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| 1 | Package:·macaulay2-common | 1 | Package:·macaulay2-common |
| 2 | Source:·macaulay2 | 2 | Source:·macaulay2 |
| 3 | Version:·1.24.11+ds-3 | 3 | Version:·1.24.11+ds-3 |
| 4 | Architecture:·all | 4 | Architecture:·all |
| 5 | Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org> | 5 | Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org> |
| 6 | Installed-Size:·28745 | 6 | Installed-Size:·287459 |
| 7 | Depends:·fonts-glyphicons-halflings·(>=·1.009~3.4.1+dfsg),·fonts-katex·(>=·0.16.10+~cs6.1.0),·libjs-bootsidemenu·(>=·1.0.0),·libjs-bootstrap·(>=·3.4.1+dfsg),·libjs-d3·(>=·3.5.17),·libjs-jquery·(>=·3.6.1+dfsg+~3.5.14),·libjs-katex·(>=·0.16.10+~cs6.1.0),·libjs-nouislider·(>=·15.8.1+ds),·libjs-three·(>=·111+dfsg1),·node-clipboard·(>=·2.0.11+ds+~cs9.6.11) | 7 | Depends:·fonts-glyphicons-halflings·(>=·1.009~3.4.1+dfsg),·fonts-katex·(>=·0.16.10+~cs6.1.0),·libjs-bootsidemenu·(>=·1.0.0),·libjs-bootstrap·(>=·3.4.1+dfsg),·libjs-d3·(>=·3.5.17),·libjs-jquery·(>=·3.6.1+dfsg+~3.5.14),·libjs-katex·(>=·0.16.10+~cs6.1.0),·libjs-nouislider·(>=·15.8.1+ds),·libjs-three·(>=·111+dfsg1),·node-clipboard·(>=·2.0.11+ds+~cs9.6.11) |
| 8 | Section:·math | 8 | Section:·math |
| 9 | Priority:·optional | 9 | Priority:·optional |
| 10 | Multi-Arch:·foreign | 10 | Multi-Arch:·foreign |
| 11 | Homepage:·http://macaulay2.com | 11 | Homepage:·http://macaulay2.com |
| 12 | Description:·Software·system·for·algebraic·geometry·research·(common·files) | 12 | Description:·Software·system·for·algebraic·geometry·research·(common·files) |
| 13 | ·Macaulay·2·is·a·software·system·for·algebraic·geometry·research,·written·by | 13 | ·Macaulay·2·is·a·software·system·for·algebraic·geometry·research,·written·by |
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| 13 | i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) | 13 | i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) |
| 14 | ·--·1. | 14 | ·--·1.54734s·elapsed |
| 15 | ······1······3······9······27······81······243······729······2187 | 15 | ······1······3······9······27······81······243······729······2187 |
| 16 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 16 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 17 | ····························································· | 17 | ····························································· |
| 18 | ·····0······1······2······3·······4·······5········6········7 | 18 | ·····0······1······2······3·······4·······5········6········7 |
| 19 | o3·:·Complex | 19 | o3·:·Complex |
| 20 | i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) | 20 | i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) |
| 21 | ·--· | 21 | ·--·2.27972s·elapsed |
| 22 | ······1······3······9······27······81······243······729······2187 | 22 | ······1······3······9······27······81······243······729······2187 |
| 23 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 23 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 24 | ····························································· | 24 | ····························································· |
| 25 | ·····0······1······2······3·······4·······5········6········7 | 25 | ·····0······1······2······3·······4·······5········6········7 |
| 26 | o4·:·Complex | 26 | o4·:·Complex |
| Offset 86, 26 lines modified | Offset 86, 26 lines modified | ||
| 86 | o2·=·cokernel·|·a·b·c·| | 86 | o2·=·cokernel·|·a·b·c·| |
| 87 | ····························1 | 87 | ····························1 |
| 88 | o2·:·R-module,·quotient·of·R</code></pre> | 88 | o2·:·R-module,·quotient·of·R</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) |
| 92 | ·--·1. | 92 | ·--·1.54734s·elapsed |
| 93 | ······1······3······9······27······81······243······729······2187 | 93 | ······1······3······9······27······81······243······729······2187 |
| 94 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 94 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 95 | ····························································· | 95 | ····························································· |
| 96 | ·····0······1······2······3·······4·······5········6········7 | 96 | ·····0······1······2······3·······4·······5········6········7 |
| 97 | o3·:·Complex</code></pre> | 97 | o3·:·Complex</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) |
| 101 | ·--· | 101 | ·--·2.27972s·elapsed |
| 102 | ······1······3······9······27······81······243······729······2187 | 102 | ······1······3······9······27······81······243······729······2187 |
| 103 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 103 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 104 | ····························································· | 104 | ····························································· |
| 105 | ·····0······1······2······3·······4·······5········6········7 | 105 | ·····0······1······2······3·······4·······5········6········7 |
| 106 | o4·:·Complex</code></pre> | 106 | o4·:·Complex</code></pre> |
| Offset 24, 24 lines modified | Offset 24, 24 lines modified | ||
| 24 | i2·:·M·=·coker·vars·R | 24 | i2·:·M·=·coker·vars·R |
| 25 | o2·=·cokernel·|·a·b·c·| | 25 | o2·=·cokernel·|·a·b·c·| |
| 26 | ····························1 | 26 | ····························1 |
| 27 | o2·:·R-module,·quotient·of·R | 27 | o2·:·R-module,·quotient·of·R |
| 28 | i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) | 28 | i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) |
| 29 | ·--·1. | 29 | ·--·1.54734s·elapsed |
| 30 | ······1······3······9······27······81······243······729······2187 | 30 | ······1······3······9······27······81······243······729······2187 |
| 31 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 31 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 32 | ·····0······1······2······3·······4·······5········6········7 | 32 | ·····0······1······2······3·······4·······5········6········7 |
| 33 | o3·:·Complex | 33 | o3·:·Complex |
| 34 | i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) | 34 | i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) |
| 35 | ·--· | 35 | ·--·2.27972s·elapsed |
| 36 | ······1······3······9······27······81······243······729······2187 | 36 | ······1······3······9······27······81······243······729······2187 |
| 37 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 37 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 38 | ·····0······1······2······3·······4·······5········6········7 | 38 | ·····0······1······2······3·······4·······5········6········7 |
| 39 | o4·:·Complex | 39 | o4·:·Complex |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=92 | 7 | #:len=92 |
| 8 | aW5kdWNlZFJlZHVjZWRTaW1wbGljaWFsQ2hhaW5Db21wbGV4TWFwKEFic3RyYWN0U2ltcGxpY2lh | 8 | aW5kdWNlZFJlZHVjZWRTaW1wbGljaWFsQ2hhaW5Db21wbGV4TWFwKEFic3RyYWN0U2ltcGxpY2lh |
| 9 | bENvbXBsZXgsQWJzdHJhY3RTaW1wbGljaWFsQ29tcGxleCk= | 9 | bENvbXBsZXgsQWJzdHJhY3RTaW1wbGljaWFsQ29tcGxleCk= |
| 10 | #:len=502 | 10 | #:len=502 |
| 11 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzMyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 11 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzMyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| Offset 1, 18 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·6456613336951100320 | 1 | --·-*-·M2-comint·-*-·hash:·6456613336951100320 |
| 2 | i1·:·setRandomSeed(currentTime()); | 2 | i1·:·setRandomSeed(currentTime()); |
| 3 | i2·:·K·=·randomAbstractSimplicialComplex(4) | 3 | i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 4 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 4 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 5 | ·······························0·=>·{{1},·{ | 5 | ·······························0·=>·{{1},·{3}} |
| 6 | ·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}} | ||
| 7 | ·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,·4}} | ||
| 8 | ······························· | 6 | ·······························1·=>·{{1,·3}} |
| 9 | o2·:·AbstractSimplicialComplex | 7 | o2·:·AbstractSimplicialComplex |
| 10 | i3·:·prune·HH·simplicialChainComplex·K | 8 | i3·:·prune·HH·simplicialChainComplex·K |
| 11 | ·······1 | 9 | ·······1 |
| 12 | o3·=·ZZ | 10 | o3·=·ZZ |
| Offset 22, 17 lines modified | Offset 20, 17 lines modified | ||
| 22 | o3·:·Complex | 20 | o3·:·Complex |
| 23 | i4·:·setRandomSeed(currentTime()); | 21 | i4·:·setRandomSeed(currentTime()); |
| 24 | i5·:·L·=·randomAbstractSimplicialComplex(6,3) | 22 | i5·:·L·=·randomAbstractSimplicialComplex(6,3) |
| 25 | o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················} | 23 | o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················} |
| 26 | ·······························0·=>·{{ | 24 | ·······························0·=>·{{1},·{4},·{5}} |
| 27 | ·······························1·=>·{{ | 25 | ·······························1·=>·{{1,·4},·{1,·5},·{4,·5}} |
| 28 | ·······························2·=>·{{ | 26 | ·······························2·=>·{{1,·4,·5}} |
| 29 | o5·:·AbstractSimplicialComplex | 27 | o5·:·AbstractSimplicialComplex |
| 30 | i6·:·prune·HH·simplicialChainComplex·L | 28 | i6·:·prune·HH·simplicialChainComplex·L |
| 31 | ·······1 | 29 | ·······1 |
| 32 | o6·=·ZZ | 30 | o6·=·ZZ |
| Offset 41, 18 lines modified | Offset 39, 18 lines modified | ||
| 41 | o6·:·Complex | 39 | o6·:·Complex |
| 42 | i7·:·setRandomSeed(currentTime()); | 40 | i7·:·setRandomSeed(currentTime()); |
| 43 | i8·:·M·=·randomAbstractSimplicialComplex(6,3,2) | 41 | i8·:·M·=·randomAbstractSimplicialComplex(6,3,2) |
| 44 | o8·=·AbstractSimplicialComplex{-1·=>·{{}}··································· | 42 | o8·=·AbstractSimplicialComplex{-1·=>·{{}}···································} |
| 45 | ·······························0·=>·{{1},·{ | 43 | ·······························0·=>·{{1},·{2},·{3},·{5}} |
| 46 | ·······························1·=>·{{1,·3},·{1,·4},·{1,·5},·{3,·5},·{3,·6},·{4,·5},·{5,·6}} | ||
| 47 | ······························· | 44 | ·······························1·=>·{{1,·2},·{1,·3},·{2,·3},·{2,·5},·{3,·5}} |
| 45 | ·······························2·=>·{{1,·2,·3},·{2,·3,·5}} | ||
| 48 | o8·:·AbstractSimplicialComplex | 46 | o8·:·AbstractSimplicialComplex |
| 49 | i9·:·prune·HH·simplicialChainComplex·M | 47 | i9·:·prune·HH·simplicialChainComplex·M |
| 50 | ·······1 | 48 | ·······1 |
| 51 | o9·=·ZZ | 49 | o9·=·ZZ |
| Offset 61, 57 lines modified | Offset 59, 35 lines modified | ||
| 61 | o9·:·Complex | 59 | o9·:·Complex |
| 62 | i10·:·setRandomSeed(currentTime()); | 60 | i10·:·setRandomSeed(currentTime()); |
| 63 | i11·:·K·=·randomAbstractSimplicialComplex(4) | 61 | i11·:·K·=·randomAbstractSimplicialComplex(4) |
| 64 | o11·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 62 | o11·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 65 | ································0·=>·{{1},·{ | 63 | ································0·=>·{{1},·{3}} |
| 66 | ································1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}} | ||
| 67 | ································2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,·4}} | ||
| 68 | ································ | 64 | ································1·=>·{{1,·3}} |
| 69 | o11·:·AbstractSimplicialComplex | 65 | o11·:·AbstractSimplicialComplex |
| 70 | i12·:·J·=·randomSubSimplicialComplex(K) | 66 | i12·:·J·=·randomSubSimplicialComplex(K) |
| 71 | o12·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 67 | o12·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 72 | ································0·=>·{{1},·{ | 68 | ································0·=>·{{1},·{3}} |
| 73 | ································1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}} | ||
| 74 | ································2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,·4}} | ||
| 75 | ································ | 69 | ································1·=>·{{1,·3}} |
| 76 | o12·:·AbstractSimplicialComplex | 70 | o12·:·AbstractSimplicialComplex |
| 77 | i13·:·inducedSimplicialChainComplexMap(K,J) | 71 | i13·:·inducedSimplicialChainComplexMap(K,J) |
| 78 | ············ | 72 | ············2················2 |
| 79 | o13·=·0·:·ZZ··<----------- | 73 | o13·=·0·:·ZZ··<-----------·ZZ··:·0 |
| 80 | ·················|·1·0· | 74 | ·················|·1·0·| |
| 81 | ·················|·0·1· | 75 | ·················|·0·1·| |
| 82 | ·················|·0·0·1·0·| | ||
| 83 | ·················|·0·0·0·1·| | ||
| 84 | ············6························6 | ||
| 85 | ······1·:·ZZ··<-------------------·ZZ··:·1 | ||
| 86 | ·················|·1·0·0·0·0·0·| | ||
| 87 | ·················|·0·1·0·0·0·0·| | ||
| 88 | ·················|·0·0·1·0·0·0·| | ||
| 89 | ·················|·0·0·0·1·0·0·| | ||
| 90 | ·················|·0·0·0·0·1·0·| | ||
| 91 | ·················|·0·0·0·0·0·1·| | ||
| 92 | ············4····················4 | ||
| 93 | ······2·:·ZZ··<---------------·ZZ··:·2 | ||
| 94 | ·················|·1·0·0·0·| | ||
| 95 | ·················|·0·1·0·0·| | ||
| 96 | ·················|·0·0·1·0·| | ||
| 97 | ·················|·0·0·0·1·| | ||
| 98 | ············1··············1 | 76 | ············1··············1 |
| 99 | ······ | 77 | ······1·:·ZZ··<---------·ZZ··:·1 |
| 100 | ·················|·1·| | 78 | ·················|·1·| |
| 101 | o13·:·ComplexMap | 79 | o13·:·ComplexMap |
| 102 | i14·:· | 80 | i14·:· |
| Offset 1, 34 lines modified | Offset 1, 35 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·9222441599761629245 | 1 | --·-*-·M2-comint·-*-·hash:·9222441599761629245 |
| 2 | i1·:·setRandomSeed(currentTime()); | 2 | i1·:·setRandomSeed(currentTime()); |
| 3 | i2·:·K·=·randomAbstractSimplicialComplex(4) | 3 | i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 4 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}} | 4 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 5 | ·······························0·=>·{{4}} | 5 | ·······························0·=>·{{1},·{4}} |
| 6 | ·······························1·=>·{{1,·4}} | ||
| 6 | o2·:·AbstractSimplicialComplex | 7 | o2·:·AbstractSimplicialComplex |
| 7 | i3·:·setRandomSeed(currentTime()); | 8 | i3·:·setRandomSeed(currentTime()); |
| 8 | i4·:·L·=·randomAbstractSimplicialComplex(6,3) | 9 | i4·:·L·=·randomAbstractSimplicialComplex(6,3) |
| 9 | o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················} | 10 | o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················} |
| 10 | ·······························0·=>·{{1},·{ | 11 | ·······························0·=>·{{1},·{3},·{5}} |
| 11 | ·······························1·=>·{{1,· | 12 | ·······························1·=>·{{1,·3},·{1,·5},·{3,·5}} |
| 12 | ·······························2·=>·{{1,· | 13 | ·······························2·=>·{{1,·3,·5}} |
| 13 | o4·:·AbstractSimplicialComplex | 14 | o4·:·AbstractSimplicialComplex |
| 14 | i5·:·setRandomSeed(currentTime()); | 15 | i5·:·setRandomSeed(currentTime()); |
| 15 | i6·:·M·=·randomAbstractSimplicialComplex(6,3,2) | 16 | i6·:·M·=·randomAbstractSimplicialComplex(6,3,2) |
| 16 | o6·=·AbstractSimplicialComplex{-1·=>·{{}}···················································} | 17 | o6·=·AbstractSimplicialComplex{-1·=>·{{}}···················································} |
| 17 | ·······························0·=>·{{1},·{2},·{ | 18 | ·······························0·=>·{{1},·{2},·{3},·{4},·{6}} |
| 18 | ·······························1·=>·{{1,· | 19 | ·······························1·=>·{{1,·2},·{1,·3},·{2,·3},·{2,·6},·{3,·4},·{3,·6},·{4,·6}} |
| 19 | ·······························2·=>·{{1,· | 20 | ·······························2·=>·{{1,·2,·3},·{2,·3,·6},·{3,·4,·6}} |
| 20 | o6·:·AbstractSimplicialComplex | 21 | o6·:·AbstractSimplicialComplex |
| 21 | i7·:· | 22 | i7·:· |
| Offset 1, 22 lines modified | Offset 1, 20 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·13473104809235542297 | 1 | --·-*-·M2-comint·-*-·hash:·13473104809235542297 |
| 2 | i1·:·setRandomSeed(currentTime()); | 2 | i1·:·setRandomSeed(currentTime()); |
| 3 | i2·:·K·=·randomAbstractSimplicialComplex(4) | 3 | i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 4 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 4 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 5 | ·······························0·=>·{{1},·{ | 5 | ·······························0·=>·{{1},·{4}} |
| 6 | ·······························1·=>·{{1,·2},·{1,·4},·{2,·4}} | ||
| 7 | ······························· | 6 | ·······························1·=>·{{1,·4}} |
| 8 | o2·:·AbstractSimplicialComplex | 7 | o2·:·AbstractSimplicialComplex |
| 9 | i3·:·J·=·randomSubSimplicialComplex(K) | 8 | i3·:·J·=·randomSubSimplicialComplex(K) |
| 10 | o3·=·AbstractSimplicialComplex{-1·=>·{{}} | 9 | o3·=·AbstractSimplicialComplex{-1·=>·{{}}} |
| 11 | ·······························0·=>·{{ | 10 | ·······························0·=>·{{4}} |
| 12 | ·······························1·=>·{{1,·2}} | ||
| 13 | o3·:·AbstractSimplicialComplex | 11 | o3·:·AbstractSimplicialComplex |
| 14 | i4·:· | 12 | i4·:· |
| Offset 52, 19 lines modified | Offset 52, 17 lines modified | ||
| 52 | ········<table·class="examples"> | 52 | ········<table·class="examples"> |
| 53 | ··········<tr> | 53 | ··········<tr> |
| 54 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre> | 54 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre> |
| 55 | </td>··········</tr> | 55 | </td>··········</tr> |
| 56 | ··········<tr> | 56 | ··········<tr> |
| 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4) | 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 58 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 58 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 59 | ·······························0·=>·{{1},·{ | 59 | ·······························0·=>·{{1},·{3}} |
| 60 | ·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}} | ||
| 61 | ·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,·4}} | ||
| 62 | ······························· | 60 | ·······························1·=>·{{1,·3}} |
| 63 | o2·:·AbstractSimplicialComplex</code></pre> | 61 | o2·:·AbstractSimplicialComplex</code></pre> |
| 64 | </td>··········</tr> | 62 | </td>··········</tr> |
| 65 | ··········<tr> | 63 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·prune·HH·simplicialChainComplex·K | 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·prune·HH·simplicialChainComplex·K |
| 67 | ·······1 | 65 | ·······1 |
| Offset 82, 17 lines modified | Offset 80, 17 lines modified | ||
| 82 | ··········<tr> | 80 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·setRandomSeed(currentTime());</code></pre> | 81 | <td>··············<pre><code·class="language-macaulay2">i4·:·setRandomSeed(currentTime());</code></pre> |
| 84 | </td>··········</tr> | 82 | </td>··········</tr> |
| 85 | ··········<tr> | 83 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i5·:·L·=·randomAbstractSimplicialComplex(6,3) | 84 | <td>··············<pre><code·class="language-macaulay2">i5·:·L·=·randomAbstractSimplicialComplex(6,3) |
| 87 | o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················} | 85 | o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················} |
| 88 | ·······························0·=>·{{ | 86 | ·······························0·=>·{{1},·{4},·{5}} |
| 89 | ·······························1·=>·{{ | 87 | ·······························1·=>·{{1,·4},·{1,·5},·{4,·5}} |
| 90 | ·······························2·=>·{{ | 88 | ·······························2·=>·{{1,·4,·5}} |
| 91 | o5·:·AbstractSimplicialComplex</code></pre> | 89 | o5·:·AbstractSimplicialComplex</code></pre> |
| 92 | </td>··········</tr> | 90 | </td>··········</tr> |
| 93 | ··········<tr> | 91 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·prune·HH·simplicialChainComplex·L | 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·prune·HH·simplicialChainComplex·L |
| 95 | ·······1 | 93 | ·······1 |
| Offset 109, 18 lines modified | Offset 107, 18 lines modified | ||
| 109 | ········<table·class="examples"> | 107 | ········<table·class="examples"> |
| 110 | ··········<tr> | 108 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·setRandomSeed(currentTime());</code></pre> | 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·setRandomSeed(currentTime());</code></pre> |
| 112 | </td>··········</tr> | 110 | </td>··········</tr> |
| 113 | ··········<tr> | 111 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i8·:·M·=·randomAbstractSimplicialComplex(6,3,2) | 112 | <td>··············<pre><code·class="language-macaulay2">i8·:·M·=·randomAbstractSimplicialComplex(6,3,2) |
| 115 | o8·=·AbstractSimplicialComplex{-1·=>·{{}}··································· | 113 | o8·=·AbstractSimplicialComplex{-1·=>·{{}}···································} |
| 116 | ·······························0·=>·{{1},·{ | 114 | ·······························0·=>·{{1},·{2},·{3},·{5}} |
| 117 | ·······························1·=>·{{1,·3},·{1,·4},·{1,·5},·{3,·5},·{3,·6},·{4,·5},·{5,·6}} | ||
| 118 | ······························· | 115 | ·······························1·=>·{{1,·2},·{1,·3},·{2,·3},·{2,·5},·{3,·5}} |
| 116 | ·······························2·=>·{{1,·2,·3},·{2,·3,·5}} | ||
| 119 | o8·:·AbstractSimplicialComplex</code></pre> | 117 | o8·:·AbstractSimplicialComplex</code></pre> |
| 120 | </td>··········</tr> | 118 | </td>··········</tr> |
| 121 | ··········<tr> | 119 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i9·:·prune·HH·simplicialChainComplex·M | 120 | <td>··············<pre><code·class="language-macaulay2">i9·:·prune·HH·simplicialChainComplex·M |
| 123 | ·······1 | 121 | ·······1 |
| Offset 137, 61 lines modified | Offset 135, 39 lines modified | ||
| 137 | ········<table·class="examples"> | 135 | ········<table·class="examples"> |
| 138 | ··········<tr> | 136 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i10·:·setRandomSeed(currentTime());</code></pre> | 137 | <td>··············<pre><code·class="language-macaulay2">i10·:·setRandomSeed(currentTime());</code></pre> |
| 140 | </td>··········</tr> | 138 | </td>··········</tr> |
| 141 | ··········<tr> | 139 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i11·:·K·=·randomAbstractSimplicialComplex(4) | 140 | <td>··············<pre><code·class="language-macaulay2">i11·:·K·=·randomAbstractSimplicialComplex(4) |
| 143 | o11·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 141 | o11·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 144 | ································0·=>·{{1},·{ | 142 | ································0·=>·{{1},·{3}} |
| 145 | ································1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}} | ||
| 146 | ································2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,·4}} | ||
| 147 | ································ | 143 | ································1·=>·{{1,·3}} |
| 148 | o11·:·AbstractSimplicialComplex</code></pre> | 144 | o11·:·AbstractSimplicialComplex</code></pre> |
| 149 | </td>··········</tr> | 145 | </td>··········</tr> |
| 150 | ··········<tr> | 146 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i12·:·J·=·randomSubSimplicialComplex(K) | 147 | <td>··············<pre><code·class="language-macaulay2">i12·:·J·=·randomSubSimplicialComplex(K) |
| 152 | o12·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 148 | o12·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 153 | ································0·=>·{{1},·{ | 149 | ································0·=>·{{1},·{3}} |
| 154 | ································1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}} | ||
| 155 | ································2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,·4}} | ||
| 156 | ································ | 150 | ································1·=>·{{1,·3}} |
| 157 | o12·:·AbstractSimplicialComplex</code></pre> | 151 | o12·:·AbstractSimplicialComplex</code></pre> |
| 158 | </td>··········</tr> | 152 | </td>··········</tr> |
| 159 | ··········<tr> | 153 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i13·:·inducedSimplicialChainComplexMap(K,J) | 154 | <td>··············<pre><code·class="language-macaulay2">i13·:·inducedSimplicialChainComplexMap(K,J) |
| 161 | ············ | 155 | ············2················2 |
| 162 | o13·=·0·:·ZZ··<----------- | 156 | o13·=·0·:·ZZ··<-----------·ZZ··:·0 |
| 163 | ·················|·1·0· | 157 | ·················|·1·0·| |
| 164 | ·················|·0·1· | 158 | ·················|·0·1·| |
| 165 | ·················|·0·0·1·0·| | ||
| 166 | ·················|·0·0·0·1·| | ||
| 167 | ············6························6 | ||
| 168 | ······1·:·ZZ··<-------------------·ZZ··:·1 | ||
| 169 | ·················|·1·0·0·0·0·0·| | ||
| 170 | ·················|·0·1·0·0·0·0·| | ||
| 171 | ·················|·0·0·1·0·0·0·| | ||
| 172 | ·················|·0·0·0·1·0·0·| | ||
| 173 | ·················|·0·0·0·0·1·0·| | ||
| 174 | ·················|·0·0·0·0·0·1·| | ||
| 175 | ············4····················4 | ||
| 176 | ······2·:·ZZ··<---------------·ZZ··:·2 | ||
| 177 | ·················|·1·0·0·0·| | ||
| 178 | ·················|·0·1·0·0·| | ||
| 179 | ·················|·0·0·1·0·| | ||
| 180 | ·················|·0·0·0·1·| | ||
| 181 | ············1··············1 | 159 | ············1··············1 |
| 182 | ······ | 160 | ······1·:·ZZ··<---------·ZZ··:·1 |
| 183 | ·················|·1·| | 161 | ·················|·1·| |
| 184 | o13·:·ComplexMap</code></pre> | 162 | o13·:·ComplexMap</code></pre> |
| 185 | </td>··········</tr> | 163 | </td>··········</tr> |
| 186 | ········</table> | 164 | ········</table> |
| 187 | ······</div> | 165 | ······</div> |
| 188 | ····</div> | 166 | ····</div> |
| Offset 9, 22 lines modified | Offset 9, 17 lines modified | ||
| 9 | In·what·follows·we·illustrate·a·collection·of·homological·calculations·that·can | 9 | In·what·follows·we·illustrate·a·collection·of·homological·calculations·that·can |
| 10 | be·performed·on·random·simplicial·complexes. | 10 | be·performed·on·random·simplicial·complexes. |
| 11 | Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset | 11 | Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset |
| 12 | of·[n]·=·{1,...,n}. | 12 | of·[n]·=·{1,...,n}. |
| 13 | i1·:·setRandomSeed(currentTime()); | 13 | i1·:·setRandomSeed(currentTime()); |
| 14 | i2·:·K·=·randomAbstractSimplicialComplex(4) | 14 | i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 15 | o2·=·AbstractSimplicialComplex{-1·=>·{{}} | 15 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 16 | } | ||
| 17 | ·······························0·=>·{{1},·{ | 16 | ·······························0·=>·{{1},·{3}} |
| 18 | ·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4}, | ||
| 19 | {3,·4}} | ||
| 20 | ·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3, | ||
| 21 | 4}} | ||
| 22 | ······························· | 17 | ·······························1·=>·{{1,·3}} |
| 23 | o2·:·AbstractSimplicialComplex | 18 | o2·:·AbstractSimplicialComplex |
| 24 | i3·:·prune·HH·simplicialChainComplex·K | 19 | i3·:·prune·HH·simplicialChainComplex·K |
| 25 | ·······1 | 20 | ·······1 |
| 26 | o3·=·ZZ | 21 | o3·=·ZZ |
| Offset 32, 17 lines modified | Offset 27, 17 lines modified | ||
| 32 | o3·:·Complex | 27 | o3·:·Complex |
| 33 | Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r. | 28 | Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r. |
| 34 | i4·:·setRandomSeed(currentTime()); | 29 | i4·:·setRandomSeed(currentTime()); |
| 35 | i5·:·L·=·randomAbstractSimplicialComplex(6,3) | 30 | i5·:·L·=·randomAbstractSimplicialComplex(6,3) |
| 36 | o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················} | 31 | o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················} |
| 37 | ·······························0·=>·{{ | 32 | ·······························0·=>·{{1},·{4},·{5}} |
| 38 | ·······························1·=>·{{ | 33 | ·······························1·=>·{{1,·4},·{1,·5},·{4,·5}} |
| 39 | ·······························2·=>·{{ | 34 | ·······························2·=>·{{1,·4,·5}} |
| 40 | o5·:·AbstractSimplicialComplex | 35 | o5·:·AbstractSimplicialComplex |
| 41 | i6·:·prune·HH·simplicialChainComplex·L | 36 | i6·:·prune·HH·simplicialChainComplex·L |
| 42 | ·······1 | 37 | ·······1 |
| 43 | o6·=·ZZ | 38 | o6·=·ZZ |
| Offset 51, 79 lines modified | Offset 46, 49 lines modified | ||
| 51 | o6·:·Complex | 46 | o6·:·Complex |
| 52 | Create·the·random·complex·Y_d(n,m)·which·has·vertex·set·[n]·and·complete·(d·â | 47 | Create·the·random·complex·Y_d(n,m)·which·has·vertex·set·[n]·and·complete·(d·â |
| 53 | 1)-skeleton,·and·has·exactly·m·dimension·d·faces,·chosen·at·random·from·all | 48 | 1)-skeleton,·and·has·exactly·m·dimension·d·faces,·chosen·at·random·from·all |
| 54 | binomial(binomial(n,d+1),m)·possibilities. | 49 | binomial(binomial(n,d+1),m)·possibilities. |
| 55 | i7·:·setRandomSeed(currentTime()); | 50 | i7·:·setRandomSeed(currentTime()); |
| 56 | i8·:·M·=·randomAbstractSimplicialComplex(6,3,2) | 51 | i8·:·M·=·randomAbstractSimplicialComplex(6,3,2) |
| 52 | o8·=·AbstractSimplicialComplex{-1·=>·{{}}···································} | ||
| 57 | o8·=·AbstractSimplicialComplex{-1·=>·{{}} | ||
| 58 | } | ||
| 59 | ·······························0·=>·{{1},·{ | 53 | ·······························0·=>·{{1},·{2},·{3},·{5}} |
| 60 | ·······························1·=>·{{1,· | 54 | ·······························1·=>·{{1,·2},·{1,·3},·{2,·3},·{2,·5},·{3,·5}} |
| 55 | ·······························2·=>·{{1,·2,·3},·{2,·3,·5}} | ||
| 61 | {4,·5},·{5,·6}} | ||
| 62 | ·······························2·=>·{{1,·3,·5},·{1,·4,·5},·{3,·5,·6}} | ||
| 63 | o8·:·AbstractSimplicialComplex | 56 | o8·:·AbstractSimplicialComplex |
| 64 | i9·:·prune·HH·simplicialChainComplex·M | 57 | i9·:·prune·HH·simplicialChainComplex·M |
| 65 | ·······1 | 58 | ·······1 |
| 66 | o9·=·ZZ | 59 | o9·=·ZZ |
| 67 | ·····0 | 60 | ·····0 |
| 68 | o9·:·Complex | 61 | o9·:·Complex |
| 69 | Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex. | 62 | Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex. |
| 70 | i10·:·setRandomSeed(currentTime()); | 63 | i10·:·setRandomSeed(currentTime()); |
| 71 | i11·:·K·=·randomAbstractSimplicialComplex(4) | 64 | i11·:·K·=·randomAbstractSimplicialComplex(4) |
| 72 | o11·=·AbstractSimplicialComplex{-1·=>·{{}} | 65 | o11·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 73 | } | ||
| 74 | ································0·=>·{{1},·{ | 66 | ································0·=>·{{1},·{3}} |
| 75 | ································1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4}, | ||
| 76 | {3,·4}} | ||
| 77 | ································2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3, | ||
| 78 | 4}} | ||
| 79 | ································ | 67 | ································1·=>·{{1,·3}} |
| 80 | o11·:·AbstractSimplicialComplex | 68 | o11·:·AbstractSimplicialComplex |
| 81 | i12·:·J·=·randomSubSimplicialComplex(K) | 69 | i12·:·J·=·randomSubSimplicialComplex(K) |
| 82 | o12·=·AbstractSimplicialComplex{-1·=>·{{}} | 70 | o12·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 83 | } | ||
| 84 | ································0·=>·{{1},·{ | 71 | ································0·=>·{{1},·{3}} |
| 85 | ································1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4}, | ||
| 86 | {3,·4}} | ||
| 87 | ································2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3, | ||
| 88 | 4}} | ||
| 89 | ································ | 72 | ································1·=>·{{1,·3}} |
| 90 | o12·:·AbstractSimplicialComplex | 73 | o12·:·AbstractSimplicialComplex |
| 91 | i13·:·inducedSimplicialChainComplexMap(K,J) | 74 | i13·:·inducedSimplicialChainComplexMap(K,J) |
| 92 | ············ | 75 | ············2················2 |
| 93 | o13·=·0·:·ZZ··<----------- | 76 | o13·=·0·:·ZZ··<-----------·ZZ··:·0 |
| 94 | ·················|·1·0· | 77 | ·················|·1·0·| |
| 95 | ·················|·0·1· | 78 | ·················|·0·1·| |
| 96 | ·················|·0·0·1·0·| | ||
| 97 | ·················|·0·0·0·1·| | ||
| 98 | ············6························6 | ||
| 99 | ······1·:·ZZ··<-------------------·ZZ··:·1 | ||
| 100 | ·················|·1·0·0·0·0·0·| | ||
| 101 | ·················|·0·1·0·0·0·0·| | ||
| 102 | ·················|·0·0·1·0·0·0·| | ||
| 103 | ·················|·0·0·0·1·0·0·| | ||
| 104 | ·················|·0·0·0·0·1·0·| | ||
| 105 | ·················|·0·0·0·0·0·1·| | ||
| 106 | ············4····················4 | ||
| 107 | ······2·:·ZZ··<---------------·ZZ··:·2 | ||
| 108 | ·················|·1·0·0·0·| | ||
| 109 | ·················|·0·1·0·0·| | ||
| 110 | ·················|·0·0·1·0·| | ||
| 111 | ·················|·0·0·0·1·| | ||
| 112 | ············1··············1 | 79 | ············1··············1 |
| 113 | ······ | 80 | ······1·:·ZZ··<---------·ZZ··:·1 |
| 114 | ·················|·1·| | 81 | ·················|·1·| |
| 115 | o13·:·ComplexMap | 82 | o13·:·ComplexMap |
| Offset 50, 16 lines modified | Offset 50, 17 lines modified | ||
| 50 | ········<table·class="examples"> | 50 | ········<table·class="examples"> |
| 51 | ··········<tr> | 51 | ··········<tr> |
| 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre> | 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre> |
| 53 | </td>··········</tr> | 53 | </td>··········</tr> |
| 54 | ··········<tr> | 54 | ··········<tr> |
| 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4) | 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 56 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}} | 56 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 57 | ·······························0·=>·{{4}} | 57 | ·······························0·=>·{{1},·{4}} |
| 58 | ·······························1·=>·{{1,·4}} | ||
| 58 | o2·:·AbstractSimplicialComplex</code></pre> | 59 | o2·:·AbstractSimplicialComplex</code></pre> |
| 59 | </td>··········</tr> | 60 | </td>··········</tr> |
| 60 | ········</table> | 61 | ········</table> |
| 61 | ········<div> | 62 | ········<div> |
| 62 | ··········<p>Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.</p> | 63 | ··········<p>Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.</p> |
| 63 | ········</div> | 64 | ········</div> |
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| 67 | ··········<tr> | 68 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·setRandomSeed(currentTime());</code></pre> | 69 | <td>··············<pre><code·class="language-macaulay2">i3·:·setRandomSeed(currentTime());</code></pre> |
| 69 | </td>··········</tr> | 70 | </td>··········</tr> |
| 70 | ··········<tr> | 71 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i4·:·L·=·randomAbstractSimplicialComplex(6,3) | 72 | <td>··············<pre><code·class="language-macaulay2">i4·:·L·=·randomAbstractSimplicialComplex(6,3) |
| 72 | o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················} | 73 | o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················} |
| 73 | ·······························0·=>·{{1},·{ | 74 | ·······························0·=>·{{1},·{3},·{5}} |
| 74 | ·······························1·=>·{{1,· | 75 | ·······························1·=>·{{1,·3},·{1,·5},·{3,·5}} |
| 75 | ·······························2·=>·{{1,· | 76 | ·······························2·=>·{{1,·3,·5}} |
| 76 | o4·:·AbstractSimplicialComplex</code></pre> | 77 | o4·:·AbstractSimplicialComplex</code></pre> |
| 77 | </td>··········</tr> | 78 | </td>··········</tr> |
| 78 | ········</table> | 79 | ········</table> |
| 79 | ········<div> | 80 | ········<div> |
| 80 | ··········<p>Create·the·random·complex·Y_d(n,m)·which·has·vertex·set·[n]·and·complete·(d·−·1)-skeleton,·and·has·exactly·m·d-dimensional·faces,·chosen·at·random·from·all·binomial(binomial(n,d+1),m)·possibilities.</p> | 81 | ··········<p>Create·the·random·complex·Y_d(n,m)·which·has·vertex·set·[n]·and·complete·(d·−·1)-skeleton,·and·has·exactly·m·d-dimensional·faces,·chosen·at·random·from·all·binomial(binomial(n,d+1),m)·possibilities.</p> |
| 81 | ········</div> | 82 | ········</div> |
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| 85 | ··········<tr> | 86 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i5·:·setRandomSeed(currentTime());</code></pre> | 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·setRandomSeed(currentTime());</code></pre> |
| 87 | </td>··········</tr> | 88 | </td>··········</tr> |
| 88 | ··········<tr> | 89 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i6·:·M·=·randomAbstractSimplicialComplex(6,3,2) | 90 | <td>··············<pre><code·class="language-macaulay2">i6·:·M·=·randomAbstractSimplicialComplex(6,3,2) |
| 90 | o6·=·AbstractSimplicialComplex{-1·=>·{{}}···················································} | 91 | o6·=·AbstractSimplicialComplex{-1·=>·{{}}···················································} |
| 91 | ·······························0·=>·{{1},·{2},·{ | 92 | ·······························0·=>·{{1},·{2},·{3},·{4},·{6}} |
| 92 | ·······························1·=>·{{1,· | 93 | ·······························1·=>·{{1,·2},·{1,·3},·{2,·3},·{2,·6},·{3,·4},·{3,·6},·{4,·6}} |
| 93 | ·······························2·=>·{{1,· | 94 | ·······························2·=>·{{1,·2,·3},·{2,·3,·6},·{3,·4,·6}} |
| 94 | o6·:·AbstractSimplicialComplex</code></pre> | 95 | o6·:·AbstractSimplicialComplex</code></pre> |
| 95 | </td>··········</tr> | 96 | </td>··········</tr> |
| 96 | ········</table> | 97 | ········</table> |
| 97 | ······</div> | 98 | ······</div> |
| 98 | ······<div> | 99 | ······<div> |
| 99 | ········<h2>See·also</h2> | 100 | ········<h2>See·also</h2> |
| Offset 6, 40 lines modified | Offset 6, 41 lines modified | ||
| 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·s\x8se\x8et\x8t·*\x8**\x8**\x8**\x8**\x8**\x8* | 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·s\x8se\x8et\x8t·*\x8**\x8**\x8**\x8**\x8**\x8* |
| 7 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 7 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 8 | Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset | 8 | Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset |
| 9 | of·[n]·=·{1,...,n}. | 9 | of·[n]·=·{1,...,n}. |
| 10 | i1·:·setRandomSeed(currentTime()); | 10 | i1·:·setRandomSeed(currentTime()); |
| 11 | i2·:·K·=·randomAbstractSimplicialComplex(4) | 11 | i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 12 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}} | 12 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 13 | ·······························0·=>·{{4}} | 13 | ·······························0·=>·{{1},·{4}} |
| 14 | ·······························1·=>·{{1,·4}} | ||
| 14 | o2·:·AbstractSimplicialComplex | 15 | o2·:·AbstractSimplicialComplex |
| 15 | Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r. | 16 | Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r. |
| 16 | i3·:·setRandomSeed(currentTime()); | 17 | i3·:·setRandomSeed(currentTime()); |
| 17 | i4·:·L·=·randomAbstractSimplicialComplex(6,3) | 18 | i4·:·L·=·randomAbstractSimplicialComplex(6,3) |
| 18 | o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················} | 19 | o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················} |
| 19 | ·······························0·=>·{{1},·{ | 20 | ·······························0·=>·{{1},·{3},·{5}} |
| 20 | ·······························1·=>·{{1,· | 21 | ·······························1·=>·{{1,·3},·{1,·5},·{3,·5}} |
| 21 | ·······························2·=>·{{1,· | 22 | ·······························2·=>·{{1,·3,·5}} |
| 22 | o4·:·AbstractSimplicialComplex | 23 | o4·:·AbstractSimplicialComplex |
| 23 | Create·the·random·complex·Y_d(n,m)·which·has·vertex·set·[n]·and·complete·(d·â | 24 | Create·the·random·complex·Y_d(n,m)·which·has·vertex·set·[n]·and·complete·(d·â |
| 24 | 1)-skeleton,·and·has·exactly·m·d-dimensional·faces,·chosen·at·random·from·all | 25 | 1)-skeleton,·and·has·exactly·m·d-dimensional·faces,·chosen·at·random·from·all |
| 25 | binomial(binomial(n,d+1),m)·possibilities. | 26 | binomial(binomial(n,d+1),m)·possibilities. |
| 26 | i5·:·setRandomSeed(currentTime()); | 27 | i5·:·setRandomSeed(currentTime()); |
| 27 | i6·:·M·=·randomAbstractSimplicialComplex(6,3,2) | 28 | i6·:·M·=·randomAbstractSimplicialComplex(6,3,2) |
| 28 | o6·=·AbstractSimplicialComplex{-1·=>·{{}} | 29 | o6·=·AbstractSimplicialComplex{-1·=>·{{}} |
| 29 | } | 30 | } |
| 30 | ·······························0·=>·{{1},·{2},·{ | 31 | ·······························0·=>·{{1},·{2},·{3},·{4},·{6}} |
| 31 | ·······························1·=>·{{1,· | 32 | ·······························1·=>·{{1,·2},·{1,·3},·{2,·3},·{2,·6},·{3,·4}, |
| 32 | { | 33 | {3,·6},·{4,·6}} |
| 33 | ·······························2·=>·{{1,· | 34 | ·······························2·=>·{{1,·2,·3},·{2,·3,·6},·{3,·4,·6}} |
| 34 | o6·:·AbstractSimplicialComplex | 35 | o6·:·AbstractSimplicialComplex |
| 35 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 36 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·--·get·a·random·object | 37 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·--·get·a·random·object |
| 37 | ····*·randomSquareFreeMonomialIdeal·(missing·documentation) | 38 | ····*·randomSquareFreeMonomialIdeal·(missing·documentation) |
| 38 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·*\x8**\x8**\x8**\x8**\x8* | 39 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 39 | ····*·randomAbstractSimplicialComplex(ZZ) | 40 | ····*·randomAbstractSimplicialComplex(ZZ) |
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| 50 | ········<table·class="examples"> | 50 | ········<table·class="examples"> |
| 51 | ··········<tr> | 51 | ··········<tr> |
| 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre> | 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre> |
| 53 | </td>··········</tr> | 53 | </td>··········</tr> |
| 54 | ··········<tr> | 54 | ··········<tr> |
| 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4) | 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 56 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 56 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 57 | ·······························0·=>·{{1},·{ | 57 | ·······························0·=>·{{1},·{4}} |
| 58 | ·······························1·=>·{{1,·2},·{1,·4},·{2,·4}} | ||
| 59 | ······························· | 58 | ·······························1·=>·{{1,·4}} |
| 60 | o2·:·AbstractSimplicialComplex</code></pre> | 59 | o2·:·AbstractSimplicialComplex</code></pre> |
| 61 | </td>··········</tr> | 60 | </td>··········</tr> |
| 62 | ··········<tr> | 61 | ··········<tr> |
| 63 | <td>··············<pre><code·class="language-macaulay2">i3·:·J·=·randomSubSimplicialComplex(K) | 62 | <td>··············<pre><code·class="language-macaulay2">i3·:·J·=·randomSubSimplicialComplex(K) |
| 64 | o3·=·AbstractSimplicialComplex{-1·=>·{{}} | 63 | o3·=·AbstractSimplicialComplex{-1·=>·{{}}} |
| 65 | ·······························0·=>·{{ | 64 | ·······························0·=>·{{4}} |
| 66 | ·······························1·=>·{{1,·2}} | ||
| 67 | o3·:·AbstractSimplicialComplex</code></pre> | 65 | o3·:·AbstractSimplicialComplex</code></pre> |
| 68 | </td>··········</tr> | 66 | </td>··········</tr> |
| 69 | ········</table> | 67 | ········</table> |
| 70 | ······</div> | 68 | ······</div> |
| 71 | ······<div·class="waystouse"> | 69 | ······<div·class="waystouse"> |
| 72 | ········<h2>Ways·to·use·<span·class="tt">randomSubSimplicialComplex</span>:</h2> | 70 | ········<h2>Ways·to·use·<span·class="tt">randomSubSimplicialComplex</span>:</h2> |
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| 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8su\x8ub\x8b-\x8-s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·c\x8co\x8om\x8mp\x8pl\x8le\x8ex\x8x | 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8su\x8ub\x8b-\x8-s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·c\x8co\x8om\x8mp\x8pl\x8le\x8ex\x8x |
| 7 | *\x8**\x8**\x8**\x8**\x8**\x8* | 7 | *\x8**\x8**\x8**\x8**\x8**\x8* |
| 8 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 8 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 9 | Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex. | 9 | Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex. |
| 10 | i1·:·setRandomSeed(currentTime()); | 10 | i1·:·setRandomSeed(currentTime()); |
| 11 | i2·:·K·=·randomAbstractSimplicialComplex(4) | 11 | i2·:·K·=·randomAbstractSimplicialComplex(4) |
| 12 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}····· | 12 | o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····} |
| 13 | ·······························0·=>·{{1},·{ | 13 | ·······························0·=>·{{1},·{4}} |
| 14 | ·······························1·=>·{{1,·2},·{1,·4},·{2,·4}} | ||
| 15 | ······························· | 14 | ·······························1·=>·{{1,·4}} |
| 16 | o2·:·AbstractSimplicialComplex | 15 | o2·:·AbstractSimplicialComplex |
| 17 | i3·:·J·=·randomSubSimplicialComplex(K) | 16 | i3·:·J·=·randomSubSimplicialComplex(K) |
| 18 | o3·=·AbstractSimplicialComplex{-1·=>·{{}} | 17 | o3·=·AbstractSimplicialComplex{-1·=>·{{}}} |
| 19 | ·······························0·=>·{{ | 18 | ·······························0·=>·{{4}} |
| 20 | ·······························1·=>·{{1,·2}} | ||
| 21 | o3·:·AbstractSimplicialComplex | 19 | o3·:·AbstractSimplicialComplex |
| 22 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·*\x8**\x8**\x8**\x8**\x8* | 20 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 23 | ····*·randomSubSimplicialComplex(AbstractSimplicialComplex) | 21 | ····*·randomSubSimplicialComplex(AbstractSimplicialComplex) |
| 24 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 22 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 25 | The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8u_\x8b_\x8S_\x8i_\x8m_\x8p_\x8l_\x8i_\x8c_\x8i_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 23 | The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8u_\x8b_\x8S_\x8i_\x8m_\x8p_\x8l_\x8i_\x8c_\x8i_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | QWJzdHJhY3RUb3JpY1ZhcmlldGllcw== | 8 | QWJzdHJhY3RUb3JpY1ZhcmlldGllcw== |
| 9 | #:len=379 | 9 | #:len=379 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | dHJhY2VNYXRyaXgoSWRlYWwsTWF0cml4KQ== | 8 | dHJhY2VNYXRyaXgoSWRlYWwsTWF0cml4KQ== |
| 9 | #:len=268 | 9 | #:len=268 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTE2MCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTE2MCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodHJhY2VNYXRyaXgsSWRlYWwsTWF0cml4KSwidHJh | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodHJhY2VNYXRyaXgsSWRlYWwsTWF0cml4KSwidHJh |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=27 | 7 | #:len=27 |
| 8 | YWRqdW5jdGlvblByb2Nlc3MoSWRlYWwsWlop | 8 | YWRqdW5jdGlvblByb2Nlc3MoSWRlYWwsWlop |
| 9 | #:len=310 | 9 | #:len=310 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjc3LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjc3LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGp1bmN0aW9uUHJvY2VzcyxJZGVhbCxaWiksImFk | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGp1bmN0aW9uUHJvY2VzcyxJZGVhbCxaWiksImFk |
| Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
| 49 | o8·:·BettiTally | 49 | o8·:·BettiTally |
| 50 | i9·:·c=codim·I | 50 | i9·:·c=codim·I |
| 51 | o9·=·4 | 51 | o9·=·4 |
| 52 | i10·:·elapsedTime·fI=res·I | 52 | i10·:·elapsedTime·fI=res·I |
| 53 | ·--·.0 | 53 | ·--·.0207379s·elapsed |
| 54 | ········1·······14·······33·······28·······8 | 54 | ········1·······14·······33·······28·······8 |
| 55 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 | 55 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 |
| 56 | ·················································· | 56 | ·················································· |
| 57 | ······0·······1········2········3········4·······5 | 57 | ······0·······1········2········3········4·······5 |
| 58 | o10·:·ChainComplex | 58 | o10·:·ChainComplex |
| Offset 87, 30 lines modified | Offset 87, 30 lines modified | ||
| 87 | o13·:·BettiTally | 87 | o13·:·BettiTally |
| 88 | i14·:·phi=map(P2,Pn,H); | 88 | i14·:·phi=map(P2,Pn,H); |
| 89 | o14·:·RingMap·P2·<--·Pn | 89 | o14·:·RingMap·P2·<--·Pn |
| 90 | i15·:·elapsedTime·betti(I'=trim·ker·phi) | 90 | i15·:·elapsedTime·betti(I'=trim·ker·phi) |
| 91 | ·--·. | 91 | ·--·.519233s·elapsed |
| 92 | ·············0··1 | 92 | ·············0··1 |
| 93 | o15·=·total:·1·11 | 93 | o15·=·total:·1·11 |
| 94 | ··········0:·1··. | 94 | ··········0:·1··. |
| 95 | ··········1:·.··3 | 95 | ··········1:·.··3 |
| 96 | ··········2:·.··8 | 96 | ··········2:·.··8 |
| 97 | o15·:·BettiTally | 97 | o15·:·BettiTally |
| 98 | i16·:·I'==·I | 98 | i16·:·I'==·I |
| 99 | o16·=·true | 99 | o16·=·true |
| 100 | i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 100 | i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 101 | ·--· | 101 | ·--·5.478s·elapsed |
| 102 | i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 102 | i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 103 | ··························0·1 | 103 | ··························0·1 |
| 104 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} | 104 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} |
| 105 | ·······················0:·1·2 | 105 | ·······················0:·1·2 |
| 106 | ··························0·1 | 106 | ··························0·1 |
| Offset 79, 40 lines modified | Offset 79, 40 lines modified | ||
| 79 | ··········1:·.·. | 79 | ··········1:·.·. |
| 80 | ··········2:·.·. | 80 | ··········2:·.·. |
| 81 | ··········3:·.·8 | 81 | ··········3:·.·8 |
| 82 | o13·:·BettiTally | 82 | o13·:·BettiTally |
| 83 | i14·:·elapsedTime·sub(I,H) | 83 | i14·:·elapsedTime·sub(I,H) |
| 84 | ·--·.0 | 84 | ·--·.0275377s·elapsed |
| 85 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) | 85 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) |
| 86 | o14·:·Ideal·of·P2 | 86 | o14·:·Ideal·of·P2 |
| 87 | i15·:·phi=map(P2,Pn,H); | 87 | i15·:·phi=map(P2,Pn,H); |
| 88 | o15·:·RingMap·P2·<--·Pn | 88 | o15·:·RingMap·P2·<--·Pn |
| 89 | i16·:·elapsedTime·betti(I'=trim·ker·phi) | 89 | i16·:·elapsedTime·betti(I'=trim·ker·phi) |
| 90 | ·--·.0 | 90 | ·--·.0705611s·elapsed |
| 91 | ·············0··1 | 91 | ·············0··1 |
| 92 | o16·=·total:·1·12 | 92 | o16·=·total:·1·12 |
| 93 | ··········0:·1··. | 93 | ··········0:·1··. |
| 94 | ··········1:·.·12 | 94 | ··········1:·.·12 |
| 95 | o16·:·BettiTally | 95 | o16·:·BettiTally |
| 96 | i17·:·I'==·I | 96 | i17·:·I'==·I |
| 97 | o17·=·true | 97 | o17·=·true |
| 98 | i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 98 | i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 99 | ·--·1. | 99 | ·--·1.76866s·elapsed |
| 100 | i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 100 | i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 101 | ···························0··1 | 101 | ···························0··1 |
| 102 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} | 102 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} |
| 103 | ························0:·1··. | 103 | ························0:·1··. |
| 104 | ························1:·.··. | 104 | ························1:·.··. |
| Offset 130, 15 lines modified | Offset 130, 15 lines modified | ||
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·c=codim·I | 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·c=codim·I |
| 132 | o9·=·4</code></pre> | 132 | o9·=·4</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I | 135 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I |
| 136 | ·--·.0 | 136 | ·--·.0207379s·elapsed |
| 137 | ········1·······14·······33·······28·······8 | 137 | ········1·······14·······33·······28·······8 |
| 138 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 | 138 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 |
| 139 | ·················································· | 139 | ·················································· |
| 140 | ······0·······1········2········3········4·······5 | 140 | ······0·······1········2········3········4·······5 |
| 141 | o10·:·ChainComplex</code></pre> | 141 | o10·:·ChainComplex</code></pre> |
| Offset 55, 15 lines modified | Offset 55, 15 lines modified | ||
| 55 | ·········2:·.·12 | 55 | ·········2:·.·12 |
| 56 | o8·:·BettiTally | 56 | o8·:·BettiTally |
| 57 | i9·:·c=codim·I | 57 | i9·:·c=codim·I |
| 58 | o9·=·4 | 58 | o9·=·4 |
| 59 | i10·:·elapsedTime·fI=res·I | 59 | i10·:·elapsedTime·fI=res·I |
| 60 | ·--·.0 | 60 | ·--·.0207379s·elapsed |
| 61 | ········1·······14·······33·······28·······8 | 61 | ········1·······14·······33·······28·······8 |
| 62 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 | 62 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 |
| 63 | ······0·······1········2········3········4·······5 | 63 | ······0·······1········2········3········4·······5 |
| 64 | o10·:·ChainComplex | 64 | o10·:·ChainComplex |
| Offset 192, 15 lines modified | Offset 192, 15 lines modified | ||
| 192 | ··········<tr> | 192 | ··········<tr> |
| 193 | <td>··············<pre><code·class="language-macaulay2">i14·:·phi=map(P2,Pn,H); | 193 | <td>··············<pre><code·class="language-macaulay2">i14·:·phi=map(P2,Pn,H); |
| 194 | o14·:·RingMap·P2·<--·Pn</code></pre> | 194 | o14·:·RingMap·P2·<--·Pn</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi) | 197 | <td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi) |
| 198 | ·--·. | 198 | ·--·.519233s·elapsed |
| 199 | ·············0··1 | 199 | ·············0··1 |
| 200 | o15·=·total:·1·11 | 200 | o15·=·total:·1·11 |
| 201 | ··········0:·1··. | 201 | ··········0:·1··. |
| 202 | ··········1:·.··3 | 202 | ··········1:·.··3 |
| 203 | ··········2:·.··8 | 203 | ··········2:·.··8 |
| Offset 209, 15 lines modified | Offset 209, 15 lines modified | ||
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i16·:·I'==·I | 210 | <td>··············<pre><code·class="language-macaulay2">i16·:·I'==·I |
| 211 | o16·=·true</code></pre> | 211 | o16·=·true</code></pre> |
| 212 | </td>··········</tr> | 212 | </td>··········</tr> |
| 213 | ··········<tr> | 213 | ··········<tr> |
| 214 | <td>··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 214 | <td>··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 215 | ·--· | 215 | ·--·5.478s·elapsed</code></pre> |
| 216 | </td>··········</tr> | 216 | </td>··········</tr> |
| 217 | ··········<tr> | 217 | ··········<tr> |
| 218 | <td>··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 218 | <td>··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 219 | ··························0·1 | 219 | ··························0·1 |
| 220 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} | 220 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} |
| 221 | ·······················0:·1·2 | 221 | ·······················0:·1·2 |
| Offset 111, 28 lines modified | Offset 111, 28 lines modified | ||
| 111 | ··········6:·.·7 | 111 | ··········6:·.·7 |
| 112 | o13·:·BettiTally | 112 | o13·:·BettiTally |
| 113 | i14·:·phi=map(P2,Pn,H); | 113 | i14·:·phi=map(P2,Pn,H); |
| 114 | o14·:·RingMap·P2·<--·Pn | 114 | o14·:·RingMap·P2·<--·Pn |
| 115 | i15·:·elapsedTime·betti(I'=trim·ker·phi) | 115 | i15·:·elapsedTime·betti(I'=trim·ker·phi) |
| 116 | ·--·. | 116 | ·--·.519233s·elapsed |
| 117 | ·············0··1 | 117 | ·············0··1 |
| 118 | o15·=·total:·1·11 | 118 | o15·=·total:·1·11 |
| 119 | ··········0:·1··. | 119 | ··········0:·1··. |
| 120 | ··········1:·.··3 | 120 | ··········1:·.··3 |
| 121 | ··········2:·.··8 | 121 | ··········2:·.··8 |
| 122 | o15·:·BettiTally | 122 | o15·:·BettiTally |
| 123 | i16·:·I'==·I | 123 | i16·:·I'==·I |
| 124 | o16·=·true | 124 | o16·=·true |
| 125 | i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 125 | i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 126 | ·--· | 126 | ·--·5.478s·elapsed |
| 127 | i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 127 | i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 128 | ··························0·1 | 128 | ··························0·1 |
| 129 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} | 129 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} |
| 130 | ·······················0:·1·2 | 130 | ·······················0:·1·2 |
| 131 | ··························0·1 | 131 | ··························0·1 |
| 132 | ············(1,·3,·total:·1·3)·=>·8 | 132 | ············(1,·3,·total:·1·3)·=>·8 |
| Offset 167, 28 lines modified | Offset 167, 28 lines modified | ||
| 167 | ··········2:·.·. | 167 | ··········2:·.·. |
| 168 | ··········3:·.·8 | 168 | ··········3:·.·8 |
| 169 | o13·:·BettiTally</code></pre> | 169 | o13·:·BettiTally</code></pre> |
| 170 | </td>··········</tr> | 170 | </td>··········</tr> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H) | 172 | <td>··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H) |
| 173 | ·--·.0 | 173 | ·--·.0275377s·elapsed |
| 174 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) | 174 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) |
| 175 | o14·:·Ideal·of·P2</code></pre> | 175 | o14·:·Ideal·of·P2</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ··········<tr> | 177 | ··········<tr> |
| 178 | <td>··············<pre><code·class="language-macaulay2">i15·:·phi=map(P2,Pn,H); | 178 | <td>··············<pre><code·class="language-macaulay2">i15·:·phi=map(P2,Pn,H); |
| 179 | o15·:·RingMap·P2·<--·Pn</code></pre> | 179 | o15·:·RingMap·P2·<--·Pn</code></pre> |
| 180 | </td>··········</tr> | 180 | </td>··········</tr> |
| 181 | ··········<tr> | 181 | ··········<tr> |
| 182 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi) | 182 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi) |
| 183 | ·--·.0 | 183 | ·--·.0705611s·elapsed |
| 184 | ·············0··1 | 184 | ·············0··1 |
| 185 | o16·=·total:·1·12 | 185 | o16·=·total:·1·12 |
| 186 | ··········0:·1··. | 186 | ··········0:·1··. |
| 187 | ··········1:·.·12 | 187 | ··········1:·.·12 |
| 188 | o16·:·BettiTally</code></pre> | 188 | o16·:·BettiTally</code></pre> |
| Offset 196, 15 lines modified | Offset 196, 15 lines modified | ||
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i17·:·I'==·I | 197 | <td>··············<pre><code·class="language-macaulay2">i17·:·I'==·I |
| 198 | o17·=·true</code></pre> | 198 | o17·=·true</code></pre> |
| 199 | </td>··········</tr> | 199 | </td>··········</tr> |
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 201 | <td>··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 202 | ·--·1. | 202 | ·--·1.76866s·elapsed</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 205 | <td>··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 206 | ···························0··1 | 206 | ···························0··1 |
| 207 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} | 207 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} |
| 208 | ························0:·1··. | 208 | ························0:·1··. |
| Offset 83, 36 lines modified | Offset 83, 36 lines modified | ||
| 83 | ··········0:·1·. | 83 | ··········0:·1·. |
| 84 | ··········1:·.·. | 84 | ··········1:·.·. |
| 85 | ··········2:·.·. | 85 | ··········2:·.·. |
| 86 | ··········3:·.·8 | 86 | ··········3:·.·8 |
| 87 | o13·:·BettiTally | 87 | o13·:·BettiTally |
| 88 | i14·:·elapsedTime·sub(I,H) | 88 | i14·:·elapsedTime·sub(I,H) |
| 89 | ·--·.0 | 89 | ·--·.0275377s·elapsed |
| 90 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) | 90 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) |
| 91 | o14·:·Ideal·of·P2 | 91 | o14·:·Ideal·of·P2 |
| 92 | i15·:·phi=map(P2,Pn,H); | 92 | i15·:·phi=map(P2,Pn,H); |
| 93 | o15·:·RingMap·P2·<--·Pn | 93 | o15·:·RingMap·P2·<--·Pn |
| 94 | i16·:·elapsedTime·betti(I'=trim·ker·phi) | 94 | i16·:·elapsedTime·betti(I'=trim·ker·phi) |
| 95 | ·--·.0 | 95 | ·--·.0705611s·elapsed |
| 96 | ·············0··1 | 96 | ·············0··1 |
| 97 | o16·=·total:·1·12 | 97 | o16·=·total:·1·12 |
| 98 | ··········0:·1··. | 98 | ··········0:·1··. |
| 99 | ··········1:·.·12 | 99 | ··········1:·.·12 |
| 100 | o16·:·BettiTally | 100 | o16·:·BettiTally |
| 101 | i17·:·I'==·I | 101 | i17·:·I'==·I |
| 102 | o17·=·true | 102 | o17·=·true |
| 103 | i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 103 | i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 104 | ·--·1. | 104 | ·--·1.76866s·elapsed |
| 105 | i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 105 | i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 106 | ···························0··1 | 106 | ···························0··1 |
| 107 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} | 107 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} |
| 108 | ························0:·1··. | 108 | ························0:·1··. |
| 109 | ························1:·.··. | 109 | ························1:·.··. |
| 110 | ························2:·.··. | 110 | ························2:·.··. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | c3RhbmxleVJlaXNuZXIoTGlzdCxMaXN0KQ== | 8 | c3RhbmxleVJlaXNuZXIoTGlzdCxMaXN0KQ== |
| 9 | #:len=286 | 9 | #:len=286 |
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| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3RhbmxleVJlaXNuZXIsTGlzdCxMaXN0KSwic3Rh | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3RhbmxleVJlaXNuZXIsTGlzdCxMaXN0KSwic3Rh |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=15 | 7 | #:len=15 |
| 8 | YW5hbHl6ZShNb2R1bGUp | 8 | YW5hbHl6ZShNb2R1bGUp |
| 9 | #:len=251 | 9 | #:len=251 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbmFseXplLE1vZHVsZSksImFuYWx5emUoTW9kdWxl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbmFseXplLE1vZHVsZSksImFuYWx5emUoTW9kdWxl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | c2VxdWVuY2VUb1ZhcmlhYmxlU3ltYm9scw== | 8 | c2VxdWVuY2VUb1ZhcmlhYmxlU3ltYm9scw== |
| 9 | #:len=228 | 9 | #:len=228 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgsICJ1bmRvY3VtZW50ZWQiID0+IHRy | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgsICJ1bmRvY3VtZW50ZWQiID0+IHRy |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | dGF0ZVJlc29sdXRpb24= | 8 | dGF0ZVJlc29sdXRpb24= |
| 9 | #:len=2024 | 9 | #:len=2024 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluaXRlIHBpZWNlIG9mIHRoZSBUYXRl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluaXRlIHBpZWNlIG9mIHRoZSBUYXRl |
| 11 | IHJlc29sdXRpb24iLCAibGluZW51bSIgPT4gNzY5LCBJbnB1dHMgPT4ge1NQQU57VFR7Im0ifSwi | 11 | IHJlc29sdXRpb24iLCAibGluZW51bSIgPT4gNzY5LCBJbnB1dHMgPT4ge1NQQU57VFR7Im0ifSwi |
| Offset 114, 26 lines modified | Offset 114, 26 lines modified | ||
| 114 | ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··| | 114 | ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··| |
| 115 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| | 115 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| |
| 116 | ··············4······4 | 116 | ··············4······4 |
| 117 | o13·:·Matrix·A··<--·A | 117 | o13·:·Matrix·A··<--·A |
| 118 | i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) | 118 | i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) |
| 119 | ·--·used·0. | 119 | ·--·used·0.527137s·(cpu);·0.330387s·(thread);·0s·(gc) |
| 120 | ·············0·1·2 | 120 | ·············0·1·2 |
| 121 | o14·=·total:·3·6·3 | 121 | o14·=·total:·3·6·3 |
| 122 | ··········0:·3·.·. | 122 | ··········0:·3·.·. |
| 123 | ··········1:·.·6·. | 123 | ··········1:·.·6·. |
| 124 | ··········2:·.·.·3 | 124 | ··········2:·.·.·3 |
| 125 | o14·:·BettiTally | 125 | o14·:·BettiTally |
| 126 | i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) | 126 | i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) |
| 127 | ·--·used·0. | 127 | ·--·used·0.585122s·(cpu);·0.385726s·(thread);·0s·(gc) |
| 128 | ·············0·1·2 | 128 | ·············0·1·2 |
| 129 | o15·=·total:·3·6·3 | 129 | o15·=·total:·3·6·3 |
| 130 | ··········0:·3·.·. | 130 | ··········0:·3·.·. |
| 131 | ··········1:·.·6·. | 131 | ··········1:·.·6·. |
| 132 | ··········2:·.·.·3 | 132 | ··········2:·.·.·3 |
| Offset 228, 15 lines modified | Offset 228, 15 lines modified | ||
| 228 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| | 228 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| |
| 229 | ··············4······4 | 229 | ··············4······4 |
| 230 | o13·:·Matrix·A··<--·A</code></pre> | 230 | o13·:·Matrix·A··<--·A</code></pre> |
| 231 | </td>··········</tr> | 231 | </td>··········</tr> |
| 232 | ··········<tr> | 232 | ··········<tr> |
| 233 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) | 233 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) |
| 234 | ·--·used·0. | 234 | ·--·used·0.527137s·(cpu);·0.330387s·(thread);·0s·(gc) |
| 235 | ·············0·1·2 | 235 | ·············0·1·2 |
| 236 | o14·=·total:·3·6·3 | 236 | o14·=·total:·3·6·3 |
| 237 | ··········0:·3·.·. | 237 | ··········0:·3·.·. |
| 238 | ··········1:·.·6·. | 238 | ··········1:·.·6·. |
| 239 | ··········2:·.·.·3 | 239 | ··········2:·.·.·3 |
| Offset 245, 15 lines modified | Offset 245, 15 lines modified | ||
| 245 | ········</table> | 245 | ········</table> |
| 246 | ········<div> | 246 | ········<div> |
| 247 | ··········<p>With·the·form·<span·class="tt">pureResolution(p,q,D)</span>·we·can·directly·create·the·situation·of·<span·class="tt">pureResolution(M,D)</span>·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of·linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables·of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in·A·this·runs·much·faster·than·taking·a·random·matrix·M.</p> | 247 | ··········<p>With·the·form·<span·class="tt">pureResolution(p,q,D)</span>·we·can·directly·create·the·situation·of·<span·class="tt">pureResolution(M,D)</span>·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of·linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables·of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in·A·this·runs·much·faster·than·taking·a·random·matrix·M.</p> |
| 248 | ········</div> | 248 | ········</div> |
| 249 | ········<table·class="examples"> | 249 | ········<table·class="examples"> |
| 250 | ··········<tr> | 250 | ··········<tr> |
| 251 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) | 251 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) |
| 252 | ·--·used·0. | 252 | ·--·used·0.585122s·(cpu);·0.385726s·(thread);·0s·(gc) |
| 253 | ·············0·1·2 | 253 | ·············0·1·2 |
| 254 | o15·=·total:·3·6·3 | 254 | o15·=·total:·3·6·3 |
| 255 | ··········0:·3·.·. | 255 | ··········0:·3·.·. |
| 256 | ··········1:·.·6·. | 256 | ··········1:·.·6·. |
| 257 | ··········2:·.·.·3 | 257 | ··········2:·.·.·3 |
| Offset 162, 30 lines modified | Offset 162, 30 lines modified | ||
| 162 | ······|·-30a-29b·-29a-24b·-47a-39b·38a+2b···| | 162 | ······|·-30a-29b·-29a-24b·-47a-39b·38a+2b···| |
| 163 | ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··| | 163 | ······|·19a+19b··-38a-16b·-18a-13b·16a+22b··| |
| 164 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| | 164 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| |
| 165 | ··············4······4 | 165 | ··············4······4 |
| 166 | o13·:·Matrix·A··<--·A | 166 | o13·:·Matrix·A··<--·A |
| 167 | i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) | 167 | i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) |
| 168 | ·--·used·0. | 168 | ·--·used·0.527137s·(cpu);·0.330387s·(thread);·0s·(gc) |
| 169 | ·············0·1·2 | 169 | ·············0·1·2 |
| 170 | o14·=·total:·3·6·3 | 170 | o14·=·total:·3·6·3 |
| 171 | ··········0:·3·.·. | 171 | ··········0:·3·.·. |
| 172 | ··········1:·.·6·. | 172 | ··········1:·.·6·. |
| 173 | ··········2:·.·.·3 | 173 | ··········2:·.·.·3 |
| 174 | o14·:·BettiTally | 174 | o14·:·BettiTally |
| 175 | With·the·form·pureResolution(p,q,D)·we·can·directly·create·the·situation·of | 175 | With·the·form·pureResolution(p,q,D)·we·can·directly·create·the·situation·of |
| 176 | pureResolution(M,D)·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of | 176 | pureResolution(M,D)·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of |
| 177 | linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables | 177 | linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables |
| 178 | of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in | 178 | of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in |
| 179 | A·this·runs·much·faster·than·taking·a·random·matrix·M. | 179 | A·this·runs·much·faster·than·taking·a·random·matrix·M. |
| 180 | i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) | 180 | i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) |
| 181 | ·--·used·0. | 181 | ·--·used·0.585122s·(cpu);·0.385726s·(thread);·0s·(gc) |
| 182 | ·············0·1·2 | 182 | ·············0·1·2 |
| 183 | o15·=·total:·3·6·3 | 183 | o15·=·total:·3·6·3 |
| 184 | ··········0:·3·.·. | 184 | ··········0:·3·.·. |
| 185 | ··········1:·.·6·. | 185 | ··········1:·.·6·. |
| 186 | ··········2:·.·.·3 | 186 | ··········2:·.·.·3 |
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| 1 | --·-*-·M2-comint·-*-·hash:·1330545576567 | 1 | --·-*-·M2-comint·-*-·hash:·1330545576567 |
| 2 | i1·:·runBenchmarks·"res39" | 2 | i1·:·runBenchmarks·"res39" |
| 3 | --·beginning·computation· | 3 | --·beginning·computation·Wed·Dec·17·10:04:31·+14·2025 |
| 4 | --·Linux·i | 4 | --·Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 5 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz· | 5 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·1996.250·· |
| 6 | --·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0 | 6 | --·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0 |
| 7 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·. | 7 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.182448·seconds |
| 8 | i2·:· | 8 | i2·:· |
| Offset 73, 19 lines modified | Offset 73, 19 lines modified | ||
| 73 | ········<h2>Description</h2> | 73 | ········<h2>Description</h2> |
| 74 | ········<div> | 74 | ········<div> |
| 75 | ··········<p>The·tests·available·are:·<br>"deg2generic"·--·gb·of·a·generic·ideal·of·codimension·2·and·degree·2<br>"gb4by4comm"·--·gb·of·the·ideal·of·generic·commuting·4·by·4·matrices·over·ZZ/101<br>"gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables<br>"gbB148"·--·gb·of·Bayesian·graph·ideal·#148<br>"res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101<br>"resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)<br>"yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory<br>"yang-subring"·--·an·example·of·Yang-Hui·He<br></p> | 75 | ··········<p>The·tests·available·are:·<br>"deg2generic"·--·gb·of·a·generic·ideal·of·codimension·2·and·degree·2<br>"gb4by4comm"·--·gb·of·the·ideal·of·generic·commuting·4·by·4·matrices·over·ZZ/101<br>"gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables<br>"gbB148"·--·gb·of·Bayesian·graph·ideal·#148<br>"res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101<br>"resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)<br>"yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory<br>"yang-subring"·--·an·example·of·Yang-Hui·He<br></p> |
| 76 | ········</div> | 76 | ········</div> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·"res39" | 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·"res39" |
| 80 | --·beginning·computation· | 80 | --·beginning·computation·Wed·Dec·17·10:04:31·+14·2025 |
| 81 | --·Linux·i | 81 | --·Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 82 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz· | 82 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·1996.250·· |
| 83 | --·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0 | 83 | --·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0 |
| 84 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·. | 84 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.182448·seconds</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ········</table> | 86 | ········</table> |
| 87 | ······</div> | 87 | ······</div> |
| 88 | ······<div·class="waystouse"> | 88 | ······<div·class="waystouse"> |
| 89 | ········<h2>For·the·programmer</h2> | 89 | ········<h2>For·the·programmer</h2> |
| 90 | ········<p>The·object·<a·href="_run__Benchmarks.html">runBenchmarks</a>·is·<span>a·<a·title="the·class·of·all·commands"·href="../../Macaulay2Doc/html/___Command.html">command</a></span>.</p> | 90 | ········<p>The·object·<a·href="_run__Benchmarks.html">runBenchmarks</a>·is·<span>a·<a·title="the·class·of·all·commands"·href="../../Macaulay2Doc/html/___Command.html">command</a></span>.</p> |
| 91 | ······</div> | 91 | ······</div> |
| Offset 24, 15 lines modified | Offset 24, 15 lines modified | ||
| 24 | "gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables | 24 | "gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables |
| 25 | "gbB148"·--·gb·of·Bayesian·graph·ideal·#148 | 25 | "gbB148"·--·gb·of·Bayesian·graph·ideal·#148 |
| 26 | "res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101 | 26 | "res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101 |
| 27 | "resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5) | 27 | "resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5) |
| 28 | "yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory | 28 | "yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory |
| 29 | "yang-subring"·--·an·example·of·Yang-Hui·He | 29 | "yang-subring"·--·an·example·of·Yang-Hui·He |
| 30 | i1·:·runBenchmarks·"res39" | 30 | i1·:·runBenchmarks·"res39" |
| 31 | --·beginning·computation·Tue·Nov·12·23:39:47·-12·2024 | ||
| 32 | --· | 31 | --·beginning·computation·Wed·Dec·17·10:04:31·+14·2025 |
| 32 | --·Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian | ||
| 33 | 6.1.11 | 33 | 6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 34 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz· | 34 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·1996.250 |
| 35 | --·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0 | 35 | --·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0 |
| 36 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·. | 36 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.182448·seconds |
| 37 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 37 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 38 | The·object·_\x8r_\x8u_\x8n_\x8B_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k_\x8s·is·a·_\x8c_\x8o_\x8m_\x8m_\x8a_\x8n_\x8d. | 38 | The·object·_\x8r_\x8u_\x8n_\x8B_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k_\x8s·is·a·_\x8c_\x8o_\x8m_\x8m_\x8a_\x8n_\x8d. |
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| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]--> | 82 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]--> |
| 83 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> | 83 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> |
| 84 | ··············<li> | 84 | ··············<li> |
| 85 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> | 85 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> |
| 86 | ··············<li> | 86 | ··············<li> |
| 87 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> | 87 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> |
| 88 | ··············<li> | 88 | ··············<li> |
| 89 | <span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2- | 89 | <span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-3667083-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li> |
| 90 | ··············<li> | 90 | ··············<li> |
| 91 | <span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li> | 91 | <span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li> |
| 92 | ············</ul> | 92 | ············</ul> |
| 93 | ··········</li> | 93 | ··········</li> |
| 94 | ··········<li> | 94 | ··········<li> |
| 95 | Outputs:············<ul> | 95 | Outputs:············<ul> |
| 96 | ··············<li> | 96 | ··············<li> |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | ············"OutPoints", | 27 | ············"OutPoints", |
| 28 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates | 28 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates |
| 29 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real | 29 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real |
| 30 | ············number·or·random·complex·number | 30 | ············number·or·random·complex·number |
| 31 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates | 31 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates |
| 32 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real | 32 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real |
| 33 | ············number·or·random·complex·number | 33 | ············number·or·random·complex·number |
| 34 | ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2- | 34 | ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-3667083-0/0",·Option·to |
| 35 | ············change·directory·for·file·storage. | 35 | ············change·directory·for·file·storage. |
| 36 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional | 36 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional |
| 37 | ············output | 37 | ············output |
| 38 | ····*·Outputs: | 38 | ····*·Outputs: |
| 39 | ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·whose·entries·are·lists·of·solutions·for·each | 39 | ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·whose·entries·are·lists·of·solutions·for·each |
| 40 | ············target·system | 40 | ············target·system |
| 41 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 41 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| Offset 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | ··············<li> | 88 | ··············<li> |
| 89 | <span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]--> | 89 | <span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]--> |
| 90 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> | 90 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> |
| 91 | ··············<li> | 91 | ··············<li> |
| 92 | <span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]--> | 92 | <span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]--> |
| 93 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> | 93 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> |
| 94 | ··············<li> | 94 | ··············<li> |
| 95 | <span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2- | 95 | <span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-3667083-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li> |
| 96 | ··············<li> | 96 | ··············<li> |
| 97 | <span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li> | 97 | <span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li> |
| 98 | ············</ul> | 98 | ············</ul> |
| 99 | ··········</li> | 99 | ··········</li> |
| 100 | ··········<li> | 100 | ··········<li> |
| 101 | Outputs:············<ul> | 101 | Outputs:············<ul> |
| 102 | ··············<li> | 102 | ··············<li> |
| Offset 22, 15 lines modified | Offset 22, 15 lines modified | ||
| 22 | ············value·{}, | 22 | ············value·{}, |
| 23 | ··········o·HomVariableGroup·(missing·documentation)·=>·...,·default·value·{}, | 23 | ··········o·HomVariableGroup·(missing·documentation)·=>·...,·default·value·{}, |
| 24 | ··········o·M2Precision·(missing·documentation)·=>·...,·default·value·53, | 24 | ··········o·M2Precision·(missing·documentation)·=>·...,·default·value·53, |
| 25 | ··········o·OutputStyle·(missing·documentation)·=>·...,·default·value | 25 | ··········o·OutputStyle·(missing·documentation)·=>·...,·default·value |
| 26 | ············"OutPoints", | 26 | ············"OutPoints", |
| 27 | ··········o·RandomComplex·(missing·documentation)·=>·...,·default·value·{}, | 27 | ··········o·RandomComplex·(missing·documentation)·=>·...,·default·value·{}, |
| 28 | ··········o·RandomReal·(missing·documentation)·=>·...,·default·value·{}, | 28 | ··········o·RandomReal·(missing·documentation)·=>·...,·default·value·{}, |
| 29 | ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2- | 29 | ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-3667083-0/0",·Option·to |
| 30 | ············change·directory·for·file·storage. | 30 | ············change·directory·for·file·storage. |
| 31 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional | 31 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional |
| 32 | ············output | 32 | ············output |
| 33 | ····*·Outputs: | 33 | ····*·Outputs: |
| 34 | ··········o·S0,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·solutions·to·the·target·system | 34 | ··········o·S0,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·solutions·to·the·target·system |
| 35 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 35 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 36 | This·method·calls·Bertini·to·track·a·user-defined·homotopy.·The·user·needs·to | 36 | This·method·calls·Bertini·to·track·a·user-defined·homotopy.·The·user·needs·to |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]--> | 91 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]--> |
| 92 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> | 92 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> |
| 93 | ··············<li> | 93 | ··············<li> |
| 94 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> | 94 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> |
| 95 | ··············<li> | 95 | ··············<li> |
| 96 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> | 96 | <span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li> |
| 97 | ··············<li> | 97 | ··············<li> |
| 98 | <span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2- | 98 | <span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-3667083-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li> |
| 99 | ··············<li> | 99 | ··············<li> |
| 100 | <span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]--> | 100 | <span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]--> |
| 101 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span>··············</li> | 101 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span>··············</li> |
| 102 | ··············<li> | 102 | ··············<li> |
| 103 | <span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li> | 103 | <span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li> |
| 104 | ············</ul> | 104 | ············</ul> |
| 105 | ··········</li> | 105 | ··········</li> |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | ············"OutPoints", | 33 | ············"OutPoints", |
| 34 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates | 34 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates |
| 35 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real | 35 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real |
| 36 | ············number·or·random·complex·number | 36 | ············number·or·random·complex·number |
| 37 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates | 37 | ··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates |
| 38 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real | 38 | ············symbols/strings/variables·that·will·be·set·to·be·a·random·real |
| 39 | ············number·or·random·complex·number | 39 | ············number·or·random·complex·number |
| 40 | ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2- | 40 | ··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-3667083-0/0",·Option·to |
| 41 | ············change·directory·for·file·storage. | 41 | ············change·directory·for·file·storage. |
| 42 | ··········o·UseRegeneration·(missing·documentation)·=>·...,·default·value·-1, | 42 | ··········o·UseRegeneration·(missing·documentation)·=>·...,·default·value·-1, |
| 43 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional | 43 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional |
| 44 | ············output | 44 | ············output |
| 45 | ····*·Outputs: | 45 | ····*·Outputs: |
| 46 | ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·points·that·are·contained·in·the·variety·of·F | 46 | ··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·points·that·are·contained·in·the·variety·of·F |
| 47 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 47 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | aW52ZXJzZVJpbmdBY3RvcnMoLi4uLFN1Yj0+Li4uKQ== | 8 | aW52ZXJzZVJpbmdBY3RvcnMoLi4uLFN1Yj0+Li4uKQ== |
| 9 | #:len=264 | 9 | #:len=264 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjg0OCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjg0OCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaW52ZXJzZVJpbmdBY3RvcnMsU3ViXSwiaW52ZXJz | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaW52ZXJzZVJpbmdBY3RvcnMsU3ViXSwiaW52ZXJz |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | i8·:·A·=·action(RI,S7) | 76 | i8·:·A·=·action(RI,S7) |
| 77 | o8·=·ChainComplex·with·15·actors | 77 | o8·=·ChainComplex·with·15·actors |
| 78 | o8·:·ActionOnComplex | 78 | o8·:·ActionOnComplex |
| 79 | i9·:·elapsedTime·c·=·character·A | 79 | i9·:·elapsedTime·c·=·character·A |
| 80 | ·--·. | 80 | ·--·.632303s·elapsed |
| 81 | o9·=·Character·over·R | 81 | o9·=·Character·over·R |
| 82 | ······ | 82 | ······ |
| 83 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| | 83 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| |
| 84 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| | 84 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| |
| 85 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| | 85 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| |
| 86 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| | 86 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | i6·:·A=action(RI,S6) | 100 | i6·:·A=action(RI,S6) |
| 101 | o6·=·ChainComplex·with·11·actors | 101 | o6·=·ChainComplex·with·11·actors |
| 102 | o6·:·ActionOnComplex | 102 | o6·:·ActionOnComplex |
| 103 | i7·:·elapsedTime·c=character·A | 103 | i7·:·elapsedTime·c=character·A |
| 104 | ·--·.4 | 104 | ·--·.453337s·elapsed |
| 105 | o7·=·Character·over·R | 105 | o7·=·Character·over·R |
| 106 | ······ | 106 | ······ |
| 107 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| | 107 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| |
| 108 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| | 108 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| |
| 109 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| | 109 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| |
| 110 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| | 110 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| |
| Offset 187, 27 lines modified | Offset 187, 27 lines modified | ||
| 187 | i19·:·A2·=·action(RI2,G,Sub=>false) | 187 | i19·:·A2·=·action(RI2,G,Sub=>false) |
| 188 | o19·=·ChainComplex·with·6·actors | 188 | o19·=·ChainComplex·with·6·actors |
| 189 | o19·:·ActionOnComplex | 189 | o19·:·ActionOnComplex |
| 190 | i20·:·elapsedTime·a1·=·character·A1 | 190 | i20·:·elapsedTime·a1·=·character·A1 |
| 191 | ·--· | 191 | ·--·.939647s·elapsed |
| 192 | o20·=·Character·over·R | 192 | o20·=·Character·over·R |
| 193 | ······· | 193 | ······· |
| 194 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 194 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 195 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 195 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 196 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| | 196 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| |
| 197 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| | 197 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| |
| 198 | o20·:·Character | 198 | o20·:·Character |
| 199 | i21·:·elapsedTime·a2·=·character·A2 | 199 | i21·:·elapsedTime·a2·=·character·A2 |
| 200 | ·--·3 | 200 | ·--·39.6342s·elapsed |
| 201 | o21·=·Character·over·R | 201 | o21·=·Character·over·R |
| 202 | ······· | 202 | ······· |
| 203 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 203 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 204 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| | 204 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| |
| 205 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 205 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 206 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 206 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| Offset 297, 15 lines modified | Offset 297, 15 lines modified | ||
| 297 | i31·:·B·=·action(M,G,Sub=>false) | 297 | i31·:·B·=·action(M,G,Sub=>false) |
| 298 | o31·=·Module·with·6·actors | 298 | o31·=·Module·with·6·actors |
| 299 | o31·:·ActionOnGradedModule | 299 | o31·:·ActionOnGradedModule |
| 300 | i32·:·elapsedTime·b·=·character(B,21) | 300 | i32·:·elapsedTime·b·=·character(B,21) |
| 301 | ·--·1 | 301 | ·--·18.7836s·elapsed |
| 302 | o32·=·Character·over·R | 302 | o32·=·Character·over·R |
| 303 | ······· | 303 | ······· |
| 304 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| | 304 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| |
| 305 | o32·:·Character | 305 | o32·:·Character |
| Offset 138, 15 lines modified | Offset 138, 15 lines modified | ||
| 138 | o8·=·ChainComplex·with·15·actors | 138 | o8·=·ChainComplex·with·15·actors |
| 139 | o8·:·ActionOnComplex</code></pre> | 139 | o8·:·ActionOnComplex</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·c·=·character·A | 142 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·c·=·character·A |
| 143 | ·--·. | 143 | ·--·.632303s·elapsed |
| 144 | o9·=·Character·over·R | 144 | o9·=·Character·over·R |
| 145 | ······ | 145 | ······ |
| 146 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| | 146 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| |
| 147 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| | 147 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| |
| 148 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| | 148 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| |
| 149 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| | 149 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | o7·:·List | 91 | o7·:·List |
| 92 | i8·:·A·=·action(RI,S7) | 92 | i8·:·A·=·action(RI,S7) |
| 93 | o8·=·ChainComplex·with·15·actors | 93 | o8·=·ChainComplex·with·15·actors |
| 94 | o8·:·ActionOnComplex | 94 | o8·:·ActionOnComplex |
| 95 | i9·:·elapsedTime·c·=·character·A | 95 | i9·:·elapsedTime·c·=·character·A |
| 96 | ·--·. | 96 | ·--·.632303s·elapsed |
| 97 | o9·=·Character·over·R | 97 | o9·=·Character·over·R |
| 98 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| | 98 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| |
| 99 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| | 99 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| |
| 100 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| | 100 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| |
| 101 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| | 101 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| |
| Offset 160, 15 lines modified | Offset 160, 15 lines modified | ||
| 160 | o6·=·ChainComplex·with·11·actors | 160 | o6·=·ChainComplex·with·11·actors |
| 161 | o6·:·ActionOnComplex</code></pre> | 161 | o6·:·ActionOnComplex</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·c=character·A | 164 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·c=character·A |
| 165 | ·--·.4 | 165 | ·--·.453337s·elapsed |
| 166 | o7·=·Character·over·R | 166 | o7·=·Character·over·R |
| 167 | ······ | 167 | ······ |
| 168 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| | 168 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| |
| 169 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| | 169 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| |
| 170 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| | 170 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| |
| 171 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| | 171 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| |
| Offset 113, 15 lines modified | Offset 113, 15 lines modified | ||
| 113 | o5·:·List | 113 | o5·:·List |
| 114 | i6·:·A=action(RI,S6) | 114 | i6·:·A=action(RI,S6) |
| 115 | o6·=·ChainComplex·with·11·actors | 115 | o6·=·ChainComplex·with·11·actors |
| 116 | o6·:·ActionOnComplex | 116 | o6·:·ActionOnComplex |
| 117 | i7·:·elapsedTime·c=character·A | 117 | i7·:·elapsedTime·c=character·A |
| 118 | ·--·.4 | 118 | ·--·.453337s·elapsed |
| 119 | o7·=·Character·over·R | 119 | o7·=·Character·over·R |
| 120 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| | 120 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| |
| 121 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| | 121 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| |
| 122 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| | 122 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| |
| 123 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| | 123 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| |
| Offset 264, 28 lines modified | Offset 264, 28 lines modified | ||
| 264 | o19·=·ChainComplex·with·6·actors | 264 | o19·=·ChainComplex·with·6·actors |
| 265 | o19·:·ActionOnComplex</code></pre> | 265 | o19·:·ActionOnComplex</code></pre> |
| 266 | </td>··········</tr> | 266 | </td>··········</tr> |
| 267 | ··········<tr> | 267 | ··········<tr> |
| 268 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·a1·=·character·A1 | 268 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·a1·=·character·A1 |
| 269 | ·--· | 269 | ·--·.939647s·elapsed |
| 270 | o20·=·Character·over·R | 270 | o20·=·Character·over·R |
| 271 | ······· | 271 | ······· |
| 272 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 272 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 273 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 273 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 274 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| | 274 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| |
| 275 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| | 275 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| |
| 276 | o20·:·Character</code></pre> | 276 | o20·:·Character</code></pre> |
| 277 | </td>··········</tr> | 277 | </td>··········</tr> |
| 278 | ··········<tr> | 278 | ··········<tr> |
| 279 | <td>··············<pre><code·class="language-macaulay2">i21·:·elapsedTime·a2·=·character·A2 | 279 | <td>··············<pre><code·class="language-macaulay2">i21·:·elapsedTime·a2·=·character·A2 |
| 280 | ·--·3 | 280 | ·--·39.6342s·elapsed |
| 281 | o21·=·Character·over·R | 281 | o21·=·Character·over·R |
| 282 | ······· | 282 | ······· |
| 283 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 283 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 284 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| | 284 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| |
| 285 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 285 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 286 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 286 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| Offset 397, 15 lines modified | Offset 397, 15 lines modified | ||
| 397 | o31·=·Module·with·6·actors | 397 | o31·=·Module·with·6·actors |
| 398 | o31·:·ActionOnGradedModule</code></pre> | 398 | o31·:·ActionOnGradedModule</code></pre> |
| 399 | </td>··········</tr> | 399 | </td>··········</tr> |
| 400 | ··········<tr> | 400 | ··········<tr> |
| 401 | <td>··············<pre><code·class="language-macaulay2">i32·:·elapsedTime·b·=·character(B,21) | 401 | <td>··············<pre><code·class="language-macaulay2">i32·:·elapsedTime·b·=·character(B,21) |
| 402 | ·--·1 | 402 | ·--·18.7836s·elapsed |
| 403 | o32·=·Character·over·R | 403 | o32·=·Character·over·R |
| 404 | ······· | 404 | ······· |
| 405 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| | 405 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| |
| 406 | o32·:·Character</code></pre> | 406 | o32·:·Character</code></pre> |
| 407 | </td>··········</tr> | 407 | </td>··········</tr> |
| Offset 192, 26 lines modified | Offset 192, 26 lines modified | ||
| 192 | o18·:·ActionOnComplex | 192 | o18·:·ActionOnComplex |
| 193 | i19·:·A2·=·action(RI2,G,Sub=>false) | 193 | i19·:·A2·=·action(RI2,G,Sub=>false) |
| 194 | o19·=·ChainComplex·with·6·actors | 194 | o19·=·ChainComplex·with·6·actors |
| 195 | o19·:·ActionOnComplex | 195 | o19·:·ActionOnComplex |
| 196 | i20·:·elapsedTime·a1·=·character·A1 | 196 | i20·:·elapsedTime·a1·=·character·A1 |
| 197 | ·--· | 197 | ·--·.939647s·elapsed |
| 198 | o20·=·Character·over·R | 198 | o20·=·Character·over·R |
| 199 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 199 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 200 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 200 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 201 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| | 201 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| |
| 202 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| | 202 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| |
| 203 | o20·:·Character | 203 | o20·:·Character |
| 204 | i21·:·elapsedTime·a2·=·character·A2 | 204 | i21·:·elapsedTime·a2·=·character·A2 |
| 205 | ·--·3 | 205 | ·--·39.6342s·elapsed |
| 206 | o21·=·Character·over·R | 206 | o21·=·Character·over·R |
| 207 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 207 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 208 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| | 208 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| |
| 209 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 209 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 210 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 210 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| Offset 308, 15 lines modified | Offset 308, 15 lines modified | ||
| 308 | i30·:·M·=·Is2·/·I2; | 308 | i30·:·M·=·Is2·/·I2; |
| 309 | i31·:·B·=·action(M,G,Sub=>false) | 309 | i31·:·B·=·action(M,G,Sub=>false) |
| 310 | o31·=·Module·with·6·actors | 310 | o31·=·Module·with·6·actors |
| 311 | o31·:·ActionOnGradedModule | 311 | o31·:·ActionOnGradedModule |
| 312 | i32·:·elapsedTime·b·=·character(B,21) | 312 | i32·:·elapsedTime·b·=·character(B,21) |
| 313 | ·--·1 | 313 | ·--·18.7836s·elapsed |
| 314 | o32·=·Character·over·R | 314 | o32·=·Character·over·R |
| 315 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| | 315 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| |
| 316 | o32·:·Character | 316 | o32·:·Character |
| 317 | i33·:·b/T | 317 | i33·:·b/T |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 9 | #:len=397 | 9 | #:len=397 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBtZXRob2QgZm9yIGJyb3dzaW5nIGFu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBtZXRob2QgZm9yIGJyb3dzaW5nIGFu |
| 11 | ZCBleGFtaW5pbmcgTWFjYXVsYXkyIGRhdGEgc3RydWN0dXJlcyIsIERlc2NyaXB0aW9uID0+ICgi | 11 | ZCBleGFtaW5pbmcgTWFjYXVsYXkyIGRhdGEgc3RydWN0dXJlcyIsIERlc2NyaXB0aW9uID0+ICgi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=19 | 7 | #:len=19 |
| 8 | aXNTeXp5Z3koTW9kdWxlLFpaKQ== | 8 | aXNTeXp5Z3koTW9kdWxlLFpaKQ== |
| 9 | #:len=228 | 9 | #:len=228 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDYyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDYyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpc1N5enlneSxNb2R1bGUsWlopLCJpc1N5enlneShN | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpc1N5enlneSxNb2R1bGUsWlopLCJpc1N5enlneShN |
| Offset 230, 15 lines modified | Offset 230, 15 lines modified | ||
| 230 | ··········0:·1·.·.·.·. | 230 | ··········0:·1·.·.·.·. |
| 231 | ··········1:·.·4·2·.·. | 231 | ··········1:·.·4·2·.·. |
| 232 | ··········2:·.·1·6·5·1 | 232 | ··········2:·.·1·6·5·1 |
| 233 | o22·:·BettiTally | 233 | o22·:·BettiTally |
| 234 | i23·:·time·j=bruns·F.dd_3; | 234 | i23·:·time·j=bruns·F.dd_3; |
| 235 | ·--·used·0. | 235 | ·--·used·0.232378s·(cpu);·0.19161s·(thread);·0s·(gc) |
| 236 | o23·:·Ideal·of·S | 236 | o23·:·Ideal·of·S |
| 237 | i24·:·betti·res·j | 237 | i24·:·betti·res·j |
| 238 | ·············0·1·2·3·4 | 238 | ·············0·1·2·3·4 |
| 239 | o24·=·total:·1·3·6·5·1 | 239 | o24·=·total:·1·3·6·5·1 |
| Offset 336, 15 lines modified | Offset 336, 15 lines modified | ||
| 336 | ··········1:·.·4·2·.·. | 336 | ··········1:·.·4·2·.·. |
| 337 | ··········2:·.·1·6·5·1 | 337 | ··········2:·.·1·6·5·1 |
| 338 | o22·:·BettiTally</code></pre> | 338 | o22·:·BettiTally</code></pre> |
| 339 | </td>··········</tr> | 339 | </td>··········</tr> |
| 340 | ··········<tr> | 340 | ··········<tr> |
| 341 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·j=bruns·F.dd_3; | 341 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·j=bruns·F.dd_3; |
| 342 | ·--·used·0. | 342 | ·--·used·0.232378s·(cpu);·0.19161s·(thread);·0s·(gc) |
| 343 | o23·:·Ideal·of·S</code></pre> | 343 | o23·:·Ideal·of·S</code></pre> |
| 344 | </td>··········</tr> | 344 | </td>··········</tr> |
| 345 | ··········<tr> | 345 | ··········<tr> |
| 346 | <td>··············<pre><code·class="language-macaulay2">i24·:·betti·res·j | 346 | <td>··············<pre><code·class="language-macaulay2">i24·:·betti·res·j |
| 347 | ·············0·1·2·3·4 | 347 | ·············0·1·2·3·4 |
| Offset 231, 15 lines modified | Offset 231, 15 lines modified | ||
| 231 | o22·=·total:·1·5·8·5·1 | 231 | o22·=·total:·1·5·8·5·1 |
| 232 | ··········0:·1·.·.·.·. | 232 | ··········0:·1·.·.·.·. |
| 233 | ··········1:·.·4·2·.·. | 233 | ··········1:·.·4·2·.·. |
| 234 | ··········2:·.·1·6·5·1 | 234 | ··········2:·.·1·6·5·1 |
| 235 | o22·:·BettiTally | 235 | o22·:·BettiTally |
| 236 | i23·:·time·j=bruns·F.dd_3; | 236 | i23·:·time·j=bruns·F.dd_3; |
| 237 | ·--·used·0. | 237 | ·--·used·0.232378s·(cpu);·0.19161s·(thread);·0s·(gc) |
| 238 | o23·:·Ideal·of·S | 238 | o23·:·Ideal·of·S |
| 239 | i24·:·betti·res·j | 239 | i24·:·betti·res·j |
| 240 | ·············0·1·2·3·4 | 240 | ·············0·1·2·3·4 |
| 241 | o24·=·total:·1·3·6·5·1 | 241 | o24·=·total:·1·3·6·5·1 |
| 242 | ··········0:·1·.·.·.·. | 242 | ··········0:·1·.·.·.·. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=28 | 7 | #:len=28 |
| 8 | c3ViY29tcGxleChDZWxsQ29tcGxleCxMaXN0KQ== | 8 | c3ViY29tcGxleChDZWxsQ29tcGxleCxMaXN0KQ== |
| 9 | #:len=297 | 9 | #:len=297 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTUwNCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTUwNCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ViY29tcGxleCxDZWxsQ29tcGxleCxMaXN0KSwi | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ViY29tcGxleCxDZWxsQ29tcGxleCxMaXN0KSwi |
| Offset 20, 18 lines modified | Offset 20, 18 lines modified | ||
| 20 | i10·:·f·=·newCell({e12,e23,e34,e41}); | 20 | i10·:·f·=·newCell({e12,e23,e34,e41}); |
| 21 | i11·:·C·=·cellComplex(R,{f}); | 21 | i11·:·C·=·cellComplex(R,{f}); |
| 22 | i12·:·facePoset·C | 22 | i12·:·facePoset·C |
| 23 | o12·=·Relation·Matrix:·|·1·0·0·0· | 23 | o12·=·Relation·Matrix:·|·1·0·0·0·1·0·1·0·1·| |
| 24 | ·······················|·0·1·0·0·0·1· | 24 | ·······················|·0·1·0·0·0·1·1·0·1·| |
| 25 | ·······················|·0·0·1·0· | 25 | ·······················|·0·0·1·0·0·1·0·1·1·| |
| 26 | ·······················|·0·0·0·1·1·0· | 26 | ·······················|·0·0·0·1·1·0·0·1·1·| |
| 27 | ·······················|·0·0·0·0·1·0·0·0·1·| | 27 | ·······················|·0·0·0·0·1·0·0·0·1·| |
| 28 | ·······················|·0·0·0·0·0·1·0·0·1·| | 28 | ·······················|·0·0·0·0·0·1·0·0·1·| |
| 29 | ·······················|·0·0·0·0·0·0·1·0·1·| | 29 | ·······················|·0·0·0·0·0·0·1·0·1·| |
| 30 | ·······················|·0·0·0·0·0·0·0·1·1·| | 30 | ·······················|·0·0·0·0·0·0·0·1·1·| |
| 31 | ·······················|·0·0·0·0·0·0·0·0·1·| | 31 | ·······················|·0·0·0·0·0·0·0·0·1·| |
| 32 | o12·:·Poset | 32 | o12·:·Poset |
| Offset 19, 16 lines modified | Offset 19, 16 lines modified | ||
| 19 | ··························· | 19 | ··························· |
| 20 | ·····-1·····0······1······2 | 20 | ·····-1·····0······1······2 |
| 21 | o4·:·Complex | 21 | o4·:·Complex |
| 22 | i5·:·cells(1,H)/cellLabel | 22 | i5·:·cells(1,H)/cellLabel |
| 23 | ·······3·5····4·5···2········2····4·4····5·3 | 23 | ·······5·4···3·5····4·5···2········2····4·4····5·3 |
| 24 | o5·=·{x·y· | 24 | o5·=·{x·y·,·x·y·z,·x·y·,·x·y*z,·x*y·z,·x·y·z,·x·y·z} |
| 25 | o5·:·List | 25 | o5·:·List |
| 26 | i6·:·cells(2,H)/cellLabel | 26 | i6·:·cells(2,H)/cellLabel |
| 27 | ·······5·4····4·5 | 27 | ·······5·4····4·5 |
| 28 | o6·=·{x·y·z,·x·y·z} | 28 | o6·=·{x·y·z,·x·y·z} |
| Offset 22, 20 lines modified | Offset 22, 20 lines modified | ||
| 22 | i11·:·T·=·new·HashTable·from·{v0·=>·a^2*b,·v1·=>·b*c^2,·v2·=>·b^2,·v3·=>·a*c}; | 22 | i11·:·T·=·new·HashTable·from·{v0·=>·a^2*b,·v1·=>·b*c^2,·v2·=>·b^2,·v3·=>·a*c}; |
| 23 | i12·:·relabeledC·=·relabelCellComplex(C,T); | 23 | i12·:·relabeledC·=·relabelCellComplex(C,T); |
| 24 | i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) | 24 | i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) |
| 25 | ········ | 25 | ··········2···2········2 |
| 26 | o13·=·{b·,· | 26 | o13·=·{b*c·,·b·,·a*c,·a·b} |
| 27 | o13·:·List | 27 | o13·:·List |
| 28 | i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) | 28 | i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) |
| 29 | ········2·2··· | 29 | ········2·2·······2·····2····2···2···2·2 |
| 30 | o14·=·{ | 30 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} |
| 31 | o14·:·List | 31 | o14·:·List |
| 32 | i15·:· | 32 | i15·:· |
| Offset 19, 16 lines modified | Offset 19, 16 lines modified | ||
| 19 | ···················· | 19 | ···················· |
| 20 | ·····-1·····0······1 | 20 | ·····-1·····0······1 |
| 21 | o4·:·Complex | 21 | o4·:·Complex |
| 22 | i5·:·cells(1,C)/cellLabel | 22 | i5·:·cells(1,C)/cellLabel |
| 23 | ······· | 23 | ·········2····4·5···2······5·4 |
| 24 | o5·=·{x | 24 | o5·=·{x*y·z,·x·y·,·x·y*z,·x·y·} |
| 25 | o5·:·List | 25 | o5·:·List |
| 26 | i6·:·cells(2,C)/cellLabel | 26 | i6·:·cells(2,C)/cellLabel |
| 27 | o6·=·{} | 27 | o6·=·{} |
| Offset 105, 18 lines modified | Offset 105, 18 lines modified | ||
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i11·:·C·=·cellComplex(R,{f});</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i11·:·C·=·cellComplex(R,{f});</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i12·:·facePoset·C | 110 | <td>··············<pre><code·class="language-macaulay2">i12·:·facePoset·C |
| 111 | o12·=·Relation·Matrix:·|·1·0·0·0· | 111 | o12·=·Relation·Matrix:·|·1·0·0·0·1·0·1·0·1·| |
| 112 | ·······················|·0·1·0·0·0·1· | 112 | ·······················|·0·1·0·0·0·1·1·0·1·| |
| 113 | ·······················|·0·0·1·0· | 113 | ·······················|·0·0·1·0·0·1·0·1·1·| |
| 114 | ·······················|·0·0·0·1·1·0· | 114 | ·······················|·0·0·0·1·1·0·0·1·1·| |
| 115 | ·······················|·0·0·0·0·1·0·0·0·1·| | 115 | ·······················|·0·0·0·0·1·0·0·0·1·| |
| 116 | ·······················|·0·0·0·0·0·1·0·0·1·| | 116 | ·······················|·0·0·0·0·0·1·0·0·1·| |
| 117 | ·······················|·0·0·0·0·0·0·1·0·1·| | 117 | ·······················|·0·0·0·0·0·0·1·0·1·| |
| 118 | ·······················|·0·0·0·0·0·0·0·1·1·| | 118 | ·······················|·0·0·0·0·0·0·0·1·1·| |
| 119 | ·······················|·0·0·0·0·0·0·0·0·1·| | 119 | ·······················|·0·0·0·0·0·0·0·0·1·| |
| 120 | o12·:·Poset</code></pre> | 120 | o12·:·Poset</code></pre> |
| Offset 26, 18 lines modified | Offset 26, 18 lines modified | ||
| 26 | i7·:·e23·=·newCell({v2,v3}); | 26 | i7·:·e23·=·newCell({v2,v3}); |
| 27 | i8·:·e34·=·newCell({v3,v4}); | 27 | i8·:·e34·=·newCell({v3,v4}); |
| 28 | i9·:·e41·=·newCell({v4,v1}); | 28 | i9·:·e41·=·newCell({v4,v1}); |
| 29 | i10·:·f·=·newCell({e12,e23,e34,e41}); | 29 | i10·:·f·=·newCell({e12,e23,e34,e41}); |
| 30 | i11·:·C·=·cellComplex(R,{f}); | 30 | i11·:·C·=·cellComplex(R,{f}); |
| 31 | i12·:·facePoset·C | 31 | i12·:·facePoset·C |
| 32 | o12·=·Relation·Matrix:·|·1·0·0·0· | 32 | o12·=·Relation·Matrix:·|·1·0·0·0·1·0·1·0·1·| |
| 33 | ·······················|·0·1·0·0·0·1· | 33 | ·······················|·0·1·0·0·0·1·1·0·1·| |
| 34 | ·······················|·0·0·1·0· | 34 | ·······················|·0·0·1·0·0·1·0·1·1·| |
| 35 | ·······················|·0·0·0·1·1·0· | 35 | ·······················|·0·0·0·1·1·0·0·1·1·| |
| 36 | ·······················|·0·0·0·0·1·0·0·0·1·| | 36 | ·······················|·0·0·0·0·1·0·0·0·1·| |
| 37 | ·······················|·0·0·0·0·0·1·0·0·1·| | 37 | ·······················|·0·0·0·0·0·1·0·0·1·| |
| 38 | ·······················|·0·0·0·0·0·0·1·0·1·| | 38 | ·······················|·0·0·0·0·0·0·1·0·1·| |
| 39 | ·······················|·0·0·0·0·0·0·0·1·1·| | 39 | ·······················|·0·0·0·0·0·0·0·1·1·| |
| 40 | ·······················|·0·0·0·0·0·0·0·0·1·| | 40 | ·······················|·0·0·0·0·0·0·0·0·1·| |
| 41 | o12·:·Poset | 41 | o12·:·Poset |
| Offset 101, 16 lines modified | Offset 101, 16 lines modified | ||
| 101 | ·····-1·····0······1······2 | 101 | ·····-1·····0······1······2 |
| 102 | o4·:·Complex</code></pre> | 102 | o4·:·Complex</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·cells(1,H)/cellLabel | 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·cells(1,H)/cellLabel |
| 106 | ·······3·5····4·5···2········2····4·4····5·3 | 106 | ·······5·4···3·5····4·5···2········2····4·4····5·3 |
| 107 | o5·=·{x·y· | 107 | o5·=·{x·y·,·x·y·z,·x·y·,·x·y*z,·x*y·z,·x·y·z,·x·y·z} |
| 108 | o5·:·List</code></pre> | 108 | o5·:·List</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·cells(2,H)/cellLabel | 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·cells(2,H)/cellLabel |
| 112 | ·······5·4····4·5 | 112 | ·······5·4····4·5 |
| Offset 40, 16 lines modified | Offset 40, 16 lines modified | ||
| 40 | o4·=·S··<--·S··<--·S··<--·S | 40 | o4·=·S··<--·S··<--·S··<--·S |
| 41 | ·····-1·····0······1······2 | 41 | ·····-1·····0······1······2 |
| 42 | o4·:·Complex | 42 | o4·:·Complex |
| 43 | i5·:·cells(1,H)/cellLabel | 43 | i5·:·cells(1,H)/cellLabel |
| 44 | ·······3·5····4·5···2········2····4·4····5·3 | 44 | ·······5·4···3·5····4·5···2········2····4·4····5·3 |
| 45 | o5·=·{x·y· | 45 | o5·=·{x·y·,·x·y·z,·x·y·,·x·y*z,·x*y·z,·x·y·z,·x·y·z} |
| 46 | o5·:·List | 46 | o5·:·List |
| 47 | i6·:·cells(2,H)/cellLabel | 47 | i6·:·cells(2,H)/cellLabel |
| 48 | ·······5·4····4·5 | 48 | ·······5·4····4·5 |
| 49 | o6·=·{x·y·z,·x·y·z} | 49 | o6·=·{x·y·z,·x·y·z} |
| Offset 114, 24 lines modified | Offset 114, 24 lines modified | ||
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i12·:·relabeledC·=·relabelCellComplex(C,T);</code></pre> | 116 | <td>··············<pre><code·class="language-macaulay2">i12·:·relabeledC·=·relabelCellComplex(C,T);</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) | 119 | <td>··············<pre><code·class="language-macaulay2">i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) |
| 120 | ········ | 120 | ··········2···2········2 |
| 121 | o13·=·{b·,· | 121 | o13·=·{b*c·,·b·,·a*c,·a·b} |
| 122 | o13·:·List</code></pre> | 122 | o13·:·List</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) | 125 | <td>··············<pre><code·class="language-macaulay2">i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) |
| 126 | ········2·2··· | 126 | ········2·2·······2·····2····2···2···2·2 |
| 127 | o14·=·{ | 127 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} |
| 128 | o14·:·List</code></pre> | 128 | o14·:·List</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ········</table> | 130 | ········</table> |
| 131 | ······</div> | 131 | ······</div> |
| 132 | ······<div> | 132 | ······<div> |
| 133 | ········<h2>See·also</h2> | 133 | ········<h2>See·also</h2> |
| Offset 32, 22 lines modified | Offset 32, 22 lines modified | ||
| 32 | i8·:·v1·=·verts#1; | 32 | i8·:·v1·=·verts#1; |
| 33 | i9·:·v2·=·verts#2; | 33 | i9·:·v2·=·verts#2; |
| 34 | i10·:·v3·=·verts#3; | 34 | i10·:·v3·=·verts#3; |
| 35 | i11·:·T·=·new·HashTable·from·{v0·=>·a^2*b,·v1·=>·b*c^2,·v2·=>·b^2,·v3·=>·a*c}; | 35 | i11·:·T·=·new·HashTable·from·{v0·=>·a^2*b,·v1·=>·b*c^2,·v2·=>·b^2,·v3·=>·a*c}; |
| 36 | i12·:·relabeledC·=·relabelCellComplex(C,T); | 36 | i12·:·relabeledC·=·relabelCellComplex(C,T); |
| 37 | i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) | 37 | i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) |
| 38 | ········ | 38 | ··········2···2········2 |
| 39 | o13·=·{b·,· | 39 | o13·=·{b*c·,·b·,·a*c,·a·b} |
| 40 | o13·:·List | 40 | o13·:·List |
| 41 | i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) | 41 | i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) |
| 42 | ········2·2··· | 42 | ········2·2·······2·····2····2···2···2·2 |
| 43 | o14·=·{ | 43 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} |
| 44 | o14·:·List | 44 | o14·:·List |
| 45 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 45 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 46 | ····*·_\x8c_\x8e_\x8l_\x8l_\x8L_\x8a_\x8b_\x8e_\x8l·--·return·the·label·of·a·cell | 46 | ····*·_\x8c_\x8e_\x8l_\x8l_\x8L_\x8a_\x8b_\x8e_\x8l·--·return·the·label·of·a·cell |
| 47 | ····*·_\x8R_\x8i_\x8n_\x8g_\x8M_\x8a_\x8p_\x8·_\x8*_\x8*_\x8·_\x8C_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·--·tensors·labels·via·a·ring·map | 47 | ····*·_\x8R_\x8i_\x8n_\x8g_\x8M_\x8a_\x8p_\x8·_\x8*_\x8*_\x8·_\x8C_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·--·tensors·labels·via·a·ring·map |
| 48 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8re\x8el\x8la\x8ab\x8be\x8el\x8lC\x8Ce\x8el\x8ll\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·*\x8**\x8**\x8**\x8**\x8* | 48 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8re\x8el\x8la\x8ab\x8be\x8el\x8lC\x8Ce\x8el\x8ll\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 49 | ····*·relabelCellComplex(CellComplex,HashTable) | 49 | ····*·relabelCellComplex(CellComplex,HashTable) |
| Offset 95, 16 lines modified | Offset 95, 16 lines modified | ||
| 95 | ·····-1·····0······1 | 95 | ·····-1·····0······1 |
| 96 | o4·:·Complex</code></pre> | 96 | o4·:·Complex</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·cells(1,C)/cellLabel | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·cells(1,C)/cellLabel |
| 100 | ······· | 100 | ·········2····4·5···2······5·4 |
| 101 | o5·=·{x | 101 | o5·=·{x*y·z,·x·y·,·x·y*z,·x·y·} |
| 102 | o5·:·List</code></pre> | 102 | o5·:·List</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·cells(2,C)/cellLabel | 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·cells(2,C)/cellLabel |
| 106 | o6·=·{} | 106 | o6·=·{} |
| Offset 30, 16 lines modified | Offset 30, 16 lines modified | ||
| 30 | o4·=·S··<--·S··<--·S | 30 | o4·=·S··<--·S··<--·S |
| 31 | ·····-1·····0······1 | 31 | ·····-1·····0······1 |
| 32 | o4·:·Complex | 32 | o4·:·Complex |
| 33 | i5·:·cells(1,C)/cellLabel | 33 | i5·:·cells(1,C)/cellLabel |
| 34 | ······· | 34 | ·········2····4·5···2······5·4 |
| 35 | o5·=·{x | 35 | o5·=·{x*y·z,·x·y·,·x·y*z,·x·y·} |
| 36 | o5·:·List | 36 | o5·:·List |
| 37 | i6·:·cells(2,C)/cellLabel | 37 | i6·:·cells(2,C)/cellLabel |
| 38 | o6·=·{} | 38 | o6·=·{} |
| 39 | o6·:·List | 39 | o6·:·List |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=30 | 7 | #:len=30 |
| 8 | SG9tKENoYWluQ29tcGxleCxDaGFpbkNvbXBsZXgp | 8 | SG9tKENoYWluQ29tcGxleCxDaGFpbkNvbXBsZXgp |
| 9 | #:len=1256 | 9 | #:len=1256 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ3JlYXRlIHRoZSBob21vbW9ycGhpc20g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ3JlYXRlIHRoZSBob21vbW9ycGhpc20g |
| 11 | Y29tcGxleCBvZiBhIHBhaXIgb2YgY2hhaW4gY29tcGxleGVzLiIsICJsaW5lbnVtIiA9PiA4MDcs | 11 | Y29tcGxleCBvZiBhIHBhaXIgb2YgY2hhaW4gY29tcGxleGVzLiIsICJsaW5lbnVtIiA9PiA4MDcs |
| Offset 63, 15 lines modified | Offset 63, 15 lines modified | ||
| 63 | o11·:·ChainComplex | 63 | o11·:·ChainComplex |
| 64 | i12·:·isMinimalChainComplex·E | 64 | i12·:·isMinimalChainComplex·E |
| 65 | o12·=·false | 65 | o12·=·false |
| 66 | i13·:·time·m·=·minimize·(E[1]); | 66 | i13·:·time·m·=·minimize·(E[1]); |
| 67 | ·--·used·0.2 | 67 | ·--·used·0.260431s·(cpu);·0.201973s·(thread);·0s·(gc) |
| 68 | i14·:·isQuasiIsomorphism·m | 68 | i14·:·isQuasiIsomorphism·m |
| 69 | o14·=·true | 69 | o14·=·true |
| 70 | i15·:·E[1]·==·source·m | 70 | i15·:·E[1]·==·source·m |
| Offset 27, 18 lines modified | Offset 27, 18 lines modified | ||
| 27 | i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5); | 27 | i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5); |
| 28 | i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i); | 28 | i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i); |
| 29 | i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S)); | 29 | i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S)); |
| 30 | i8·:·time·m·=·resolutionOfChainComplex·C; | 30 | i8·:·time·m·=·resolutionOfChainComplex·C; |
| 31 | ·--·used·0.1 | 31 | ·--·used·0.148572s·(cpu);·0.104796s·(thread);·0s·(gc) |
| 32 | i9·:·time·n·=·cartanEilenbergResolution·C; | 32 | i9·:·time·n·=·cartanEilenbergResolution·C; |
| 33 | ·--·used·0.1 | 33 | ·--·used·0.126174s·(cpu);·0.126796s·(thread);·0s·(gc) |
| 34 | i10·:·betti·source·m | 34 | i10·:·betti·source·m |
| 35 | ·············0··1··2···3···4···5···6···7 | 35 | ·············0··1··2···3···4···5···6···7 |
| 36 | o10·=·total:·1·19·80·181·312·484·447·156 | 36 | o10·=·total:·1·19·80·181·312·484·447·156 |
| 37 | ··········0:·1··3··3···1···.···.···.···. | 37 | ··········0:·1··3··3···1···.···.···.···. |
| 38 | ··········1:·.··.··1···3···3···.···.···. | 38 | ··········1:·.··.··1···3···3···.···.···. |
| Offset 155, 15 lines modified | Offset 155, 15 lines modified | ||
| 155 | ········</table> | 155 | ········</table> |
| 156 | ········<div> | 156 | ········<div> |
| 157 | ··········<p>Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero,·and·thus·is·part·of·the·minimization.</p> | 157 | ··········<p>Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero,·and·thus·is·part·of·the·minimization.</p> |
| 158 | ········</div> | 158 | ········</div> |
| 159 | ········<table·class="examples"> | 159 | ········<table·class="examples"> |
| 160 | ··········<tr> | 160 | ··········<tr> |
| 161 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·m·=·minimize·(E[1]); | 161 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·m·=·minimize·(E[1]); |
| 162 | ·--·used·0.2 | 162 | ·--·used·0.260431s·(cpu);·0.201973s·(thread);·0s·(gc)</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i14·:·isQuasiIsomorphism·m | 165 | <td>··············<pre><code·class="language-macaulay2">i14·:·isQuasiIsomorphism·m |
| 166 | o14·=·true</code></pre> | 166 | o14·=·true</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | o11·:·ChainComplex | 80 | o11·:·ChainComplex |
| 81 | i12·:·isMinimalChainComplex·E | 81 | i12·:·isMinimalChainComplex·E |
| 82 | o12·=·false | 82 | o12·=·false |
| 83 | Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero, | 83 | Now·we·minimize·the·result.·The·free·summand·we·added·to·the·end·maps·to·zero, |
| 84 | and·thus·is·part·of·the·minimization. | 84 | and·thus·is·part·of·the·minimization. |
| 85 | i13·:·time·m·=·minimize·(E[1]); | 85 | i13·:·time·m·=·minimize·(E[1]); |
| 86 | ·--·used·0.2 | 86 | ·--·used·0.260431s·(cpu);·0.201973s·(thread);·0s·(gc) |
| 87 | i14·:·isQuasiIsomorphism·m | 87 | i14·:·isQuasiIsomorphism·m |
| 88 | o14·=·true | 88 | o14·=·true |
| 89 | i15·:·E[1]·==·source·m | 89 | i15·:·E[1]·==·source·m |
| 90 | o15·=·true | 90 | o15·=·true |
| 91 | i16·:·E'·=·target·m | 91 | i16·:·E'·=·target·m |
| Offset 116, 19 lines modified | Offset 116, 19 lines modified | ||
| 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);</code></pre> | 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S));</code></pre> | 119 | <td>··············<pre><code·class="language-macaulay2">i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i-1),mods_i,substitute(matrix·C.dd_i,S));</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·m·=·resolutionOfChainComplex·C; | 122 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·m·=·resolutionOfChainComplex·C; |
| 123 | ·--·used·0.1 | 123 | ·--·used·0.148572s·(cpu);·0.104796s·(thread);·0s·(gc)</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·n·=·cartanEilenbergResolution·C; | 126 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·n·=·cartanEilenbergResolution·C; |
| 127 | ·--·used·0.1 | 127 | ·--·used·0.126174s·(cpu);·0.126796s·(thread);·0s·(gc)</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i10·:·betti·source·m | 130 | <td>··············<pre><code·class="language-macaulay2">i10·:·betti·source·m |
| 131 | ·············0··1··2···3···4···5···6···7 | 131 | ·············0··1··2···3···4···5···6···7 |
| 132 | o10·=·total:·1·19·80·181·312·484·447·156 | 132 | o10·=·total:·1·19·80·181·312·484·447·156 |
| 133 | ··········0:·1··3··3···1···.···.···.···. | 133 | ··········0:·1··3··3···1···.···.···.···. |
| Offset 50, 17 lines modified | Offset 50, 17 lines modified | ||
| 50 | o4·:·RingMap·R·<--·S | 50 | o4·:·RingMap·R·<--·S |
| 51 | i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5); | 51 | i5·:·C·=·res(R^1/(ideal·vars·R))**(R^1/(ideal·vars·R)^5); |
| 52 | i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i); | 52 | i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i); |
| 53 | i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i- | 53 | i7·:·C·=·chainComplex·for·i·from·min·C+1·to·max·C·list·map(mods_(i- |
| 54 | 1),mods_i,substitute(matrix·C.dd_i,S)); | 54 | 1),mods_i,substitute(matrix·C.dd_i,S)); |
| 55 | i8·:·time·m·=·resolutionOfChainComplex·C; | 55 | i8·:·time·m·=·resolutionOfChainComplex·C; |
| 56 | ·--·used·0.1 | 56 | ·--·used·0.148572s·(cpu);·0.104796s·(thread);·0s·(gc) |
| 57 | i9·:·time·n·=·cartanEilenbergResolution·C; | 57 | i9·:·time·n·=·cartanEilenbergResolution·C; |
| 58 | ·--·used·0.1 | 58 | ·--·used·0.126174s·(cpu);·0.126796s·(thread);·0s·(gc) |
| 59 | i10·:·betti·source·m | 59 | i10·:·betti·source·m |
| 60 | ·············0··1··2···3···4···5···6···7 | 60 | ·············0··1··2···3···4···5···6···7 |
| 61 | o10·=·total:·1·19·80·181·312·484·447·156 | 61 | o10·=·total:·1·19·80·181·312·484·447·156 |
| 62 | ··········0:·1··3··3···1···.···.···.···. | 62 | ··········0:·1··3··3···1···.···.···.···. |
| 63 | ··········1:·.··.··1···3···3···.···.···. | 63 | ··········1:·.··.··1···3···3···.···.···. |
| 64 | ··········2:·.··1··3···3···2···.···.···. | 64 | ··········2:·.··1··3···3···2···.···.···. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=41 | 7 | #:len=41 |
| 8 | cmV2ZXJzZUZhY3RvcnMoQ2hhaW5Db21wbGV4LENoYWluQ29tcGxleCk= | 8 | cmV2ZXJzZUZhY3RvcnMoQ2hhaW5Db21wbGV4LENoYWluQ29tcGxleCk= |
| 9 | #:len=335 | 9 | #:len=335 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjEzLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjEzLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyZXZlcnNlRmFjdG9ycyxDaGFpbkNvbXBsZXgsQ2hh | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyZXZlcnNlRmFjdG9ycyxDaGFpbkNvbXBsZXgsQ2hh |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | TXVsdGlQcm9qQ29vcmRSaW5n | 8 | TXVsdGlQcm9qQ29vcmRSaW5n |
| 9 | #:len=2206 | 9 | #:len=2206 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQSBxdWljayB3YXkgdG8gYnVpbGQgdGhl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQSBxdWljayB3YXkgdG8gYnVpbGQgdGhl |
| 11 | IGNvb3JkaW5hdGUgcmluZyBvZiBhIHByb2R1Y3Qgb2YgcHJvamVjdGl2ZSBzcGFjZXMiLCAibGlu | 11 | IGNvb3JkaW5hdGUgcmluZyBvZiBhIHByb2R1Y3Qgb2YgcHJvamVjdGl2ZSBzcGFjZXMiLCAibGlu |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | ··············2··············2 | 83 | ··············2··············2 |
| 84 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) | 84 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) |
| 85 | ··············0·3····1·2·4···2·5 | 85 | ··············0·3····1·2·4···2·5 |
| 86 | o14·:·Ideal·of·R | 86 | o14·:·Ideal·of·R |
| 87 | i15·:·time·csmK=CSM(A,K) | 87 | i15·:·time·csmK=CSM(A,K) |
| 88 | ·--·used· | 88 | ·--·used·2.2165s·(cpu);·0.499524s·(thread);·0s·(gc) |
| 89 | ········2·2·····2·········2····2············2 | 89 | ········2·2·····2·········2····2············2 |
| 90 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 90 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 91 | ········1·2·····1·2·····1·2····1·····1·2····2 | 91 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 92 | o15·:·A | 92 | o15·:·A |
| Offset 124, 15 lines modified | Offset 124, 15 lines modified | ||
| 124 | ········2·2·····2·········2·····2·············2 | 124 | ········2·2·····2·········2·····2·············2 |
| 125 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h | 125 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h |
| 126 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 | 126 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 |
| 127 | o21·:·A | 127 | o21·:·A |
| 128 | i22·:·time·CSM(A,K,m) | 128 | i22·:·time·CSM(A,K,m) |
| 129 | ·--·used·0. | 129 | ·--·used·0.237307s·(cpu);·0.100396s·(thread);·0s·(gc) |
| 130 | ········2·2·····2·········2····2············2 | 130 | ········2·2·····2·········2····2············2 |
| 131 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 131 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 132 | ········1·2·····1·2·····1·2····1·····1·2····2 | 132 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 133 | o22·:·A | 133 | o22·:·A |
| Offset 9, 28 lines modified | Offset 9, 28 lines modified | ||
| 9 | i2·:·U·=·toricProjectiveSpace·7 | 9 | i2·:·U·=·toricProjectiveSpace·7 |
| 10 | o2·=·U | 10 | o2·=·U |
| 11 | o2·:·NormalToricVariety | 11 | o2·:·NormalToricVariety |
| 12 | i3·:·time·CSM·U | 12 | i3·:·time·CSM·U |
| 13 | ·--·used·0.1 | 13 | ·--·used·0.193418s·(cpu);·0.102879s·(thread);·0s·(gc) |
| 14 | ·······7······6······5······4······3······2 | 14 | ·······7······6······5······4······3······2 |
| 15 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 15 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 16 | ·······7······7······7······7······7······7·····7 | 16 | ·······7······7······7······7······7······7·····7 |
| 17 | ················································ZZ[x·..x·] | 17 | ················································ZZ[x·..x·] |
| 18 | ····················································0···7 | 18 | ····················································0···7 |
| 19 | o3·:·----------------------------------------------------------------------------------------------- | 19 | o3·:·----------------------------------------------------------------------------------------------- |
| 20 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·) | 20 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·) |
| 21 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7 | 21 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7 |
| 22 | i4·:·time·CSM(U,CheckSmooth=>false) | 22 | i4·:·time·CSM(U,CheckSmooth=>false) |
| 23 | ·--·used·0. | 23 | ·--·used·0.447512s·(cpu);·0.244803s·(thread);·0s·(gc) |
| 24 | ·······7······6······5······4······3······2 | 24 | ·······7······6······5······4······3······2 |
| 25 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 25 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 26 | ·······7······7······7······7······7······7·····7 | 26 | ·······7······7······7······7······7······7·····7 |
| 27 | ················································ZZ[x·..x·] | 27 | ················································ZZ[x·..x·] |
| 28 | ····················································0···7 | 28 | ····················································0···7 |
| Offset 18, 29 lines modified | Offset 18, 29 lines modified | ||
| 18 | i3·:·R=ZZ/32749[v_0..v_5]; | 18 | i3·:·R=ZZ/32749[v_0..v_5]; |
| 19 | i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3)); | 19 | i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3)); |
| 20 | o4·:·Ideal·of·R | 20 | o4·:·Ideal·of·R |
| 21 | i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) | 21 | i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) |
| 22 | ·--·used· | 22 | ·--·used·1.08487s·(cpu);·0.367339s·(thread);·0s·(gc) |
| 23 | ·······5······4······3······2 | 23 | ·······5······4······3······2 |
| 24 | o5·=·6h··+·14h··+·14h··+·10h | 24 | o5·=·6h··+·14h··+·14h··+·10h |
| 25 | ·······1······1······1······1 | 25 | ·······1······1······1······1 |
| 26 | ·····ZZ[h·] | 26 | ·····ZZ[h·] |
| 27 | ·········1 | 27 | ·········1 |
| 28 | o5·:·------ | 28 | o5·:·------ |
| 29 | ········6 | 29 | ········6 |
| 30 | ·······h | 30 | ·······h |
| 31 | ········1 | 31 | ········1 |
| 32 | i6·:·time·CSM(I,CompMethod=>PnResidual) | 32 | i6·:·time·CSM(I,CompMethod=>PnResidual) |
| 33 | ·--·used· | 33 | ·--·used·2.15673s·(cpu);·1.89646s·(thread);·0s·(gc) |
| 34 | ·······5······4······3······2 | 34 | ·······5······4······3······2 |
| 35 | o6·=·6H··+·14H··+·14H··+·10H | 35 | o6·=·6H··+·14H··+·14H··+·10H |
| 36 | ·····ZZ[H] | 36 | ·····ZZ[H] |
| 37 | o6·:·----- | 37 | o6·:·----- |
| 38 | ········6 | 38 | ········6 |
| Offset 53, 29 lines modified | Offset 53, 29 lines modified | ||
| 53 | i8·:·S=QQ[s_0..s_3]; | 53 | i8·:·S=QQ[s_0..s_3]; |
| 54 | i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3)); | 54 | i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3)); |
| 55 | o9·:·Ideal·of·S | 55 | o9·:·Ideal·of·S |
| 56 | i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) | 56 | i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) |
| 57 | ·--·used·0. | 57 | ·--·used·0.423849s·(cpu);·0.210667s·(thread);·0s·(gc) |
| 58 | ········3·····2 | 58 | ········3·····2 |
| 59 | o10·=·3h··+·5h | 59 | o10·=·3h··+·5h |
| 60 | ········1·····1 | 60 | ········1·····1 |
| 61 | ······ZZ[h·] | 61 | ······ZZ[h·] |
| 62 | ··········1 | 62 | ··········1 |
| 63 | o10·:·------ | 63 | o10·:·------ |
| 64 | ·········4 | 64 | ·········4 |
| 65 | ········h | 65 | ········h |
| 66 | ·········1 | 66 | ·········1 |
| 67 | i11·:·time·CSM(K,CompMethod=>PnResidual) | 67 | i11·:·time·CSM(K,CompMethod=>PnResidual) |
| 68 | ·--·used·0. | 68 | ·--·used·0.22171s·(cpu);·0.114416s·(thread);·0s·(gc) |
| 69 | ········3·····2 | 69 | ········3·····2 |
| 70 | o11·=·3H··+·5H | 70 | o11·=·3H··+·5H |
| 71 | ······ZZ[H] | 71 | ······ZZ[H] |
| 72 | o11·:·----- | 72 | o11·:·----- |
| 73 | ·········4 | 73 | ·········4 |
| Offset 21, 20 lines modified | Offset 21, 20 lines modified | ||
| 21 | ·············2························································2 | 21 | ·············2························································2 |
| 22 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) | 22 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) |
| 23 | ·············3·········0·4········1·4·········2·4·········3·4·········4 | 23 | ·············3·········0·4········1·4·········2·4·········3·4·········4 |
| 24 | o3·:·Ideal·of·R | 24 | o3·:·Ideal·of·R |
| 25 | i4·:·time·Euler(I,InputIsSmooth=>true) | 25 | i4·:·time·Euler(I,InputIsSmooth=>true) |
| 26 | ·--·used·0. | 26 | ·--·used·0.162477s·(cpu);·0.0700406s·(thread);·0s·(gc) |
| 27 | o4·=·4 | 27 | o4·=·4 |
| 28 | i5·:·time·Euler·I | 28 | i5·:·time·Euler·I |
| 29 | ·--·used·0.2 | 29 | ·--·used·0.276327s·(cpu);·0.147121s·(thread);·0s·(gc) |
| 30 | o5·=·4 | 30 | o5·=·4 |
| 31 | i6·:·EulerIHash=Euler(I,Output=>HashForm); | 31 | i6·:·EulerIHash=Euler(I,Output=>HashForm); |
| 32 | i7·:·A=ring·EulerIHash#"CSM" | 32 | i7·:·A=ring·EulerIHash#"CSM" |
| Offset 62, 20 lines modified | Offset 62, 20 lines modified | ||
| 62 | ·····------------------------------------------------------------------------ | 62 | ·····------------------------------------------------------------------------ |
| 63 | ·····-·x·x·) | 63 | ·····-·x·x·) |
| 64 | ········0·3 | 64 | ········0·3 |
| 65 | o9·:·Ideal·of·R | 65 | o9·:·Ideal·of·R |
| 66 | i10·:·time·Euler(J,Method=>DirectCompleteInt) | 66 | i10·:·time·Euler(J,Method=>DirectCompleteInt) |
| 67 | ·--·used·0. | 67 | ·--·used·0.41416s·(cpu);·0.10607s·(thread);·0s·(gc) |
| 68 | o10·=·2 | 68 | o10·=·2 |
| 69 | i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) | 69 | i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) |
| 70 | ·--·used·0. | 70 | ·--·used·0.251136s·(cpu);·0.0756807s·(thread);·0s·(gc) |
| 71 | o11·=·2 | 71 | o11·=·2 |
| 72 | i12·:·R=MultiProjCoordRing({2,2}) | 72 | i12·:·R=MultiProjCoordRing({2,2}) |
| 73 | o12·=·R | 73 | o12·=·R |
| Offset 7, 29 lines modified | Offset 7, 29 lines modified | ||
| 7 | o1·:·PolynomialRing | 7 | o1·:·PolynomialRing |
| 8 | i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R)); | 8 | i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R)); |
| 9 | o2·:·Ideal·of·R | 9 | o2·:·Ideal·of·R |
| 10 | i3·:·time·CSM(I,Method=>DirectCompletInt) | 10 | i3·:·time·CSM(I,Method=>DirectCompletInt) |
| 11 | ·--·used· | 11 | ·--·used·4.6779s·(cpu);·1.28724s·(thread);·0s·(gc) |
| 12 | ·······2·2·····2·········2 | 12 | ·······2·2·····2·········2 |
| 13 | o3·=·2h·h··+·2h·h··+·5h·h | 13 | o3·=·2h·h··+·2h·h··+·5h·h |
| 14 | ·······1·2·····1·2·····1·2 | 14 | ·······1·2·····1·2·····1·2 |
| 15 | ·····ZZ[h·..h·] | 15 | ·····ZZ[h·..h·] |
| 16 | ·········1···2 | 16 | ·········1···2 |
| 17 | o3·:·---------- | 17 | o3·:·---------- |
| 18 | ········3···3 | 18 | ········3···3 |
| 19 | ······(h·,·h·) | 19 | ······(h·,·h·) |
| 20 | ········1···2 | 20 | ········1···2 |
| 21 | i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) | 21 | i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) |
| 22 | ·--·used· | 22 | ·--·used·4.43929s·(cpu);·1.26914s·(thread);·0s·(gc) |
| 23 | ·······2·2·····2·········2 | 23 | ·······2·2·····2·········2 |
| 24 | o4·=·2h·h··+·2h·h··+·5h·h | 24 | o4·=·2h·h··+·2h·h··+·5h·h |
| 25 | ·······1·2·····1·2·····1·2 | 25 | ·······1·2·····1·2·····1·2 |
| 26 | ·····ZZ[h·..h·] | 26 | ·····ZZ[h·..h·] |
| 27 | ·········1···2 | 27 | ·········1···2 |
| Offset 3, 43 lines modified | Offset 3, 43 lines modified | ||
| 3 | i1·:·R·=·ZZ/32749[x_0..x_4]; | 3 | i1·:·R·=·ZZ/32749[x_0..x_4]; |
| 4 | i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); | 4 | i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); |
| 5 | o2·:·Ideal·of·R | 5 | o2·:·Ideal·of·R |
| 6 | i3·:·time·CSM·I | 6 | i3·:·time·CSM·I |
| 7 | ·--·used· | 7 | ·--·used·1.12499s·(cpu);·0.47701s·(thread);·0s·(gc) |
| 8 | ·······3 | 8 | ·······3 |
| 9 | o3·=·4h | 9 | o3·=·4h |
| 10 | ·······1 | 10 | ·······1 |
| 11 | ·····ZZ[h·] | 11 | ·····ZZ[h·] |
| 12 | ·········1 | 12 | ·········1 |
| 13 | o3·:·------ | 13 | o3·:·------ |
| 14 | ········5 | 14 | ········5 |
| 15 | ·······h | 15 | ·······h |
| 16 | ········1 | 16 | ········1 |
| 17 | i4·:·time·CSM(I,InputIsSmooth=>true) | 17 | i4·:·time·CSM(I,InputIsSmooth=>true) |
| 18 | ·--·used·0. | 18 | ·--·used·0.18877s·(cpu);·0.0569748s·(thread);·0s·(gc) |
| 19 | ·······3 | 19 | ·······3 |
| 20 | o4·=·4h | 20 | o4·=·4h |
| 21 | ·······1 | 21 | ·······1 |
| 22 | ·····ZZ[h·] | 22 | ·····ZZ[h·] |
| 23 | ·········1 | 23 | ·········1 |
| 24 | o4·:·------ | 24 | o4·:·------ |
| 25 | ········5 | 25 | ········5 |
| 26 | ·······h | 26 | ·······h |
| 27 | ········1 | 27 | ········1 |
| 28 | i5·:·time·Chern·I | 28 | i5·:·time·Chern·I |
| 29 | ·--·used·0.0 | 29 | ·--·used·0.0533118s·(cpu);·0.0392388s·(thread);·0s·(gc) |
| 30 | ·······3 | 30 | ·······3 |
| 31 | o5·=·4h | 31 | o5·=·4h |
| 32 | ·······1 | 32 | ·······1 |
| 33 | ·····ZZ[h·] | 33 | ·····ZZ[h·] |
| 34 | ·········1 | 34 | ·········1 |
| Offset 7, 29 lines modified | Offset 7, 29 lines modified | ||
| 7 | o1·:·PolynomialRing | 7 | o1·:·PolynomialRing |
| 8 | i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); | 8 | i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); |
| 9 | o2·:·Ideal·of·R | 9 | o2·:·Ideal·of·R |
| 10 | i3·:·time·CSM·I | 10 | i3·:·time·CSM·I |
| 11 | ·--·used· | 11 | ·--·used·2.47526s·(cpu);·0.990371s·(thread);·0s·(gc) |
| 12 | ········5······4·····3 | 12 | ········5······4·····3 |
| 13 | o3·=·12h··+·10h··+·6h | 13 | o3·=·12h··+·10h··+·6h |
| 14 | ········1······1·····1 | 14 | ········1······1·····1 |
| 15 | ·····ZZ[h·] | 15 | ·····ZZ[h·] |
| 16 | ·········1 | 16 | ·········1 |
| 17 | o3·:·------ | 17 | o3·:·------ |
| 18 | ········7 | 18 | ········7 |
| 19 | ·······h | 19 | ·······h |
| 20 | ········1 | 20 | ········1 |
| 21 | i4·:·time·CSM(I,Method=>DirectCompleteInt) | 21 | i4·:·time·CSM(I,Method=>DirectCompleteInt) |
| 22 | ·--·used·0. | 22 | ·--·used·0.727905s·(cpu);·0.242391s·(thread);·0s·(gc) |
| 23 | ········5······4·····3 | 23 | ········5······4·····3 |
| 24 | o4·=·12h··+·10h··+·6h | 24 | o4·=·12h··+·10h··+·6h |
| 25 | ········1······1·····1 | 25 | ········1······1·····1 |
| 26 | ·····ZZ[h·] | 26 | ·····ZZ[h·] |
| 27 | ·········1 | 27 | ·········1 |
| Offset 221, 15 lines modified | Offset 221, 15 lines modified | ||
| 221 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) | 221 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) |
| 222 | ··············0·3····1·2·4···2·5 | 222 | ··············0·3····1·2·4···2·5 |
| 223 | o14·:·Ideal·of·R</code></pre> | 223 | o14·:·Ideal·of·R</code></pre> |
| 224 | </td>··········</tr> | 224 | </td>··········</tr> |
| 225 | ··········<tr> | 225 | ··········<tr> |
| 226 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·csmK=CSM(A,K) | 226 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·csmK=CSM(A,K) |
| 227 | ·--·used· | 227 | ·--·used·2.2165s·(cpu);·0.499524s·(thread);·0s·(gc) |
| 228 | ········2·2·····2·········2····2············2 | 228 | ········2·2·····2·········2····2············2 |
| 229 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 229 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 230 | ········1·2·····1·2·····1·2····1·····1·2····2 | 230 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 231 | o15·:·A</code></pre> | 231 | o15·:·A</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| Offset 274, 15 lines modified | Offset 274, 15 lines modified | ||
| 274 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h | 274 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h |
| 275 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 | 275 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 |
| 276 | o21·:·A</code></pre> | 276 | o21·:·A</code></pre> |
| 277 | </td>··········</tr> | 277 | </td>··········</tr> |
| 278 | ··········<tr> | 278 | ··········<tr> |
| 279 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·CSM(A,K,m) | 279 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·CSM(A,K,m) |
| 280 | ·--·used·0. | 280 | ·--·used·0.237307s·(cpu);·0.100396s·(thread);·0s·(gc) |
| 281 | ········2·2·····2·········2····2············2 | 281 | ········2·2·····2·········2····2············2 |
| 282 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 282 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 283 | ········1·2·····1·2·····1·2····1·····1·2····2 | 283 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 284 | o22·:·A</code></pre> | 284 | o22·:·A</code></pre> |
| 285 | </td>··········</tr> | 285 | </td>··········</tr> |
| Offset 161, 15 lines modified | Offset 161, 15 lines modified | ||
| 161 | ··············2··············2 | 161 | ··············2··············2 |
| 162 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) | 162 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) |
| 163 | ··············0·3····1·2·4···2·5 | 163 | ··············0·3····1·2·4···2·5 |
| 164 | o14·:·Ideal·of·R | 164 | o14·:·Ideal·of·R |
| 165 | i15·:·time·csmK=CSM(A,K) | 165 | i15·:·time·csmK=CSM(A,K) |
| 166 | ·--·used· | 166 | ·--·used·2.2165s·(cpu);·0.499524s·(thread);·0s·(gc) |
| 167 | ········2·2·····2·········2····2············2 | 167 | ········2·2·····2·········2····2············2 |
| 168 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 168 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 169 | ········1·2·····1·2·····1·2····1·····1·2····2 | 169 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 170 | o15·:·A | 170 | o15·:·A |
| 171 | i16·:·csmKHash=·CSM(A,K,Output=>HashForm) | 171 | i16·:·csmKHash=·CSM(A,K,Output=>HashForm) |
| Offset 200, 15 lines modified | Offset 200, 15 lines modified | ||
| 200 | ········2·2·····2·········2·····2·············2 | 200 | ········2·2·····2·········2·····2·············2 |
| 201 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h | 201 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h |
| 202 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 | 202 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 |
| 203 | o21·:·A | 203 | o21·:·A |
| 204 | i22·:·time·CSM(A,K,m) | 204 | i22·:·time·CSM(A,K,m) |
| 205 | ·--·used·0. | 205 | ·--·used·0.237307s·(cpu);·0.100396s·(thread);·0s·(gc) |
| 206 | ········2·2·····2·········2····2············2 | 206 | ········2·2·····2·········2····2············2 |
| 207 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 207 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 208 | ········1·2·····1·2·····1·2····1·····1·2····2 | 208 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 209 | o22·:·A | 209 | o22·:·A |
| 210 | In·the·case·where·the·ambient·space·is·a·toric·variety·which·is·not·a·product | 210 | In·the·case·where·the·ambient·space·is·a·toric·variety·which·is·not·a·product |
| Offset 60, 29 lines modified | Offset 60, 29 lines modified | ||
| 60 | o2·=·U | 60 | o2·=·U |
| 61 | o2·:·NormalToricVariety</code></pre> | 61 | o2·:·NormalToricVariety</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·U | 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·U |
| 65 | ·--·used·0.1 | 65 | ·--·used·0.193418s·(cpu);·0.102879s·(thread);·0s·(gc) |
| 66 | ·······7······6······5······4······3······2 | 66 | ·······7······6······5······4······3······2 |
| 67 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 67 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 68 | ·······7······7······7······7······7······7·····7 | 68 | ·······7······7······7······7······7······7·····7 |
| 69 | ················································ZZ[x·..x·] | 69 | ················································ZZ[x·..x·] |
| 70 | ····················································0···7 | 70 | ····················································0···7 |
| 71 | o3·:·----------------------------------------------------------------------------------------------- | 71 | o3·:·----------------------------------------------------------------------------------------------- |
| 72 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·) | 72 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·) |
| 73 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7</code></pre> | 73 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(U,CheckSmooth=>false) | 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(U,CheckSmooth=>false) |
| 77 | ·--·used·0. | 77 | ·--·used·0.447512s·(cpu);·0.244803s·(thread);·0s·(gc) |
| 78 | ·······7······6······5······4······3······2 | 78 | ·······7······6······5······4······3······2 |
| 79 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 79 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 80 | ·······7······7······7······7······7······7·····7 | 80 | ·······7······7······7······7······7······7·····7 |
| 81 | ················································ZZ[x·..x·] | 81 | ················································ZZ[x·..x·] |
| 82 | ····················································0···7 | 82 | ····················································0···7 |
| Offset 16, 30 lines modified | Offset 16, 30 lines modified | ||
| 16 | o1·:·Package | 16 | o1·:·Package |
| 17 | i2·:·U·=·toricProjectiveSpace·7 | 17 | i2·:·U·=·toricProjectiveSpace·7 |
| 18 | o2·=·U | 18 | o2·=·U |
| 19 | o2·:·NormalToricVariety | 19 | o2·:·NormalToricVariety |
| 20 | i3·:·time·CSM·U | 20 | i3·:·time·CSM·U |
| 21 | ·--·used·0.1 | 21 | ·--·used·0.193418s·(cpu);·0.102879s·(thread);·0s·(gc) |
| 22 | ·······7······6······5······4······3······2 | 22 | ·······7······6······5······4······3······2 |
| 23 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 23 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 24 | ·······7······7······7······7······7······7·····7 | 24 | ·······7······7······7······7······7······7·····7 |
| 25 | ················································ZZ[x·..x·] | 25 | ················································ZZ[x·..x·] |
| 26 | ····················································0···7 | 26 | ····················································0···7 |
| 27 | o3·:·-------------------------------------------------------------------------- | 27 | o3·:·-------------------------------------------------------------------------- |
| 28 | --------------------- | 28 | --------------------- |
| 29 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·, | 29 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·, |
| 30 | -·x··+·x·,·-·x··+·x·) | 30 | -·x··+·x·,·-·x··+·x·) |
| 31 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5 | 31 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5 |
| 32 | 0····6·····0····7 | 32 | 0····6·····0····7 |
| 33 | i4·:·time·CSM(U,CheckSmooth=>false) | 33 | i4·:·time·CSM(U,CheckSmooth=>false) |
| 34 | ·--·used·0. | 34 | ·--·used·0.447512s·(cpu);·0.244803s·(thread);·0s·(gc) |
| 35 | ·······7······6······5······4······3······2 | 35 | ·······7······6······5······4······3······2 |
| 36 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 36 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 37 | ·······7······7······7······7······7······7·····7 | 37 | ·······7······7······7······7······7······7·····7 |
| 38 | ················································ZZ[x·..x·] | 38 | ················································ZZ[x·..x·] |
| 39 | ····················································0···7 | 39 | ····················································0···7 |
| Offset 76, 30 lines modified | Offset 76, 30 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3)); | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3)); |
| 78 | o4·:·Ideal·of·R</code></pre> | 78 | o4·:·Ideal·of·R</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) | 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) |
| 82 | ·--·used· | 82 | ·--·used·1.08487s·(cpu);·0.367339s·(thread);·0s·(gc) |
| 83 | ·······5······4······3······2 | 83 | ·······5······4······3······2 |
| 84 | o5·=·6h··+·14h··+·14h··+·10h | 84 | o5·=·6h··+·14h··+·14h··+·10h |
| 85 | ·······1······1······1······1 | 85 | ·······1······1······1······1 |
| 86 | ·····ZZ[h·] | 86 | ·····ZZ[h·] |
| 87 | ·········1 | 87 | ·········1 |
| 88 | o5·:·------ | 88 | o5·:·------ |
| 89 | ········6 | 89 | ········6 |
| 90 | ·······h | 90 | ·······h |
| 91 | ········1</code></pre> | 91 | ········1</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·CSM(I,CompMethod=>PnResidual) | 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·CSM(I,CompMethod=>PnResidual) |
| 95 | ·--·used· | 95 | ·--·used·2.15673s·(cpu);·1.89646s·(thread);·0s·(gc) |
| 96 | ·······5······4······3······2 | 96 | ·······5······4······3······2 |
| 97 | o6·=·6H··+·14H··+·14H··+·10H | 97 | o6·=·6H··+·14H··+·14H··+·10H |
| 98 | ·····ZZ[H] | 98 | ·····ZZ[H] |
| 99 | o6·:·----- | 99 | o6·:·----- |
| 100 | ········6 | 100 | ········6 |
| Offset 116, 30 lines modified | Offset 116, 30 lines modified | ||
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3)); | 117 | <td>··············<pre><code·class="language-macaulay2">i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3)); |
| 118 | o9·:·Ideal·of·S</code></pre> | 118 | o9·:·Ideal·of·S</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) | 121 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) |
| 122 | ·--·used·0. | 122 | ·--·used·0.423849s·(cpu);·0.210667s·(thread);·0s·(gc) |
| 123 | ········3·····2 | 123 | ········3·····2 |
| 124 | o10·=·3h··+·5h | 124 | o10·=·3h··+·5h |
| 125 | ········1·····1 | 125 | ········1·····1 |
| 126 | ······ZZ[h·] | 126 | ······ZZ[h·] |
| 127 | ··········1 | 127 | ··········1 |
| 128 | o10·:·------ | 128 | o10·:·------ |
| 129 | ·········4 | 129 | ·········4 |
| 130 | ········h | 130 | ········h |
| 131 | ·········1</code></pre> | 131 | ·········1</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·CSM(K,CompMethod=>PnResidual) | 134 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·CSM(K,CompMethod=>PnResidual) |
| 135 | ·--·used·0. | 135 | ·--·used·0.22171s·(cpu);·0.114416s·(thread);·0s·(gc) |
| 136 | ········3·····2 | 136 | ········3·····2 |
| 137 | o11·=·3H··+·5H | 137 | o11·=·3H··+·5H |
| 138 | ······ZZ[H] | 138 | ······ZZ[H] |
| 139 | o11·:·----- | 139 | o11·:·----- |
| 140 | ·········4 | 140 | ·········4 |
| Offset 32, 28 lines modified | Offset 32, 28 lines modified | ||
| 32 | using·the·regenerative·cascade·implemented·in·Bertini.·This·is·done·by·choosing | 32 | using·the·regenerative·cascade·implemented·in·Bertini.·This·is·done·by·choosing |
| 33 | the·option·bertini,·provided·Bertini·is·_\x8i_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8e_\x8d_\x8·_\x8a_\x8n_\x8d_\x8·_\x8c_\x8o_\x8n_\x8f_\x8i_\x8g_\x8u_\x8r_\x8e_\x8d. | 33 | the·option·bertini,·provided·Bertini·is·_\x8i_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8e_\x8d_\x8·_\x8a_\x8n_\x8d_\x8·_\x8c_\x8o_\x8n_\x8f_\x8i_\x8g_\x8u_\x8r_\x8e_\x8d. |
| 34 | i3·:·R=ZZ/32749[v_0..v_5]; | 34 | i3·:·R=ZZ/32749[v_0..v_5]; |
| 35 | i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3)); | 35 | i4·:·I=ideal(4*v_3*v_1*v_2-8*v_1*v_3^2,v_5*(v_0*v_1*v_4-v_2^3)); |
| 36 | o4·:·Ideal·of·R | 36 | o4·:·Ideal·of·R |
| 37 | i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) | 37 | i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) |
| 38 | ·--·used· | 38 | ·--·used·1.08487s·(cpu);·0.367339s·(thread);·0s·(gc) |
| 39 | ·······5······4······3······2 | 39 | ·······5······4······3······2 |
| 40 | o5·=·6h··+·14h··+·14h··+·10h | 40 | o5·=·6h··+·14h··+·14h··+·10h |
| 41 | ·······1······1······1······1 | 41 | ·······1······1······1······1 |
| 42 | ·····ZZ[h·] | 42 | ·····ZZ[h·] |
| 43 | ·········1 | 43 | ·········1 |
| 44 | o5·:·------ | 44 | o5·:·------ |
| 45 | ········6 | 45 | ········6 |
| 46 | ·······h | 46 | ·······h |
| 47 | ········1 | 47 | ········1 |
| 48 | i6·:·time·CSM(I,CompMethod=>PnResidual) | 48 | i6·:·time·CSM(I,CompMethod=>PnResidual) |
| 49 | ·--·used· | 49 | ·--·used·2.15673s·(cpu);·1.89646s·(thread);·0s·(gc) |
| 50 | ·······5······4······3······2 | 50 | ·······5······4······3······2 |
| 51 | o6·=·6H··+·14H··+·14H··+·10H | 51 | o6·=·6H··+·14H··+·14H··+·10H |
| 52 | ·····ZZ[H] | 52 | ·····ZZ[H] |
| 53 | o6·:·----- | 53 | o6·:·----- |
| 54 | ········6 | 54 | ········6 |
| Offset 62, 28 lines modified | Offset 62, 28 lines modified | ||
| 62 | o7·=·2 | 62 | o7·=·2 |
| 63 | i8·:·S=QQ[s_0..s_3]; | 63 | i8·:·S=QQ[s_0..s_3]; |
| 64 | i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3)); | 64 | i9·:·K=ideal(4*s_3*s_2-s_2^2,(s_0*s_1*s_3-s_2^3)); |
| 65 | o9·:·Ideal·of·S | 65 | o9·:·Ideal·of·S |
| 66 | i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) | 66 | i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) |
| 67 | ·--·used·0. | 67 | ·--·used·0.423849s·(cpu);·0.210667s·(thread);·0s·(gc) |
| 68 | ········3·····2 | 68 | ········3·····2 |
| 69 | o10·=·3h··+·5h | 69 | o10·=·3h··+·5h |
| 70 | ········1·····1 | 70 | ········1·····1 |
| 71 | ······ZZ[h·] | 71 | ······ZZ[h·] |
| 72 | ··········1 | 72 | ··········1 |
| 73 | o10·:·------ | 73 | o10·:·------ |
| 74 | ·········4 | 74 | ·········4 |
| 75 | ········h | 75 | ········h |
| 76 | ·········1 | 76 | ·········1 |
| 77 | i11·:·time·CSM(K,CompMethod=>PnResidual) | 77 | i11·:·time·CSM(K,CompMethod=>PnResidual) |
| 78 | ·--·used·0. | 78 | ·--·used·0.22171s·(cpu);·0.114416s·(thread);·0s·(gc) |
| 79 | ········3·····2 | 79 | ········3·····2 |
| 80 | o11·=·3H··+·5H | 80 | o11·=·3H··+·5H |
| 81 | ······ZZ[H] | 81 | ······ZZ[H] |
| 82 | o11·:·----- | 82 | o11·:·----- |
| 83 | ·········4 | 83 | ·········4 |
| Offset 130, 21 lines modified | Offset 130, 21 lines modified | ||
| 130 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) | 130 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) |
| 131 | ·············3·········0·4········1·4·········2·4·········3·4·········4 | 131 | ·············3·········0·4········1·4·········2·4·········3·4·········4 |
| 132 | o3·:·Ideal·of·R</code></pre> | 132 | o3·:·Ideal·of·R</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Euler(I,InputIsSmooth=>true) | 135 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Euler(I,InputIsSmooth=>true) |
| 136 | ·--·used·0. | 136 | ·--·used·0.162477s·(cpu);·0.0700406s·(thread);·0s·(gc) |
| 137 | o4·=·4</code></pre> | 137 | o4·=·4</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Euler·I | 140 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Euler·I |
| 141 | ·--·used·0.2 | 141 | ·--·used·0.276327s·(cpu);·0.147121s·(thread);·0s·(gc) |
| 142 | o5·=·4</code></pre> | 142 | o5·=·4</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i6·:·EulerIHash=Euler(I,Output=>HashForm);</code></pre> | 145 | <td>··············<pre><code·class="language-macaulay2">i6·:·EulerIHash=Euler(I,Output=>HashForm);</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| Offset 182, 21 lines modified | Offset 182, 21 lines modified | ||
| 182 | ········</table> | 182 | ········</table> |
| 183 | ········<div> | 183 | ········<div> |
| 184 | ··········<p>Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the·method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that·the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and·input·this·information·into·the·method.·This·may·also·improve·computation·speed.</p> | 184 | ··········<p>Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the·method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that·the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and·input·this·information·into·the·method.·This·may·also·improve·computation·speed.</p> |
| 185 | ········</div> | 185 | ········</div> |
| 186 | ········<table·class="examples"> | 186 | ········<table·class="examples"> |
| 187 | ··········<tr> | 187 | ··········<tr> |
| 188 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Euler(J,Method=>DirectCompleteInt) | 188 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Euler(J,Method=>DirectCompleteInt) |
| 189 | ·--·used·0. | 189 | ·--·used·0.41416s·(cpu);·0.10607s·(thread);·0s·(gc) |
| 190 | o10·=·2</code></pre> | 190 | o10·=·2</code></pre> |
| 191 | </td>··········</tr> | 191 | </td>··········</tr> |
| 192 | ··········<tr> | 192 | ··········<tr> |
| 193 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) | 193 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) |
| 194 | ·--·used·0. | 194 | ·--·used·0.251136s·(cpu);·0.0756807s·(thread);·0s·(gc) |
| 195 | o11·=·2</code></pre> | 195 | o11·=·2</code></pre> |
| 196 | </td>··········</tr> | 196 | </td>··········</tr> |
| 197 | ········</table> | 197 | ········</table> |
| 198 | ········<div> | 198 | ········<div> |
| 199 | ··········<p>Now·consider·an·example·in·\PP^2·\times·\PP^2.</p> | 199 | ··········<p>Now·consider·an·example·in·\PP^2·\times·\PP^2.</p> |
| 200 | ········</div> | 200 | ········</div> |
| Offset 75, 19 lines modified | Offset 75, 19 lines modified | ||
| 75 | ·····------------------------------------------------------------------------ | 75 | ·····------------------------------------------------------------------------ |
| 76 | ·············2························································2 | 76 | ·············2························································2 |
| 77 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) | 77 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) |
| 78 | ·············3·········0·4········1·4·········2·4·········3·4·········4 | 78 | ·············3·········0·4········1·4·········2·4·········3·4·········4 |
| 79 | o3·:·Ideal·of·R | 79 | o3·:·Ideal·of·R |
| 80 | i4·:·time·Euler(I,InputIsSmooth=>true) | 80 | i4·:·time·Euler(I,InputIsSmooth=>true) |
| 81 | ·--·used·0. | 81 | ·--·used·0.162477s·(cpu);·0.0700406s·(thread);·0s·(gc) |
| 82 | o4·=·4 | 82 | o4·=·4 |
| 83 | i5·:·time·Euler·I | 83 | i5·:·time·Euler·I |
| 84 | ·--·used·0.2 | 84 | ·--·used·0.276327s·(cpu);·0.147121s·(thread);·0s·(gc) |
| 85 | o5·=·4 | 85 | o5·=·4 |
| 86 | i6·:·EulerIHash=Euler(I,Output=>HashForm); | 86 | i6·:·EulerIHash=Euler(I,Output=>HashForm); |
| 87 | i7·:·A=ring·EulerIHash#"CSM" | 87 | i7·:·A=ring·EulerIHash#"CSM" |
| 88 | o7·=·A | 88 | o7·=·A |
| Offset 115, 19 lines modified | Offset 115, 19 lines modified | ||
| 115 | o9·:·Ideal·of·R | 115 | o9·:·Ideal·of·R |
| 116 | Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the | 116 | Note·that·the·ideal·J·above·is·a·complete·intersection,·thus·we·may·change·the |
| 117 | method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that | 117 | method·option·which·may·speed·computation·in·some·cases.·We·may·also·note·that |
| 118 | the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and | 118 | the·ideal·generated·by·the·first·2·generators·of·I·defines·a·smooth·scheme·and |
| 119 | input·this·information·into·the·method.·This·may·also·improve·computation | 119 | input·this·information·into·the·method.·This·may·also·improve·computation |
| 120 | speed. | 120 | speed. |
| 121 | i10·:·time·Euler(J,Method=>DirectCompleteInt) | 121 | i10·:·time·Euler(J,Method=>DirectCompleteInt) |
| 122 | ·--·used·0. | 122 | ·--·used·0.41416s·(cpu);·0.10607s·(thread);·0s·(gc) |
| 123 | o10·=·2 | 123 | o10·=·2 |
| 124 | i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) | 124 | i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) |
| 125 | ·--·used·0. | 125 | ·--·used·0.251136s·(cpu);·0.0756807s·(thread);·0s·(gc) |
| 126 | o11·=·2 | 126 | o11·=·2 |
| 127 | Now·consider·an·example·in·\PP^2·\times·\PP^2. | 127 | Now·consider·an·example·in·\PP^2·\times·\PP^2. |
| 128 | i12·:·R=MultiProjCoordRing({2,2}) | 128 | i12·:·R=MultiProjCoordRing({2,2}) |
| 129 | o12·=·R | 129 | o12·=·R |
| Offset 58, 30 lines modified | Offset 58, 30 lines modified | ||
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R)); | 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R)); |
| 60 | o2·:·Ideal·of·R</code></pre> | 60 | o2·:·Ideal·of·R</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ··········<tr> | 62 | ··········<tr> |
| 63 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM(I,Method=>DirectCompletInt) | 63 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM(I,Method=>DirectCompletInt) |
| 64 | ·--·used· | 64 | ·--·used·4.6779s·(cpu);·1.28724s·(thread);·0s·(gc) |
| 65 | ·······2·2·····2·········2 | 65 | ·······2·2·····2·········2 |
| 66 | o3·=·2h·h··+·2h·h··+·5h·h | 66 | o3·=·2h·h··+·2h·h··+·5h·h |
| 67 | ·······1·2·····1·2·····1·2 | 67 | ·······1·2·····1·2·····1·2 |
| 68 | ·····ZZ[h·..h·] | 68 | ·····ZZ[h·..h·] |
| 69 | ·········1···2 | 69 | ·········1···2 |
| 70 | o3·:·---------- | 70 | o3·:·---------- |
| 71 | ········3···3 | 71 | ········3···3 |
| 72 | ······(h·,·h·) | 72 | ······(h·,·h·) |
| 73 | ········1···2</code></pre> | 73 | ········1···2</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) | 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) |
| 77 | ·--·used· | 77 | ·--·used·4.43929s·(cpu);·1.26914s·(thread);·0s·(gc) |
| 78 | ·······2·2·····2·········2 | 78 | ·······2·2·····2·········2 |
| 79 | o4·=·2h·h··+·2h·h··+·5h·h | 79 | o4·=·2h·h··+·2h·h··+·5h·h |
| 80 | ·······1·2·····1·2·····1·2 | 80 | ·······1·2·····1·2·····1·2 |
| 81 | ·····ZZ[h·..h·] | 81 | ·····ZZ[h·..h·] |
| 82 | ·········1···2 | 82 | ·········1···2 |
| Offset 16, 28 lines modified | Offset 16, 28 lines modified | ||
| 16 | o1·=·R | 16 | o1·=·R |
| 17 | o1·:·PolynomialRing | 17 | o1·:·PolynomialRing |
| 18 | i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R)); | 18 | i2·:·I=ideal(R_0*R_1*R_3-R_0^2*R_3,random({0,1},R),random({1,2},R)); |
| 19 | o2·:·Ideal·of·R | 19 | o2·:·Ideal·of·R |
| 20 | i3·:·time·CSM(I,Method=>DirectCompletInt) | 20 | i3·:·time·CSM(I,Method=>DirectCompletInt) |
| 21 | ·--·used· | 21 | ·--·used·4.6779s·(cpu);·1.28724s·(thread);·0s·(gc) |
| 22 | ·······2·2·····2·········2 | 22 | ·······2·2·····2·········2 |
| 23 | o3·=·2h·h··+·2h·h··+·5h·h | 23 | o3·=·2h·h··+·2h·h··+·5h·h |
| 24 | ·······1·2·····1·2·····1·2 | 24 | ·······1·2·····1·2·····1·2 |
| 25 | ·····ZZ[h·..h·] | 25 | ·····ZZ[h·..h·] |
| 26 | ·········1···2 | 26 | ·········1···2 |
| 27 | o3·:·---------- | 27 | o3·:·---------- |
| 28 | ········3···3 | 28 | ········3···3 |
| 29 | ······(h·,·h·) | 29 | ······(h·,·h·) |
| 30 | ········1···2 | 30 | ········1···2 |
| 31 | i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) | 31 | i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) |
| 32 | ·--·used· | 32 | ·--·used·4.43929s·(cpu);·1.26914s·(thread);·0s·(gc) |
| 33 | ·······2·2·····2·········2 | 33 | ·······2·2·····2·········2 |
| 34 | o4·=·2h·h··+·2h·h··+·5h·h | 34 | o4·=·2h·h··+·2h·h··+·5h·h |
| 35 | ·······1·2·····1·2·····1·2 | 35 | ·······1·2·····1·2·····1·2 |
| 36 | ·····ZZ[h·..h·] | 36 | ·····ZZ[h·..h·] |
| 37 | ·········1···2 | 37 | ·········1···2 |
| Offset 54, 30 lines modified | Offset 54, 30 lines modified | ||
| 54 | ··········<tr> | 54 | ··········<tr> |
| 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); | 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); |
| 56 | o2·:·Ideal·of·R</code></pre> | 56 | o2·:·Ideal·of·R</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I |
| 60 | ·--·used· | 60 | ·--·used·1.12499s·(cpu);·0.47701s·(thread);·0s·(gc) |
| 61 | ·······3 | 61 | ·······3 |
| 62 | o3·=·4h | 62 | o3·=·4h |
| 63 | ·······1 | 63 | ·······1 |
| 64 | ·····ZZ[h·] | 64 | ·····ZZ[h·] |
| 65 | ·········1 | 65 | ·········1 |
| 66 | o3·:·------ | 66 | o3·:·------ |
| 67 | ········5 | 67 | ········5 |
| 68 | ·······h | 68 | ·······h |
| 69 | ········1</code></pre> | 69 | ········1</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,InputIsSmooth=>true) | 72 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,InputIsSmooth=>true) |
| 73 | ·--·used·0. | 73 | ·--·used·0.18877s·(cpu);·0.0569748s·(thread);·0s·(gc) |
| 74 | ·······3 | 74 | ·······3 |
| 75 | o4·=·4h | 75 | o4·=·4h |
| 76 | ·······1 | 76 | ·······1 |
| 77 | ·····ZZ[h·] | 77 | ·····ZZ[h·] |
| 78 | ·········1 | 78 | ·········1 |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | ········</table> | 89 | ········</table> |
| 90 | ········<div> | 90 | ········<div> |
| 91 | ··········<p>Note·that·one·could,·equivalently,·use·the·command·<a·title="The·Chern·class"·href="___Chern.html">Chern</a>·instead·in·this·case.</p> | 91 | ··········<p>Note·that·one·could,·equivalently,·use·the·command·<a·title="The·Chern·class"·href="___Chern.html">Chern</a>·instead·in·this·case.</p> |
| 92 | ········</div> | 92 | ········</div> |
| 93 | ········<table·class="examples"> | 93 | ········<table·class="examples"> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Chern·I | 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Chern·I |
| 96 | ·--·used·0.0 | 96 | ·--·used·0.0533118s·(cpu);·0.0392388s·(thread);·0s·(gc) |
| 97 | ·······3 | 97 | ·······3 |
| 98 | o5·=·4h | 98 | o5·=·4h |
| 99 | ·······1 | 99 | ·······1 |
| 100 | ·····ZZ[h·] | 100 | ·····ZZ[h·] |
| 101 | ·········1 | 101 | ·········1 |
| Offset 9, 42 lines modified | Offset 9, 42 lines modified | ||
| 9 | input·ideal·is·known·to·define·a·smooth·subscheme·setting·this·option·to·true | 9 | input·ideal·is·known·to·define·a·smooth·subscheme·setting·this·option·to·true |
| 10 | will·speed·up·computations·(it·is·set·to·false·by·default). | 10 | will·speed·up·computations·(it·is·set·to·false·by·default). |
| 11 | i1·:·R·=·ZZ/32749[x_0..x_4]; | 11 | i1·:·R·=·ZZ/32749[x_0..x_4]; |
| 12 | i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); | 12 | i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); |
| 13 | o2·:·Ideal·of·R | 13 | o2·:·Ideal·of·R |
| 14 | i3·:·time·CSM·I | 14 | i3·:·time·CSM·I |
| 15 | ·--·used· | 15 | ·--·used·1.12499s·(cpu);·0.47701s·(thread);·0s·(gc) |
| 16 | ·······3 | 16 | ·······3 |
| 17 | o3·=·4h | 17 | o3·=·4h |
| 18 | ·······1 | 18 | ·······1 |
| 19 | ·····ZZ[h·] | 19 | ·····ZZ[h·] |
| 20 | ·········1 | 20 | ·········1 |
| 21 | o3·:·------ | 21 | o3·:·------ |
| 22 | ········5 | 22 | ········5 |
| 23 | ·······h | 23 | ·······h |
| 24 | ········1 | 24 | ········1 |
| 25 | i4·:·time·CSM(I,InputIsSmooth=>true) | 25 | i4·:·time·CSM(I,InputIsSmooth=>true) |
| 26 | ·--·used·0. | 26 | ·--·used·0.18877s·(cpu);·0.0569748s·(thread);·0s·(gc) |
| 27 | ·······3 | 27 | ·······3 |
| 28 | o4·=·4h | 28 | o4·=·4h |
| 29 | ·······1 | 29 | ·······1 |
| 30 | ·····ZZ[h·] | 30 | ·····ZZ[h·] |
| 31 | ·········1 | 31 | ·········1 |
| 32 | o4·:·------ | 32 | o4·:·------ |
| 33 | ········5 | 33 | ········5 |
| 34 | ·······h | 34 | ·······h |
| 35 | ········1 | 35 | ········1 |
| 36 | Note·that·one·could,·equivalently,·use·the·command·_\x8C_\x8h_\x8e_\x8r_\x8n·instead·in·this·case. | 36 | Note·that·one·could,·equivalently,·use·the·command·_\x8C_\x8h_\x8e_\x8r_\x8n·instead·in·this·case. |
| 37 | i5·:·time·Chern·I | 37 | i5·:·time·Chern·I |
| 38 | ·--·used·0.0 | 38 | ·--·used·0.0533118s·(cpu);·0.0392388s·(thread);·0s·(gc) |
| 39 | ·······3 | 39 | ·······3 |
| 40 | o5·=·4h | 40 | o5·=·4h |
| 41 | ·······1 | 41 | ·······1 |
| 42 | ·····ZZ[h·] | 42 | ·····ZZ[h·] |
| 43 | ·········1 | 43 | ·········1 |
| Offset 58, 30 lines modified | Offset 58, 30 lines modified | ||
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); | 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); |
| 60 | o2·:·Ideal·of·R</code></pre> | 60 | o2·:·Ideal·of·R</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ··········<tr> | 62 | ··········<tr> |
| 63 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I | 63 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I |
| 64 | ·--·used· | 64 | ·--·used·2.47526s·(cpu);·0.990371s·(thread);·0s·(gc) |
| 65 | ········5······4·····3 | 65 | ········5······4·····3 |
| 66 | o3·=·12h··+·10h··+·6h | 66 | o3·=·12h··+·10h··+·6h |
| 67 | ········1······1·····1 | 67 | ········1······1·····1 |
| 68 | ·····ZZ[h·] | 68 | ·····ZZ[h·] |
| 69 | ·········1 | 69 | ·········1 |
| 70 | o3·:·------ | 70 | o3·:·------ |
| 71 | ········7 | 71 | ········7 |
| 72 | ·······h | 72 | ·······h |
| 73 | ········1</code></pre> | 73 | ········1</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompleteInt) | 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompleteInt) |
| 77 | ·--·used·0. | 77 | ·--·used·0.727905s·(cpu);·0.242391s·(thread);·0s·(gc) |
| 78 | ········5······4·····3 | 78 | ········5······4·····3 |
| 79 | o4·=·12h··+·10h··+·6h | 79 | o4·=·12h··+·10h··+·6h |
| 80 | ········1······1·····1 | 80 | ········1······1·····1 |
| 81 | ·····ZZ[h·] | 81 | ·····ZZ[h·] |
| 82 | ·········1 | 82 | ·········1 |
| Offset 18, 28 lines modified | Offset 18, 28 lines modified | ||
| 18 | o1·=·R | 18 | o1·=·R |
| 19 | o1·:·PolynomialRing | 19 | o1·:·PolynomialRing |
| 20 | i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); | 20 | i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); |
| 21 | o2·:·Ideal·of·R | 21 | o2·:·Ideal·of·R |
| 22 | i3·:·time·CSM·I | 22 | i3·:·time·CSM·I |
| 23 | ·--·used· | 23 | ·--·used·2.47526s·(cpu);·0.990371s·(thread);·0s·(gc) |
| 24 | ········5······4·····3 | 24 | ········5······4·····3 |
| 25 | o3·=·12h··+·10h··+·6h | 25 | o3·=·12h··+·10h··+·6h |
| 26 | ········1······1·····1 | 26 | ········1······1·····1 |
| 27 | ·····ZZ[h·] | 27 | ·····ZZ[h·] |
| 28 | ·········1 | 28 | ·········1 |
| 29 | o3·:·------ | 29 | o3·:·------ |
| 30 | ········7 | 30 | ········7 |
| 31 | ·······h | 31 | ·······h |
| 32 | ········1 | 32 | ········1 |
| 33 | i4·:·time·CSM(I,Method=>DirectCompleteInt) | 33 | i4·:·time·CSM(I,Method=>DirectCompleteInt) |
| 34 | ·--·used·0. | 34 | ·--·used·0.727905s·(cpu);·0.242391s·(thread);·0s·(gc) |
| 35 | ········5······4·····3 | 35 | ········5······4·····3 |
| 36 | o4·=·12h··+·10h··+·6h | 36 | o4·=·12h··+·10h··+·6h |
| 37 | ········1······1·····1 | 37 | ········1······1·····1 |
| 38 | ·····ZZ[h·] | 38 | ·····ZZ[h·] |
| 39 | ·········1 | 39 | ·········1 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | UmluZ01hcCBDaG9yZGFsTmV0 | 8 | UmluZ01hcCBDaG9yZGFsTmV0 |
| 9 | #:len=1424 | 9 | #:len=1424 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYXBwbHkgcmluZyBtYXAgdG8gYSBjaG9y | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYXBwbHkgcmluZyBtYXAgdG8gYSBjaG9y |
| 11 | ZGFsIG5ldHdvcmsiLCAibGluZW51bSIgPT4gODg5LCBJbnB1dHMgPT4ge1NQQU57VFR7ImYifSwi | 11 | ZGFsIG5ldHdvcmsiLCAibGluZW51bSIgPT4gODg5LCBJbnB1dHMgPT4ge1NQQU57VFR7ImYifSwi |
| Offset 27, 14 lines modified | Offset 27, 14 lines modified | ||
| 27 | o5·:·HashTable | 27 | o5·:·HashTable |
| 28 | i6·:·components(N) | 28 | i6·:·components(N) |
| 29 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)}················································································································································································} | 29 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)}················································································································································································} |
| 30 | ·····························1···3···5···7···········2···4···6···8 | 30 | ·····························1···3···5···7···········2···4···6···8 |
| 31 | ···············5·=>·{ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·)} | 31 | ···············5·=>·{ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·)} |
| 32 | ·····························1··· | 32 | ·····························1···2···4···5···7···········1···3···4···6···7···········1···2···4···6···7···········2···3···5···7···8···········2···4···5···7···8···········2···3···5···6···8···········1···3···5···6···8···········1···3···4···6···8 |
| 33 | ···············6·=>·{} | 33 | ···············6·=>·{} |
| 34 | ···············7·=>·{} | 34 | ···············7·=>·{} |
| 35 | o6·:·HashTable | 35 | o6·:·HashTable |
| 36 | i7·:· | 36 | i7·:· |
| Offset 109, 15 lines modified | Offset 109, 15 lines modified | ||
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·components(N) | 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·components(N) |
| 112 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)}················································································································································································} | 112 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)}················································································································································································} |
| 113 | ·····························1···3···5···7···········2···4···6···8 | 113 | ·····························1···3···5···7···········2···4···6···8 |
| 114 | ···············5·=>·{ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·)} | 114 | ···············5·=>·{ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·)} |
| 115 | ·····························1··· | 115 | ·····························1···2···4···5···7···········1···3···4···6···7···········1···2···4···6···7···········2···3···5···7···8···········2···4···5···7···8···········2···3···5···6···8···········1···3···5···6···8···········1···3···4···6···8 |
| 116 | ···············6·=>·{} | 116 | ···············6·=>·{} |
| 117 | ···············7·=>·{} | 117 | ···············7·=>·{} |
| 118 | o6·:·HashTable</code></pre> | 118 | o6·:·HashTable</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ········</table> | 120 | ········</table> |
| 121 | ········<pre></pre> | 121 | ········<pre></pre> |
| Offset 44, 17 lines modified | Offset 44, 17 lines modified | ||
| 44 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)} | 44 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)} |
| 45 | } | 45 | } |
| 46 | ·····························1···3···5···7···········2···4···6···8 | 46 | ·····························1···3···5···7···········2···4···6···8 |
| 47 | ···············5·=>·{ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·), | 47 | ···············5·=>·{ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·), |
| 48 | ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·, | 48 | ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·, |
| 49 | x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·, | 49 | x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·, |
| 50 | x·,·x·)} | 50 | x·,·x·)} |
| 51 | ·····························1··· | 51 | ·····························1···2···4···5···7···········1···3···4···6···7 |
| 52 | 1···2···4··· | 52 | 1···2···4···6···7···········2···3···5···7···8···········2···4···5···7···8 |
| 53 | 53 | 2···3···5···6···8···········1···3···5···6···8···········1···3···4···6···8 | |
| 54 | ···············6·=>·{} | 54 | ···············6·=>·{} |
| 55 | ···············7·=>·{} | 55 | ···············7·=>·{} |
| 56 | o6·:·HashTable | 56 | o6·:·HashTable |
| 57 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 57 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 58 | It·is·assumed·that·the·_\x8c_\x8h_\x8a_\x8i_\x8n_\x8s·of·the·network·define·prime·ideals. | 58 | It·is·assumed·that·the·_\x8c_\x8h_\x8a_\x8i_\x8n_\x8s·of·the·network·define·prime·ideals. |
| 59 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 59 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | bW9ub21pYWxJZGVhbChTdHJpbmcp | 8 | bW9ub21pYWxJZGVhbChTdHJpbmcp |
| 9 | #:len=1149 | 9 | #:len=1149 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibWFrZSBhIG1vbm9taWFsIGlkZWFsIHVz | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibWFrZSBhIG1vbm9taWFsIGlkZWFsIHVz |
| 11 | aW5nIGNsYXNzaWMgTWFjYXVsYXkgc3ludGF4IiwgImxpbmVudW0iID0+IDE0NCwgSW5wdXRzID0+ | 11 | aW5nIGNsYXNzaWMgTWFjYXVsYXkgc3ludGF4IiwgImxpbmVudW0iID0+IDE0NCwgSW5wdXRzID0+ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | VmFuaXNoaW5nSWRlYWw= | 8 | VmFuaXNoaW5nSWRlYWw= |
| 9 | #:len=1237 | 9 | #:len=1237 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmFuaXNoaW5nIGlkZWFsIG9mIGFuIGV2 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmFuaXNoaW5nIGlkZWFsIG9mIGFuIGV2 |
| 11 | YWx1YXRpb24gY29kZSIsICJsaW5lbnVtIiA9PiA1MTU4LCBJbnB1dHMgPT4ge1NQQU57VFR7IkMi | 11 | YWx1YXRpb24gY29kZSIsICJsaW5lbnVtIiA9PiA1MTU4LCBJbnB1dHMgPT4ge1NQQU57VFR7IkMi |
| Offset 2, 15 lines modified | Offset 2, 15 lines modified | ||
| 2 | i1·:·F=GF(4,Variable=>a); | 2 | i1·:·F=GF(4,Variable=>a); |
| 3 | i2·:·R=linearCode(F,{{1,1,1}}); | 3 | i2·:·R=linearCode(F,{{1,1,1}}); |
| 4 | i3·:·messages·R | 4 | i3·:·messages·R |
| 5 | o3·=·{{ | 5 | o3·=·{{0},·{1},·{a},·{a·+·1}} |
| 6 | o3·:·List | 6 | o3·:·List |
| 7 | i4·:·messages·hammingCode(2,3) | 7 | i4·:·messages·hammingCode(2,3) |
| 8 | o4·=·{{1,·0,·0,·0},·{1,·0,·0,·1},·{1,·0,·1,·0},·{1,·0,·1,·1},·{1,·1,·1,·0}, | 8 | o4·=·{{1,·0,·0,·0},·{1,·0,·0,·1},·{1,·0,·1,·0},·{1,·0,·1,·1},·{1,·1,·1,·0}, |
| 9 | ·····------------------------------------------------------------------------ | 9 | ·····------------------------------------------------------------------------ |
| Offset 2, 30 lines modified | Offset 2, 30 lines modified | ||
| 2 | i1·:·C·=·hammingCode(2,·3) | 2 | i1·:·C·=·hammingCode(2,·3) |
| 3 | ·······································7 | 3 | ·······································7 |
| 4 | o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································} | 4 | o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································} |
| 5 | ················BaseField·=>·GF·2 | 5 | ················BaseField·=>·GF·2 |
| 6 | ················cache·=>·CacheTable{} | 6 | ················cache·=>·CacheTable{} |
| 7 | ················Code·=>·image·|·1· | 7 | ················Code·=>·image·|·1·0·1·1·| |
| 8 | ······························|·1· | 8 | ······························|·1·1·0·1·| |
| 9 | ······························|·1·1·1·0·| | 9 | ······························|·1·1·1·0·| |
| 10 | ······························|·1·0·0·0·| | 10 | ······························|·1·0·0·0·| |
| 11 | ······························|·0·1·0·0·| | 11 | ······························|·0·1·0·0·| |
| 12 | ······························|·0·0·1·0·| | 12 | ······························|·0·0·1·0·| |
| 13 | ······························|·0·0·0·1·| | 13 | ······························|·0·0·0·1·| |
| 14 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| | 14 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| |
| 15 | ···································|· | 15 | ···································|·0·1·1·0·1·0·0·| |
| 16 | ···································|· | 16 | ···································|·1·0·1·0·0·1·0·| |
| 17 | ···································|·1·1·0·0·0·0·1·| | 17 | ···································|·1·1·0·0·0·0·1·| |
| 18 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{ | 18 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·0,·0},·{1,·0,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}} |
| 19 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| | 19 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| |
| 20 | ·····································|·0·0·1·1·1·1·0·| | 20 | ·····································|·0·0·1·1·1·1·0·| |
| 21 | ·····································|·0·1·0·1· | 21 | ·····································|·0·1·0·1·1·0·1·| |
| 22 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,· | 22 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·1,·0,·1}} |
| 23 | o1·:·LinearCode | 23 | o1·:·LinearCode |
| 24 | i2·:·ring(C) | 24 | i2·:·ring(C) |
| 25 | o2·=·GF·2 | 25 | o2·=·GF·2 |
| Offset 37, 23 lines modified | Offset 37, 23 lines modified | ||
| 37 | ························|·0·| | 37 | ························|·0·| |
| 38 | ························|·0·| | 38 | ························|·0·| |
| 39 | ························|·1·| | 39 | ························|·1·| |
| 40 | ···············|·0·|·=>·|·0·| | 40 | ···············|·0·|·=>·|·0·| |
| 41 | ···············|·1·|····|·0·| | 41 | ···············|·1·|····|·0·| |
| 42 | ···············|·0·|····|·0·| | 42 | ···············|·0·|····|·0·| |
| 43 | ························|·0·| | 43 | ························|·0·| |
| 44 | ························|·0·| | ||
| 45 | ························|·1·| | 44 | ························|·1·| |
| 46 | ························|·0·| | 45 | ························|·0·| |
| 46 | ························|·0·| | ||
| 47 | ···············|·0·|·=>·|·0·| | 47 | ···············|·0·|·=>·|·0·| |
| 48 | ···············|·1·|····|·0·| | 48 | ···············|·1·|····|·0·| |
| 49 | ···············|·1·|····|·0·| | 49 | ···············|·1·|····|·0·| |
| 50 | ························|·0·| | 50 | ························|·0·| |
| 51 | ························|·1·| | ||
| 52 | ························|·0·| | 51 | ························|·0·| |
| 52 | ························|·1·| | ||
| 53 | ························|·0·| | 53 | ························|·0·| |
| 54 | ···············|·1·|·=>·|·1·| | 54 | ···············|·1·|·=>·|·1·| |
| 55 | ···············|·0·|····|·0·| | 55 | ···············|·0·|····|·0·| |
| 56 | ···············|·0·|····|·0·| | 56 | ···············|·0·|····|·0·| |
| 57 | ························|·0·| | 57 | ························|·0·| |
| 58 | ························|·0·| | 58 | ························|·0·| |
| 59 | ························|·0·| | 59 | ························|·0·| |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·2210985853493542567 | 1 | --·-*-·M2-comint·-*-·hash:·2210985853493542567 |
| 2 | i1·:·H·=·hammingCode(2,3); | 2 | i1·:·H·=·hammingCode(2,3); |
| 3 | i2·:·vectorSpace·H | 3 | i2·:·vectorSpace·H |
| 4 | o2·=·image·|·1·0·1·1·| | 4 | o2·=·image·|·1·0·1·1·| |
| 5 | ···········|·1·1·0·1·| | ||
| 6 | ···········|·1·1·1·0·| | 5 | ···········|·1·1·1·0·| |
| 6 | ···········|·1·1·0·1·| | ||
| 7 | ···········|·1·0·0·0·| | 7 | ···········|·1·0·0·0·| |
| 8 | ···········|·0·1·0·0·| | 8 | ···········|·0·1·0·0·| |
| 9 | ···········|·0·0·1·0·| | 9 | ···········|·0·0·1·0·| |
| 10 | ···········|·0·0·0·1·| | 10 | ···········|·0·0·0·1·| |
| 11 | ·····································7 | 11 | ·····································7 |
| 12 | o2·:·GF·2-module,·submodule·of·(GF·2) | 12 | o2·:·GF·2-module,·submodule·of·(GF·2) |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·R=linearCode(F,{{1,1,1}});</code></pre> | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·R=linearCode(F,{{1,1,1}});</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·messages·R | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·messages·R |
| 82 | o3·=·{{ | 82 | o3·=·{{0},·{1},·{a},·{a·+·1}} |
| 83 | o3·:·List</code></pre> | 83 | o3·:·List</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ········</table> | 85 | ········</table> |
| 86 | ········<table·class="examples"> | 86 | ········<table·class="examples"> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·messages·hammingCode(2,3) | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·messages·hammingCode(2,3) |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | Given·a·code·C·of·dimension·$k$·over·a·finite·field·$F$,·this·function·returns | 15 | Given·a·code·C·of·dimension·$k$·over·a·finite·field·$F$,·this·function·returns |
| 16 | the·list·that·contains·all·the·elements·of·$F^k$.·Every·element·of·the·list·can | 16 | the·list·that·contains·all·the·elements·of·$F^k$.·Every·element·of·the·list·can |
| 17 | be·used·to·encode·a·message·using·the·linear·code·C. | 17 | be·used·to·encode·a·message·using·the·linear·code·C. |
| 18 | i1·:·F=GF(4,Variable=>a); | 18 | i1·:·F=GF(4,Variable=>a); |
| 19 | i2·:·R=linearCode(F,{{1,1,1}}); | 19 | i2·:·R=linearCode(F,{{1,1,1}}); |
| 20 | i3·:·messages·R | 20 | i3·:·messages·R |
| 21 | o3·=·{{ | 21 | o3·=·{{0},·{1},·{a},·{a·+·1}} |
| 22 | o3·:·List | 22 | o3·:·List |
| 23 | i4·:·messages·hammingCode(2,3) | 23 | i4·:·messages·hammingCode(2,3) |
| 24 | o4·=·{{1,·0,·0,·0},·{1,·0,·0,·1},·{1,·0,·1,·0},·{1,·0,·1,·1},·{1,·1,·1,·0}, | 24 | o4·=·{{1,·0,·0,·0},·{1,·0,·0,·1},·{1,·0,·1,·0},·{1,·0,·1,·1},·{1,·1,·1,·0}, |
| 25 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 26 | ·····{1,·1,·1,·1},·{0,·1,·1,·0},·{0,·1,·0,·1},·{0,·1,·0,·0},·{0,·1,·1,·1}, | 26 | ·····{1,·1,·1,·1},·{0,·1,·1,·0},·{0,·1,·0,·1},·{0,·1,·0,·0},·{0,·1,·1,·1}, |
| Offset 76, 30 lines modified | Offset 76, 30 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·C·=·hammingCode(2,·3) | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·C·=·hammingCode(2,·3) |
| 78 | ·······································7 | 78 | ·······································7 |
| 79 | o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································} | 79 | o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································} |
| 80 | ················BaseField·=>·GF·2 | 80 | ················BaseField·=>·GF·2 |
| 81 | ················cache·=>·CacheTable{} | 81 | ················cache·=>·CacheTable{} |
| 82 | ················Code·=>·image·|·1· | 82 | ················Code·=>·image·|·1·0·1·1·| |
| 83 | ······························|·1· | 83 | ······························|·1·1·0·1·| |
| 84 | ······························|·1·1·1·0·| | 84 | ······························|·1·1·1·0·| |
| 85 | ······························|·1·0·0·0·| | 85 | ······························|·1·0·0·0·| |
| 86 | ······························|·0·1·0·0·| | 86 | ······························|·0·1·0·0·| |
| 87 | ······························|·0·0·1·0·| | 87 | ······························|·0·0·1·0·| |
| 88 | ······························|·0·0·0·1·| | 88 | ······························|·0·0·0·1·| |
| 89 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| | 89 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| |
| 90 | ···································|· | 90 | ···································|·0·1·1·0·1·0·0·| |
| 91 | ···································|· | 91 | ···································|·1·0·1·0·0·1·0·| |
| 92 | ···································|·1·1·0·0·0·0·1·| | 92 | ···································|·1·1·0·0·0·0·1·| |
| 93 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{ | 93 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·0,·0},·{1,·0,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}} |
| 94 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| | 94 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| |
| 95 | ·····································|·0·0·1·1·1·1·0·| | 95 | ·····································|·0·0·1·1·1·1·0·| |
| 96 | ·····································|·0·1·0·1· | 96 | ·····································|·0·1·0·1·1·0·1·| |
| 97 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,· | 97 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·1,·0,·1}} |
| 98 | o1·:·LinearCode</code></pre> | 98 | o1·:·LinearCode</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·ring(C) | 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·ring(C) |
| 102 | o2·=·GF·2 | 102 | o2·=·GF·2 |
| Offset 18, 32 lines modified | Offset 18, 32 lines modified | ||
| 18 | i1·:·C·=·hammingCode(2,·3) | 18 | i1·:·C·=·hammingCode(2,·3) |
| 19 | ·······································7 | 19 | ·······································7 |
| 20 | o1·=·LinearCode{AmbientModule·=>·(GF·2) | 20 | o1·=·LinearCode{AmbientModule·=>·(GF·2) |
| 21 | } | 21 | } |
| 22 | ················BaseField·=>·GF·2 | 22 | ················BaseField·=>·GF·2 |
| 23 | ················cache·=>·CacheTable{} | 23 | ················cache·=>·CacheTable{} |
| 24 | ················Code·=>·image·|·1· | 24 | ················Code·=>·image·|·1·0·1·1·| |
| 25 | ······························|·1· | 25 | ······························|·1·1·0·1·| |
| 26 | ······························|·1·1·1·0·| | 26 | ······························|·1·1·1·0·| |
| 27 | ······························|·1·0·0·0·| | 27 | ······························|·1·0·0·0·| |
| 28 | ······························|·0·1·0·0·| | 28 | ······························|·0·1·0·0·| |
| 29 | ······························|·0·0·1·0·| | 29 | ······························|·0·0·1·0·| |
| 30 | ······························|·0·0·0·1·| | 30 | ······························|·0·0·0·1·| |
| 31 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| | 31 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| |
| 32 | ···································|· | 32 | ···································|·0·1·1·0·1·0·0·| |
| 33 | ···································|· | 33 | ···································|·1·0·1·0·0·1·0·| |
| 34 | ···································|·1·1·0·0·0·0·1·| | 34 | ···································|·1·1·0·0·0·0·1·| |
| 35 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{ | 35 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·1,·1,·0,·1,·0,·0}, |
| 36 | { | 36 | {1,·0,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}} |
| 37 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| | 37 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| |
| 38 | ·····································|·0·0·1·1·1·1·0·| | 38 | ·····································|·0·0·1·1·1·1·0·| |
| 39 | ·····································|·0·1·0·1· | 39 | ·····································|·0·1·0·1·1·0·1·| |
| 40 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1, | 40 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1, |
| 41 | 0},·{0,·1,·0,·1,· | 41 | 0},·{0,·1,·0,·1,·1,·0,·1}} |
| 42 | o1·:·LinearCode | 42 | o1·:·LinearCode |
| 43 | i2·:·ring(C) | 43 | i2·:·ring(C) |
| 44 | o2·=·GF·2 | 44 | o2·=·GF·2 |
| 45 | o2·:·GaloisField | 45 | o2·:·GaloisField |
| Offset 119, 23 lines modified | Offset 119, 23 lines modified | ||
| 119 | ························|·0·| | 119 | ························|·0·| |
| 120 | ························|·0·| | 120 | ························|·0·| |
| 121 | ························|·1·| | 121 | ························|·1·| |
| 122 | ···············|·0·|·=>·|·0·| | 122 | ···············|·0·|·=>·|·0·| |
| 123 | ···············|·1·|····|·0·| | 123 | ···············|·1·|····|·0·| |
| 124 | ···············|·0·|····|·0·| | 124 | ···············|·0·|····|·0·| |
| 125 | ························|·0·| | 125 | ························|·0·| |
| 126 | ························|·0·| | ||
| 127 | ························|·1·| | 126 | ························|·1·| |
| 128 | ························|·0·| | 127 | ························|·0·| |
| 128 | ························|·0·| | ||
| 129 | ···············|·0·|·=>·|·0·| | 129 | ···············|·0·|·=>·|·0·| |
| 130 | ···············|·1·|····|·0·| | 130 | ···············|·1·|····|·0·| |
| 131 | ···············|·1·|····|·0·| | 131 | ···············|·1·|····|·0·| |
| 132 | ························|·0·| | 132 | ························|·0·| |
| 133 | ························|·1·| | ||
| 134 | ························|·0·| | 133 | ························|·0·| |
| 134 | ························|·1·| | ||
| 135 | ························|·0·| | 135 | ························|·0·| |
| 136 | ···············|·1·|·=>·|·1·| | 136 | ···············|·1·|·=>·|·1·| |
| 137 | ···············|·0·|····|·0·| | 137 | ···············|·0·|····|·0·| |
| 138 | ···············|·0·|····|·0·| | 138 | ···············|·0·|····|·0·| |
| 139 | ························|·0·| | 139 | ························|·0·| |
| 140 | ························|·0·| | 140 | ························|·0·| |
| 141 | ························|·0·| | 141 | ························|·0·| |
| Offset 52, 23 lines modified | Offset 52, 23 lines modified | ||
| 52 | ························|·0·| | 52 | ························|·0·| |
| 53 | ························|·0·| | 53 | ························|·0·| |
| 54 | ························|·1·| | 54 | ························|·1·| |
| 55 | ···············|·0·|·=>·|·0·| | 55 | ···············|·0·|·=>·|·0·| |
| 56 | ···············|·1·|····|·0·| | 56 | ···············|·1·|····|·0·| |
| 57 | ···············|·0·|····|·0·| | 57 | ···············|·0·|····|·0·| |
| 58 | ························|·0·| | 58 | ························|·0·| |
| 59 | ························|·0·| | ||
| 60 | ························|·1·| | 59 | ························|·1·| |
| 61 | ························|·0·| | 60 | ························|·0·| |
| 61 | ························|·0·| | ||
| 62 | ···············|·0·|·=>·|·0·| | 62 | ···············|·0·|·=>·|·0·| |
| 63 | ···············|·1·|····|·0·| | 63 | ···············|·1·|····|·0·| |
| 64 | ···············|·1·|····|·0·| | 64 | ···············|·1·|····|·0·| |
| 65 | ························|·0·| | 65 | ························|·0·| |
| 66 | ························|·1·| | ||
| 67 | ························|·0·| | 66 | ························|·0·| |
| 67 | ························|·1·| | ||
| 68 | ························|·0·| | 68 | ························|·0·| |
| 69 | ···············|·1·|·=>·|·1·| | 69 | ···············|·1·|·=>·|·1·| |
| 70 | ···············|·0·|····|·0·| | 70 | ···············|·0·|····|·0·| |
| 71 | ···············|·0·|····|·0·| | 71 | ···············|·0·|····|·0·| |
| 72 | ························|·0·| | 72 | ························|·0·| |
| 73 | ························|·0·| | 73 | ························|·0·| |
| 74 | ························|·0·| | 74 | ························|·0·| |
| Offset 74, 16 lines modified | Offset 74, 16 lines modified | ||
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·H·=·hammingCode(2,3);</code></pre> | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·H·=·hammingCode(2,3);</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·vectorSpace·H | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·vectorSpace·H |
| 79 | o2·=·image·|·1·0·1·1·| | 79 | o2·=·image·|·1·0·1·1·| |
| 80 | ···········|·1·1·0·1·| | ||
| 81 | ···········|·1·1·1·0·| | 80 | ···········|·1·1·1·0·| |
| 81 | ···········|·1·1·0·1·| | ||
| 82 | ···········|·1·0·0·0·| | 82 | ···········|·1·0·0·0·| |
| 83 | ···········|·0·1·0·0·| | 83 | ···········|·0·1·0·0·| |
| 84 | ···········|·0·0·1·0·| | 84 | ···········|·0·0·1·0·| |
| 85 | ···········|·0·0·0·1·| | 85 | ···········|·0·0·0·1·| |
| 86 | ·····································7 | 86 | ·····································7 |
| 87 | o2·:·GF·2-module,·submodule·of·(GF·2)</code></pre> | 87 | o2·:·GF·2-module,·submodule·of·(GF·2)</code></pre> |
| Offset 14, 16 lines modified | Offset 14, 16 lines modified | ||
| 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 15 | Given·a·linear·code·C,·this·function·returns·$V$,·the·vector·space·spanned·by | 15 | Given·a·linear·code·C,·this·function·returns·$V$,·the·vector·space·spanned·by |
| 16 | the·rows·of·a·generator·matrix·of·C. | 16 | the·rows·of·a·generator·matrix·of·C. |
| 17 | i1·:·H·=·hammingCode(2,3); | 17 | i1·:·H·=·hammingCode(2,3); |
| 18 | i2·:·vectorSpace·H | 18 | i2·:·vectorSpace·H |
| 19 | o2·=·image·|·1·0·1·1·| | 19 | o2·=·image·|·1·0·1·1·| |
| 20 | ···········|·1·1·0·1·| | ||
| 21 | ···········|·1·1·1·0·| | 20 | ···········|·1·1·1·0·| |
| 21 | ···········|·1·1·0·1·| | ||
| 22 | ···········|·1·0·0·0·| | 22 | ···········|·1·0·0·0·| |
| 23 | ···········|·0·1·0·0·| | 23 | ···········|·0·1·0·0·| |
| 24 | ···········|·0·0·1·0·| | 24 | ···········|·0·0·1·0·| |
| 25 | ···········|·0·0·0·1·| | 25 | ···········|·0·0·0·1·| |
| 26 | ·····································7 | 26 | ·····································7 |
| 27 | o2·:·GF·2-module,·submodule·of·(GF·2) | 27 | o2·:·GF·2-module,·submodule·of·(GF·2) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=29 | 7 | #:len=29 |
| 8 | Y29ob21DYWxnKE5vcm1hbFRvcmljVmFyaWV0eSk= | 8 | Y29ob21DYWxnKE5vcm1hbFRvcmljVmFyaWV0eSk= |
| 9 | #:len=2221 | 9 | #:len=2221 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibG9jYWxseSBzdGFzaGVkIGNvaG9tb2xv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibG9jYWxseSBzdGFzaGVkIGNvaG9tb2xv |
| 11 | Z3kgdmVjdG9ycyBmcm9tIENvaG9tQ2FsZyIsICJsaW5lbnVtIiA9PiAyODIsIElucHV0cyA9PiB7 | 11 | Z3kgdmVjdG9ycyBmcm9tIENvaG9tQ2FsZyIsICJsaW5lbnVtIiA9PiAyODIsIElucHV0cyA9PiB7 |
| Offset 184, 15 lines modified | Offset 184, 15 lines modified | ||
| 184 | ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0, | 184 | ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0, |
| 185 | ······----------------------------------------------------------------------- | 185 | ······----------------------------------------------------------------------- |
| 186 | ······0,·0,·0,·-1,·-1}} | 186 | ······0,·0,·0,·-1,·-1}} |
| 187 | o19·:·List | 187 | o19·:·List |
| 188 | i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) | 188 | i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) |
| 189 | ·--· | 189 | ·--·3.46171s·elapsed |
| 190 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, | 190 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, |
| 191 | ······----------------------------------------------------------------------- | 191 | ······----------------------------------------------------------------------- |
| 192 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, | 192 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, |
| 193 | ······----------------------------------------------------------------------- | 193 | ······----------------------------------------------------------------------- |
| 194 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, | 194 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, |
| 195 | ······----------------------------------------------------------------------- | 195 | ······----------------------------------------------------------------------- |
| Offset 265, 45 lines modified | Offset 265, 45 lines modified | ||
| 265 | i22·:·degree(X_3·+·X_7·+·X_8) | 265 | i22·:·degree(X_3·+·X_7·+·X_8) |
| 266 | o22·=·{0,·0,·1,·2,·0,·-1} | 266 | o22·=·{0,·0,·1,·2,·0,·-1} |
| 267 | o22·:·List | 267 | o22·:·List |
| 268 | i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) | 268 | i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) |
| 269 | ·--·. | 269 | ·--·.588481s·elapsed |
| 270 | o23·=·{1,·0,·0,·0,·0} | 270 | o23·=·{1,·0,·0,·0,·0} |
| 271 | o23·:·List | 271 | o23·:·List |
| 272 | i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1)) | 272 | i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1)) |
| 273 | ·--· | 273 | ·--·125.286s·elapsed |
| 274 | o24·=·{1,·0,·0,·0,·0} | 274 | o24·=·{1,·0,·0,·0,·0} |
| 275 | o24·:·List | 275 | o24·:·List |
| 276 | i25·:·assert(cohomvec1·==·cohomvec2) | 276 | i25·:·assert(cohomvec1·==·cohomvec2) |
| 277 | i26·:·degree(X_3·+·X_7·-·X_8) | 277 | i26·:·degree(X_3·+·X_7·-·X_8) |
| 278 | o26·=·{0,·0,·1,·2,·-2,·-1} | 278 | o26·=·{0,·0,·1,·2,·-2,·-1} |
| 279 | o26·:·List | 279 | o26·:·List |
| 280 | i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) | 280 | i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) |
| 281 | ·--·. | 281 | ·--·.532626s·elapsed |
| 282 | o27·=·{0,·0,·0,·0,·0} | 282 | o27·=·{0,·0,·0,·0,·0} |
| 283 | o27·:·List | 283 | o27·:·List |
| 284 | i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1)) | 284 | i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1)) |
| 285 | ·--·.3 | 285 | ·--·.35927s·elapsed |
| 286 | ·--·.3 | 286 | ·--·.359313s·elapsed |
| 287 | o28·=·{0,·0,·0,·0,·0} | 287 | o28·=·{0,·0,·0,·0,·0} |
| 288 | o28·:·List | 288 | o28·:·List |
| 289 | i29·:·assert(cohomvec1·==·cohomvec2) | 289 | i29·:·assert(cohomvec1·==·cohomvec2) |
| Offset 263, 15 lines modified | Offset 263, 15 lines modified | ||
| 263 | ······----------------------------------------------------------------------- | 263 | ······----------------------------------------------------------------------- |
| 264 | ······0,·0,·0,·-1,·-1}} | 264 | ······0,·0,·0,·-1,·-1}} |
| 265 | o19·:·List</code></pre> | 265 | o19·:·List</code></pre> |
| 266 | </td>··········</tr> | 266 | </td>··········</tr> |
| 267 | ··········<tr> | 267 | ··········<tr> |
| 268 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) | 268 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) |
| 269 | ·--· | 269 | ·--·3.46171s·elapsed |
| 270 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, | 270 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, |
| 271 | ······----------------------------------------------------------------------- | 271 | ······----------------------------------------------------------------------- |
| 272 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, | 272 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, |
| 273 | ······----------------------------------------------------------------------- | 273 | ······----------------------------------------------------------------------- |
| 274 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, | 274 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, |
| 275 | ······----------------------------------------------------------------------- | 275 | ······----------------------------------------------------------------------- |
| Offset 347, 23 lines modified | Offset 347, 23 lines modified | ||
| 347 | o22·=·{0,·0,·1,·2,·0,·-1} | 347 | o22·=·{0,·0,·1,·2,·0,·-1} |
| 348 | o22·:·List</code></pre> | 348 | o22·:·List</code></pre> |
| 349 | </td>··········</tr> | 349 | </td>··········</tr> |
| 350 | ··········<tr> | 350 | ··········<tr> |
| 351 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) | 351 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) |
| 352 | ·--·. | 352 | ·--·.588481s·elapsed |
| 353 | o23·=·{1,·0,·0,·0,·0} | 353 | o23·=·{1,·0,·0,·0,·0} |
| 354 | o23·:·List</code></pre> | 354 | o23·:·List</code></pre> |
| 355 | </td>··········</tr> | 355 | </td>··········</tr> |
| 356 | ··········<tr> | 356 | ··········<tr> |
| 357 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1)) | 357 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,0,-1)) |
| 358 | ·--· | 358 | ·--·125.286s·elapsed |
| 359 | o24·=·{1,·0,·0,·0,·0} | 359 | o24·=·{1,·0,·0,·0,·0} |
| 360 | o24·:·List</code></pre> | 360 | o24·:·List</code></pre> |
| 361 | </td>··········</tr> | 361 | </td>··········</tr> |
| 362 | ··········<tr> | 362 | ··········<tr> |
| 363 | <td>··············<pre><code·class="language-macaulay2">i25·:·assert(cohomvec1·==·cohomvec2)</code></pre> | 363 | <td>··············<pre><code·class="language-macaulay2">i25·:·assert(cohomvec1·==·cohomvec2)</code></pre> |
| Offset 373, 24 lines modified | Offset 373, 24 lines modified | ||
| 373 | o26·=·{0,·0,·1,·2,·-2,·-1} | 373 | o26·=·{0,·0,·1,·2,·-2,·-1} |
| 374 | o26·:·List</code></pre> | 374 | o26·:·List</code></pre> |
| 375 | </td>··········</tr> | 375 | </td>··········</tr> |
| 376 | ··········<tr> | 376 | ··········<tr> |
| 377 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) | 377 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) |
| 378 | ·--·. | 378 | ·--·.532626s·elapsed |
| 379 | o27·=·{0,·0,·0,·0,·0} | 379 | o27·=·{0,·0,·0,·0,·0} |
| 380 | o27·:·List</code></pre> | 380 | o27·:·List</code></pre> |
| 381 | </td>··········</tr> | 381 | </td>··········</tr> |
| 382 | ··········<tr> | 382 | ··········<tr> |
| 383 | <td>··············<pre><code·class="language-macaulay2">i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1)) | 383 | <td>··············<pre><code·class="language-macaulay2">i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X(0,0,1,2,-2,-1)) |
| 384 | ·--·.3 | 384 | ·--·.35927s·elapsed |
| 385 | ·--·.3 | 385 | ·--·.359313s·elapsed |
| 386 | o28·=·{0,·0,·0,·0,·0} | 386 | o28·=·{0,·0,·0,·0,·0} |
| 387 | o28·:·List</code></pre> | 387 | o28·:·List</code></pre> |
| 388 | </td>··········</tr> | 388 | </td>··········</tr> |
| 389 | ··········<tr> | 389 | ··········<tr> |
| 390 | <td>··············<pre><code·class="language-macaulay2">i29·:·assert(cohomvec1·==·cohomvec2)</code></pre> | 390 | <td>··············<pre><code·class="language-macaulay2">i29·:·assert(cohomvec1·==·cohomvec2)</code></pre> |
| Offset 182, 15 lines modified | Offset 182, 15 lines modified | ||
| 182 | ······----------------------------------------------------------------------- | 182 | ······----------------------------------------------------------------------- |
| 183 | ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0, | 183 | ······{0,·-1,·0,·0,·0,·-1},·{0,·0,·-1,·0,·0,·-1},·{0,·0,·0,·-1,·0,·-1},·{0, |
| 184 | ······----------------------------------------------------------------------- | 184 | ······----------------------------------------------------------------------- |
| 185 | ······0,·0,·0,·-1,·-1}} | 185 | ······0,·0,·0,·-1,·-1}} |
| 186 | o19·:·List | 186 | o19·:·List |
| 187 | i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) | 187 | i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) |
| 188 | ·--· | 188 | ·--·3.46171s·elapsed |
| 189 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, | 189 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, |
| 190 | ······----------------------------------------------------------------------- | 190 | ······----------------------------------------------------------------------- |
| 191 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, | 191 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, |
| 192 | ······----------------------------------------------------------------------- | 192 | ······----------------------------------------------------------------------- |
| 193 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, | 193 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, |
| 194 | ······----------------------------------------------------------------------- | 194 | ······----------------------------------------------------------------------- |
| Offset 262, 42 lines modified | Offset 262, 42 lines modified | ||
| 262 | ·······················{2,·2,·3,·1,·-4,·-6}·=>·{{0,·1,·0,·0,·0},·{{1,·1x1*x2}}} | 262 | ·······················{2,·2,·3,·1,·-4,·-6}·=>·{{0,·1,·0,·0,·0},·{{1,·1x1*x2}}} |
| 263 | i22·:·degree(X_3·+·X_7·+·X_8) | 263 | i22·:·degree(X_3·+·X_7·+·X_8) |
| 264 | o22·=·{0,·0,·1,·2,·0,·-1} | 264 | o22·=·{0,·0,·1,·2,·0,·-1} |
| 265 | o22·:·List | 265 | o22·:·List |
| 266 | i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) | 266 | i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) |
| 267 | ·--·. | 267 | ·--·.588481s·elapsed |
| 268 | o23·=·{1,·0,·0,·0,·0} | 268 | o23·=·{1,·0,·0,·0,·0} |
| 269 | o23·:·List | 269 | o23·:·List |
| 270 | i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X | 270 | i24·:·elapsedTime·cohomvec2·=·for·j·from·0·to·dim·X·list·rank·HH^j(X,·OO_X |
| 271 | (0,0,1,2,0,-1)) | 271 | (0,0,1,2,0,-1)) |
| 272 | ·--· | 272 | ·--·125.286s·elapsed |
| 273 | o24·=·{1,·0,·0,·0,·0} | 273 | o24·=·{1,·0,·0,·0,·0} |
| 274 | o24·:·List | 274 | o24·:·List |
| 275 | i25·:·assert(cohomvec1·==·cohomvec2) | 275 | i25·:·assert(cohomvec1·==·cohomvec2) |
| 276 | i26·:·degree(X_3·+·X_7·-·X_8) | 276 | i26·:·degree(X_3·+·X_7·-·X_8) |
| 277 | o26·=·{0,·0,·1,·2,·-2,·-1} | 277 | o26·=·{0,·0,·1,·2,·-2,·-1} |
| 278 | o26·:·List | 278 | o26·:·List |
| 279 | i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) | 279 | i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) |
| 280 | ·--·. | 280 | ·--·.532626s·elapsed |
| 281 | o27·=·{0,·0,·0,·0,·0} | 281 | o27·=·{0,·0,·0,·0,·0} |
| 282 | o27·:·List | 282 | o27·:·List |
| 283 | i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j | 283 | i28·:·elapsedTime·cohomvec2·=·elapsedTime·for·j·from·0·to·dim·X·list·rank·HH^j |
| 284 | (X,·OO_X(0,0,1,2,-2,-1)) | 284 | (X,·OO_X(0,0,1,2,-2,-1)) |
| 285 | ·--·.3 | 285 | ·--·.35927s·elapsed |
| 286 | ·--·.3 | 286 | ·--·.359313s·elapsed |
| 287 | o28·=·{0,·0,·0,·0,·0} | 287 | o28·=·{0,·0,·0,·0,·0} |
| 288 | o28·:·List | 288 | o28·:·List |
| 289 | i29·:·assert(cohomvec1·==·cohomvec2) | 289 | i29·:·assert(cohomvec1·==·cohomvec2) |
| 290 | _\x8c_\x8o_\x8h_\x8o_\x8m_\x8C_\x8a_\x8l_\x8g·computes·cohomology·vectors·by·calling·CohomCalg.·It·also·stashes | 290 | _\x8c_\x8o_\x8h_\x8o_\x8m_\x8C_\x8a_\x8l_\x8g·computes·cohomology·vectors·by·calling·CohomCalg.·It·also·stashes |
| 291 | it's·results·in·the·toric·variety's·cache·table,·so·computations·need·not·be | 291 | it's·results·in·the·toric·variety's·cache·table,·so·computations·need·not·be |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=24 | 7 | #:len=24 |
| 8 | Y29tcGxleHJhbmsoUmluZ0VsZW1lbnQp | 8 | Y29tcGxleHJhbmsoUmluZ0VsZW1lbnQp |
| 9 | #:len=297 | 9 | #:len=297 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV4cmFuayxSaW5nRWxlbWVudCksImNvbXBs | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV4cmFuayxSaW5nRWxlbWVudCksImNvbXBs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=28 | 7 | #:len=28 |
| 8 | RWlzZW5idWRTaGFtYXNoVG90YWwoTW9kdWxlKQ== | 8 | RWlzZW5idWRTaGFtYXNoVG90YWwoTW9kdWxlKQ== |
| 9 | #:len=349 | 9 | #:len=349 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTE2NSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTE2NSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoRWlzZW5idWRTaGFtYXNoVG90YWwsTW9kdWxlKSwi | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoRWlzZW5idWRTaGFtYXNoVG90YWwsTW9kdWxlKSwi |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | o5·:·QuotientRing | 35 | o5·:·QuotientRing |
| 36 | i6·:·len·=·10 | 36 | i6·:·len·=·10 |
| 37 | o6·=·10 | 37 | o6·=·10 |
| 38 | i7·:·time·G·=·EisenbudShamash(ff,F,len) | 38 | i7·:·time·G·=·EisenbudShamash(ff,F,len) |
| 39 | ·--·used· | 39 | ·--·used·8.71608s·(cpu);·5.48522s·(thread);·0s·(gc) |
| 40 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76 | 40 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76 |
| 41 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------| | 41 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------| |
| 42 | ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·| | 42 | ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·| |
| 43 | ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)| | 43 | ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)| |
| 44 | ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/ | 44 | ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/ |
| 45 | ·············································································································································································· | 45 | ·············································································································································································· |
| Offset 140, 37 lines modified | Offset 140, 37 lines modified | ||
| 140 | i19·:·R1·=·R/ideal·ff | 140 | i19·:·R1·=·R/ideal·ff |
| 141 | o19·=·R1 | 141 | o19·=·R1 |
| 142 | o19·:·QuotientRing | 142 | o19·:·QuotientRing |
| 143 | i20·:·FF·=·time·Shamash(R1,F,4) | 143 | i20·:·FF·=·time·Shamash(R1,F,4) |
| 144 | ·--·used·0.1 | 144 | ·--·used·0.136054s·(cpu);·0.0842077s·(thread);·0s·(gc) |
| 145 | ········1·······6·······18·······38·······66 | 145 | ········1·······6·······18·······38·······66 |
| 146 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 146 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 147 | ········································· | 147 | ········································· |
| 148 | ······0·······1·······2········3········4 | 148 | ······0·······1·······2········3········4 |
| 149 | o20·:·ChainComplex | 149 | o20·:·ChainComplex |
| 150 | i21·:·GG·=·time·EisenbudShamash(ff,F,4) | 150 | i21·:·GG·=·time·EisenbudShamash(ff,F,4) |
| 151 | ·--·used·1. | 151 | ·--·used·1.28981s·(cpu);·0.85591s·(thread);·0s·(gc) |
| 152 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 | 152 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 |
| 153 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| | 153 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| |
| 154 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| | 154 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| |
| 155 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ | 155 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ |
| 156 | ················································· | 156 | ················································· |
| 157 | ······0·········1·········2··········3··········4 | 157 | ······0·········1·········2··········3··········4 |
| 158 | o21·:·ChainComplex | 158 | o21·:·ChainComplex |
| 159 | i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) | 159 | i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) |
| 160 | ·--·used·1. | 160 | ·--·used·1.33999s·(cpu);·0.816011s·(thread);·0s·(gc) |
| 161 | ········1·······6·······18·······38·······66 | 161 | ········1·······6·······18·······38·······66 |
| 162 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 162 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 163 | ········································· | 163 | ········································· |
| 164 | ······-2······-1······0········1········2 | 164 | ······-2······-1······0········1········2 |
| 165 | o22·:·ChainComplex | 165 | o22·:·ChainComplex |
| Offset 1, 17 lines modified | Offset 1, 17 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731741365432311614 | 1 | --·-*-·M2-comint·-*-·hash:·1731741365432311614 |
| 2 | i1·:·setRandomSeed·0 | 2 | i1·:·setRandomSeed·0 |
| 3 | o1·=·0 | 3 | o1·=·0 |
| 4 | i2·:·sumTwoMonomials(2,3) | 4 | i2·:·sumTwoMonomials(2,3) |
| 5 | ·--·used·1.2 | 5 | ·--·used·1.24063s·(cpu);·0.415842s·(thread);·0s·(gc) |
| 6 | ·--·used·0.426 | 6 | ·--·used·0.452653s·(cpu);·0.154356s·(thread);·0s·(gc) |
| 7 | ·--·used·0.0001 | 7 | ·--·used·0.000117801s·(cpu);·2.034e-06s·(thread);·0s·(gc) |
| 8 | 2 | 8 | 2 |
| 9 | Tally{{{2,·2},·{1,·2}}·=>·3} | 9 | Tally{{{2,·2},·{1,·2}}·=>·3} |
| 10 | 3 | 10 | 3 |
| 11 | Tally{{{2,·2},·{1,·2}}·=>·1} | 11 | Tally{{{2,·2},·{1,·2}}·=>·1} |
| 12 | 4 | 12 | 4 |
| Offset 1, 23 lines modified | Offset 1, 23 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731741366884359753 | 1 | --·-*-·M2-comint·-*-·hash:·1731741366884359753 |
| 2 | i1·:·setRandomSeed·0 | 2 | i1·:·setRandomSeed·0 |
| 3 | o1·=·0 | 3 | o1·=·0 |
| 4 | i2·:·twoMonomials(2,3) | 4 | i2·:·twoMonomials(2,3) |
| 5 | ·--·used·2.29 | 5 | ·--·used·2.2935s·(cpu);·0.729454s·(thread);·0s·(gc) |
| 6 | 2 | 6 | 2 |
| 7 | Tally{{{1,·1}}·=>·2········} | 7 | Tally{{{1,·1}}·=>·2········} |
| 8 | ······{{2,·2},·{1,·2}}·=>·4 | 8 | ······{{2,·2},·{1,·2}}·=>·4 |
| 9 | ·--·used·1. | 9 | ·--·used·1.3127s·(cpu);·0.506679s·(thread);·0s·(gc) |
| 10 | 3 | 10 | 3 |
| 11 | Tally{{{2,·2},·{1,·2}}·=>·2} | 11 | Tally{{{2,·2},·{1,·2}}·=>·2} |
| 12 | ······{{3,·3},·{2,·3}}·=>·1 | 12 | ······{{3,·3},·{2,·3}}·=>·1 |
| 13 | ·--·used·0.4 | 13 | ·--·used·0.440456s·(cpu);·0.156264s·(thread);·0s·(gc) |
| 14 | 4 | 14 | 4 |
| 15 | Tally{{{2,·2},·{1,·2}}·=>·1} | 15 | Tally{{{2,·2},·{1,·2}}·=>·1} |
| 16 | i3·:· | 16 | i3·:· |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i6·:·len·=·10 | 122 | <td>··············<pre><code·class="language-macaulay2">i6·:·len·=·10 |
| 123 | o6·=·10</code></pre> | 123 | o6·=·10</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·G·=·EisenbudShamash(ff,F,len) | 126 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·G·=·EisenbudShamash(ff,F,len) |
| 127 | ·--·used· | 127 | ·--·used·8.71608s·(cpu);·5.48522s·(thread);·0s·(gc) |
| 128 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76 | 128 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76 |
| 129 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------| | 129 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------| |
| 130 | ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·| | 130 | ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·| |
| 131 | ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)| | 131 | ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)| |
| 132 | ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/ | 132 | ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/ |
| 133 | ·············································································································································································· | 133 | ·············································································································································································· |
| Offset 259, 26 lines modified | Offset 259, 26 lines modified | ||
| 259 | o19·=·R1 | 259 | o19·=·R1 |
| 260 | o19·:·QuotientRing</code></pre> | 260 | o19·:·QuotientRing</code></pre> |
| 261 | </td>··········</tr> | 261 | </td>··········</tr> |
| 262 | ··········<tr> | 262 | ··········<tr> |
| 263 | <td>··············<pre><code·class="language-macaulay2">i20·:·FF·=·time·Shamash(R1,F,4) | 263 | <td>··············<pre><code·class="language-macaulay2">i20·:·FF·=·time·Shamash(R1,F,4) |
| 264 | ·--·used·0.1 | 264 | ·--·used·0.136054s·(cpu);·0.0842077s·(thread);·0s·(gc) |
| 265 | ········1·······6·······18·······38·······66 | 265 | ········1·······6·······18·······38·······66 |
| 266 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 266 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 267 | ········································· | 267 | ········································· |
| 268 | ······0·······1·······2········3········4 | 268 | ······0·······1·······2········3········4 |
| 269 | o20·:·ChainComplex</code></pre> | 269 | o20·:·ChainComplex</code></pre> |
| 270 | </td>··········</tr> | 270 | </td>··········</tr> |
| 271 | ··········<tr> | 271 | ··········<tr> |
| 272 | <td>··············<pre><code·class="language-macaulay2">i21·:·GG·=·time·EisenbudShamash(ff,F,4) | 272 | <td>··············<pre><code·class="language-macaulay2">i21·:·GG·=·time·EisenbudShamash(ff,F,4) |
| 273 | ·--·used·1. | 273 | ·--·used·1.28981s·(cpu);·0.85591s·(thread);·0s·(gc) |
| 274 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 | 274 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 |
| 275 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| | 275 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| |
| 276 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| | 276 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| |
| 277 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ | 277 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ |
| 278 | ················································· | 278 | ················································· |
| 279 | ······0·········1·········2··········3··········4 | 279 | ······0·········1·········2··········3··········4 |
| Offset 288, 15 lines modified | Offset 288, 15 lines modified | ||
| 288 | ········</table> | 288 | ········</table> |
| 289 | ········<div> | 289 | ········<div> |
| 290 | ··········<p>The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:</p> | 290 | ··········<p>The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:</p> |
| 291 | ········</div> | 291 | ········</div> |
| 292 | ········<table·class="examples"> | 292 | ········<table·class="examples"> |
| 293 | ··········<tr> | 293 | ··········<tr> |
| 294 | <td>··············<pre><code·class="language-macaulay2">i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) | 294 | <td>··············<pre><code·class="language-macaulay2">i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) |
| 295 | ·--·used·1. | 295 | ·--·used·1.33999s·(cpu);·0.816011s·(thread);·0s·(gc) |
| 296 | ········1·······6·······18·······38·······66 | 296 | ········1·······6·······18·······38·······66 |
| 297 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 297 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 298 | ········································· | 298 | ········································· |
| 299 | ······-2······-1······0········1········2 | 299 | ······-2······-1······0········1········2 |
| 300 | o22·:·ChainComplex</code></pre> | 300 | o22·:·ChainComplex</code></pre> |
| Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
| 51 | o5·=·R | 51 | o5·=·R |
| 52 | o5·:·QuotientRing | 52 | o5·:·QuotientRing |
| 53 | i6·:·len·=·10 | 53 | i6·:·len·=·10 |
| 54 | o6·=·10 | 54 | o6·=·10 |
| 55 | i7·:·time·G·=·EisenbudShamash(ff,F,len) | 55 | i7·:·time·G·=·EisenbudShamash(ff,F,len) |
| 56 | ·--·used· | 56 | ·--·used·8.71608s·(cpu);·5.48522s·(thread);·0s·(gc) |
| 57 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S | 57 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S |
| 58 | \28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/ | 58 | \28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/ |
| 59 | S···\68·····/····S···\76 | 59 | S···\68·····/····S···\76 |
| 60 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|------- | 60 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|------- |
| 61 | -|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|- | 61 | -|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|- |
| 62 | -------|···<--·|--------| | 62 | -------|···<--·|--------| |
| Offset 167, 36 lines modified | Offset 167, 36 lines modified | ||
| 167 | o18·:·Matrix·R··<--·R | 167 | o18·:·Matrix·R··<--·R |
| 168 | i19·:·R1·=·R/ideal·ff | 168 | i19·:·R1·=·R/ideal·ff |
| 169 | o19·=·R1 | 169 | o19·=·R1 |
| 170 | o19·:·QuotientRing | 170 | o19·:·QuotientRing |
| 171 | i20·:·FF·=·time·Shamash(R1,F,4) | 171 | i20·:·FF·=·time·Shamash(R1,F,4) |
| 172 | ·--·used·0.1 | 172 | ·--·used·0.136054s·(cpu);·0.0842077s·(thread);·0s·(gc) |
| 173 | ········1·······6·······18·······38·······66 | 173 | ········1·······6·······18·······38·······66 |
| 174 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 174 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 175 | ······0·······1·······2········3········4 | 175 | ······0·······1·······2········3········4 |
| 176 | o20·:·ChainComplex | 176 | o20·:·ChainComplex |
| 177 | i21·:·GG·=·time·EisenbudShamash(ff,F,4) | 177 | i21·:·GG·=·time·EisenbudShamash(ff,F,4) |
| 178 | ·--·used·1. | 178 | ·--·used·1.28981s·(cpu);·0.85591s·(thread);·0s·(gc) |
| 179 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 | 179 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 |
| 180 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| | 180 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| |
| 181 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| | 181 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| |
| 182 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ | 182 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ |
| 183 | ······0·········1·········2··········3··········4 | 183 | ······0·········1·········2··········3··········4 |
| 184 | o21·:·ChainComplex | 184 | o21·:·ChainComplex |
| 185 | The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0: | 185 | The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0: |
| 186 | i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) | 186 | i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) |
| 187 | ·--·used·1. | 187 | ·--·used·1.33999s·(cpu);·0.816011s·(thread);·0s·(gc) |
| 188 | ········1·······6·······18·······38·······66 | 188 | ········1·······6·······18·······38·······66 |
| 189 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 189 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 190 | ······-2······-1······0········1········2 | 190 | ······-2······-1······0········1········2 |
| 191 | o22·:·ChainComplex | 191 | o22·:·ChainComplex |
| Offset 76, 17 lines modified | Offset 76, 17 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 |
| 78 | o1·=·0</code></pre> | 78 | o1·=·0</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·sumTwoMonomials(2,3) | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·sumTwoMonomials(2,3) |
| 82 | ·--·used·1.2 | 82 | ·--·used·1.24063s·(cpu);·0.415842s·(thread);·0s·(gc) |
| 83 | ·--·used·0.426 | 83 | ·--·used·0.452653s·(cpu);·0.154356s·(thread);·0s·(gc) |
| 84 | ·--·used·0.0001 | 84 | ·--·used·0.000117801s·(cpu);·2.034e-06s·(thread);·0s·(gc) |
| 85 | 2 | 85 | 2 |
| 86 | Tally{{{2,·2},·{1,·2}}·=>·3} | 86 | Tally{{{2,·2},·{1,·2}}·=>·3} |
| 87 | 3 | 87 | 3 |
| 88 | Tally{{{2,·2},·{1,·2}}·=>·1} | 88 | Tally{{{2,·2},·{1,·2}}·=>·1} |
| 89 | 4 | 89 | 4 |
| Offset 18, 17 lines modified | Offset 18, 17 lines modified | ||
| 18 | =·S/(d-th·powers·of·the·variables),·with·full·complexity·(=c);·that·is,·for·an | 18 | =·S/(d-th·powers·of·the·variables),·with·full·complexity·(=c);·that·is,·for·an |
| 19 | appropriate·syzygy·M·of·M0·=·R/(m1+m2)·where·m1·and·m2·are·monomials·of·the | 19 | appropriate·syzygy·M·of·M0·=·R/(m1+m2)·where·m1·and·m2·are·monomials·of·the |
| 20 | same·degree. | 20 | same·degree. |
| 21 | i1·:·setRandomSeed·0 | 21 | i1·:·setRandomSeed·0 |
| 22 | o1·=·0 | 22 | o1·=·0 |
| 23 | i2·:·sumTwoMonomials(2,3) | 23 | i2·:·sumTwoMonomials(2,3) |
| 24 | ·--·used·1.2 | 24 | ·--·used·1.24063s·(cpu);·0.415842s·(thread);·0s·(gc) |
| 25 | ·--·used·0.426 | 25 | ·--·used·0.452653s·(cpu);·0.154356s·(thread);·0s·(gc) |
| 26 | ·--·used·0.0001 | 26 | ·--·used·0.000117801s·(cpu);·2.034e-06s·(thread);·0s·(gc) |
| 27 | 2 | 27 | 2 |
| 28 | Tally{{{2,·2},·{1,·2}}·=>·3} | 28 | Tally{{{2,·2},·{1,·2}}·=>·3} |
| 29 | 3 | 29 | 3 |
| 30 | Tally{{{2,·2},·{1,·2}}·=>·1} | 30 | Tally{{{2,·2},·{1,·2}}·=>·1} |
| 31 | 4 | 31 | 4 |
| Offset 82, 25 lines modified | Offset 82, 25 lines modified | ||
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 | 83 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 |
| 84 | o1·=·0</code></pre> | 84 | o1·=·0</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·twoMonomials(2,3) | 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·twoMonomials(2,3) |
| 88 | ·--·used·2.29 | 88 | ·--·used·2.2935s·(cpu);·0.729454s·(thread);·0s·(gc) |
| 89 | 2 | 89 | 2 |
| 90 | Tally{{{1,·1}}·=>·2········} | 90 | Tally{{{1,·1}}·=>·2········} |
| 91 | ······{{2,·2},·{1,·2}}·=>·4 | 91 | ······{{2,·2},·{1,·2}}·=>·4 |
| 92 | ·--·used·1. | 92 | ·--·used·1.3127s·(cpu);·0.506679s·(thread);·0s·(gc) |
| 93 | 3 | 93 | 3 |
| 94 | Tally{{{2,·2},·{1,·2}}·=>·2} | 94 | Tally{{{2,·2},·{1,·2}}·=>·2} |
| 95 | ······{{3,·3},·{2,·3}}·=>·1 | 95 | ······{{3,·3},·{2,·3}}·=>·1 |
| 96 | ·--·used·0.4 | 96 | ·--·used·0.440456s·(cpu);·0.156264s·(thread);·0s·(gc) |
| 97 | 4 | 97 | 4 |
| 98 | Tally{{{2,·2},·{1,·2}}·=>·1}</code></pre> | 98 | Tally{{{2,·2},·{1,·2}}·=>·1}</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ········</table> | 100 | ········</table> |
| 101 | ······</div> | 101 | ······</div> |
| 102 | ······<div> | 102 | ······<div> |
| 103 | ········<h2>See·also</h2> | 103 | ········<h2>See·also</h2> |
| Offset 20, 25 lines modified | Offset 20, 25 lines modified | ||
| 20 | monomials·in·R·=·S/(d-th·powers·of·the·variables),·with·full·complexity·(=c); | 20 | monomials·in·R·=·S/(d-th·powers·of·the·variables),·with·full·complexity·(=c); |
| 21 | that·is,·for·an·appropriate·syzygy·M·of·M0·=·R/(m1,·m2)·where·m1·and·m2·are | 21 | that·is,·for·an·appropriate·syzygy·M·of·M0·=·R/(m1,·m2)·where·m1·and·m2·are |
| 22 | monomials·of·the·same·degree. | 22 | monomials·of·the·same·degree. |
| 23 | i1·:·setRandomSeed·0 | 23 | i1·:·setRandomSeed·0 |
| 24 | o1·=·0 | 24 | o1·=·0 |
| 25 | i2·:·twoMonomials(2,3) | 25 | i2·:·twoMonomials(2,3) |
| 26 | ·--·used·2.29 | 26 | ·--·used·2.2935s·(cpu);·0.729454s·(thread);·0s·(gc) |
| 27 | 2 | 27 | 2 |
| 28 | Tally{{{1,·1}}·=>·2········} | 28 | Tally{{{1,·1}}·=>·2········} |
| 29 | ······{{2,·2},·{1,·2}}·=>·4 | 29 | ······{{2,·2},·{1,·2}}·=>·4 |
| 30 | ·--·used·1. | 30 | ·--·used·1.3127s·(cpu);·0.506679s·(thread);·0s·(gc) |
| 31 | 3 | 31 | 3 |
| 32 | Tally{{{2,·2},·{1,·2}}·=>·2} | 32 | Tally{{{2,·2},·{1,·2}}·=>·2} |
| 33 | ······{{3,·3},·{2,·3}}·=>·1 | 33 | ······{{3,·3},·{2,·3}}·=>·1 |
| 34 | ·--·used·0.4 | 34 | ·--·used·0.440456s·(cpu);·0.156264s·(thread);·0s·(gc) |
| 35 | 4 | 35 | 4 |
| 36 | Tally{{{2,·2},·{1,·2}}·=>·1} | 36 | Tally{{{2,·2},·{1,·2}}·=>·1} |
| 37 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 37 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 38 | ····*·_\x8t_\x8w_\x8o_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·tally·the·sequences·of·BRanks·for·certain·examples | 38 | ····*·_\x8t_\x8w_\x8o_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·tally·the·sequences·of·BRanks·for·certain·examples |
| 39 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8tw\x8wo\x8oM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8ls\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 39 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8tw\x8wo\x8oM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8ls\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 40 | ····*·twoMonomials(ZZ,ZZ) | 40 | ····*·twoMonomials(ZZ,ZZ) |
| 41 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 41 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=19 | 7 | #:len=19 |
| 8 | SG9tKE1hdHJpeCxDb21wbGV4KQ== | 8 | SG9tKE1hdHJpeCxDb21wbGV4KQ== |
| 9 | #:len=295 | 9 | #:len=295 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 6 | #·End·of·header | 6 | #·End·of·header |
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| 9 | #:len=1172 | 9 | #:len=1172 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 7 | #:len=33 | 7 | #:len=33 |
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| 9 | #:len=273 | 9 | #:len=273 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | Y29ud2F5UG9seW5vbWlhbA== | 8 | Y29ud2F5UG9seW5vbWlhbA== |
| 9 | #:len=1659 | 9 | #:len=1659 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJvdmlkZSBhIENvbndheSBwb2x5bm9t | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJvdmlkZSBhIENvbndheSBwb2x5bm9t |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=52 | 7 | #:len=52 |
| 8 | cHJvZHVjdE9mUHJvamVjdGl2ZVNwYWNlcyguLi4sQ29lZmZpY2llbnRGaWVsZD0+Li4uKQ== | 8 | cHJvZHVjdE9mUHJvamVjdGl2ZVNwYWNlcyguLi4sQ29lZmZpY2llbnRGaWVsZD0+Li4uKQ== |
| 9 | #:len=367 | 9 | #:len=367 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzcwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzcwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=6 | 7 | #:len=6 |
| 8 | TGFiZWxz | 8 | TGFiZWxz |
| 9 | #:len=183 | 9 | #:len=183 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA3LCAidW5kb2N1bWVudGVkIiA9PiB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA3LCAidW5kb2N1bWVudGVkIiA9PiB0 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | ZGVzY3JpYmUoUmF0aW9uYWxNYXAp | 8 | ZGVzY3JpYmUoUmF0aW9uYWxNYXAp |
| 9 | #:len=1096 | 9 | #:len=1096 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGVzY3JpYmUgYSByYXRpb25hbCBtYXAi | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGVzY3JpYmUgYSByYXRpb25hbCBtYXAi |
| 11 | LCAibGluZW51bSIgPT4gOTgzLCBJbnB1dHMgPT4ge1NQQU57VFR7InBoaSJ9LCIsICIsU1BBTnsi | 11 | LCAibGluZW51bSIgPT4gOTgzLCBJbnB1dHMgPT4ge1NQQU57VFR7InBoaSJ9LCIsICIsU1BBTnsi |
| Offset 13, 26 lines modified | Offset 13, 26 lines modified | ||
| 13 | o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·) | 13 | o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·) |
| 14 | ···············1····0·2·····1·2····0·3·····2····1·3 | 14 | ···············1····0·2·····1·2····0·3·····2····1·3 |
| 15 | o2·:·Ideal·of·GF·78125[x·..x·] | 15 | o2·:·Ideal·of·GF·78125[x·..x·] |
| 16 | ························0···4 | 16 | ························0···4 |
| 17 | i3·:·time·ChernSchwartzMacPherson·C | 17 | i3·:·time·ChernSchwartzMacPherson·C |
| 18 | ·--·used·1. | 18 | ·--·used·1.37237s·(cpu);·0.925571s·(thread);·0s·(gc) |
| 19 | ·······4·····3·····2 | 19 | ·······4·····3·····2 |
| 20 | o3·=·3H··+·5H··+·3H | 20 | o3·=·3H··+·5H··+·3H |
| 21 | ·····ZZ[H] | 21 | ·····ZZ[H] |
| 22 | o3·:·----- | 22 | o3·:·----- |
| 23 | ········5 | 23 | ········5 |
| 24 | ·······H | 24 | ·······H |
| 25 | i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) | 25 | i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) |
| 26 | ·--·used·2. | 26 | ·--·used·2.48176s·(cpu);·0.957935s·(thread);·0s·(gc) |
| 27 | Certify:·output·certified! | 27 | Certify:·output·certified! |
| 28 | ·······4·····3·····2 | 28 | ·······4·····3·····2 |
| 29 | o4·=·3H··+·5H··+·3H | 29 | o4·=·3H··+·5H··+·3H |
| 30 | ·····ZZ[H] | 30 | ·····ZZ[H] |
| 31 | o4·:·----- | 31 | o4·:·----- |
| Offset 62, 26 lines modified | Offset 62, 26 lines modified | ||
| 62 | ········0,2·1,3····0,1·2,3 | 62 | ········0,2·1,3····0,1·2,3 |
| 63 | ················ZZ | 63 | ················ZZ |
| 64 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] | 64 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] |
| 65 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 | 65 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 |
| 66 | i9·:·time·ChernClass·G | 66 | i9·:·time·ChernClass·G |
| 67 | ·--·used·0.1 | 67 | ·--·used·0.171453s·(cpu);·0.125004s·(thread);·0s·(gc) |
| 68 | ········9······8······7······6······5······4·····3 | 68 | ········9······8······7······6······5······4·····3 |
| 69 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 69 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 70 | ·····ZZ[H] | 70 | ·····ZZ[H] |
| 71 | o9·:·----- | 71 | o9·:·----- |
| 72 | ·······10 | 72 | ·······10 |
| 73 | ······H | 73 | ······H |
| 74 | i10·:·time·ChernClass(G,Certify=>true) | 74 | i10·:·time·ChernClass(G,Certify=>true) |
| 75 | ·--·used·0.2 | 75 | ·--·used·0.211593s·(cpu);·0.0269365s·(thread);·0s·(gc) |
| 76 | Certify:·output·certified! | 76 | Certify:·output·certified! |
| 77 | ·········9······8······7······6······5······4·····3 | 77 | ·········9······8······7······6······5······4·····3 |
| 78 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 78 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 79 | ······ZZ[H] | 79 | ······ZZ[H] |
| 80 | o10·:·----- | 80 | o10·:·----- |
| Offset 1, 56 lines modified | Offset 1, 56 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·10433409267944421825 | 1 | --·-*-·M2-comint·-*-·hash:·10433409267944421825 |
| 2 | i1·:·ZZ/300007[t_0..t_6]; | 2 | i1·:·ZZ/300007[t_0..t_6]; |
| 3 | i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) | 3 | i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) |
| 4 | ·--·used·0.0040 | 4 | ·--·used·0.00401078s·(cpu);·0.00373695s·(thread);·0s·(gc) |
| 5 | ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 | 5 | ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 |
| 6 | o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) | 6 | o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) |
| 7 | ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 | 7 | ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 |
| 8 | ···············ZZ·················ZZ | 8 | ···············ZZ·················ZZ |
| 9 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] | 9 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] |
| 10 | ·············300007··0···6······300007··0···9 | 10 | ·············300007··0···6······300007··0···9 |
| 11 | i3·:·time·J·=·kernel(phi,2) | 11 | i3·:·time·J·=·kernel(phi,2) |
| 12 | ·--·used·0.03 | 12 | ·--·used·0.0362442s·(cpu);·0.037683s·(thread);·0s·(gc) |
| 13 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x· | 13 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x· |
| 14 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 | 14 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 |
| 15 | ·····------------------------------------------------------------------------ | 15 | ·····------------------------------------------------------------------------ |
| 16 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 16 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 17 | ········1·6····0·8···2·4····1·5····0·7 | 17 | ········1·6····0·8···2·4····1·5····0·7 |
| 18 | ················ZZ | 18 | ················ZZ |
| 19 | o3·:·Ideal·of·------[x·..x·] | 19 | o3·:·Ideal·of·------[x·..x·] |
| 20 | ··············300007··0···9 | 20 | ··············300007··0···9 |
| 21 | i4·:·time·degreeMap·phi | 21 | i4·:·time·degreeMap·phi |
| 22 | ·--·used·0.0 | 22 | ·--·used·0.0812392s·(cpu);·0.0356259s·(thread);·0s·(gc) |
| 23 | o4·=·1 | 23 | o4·=·1 |
| 24 | i5·:·time·projectiveDegrees·phi | 24 | i5·:·time·projectiveDegrees·phi |
| 25 | ·--·used·0.3 | 25 | ·--·used·0.375054s·(cpu);·0.339625s·(thread);·0s·(gc) |
| 26 | o5·=·{1,·3,·9,·17,·21,·15,·5} | 26 | o5·=·{1,·3,·9,·17,·21,·15,·5} |
| 27 | o5·:·List | 27 | o5·:·List |
| 28 | i6·:·time·projectiveDegrees(phi,NumDegrees=>0) | 28 | i6·:·time·projectiveDegrees(phi,NumDegrees=>0) |
| 29 | ·--·used·0.0 | 29 | ·--·used·0.0627803s·(cpu);·0.0626703s·(thread);·0s·(gc) |
| 30 | o6·=·{5} | 30 | o6·=·{5} |
| 31 | o6·:·List | 31 | o6·:·List |
| 32 | i7·:·time·phi·=·toMap(phi,Dominant=>J) | 32 | i7·:·time·phi·=·toMap(phi,Dominant=>J) |
| 33 | ·--·used·0.000 | 33 | ·--·used·0.000242715s·(cpu);·0.00237005s·(thread);·0s·(gc) |
| 34 | ·······································································ZZ | 34 | ·······································································ZZ |
| 35 | ·····································································------[x·..x·] | 35 | ·····································································------[x·..x·] |
| 36 | ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 | 36 | ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 |
| 37 | o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) | 37 | o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) |
| 38 | ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 | 38 | ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 |
| 39 | ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 39 | ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 59 | ···········································································------[x·..x·] | 59 | ···········································································------[x·..x·] |
| 60 | ···············ZZ··························································300007··0···9 | 60 | ···············ZZ··························································300007··0···9 |
| 61 | o7·:·RingMap·------[t·..t·]·<--·---------------------------------------------------------------------------------------------------- | 61 | o7·:·RingMap·------[t·..t·]·<--·---------------------------------------------------------------------------------------------------- |
| 62 | ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 62 | ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 63 | ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 63 | ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| 64 | i8·:·time·psi·=·inverseMap·phi | 64 | i8·:·time·psi·=·inverseMap·phi |
| 65 | ·--·used·0.37 | 65 | ·--·used·0.437051s·(cpu);·0.384559s·(thread);·0s·(gc) |
| 66 | ·······················································ZZ | 66 | ·······················································ZZ |
| 67 | ·····················································------[x·..x·] | 67 | ·····················································------[x·..x·] |
| 68 | ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2 | 68 | ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2 |
| 69 | o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·}) | 69 | o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·}) |
| 70 | ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9 | 70 | ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9 |
| 71 | ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 71 | ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| Offset 76, 32 lines modified | Offset 76, 32 lines modified | ||
| 76 | ························································------[x·..x·] | 76 | ························································------[x·..x·] |
| 77 | ························································300007··0···9···················································ZZ | 77 | ························································300007··0···9···················································ZZ |
| 78 | o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·] | 78 | o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·] |
| 79 | ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6 | 79 | ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6 |
| 80 | ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 80 | ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| 81 | i9·:·time·isInverseMap(phi,psi) | 81 | i9·:·time·isInverseMap(phi,psi) |
| 82 | ·--·used·0.00 | 82 | ·--·used·0.00737805s·(cpu);·0.00798491s·(thread);·0s·(gc) |
| 83 | o9·=·true | 83 | o9·=·true |
| 84 | i10·:·time·degreeMap·psi | 84 | i10·:·time·degreeMap·psi |
| 85 | ·--·used·0.18 | 85 | ·--·used·0.218521s·(cpu);·0.16695s·(thread);·0s·(gc) |
| 86 | o10·=·1 | 86 | o10·=·1 |
| 87 | i11·:·time·projectiveDegrees·psi | 87 | i11·:·time·projectiveDegrees·psi |
| 88 | ·--·used· | 88 | ·--·used·5.11597s·(cpu);·4.7932s·(thread);·0s·(gc) |
| 89 | o11·=·{5,·15,·21,·17,·9,·3,·1} | 89 | o11·=·{5,·15,·21,·17,·9,·3,·1} |
| 90 | o11·:·List | 90 | o11·:·List |
| 91 | i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) | 91 | i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) |
| 92 | ·--·used·0.00 | 92 | ·--·used·0.000742082s·(cpu);·0.00252711s·(thread);·0s·(gc) |
| 93 | o12·=·--·rational·map·-- | 93 | o12·=·--·rational·map·-- |
| 94 | ·····················ZZ | 94 | ·····················ZZ |
| 95 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 95 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 96 | ···················300007··0···1···2···3···4···5···6 | 96 | ···················300007··0···1···2···3···4···5···6 |
| 97 | ·····················ZZ | 97 | ·····················ZZ |
| 98 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 98 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 147, 15 lines modified | Offset 147, 15 lines modified | ||
| 147 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t | 147 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t |
| 148 | ··························4·····3·4·5····2·5····3·6····2·4·6 | 148 | ··························4·····3·4·5····2·5····3·6····2·4·6 |
| 149 | ······················} | 149 | ······················} |
| 150 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9) | 150 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9) |
| 151 | i13·:·time·phi·=·rationalMap(phi,Dominant=>2) | 151 | i13·:·time·phi·=·rationalMap(phi,Dominant=>2) |
| 152 | ·--·used·0.1 | 152 | ·--·used·0.131657s·(cpu);·0.0892685s·(thread);·0s·(gc) |
| 153 | o13·=·--·rational·map·-- | 153 | o13·=·--·rational·map·-- |
| 154 | ·····················ZZ | 154 | ·····················ZZ |
| 155 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 155 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 156 | ···················300007··0···1···2···3···4···5···6 | 156 | ···················300007··0···1···2···3···4···5···6 |
| 157 | ···································ZZ | 157 | ···································ZZ |
| 158 | ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])·defined·by | 158 | ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·])·defined·by |
| Offset 217, 15 lines modified | Offset 217, 15 lines modified | ||
| 217 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t | 217 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t |
| 218 | ··························4·····3·4·5····2·5····3·6····2·4·6 | 218 | ··························4·····3·4·5····2·5····3·6····2·4·6 |
| 219 | ······················} | 219 | ······················} |
| 220 | o13·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) | 220 | o13·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) |
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| Offset 3, 18 lines modified | Offset 3, 18 lines modified | ||
| 3 | i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181); | 3 | i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181); |
| 4 | ················ZZ | 4 | ················ZZ |
| 5 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] | 5 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] |
| 6 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 | 6 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 |
| 7 | i2·:·time·EulerCharacteristic·I | 7 | i2·:·time·EulerCharacteristic·I |
| 8 | ·--·used·0. | 8 | ·--·used·0.261286s·(cpu);·0.158778s·(thread);·0s·(gc) |
| 9 | o2·=·10 | 9 | o2·=·10 |
| 10 | i3·:·time·EulerCharacteristic(I,Certify=>true) | 10 | i3·:·time·EulerCharacteristic(I,Certify=>true) |
| 11 | ·--·used·0.2 | 11 | ·--·used·0.242871s·(cpu);·0.0360588s·(thread);·0s·(gc) |
| 12 | Certify:·output·certified! | 12 | Certify:·output·certified! |
| 13 | o3·=·10 | 13 | o3·=·10 |
| 14 | i4·:· | 14 | i4·:· |
| Offset 8, 15 lines modified | Offset 8, 15 lines modified | ||
| 8 | o3·=·rational·map·defined·by·forms·of·degree·2 | 8 | o3·=·rational·map·defined·by·forms·of·degree·2 |
| 9 | ·····source·variety:·PP^5 | 9 | ·····source·variety:·PP^5 |
| 10 | ·····target·variety:·PP^5 | 10 | ·····target·variety:·PP^5 |
| 11 | ·····coefficient·ring:·QQ | 11 | ·····coefficient·ring:·QQ |
| 12 | i4·:·time·phi!·; | 12 | i4·:·time·phi!·; |
| 13 | ·--·used·0. | 13 | ·--·used·0.36002s·(cpu);·0.0853657s·(thread);·0s·(gc) |
| 14 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2)) | 14 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2)) |
| 15 | i5·:·describe·phi | 15 | i5·:·describe·phi |
| 16 | o5·=·rational·map·defined·by·forms·of·degree·2 | 16 | o5·=·rational·map·defined·by·forms·of·degree·2 |
| 17 | ·····source·variety:·PP^5 | 17 | ·····source·variety:·PP^5 |
| Offset 37, 15 lines modified | Offset 37, 15 lines modified | ||
| 37 | o8·=·rational·map·defined·by·forms·of·degree·2 | 37 | o8·=·rational·map·defined·by·forms·of·degree·2 |
| 38 | ·····source·variety:·PP^4 | 38 | ·····source·variety:·PP^4 |
| 39 | ·····target·variety:·PP^5 | 39 | ·····target·variety:·PP^5 |
| 40 | ·····coefficient·ring:·QQ | 40 | ·····coefficient·ring:·QQ |
| 41 | i9·:·time·phi!·; | 41 | i9·:·time·phi!·; |
| 42 | ·--·used·0.2 | 42 | ·--·used·0.24123s·(cpu);·0.0501771s·(thread);·0s·(gc) |
| 43 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5) | 43 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5) |
| 44 | i10·:·describe·phi | 44 | i10·:·describe·phi |
| 45 | o10·=·rational·map·defined·by·forms·of·degree·2 | 45 | o10·=·rational·map·defined·by·forms·of·degree·2 |
| 46 | ······source·variety:·PP^4 | 46 | ······source·variety:·PP^4 |
| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | ·····-·a*c·+·e·········-·b*c·+·f | 67 | ·····-·a*c·+·e·········-·b*c·+·f |
| 68 | ·····----------*v,·x·+·----------*v) | 68 | ·····----------*v,·x·+·----------*v) |
| 69 | ······d*e·-·a*f·········d*e·-·a*f | 69 | ······d*e·-·a*f·········d*e·-·a*f |
| 70 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] | 70 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] |
| 71 | i6·:·time·phi^**·q | 71 | i6·:·time·phi^**·q |
| 72 | ·--·used·0. | 72 | ·--·used·0.221078s·(cpu);·0.166008s·(thread);·0s·(gc) |
| 73 | ················-e········-d········-c········-b········-a | 73 | ················-e········-d········-c········-b········-a |
| 74 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) | 74 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) |
| 75 | ·················f·········f·········f·········f·········f | 75 | ·················f·········f·········f·········f·········f |
| 76 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] | 76 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] |
| Offset 47, 49 lines modified | Offset 47, 49 lines modified | ||
| 47 | ··········································································P7 | 47 | ··········································································P7 |
| 48 | o3·:·Ideal·of·------------------------------------------------------------------------------------------------------------------------- | 48 | o3·:·Ideal·of·------------------------------------------------------------------------------------------------------------------------- |
| 49 | ···············2·2················2·2········································2·2····················································2·2 | 49 | ···············2·2················2·2········································2·2····················································2·2 |
| 50 | ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x | 50 | ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x |
| 51 | ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7 | 51 | ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7 |
| 52 | i4·:·time·SegreClass·X | 52 | i4·:·time·SegreClass·X |
| 53 | ·--·used·0. | 53 | ·--·used·0.499862s·(cpu);·0.414248s·(thread);·0s·(gc) |
| 54 | ··········7········6·······5·······4······3 | 54 | ··········7········6·······5·······4······3 |
| 55 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H | 55 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 56 | ·····ZZ[H] | 56 | ·····ZZ[H] |
| 57 | o4·:·----- | 57 | o4·:·----- |
| 58 | ········8 | 58 | ········8 |
| 59 | ·······H | 59 | ·······H |
| 60 | i5·:·time·SegreClass·lift(X,P7) | 60 | i5·:·time·SegreClass·lift(X,P7) |
| 61 | ·--·used·0.2 | 61 | ·--·used·0.28225s·(cpu);·0.237108s·(thread);·0s·(gc) |
| 62 | ··········7········6·······5······4······3 | 62 | ··········7········6·······5······4······3 |
| 63 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H | 63 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 64 | ·····ZZ[H] | 64 | ·····ZZ[H] |
| 65 | o5·:·----- | 65 | o5·:·----- |
| 66 | ········8 | 66 | ········8 |
| 67 | ·······H | 67 | ·······H |
| 68 | i6·:·time·SegreClass(X,Certify=>true) | 68 | i6·:·time·SegreClass(X,Certify=>true) |
| 69 | ·--·used·0.2 | 69 | ·--·used·0.228484s·(cpu);·0.0406714s·(thread);·0s·(gc) |
| 70 | Certify:·output·certified! | 70 | Certify:·output·certified! |
| 71 | ··········7········6·······5·······4······3 | 71 | ··········7········6·······5·······4······3 |
| 72 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H | 72 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 73 | ·····ZZ[H] | 73 | ·····ZZ[H] |
| 74 | o6·:·----- | 74 | o6·:·----- |
| 75 | ········8 | 75 | ········8 |
| 76 | ·······H | 76 | ·······H |
| 77 | i7·:·time·SegreClass(lift(X,P7),Certify=>true) | 77 | i7·:·time·SegreClass(lift(X,P7),Certify=>true) |
| 78 | ·--·used·0. | 78 | ·--·used·0.400211s·(cpu);·0.150632s·(thread);·0s·(gc) |
| 79 | Certify:·output·certified! | 79 | Certify:·output·certified! |
| 80 | ··········7········6·······5······4······3 | 80 | ··········7········6·······5······4······3 |
| 81 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H | 81 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 82 | ·····ZZ[H] | 82 | ·····ZZ[H] |
| 83 | o7·:·----- | 83 | o7·:·----- |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | ·······ZZ | 105 | ·······ZZ |
| 106 | o9·=·------[x·..x·] | 106 | o9·=·------[x·..x·] |
| 107 | ·····100003··0···6 | 107 | ·····100003··0···6 |
| 108 | o9·:·PolynomialRing | 108 | o9·:·PolynomialRing |
| 109 | i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2) | 109 | i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2) |
| 110 | ·--·used·0.0 | 110 | ·--·used·0.0642405s·(cpu);·0.064913s·(thread);·0s·(gc) |
| 111 | ························································ZZ | 111 | ························································ZZ |
| 112 | ······················································------[y·..y·] | 112 | ······················································------[y·..y·] |
| 113 | ······················································100003··0···9················································ZZ··············2······························2 | 113 | ······················································100003··0···9················································ZZ··············2······························2 |
| 114 | o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·}) | 114 | o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·}) |
| 115 | ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9 | 115 | ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9 |
| 116 | ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 | 116 | ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 |
| Offset 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ·························································------[y·..y·] | 122 | ·························································------[y·..y·] |
| 123 | ·························································100003··0···9···················································ZZ | 123 | ·························································100003··0···9···················································ZZ |
| 124 | o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·] | 124 | o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·] |
| 125 | ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6 | 125 | ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6 |
| 126 | ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 | 126 | ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 |
| 127 | i11·:·time·SegreClass·phi | 127 | i11·:·time·SegreClass·phi |
| 128 | ·--·used·0. | 128 | ·--·used·0.331994s·(cpu);·0.217052s·(thread);·0s·(gc) |
| 129 | ·········9······8······7······6·····5 | 129 | ·········9······8······7······6·····5 |
| 130 | o11·=·23H··-·42H··+·36H··-·22H··+·9H | 130 | o11·=·23H··-·42H··+·36H··-·22H··+·9H |
| 131 | ······ZZ[H] | 131 | ······ZZ[H] |
| 132 | o11·:·----- | 132 | o11·:·----- |
| 133 | ········10 | 133 | ········10 |
| Offset 150, 27 lines modified | Offset 150, 27 lines modified | ||
| 150 | ··························································100003··0···9 | 150 | ··························································100003··0···9 |
| 151 | o12·:·Ideal·of·---------------------------------------------------------------------------------------------------- | 151 | o12·:·Ideal·of·---------------------------------------------------------------------------------------------------- |
| 152 | ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) | 152 | ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) |
| 153 | ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 | 153 | ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 |
| 154 | i13·:·--·Segre·class·of·B·in·G(1,4) | 154 | i13·:·--·Segre·class·of·B·in·G(1,4) |
| 155 | ······time·SegreClass·B | 155 | ······time·SegreClass·B |
| 156 | ·--·used·0.2 | 156 | ·--·used·0.281258s·(cpu);·0.22194s·(thread);·0s·(gc) |
| 157 | ·········9······8······7······6·····5 | 157 | ·········9······8······7······6·····5 |
| 158 | o13·=·23H··-·42H··+·36H··-·22H··+·9H | 158 | o13·=·23H··-·42H··+·36H··-·22H··+·9H |
| 159 | ······ZZ[H] | 159 | ······ZZ[H] |
| 160 | o13·:·----- | 160 | o13·:·----- |
| 161 | ········10 | 161 | ········10 |
| 162 | ·······H | 162 | ·······H |
| 163 | i14·:·--·Segre·class·of·B·in·P^9 | 163 | i14·:·--·Segre·class·of·B·in·P^9 |
| 164 | ······time·SegreClass·lift(B,ambient·ring·B) | 164 | ······time·SegreClass·lift(B,ambient·ring·B) |
| 165 | ·--·used·0. | 165 | ·--·used·0.918915s·(cpu);·0.732797s·(thread);·0s·(gc) |
| 166 | ···········9·······8·······7······6·····5 | 166 | ···········9·······8·······7······6·····5 |
| 167 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H | 167 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H |
| 168 | ······ZZ[H] | 168 | ······ZZ[H] |
| 169 | o14·:·----- | 169 | o14·:·----- |
| 170 | ········10 | 170 | ········10 |
| Offset 17, 32 lines modified | Offset 17, 32 lines modified | ||
| 17 | o3·=·QQ[u·..u·] | 17 | o3·=·QQ[u·..u·] |
| 18 | ·········0···5 | 18 | ·········0···5 |
| 19 | o3·:·PolynomialRing | 19 | o3·:·PolynomialRing |
| 20 | i4·:·time·psi·=·abstractRationalMap(P4,P5,f) | 20 | i4·:·time·psi·=·abstractRationalMap(P4,P5,f) |
| 21 | ·--·used·0.00 | 21 | ·--·used·0.00322296s·(cpu);·0.000310733s·(thread);·0s·(gc) |
| 22 | o4·=·--·rational·map·-- | 22 | o4·=·--·rational·map·-- |
| 23 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 23 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 24 | ······················0···1···2···3···4 | 24 | ······················0···1···2···3···4 |
| 25 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 25 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 26 | ······················0···1···2···3···4···5 | 26 | ······················0···1···2···3···4···5 |
| 27 | ·····defining·forms:·given·by·a·function | 27 | ·····defining·forms:·given·by·a·function |
| 28 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5) | 28 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5) |
| 29 | i5·:·time·projectiveDegrees(psi,3) | 29 | i5·:·time·projectiveDegrees(psi,3) |
| 30 | ·--·used·0.1 | 30 | ·--·used·0.191268s·(cpu);·0.142661s·(thread);·0s·(gc) |
| 31 | o5·=·2 | 31 | o5·=·2 |
| 32 | i6·:·time·rationalMap·psi | 32 | i6·:·time·rationalMap·psi |
| 33 | ·--·used·0. | 33 | ·--·used·0.341785s·(cpu);·0.299419s·(thread);·0s·(gc) |
| 34 | o6·=·--·rational·map·-- | 34 | o6·=·--·rational·map·-- |
| 35 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 35 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 36 | ······················0···1···2···3···4 | 36 | ······················0···1···2···3···4 |
| 37 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 37 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 38 | ······················0···1···2···3···4···5 | 38 | ······················0···1···2···3···4···5 |
| 39 | ·····defining·forms:·{ | 39 | ·····defining·forms:·{ |
| Offset 113, 48 lines modified | Offset 113, 48 lines modified | ||
| 113 | ················1····0·2·····1·2····0·3·····2····1·3 | 113 | ················1····0·2·····1·2····0·3·····2····1·3 |
| 114 | ·················ZZ | 114 | ·················ZZ |
| 115 | o13·:·Ideal·of·-----[x·..x·] | 115 | o13·:·Ideal·of·-----[x·..x·] |
| 116 | ···············65521··0···3 | 116 | ···············65521··0···3 |
| 117 | i14·:·time·T·=·abstractRationalMap(I,"OADP") | 117 | i14·:·time·T·=·abstractRationalMap(I,"OADP") |
| 118 | ·--·used·0.03 | 118 | ·--·used·0.0360003s·(cpu);·0.0344904s·(thread);·0s·(gc) |
| 119 | o14·=·--·rational·map·-- | 119 | o14·=·--·rational·map·-- |
| 120 | ·····················ZZ | 120 | ·····················ZZ |
| 121 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 121 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 122 | ···················65521··0···1···2···3 | 122 | ···················65521··0···1···2···3 |
| 123 | ·····················ZZ | 123 | ·····················ZZ |
| 124 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 124 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| 125 | ···················65521··0···1···2···3 | 125 | ···················65521··0···1···2···3 |
| 126 | ······defining·forms:·given·by·a·function | 126 | ······defining·forms:·given·by·a·function |
| 127 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) | 127 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) |
| 128 | i15·:·time·projectiveDegrees(T,2) | 128 | i15·:·time·projectiveDegrees(T,2) |
| 129 | ·--·used·2. | 129 | ·--·used·2.63059s·(cpu);·1.66126s·(thread);·0s·(gc) |
| 130 | o15·=·3 | 130 | o15·=·3 |
| 131 | i16·:·time·T2·=·T·*·T | 131 | i16·:·time·T2·=·T·*·T |
| 132 | ·--·used·0.0001 | 132 | ·--·used·0.00014931s·(cpu);·1.9707e-05s·(thread);·0s·(gc) |
| 133 | o16·=·--·rational·map·-- | 133 | o16·=·--·rational·map·-- |
| 134 | ·····················ZZ | 134 | ·····················ZZ |
| 135 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 135 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 136 | ···················65521··0···1···2···3 | 136 | ···················65521··0···1···2···3 |
| 137 | ·····················ZZ | 137 | ·····················ZZ |
| 138 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 138 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| 139 | ···················65521··0···1···2···3 | 139 | ···················65521··0···1···2···3 |
| 140 | ······defining·forms:·given·by·a·function | 140 | ······defining·forms:·given·by·a·function |
| 141 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) | 141 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) |
| 142 | i17·:·time·projectiveDegrees(T2,2) | 142 | i17·:·time·projectiveDegrees(T2,2) |
| 143 | ·--·used· | 143 | ·--·used·4.00796s·(cpu);·2.53047s·(thread);·0s·(gc) |
| 144 | o17·=·1 | 144 | o17·=·1 |
| 145 | i18·:·p·=·apply(3,i->random(ZZ/65521))|{1} | 145 | i18·:·p·=·apply(3,i->random(ZZ/65521))|{1} |
| 146 | o18·=·{28963,·31975,·-30172,·1} | 146 | o18·=·{28963,·31975,·-30172,·1} |
| Offset 169, 15 lines modified | Offset 169, 15 lines modified | ||
| 169 | i20·:·T·q | 169 | i20·:·T·q |
| 170 | o20·=·{28963,·31975,·-30172,·1} | 170 | o20·=·{28963,·31975,·-30172,·1} |
| 171 | o20·:·List | 171 | o20·:·List |
| 172 | i21·:·time·f·=·rationalMap·T | 172 | i21·:·time·f·=·rationalMap·T |
| 173 | ·--·used· | 173 | ·--·used·3.53929s·(cpu);·2.34378s·(thread);·0s·(gc) |
| 174 | o21·=·--·rational·map·-- | 174 | o21·=·--·rational·map·-- |
| 175 | ·····················ZZ | 175 | ·····················ZZ |
| 176 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 176 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 177 | ···················65521··0···1···2···3 | 177 | ···················65521··0···1···2···3 |
| 178 | ·····················ZZ | 178 | ·····················ZZ |
| 179 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 179 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| Offset 44, 15 lines modified | Offset 44, 15 lines modified | ||
| 44 | ······················x·x··-·x·x | 44 | ······················x·x··-·x·x |
| 45 | ·······················1·2····0·4 | 45 | ·······················1·2····0·4 |
| 46 | ·····················} | 46 | ·····················} |
| 47 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8) | 47 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8) |
| 48 | i3·:·time·psi·=·approximateInverseMap·phi | 48 | i3·:·time·psi·=·approximateInverseMap·phi |
| 49 | ·--·used·0. | 49 | ·--·used·0.241364s·(cpu);·0.204377s·(thread);·0s·(gc) |
| 50 | --·approximateInverseMap:·step·1·of·10 | 50 | --·approximateInverseMap:·step·1·of·10 |
| 51 | --·approximateInverseMap:·step·2·of·10 | 51 | --·approximateInverseMap:·step·2·of·10 |
| 52 | --·approximateInverseMap:·step·3·of·10 | 52 | --·approximateInverseMap:·step·3·of·10 |
| 53 | --·approximateInverseMap:·step·4·of·10 | 53 | --·approximateInverseMap:·step·4·of·10 |
| 54 | --·approximateInverseMap:·step·5·of·10 | 54 | --·approximateInverseMap:·step·5·of·10 |
| 55 | --·approximateInverseMap:·step·6·of·10 | 55 | --·approximateInverseMap:·step·6·of·10 |
| 56 | --·approximateInverseMap:·step·7·of·10 | 56 | --·approximateInverseMap:·step·7·of·10 |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | ·····················} | 106 | ·····················} |
| 107 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) | 107 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) |
| 108 | i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1) | 108 | i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1) |
| 109 | i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); | 109 | i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); |
| 110 | ·--·used·0.1 | 110 | ·--·used·0.197017s·(cpu);·0.150704s·(thread);·0s·(gc) |
| 111 | --·approximateInverseMap:·step·1·of·3 | 111 | --·approximateInverseMap:·step·1·of·3 |
| 112 | --·approximateInverseMap:·step·2·of·3 | 112 | --·approximateInverseMap:·step·2·of·3 |
| 113 | --·approximateInverseMap:·step·3·of·3 | 113 | --·approximateInverseMap:·step·3·of·3 |
| 114 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) | 114 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) |
| 115 | i6·:·assert(psi·==·psi') | 115 | i6·:·assert(psi·==·psi') |
| Offset 189, 15 lines modified | Offset 189, 15 lines modified | ||
| 189 | ·······················0······1·4······0·5······1·5·····2·5······3·5······4·5······5······0·6······1·6······2·6······4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8······5·8······6·8·····7·8 | 189 | ·······················0······1·4······0·5······1·5·····2·5······3·5······4·5······5······0·6······1·6······2·6······4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8······5·8······6·8·····7·8 |
| 190 | ·····················} | 190 | ·····················} |
| 191 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11) | 191 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11) |
| 192 | i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time· | 192 | i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time· |
| 193 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) | 193 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) |
| 194 | ·--·used·1. | 194 | ·--·used·1.93705s·(cpu);·1.66113s·(thread);·0s·(gc) |
| 195 | --·approximateInverseMap:·step·1·of·3 | 195 | --·approximateInverseMap:·step·1·of·3 |
| 196 | --·approximateInverseMap:·step·2·of·3 | 196 | --·approximateInverseMap:·step·2·of·3 |
| 197 | --·approximateInverseMap:·step·3·of·3 | 197 | --·approximateInverseMap:·step·3·of·3 |
| 198 | o8·=·--·rational·map·-- | 198 | o8·=·--·rational·map·-- |
| 199 | ································ZZ | 199 | ································ZZ |
| 200 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by | 200 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by |
| Offset 254, 15 lines modified | Offset 254, 15 lines modified | ||
| 254 | i9·:·--·but... | 254 | i9·:·--·but... |
| 255 | ·····phi·*·psi·==·1 | 255 | ·····phi·*·psi·==·1 |
| 256 | o9·=·false | 256 | o9·=·false |
| 257 | i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify | 257 | i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify |
| 258 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) | 258 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) |
| 259 | ·--·used·2. | 259 | ·--·used·2.89006s·(cpu);·2.51569s·(thread);·0s·(gc) |
| 260 | --·approximateInverseMap:·step·1·of·3 | 260 | --·approximateInverseMap:·step·1·of·3 |
| 261 | --·approximateInverseMap:·step·2·of·3 | 261 | --·approximateInverseMap:·step·2·of·3 |
| 262 | --·approximateInverseMap:·step·3·of·3 | 262 | --·approximateInverseMap:·step·3·of·3 |
| 263 | Certify:·output·certified! | 263 | Certify:·output·certified! |
| 264 | o10·=·--·rational·map·-- | 264 | o10·=·--·rational·map·-- |
| 265 | ·································ZZ | 265 | ·································ZZ |
| Offset 9, 27 lines modified | Offset 9, 27 lines modified | ||
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| 9 | 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| 10 | o4·=·map·(ringP8,·ringP14,·{-·95x··+·181x·x··+·1028x··-·1384x·x··-·1455x·x··+·559x··-·502x·x··+·1264x·x··-·162x·x··+·1209x··-·180x·x··-·504x·x··-·1168x·x··-·676x·x··+·501x··+·73x·x··+·1263x·x··+·1035x·x··+·844x·x··+·1593x·x··+·785x··+·982x·x··-·412x·x··+·1335x·x··+·1136x·x··+·826x·x··+·1078x·x··+·1158x··+·335x·x··-·982x·x··-·1479x·x··-·15x·x··+·1363x·x··+·1397x·x··-·575x·x··-·71x··+·1255x·x··-·1138x·x··-·1590x·x··+·604x·x··+·1182x·x··-·63x·x··-·1382x·x··-·1255x·x··-·613x·,·-·1444x··+·575x·x··+·767x··-·1495x·x··+·1631x·x··-·217x··-·294x·x··-·1511x·x··-·504x·x··-·1284x··-·1459x·x··+·152x·x··+·141x·x··-·10x·x··-·95x··+·1056x·x··+·654x·x··+·1397x·x··-·930x·x··+·578x·x··-·696x··+·759x·x··+·733x·x··+·505x·x··-·609x·x··+·526x·x··-·659x·x··+·846x··+·1253x·x··-·1519x·x··+·635x·x··+·576x·x··+·54x·x··-·1261x·x··-·822x·x··-·257x··-·986x·x··+·356x·x··-·1488x·x··-·1561x·x··-·850x·x··-·85x·x··-·1350x·x··-·783x·x··-·1335x·,·-·871x··+·1006x·x··-·1399x··-·1636x·x··-·699x·x··-·769x··-·307x·x··-·1645x·x··-·502x·x··-·719x··+·1405x·x··+·870x·x··-·1133x·x··+·425x·x··-·1203x··-·1601x·x··+·117x·x··-·382x·x··+·318x·x··-·117x·x··-·560x··+·1135x·x··+·1468x·x··+·869x·x··-·943x·x··-·335x·x··-·1218x·x··+·201x··-·11x·x··+·540x·x··-·710x·x··-·489x·x··+·1605x·x··+·1663x·x··-·423x·x··+·1246x··+·97x·x··-·644x·x··+·1655x·x··+·1219x·x··+·1476x·x··+·1355x·x··+·1594x·x··+·893x·x··+·1150x·,·-·143x··+·1240x·x··-·1042x··+·1649x·x··+·1024x·x··+·794x··+·1442x·x··-·1263x·x··+·537x·x··-·82x··-·734x·x··-·1569x·x··-·798x·x··-·366x·x··+·1289x··-·569x·x··-·254x·x··+·237x·x··-·1234x·x··-·807x·x··+·264x··-·202x·x··-·616x·x··+·44x·x··+·1465x·x··+·685x·x··+·1630x·x··-·406x··-·123x·x··-·4x·x··+·1583x·x··+·1235x·x··+·162x·x··+·1034x·x··-·1035x·x··+·737x··+·660x·x··+·1459x·x··-·359x·x··-·1291x·x··+·1638x·x··-·325x·x··-·631x·x··+·73x·x··-·1471x·,·-·1340x··+·31x·x··-·994x··-·880x·x··-·89x·x··+·574x··+·760x·x··-·1054x·x··+·772x·x··-·239x··-·443x·x··+·1240x·x··+·637x·x··-·1423x·x··+·320x··-·1363x·x··-·1139x·x··-·158x·x··-·325x·x··-·1578x·x··+·32x··+·695x·x··+·305x·x··+·1012x·x··+·1492x·x··+·1290x·x··+·1579x·x··-·342x··-·83x·x··-·104x·x··+·998x·x··-·92x·x··+·1554x·x··+·201x·x··-·237x·x··+·160x··-·228x·x··-·543x·x··-·1147x·x··-·376x·x··+·1313x·x··+·603x·x··+·106x·x··-·1361x·x··+·699x·,·-·228x··-·1510x·x··+·277x··-·4x·x··-·22x·x··-·1526x··+·234x·x··+·969x·x··+·1253x·x··-·1426x··-·1474x·x··+·947x·x··+·194x·x··-·316x·x··-·988x··-·1211x·x··+·1087x·x··+·536x·x··-·491x·x··+·870x·x··-·659x··+·1490x·x··-·469x·x··+·1190x·x··+·807x·x··+·650x·x··+·448x·x··-·1353x··-·218x·x··+·759x·x··-·253x·x··+·830x·x··-·1080x·x··-·143x·x··-·1313x·x··-·374x··-·180x·x··+·741x·x··+·742x·x··-·1254x·x··+·458x·x··-·345x·x··+·597x·x··+·1567x·x··-·31x·,·1120x··+·709x·x··-·1538x··-·1048x·x··-·162x·x··-·1518x··-·73x·x··+·380x·x··+·533x·x··-·286x··+·1374x·x··-·74x·x··-·22x·x··+·1535x·x··-·1071x··-·839x·x··-·560x·x··+·928x·x··+·335x·x··-·1008x·x··+·810x··-·448x·x··-·357x·x··-·107x·x··+·40x·x··+·784x·x··-·1423x·x··+·1276x··+·147x·x··+·443x·x··-·598x·x··-·1077x·x··-·1214x·x··+·322x·x··-·1408x·x··+·72x··-·63x·x··-·1513x·x··-·791x·x··+·11x·x··+·77x·x··+·836x·x··-·1100x·x··+·1637x·x··-·788x·,·1331x··+·318x·x··-·704x··+·51x·x··+·275x·x··+·1149x··+·1526x·x··+·768x·x··+·414x·x··-·782x··-·262x·x··+·686x·x··-·380x·x··+·1377x·x··+·1077x··+·1650x·x··-·1129x·x··-·508x·x··+·846x·x··+·1513x·x··+·460x··-·1626x·x··-·1024x·x··+·862x·x··+·1352x·x··-·188x·x··-·1382x·x··-·650x··+·55x·x··-·326x·x··+·1037x·x··+·705x·x··-·667x·x··+·1483x·x··+·1661x·x··-·1652x··-·1052x·x··-·692x·x··-·542x·x··+·162x·x··+·582x·x··-·1369x·x··+·934x·x··+·1392x·x··+·1227x·,·-·346x··+·1408x·x··-·1225x··-·1536x·x··-·1028x·x··-·985x··-·210x·x··-·1312x·x··+·915x·x··+·1633x··-·202x·x··-·1636x·x··-·1653x·x··-·480x·x··-·1260x··-·813x·x··-·1623x·x··-·1429x·x··+·1094x·x··-·747x·x··+·955x··+·898x·x··-·795x·x··-·35x·x··-·566x·x··+·1631x·x··-·324x·x··+·926x··-·132x·x··-·9x·x··-·1290x·x··-·543x·x··+·902x·x··+·735x·x··-·342x·x··-·400x··+·900x·x··-·463x·x··+·694x·x··-·1262x·x··-·1449x·x··-·448x·x··-·1402x·x··-·731x·x··-·996x·,·301x··+·166x·x··-·955x··-·739x·x··-·1199x·x··-·319x··+·1047x·x··-·532x·x··+·902x·x··+·1195x··-·663x·x··+·1215x·x··-·534x·x··-·332x·x··-·973x··+·772x·x··-·308x·x··+·315x·x··-·454x·x··-·483x·x··-·239x··-·1313x·x··-·419x·x··-·1340x·x··-·1388x·x··-·1340x·x··-·1665x·x··-·333x··-·465x·x··-·1084x·x··+·676x·x··-·1612x·x··-·288x·x··+·11x·x··-·1170x·x··-·189x··+·498x·x··-·889x·x··+·693x·x··+·1460x·x··-·473x·x··-·414x·x··-·122x·x··-·1659x·x··-·1421x·,·14x··-·1049x·x··+·1506x··+·1235x·x··+·642x·x··-·1034x··+·460x·x··+·150x·x··+·760x·x··-·1246x··-·1407x·x··+·1570x·x··+·1403x·x··-·1610x·x··-·431x··+·574x·x··+·893x·x··-·657x·x··+·417x·x··+·1362x·x··+·224x··+·268x·x··+·1097x·x··+·1132x·x··+·148x·x··+·1331x·x··-·77x·x··-·756x··+·228x·x··+·136x·x··-·1484x·x··-·1478x·x··-·13x·x··+·1620x·x··-·701x·x··-·769x··-·760x·x··-·492x·x··-·1077x·x··-·1249x·x··-·834x·x··-·395x·x··-·1358x·x··-·988x·x··+·113x·,·-·1634x··-·13x·x··+·805x··-·21x·x··-·1655x·x··+·1479x··-·1510x·x··-·646x·x··+·225x·x··-·1411x··+·1227x·x··-·1108x·x··+·1291x·x··-·59x·x··-·142x··+·586x·x··-·676x·x··+·655x·x··-·1476x·x··+·453x·x··-·1076x··-·1152x·x··+·1373x·x··-·1191x·x··-·416x·x··+·699x·x··+·317x·x··+·825x··-·1560x·x··-·488x·x··-·1035x·x··-·1561x·x··-·644x·x··-·1178x·x··-·1320x·x··+·158x··+·889x·x··+·1444x·x··-·1486x·x··-·1211x·x··+·1269x·x··-·1228x·x··+·568x·x··+·1591x·x··+·1207x·,·105x··-·538x·x··-·1222x··-·277x·x··+·716x·x··-·1067x··-·428x·x··+·154x·x··-·469x·x··+·77x··+·538x·x··-·179x·x··+·921x·x··-·223x·x··+·1093x··-·262x·x··+·1299x·x··+·631x·x··+·1486x·x··-·1280x·x··-·121x··-·50x·x··-·978x·x··-·694x·x··-·531x·x··+·505x·x··+·1412x·x··-·1061x··+·1202x·x··+·448x·x··-·187x·x··+·1276x·x··-·121x·x··+·1361x·x··+·697x·x··+·682x··+·1592x·x··+·705x·x··-·227x·x··-·7x·x··-·1423x·x··-·1446x·x··-·1578x·x··+·1511x·x··+·917x·,·1270x··-·391x·x··-·1116x··-·287x·x··+·653x·x··+·1643x··+·1623x·x··+·514x·x··-·14x·x··-·90x··+·1232x·x··-·1434x·x··+·1296x·x··+·1522x·x··+·136x··-·623x·x··-·607x·x··+·18x·x··+·896x·x··-·29x·x··+·1059x··-·1053x·x··+·1643x·x··+·1652x·x··-·1190x·x··-·1073x·x··+·1470x·x··-·944x··-·93x·x··-·187x·x··-·994x·x··-·1415x·x··-·229x·x··-·796x·x··+·1642x·x··+·1600x··-·344x·x··+·905x·x··+·1032x·x··-·538x·x··-·891x·x··+·1243x·x··+·1290x·x··+·490x·x··-·1148x·,·1613x··+·175x·x··-·1346x··-·1000x·x··-·1217x·x··-·729x··-·1296x·x··+·1456x·x··+·745x·x··+·539x··+·525x·x··-·811x·x··+·753x·x··+·1362x·x··+·1629x··-·840x·x··+·513x·x··+·429x·x··+·842x·x··+·1414x·x··-·308x··+·1415x·x··-·1461x·x··-·1135x·x··+·701x·x··+·766x·x··+·785x·x··+·1503x··+·147x·x··+·929x·x··-·1220x·x··-·853x·x··+·493x·x··+·226x·x··+·1416x·x··+·280x··-·7x·x··+·1632x·x··+·520x·x··+·1259x·x··+·157x·x··+·1596x·x··+·655x·x··-·42x·x··-·586x·}) | 10 | o4·=·map·(ringP8,·ringP14,·{-·95x··+·181x·x··+·1028x··-·1384x·x··-·1455x·x··+·559x··-·502x·x··+·1264x·x··-·162x·x··+·1209x··-·180x·x··-·504x·x··-·1168x·x··-·676x·x··+·501x··+·73x·x··+·1263x·x··+·1035x·x··+·844x·x··+·1593x·x··+·785x··+·982x·x··-·412x·x··+·1335x·x··+·1136x·x··+·826x·x··+·1078x·x··+·1158x··+·335x·x··-·982x·x··-·1479x·x··-·15x·x··+·1363x·x··+·1397x·x··-·575x·x··-·71x··+·1255x·x··-·1138x·x··-·1590x·x··+·604x·x··+·1182x·x··-·63x·x··-·1382x·x··-·1255x·x··-·613x·,·-·1444x··+·575x·x··+·767x··-·1495x·x··+·1631x·x··-·217x··-·294x·x··-·1511x·x··-·504x·x··-·1284x··-·1459x·x··+·152x·x··+·141x·x··-·10x·x··-·95x··+·1056x·x··+·654x·x··+·1397x·x··-·930x·x··+·578x·x··-·696x··+·759x·x··+·733x·x··+·505x·x··-·609x·x··+·526x·x··-·659x·x··+·846x··+·1253x·x··-·1519x·x··+·635x·x··+·576x·x··+·54x·x··-·1261x·x··-·822x·x··-·257x··-·986x·x··+·356x·x··-·1488x·x··-·1561x·x··-·850x·x··-·85x·x··-·1350x·x··-·783x·x··-·1335x·,·-·871x··+·1006x·x··-·1399x··-·1636x·x··-·699x·x··-·769x··-·307x·x··-·1645x·x··-·502x·x··-·719x··+·1405x·x··+·870x·x··-·1133x·x··+·425x·x··-·1203x··-·1601x·x··+·117x·x··-·382x·x··+·318x·x··-·117x·x··-·560x··+·1135x·x··+·1468x·x··+·869x·x··-·943x·x··-·335x·x··-·1218x·x··+·201x··-·11x·x··+·540x·x··-·710x·x··-·489x·x··+·1605x·x··+·1663x·x··-·423x·x··+·1246x··+·97x·x··-·644x·x··+·1655x·x··+·1219x·x··+·1476x·x··+·1355x·x··+·1594x·x··+·893x·x··+·1150x·,·-·143x··+·1240x·x··-·1042x··+·1649x·x··+·1024x·x··+·794x··+·1442x·x··-·1263x·x··+·537x·x··-·82x··-·734x·x··-·1569x·x··-·798x·x··-·366x·x··+·1289x··-·569x·x··-·254x·x··+·237x·x··-·1234x·x··-·807x·x··+·264x··-·202x·x··-·616x·x··+·44x·x··+·1465x·x··+·685x·x··+·1630x·x··-·406x··-·123x·x··-·4x·x··+·1583x·x··+·1235x·x··+·162x·x··+·1034x·x··-·1035x·x··+·737x··+·660x·x··+·1459x·x··-·359x·x··-·1291x·x··+·1638x·x··-·325x·x··-·631x·x··+·73x·x··-·1471x·,·-·1340x··+·31x·x··-·994x··-·880x·x··-·89x·x··+·574x··+·760x·x··-·1054x·x··+·772x·x··-·239x··-·443x·x··+·1240x·x··+·637x·x··-·1423x·x··+·320x··-·1363x·x··-·1139x·x··-·158x·x··-·325x·x··-·1578x·x··+·32x··+·695x·x··+·305x·x··+·1012x·x··+·1492x·x··+·1290x·x··+·1579x·x··-·342x··-·83x·x··-·104x·x··+·998x·x··-·92x·x··+·1554x·x··+·201x·x··-·237x·x··+·160x··-·228x·x··-·543x·x··-·1147x·x··-·376x·x··+·1313x·x··+·603x·x··+·106x·x··-·1361x·x··+·699x·,·-·228x··-·1510x·x··+·277x··-·4x·x··-·22x·x··-·1526x··+·234x·x··+·969x·x··+·1253x·x··-·1426x··-·1474x·x··+·947x·x··+·194x·x··-·316x·x··-·988x··-·1211x·x··+·1087x·x··+·536x·x··-·491x·x··+·870x·x··-·659x··+·1490x·x··-·469x·x··+·1190x·x··+·807x·x··+·650x·x··+·448x·x··-·1353x··-·218x·x··+·759x·x··-·253x·x··+·830x·x··-·1080x·x··-·143x·x··-·1313x·x··-·374x··-·180x·x··+·741x·x··+·742x·x··-·1254x·x··+·458x·x··-·345x·x··+·597x·x··+·1567x·x··-·31x·,·1120x··+·709x·x··-·1538x··-·1048x·x··-·162x·x··-·1518x··-·73x·x··+·380x·x··+·533x·x··-·286x··+·1374x·x··-·74x·x··-·22x·x··+·1535x·x··-·1071x··-·839x·x··-·560x·x··+·928x·x··+·335x·x··-·1008x·x··+·810x··-·448x·x··-·357x·x··-·107x·x··+·40x·x··+·784x·x··-·1423x·x··+·1276x··+·147x·x··+·443x·x··-·598x·x··-·1077x·x··-·1214x·x··+·322x·x··-·1408x·x··+·72x··-·63x·x··-·1513x·x··-·791x·x··+·11x·x··+·77x·x··+·836x·x··-·1100x·x··+·1637x·x··-·788x·,·1331x··+·318x·x··-·704x··+·51x·x··+·275x·x··+·1149x··+·1526x·x··+·768x·x··+·414x·x··-·782x··-·262x·x··+·686x·x··-·380x·x··+·1377x·x··+·1077x··+·1650x·x··-·1129x·x··-·508x·x··+·846x·x··+·1513x·x··+·460x··-·1626x·x··-·1024x·x··+·862x·x··+·1352x·x··-·188x·x··-·1382x·x··-·650x··+·55x·x··-·326x·x··+·1037x·x··+·705x·x··-·667x·x··+·1483x·x··+·1661x·x··-·1652x··-·1052x·x··-·692x·x··-·542x·x··+·162x·x··+·582x·x··-·1369x·x··+·934x·x··+·1392x·x··+·1227x·,·-·346x··+·1408x·x··-·1225x··-·1536x·x··-·1028x·x··-·985x··-·210x·x··-·1312x·x··+·915x·x··+·1633x··-·202x·x··-·1636x·x··-·1653x·x··-·480x·x··-·1260x··-·813x·x··-·1623x·x··-·1429x·x··+·1094x·x··-·747x·x··+·955x··+·898x·x··-·795x·x··-·35x·x··-·566x·x··+·1631x·x··-·324x·x··+·926x··-·132x·x··-·9x·x··-·1290x·x··-·543x·x··+·902x·x··+·735x·x··-·342x·x··-·400x··+·900x·x··-·463x·x··+·694x·x··-·1262x·x··-·1449x·x··-·448x·x··-·1402x·x··-·731x·x··-·996x·,·301x··+·166x·x··-·955x··-·739x·x··-·1199x·x··-·319x··+·1047x·x··-·532x·x··+·902x·x··+·1195x··-·663x·x··+·1215x·x··-·534x·x··-·332x·x··-·973x··+·772x·x··-·308x·x··+·315x·x··-·454x·x··-·483x·x··-·239x··-·1313x·x··-·419x·x··-·1340x·x··-·1388x·x··-·1340x·x··-·1665x·x··-·333x··-·465x·x··-·1084x·x··+·676x·x··-·1612x·x··-·288x·x··+·11x·x··-·1170x·x··-·189x··+·498x·x··-·889x·x··+·693x·x··+·1460x·x··-·473x·x··-·414x·x··-·122x·x··-·1659x·x··-·1421x·,·14x··-·1049x·x··+·1506x··+·1235x·x··+·642x·x··-·1034x··+·460x·x··+·150x·x··+·760x·x··-·1246x··-·1407x·x··+·1570x·x··+·1403x·x··-·1610x·x··-·431x··+·574x·x··+·893x·x··-·657x·x··+·417x·x··+·1362x·x··+·224x··+·268x·x··+·1097x·x··+·1132x·x··+·148x·x··+·1331x·x··-·77x·x··-·756x··+·228x·x··+·136x·x··-·1484x·x··-·1478x·x··-·13x·x··+·1620x·x··-·701x·x··-·769x··-·760x·x··-·492x·x··-·1077x·x··-·1249x·x··-·834x·x··-·395x·x··-·1358x·x··-·988x·x··+·113x·,·-·1634x··-·13x·x··+·805x··-·21x·x··-·1655x·x··+·1479x··-·1510x·x··-·646x·x··+·225x·x··-·1411x··+·1227x·x··-·1108x·x··+·1291x·x··-·59x·x··-·142x··+·586x·x··-·676x·x··+·655x·x··-·1476x·x··+·453x·x··-·1076x··-·1152x·x··+·1373x·x··-·1191x·x··-·416x·x··+·699x·x··+·317x·x··+·825x··-·1560x·x··-·488x·x··-·1035x·x··-·1561x·x··-·644x·x··-·1178x·x··-·1320x·x··+·158x··+·889x·x··+·1444x·x··-·1486x·x··-·1211x·x··+·1269x·x··-·1228x·x··+·568x·x··+·1591x·x··+·1207x·,·105x··-·538x·x··-·1222x··-·277x·x··+·716x·x··-·1067x··-·428x·x··+·154x·x··-·469x·x··+·77x··+·538x·x··-·179x·x··+·921x·x··-·223x·x··+·1093x··-·262x·x··+·1299x·x··+·631x·x··+·1486x·x··-·1280x·x··-·121x··-·50x·x··-·978x·x··-·694x·x··-·531x·x··+·505x·x··+·1412x·x··-·1061x··+·1202x·x··+·448x·x··-·187x·x··+·1276x·x··-·121x·x··+·1361x·x··+·697x·x··+·682x··+·1592x·x··+·705x·x··-·227x·x··-·7x·x··-·1423x·x··-·1446x·x··-·1578x·x··+·1511x·x··+·917x·,·1270x··-·391x·x··-·1116x··-·287x·x··+·653x·x··+·1643x··+·1623x·x··+·514x·x··-·14x·x··-·90x··+·1232x·x··-·1434x·x··+·1296x·x··+·1522x·x··+·136x··-·623x·x··-·607x·x··+·18x·x··+·896x·x··-·29x·x··+·1059x··-·1053x·x··+·1643x·x··+·1652x·x··-·1190x·x··-·1073x·x··+·1470x·x··-·944x··-·93x·x··-·187x·x··-·994x·x··-·1415x·x··-·229x·x··-·796x·x··+·1642x·x··+·1600x··-·344x·x··+·905x·x··+·1032x·x··-·538x·x··-·891x·x··+·1243x·x··+·1290x·x··+·490x·x··-·1148x·,·1613x··+·175x·x··-·1346x··-·1000x·x··-·1217x·x··-·729x··-·1296x·x··+·1456x·x··+·745x·x··+·539x··+·525x·x··-·811x·x··+·753x·x··+·1362x·x··+·1629x··-·840x·x··+·513x·x··+·429x·x··+·842x·x··+·1414x·x··-·308x··+·1415x·x··-·1461x·x··-·1135x·x··+·701x·x··+·766x·x··+·785x·x··+·1503x··+·147x·x··+·929x·x··-·1220x·x··-·853x·x··+·493x·x··+·226x·x··+·1416x·x··+·280x··-·7x·x··+·1632x·x··+·520x·x··+·1259x·x··+·157x·x··+·1596x·x··+·655x·x··-·42x·x··-·586x·}) 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| 11 | ·································0·······0·1········1········0·2········1·2·······2·······0·3········1·3·······2·3········3·······0·4·······1·4········2·4·······3·4·······4······0·5········1·5········2·5·······3·5········4·5·······5·······0·6·······1·6········2·6········3·6·······4·6········5·6········6·······0·7·······1·7········2·7······3·7········4·7········5·7·······6·7······7········0·8········1·8········2·8·······3·8········4·8······5·8········6·8········7·8·······8·········0·······0·1·······1········0·2········1·2·······2·······0·3········1·3·······2·3········3········0·4·······1·4·······2·4······3·4······4········0·5·······1·5········2·5·······3·5·······4·5·······5·······0·6·······1·6·······2·6·······3·6·······4·6·······5·6·······6········0·7········1·7·······2·7·······3·7······4·7········5·7·······6·7·······7·······0·8·······1·8········2·8········3·8·······4·8······5·8········6·8·······7·8········8········0········0·1········1········0·2·······1·2·······2·······0·3········1·3·······2·3·······3········0·4·······1·4········2·4·······3·4········4········0·5·······1·5·······2·5·······3·5·······4·5·······5········0·6········1·6·······2·6·······3·6·······4·6········5·6·······6······0·7·······1·7·······2·7·······3·7········4·7········5·7·······6·7········7······0·8·······1·8········2·8········3·8········4·8········5·8········6·8·······7·8········8········0········0·1········1········0·2········1·2·······2········0·3········1·3·······2·3······3·······0·4········1·4·······2·4·······3·4········4·······0·5·······1·5·······2·5········3·5·······4·5·······5·······0·6·······1·6······2·6········3·6·······4·6········5·6·······6·······0·7·····1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8·······2·8········3·8········4·8·······5·8·······6·8······7·8········8·········0······0·1·······1·······0·2······1·2·······2·······0·3········1·3·······2·3·······3·······0·4········1·4·······2·4········3·4·······4········0·5········1·5·······2·5·······3·5········4·5······5·······0·6·······1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7······3·7········4·7·······5·7·······6·7·······7·······0·8·······1·8········2·8·······3·8········4·8·······5·8·······6·8········7·8·······8········0········0·1·······1·····0·2······1·2········2·······0·3·······1·3········2·3········3········0·4·······1·4·······2·4·······3·4·······4········0·5········1·5·······2·5·······3·5·······4·5·······5········0·6·······1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7·······2·7·······3·7········4·7·······5·7········6·7·······7·······0·8·······1·8·······2·8········3·8·······4·8·······5·8·······6·8········7·8······8·······0·······0·1········1········0·2·······1·2········2······0·3·······1·3·······2·3·······3········0·4······1·4······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5·······0·6·······1·6·······2·6······3·6·······4·6········5·6········6·······0·7·······1·7·······2·7········3·7········4·7·······5·7········6·7······7······0·8········1·8·······2·8······3·8······4·8·······5·8········6·8········7·8·······8·······0·······0·1·······1······0·2·······1·2········2········0·3·······1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4········0·5········1·5·······2·5·······3·5········4·5·······5········0·6········1·6·······2·6········3·6·······4·6········5·6·······6······0·7·······1·7········2·7·······3·7·······4·7········5·7········6·7········7········0·8·······1·8·······2·8·······3·8·······4·8········5·8·······6·8········7·8········8········0········0·1········1········0·2········1·2·······2·······0·3········1·3·······2·3········3·······0·4········1·4········2·4·······3·4········4·······0·5········1·5········2·5········3·5·······4·5·······5·······0·6·······1·6······2·6·······3·6········4·6·······5·6·······6·······0·7·····1·7········2·7·······3·7·······4·7·······5·7·······6·7·······7·······0·8·······1·8·······2·8········3·8········4·8·······5·8········6·8·······7·8·······8······0·······0·1·······1·······0·2········1·2·······2········0·3·······1·3·······2·3········3·······0·4········1·4·······2·4·······3·4·······4·······0·5·······1·5·······2·5·······3·5·······4·5·······5········0·6·······1·6········2·6········3·6········4·6········5·6·······6·······0·7········1·7·······2·7········3·7·······4·7······5·7········6·7·······7·······0·8·······1·8·······2·8········3·8·······4·8·······5·8·······6·8········7·8········8·····0········0·1········1········0·2·······1·2········2·······0·3·······1·3·······2·3········3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5·······2·5·······3·5········4·5·······5·······0·6········1·6········2·6·······3·6········4·6······5·6·······6·······0·7·······1·7········2·7········3·7······4·7········5·7·······6·7·······7·······0·8·······1·8········2·8········3·8·······4·8·······5·8········6·8·······7·8·······8·········0······0·1·······1······0·2········1·2········2········0·3·······1·3·······2·3········3········0·4········1·4········2·4······3·4·······4·······0·5·······1·5·······2·5········3·5·······4·5········5········0·6········1·6········2·6·······3·6·······4·6·······5·6·······6········0·7·······1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8········2·8········3·8········4·8········5·8·······6·8········7·8········8······0·······0·1········1·······0·2·······1·2········2·······0·3·······1·3·······2·3······3·······0·4·······1·4·······2·4·······3·4········4·······0·5········1·5·······2·5········3·5········4·5·······5······0·6·······1·6·······2·6·······3·6·······4·6········5·6········6········0·7·······1·7·······2·7········3·7·······4·7········5·7·······6·7·······7········0·8·······1·8·······2·8·····3·8········4·8········5·8········6·8········7·8·······8·······0·······0·1········1·······0·2·······1·2········2········0·3·······1·3······2·3······3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5······2·5·······3·5······4·5········5········0·6········1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7········3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8·······4·8········5·8········6·8·······7·8········8·······0·······0·1········1········0·2········1·2·······2········0·3········1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6········1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7········2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2·8········3·8·······4·8········5·8·······6·8······7·8·······8 | 11 | ·································0·······0·1········1········0·2········1·2·······2·······0·3········1·3·······2·3········3·······0·4·······1·4········2·4·······3·4·······4······0·5········1·5········2·5·······3·5········4·5·······5·······0·6·······1·6········2·6········3·6·······4·6········5·6········6·······0·7·······1·7········2·7······3·7········4·7········5·7·······6·7······7········0·8········1·8········2·8·······3·8········4·8······5·8········6·8········7·8·······8·········0·······0·1·······1········0·2········1·2·······2·······0·3········1·3·······2·3········3········0·4·······1·4·······2·4······3·4······4········0·5·······1·5········2·5·······3·5·······4·5·······5·······0·6·······1·6·······2·6·······3·6·······4·6·······5·6·······6········0·7········1·7·······2·7·······3·7······4·7········5·7·······6·7·······7·······0·8·······1·8········2·8········3·8·······4·8······5·8········6·8·······7·8········8········0········0·1········1········0·2·······1·2·······2·······0·3········1·3·······2·3·······3········0·4·······1·4········2·4·······3·4········4········0·5·······1·5·······2·5·······3·5·······4·5·······5········0·6········1·6·······2·6·······3·6·······4·6········5·6·······6······0·7·······1·7·······2·7·······3·7········4·7········5·7·······6·7········7······0·8·······1·8········2·8········3·8········4·8········5·8········6·8·······7·8········8········0········0·1········1········0·2········1·2·······2········0·3········1·3·······2·3······3·······0·4········1·4·······2·4·······3·4········4·······0·5·······1·5·······2·5········3·5·······4·5·······5·······0·6·······1·6······2·6········3·6·······4·6········5·6·······6·······0·7·····1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8·······2·8········3·8········4·8·······5·8·······6·8······7·8········8·········0······0·1·······1·······0·2······1·2·······2·······0·3········1·3·······2·3·······3·······0·4········1·4·······2·4········3·4·······4········0·5········1·5·······2·5·······3·5········4·5······5·······0·6·······1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7······3·7········4·7·······5·7·······6·7·······7·······0·8·······1·8········2·8·······3·8········4·8·······5·8·······6·8········7·8·······8········0········0·1·······1·····0·2······1·2········2·······0·3·······1·3········2·3········3········0·4·······1·4·······2·4·······3·4·······4········0·5········1·5·······2·5·······3·5·······4·5·······5········0·6·······1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7·······2·7·······3·7········4·7·······5·7········6·7·······7·······0·8·······1·8·······2·8········3·8·······4·8·······5·8·······6·8········7·8······8·······0·······0·1········1········0·2·······1·2········2······0·3·······1·3·······2·3·······3········0·4······1·4······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5·······0·6·······1·6·······2·6······3·6·······4·6········5·6········6·······0·7·······1·7·······2·7········3·7········4·7·······5·7········6·7······7······0·8········1·8·······2·8······3·8······4·8·······5·8········6·8········7·8·······8·······0·······0·1·······1······0·2·······1·2········2········0·3·······1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4········0·5········1·5·······2·5·······3·5········4·5·······5········0·6········1·6·······2·6········3·6·······4·6········5·6·······6······0·7·······1·7········2·7·······3·7·······4·7········5·7········6·7········7········0·8·······1·8·······2·8·······3·8·······4·8········5·8·······6·8········7·8········8········0········0·1········1········0·2········1·2·······2·······0·3········1·3·······2·3········3·······0·4········1·4········2·4·······3·4········4·······0·5········1·5········2·5········3·5·······4·5·······5·······0·6·······1·6······2·6·······3·6········4·6·······5·6·······6·······0·7·····1·7········2·7·······3·7·······4·7·······5·7·······6·7·······7·······0·8·······1·8·······2·8········3·8········4·8·······5·8········6·8·······7·8·······8······0·······0·1·······1·······0·2········1·2·······2········0·3·······1·3·······2·3········3·······0·4········1·4·······2·4·······3·4·······4·······0·5·······1·5·······2·5·······3·5·······4·5·······5········0·6·······1·6········2·6········3·6········4·6········5·6·······6·······0·7········1·7·······2·7········3·7·······4·7······5·7········6·7·······7·······0·8·······1·8·······2·8········3·8·······4·8·······5·8·······6·8········7·8········8·····0········0·1········1········0·2·······1·2········2·······0·3·······1·3·······2·3········3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5·······2·5·······3·5········4·5·······5·······0·6········1·6········2·6·······3·6········4·6······5·6·······6·······0·7·······1·7········2·7········3·7······4·7········5·7·······6·7·······7·······0·8·······1·8········2·8········3·8·······4·8·······5·8········6·8·······7·8·······8·········0······0·1·······1······0·2········1·2········2········0·3·······1·3·······2·3········3········0·4········1·4········2·4······3·4·······4·······0·5·······1·5·······2·5········3·5·······4·5········5········0·6········1·6········2·6·······3·6·······4·6·······5·6·······6········0·7·······1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8········2·8········3·8········4·8········5·8·······6·8········7·8········8······0·······0·1········1·······0·2·······1·2········2·······0·3·······1·3·······2·3······3·······0·4·······1·4·······2·4·······3·4········4·······0·5········1·5·······2·5········3·5········4·5·······5······0·6·······1·6·······2·6·······3·6·······4·6········5·6········6········0·7·······1·7·······2·7········3·7·······4·7········5·7·······6·7·······7········0·8·······1·8·······2·8·····3·8········4·8········5·8········6·8········7·8·······8·······0·······0·1········1·······0·2·······1·2········2········0·3·······1·3······2·3······3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5······2·5·······3·5······4·5········5········0·6········1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7········3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8·······4·8········5·8········6·8·······7·8········8·······0·······0·1········1········0·2········1·2·······2········0·3········1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6········1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7········2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2·8········3·8·······4·8········5·8·······6·8······7·8·······8 |
| 12 | o4·:·RingMap·ringP8·<--·ringP14 | 12 | o4·:·RingMap·ringP8·<--·ringP14 |
| 13 | i5·:·time·degreeMap·phi | 13 | i5·:·time·degreeMap·phi |
| 14 | ·--·used·0.08 | 14 | ·--·used·0.0889568s·(cpu);·0.0496064s·(thread);·0s·(gc) |
| 15 | o5·=·1 | 15 | o5·=·1 |
| 16 | i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14· | 16 | i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14· |
| 17 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14) | 17 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14) |
| 18 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) | 18 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) |
| 19 | ·································2··················2···························2······································2·················································2···························································2···································································2··············································································2··························································································2········2··················2······························2·······································2················································2·····························································2··································································2··············································································2····························································································2········2··················2·····························2·······································2················································2···························································2······································································2··············································································2·························································································2·········2·················2····························2·······································2··················································2·····························································2····································································2················································································2·····························································································2·······2···················2····························2·····································2················································2··························································2··································································2···················································································2····························································································2········2················2···························2······································2··················································2····························································2······································································2·················································································2··························································································2···2···················2···························2·····································2··················································2···························································2····································································2··············································································2·························································································2······2··················2···························2······································2··················································2·····························································2·······································································2··············································································2··························································································2·········2··················2····························2·····································2·················································2······························································2····································································2···············································································2························································································2 | 19 | ·································2··················2···························2······································2·················································2···························································2···································································2··············································································2··························································································2········2··················2······························2·······································2················································2·····························································2··································································2··············································································2····························································································2········2··················2·····························2·······································2················································2···························································2······································································2··············································································2·························································································2·········2·················2····························2·······································2··················································2·····························································2····································································2················································································2·····························································································2·······2···················2····························2·····································2················································2··························································2··································································2···················································································2····························································································2········2················2···························2······································2··················································2····························································2······································································2·················································································2··························································································2···2···················2···························2·····································2··················································2···························································2····································································2··············································································2·························································································2······2··················2···························2······································2··················································2·····························································2·······································································2··············································································2··························································································2·········2··················2····························2·····································2·················································2······························································2····································································2···············································································2························································································2 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| 20 | o6·=·map·(ringP8,·ringP8,·{-·780x··-·506x·x··+·1537x··-·132x·x··-·928x·x··+·386x··-·102x·x··+·422x·x··+·725x·x··-·1073x··-·905x·x··-·830x·x··+·1500x·x··+·276x·x··+·1533x··-·653x·x··+·1558x·x··+·939x·x··-·1432x·x··+·462x·x··-·329x··-·92x·x··+·661x·x··-·1298x·x··-·684x·x··+·70x·x··-·715x·x··+·1093x··+·581x·x··+·329x·x··+·454x·x··-·911x·x··-·84x·x··-·1452x·x··-·809x·x··+·1202x··+·1353x·x··+·1503x·x··+·482x·x··+·893x·x··-·643x·x··+·598x·x··+·110x·x··+·1064x·x··-·472x·,·-·522x··-·583x·x··+·1339x··+·1535x·x··-·1317x·x··+·1113x··-·169x·x··+·1440x·x··-·1657x·x··+·721x··+·40x·x··-·1576x·x··-·367x·x··+·257x·x··-·1454x··+·1612x·x··+·1529x·x··-·1068x·x··+·560x·x··-·1441x·x··+·608x··-·92x·x··-·1006x·x··+·285x·x··+·102x·x··-·397x·x··+·66x·x··-·643x··-·38x·x··+·1380x·x··+·1069x·x··-·426x·x··+·1147x·x··+·982x·x··+·10x·x··-·662x··+·16x·x··+·1561x·x··+·1597x·x··+·512x·x··+·1288x·x··-·1253x·x··+·1317x·x··+·1481x·x··-·354x·,·-·640x··-·1551x·x··+·469x··+·1482x·x··-·1593x·x··-·986x··+·471x·x··+·612x·x··+·1228x·x··+·1156x··-·731x·x··+·1503x·x··-·628x·x··+·674x·x··-·799x··+·1137x·x··+·844x·x··+·589x·x··-·666x·x··+·829x·x··-·1024x··-·170x·x··+·450x·x··+·1497x·x··+·1204x·x··-·907x·x··+·1621x·x··-·417x··+·1297x·x··+·1444x·x··+·4x·x··+·398x·x··+·996x·x··-·1031x·x··+·239x·x··+·303x··+·1215x·x··-·83x·x··+·1571x·x··-·1543x·x··-·925x·x··-·694x·x··+·151x·x··-·520x·x··+·880x·,·-·1210x··-·222x·x··+·185x··+·245x·x··+·1059x·x··-·322x··+·238x·x··+·962x·x··+·1260x·x··-·1581x··+·50x·x··+·1352x·x··-·1465x·x··+·1555x·x··+·1333x··+·1362x·x··+·1365x·x··+·1168x·x··-·1401x·x··+·149x·x··-·652x··+·1378x·x··-·557x·x··-·112x·x··+·26x·x··+·315x·x··+·111x·x··+·1592x··-·283x·x··-·1454x·x··+·907x·x··+·212x·x··+·400x·x··+·1049x·x··-·882x·x··-·1429x··-·183x·x··+·1571x·x··-·1286x·x··-·1179x·x··+·1319x·x··+·240x·x··-·1100x·x··+·1500x·x··-·348x·,·1051x··-·1325x·x··+·1354x··-·346x·x··-·1532x·x··-·466x··+·163x·x··-·659x·x··-·291x·x··+·966x··+·789x·x··+·393x·x··+·403x·x··-·1199x·x··-·570x··-·93x·x··-·492x·x··-·418x·x··+·713x·x··-·1323x·x··-·1384x··-·830x·x··-·54x·x··-·306x·x··+·709x·x··+·421x·x··-·954x·x··-·299x··+·1053x·x··-·1080x·x··+·686x·x··+·170x·x··-·1272x·x··-·1661x·x··+·1235x·x··+·1553x··-·1454x·x··-·1411x·x··-·1195x·x··-·962x·x··+·737x·x··-·390x·x··+·957x·x··+·1538x·x··+·1234x·,·-·509x··+·9x·x··-·1563x··-·710x·x··-·642x·x··+·541x··+·220x·x··-·1214x·x··-·16x·x··+·1008x··-·1088x·x··+·755x·x··-·886x·x··-·1433x·x··+·1154x··+·1627x·x··-·1547x·x··-·951x·x··+·866x·x··+·163x·x··-·1142x··-·668x·x··+·1361x·x··+·1324x·x··-·490x·x··+·282x·x··-·1133x·x··-·612x··+·805x·x··-·126x·x··+·1296x·x··-·973x·x··+·1271x·x··-·1646x·x··+·844x·x··+·1073x··-·1452x·x··-·1112x·x··-·141x·x··+·176x·x··-·1579x·x··-·78x·x··+·848x·x··-·1365x·x··+·711x·,·x··+·1543x·x··-·1076x··+·493x·x··-·526x·x··+·868x··-·582x·x··-·996x·x··+·206x·x··-·419x··+·1258x·x··-·391x·x··+·1002x·x··-·1539x·x··+·931x··-·1504x·x··+·810x·x··+·324x·x··+·1356x·x··+·313x·x··+·772x··+·299x·x··+·1186x·x··+·718x·x··+·407x·x··-·64x·x··-·828x·x··-·1393x··+·94x·x··-·290x·x··-·766x·x··+·950x·x··-·640x·x··+·265x·x··-·1640x·x··-·1403x··-·126x·x··+·891x·x··-·1519x·x··-·927x·x··-·1335x·x··-·1448x·x··-·x·x··-·1103x·x··-·1152x·,·821x··+·558x·x··-·1174x··-·168x·x··+·986x·x··+·790x··+·549x·x··+·817x·x··+·1396x·x··+·695x··+·1211x·x··+·878x·x··-·1061x·x··-·1244x·x··-·880x··+·1409x·x··-·567x·x··+·1240x·x··+·1126x·x··-·1262x·x··+·490x··+·1553x·x··+·1276x·x··+·805x·x··+·576x·x··-·1076x·x··+·1617x·x··-·495x··-·750x·x··-·277x·x··+·544x·x··+·1479x·x··-·784x·x··-·64x·x··-·1203x·x··+·405x··+·1013x·x··+·604x·x··+·1301x·x··+·1003x·x··+·235x·x··+·696x·x··+·939x·x··-·714x·x··-·879x·,·-·1452x··+·727x·x··-·1159x··+·449x·x··-·1169x·x··+·732x··+·575x·x··-·600x·x··+·924x·x··-·837x··+·1298x·x··-·860x·x··+·1010x·x··+·774x·x··+·319x··+·1087x·x··-·1120x·x··+·1439x·x··+·1175x·x··-·1648x·x··+·985x··-·1317x·x··-·878x·x··+·399x·x··-·1339x·x··+·70x·x··-·463x·x··+·470x··-·628x·x··-·907x·x··+·748x·x··+·98x·x··+·1150x·x··+·1140x·x··+·1308x·x··+·621x··+·369x·x··-·991x·x··-·1186x·x··+·61x·x··-·907x·x··-·681x·x··-·1528x·x··+·717x·x··+·854x·}) | 20 | o6·=·map·(ringP8,·ringP8,·{-·780x··-·506x·x··+·1537x··-·132x·x··-·928x·x··+·386x··-·102x·x··+·422x·x··+·725x·x··-·1073x··-·905x·x··-·830x·x··+·1500x·x··+·276x·x··+·1533x··-·653x·x··+·1558x·x··+·939x·x··-·1432x·x··+·462x·x··-·329x··-·92x·x··+·661x·x··-·1298x·x··-·684x·x··+·70x·x··-·715x·x··+·1093x··+·581x·x··+·329x·x··+·454x·x··-·911x·x··-·84x·x··-·1452x·x··-·809x·x··+·1202x··+·1353x·x··+·1503x·x··+·482x·x··+·893x·x··-·643x·x··+·598x·x··+·110x·x··+·1064x·x··-·472x·,·-·522x··-·583x·x··+·1339x··+·1535x·x··-·1317x·x··+·1113x··-·169x·x··+·1440x·x··-·1657x·x··+·721x··+·40x·x··-·1576x·x··-·367x·x··+·257x·x··-·1454x··+·1612x·x··+·1529x·x··-·1068x·x··+·560x·x··-·1441x·x··+·608x··-·92x·x··-·1006x·x··+·285x·x··+·102x·x··-·397x·x··+·66x·x··-·643x··-·38x·x··+·1380x·x··+·1069x·x··-·426x·x··+·1147x·x··+·982x·x··+·10x·x··-·662x··+·16x·x··+·1561x·x··+·1597x·x··+·512x·x··+·1288x·x··-·1253x·x··+·1317x·x··+·1481x·x··-·354x·,·-·640x··-·1551x·x··+·469x··+·1482x·x··-·1593x·x··-·986x··+·471x·x··+·612x·x··+·1228x·x··+·1156x··-·731x·x··+·1503x·x··-·628x·x··+·674x·x··-·799x··+·1137x·x··+·844x·x··+·589x·x··-·666x·x··+·829x·x··-·1024x··-·170x·x··+·450x·x··+·1497x·x··+·1204x·x··-·907x·x··+·1621x·x··-·417x··+·1297x·x··+·1444x·x··+·4x·x··+·398x·x··+·996x·x··-·1031x·x··+·239x·x··+·303x··+·1215x·x··-·83x·x··+·1571x·x··-·1543x·x··-·925x·x··-·694x·x··+·151x·x··-·520x·x··+·880x·,·-·1210x··-·222x·x··+·185x··+·245x·x··+·1059x·x··-·322x··+·238x·x··+·962x·x··+·1260x·x··-·1581x··+·50x·x··+·1352x·x··-·1465x·x··+·1555x·x··+·1333x··+·1362x·x··+·1365x·x··+·1168x·x··-·1401x·x··+·149x·x··-·652x··+·1378x·x··-·557x·x··-·112x·x··+·26x·x··+·315x·x··+·111x·x··+·1592x··-·283x·x··-·1454x·x··+·907x·x··+·212x·x··+·400x·x··+·1049x·x··-·882x·x··-·1429x··-·183x·x··+·1571x·x··-·1286x·x··-·1179x·x··+·1319x·x··+·240x·x··-·1100x·x··+·1500x·x··-·348x·,·1051x··-·1325x·x··+·1354x··-·346x·x··-·1532x·x··-·466x··+·163x·x··-·659x·x··-·291x·x··+·966x··+·789x·x··+·393x·x··+·403x·x··-·1199x·x··-·570x··-·93x·x··-·492x·x··-·418x·x··+·713x·x··-·1323x·x··-·1384x··-·830x·x··-·54x·x··-·306x·x··+·709x·x··+·421x·x··-·954x·x··-·299x··+·1053x·x··-·1080x·x··+·686x·x··+·170x·x··-·1272x·x··-·1661x·x··+·1235x·x··+·1553x··-·1454x·x··-·1411x·x··-·1195x·x··-·962x·x··+·737x·x··-·390x·x··+·957x·x··+·1538x·x··+·1234x·,·-·509x··+·9x·x··-·1563x··-·710x·x··-·642x·x··+·541x··+·220x·x··-·1214x·x··-·16x·x··+·1008x··-·1088x·x··+·755x·x··-·886x·x··-·1433x·x··+·1154x··+·1627x·x··-·1547x·x··-·951x·x··+·866x·x··+·163x·x··-·1142x··-·668x·x··+·1361x·x··+·1324x·x··-·490x·x··+·282x·x··-·1133x·x··-·612x··+·805x·x··-·126x·x··+·1296x·x··-·973x·x··+·1271x·x··-·1646x·x··+·844x·x··+·1073x··-·1452x·x··-·1112x·x··-·141x·x··+·176x·x··-·1579x·x··-·78x·x··+·848x·x··-·1365x·x··+·711x·,·x··+·1543x·x··-·1076x··+·493x·x··-·526x·x··+·868x··-·582x·x··-·996x·x··+·206x·x··-·419x··+·1258x·x··-·391x·x··+·1002x·x··-·1539x·x··+·931x··-·1504x·x··+·810x·x··+·324x·x··+·1356x·x··+·313x·x··+·772x··+·299x·x··+·1186x·x··+·718x·x··+·407x·x··-·64x·x··-·828x·x··-·1393x··+·94x·x··-·290x·x··-·766x·x··+·950x·x··-·640x·x··+·265x·x··-·1640x·x··-·1403x··-·126x·x··+·891x·x··-·1519x·x··-·927x·x··-·1335x·x··-·1448x·x··-·x·x··-·1103x·x··-·1152x·,·821x··+·558x·x··-·1174x··-·168x·x··+·986x·x··+·790x··+·549x·x··+·817x·x··+·1396x·x··+·695x··+·1211x·x··+·878x·x··-·1061x·x··-·1244x·x··-·880x··+·1409x·x··-·567x·x··+·1240x·x··+·1126x·x··-·1262x·x··+·490x··+·1553x·x··+·1276x·x··+·805x·x··+·576x·x··-·1076x·x··+·1617x·x··-·495x··-·750x·x··-·277x·x··+·544x·x··+·1479x·x··-·784x·x··-·64x·x··-·1203x·x··+·405x··+·1013x·x··+·604x·x··+·1301x·x··+·1003x·x··+·235x·x··+·696x·x··+·939x·x··-·714x·x··-·879x·,·-·1452x··+·727x·x··-·1159x··+·449x·x··-·1169x·x··+·732x··+·575x·x··-·600x·x··+·924x·x··-·837x··+·1298x·x··-·860x·x··+·1010x·x··+·774x·x··+·319x··+·1087x·x··-·1120x·x··+·1439x·x··+·1175x·x··-·1648x·x··+·985x··-·1317x·x··-·878x·x··+·399x·x··-·1339x·x··+·70x·x··-·463x·x··+·470x··-·628x·x··-·907x·x··+·748x·x··+·98x·x··+·1150x·x··+·1140x·x··+·1308x·x··+·621x··+·369x·x··-·991x·x··-·1186x·x··+·61x·x··-·907x·x··-·681x·x··-·1528x·x··+·717x·x··+·854x·}) |
| 21 | 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|
| 22 | o6·:·RingMap·ringP8·<--·ringP8 | 22 | o6·:·RingMap·ringP8·<--·ringP8 |
| 23 | i7·:·time·degreeMap·phi' | 23 | i7·:·time·degreeMap·phi' |
| 24 | ·--·used·0. | 24 | ·--·used·0.545321s·(cpu);·0.454568s·(thread);·0s·(gc) |
| 25 | o7·=·14 | 25 | o7·=·14 |
| 26 | i8·:· | 26 | i8·:· |
| Offset 5, 14 lines modified | Offset 5, 14 lines modified | ||
| 5 | o2·:·Ideal·of·P6 | 5 | o2·:·Ideal·of·P6 |
| 6 | i3·:·Phi·=·rationalMap(X,Dominant=>2); | 6 | i3·:·Phi·=·rationalMap(X,Dominant=>2); |
| 7 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) | 7 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) |
| 8 | i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) | 8 | i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) |
| 9 | ·--·used·0.000 | 9 | ·--·used·0.000196629s·(cpu);·0.000579297s·(thread);·0s·(gc) |
| 10 | i5·:·Phi; | 10 | i5·:·Phi; |
| 11 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) | 11 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) |
| 12 | i6·:· | 12 | i6·:· |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | ······················-·x··+·x·x | 35 | ······················-·x··+·x·x |
| 36 | ·························3····2·4 | 36 | ·························3····2·4 |
| 37 | ·····················} | 37 | ·····················} |
| 38 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) | 38 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) |
| 39 | i3·:·time·(p1,p2)·=·graph·phi; | 39 | i3·:·time·(p1,p2)·=·graph·phi; |
| 40 | ·--·used·0.2 | 40 | ·--·used·0.274214s·(cpu);·0.0495487s·(thread);·0s·(gc) |
| 41 | i4·:·p1 | 41 | i4·:·p1 |
| 42 | o4·=·--·rational·map·-- | 42 | o4·=·--·rational·map·-- |
| 43 | ··································ZZ·································ZZ | 43 | ··································ZZ·································ZZ |
| 44 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by | 44 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by |
| 45 | ································190181··0···1···2···3···4··········190181··0···1···2···3···4···5 | 45 | ································190181··0···1···2···3···4··········190181··0···1···2···3···4···5 |
| Offset 173, 15 lines modified | Offset 173, 15 lines modified | ||
| 173 | i8·:·projectiveDegrees·p2 | 173 | i8·:·projectiveDegrees·p2 |
| 174 | o8·=·{51,·28,·14,·6,·2} | 174 | o8·=·{51,·28,·14,·6,·2} |
| 175 | o8·:·List | 175 | o8·:·List |
| 176 | i9·:·time·g·=·graph·p2; | 176 | i9·:·time·g·=·graph·p2; |
| 177 | ·--·used·0.2 | 177 | ·--·used·0.286291s·(cpu);·0.0657456s·(thread);·0s·(gc) |
| 178 | i10·:·g_0; | 178 | i10·:·g_0; |
| 179 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4) | 179 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4) |
| 180 | i11·:·g_1; | 180 | i11·:·g_1; |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | ······················x··-·x·x | 33 | ······················x··-·x·x |
| 34 | ·······················1····0·3 | 34 | ·······················1····0·3 |
| 35 | ·····················} | 35 | ·····················} |
| 36 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4) | 36 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4) |
| 37 | i3·:·time·ideal·phi | 37 | i3·:·time·ideal·phi |
| 38 | ·--·used·0.003 | 38 | ·--·used·0.00348825s·(cpu);·0.00327104s·(thread);·0s·(gc) |
| 39 | ·············2·····································2······················ | 39 | ·············2·····································2······················ |
| 40 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ | 40 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ |
| 41 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3·· | 41 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3·· |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ············2 | 43 | ············2 |
| 44 | ·····x·x·,·x··-·x·x·) | 44 | ·····x·x·,·x··-·x·x·) |
| Offset 108, 15 lines modified | Offset 108, 15 lines modified | ||
| 108 | ······················y | 108 | ······················y |
| 109 | ·······················4 | 109 | ·······················4 |
| 110 | ·····················} | 110 | ·····················} |
| 111 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4) | 111 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4) |
| 112 | i6·:·time·ideal·phi' | 112 | i6·:·time·ideal·phi' |
| 113 | ·--·used·0.15 | 113 | ·--·used·0.157543s·(cpu);·0.089825s·(thread);·0s·(gc) |
| 114 | o6·=·ideal·1 | 114 | o6·=·ideal·1 |
| 115 | ············································································································QQ[x·..x·,·y·..y·] | 115 | ············································································································QQ[x·..x·,·y·..y·] |
| 116 | ················································································································0···5···0···4 | 116 | ················································································································0···5···0···4 |
| 117 | o6·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 117 | o6·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 118 | ·····································································································································································································2 | 118 | ·····································································································································································································2 |
| Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | ······················w·w··-·w·w··+·w·w | 72 | ······················w·w··-·w·w··+·w·w |
| 73 | ·······················2·4····1·5····0·6 | 73 | ·······················2·4····1·5····0·6 |
| 74 | ·····················} | 74 | ·····················} |
| 75 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20) | 75 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20) |
| 76 | i2·:·time·psi·=·inverseMap·phi | 76 | i2·:·time·psi·=·inverseMap·phi |
| 77 | ·--·used·0.1 | 77 | ·--·used·0.154207s·(cpu);·0.10972s·(thread);·0s·(gc) |
| 78 | o2·=·--·rational·map·-- | 78 | o2·=·--·rational·map·-- |
| 79 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) | 79 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 80 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 | 80 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 |
| 81 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) | 81 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 82 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 | 82 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 |
| 83 | ·····defining·forms:·{ | 83 | ·····defining·forms:·{ |
| Offset 158, 15 lines modified | Offset 158, 15 lines modified | ||
| 158 | o4·=·map·(QQ[w·..w··],·QQ[w·..w··],·{w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w··-·w·w··-·w·w··+·w·w··-·w·w·}) | 158 | o4·=·map·(QQ[w·..w··],·QQ[w·..w··],·{w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···-·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···+·w··w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w··w···-·w··w···-·w··w···+·w··w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···+·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···-·w·w···+·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w···-·w·w···-·w·w···+·w·w···-·w·w··,·w·w··-·w·w··-·w·w··+·w·w··-·w·w·}) |
| 159 | ··············0···26·······0···26·····21·22····20·23····15·24····10·25····0·26···19·22····18·23····16·24····11·25····1·26···19·20····18·21····17·24····12·25····2·26···15·19····16·21····17·23····13·25····3·26···10·19····11·21····12·23····13·24····4·26···0·19····1·21····2·23····3·24····4·25···15·18····16·20····17·22····14·25····5·26···10·18····11·20····12·22····14·24····6·26···0·18····1·20····2·22····5·24····6·25···12·16····11·17····13·18····14·19····7·26···2·16····1·17····3·18····5·19····7·25···12·15····10·17····13·20····14·21····8·26···11·15····10·16····13·22····14·23····9·26···2·15····0·17····3·20····5·21····8·25···1·15····0·16····3·22····5·23····9·25···5·13····3·14····7·15····8·16····9·17···5·12····2·14····6·17····8·18····7·20···3·12····2·13····4·17····8·19····7·21···5·11····1·14····6·16····9·18····7·22···3·11····1·13····4·16····9·19····7·23···2·11····1·12····4·18····6·19····7·24···7·10····8·11····9·12····6·13····4·14···5·10····0·14····6·15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4·20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7····1·8····2·9 | 159 | ··············0···26·······0···26·····21·22····20·23····15·24····10·25····0·26···19·22····18·23····16·24····11·25····1·26···19·20····18·21····17·24····12·25····2·26···15·19····16·21····17·23····13·25····3·26···10·19····11·21····12·23····13·24····4·26···0·19····1·21····2·23····3·24····4·25···15·18····16·20····17·22····14·25····5·26···10·18····11·20····12·22····14·24····6·26···0·18····1·20····2·22····5·24····6·25···12·16····11·17····13·18····14·19····7·26···2·16····1·17····3·18····5·19····7·25···12·15····10·17····13·20····14·21····8·26···11·15····10·16····13·22····14·23····9·26···2·15····0·17····3·20····5·21····8·25···1·15····0·16····3·22····5·23····9·25···5·13····3·14····7·15····8·16····9·17···5·12····2·14····6·17····8·18····7·20···3·12····2·13····4·17····8·19····7·21···5·11····1·14····6·16····9·18····7·22···3·11····1·13····4·16····9·19····7·23···2·11····1·12····4·18····6·19····7·24···7·10····8·11····9·12····6·13····4·14···5·10····0·14····6·15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4·20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7····1·8····2·9 |
| 160 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 160 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 161 | ·················0···26··········0···26 | 161 | ·················0···26··········0···26 |
| 162 | i5·:·time·psi·=·inverseMap·phi | 162 | i5·:·time·psi·=·inverseMap·phi |
| 163 | ·--·used·0.2 | 163 | ·--·used·0.28098s·(cpu);·0.169417s·(thread);·0s·(gc) |
| 164 | o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··}) | 164 | o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··}) |
| 165 | ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12 | 165 | ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12 |
| 166 | o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 166 | o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 167 | ·················0···26··········0···26 | 167 | ·················0···26··········0···26 |
| Offset 28, 15 lines modified | Offset 28, 15 lines modified | ||
| 28 | ······················-·-----x··-·---------x·x··+·-----------x·x··+·-----------x·x··-·--------x··-·-------x·x··+·-----------x·x·x··+·-----------x·x·x··+·----------x·x··+·--------x·x··+·--------x·x·x··-·-----------x·x··-·-------x·x··-·----------x·x··-·-------x··-·------x·x··+·----------x·x·x··+·-----------x·x·x··-·----------x·x··+·---------x·x·x··+·----------x·x·x·x··+·-----------x·x·x··+·----------x·x·x··+·------------x·x·x··+·---------x·x··-·---------x·x··-·-----------x·x·x··-·-----------x·x··-·----------x·x·x··+·----------x·x·x··-·---------x·x··+·-------x·x··-·--------x·x··+·----------x·x··+·------x··-·---------x·x··-·-----------x·x·x··+·------------x·x·x··+·----------x·x··-·-----------x·x·x··-·-------------x·x·x·x··+·------------x·x·x··-·----------x·x·x··-·-----------x·x·x··-·-------x·x··+·-----------x·x·x··+·------------x·x·x·x··+·------------x·x·x··+·-----------x·x·x·x··+·--------------x·x·x·x··+·---------x·x·x··-·------------x·x·x··-·------------x·x·x··-·------------x·x·x··+·----------x·x··-·----------x·x··-·------------x·x·x··+·-----------x·x··-·----------x·x·x··-·------------x·x·x··-·---------x·x··+·------------x·x·x··-·--------x·x·x··+·------------x·x·x··+·----------x·x··-·--------x·x··-·---------x·x··-·---------x·x··+·---------x·x··-·-----x | 28 | ······················-·-----x··-·---------x·x··+·-----------x·x··+·-----------x·x··-·--------x··-·-------x·x··+·-----------x·x·x··+·-----------x·x·x··+·----------x·x··+·--------x·x··+·--------x·x·x··-·-----------x·x··-·-------x·x··-·----------x·x··-·-------x··-·------x·x··+·----------x·x·x··+·-----------x·x·x··-·----------x·x··+·---------x·x·x··+·----------x·x·x·x··+·-----------x·x·x··+·----------x·x·x··+·------------x·x·x··+·---------x·x··-·---------x·x··-·-----------x·x·x··-·-----------x·x··-·----------x·x·x··+·----------x·x·x··-·---------x·x··+·-------x·x··-·--------x·x··+·----------x·x··+·------x··-·---------x·x··-·-----------x·x·x··+·------------x·x·x··+·----------x·x··-·-----------x·x·x··-·-------------x·x·x·x··+·------------x·x·x··-·----------x·x·x··-·-----------x·x·x··-·-------x·x··+·-----------x·x·x··+·------------x·x·x·x··+·------------x·x·x··+·-----------x·x·x·x··+·--------------x·x·x·x··+·---------x·x·x··-·------------x·x·x··-·------------x·x·x··-·------------x·x·x··+·----------x·x··-·----------x·x··-·------------x·x·x··+·-----------x·x··-·----------x·x·x··-·------------x·x·x··-·---------x·x··+·------------x·x·x··-·--------x·x·x··+·------------x·x·x··+·----------x·x··-·--------x·x··-·---------x·x··-·---------x·x··+·---------x·x··-·-----x |
| 29 | ·························2800·0····6350400··0·1·····50803200··0·1·····33868800··0·1····181440··1····196000·0·2····381024000··0·1·2·····47628000··0·1·2····10160640··1·2····2268000·0·2····2126250·0·1·2····762048000··1·2····992250·0·2····31752000··1·2····529200·2····73500·0·3····28576800··0·1·3·····32659200··0·1·3·····6531840··1·3····15876000·0·2·3····21432600··0·1·2·3····137168640··1·2·3····158760000·0·2·3·····571536000··1·2·3····95256000·2·3····15876000·0·3····228614400··0·1·3·····65318400··1·3····190512000·0·2·3····95256000··1·2·3····31752000·2·3····352800·0·3····604800··1·3····31752000··2·3····15120·3····47628000·0·4····444528000··0·1·4····4267468800··0·1·4····152409600·1·4····714420000··0·2·4····16003008000··0·1·2·4····1524096000··1·2·4····95256000··0·2·4····533433600··1·2·4····211680·2·4····1000188000·0·3·4····2667168000··0·1·3·4·····457228800··1·3·4····240045120··0·2·3·4·····48009024000··1·2·3·4····14817600·2·3·4····4000752000··0·3·4····1524096000··1·3·4····2667168000··2·3·4····27216000··3·4····190512000·0·4····1778112000··0·1·4····304819200··1·4····47628000··0·2·4····1333584000··1·2·4····5292000··2·4····4000752000··0·3·4···71442000·1·3·4····1333584000··2·3·4····95256000··3·4····3969000·0·4···127008000·1·4····5292000··2·4····21168000·3·4···28000·4 | 29 | ·························2800·0····6350400··0·1·····50803200··0·1·····33868800··0·1····181440··1····196000·0·2····381024000··0·1·2·····47628000··0·1·2····10160640··1·2····2268000·0·2····2126250·0·1·2····762048000··1·2····992250·0·2····31752000··1·2····529200·2····73500·0·3····28576800··0·1·3·····32659200··0·1·3·····6531840··1·3····15876000·0·2·3····21432600··0·1·2·3····137168640··1·2·3····158760000·0·2·3·····571536000··1·2·3····95256000·2·3····15876000·0·3····228614400··0·1·3·····65318400··1·3····190512000·0·2·3····95256000··1·2·3····31752000·2·3····352800·0·3····604800··1·3····31752000··2·3····15120·3····47628000·0·4····444528000··0·1·4····4267468800··0·1·4····152409600·1·4····714420000··0·2·4····16003008000··0·1·2·4····1524096000··1·2·4····95256000··0·2·4····533433600··1·2·4····211680·2·4····1000188000·0·3·4····2667168000··0·1·3·4·····457228800··1·3·4····240045120··0·2·3·4·····48009024000··1·2·3·4····14817600·2·3·4····4000752000··0·3·4····1524096000··1·3·4····2667168000··2·3·4····27216000··3·4····190512000·0·4····1778112000··0·1·4····304819200··1·4····47628000··0·2·4····1333584000··1·2·4····5292000··2·4····4000752000··0·3·4···71442000·1·3·4····1333584000··2·3·4····95256000··3·4····3969000·0·4···127008000·1·4····5292000··2·4····21168000·3·4···28000·4 |
| 30 | ·····················} | 30 | ·····················} |
| 31 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4) | 31 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4) |
| 32 | i3·:·time·inverse·phi | 32 | i3·:·time·inverse·phi |
| 33 | ·--·used·0. | 33 | ·--·used·0.120667s·(cpu);·0.066183s·(thread);·0s·(gc) |
| 34 | o3·=·--·rational·map·-- | 34 | o3·=·--·rational·map·-- |
| 35 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 35 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 36 | ······················0···1···2···3···4 | 36 | ······················0···1···2···3···4 |
| 37 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 37 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 38 | ······················0···1···2···3···4 | 38 | ······················0···1···2···3···4 |
| 39 | ·····defining·forms:·{ | 39 | ·····defining·forms:·{ |
| Offset 40, 18 lines modified | Offset 40, 18 lines modified | ||
| 40 | ······················-·t··+·t·t | 40 | ······················-·t··+·t·t |
| 41 | ·························3····2·4 | 41 | ·························3····2·4 |
| 42 | ·····················} | 42 | ·····················} |
| 43 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) | 43 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) |
| 44 | i3·:·time·isBirational·phi | 44 | i3·:·time·isBirational·phi |
| 45 | ·--·used·0.0 | 45 | ·--·used·0.0937433s·(cpu);·0.0391452s·(thread);·0s·(gc) |
| 46 | o3·=·true | 46 | o3·=·true |
| 47 | i4·:·time·isBirational(phi,Certify=>true) | 47 | i4·:·time·isBirational(phi,Certify=>true) |
| 48 | ·--·used·0.2 | 48 | ·--·used·0.283204s·(cpu);·0.0649912s·(thread);·0s·(gc) |
| 49 | Certify:·output·certified! | 49 | Certify:·output·certified! |
| 50 | o4·=·true | 50 | o4·=·true |
| 51 | i5·:· | 51 | i5·:· |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·P8·=·ZZ/101[x_0..x_8]; | 3 | i1·:·P8·=·ZZ/101[x_0..x_8]; |
| 4 | i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},{x_4..x_8}}; | 4 | i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},{x_4..x_8}}; |
| 5 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8) | 5 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8) |
| 6 | i3·:·time·isDominant(phi,Certify=>true) | 6 | i3·:·time·isDominant(phi,Certify=>true) |
| 7 | ·--·used· | 7 | ·--·used·2.0284s·(cpu);·1.8784s·(thread);·0s·(gc) |
| 8 | Certify:·output·certified! | 8 | Certify:·output·certified! |
| 9 | o3·=·true | 9 | o3·=·true |
| 10 | i4·:·P7·=·ZZ/101[x_0..x_7]; | 10 | i4·:·P7·=·ZZ/101[x_0..x_7]; |
| 11 | i5·:·--·hyperelliptic·curve·of·genus·3 | 11 | i5·:·--·hyperelliptic·curve·of·genus·3 |
| Offset 20, 13 lines modified | Offset 20, 13 lines modified | ||
| 20 | o5·:·Ideal·of·P7 | 20 | o5·:·Ideal·of·P7 |
| 21 | i6·:·phi·=·rationalMap(C,3,2); | 21 | i6·:·phi·=·rationalMap(C,3,2); |
| 22 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7) | 22 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7) |
| 23 | i7·:·time·isDominant(phi,Certify=>true) | 23 | i7·:·time·isDominant(phi,Certify=>true) |
| 24 | ·--·used·2. | 24 | ·--·used·2.67717s·(cpu);·2.14012s·(thread);·0s·(gc) |
| 25 | Certify:·output·certified! | 25 | Certify:·output·certified! |
| 26 | o7·=·false | 26 | o7·=·false |
| 27 | i8·:· | 27 | i8·:· |
| Offset 6, 23 lines modified | Offset 6, 23 lines modified | ||
| 6 | o1·=·map·(QQ[x·..x·],·QQ[y·..y··],·{-·5x·x··+·x·x··+·x·x··+·35x·x··-·7x·x··+·x·x··-·x·x··-·49x··-·5x·x··+·2x·x··-·x·x··+·27x·x··-·4x··+·x·x··-·7x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x·,·-·x·x··-·6x·x··-·5x·x··+·2x·x··+·x·x··+·x·x··-·5x·x··-·x·x··+·2x·x··+·7x·x··-·2x·x··+·2x·x··-·3x·x·,·-·25x··+·9x·x··+·10x·x··-·2x·x··-·x··+·29x·x··-·x·x··-·7x·x··-·13x·x··+·3x·x··+·x·x··-·x·x··+·2x·x··-·x·x··+·7x·x··-·2x·x··-·8x·x··+·2x·x··-·3x·x·,·x·x··+·x·x··+·x··+·7x·x··-·9x·x··+·12x·x··-·4x··+·2x·x··+·2x·x··-·14x·x··+·4x·x··+·x·x··-·x·x··-·14x·x··+·x·x·,·-·5x·x··+·x·x··-·7x·x··+·8x·x··-·5x·x··+·2x·x··-·x·x··+·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·x·x··+·x··-·7x·x··-·8x·x··+·x·x··+·x·x··+·2x·x··-·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··+·x··-·8x·x··+·x·x··+·6x·x··-·2x··+·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··-·7x·x··+·x·x··+·x·x··-·7x·x··+·2x··-·x·x·,·-·4x·x··+·x·x··-·x··-·7x·x··+·8x·x··+·x·x··-·x·x··-·6x·x··+·2x··-·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·-·5x·x··+·2x··+·x·x··-·x··-·x·x··+·8x·x··-·10x·x··+·2x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x··+·5x·x··-·3x·x··-·2x·x··+·7x·x··-·2x·x··-·3x·x·,·-·5x·x··+·x·x··+·x·x··-·4x·x··-·x·x··+·x·x··+·x·x·,·x·x··-·x·x··+·5x·x··+·x·x··-·14x·x··-·x·x··-·8x·x··-·8x·x··+·2x·x··+·4x·x··+·2x·x··+·4x·x··+·3x·x··-·7x·x··+·2x·x··-·3x·x·}) | 6 | o1·=·map·(QQ[x·..x·],·QQ[y·..y··],·{-·5x·x··+·x·x··+·x·x··+·35x·x··-·7x·x··+·x·x··-·x·x··-·49x··-·5x·x··+·2x·x··-·x·x··+·27x·x··-·4x··+·x·x··-·7x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x·,·-·x·x··-·6x·x··-·5x·x··+·2x·x··+·x·x··+·x·x··-·5x·x··-·x·x··+·2x·x··+·7x·x··-·2x·x··+·2x·x··-·3x·x·,·-·25x··+·9x·x··+·10x·x··-·2x·x··-·x··+·29x·x··-·x·x··-·7x·x··-·13x·x··+·3x·x··+·x·x··-·x·x··+·2x·x··-·x·x··+·7x·x··-·2x·x··-·8x·x··+·2x·x··-·3x·x·,·x·x··+·x·x··+·x··+·7x·x··-·9x·x··+·12x·x··-·4x··+·2x·x··+·2x·x··-·14x·x··+·4x·x··+·x·x··-·x·x··-·14x·x··+·x·x·,·-·5x·x··+·x·x··-·7x·x··+·8x·x··-·5x·x··+·2x·x··-·x·x··+·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·x·x··+·x··-·7x·x··-·8x·x··+·x·x··+·x·x··+·2x·x··-·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··+·x··-·8x·x··+·x·x··+·6x·x··-·2x··+·x·x··+·x·x··-·7x·x··+·2x·x··+·x·x··-·7x·x··+·2x·x·,·x·x··-·7x·x··+·x·x··+·x·x··-·7x·x··+·2x··-·x·x·,·-·4x·x··+·x·x··-·x··-·7x·x··+·8x·x··+·x·x··-·x·x··-·6x·x··+·2x··-·x·x··-·x·x··+·7x·x··-·2x·x··-·x·x··+·7x·x··-·2x·x·,·-·5x·x··+·2x··+·x·x··-·x··-·x·x··+·8x·x··-·10x·x··+·2x·x··+·2x·x··-·2x·x··+·14x·x··-·4x·x··+·5x·x··-·3x·x··-·2x·x··+·7x·x··-·2x·x··-·3x·x·,·-·5x·x··+·x·x··+·x·x··-·4x·x··-·x·x··+·x·x··+·x·x·,·x·x··-·x·x··+·5x·x··+·x·x··-·14x·x··-·x·x··-·8x·x··-·8x·x··+·2x·x··+·4x·x··+·2x·x··+·4x·x··+·3x·x··-·7x·x··+·2x·x··-·3x·x·}) |
| 7 | ··············0···8·······0···11········0·3····2·4····3·4······0·5·····2·5····3·5····4·5······5·····0·6·····2·6····4·6······5·6·····6····4·7·····5·7·····6·7·····4·8······5·8·····6·8·····1·2·····1·5·····0·6·····1·6····4·6····5·6·····0·7····1·7·····2·7·····5·7·····6·7·····1·8·····7·8·······0·····0·2······0·4·····2·4····4······0·5····2·5·····4·5······0·6·····4·6····5·6····0·7·····2·7····4·7·····5·7·····6·7·····0·8·····4·8·····7·8···2·4····3·4····4·····2·5·····4·5······5·6·····6·····3·7·····4·7······5·7·····6·7····3·8····4·8······5·8····6·8······0·4····2·4·····2·5·····4·5·····0·6·····2·6····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···0·4····4·····1·5·····4·5····0·6····1·6·····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···2·3····4·····4·5····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8···1·3·····1·5····1·6····4·6·····5·6·····6····3·7······0·3····3·4····4·····0·5·····4·5····0·6····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8······0·2·····2····2·4····4····2·5·····4·5······0·6·····5·6·····2·7·····4·7······5·7·····6·7·····0·8·····2·8·····4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7···0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2·7·····0·8·····1·8·····5·8·····6·8·····7·8 | 7 | ··············0···8·······0···11········0·3····2·4····3·4······0·5·····2·5····3·5····4·5······5·····0·6·····2·6····4·6······5·6·····6····4·7·····5·7·····6·7·····4·8······5·8·····6·8·····1·2·····1·5·····0·6·····1·6····4·6····5·6·····0·7····1·7·····2·7·····5·7·····6·7·····1·8·····7·8·······0·····0·2······0·4·····2·4····4······0·5····2·5·····4·5······0·6·····4·6····5·6····0·7·····2·7····4·7·····5·7·····6·7·····0·8·····4·8·····7·8···2·4····3·4····4·····2·5·····4·5······5·6·····6·····3·7·····4·7······5·7·····6·7····3·8····4·8······5·8····6·8······0·4····2·4·····2·5·····4·5·····0·6·····2·6····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···0·4····4·····1·5·····4·5····0·6····1·6·····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···2·3····4·····4·5····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8···1·3·····1·5····1·6····4·6·····5·6·····6····3·7······0·3····3·4····4·····0·5·····4·5····0·6····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8······0·2·····2····2·4····4····2·5·····4·5······0·6·····5·6·····2·7·····4·7······5·7·····6·7·····0·8·····2·8·····4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7···0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2·7·····0·8·····1·8·····5·8·····6·8·····7·8 |
| 8 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] | 8 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] |
| 9 | ·················0···8··········0···11 | 9 | ·················0···8··········0···11 |
| 10 | i2·:·time·kernel(phi,1) | 10 | i2·:·time·kernel(phi,1) |
| 11 | ·--·used·0.01 | 11 | ·--·used·0.012553s·(cpu);·0.016148s·(thread);·0s·(gc) |
| 12 | o2·=·ideal·() | 12 | o2·=·ideal·() |
| 13 | o2·:·Ideal·of·QQ[y·..y··] | 13 | o2·:·Ideal·of·QQ[y·..y··] |
| 14 | ··················0···11 | 14 | ··················0···11 |
| 15 | i3·:·time·kernel(phi,2) | 15 | i3·:·time·kernel(phi,2) |
| 16 | ·--·used·0.3 | 16 | ·--·used·0.373972s·(cpu);·0.264096s·(thread);·0s·(gc) |
| 17 | ···························2················································ | 17 | ···························2················································ |
| 18 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- | 18 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- |
| 19 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6·· | 19 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6·· |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ··········································································· | 21 | ··········································································· |
| 22 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- | 22 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- |
| Offset 26, 15 lines modified | Offset 26, 15 lines modified | ||
| 26 | ··············8···········9 | 26 | ··············8···········9 |
| 27 | ·················ZZ | 27 | ·················ZZ |
| 28 | o2·:·Ideal·of·--------[x·..x·] | 28 | o2·:·Ideal·of·--------[x·..x·] |
| 29 | ··············10000019··0···9 | 29 | ··············10000019··0···9 |
| 30 | i3·:·time·parametrize·L | 30 | i3·:·time·parametrize·L |
| 31 | ·--·used·0.00 | 31 | ·--·used·0.00396491s·(cpu);·0.0045012s·(thread);·0s·(gc) |
| 32 | o3·=·--·rational·map·-- | 32 | o3·=·--·rational·map·-- |
| 33 | ·····················ZZ | 33 | ·····················ZZ |
| 34 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) | 34 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) |
| 35 | ··················10000019··0···1···2···3···4···5 | 35 | ··················10000019··0···1···2···3···4···5 |
| 36 | ·····················ZZ | 36 | ·····················ZZ |
| 37 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 37 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 116, 15 lines modified | Offset 116, 15 lines modified | ||
| 116 | ·············5·9···········6·9···········7·9···········8·9···········9 | 116 | ·············5·9···········6·9···········7·9···········8·9···········9 |
| 117 | ·················ZZ | 117 | ·················ZZ |
| 118 | o4·:·Ideal·of·--------[x·..x·] | 118 | o4·:·Ideal·of·--------[x·..x·] |
| 119 | ··············10000019··0···9 | 119 | ··············10000019··0···9 |
| 120 | i5·:·time·parametrize·Q | 120 | i5·:·time·parametrize·Q |
| 121 | ·--·used·0.6 | 121 | ·--·used·0.646178s·(cpu);·0.360424s·(thread);·0s·(gc) |
| 122 | o5·=·--·rational·map·-- | 122 | o5·=·--·rational·map·-- |
| 123 | ·····················ZZ | 123 | ·····················ZZ |
| 124 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 124 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 125 | ··················10000019··0···1···2···3···4···5···6 | 125 | ··················10000019··0···1···2···3···4···5···6 |
| 126 | ·····················ZZ | 126 | ·····················ZZ |
| 127 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 127 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 1, 15 lines modified | Offset 1, 15 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·3560583829489988690 | 1 | --·-*-·M2-comint·-*-·hash:·3560583829489988690 |
| 2 | i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); | 2 | i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); |
| 3 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8) | 3 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8) |
| 4 | i2·:·time·p·=·point·source·f | 4 | i2·:·time·p·=·point·source·f |
| 5 | ·--·used·0.1 | 5 | ·--·used·0.180833s·(cpu);·0.133539s·(thread);·0s·(gc) |
| 6 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ | 6 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ |
| 7 | ·············10········11···9·········11···8········11···7········11···6·· | 7 | ·············10········11···9·········11···8········11···7········11···6·· |
| 8 | ·····------------------------------------------------------------------------ | 8 | ·····------------------------------------------------------------------------ |
| 9 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- | 9 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- |
| 10 | ···········11···5········11···4········11···3·········11···2········11···1·· | 10 | ···········11···5········11···4········11···3·········11···2········11···1·· |
| 11 | ·····------------------------------------------------------------------------ | 11 | ·····------------------------------------------------------------------------ |
| Offset 20, 12 lines modified | Offset 20, 12 lines modified | ||
| 20 | ···························································-----[y·..y··] | 20 | ···························································-----[y·..y··] |
| 21 | ···························································33331··0···11 | 21 | ···························································33331··0···11 |
| 22 | o2·:·Ideal·of·------------------------------------------------------------------------------------------------------- | 22 | o2·:·Ideal·of·------------------------------------------------------------------------------------------------------- |
| 23 | ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) | 23 | ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) |
| 24 | ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7 | 24 | ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7 |
| 25 | i3·:·time·p·==·f^*·f·p | 25 | i3·:·time·p·==·f^*·f·p |
| 26 | ·--·used·0.1 | 26 | ·--·used·0.15898s·(cpu);·0.106391s·(thread);·0s·(gc) |
| 27 | o3·=·true | 27 | o3·=·true |
| 28 | i4·:· | 28 | i4·:· |
| Offset 7, 15 lines modified | Offset 7, 15 lines modified | ||
| 7 | o2·=·map·(GF·109561[t·..t·],·GF·109561[x·..x·],·{-·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a}) | 7 | o2·=·map·(GF·109561[t·..t·],·GF·109561[x·..x·],·{-·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a}) |
| 8 | ·····················0···4··············0···5·······1····0·2·····1·2····0·3·····2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4 | 8 | ·····················0···4··············0···5·······1····0·2·····1·2····0·3·····2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4 |
| 9 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] | 9 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] |
| 10 | ························0···4·················0···5 | 10 | ························0···4·················0···5 |
| 11 | i3·:·time·projectiveDegrees(phi,Certify=>true) | 11 | i3·:·time·projectiveDegrees(phi,Certify=>true) |
| 12 | ·--·used·0. | 12 | ·--·used·0.165802s·(cpu);·0.0280862s·(thread);·0s·(gc) |
| 13 | Certify:·output·certified! | 13 | Certify:·output·certified! |
| 14 | o3·=·{1,·2,·4,·4,·2} | 14 | o3·=·{1,·2,·4,·4,·2} |
| 15 | o3·:·List | 15 | o3·:·List |
| 16 | i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity)) | 16 | i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity)) |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | ··············GF·109561[x·..x·] | 29 | ··············GF·109561[x·..x·] |
| 30 | ·························0···5 | 30 | ·························0···5 |
| 31 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] | 31 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] |
| 32 | ·············x·x··-·x·x··+·x·x·················0···4 | 32 | ·············x·x··-·x·x··+·x·x·················0···4 |
| 33 | ··············2·3····1·4····0·5 | 33 | ··············2·3····1·4····0·5 |
| 34 | i5·:·time·projectiveDegrees(psi,Certify=>true) | 34 | i5·:·time·projectiveDegrees(psi,Certify=>true) |
| 35 | ·--·used·0.24 | 35 | ·--·used·0.241661s·(cpu);·0.0328156s·(thread);·0s·(gc) |
| 36 | Certify:·output·certified! | 36 | Certify:·output·certified! |
| 37 | o5·=·{2,·4,·4,·2,·1} | 37 | o5·=·{2,·4,·4,·2,·1} |
| 38 | o5·:·List | 38 | o5·:·List |
| 39 | i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a·rational·octic·surface | 39 | i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a·rational·octic·surface |
| Offset 48, 21 lines modified | Offset 48, 21 lines modified | ||
| 48 | ··········300007··0···6···300007··0···6·····2·4····1·5··········0·4··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6···2·3····0·5··········1·3··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6········0·3·········1·4·········3·4·········4··········0·5·········1·5·········2·5··········3·5··········4·5·········5·········3·6··········4·6·········5·6··········0·1··········1·········0·2··········1·2·········2··········1·4··········1·5·········2·5··········0·6·········1·6·········2·6·········0··········1·········0·2·········1·2·········2·········1·4··········4·········0·5·········1·5··········2·5··········4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6·········5·6 | 48 | ··········300007··0···6···300007··0···6·····2·4····1·5··········0·4··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6···2·3····0·5··········1·3··········1·4··········4·········0·5··········1·5·········2·5··········4·5·········5··········3·6·········4·6·········5·6········0·3·········1·4·········3·4·········4··········0·5·········1·5·········2·5··········3·5··········4·5·········5·········3·6··········4·6·········5·6··········0·1··········1·········0·2··········1·2·········2··········1·4··········1·5·········2·5··········0·6·········1·6·········2·6·········0··········1·········0·2·········1·2·········2·········1·4··········4·········0·5·········1·5··········2·5··········4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6·········5·6 |
| 49 | ···············ZZ·················ZZ | 49 | ···············ZZ·················ZZ |
| 50 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] | 50 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] |
| 51 | ·············300007··0···6······300007··0···6 | 51 | ·············300007··0···6······300007··0···6 |
| 52 | i7·:·time·projectiveDegrees·phi | 52 | i7·:·time·projectiveDegrees·phi |
| 53 | ·--·used·0.00 | 53 | ·--·used·0.000775454s·(cpu);·5.0575e-05s·(thread);·0s·(gc) |
| 54 | o7·=·{1,·2,·4,·8,·8,·4,·1} | 54 | o7·=·{1,·2,·4,·8,·8,·4,·1} |
| 55 | o7·:·List | 55 | o7·:·List |
| 56 | i8·:·time·projectiveDegrees(phi,NumDegrees=>1) | 56 | i8·:·time·projectiveDegrees(phi,NumDegrees=>1) |
| 57 | ·--·used· | 57 | ·--·used·9.9096e-05s·(cpu);·2.149e-05s·(thread);·0s·(gc) |
| 58 | o8·=·{4,·1} | 58 | o8·=·{4,·1} |
| 59 | o8·:·List | 59 | o8·:·List |
| 60 | i9·:· | 60 | i9·:· |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6); | 3 | i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3-x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6); |
| 4 | ················ZZ | 4 | ················ZZ |
| 5 | o2·:·Ideal·of·-----[x·..x·] | 5 | o2·:·Ideal·of·-----[x·..x·] |
| 6 | ··············33331··0···6 | 6 | ··············33331··0···6 |
| 7 | i3·:·time·phi·=·rationalMap(V,3,2) | 7 | i3·:·time·phi·=·rationalMap(V,3,2) |
| 8 | ·--·used·0.0 | 8 | ·--·used·0.0860963s·(cpu);·0.0860586s·(thread);·0s·(gc) |
| 9 | o3·=·--·rational·map·-- | 9 | o3·=·--·rational·map·-- |
| 10 | ····················ZZ | 10 | ····················ZZ |
| 11 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 11 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 12 | ··················33331··0···1···2···3···4···5···6 | 12 | ··················33331··0···1···2···3···4···5···6 |
| 13 | ····················ZZ | 13 | ····················ZZ |
| 14 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··]) | 14 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··]) |
| Offset 18, 15 lines modified | Offset 18, 15 lines modified | ||
| 18 | ···················0·········1·········2·········3········4·········5 | 18 | ···················0·········1·········2·········3········4·········5 |
| 19 | o4·:·Ideal·of·X | 19 | o4·:·Ideal·of·X |
| 20 | i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1}; | 20 | i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1}; |
| 21 | i6·:·time·phi·=·rationalMap·D | 21 | i6·:·time·phi·=·rationalMap·D |
| 22 | ·--·used·0.0 | 22 | ·--·used·0.031973s·(cpu);·0.0319217s·(thread);·0s·(gc) |
| 23 | o6·=·--·rational·map·-- | 23 | o6·=·--·rational·map·-- |
| 24 | ··································ZZ | 24 | ··································ZZ |
| 25 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by | 25 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by |
| 26 | ································65521··0···1···2···3···4···5 | 26 | ································65521··0···1···2···3···4···5 |
| 27 | ·············{ | 27 | ·············{ |
| 28 | ·················2··················2 | 28 | ·················2··················2 |
| Offset 123, 13 lines modified | Offset 123, 13 lines modified | ||
| 123 | ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x | 123 | ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x |
| 124 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 | 124 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 |
| 125 | ·····················} | 125 | ·····················} |
| 126 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20) | 126 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20) |
| 127 | i7·:·time·?·image(phi,"F4") | 127 | i7·:·time·?·image(phi,"F4") |
| 128 | ·--·used·0. | 128 | ·--·used·0.85525s·(cpu);·0.520579s·(thread);·0s·(gc) |
| 129 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 | 129 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 |
| 130 | ·····hypersurfaces·of·degree·2 | 130 | ·····hypersurfaces·of·degree·2 |
| 131 | i8·:· | 131 | i8·:· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1330846641081 | 1 | --·-*-·M2-comint·-*-·hash:·1330846641081 |
| 2 | i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) | 2 | i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) |
| 3 | ·--·used·0. | 3 | ·--·used·0.936673s·(cpu);·0.846677s·(thread);·0s·(gc) |
| 4 | o1·=·(rational·map·defined·by·forms·of·degree·3, | 4 | o1·=·(rational·map·defined·by·forms·of·degree·3, |
| 5 | ······source·variety:·PP^3······················ | 5 | ······source·variety:·PP^3······················ |
| 6 | ······target·variety:·PP^3······················ | 6 | ······target·variety:·PP^3······················ |
| 7 | ······dominance:·true··························· | 7 | ······dominance:·true··························· |
| 8 | ······birationality:·true······················· | 8 | ······birationality:·true······················· |
| 9 | ······projective·degrees:·{1,·3,·3,·1}·········· | 9 | ······projective·degrees:·{1,·3,·3,·1}·········· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1730018912715498288 | 1 | --·-*-·M2-comint·-*-·hash:·1730018912715498288 |
| 2 | i1·:·time·specialCubicTransformation·9 | 2 | i1·:·time·specialCubicTransformation·9 |
| 3 | ·--·used·0.0 | 3 | ·--·used·0.0728556s·(cpu);·0.0727528s·(thread);·0s·(gc) |
| 4 | o1·=·--·rational·map·-- | 4 | o1·=·--·rational·map·-- |
| 5 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 5 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 6 | ······················0···1···2···3···4···5···6 | 6 | ······················0···1···2···3···4···5···6 |
| 7 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by | 7 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by |
| 8 | ····································0···1···2···3···4···5···6···7···8···9 | 8 | ····································0···1···2···3···4···5···6···7···8···9 |
| 9 | ·············{ | 9 | ·············{ |
| Offset 62, 15 lines modified | Offset 62, 15 lines modified | ||
| 62 | ······················8x·x··-·12x·x··+·24x··-·11x·x··+·17x·x·x··-·24x·x··-·10x·x··+·11x·x··-·3x··-·6x·x··+·28x·x·x··-·70x·x··-·21x·x·x··+·47x·x·x··-·13x·x··-·14x·x··+·66x·x··-·22x·x··-·20x··+·2x·x··-·2x·x·x··-·10x·x··-·11x·x·x··+·8x·x·x··-·5x·x··+·3x·x·x··+·23x·x·x··-·11x·x·x··-·12x·x··+·3x·x··-·3x·x··-·2x·x··+·3x·x··+·x··-·11x·x··+·14x·x·x··+·34x·x··-·6x·x·x··-·16x·x·x··+·3x·x··-·15x·x·x··-·66x·x·x··+·12x·x·x··+·30x·x··-·19x·x·x··+·2x·x·x··-·5x·x·x··-·2x·x·x··-·7x·x··+·6x·x··+·21x·x··-·3x·x··-·21x·x··+·x·x··+·5x··-·8x·x··+·7x·x·x··-·32x·x··-·13x·x·x··+·28x·x·x··-·9x·x··+·70x·x·x··-·27x·x·x··-·36x·x··+·x·x·x··+·4x·x·x··-·7x·x·x··-·2x·x·x··+·3x·x··-·25x·x·x··-·23x·x·x··+·4x·x·x··+·27x·x·x··-·14x·x·x··-·9x·x··-·2x·x··+·10x·x··-·6x·x··-·10x·x··+·3x·x··-·2x·x | 62 | ······················8x·x··-·12x·x··+·24x··-·11x·x··+·17x·x·x··-·24x·x··-·10x·x··+·11x·x··-·3x··-·6x·x··+·28x·x·x··-·70x·x··-·21x·x·x··+·47x·x·x··-·13x·x··-·14x·x··+·66x·x··-·22x·x··-·20x··+·2x·x··-·2x·x·x··-·10x·x··-·11x·x·x··+·8x·x·x··-·5x·x··+·3x·x·x··+·23x·x·x··-·11x·x·x··-·12x·x··+·3x·x··-·3x·x··-·2x·x··+·3x·x··+·x··-·11x·x··+·14x·x·x··+·34x·x··-·6x·x·x··-·16x·x·x··+·3x·x··-·15x·x·x··-·66x·x·x··+·12x·x·x··+·30x·x··-·19x·x·x··+·2x·x·x··-·5x·x·x··-·2x·x·x··-·7x·x··+·6x·x··+·21x·x··-·3x·x··-·21x·x··+·x·x··+·5x··-·8x·x··+·7x·x·x··-·32x·x··-·13x·x·x··+·28x·x·x··-·9x·x··+·70x·x·x··-·27x·x·x··-·36x·x··+·x·x·x··+·4x·x·x··-·7x·x·x··-·2x·x·x··+·3x·x··-·25x·x·x··-·23x·x·x··+·4x·x·x··+·27x·x·x··-·14x·x·x··-·9x·x··-·2x·x··+·10x·x··-·6x·x··-·10x·x··+·3x·x··-·2x·x |
| 63 | ························0·1······0·1······1······0·2······0·1·2······1·2······0·2······1·2·····2·····0·3······0·1·3······1·3······0·2·3······1·2·3······2·3······0·3······1·3······2·3······3·····0·4·····0·1·4······1·4······0·2·4·····1·2·4·····2·4·····0·3·4······1·3·4······2·3·4······3·4·····0·4·····1·4·····2·4·····3·4····4······0·5······0·1·5······1·5·····0·2·5······1·2·5·····2·5······0·3·5······1·3·5······2·3·5······3·5······0·4·5·····1·4·5·····2·4·5·····3·4·5·····4·5·····0·5······1·5·····2·5······3·5····4·5·····5·····0·6·····0·1·6······1·6······0·2·6······1·2·6·····2·6······1·3·6······2·3·6······3·6····0·4·6·····1·4·6·····2·4·6·····3·4·6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6······1·6·····2·6······3·6·····4·6·····5·6 | 63 | ························0·1······0·1······1······0·2······0·1·2······1·2······0·2······1·2·····2·····0·3······0·1·3······1·3······0·2·3······1·2·3······2·3······0·3······1·3······2·3······3·····0·4·····0·1·4······1·4······0·2·4·····1·2·4·····2·4·····0·3·4······1·3·4······2·3·4······3·4·····0·4·····1·4·····2·4·····3·4····4······0·5······0·1·5······1·5·····0·2·5······1·2·5·····2·5······0·3·5······1·3·5······2·3·5······3·5······0·4·5·····1·4·5·····2·4·5·····3·4·5·····4·5·····0·5······1·5·····2·5······3·5····4·5·····5·····0·6·····0·1·6······1·6······0·2·6······1·2·6·····2·6······1·3·6······2·3·6······3·6····0·4·6·····1·4·6·····2·4·6·····3·4·6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6······1·6·····2·6······3·6·····4·6·····5·6 |
| 64 | ·····················} | 64 | ·····················} |
| 65 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) | 65 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9) |
| 66 | i2·:·time·describe·oo | 66 | i2·:·time·describe·oo |
| 67 | ·--·used·0.01 | 67 | ·--·used·0.0147798s·(cpu);·0.0149229s·(thread);·0s·(gc) |
| 68 | o2·=·rational·map·defined·by·forms·of·degree·3 | 68 | o2·=·rational·map·defined·by·forms·of·degree·3 |
| 69 | ·····source·variety:·PP^6 | 69 | ·····source·variety:·PP^6 |
| 70 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 | 70 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 |
| 71 | ·····dominance:·true | 71 | ·····dominance:·true |
| 72 | ·····birationality:·true | 72 | ·····birationality:·true |
| 73 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} | 73 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1729200582376678705 | 1 | --·-*-·M2-comint·-*-·hash:·1729200582376678705 |
| 2 | i1·:·time·specialQuadraticTransformation·4 | 2 | i1·:·time·specialQuadraticTransformation·4 |
| 3 | ·--·used·0.05 | 3 | ·--·used·0.0595821s·(cpu);·0.0593365s·(thread);·0s·(gc) |
| 4 | o1·=·--·rational·map·-- | 4 | o1·=·--·rational·map·-- |
| 5 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 5 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 6 | ······················0···1···2···3···4···5···6···7···8 | 6 | ······················0···1···2···3···4···5···6···7···8 |
| 7 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by | 7 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by |
| 8 | ····································0···1···2···3···4···5···6···7···8···9 | 8 | ····································0···1···2···3···4···5···6···7···8···9 |
| 9 | ·············{ | 9 | ·············{ |
| Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
| 50 | ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x | 50 | ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x |
| 51 | ·······················0·1····0·4····3·6····4·6····6····5·7 | 51 | ·······················0·1····0·4····3·6····4·6····6····5·7 |
| 52 | ·····················} | 52 | ·····················} |
| 53 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9) | 53 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9) |
| 54 | i2·:·time·describe·oo | 54 | i2·:·time·describe·oo |
| 55 | ·--·used·0.00 | 55 | ·--·used·0.00329983s·(cpu);·0.00575038s·(thread);·0s·(gc) |
| 56 | o2·=·rational·map·defined·by·forms·of·degree·2 | 56 | o2·=·rational·map·defined·by·forms·of·degree·2 |
| 57 | ·····source·variety:·PP^8 | 57 | ·····source·variety:·PP^8 |
| 58 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 | 58 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 |
| 59 | ·····dominance:·true | 59 | ·····dominance:·true |
| 60 | ·····birationality:·true | 60 | ·····birationality:·true |
| 61 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} | 61 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} |
| Offset 7, 34 lines modified | Offset 7, 34 lines modified | ||
| 7 | i2·:·str·=·toExternalString·phi; | 7 | i2·:·str·=·toExternalString·phi; |
| 8 | i3·:·#str | 8 | i3·:·#str |
| 9 | o3·=·6927 | 9 | o3·=·6927 |
| 10 | i4·:·time·phi'·=·value·str; | 10 | i4·:·time·phi'·=·value·str; |
| 11 | ·--·used·0.0 | 11 | ·--·used·0.0880272s·(cpu);·0.0403649s·(thread);·0s·(gc) |
| 12 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4) | 12 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4) |
| 13 | i5·:·time·describe·phi' | 13 | i5·:·time·describe·phi' |
| 14 | ·--·used·0.00 | 14 | ·--·used·0.00223309s·(cpu);·0.00564086s·(thread);·0s·(gc) |
| 15 | o5·=·rational·map·defined·by·forms·of·degree·3 | 15 | o5·=·rational·map·defined·by·forms·of·degree·3 |
| 16 | ·····source·variety:·PP^3 | 16 | ·····source·variety:·PP^3 |
| 17 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 | 17 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 18 | ·····dominance:·true | 18 | ·····dominance:·true |
| 19 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 19 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 20 | ·····projective·degrees:·{1,·3,·4,·2} | 20 | ·····projective·degrees:·{1,·3,·4,·2} |
| 21 | ·····number·of·minimal·representatives:·1 | 21 | ·····number·of·minimal·representatives:·1 |
| 22 | ·····dimension·base·locus:·1 | 22 | ·····dimension·base·locus:·1 |
| 23 | ·····degree·base·locus:·5 | 23 | ·····degree·base·locus:·5 |
| 24 | ·····coefficient·ring:·ZZ/33331 | 24 | ·····coefficient·ring:·ZZ/33331 |
| 25 | i6·:·time·describe·inverse·phi' | 25 | i6·:·time·describe·inverse·phi' |
| 26 | ·--·used·0.00 | 26 | ·--·used·0.00418856s·(cpu);·0.00490979s·(thread);·0s·(gc) |
| 27 | o6·=·rational·map·defined·by·forms·of·degree·2 | 27 | o6·=·rational·map·defined·by·forms·of·degree·2 |
| 28 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 | 28 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 29 | ·····target·variety:·PP^3 | 29 | ·····target·variety:·PP^3 |
| 30 | ·····dominance:·true | 30 | ·····dominance:·true |
| 31 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 31 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 32 | ·····projective·degrees:·{2,·4,·3,·1} | 32 | ·····projective·degrees:·{2,·4,·3,·1} |
| Offset 96, 27 lines modified | Offset 96, 27 lines modified | ||
| 96 | ···············1····0·2·····1·2····0·3·····2····1·3 | 96 | ···············1····0·2·····1·2····0·3·····2····1·3 |
| 97 | o2·:·Ideal·of·GF·78125[x·..x·] | 97 | o2·:·Ideal·of·GF·78125[x·..x·] |
| 98 | ························0···4</code></pre> | 98 | ························0···4</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ChernSchwartzMacPherson·C | 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ChernSchwartzMacPherson·C |
| 102 | ·--·used·1. | 102 | ·--·used·1.37237s·(cpu);·0.925571s·(thread);·0s·(gc) |
| 103 | ·······4·····3·····2 | 103 | ·······4·····3·····2 |
| 104 | o3·=·3H··+·5H··+·3H | 104 | o3·=·3H··+·5H··+·3H |
| 105 | ·····ZZ[H] | 105 | ·····ZZ[H] |
| 106 | o3·:·----- | 106 | o3·:·----- |
| 107 | ········5 | 107 | ········5 |
| 108 | ·······H</code></pre> | 108 | ·······H</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) | 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) |
| 112 | ·--·used·2. | 112 | ·--·used·2.48176s·(cpu);·0.957935s·(thread);·0s·(gc) |
| 113 | Certify:·output·certified! | 113 | Certify:·output·certified! |
| 114 | ·······4·····3·····2 | 114 | ·······4·····3·····2 |
| 115 | o4·=·3H··+·5H··+·3H | 115 | o4·=·3H··+·5H··+·3H |
| 116 | ·····ZZ[H] | 116 | ·····ZZ[H] |
| 117 | o4·:·----- | 117 | o4·:·----- |
| Offset 154, 27 lines modified | Offset 154, 27 lines modified | ||
| 154 | ················ZZ | 154 | ················ZZ |
| 155 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] | 155 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] |
| 156 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> | 156 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·ChernClass·G | 159 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·ChernClass·G |
| 160 | ·--·used·0.1 | 160 | ·--·used·0.171453s·(cpu);·0.125004s·(thread);·0s·(gc) |
| 161 | ········9······8······7······6······5······4·····3 | 161 | ········9······8······7······6······5······4·····3 |
| 162 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 162 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 163 | ·····ZZ[H] | 163 | ·····ZZ[H] |
| 164 | o9·:·----- | 164 | o9·:·----- |
| 165 | ·······10 | 165 | ·······10 |
| 166 | ······H</code></pre> | 166 | ······H</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·ChernClass(G,Certify=>true) | 169 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·ChernClass(G,Certify=>true) |
| 170 | ·--·used·0.2 | 170 | ·--·used·0.211593s·(cpu);·0.0269365s·(thread);·0s·(gc) |
| 171 | Certify:·output·certified! | 171 | Certify:·output·certified! |
| 172 | ·········9······8······7······6······5······4·····3 | 172 | ·········9······8······7······6······5······4·····3 |
| 173 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 173 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 174 | ······ZZ[H] | 174 | ······ZZ[H] |
| 175 | o10·:·----- | 175 | o10·:·----- |
| Offset 40, 25 lines modified | Offset 40, 25 lines modified | ||
| 40 | ···············2···························2 | 40 | ···············2···························2 |
| 41 | o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·) | 41 | o2·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·) |
| 42 | ···············1····0·2·····1·2····0·3·····2····1·3 | 42 | ···············1····0·2·····1·2····0·3·····2····1·3 |
| 43 | o2·:·Ideal·of·GF·78125[x·..x·] | 43 | o2·:·Ideal·of·GF·78125[x·..x·] |
| 44 | ························0···4 | 44 | ························0···4 |
| 45 | i3·:·time·ChernSchwartzMacPherson·C | 45 | i3·:·time·ChernSchwartzMacPherson·C |
| 46 | ·--·used·1. | 46 | ·--·used·1.37237s·(cpu);·0.925571s·(thread);·0s·(gc) |
| 47 | ·······4·····3·····2 | 47 | ·······4·····3·····2 |
| 48 | o3·=·3H··+·5H··+·3H | 48 | o3·=·3H··+·5H··+·3H |
| 49 | ·····ZZ[H] | 49 | ·····ZZ[H] |
| 50 | o3·:·----- | 50 | o3·:·----- |
| 51 | ········5 | 51 | ········5 |
| 52 | ·······H | 52 | ·······H |
| 53 | i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) | 53 | i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) |
| 54 | ·--·used·2. | 54 | ·--·used·2.48176s·(cpu);·0.957935s·(thread);·0s·(gc) |
| 55 | Certify:·output·certified! | 55 | Certify:·output·certified! |
| 56 | ·······4·····3·····2 | 56 | ·······4·····3·····2 |
| 57 | o4·=·3H··+·5H··+·3H | 57 | o4·=·3H··+·5H··+·3H |
| 58 | ·····ZZ[H] | 58 | ·····ZZ[H] |
| 59 | o4·:·----- | 59 | o4·:·----- |
| Offset 89, 25 lines modified | Offset 89, 25 lines modified | ||
| 89 | ········0,2·1,3····0,1·2,3 | 89 | ········0,2·1,3····0,1·2,3 |
| 90 | ················ZZ | 90 | ················ZZ |
| 91 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p | 91 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p |
| 92 | ] | 92 | ] |
| 93 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 | 93 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 |
| 94 | i9·:·time·ChernClass·G | 94 | i9·:·time·ChernClass·G |
| 95 | ·--·used·0.1 | 95 | ·--·used·0.171453s·(cpu);·0.125004s·(thread);·0s·(gc) |
| 96 | ········9······8······7······6······5······4·····3 | 96 | ········9······8······7······6······5······4·····3 |
| 97 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 97 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 98 | ·····ZZ[H] | 98 | ·····ZZ[H] |
| 99 | o9·:·----- | 99 | o9·:·----- |
| 100 | ·······10 | 100 | ·······10 |
| 101 | ······H | 101 | ······H |
| 102 | i10·:·time·ChernClass(G,Certify=>true) | 102 | i10·:·time·ChernClass(G,Certify=>true) |
| 103 | ·--·used·0.2 | 103 | ·--·used·0.211593s·(cpu);·0.0269365s·(thread);·0s·(gc) |
| 104 | Certify:·output·certified! | 104 | Certify:·output·certified! |
| 105 | ·········9······8······7······6······5······4·····3 | 105 | ·········9······8······7······6······5······4·····3 |
| 106 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 106 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 107 | ······ZZ[H] | 107 | ······ZZ[H] |
| 108 | o10·:·----- | 108 | o10·:·----- |
| Offset 86, 21 lines modified | Offset 86, 21 lines modified | ||
| 86 | ················ZZ | 86 | ················ZZ |
| 87 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] | 87 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] |
| 88 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> | 88 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·EulerCharacteristic·I | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·EulerCharacteristic·I |
| 92 | ·--·used·0. | 92 | ·--·used·0.261286s·(cpu);·0.158778s·(thread);·0s·(gc) |
| 93 | o2·=·10</code></pre> | 93 | o2·=·10</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·EulerCharacteristic(I,Certify=>true) | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·EulerCharacteristic(I,Certify=>true) |
| 97 | ·--·used·0.2 | 97 | ·--·used·0.242871s·(cpu);·0.0360588s·(thread);·0s·(gc) |
| 98 | Certify:·output·certified! | 98 | Certify:·output·certified! |
| 99 | o3·=·10</code></pre> | 99 | o3·=·10</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ········</table> | 101 | ········</table> |
| 102 | ······</div> | 102 | ······</div> |
| 103 | ······<div> | 103 | ······<div> |
| Offset 32, 19 lines modified | Offset 32, 19 lines modified | ||
| 32 | i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181); | 32 | i1·:·I·=·Grassmannian(1,4,CoefficientRing=>ZZ/190181); |
| 33 | ················ZZ | 33 | ················ZZ |
| 34 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p | 34 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p |
| 35 | ] | 35 | ] |
| 36 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 | 36 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 |
| 37 | i2·:·time·EulerCharacteristic·I | 37 | i2·:·time·EulerCharacteristic·I |
| 38 | ·--·used·0. | 38 | ·--·used·0.261286s·(cpu);·0.158778s·(thread);·0s·(gc) |
| 39 | o2·=·10 | 39 | o2·=·10 |
| 40 | i3·:·time·EulerCharacteristic(I,Certify=>true) | 40 | i3·:·time·EulerCharacteristic(I,Certify=>true) |
| 41 | ·--·used·0.2 | 41 | ·--·used·0.242871s·(cpu);·0.0360588s·(thread);·0s·(gc) |
| 42 | Certify:·output·certified! | 42 | Certify:·output·certified! |
| 43 | o3·=·10 | 43 | o3·=·10 |
| 44 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 44 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 45 | No·test·is·made·to·see·if·the·projective·variety·is·smooth. | 45 | No·test·is·made·to·see·if·the·projective·variety·is·smooth. |
| 46 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 46 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 47 | ····*·_\x8e_\x8u_\x8l_\x8e_\x8r_\x8(_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·topological·Euler·characteristic·of·a | 47 | ····*·_\x8e_\x8u_\x8l_\x8e_\x8r_\x8(_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·topological·Euler·characteristic·of·a |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | o3·=·rational·map·defined·by·forms·of·degree·2 | 82 | o3·=·rational·map·defined·by·forms·of·degree·2 |
| 83 | ·····source·variety:·PP^5 | 83 | ·····source·variety:·PP^5 |
| 84 | ·····target·variety:·PP^5 | 84 | ·····target·variety:·PP^5 |
| 85 | ·····coefficient·ring:·QQ</code></pre> | 85 | ·····coefficient·ring:·QQ</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi!·; | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi!·; |
| 89 | ·--·used·0. | 89 | ·--·used·0.36002s·(cpu);·0.0853657s·(thread);·0s·(gc) |
| 90 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))</code></pre> | 90 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·describe·phi | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·describe·phi |
| 94 | o5·=·rational·map·defined·by·forms·of·degree·2 | 94 | o5·=·rational·map·defined·by·forms·of·degree·2 |
| Offset 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | o8·=·rational·map·defined·by·forms·of·degree·2 | 115 | o8·=·rational·map·defined·by·forms·of·degree·2 |
| 116 | ·····source·variety:·PP^4 | 116 | ·····source·variety:·PP^4 |
| 117 | ·····target·variety:·PP^5 | 117 | ·····target·variety:·PP^5 |
| 118 | ·····coefficient·ring:·QQ</code></pre> | 118 | ·····coefficient·ring:·QQ</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·phi!·; | 121 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·phi!·; |
| 122 | ·--·used·0.2 | 122 | ·--·used·0.24123s·(cpu);·0.0501771s·(thread);·0s·(gc) |
| 123 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)</code></pre> | 123 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·describe·phi | 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·describe·phi |
| 127 | o10·=·rational·map·defined·by·forms·of·degree·2 | 127 | o10·=·rational·map·defined·by·forms·of·degree·2 |
| Offset 22, 15 lines modified | Offset 22, 15 lines modified | ||
| 22 | i3·:·describe·phi | 22 | i3·:·describe·phi |
| 23 | o3·=·rational·map·defined·by·forms·of·degree·2 | 23 | o3·=·rational·map·defined·by·forms·of·degree·2 |
| 24 | ·····source·variety:·PP^5 | 24 | ·····source·variety:·PP^5 |
| 25 | ·····target·variety:·PP^5 | 25 | ·····target·variety:·PP^5 |
| 26 | ·····coefficient·ring:·QQ | 26 | ·····coefficient·ring:·QQ |
| 27 | i4·:·time·phi!·; | 27 | i4·:·time·phi!·; |
| 28 | ·--·used·0. | 28 | ·--·used·0.36002s·(cpu);·0.0853657s·(thread);·0s·(gc) |
| 29 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2)) | 29 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2)) |
| 30 | i5·:·describe·phi | 30 | i5·:·describe·phi |
| 31 | o5·=·rational·map·defined·by·forms·of·degree·2 | 31 | o5·=·rational·map·defined·by·forms·of·degree·2 |
| 32 | ·····source·variety:·PP^5 | 32 | ·····source·variety:·PP^5 |
| 33 | ·····target·variety:·PP^5 | 33 | ·····target·variety:·PP^5 |
| Offset 48, 15 lines modified | Offset 48, 15 lines modified | ||
| 48 | i8·:·describe·phi | 48 | i8·:·describe·phi |
| 49 | o8·=·rational·map·defined·by·forms·of·degree·2 | 49 | o8·=·rational·map·defined·by·forms·of·degree·2 |
| 50 | ·····source·variety:·PP^4 | 50 | ·····source·variety:·PP^4 |
| 51 | ·····target·variety:·PP^5 | 51 | ·····target·variety:·PP^5 |
| 52 | ·····coefficient·ring:·QQ | 52 | ·····coefficient·ring:·QQ |
| 53 | i9·:·time·phi!·; | 53 | i9·:·time·phi!·; |
| 54 | ·--·used·0.2 | 54 | ·--·used·0.24123s·(cpu);·0.0501771s·(thread);·0s·(gc) |
| 55 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5) | 55 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5) |
| 56 | i10·:·describe·phi | 56 | i10·:·describe·phi |
| 57 | o10·=·rational·map·defined·by·forms·of·degree·2 | 57 | o10·=·rational·map·defined·by·forms·of·degree·2 |
| 58 | ······source·variety:·PP^4 | 58 | ······source·variety:·PP^4 |
| 59 | ······target·variety:·PP^5 | 59 | ······target·variety:·PP^5 |
| Offset 146, 15 lines modified | Offset 146, 15 lines modified | ||
| 146 | ·····----------*v,·x·+·----------*v) | 146 | ·····----------*v,·x·+·----------*v) |
| 147 | ······d*e·-·a*f·········d*e·-·a*f | 147 | ······d*e·-·a*f·········d*e·-·a*f |
| 148 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> | 148 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> |
| 149 | </td>··········</tr> | 149 | </td>··········</tr> |
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi^**·q | 151 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi^**·q |
| 152 | ·--·used·0. | 152 | ·--·used·0.221078s·(cpu);·0.166008s·(thread);·0s·(gc) |
| 153 | ················-e········-d········-c········-b········-a | 153 | ················-e········-d········-c········-b········-a |
| 154 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) | 154 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) |
| 155 | ·················f·········f·········f·········f·········f | 155 | ·················f·········f·········f·········f·········f |
| 156 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> | 156 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | ··············2·················2 | 83 | ··············2·················2 |
| 84 | ·····-·a*c·+·e·········-·b*c·+·f | 84 | ·····-·a*c·+·e·········-·b*c·+·f |
| 85 | ·····----------*v,·x·+·----------*v) | 85 | ·····----------*v,·x·+·----------*v) |
| 86 | ······d*e·-·a*f·········d*e·-·a*f | 86 | ······d*e·-·a*f·········d*e·-·a*f |
| 87 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] | 87 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] |
| 88 | i6·:·time·phi^**·q | 88 | i6·:·time·phi^**·q |
| 89 | ·--·used·0. | 89 | ·--·used·0.221078s·(cpu);·0.166008s·(thread);·0s·(gc) |
| 90 | ················-e········-d········-c········-b········-a | 90 | ················-e········-d········-c········-b········-a |
| 91 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) | 91 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) |
| 92 | ·················f·········f·········f·········f·········f | 92 | ·················f·········f·········f·········f·········f |
| 93 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] | 93 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v] |
| 94 | i7·:·oo·==·p | 94 | i7·:·oo·==·p |
| Offset 131, 52 lines modified | Offset 131, 52 lines modified | ||
| 131 | o3·:·Ideal·of·------------------------------------------------------------------------------------------------------------------------- | 131 | o3·:·Ideal·of·------------------------------------------------------------------------------------------------------------------------- |
| 132 | ···············2·2················2·2········································2·2····················································2·2 | 132 | ···············2·2················2·2········································2·2····················································2·2 |
| 133 | ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x | 133 | ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x··+·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x |
| 134 | ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7</code></pre> | 134 | ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1·6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·SegreClass·X | 137 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·SegreClass·X |
| 138 | ·--·used·0. | 138 | ·--·used·0.499862s·(cpu);·0.414248s·(thread);·0s·(gc) |
| 139 | ··········7········6·······5·······4······3 | 139 | ··········7········6·······5·······4······3 |
| 140 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H | 140 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 141 | ·····ZZ[H] | 141 | ·····ZZ[H] |
| 142 | o4·:·----- | 142 | o4·:·----- |
| 143 | ········8 | 143 | ········8 |
| 144 | ·······H</code></pre> | 144 | ·······H</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·SegreClass·lift(X,P7) | 147 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·SegreClass·lift(X,P7) |
| 148 | ·--·used·0.2 | 148 | ·--·used·0.28225s·(cpu);·0.237108s·(thread);·0s·(gc) |
| 149 | ··········7········6·······5······4······3 | 149 | ··········7········6·······5······4······3 |
| 150 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H | 150 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 151 | ·····ZZ[H] | 151 | ·····ZZ[H] |
| 152 | o5·:·----- | 152 | o5·:·----- |
| 153 | ········8 | 153 | ········8 |
| 154 | ·······H</code></pre> | 154 | ·······H</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·SegreClass(X,Certify=>true) | 157 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·SegreClass(X,Certify=>true) |
| 158 | ·--·used·0.2 | 158 | ·--·used·0.228484s·(cpu);·0.0406714s·(thread);·0s·(gc) |
| 159 | Certify:·output·certified! | 159 | Certify:·output·certified! |
| 160 | ··········7········6·······5·······4······3 | 160 | ··········7········6·······5·······4······3 |
| 161 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H | 161 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 162 | ·····ZZ[H] | 162 | ·····ZZ[H] |
| 163 | o6·:·----- | 163 | o6·:·----- |
| 164 | ········8 | 164 | ········8 |
| 165 | ·······H</code></pre> | 165 | ·······H</code></pre> |
| 166 | </td>··········</tr> | 166 | </td>··········</tr> |
| 167 | ··········<tr> | 167 | ··········<tr> |
| 168 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·SegreClass(lift(X,P7),Certify=>true) | 168 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·SegreClass(lift(X,P7),Certify=>true) |
| 169 | ·--·used·0. | 169 | ·--·used·0.400211s·(cpu);·0.150632s·(thread);·0s·(gc) |
| 170 | Certify:·output·certified! | 170 | Certify:·output·certified! |
| 171 | ··········7········6·······5······4······3 | 171 | ··········7········6·······5······4······3 |
| 172 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H | 172 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 173 | ·····ZZ[H] | 173 | ·····ZZ[H] |
| 174 | o7·:·----- | 174 | o7·:·----- |
| Offset 198, 15 lines modified | Offset 198, 15 lines modified | ||
| 198 | o9·=·------[x·..x·] | 198 | o9·=·------[x·..x·] |
| 199 | ·····100003··0···6 | 199 | ·····100003··0···6 |
| 200 | o9·:·PolynomialRing</code></pre> | 200 | o9·:·PolynomialRing</code></pre> |
| 201 | </td>··········</tr> | 201 | </td>··········</tr> |
| 202 | ··········<tr> | 202 | ··········<tr> |
| 203 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2) | 203 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5},{x_1,x_2,x_4,x_5,x_6}}),Dominant=>2) |
| 204 | ·--·used·0.0 | 204 | ·--·used·0.0642405s·(cpu);·0.064913s·(thread);·0s·(gc) |
| 205 | ························································ZZ | 205 | ························································ZZ |
| 206 | ······················································------[y·..y·] | 206 | ······················································------[y·..y·] |
| 207 | ······················································100003··0···9················································ZZ··············2······························2 | 207 | ······················································100003··0···9················································ZZ··············2······························2 |
| 208 | o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·}) | 208 | o10·=·map·(----------------------------------------------------------------------------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y·,·y··-·y·y··-·y·y·,·y·y··+·y·y··-·y·y·,·y·y··-·y·y·,·y·y··-·y·y··-·y·y·,·y·y··-·y·y··-·y·y·}) |
| 209 | ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9 | 209 | ···········(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)··100003··0···6·····3····0·5····1·6···3·4····1·7···4····2·7····0·9···2·5····3·5····1·8···4·5····1·9···4·8····2·9····3·9···7·8····4·9····6·9 |
| 210 | ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 | 210 | ·············5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5 |
| Offset 216, 15 lines modified | Offset 216, 15 lines modified | ||
| 216 | ·························································100003··0···9···················································ZZ | 216 | ·························································100003··0···9···················································ZZ |
| 217 | o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·] | 217 | o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·] |
| 218 | ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6 | 218 | ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6 |
| 219 | ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre> | 219 | ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre> |
| 220 | </td>··········</tr> | 220 | </td>··········</tr> |
| 221 | ··········<tr> | 221 | ··········<tr> |
| 222 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·SegreClass·phi | 222 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·SegreClass·phi |
| 223 | ·--·used·0. | 223 | ·--·used·0.331994s·(cpu);·0.217052s·(thread);·0s·(gc) |
| 224 | ·········9······8······7······6·····5 | 224 | ·········9······8······7······6·····5 |
| 225 | o11·=·23H··-·42H··+·36H··-·22H··+·9H | 225 | o11·=·23H··-·42H··+·36H··-·22H··+·9H |
| 226 | ······ZZ[H] | 226 | ······ZZ[H] |
| 227 | o11·:·----- | 227 | o11·:·----- |
| 228 | ········10 | 228 | ········10 |
| Offset 246, 28 lines modified | Offset 246, 28 lines modified | ||
| 246 | o12·:·Ideal·of·---------------------------------------------------------------------------------------------------- | 246 | o12·:·Ideal·of·---------------------------------------------------------------------------------------------------- |
| 247 | ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) | 247 | ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) |
| 248 | ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre> | 248 | ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6····1·7····0·8···2·3····1·4····0·5</code></pre> |
| 249 | </td>··········</tr> | 249 | </td>··········</tr> |
| 250 | ··········<tr> | 250 | ··········<tr> |
| 251 | <td>··············<pre><code·class="language-macaulay2">i13·:·--·Segre·class·of·B·in·G(1,4) | 251 | <td>··············<pre><code·class="language-macaulay2">i13·:·--·Segre·class·of·B·in·G(1,4) |
| 252 | ······time·SegreClass·B | 252 | ······time·SegreClass·B |
| 253 | ·--·used·0.2 | 253 | ·--·used·0.281258s·(cpu);·0.22194s·(thread);·0s·(gc) |
| 254 | ·········9······8······7······6·····5 | 254 | ·········9······8······7······6·····5 |
| 255 | o13·=·23H··-·42H··+·36H··-·22H··+·9H | 255 | o13·=·23H··-·42H··+·36H··-·22H··+·9H |
| 256 | ······ZZ[H] | 256 | ······ZZ[H] |
| 257 | o13·:·----- | 257 | o13·:·----- |
| 258 | ········10 | 258 | ········10 |
| 259 | ·······H</code></pre> | 259 | ·······H</code></pre> |
| 260 | </td>··········</tr> | 260 | </td>··········</tr> |
| 261 | ··········<tr> | 261 | ··········<tr> |
| 262 | <td>··············<pre><code·class="language-macaulay2">i14·:·--·Segre·class·of·B·in·P^9 | 262 | <td>··············<pre><code·class="language-macaulay2">i14·:·--·Segre·class·of·B·in·P^9 |
| 263 | ······time·SegreClass·lift(B,ambient·ring·B) | 263 | ······time·SegreClass·lift(B,ambient·ring·B) |
| 264 | ·--·used·0. | 264 | ·--·used·0.918915s·(cpu);·0.732797s·(thread);·0s·(gc) |
| 265 | ···········9·······8·······7······6·····5 | 265 | ···········9·······8·······7······6·····5 |
| 266 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H | 266 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H |
| 267 | ······ZZ[H] | 267 | ······ZZ[H] |
| 268 | o14·:·----- | 268 | o14·:·----- |
| 269 | ········10 | 269 | ········10 |
| Offset 82, 46 lines modified | Offset 82, 46 lines modified | ||
| 82 | ···············2·2················2·2········································2 | 82 | ···············2·2················2·2········································2 |
| 83 | 2····················································2·2 | 83 | 2····················································2·2 |
| 84 | ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x | 84 | ··············x·x··-·2x·x·x·x··+·x·x··-·2x·x·x·x··-·2x·x·x·x··+·4x·x·x·x··+·x·x |
| 85 | +·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x | 85 | +·4x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··-·2x·x·x·x··+·x·x |
| 86 | ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1 | 86 | ···············3·4·····2·3·4·5····2·5·····1·3·4·6·····1·2·5·6·····0·3·5·6····1 |
| 87 | 6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7 | 87 | 6·····1·2·4·7·····0·3·4·7·····0·2·5·7·····0·1·6·7····0·7 |
| 88 | i4·:·time·SegreClass·X | 88 | i4·:·time·SegreClass·X |
| 89 | ·--·used·0. | 89 | ·--·used·0.499862s·(cpu);·0.414248s·(thread);·0s·(gc) |
| 90 | ··········7········6·······5·······4······3 | 90 | ··········7········6·······5·······4······3 |
| 91 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H | 91 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 92 | ·····ZZ[H] | 92 | ·····ZZ[H] |
| 93 | o4·:·----- | 93 | o4·:·----- |
| 94 | ········8 | 94 | ········8 |
| 95 | ·······H | 95 | ·······H |
| 96 | i5·:·time·SegreClass·lift(X,P7) | 96 | i5·:·time·SegreClass·lift(X,P7) |
| 97 | ·--·used·0.2 | 97 | ·--·used·0.28225s·(cpu);·0.237108s·(thread);·0s·(gc) |
| 98 | ··········7········6·······5······4······3 | 98 | ··········7········6·······5······4······3 |
| 99 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H | 99 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 100 | ·····ZZ[H] | 100 | ·····ZZ[H] |
| 101 | o5·:·----- | 101 | o5·:·----- |
| 102 | ········8 | 102 | ········8 |
| 103 | ·······H | 103 | ·······H |
| 104 | i6·:·time·SegreClass(X,Certify=>true) | 104 | i6·:·time·SegreClass(X,Certify=>true) |
| 105 | ·--·used·0.2 | 105 | ·--·used·0.228484s·(cpu);·0.0406714s·(thread);·0s·(gc) |
| 106 | Certify:·output·certified! | 106 | Certify:·output·certified! |
| 107 | ··········7········6·······5·······4······3 | 107 | ··········7········6·······5·······4······3 |
| 108 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H | 108 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 109 | ·····ZZ[H] | 109 | ·····ZZ[H] |
| 110 | o6·:·----- | 110 | o6·:·----- |
| 111 | ········8 | 111 | ········8 |
| 112 | ·······H | 112 | ·······H |
| 113 | i7·:·time·SegreClass(lift(X,P7),Certify=>true) | 113 | i7·:·time·SegreClass(lift(X,P7),Certify=>true) |
| 114 | ·--·used·0. | 114 | ·--·used·0.400211s·(cpu);·0.150632s·(thread);·0s·(gc) |
| 115 | Certify:·output·certified! | 115 | Certify:·output·certified! |
| 116 | ··········7········6·······5······4······3 | 116 | ··········7········6·······5······4······3 |
| 117 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H | 117 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 118 | ·····ZZ[H] | 118 | ·····ZZ[H] |
| 119 | o7·:·----- | 119 | o7·:·----- |
| Offset 142, 15 lines modified | Offset 142, 15 lines modified | ||
| 142 | ·······ZZ | 142 | ·······ZZ |
| 143 | o9·=·------[x·..x·] | 143 | o9·=·------[x·..x·] |
| 144 | ·····100003··0···6 | 144 | ·····100003··0···6 |
| 145 | o9·:·PolynomialRing | 145 | o9·:·PolynomialRing |
| 146 | i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5}, | 146 | i10·:·time·phi·=·inverseMap·toMap(minors(2,matrix{{x_0,x_1,x_3,x_4,x_5}, |
| 147 | {x_1,x_2,x_4,x_5,x_6}}),Dominant=>2) | 147 | {x_1,x_2,x_4,x_5,x_6}}),Dominant=>2) |
| 148 | ·--·used·0.0 | 148 | ·--·used·0.0642405s·(cpu);·0.064913s·(thread);·0s·(gc) |
| 149 | ························································ZZ | 149 | ························································ZZ |
| 150 | ······················································------[y·..y·] | 150 | ······················································------[y·..y·] |
| 151 | ······················································100003··0···9 | 151 | ······················································100003··0···9 |
| 152 | ZZ··············2······························2 | 152 | ZZ··············2······························2 |
| 153 | o10·=·map·(-------------------------------------------------------------------- | 153 | o10·=·map·(-------------------------------------------------------------------- |
| 154 | --------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y | 154 | --------------------------------,·------[x·..x·],·{y··-·y·y··-·y·y·,·y·y··-·y·y |
| Offset 170, 15 lines modified | Offset 170, 15 lines modified | ||
| 170 | o10·:·RingMap·----------------------------------------------------------------- | 170 | o10·:·RingMap·----------------------------------------------------------------- |
| 171 | -----------------------------------·<--·------[x·..x·] | 171 | -----------------------------------·<--·------[x·..x·] |
| 172 | ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y | 172 | ··············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y |
| 173 | -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6 | 173 | -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·)·····100003··0···6 |
| 174 | ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6 | 174 | ················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2·6 |
| 175 | 1·7····0·8···2·3····1·4····0·5 | 175 | 1·7····0·8···2·3····1·4····0·5 |
| 176 | i11·:·time·SegreClass·phi | 176 | i11·:·time·SegreClass·phi |
| 177 | ·--·used·0. | 177 | ·--·used·0.331994s·(cpu);·0.217052s·(thread);·0s·(gc) |
| 178 | ·········9······8······7······6·····5 | 178 | ·········9······8······7······6·····5 |
| 179 | o11·=·23H··-·42H··+·36H··-·22H··+·9H | 179 | o11·=·23H··-·42H··+·36H··-·22H··+·9H |
| 180 | ······ZZ[H] | 180 | ······ZZ[H] |
| 181 | o11·:·----- | 181 | o11·:·----- |
| 182 | ········10 | 182 | ········10 |
| Offset 199, 26 lines modified | Offset 199, 26 lines modified | ||
| 199 | ------------------------------------ | 199 | ------------------------------------ |
| 200 | ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y | 200 | ···············(y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·,·y·y |
| 201 | -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) | 201 | -·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) |
| 202 | ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2 | 202 | ·················5·7····4·8····2·9···5·6····3·8····1·9···4·6····3·7····0·9···2 |
| 203 | 6····1·7····0·8···2·3····1·4····0·5 | 203 | 6····1·7····0·8···2·3····1·4····0·5 |
| 204 | i13·:·--·Segre·class·of·B·in·G(1,4) | 204 | i13·:·--·Segre·class·of·B·in·G(1,4) |
| 205 | ······time·SegreClass·B | 205 | ······time·SegreClass·B |
| 206 | ·--·used·0.2 | 206 | ·--·used·0.281258s·(cpu);·0.22194s·(thread);·0s·(gc) |
| 207 | ·········9······8······7······6·····5 | 207 | ·········9······8······7······6·····5 |
| 208 | o13·=·23H··-·42H··+·36H··-·22H··+·9H | 208 | o13·=·23H··-·42H··+·36H··-·22H··+·9H |
| 209 | ······ZZ[H] | 209 | ······ZZ[H] |
| 210 | o13·:·----- | 210 | o13·:·----- |
| 211 | ········10 | 211 | ········10 |
| 212 | ·······H | 212 | ·······H |
| 213 | i14·:·--·Segre·class·of·B·in·P^9 | 213 | i14·:·--·Segre·class·of·B·in·P^9 |
| 214 | ······time·SegreClass·lift(B,ambient·ring·B) | 214 | ······time·SegreClass·lift(B,ambient·ring·B) |
| 215 | ·--·used·0. | 215 | ·--·used·0.918915s·(cpu);·0.732797s·(thread);·0s·(gc) |
| 216 | ···········9·······8·······7······6·····5 | 216 | ···········9·······8·······7······6·····5 |
| 217 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H | 217 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H |
| 218 | ······ZZ[H] | 218 | ······ZZ[H] |
| 219 | o14·:·----- | 219 | o14·:·----- |
| 220 | ········10 | 220 | ········10 |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | o3·=·QQ[u·..u·] | 97 | o3·=·QQ[u·..u·] |
| 98 | ·········0···5 | 98 | ·········0···5 |
| 99 | o3·:·PolynomialRing</code></pre> | 99 | o3·:·PolynomialRing</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·psi·=·abstractRationalMap(P4,P5,f) | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·psi·=·abstractRationalMap(P4,P5,f) |
| 103 | ·--·used·0.00 | 103 | ·--·used·0.00322296s·(cpu);·0.000310733s·(thread);·0s·(gc) |
| 104 | o4·=·--·rational·map·-- | 104 | o4·=·--·rational·map·-- |
| 105 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 105 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 106 | ······················0···1···2···3···4 | 106 | ······················0···1···2···3···4 |
| 107 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 107 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 108 | ······················0···1···2···3···4···5 | 108 | ······················0···1···2···3···4···5 |
| 109 | ·····defining·forms:·given·by·a·function | 109 | ·····defining·forms:·given·by·a·function |
| Offset 113, 21 lines modified | Offset 113, 21 lines modified | ||
| 113 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)</code></pre> | 113 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ········</table> | 115 | ········</table> |
| 116 | ········<p>Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">psi</span>·and·then·the·corresponding·concrete·rational·map.</p> | 116 | ········<p>Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">psi</span>·and·then·the·corresponding·concrete·rational·map.</p> |
| 117 | ········<table·class="examples"> | 117 | ········<table·class="examples"> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,3) | 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,3) |
| 120 | ·--·used·0.1 | 120 | ·--·used·0.191268s·(cpu);·0.142661s·(thread);·0s·(gc) |
| 121 | o5·=·2</code></pre> | 121 | o5·=·2</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·rationalMap·psi | 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·rationalMap·psi |
| 125 | ·--·used·0. | 125 | ·--·used·0.341785s·(cpu);·0.299419s·(thread);·0s·(gc) |
| 126 | o6·=·--·rational·map·-- | 126 | o6·=·--·rational·map·-- |
| 127 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 127 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 128 | ······················0···1···2···3···4 | 128 | ······················0···1···2···3···4 |
| 129 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 129 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 130 | ······················0···1···2···3···4···5 | 130 | ······················0···1···2···3···4···5 |
| 131 | ·····defining·forms:·{ | 131 | ·····defining·forms:·{ |
| Offset 211, 15 lines modified | Offset 211, 15 lines modified | ||
| 211 | ·················ZZ | 211 | ·················ZZ |
| 212 | o13·:·Ideal·of·-----[x·..x·] | 212 | o13·:·Ideal·of·-----[x·..x·] |
| 213 | ···············65521··0···3</code></pre> | 213 | ···············65521··0···3</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ··········<tr> | 215 | ··········<tr> |
| 216 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·T·=·abstractRationalMap(I,"OADP") | 216 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·T·=·abstractRationalMap(I,"OADP") |
| 217 | ·--·used·0.03 | 217 | ·--·used·0.0360003s·(cpu);·0.0344904s·(thread);·0s·(gc) |
| 218 | o14·=·--·rational·map·-- | 218 | o14·=·--·rational·map·-- |
| 219 | ·····················ZZ | 219 | ·····················ZZ |
| 220 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 220 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 221 | ···················65521··0···1···2···3 | 221 | ···················65521··0···1···2···3 |
| 222 | ·····················ZZ | 222 | ·····················ZZ |
| 223 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 223 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| Offset 229, 39 lines modified | Offset 229, 39 lines modified | ||
| 229 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> | 229 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> |
| 230 | </td>··········</tr> | 230 | </td>··········</tr> |
| 231 | ········</table> | 231 | ········</table> |
| 232 | ········<p>The·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">T</span>·can·be·obtained·by·the·following·command:</p> | 232 | ········<p>The·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">T</span>·can·be·obtained·by·the·following·command:</p> |
| 233 | ········<table·class="examples"> | 233 | ········<table·class="examples"> |
| 234 | ··········<tr> | 234 | ··········<tr> |
| 235 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·projectiveDegrees(T,2) | 235 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·projectiveDegrees(T,2) |
| 236 | ·--·used·2. | 236 | ·--·used·2.63059s·(cpu);·1.66126s·(thread);·0s·(gc) |
| 237 | o15·=·3</code></pre> | 237 | o15·=·3</code></pre> |
| 238 | </td>··········</tr> | 238 | </td>··········</tr> |
| 239 | ········</table> | 239 | ········</table> |
| 240 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·is·defined·by·linear·forms:</p> | 240 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·is·defined·by·linear·forms:</p> |
| 241 | ········<table·class="examples"> | 241 | ········<table·class="examples"> |
| 242 | ··········<tr> | 242 | ··········<tr> |
| 243 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·T2·=·T·*·T | 243 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·T2·=·T·*·T |
| 244 | ·--·used·0.0001 | 244 | ·--·used·0.00014931s·(cpu);·1.9707e-05s·(thread);·0s·(gc) |
| 245 | o16·=·--·rational·map·-- | 245 | o16·=·--·rational·map·-- |
| 246 | ·····················ZZ | 246 | ·····················ZZ |
| 247 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 247 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 248 | ···················65521··0···1···2···3 | 248 | ···················65521··0···1···2···3 |
| 249 | ·····················ZZ | 249 | ·····················ZZ |
| 250 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 250 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| 251 | ···················65521··0···1···2···3 | 251 | ···················65521··0···1···2···3 |
| 252 | ······defining·forms:·given·by·a·function | 252 | ······defining·forms:·given·by·a·function |
| 253 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> | 253 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> |
| 254 | </td>··········</tr> | 254 | </td>··········</tr> |
| 255 | ··········<tr> | 255 | ··········<tr> |
| 256 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·projectiveDegrees(T2,2) | 256 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·projectiveDegrees(T2,2) |
| 257 | ·--·used· | 257 | ·--·used·4.00796s·(cpu);·2.53047s·(thread);·0s·(gc) |
| 258 | o17·=·1</code></pre> | 258 | o17·=·1</code></pre> |
| 259 | </td>··········</tr> | 259 | </td>··········</tr> |
| 260 | ········</table> | 260 | ········</table> |
| 261 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·leaves·a·random·point·fixed:</p> | 261 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·leaves·a·random·point·fixed:</p> |
| 262 | ········<table·class="examples"> | 262 | ········<table·class="examples"> |
| 263 | ··········<tr> | 263 | ··········<tr> |
| Offset 286, 15 lines modified | Offset 286, 15 lines modified | ||
| 286 | o20·:·List</code></pre> | 286 | o20·:·List</code></pre> |
| 287 | </td>··········</tr> | 287 | </td>··········</tr> |
| 288 | ········</table> | 288 | ········</table> |
| 289 | ········<p>We·now·compute·the·concrete·rational·map·corresponding·to·<span·class="tt">T</span>:</p> | 289 | ········<p>We·now·compute·the·concrete·rational·map·corresponding·to·<span·class="tt">T</span>:</p> |
| 290 | ········<table·class="examples"> | 290 | ········<table·class="examples"> |
| 291 | ··········<tr> | 291 | ··········<tr> |
| 292 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f·=·rationalMap·T | 292 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f·=·rationalMap·T |
| 293 | ·--·used· | 293 | ·--·used·3.53929s·(cpu);·2.34378s·(thread);·0s·(gc) |
| 294 | o21·=·--·rational·map·-- | 294 | o21·=·--·rational·map·-- |
| 295 | ·····················ZZ | 295 | ·····················ZZ |
| 296 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 296 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 297 | ···················65521··0···1···2···3 | 297 | ···················65521··0···1···2···3 |
| 298 | ·····················ZZ | 298 | ·····················ZZ |
| 299 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 299 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| Offset 36, 32 lines modified | Offset 36, 32 lines modified | ||
| 36 | i3·:·P5·:=·QQ[u_0..u_5] | 36 | i3·:·P5·:=·QQ[u_0..u_5] |
| 37 | o3·=·QQ[u·..u·] | 37 | o3·=·QQ[u·..u·] |
| 38 | ·········0···5 | 38 | ·········0···5 |
| 39 | o3·:·PolynomialRing | 39 | o3·:·PolynomialRing |
| 40 | i4·:·time·psi·=·abstractRationalMap(P4,P5,f) | 40 | i4·:·time·psi·=·abstractRationalMap(P4,P5,f) |
| 41 | ·--·used·0.00 | 41 | ·--·used·0.00322296s·(cpu);·0.000310733s·(thread);·0s·(gc) |
| 42 | o4·=·--·rational·map·-- | 42 | o4·=·--·rational·map·-- |
| 43 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 43 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 44 | ······················0···1···2···3···4 | 44 | ······················0···1···2···3···4 |
| 45 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 45 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 46 | ······················0···1···2···3···4···5 | 46 | ······················0···1···2···3···4···5 |
| 47 | ·····defining·forms:·given·by·a·function | 47 | ·····defining·forms:·given·by·a·function |
| 48 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5) | 48 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5) |
| 49 | Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·psi·and | 49 | Now·we·compute·first·the·degree·of·the·forms·defining·the·abstract·map·psi·and |
| 50 | then·the·corresponding·concrete·rational·map. | 50 | then·the·corresponding·concrete·rational·map. |
| 51 | i5·:·time·projectiveDegrees(psi,3) | 51 | i5·:·time·projectiveDegrees(psi,3) |
| 52 | ·--·used·0.1 | 52 | ·--·used·0.191268s·(cpu);·0.142661s·(thread);·0s·(gc) |
| 53 | o5·=·2 | 53 | o5·=·2 |
| 54 | i6·:·time·rationalMap·psi | 54 | i6·:·time·rationalMap·psi |
| 55 | ·--·used·0. | 55 | ·--·used·0.341785s·(cpu);·0.299419s·(thread);·0s·(gc) |
| 56 | o6·=·--·rational·map·-- | 56 | o6·=·--·rational·map·-- |
| 57 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 57 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 58 | ······················0···1···2···3···4 | 58 | ······················0···1···2···3···4 |
| 59 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 59 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 60 | ······················0···1···2···3···4···5 | 60 | ······················0···1···2···3···4···5 |
| 61 | ·····defining·forms:·{ | 61 | ·····defining·forms:·{ |
| Offset 140, 48 lines modified | Offset 140, 48 lines modified | ||
| 140 | o13·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·) | 140 | o13·=·ideal·(-·x··+·x·x·,·-·x·x··+·x·x·,·-·x··+·x·x·) |
| 141 | ················1····0·2·····1·2····0·3·····2····1·3 | 141 | ················1····0·2·····1·2····0·3·····2····1·3 |
| 142 | ·················ZZ | 142 | ·················ZZ |
| 143 | o13·:·Ideal·of·-----[x·..x·] | 143 | o13·:·Ideal·of·-----[x·..x·] |
| 144 | ···············65521··0···3 | 144 | ···············65521··0···3 |
| 145 | i14·:·time·T·=·abstractRationalMap(I,"OADP") | 145 | i14·:·time·T·=·abstractRationalMap(I,"OADP") |
| 146 | ·--·used·0.03 | 146 | ·--·used·0.0360003s·(cpu);·0.0344904s·(thread);·0s·(gc) |
| 147 | o14·=·--·rational·map·-- | 147 | o14·=·--·rational·map·-- |
| 148 | ·····················ZZ | 148 | ·····················ZZ |
| 149 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 149 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 150 | ···················65521··0···1···2···3 | 150 | ···················65521··0···1···2···3 |
| 151 | ·····················ZZ | 151 | ·····················ZZ |
| 152 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 152 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| 153 | ···················65521··0···1···2···3 | 153 | ···················65521··0···1···2···3 |
| 154 | ······defining·forms:·given·by·a·function | 154 | ······defining·forms:·given·by·a·function |
| 155 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) | 155 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) |
| 156 | The·degree·of·the·forms·defining·the·abstract·map·T·can·be·obtained·by·the | 156 | The·degree·of·the·forms·defining·the·abstract·map·T·can·be·obtained·by·the |
| 157 | following·command: | 157 | following·command: |
| 158 | i15·:·time·projectiveDegrees(T,2) | 158 | i15·:·time·projectiveDegrees(T,2) |
| 159 | ·--·used·2. | 159 | ·--·used·2.63059s·(cpu);·1.66126s·(thread);·0s·(gc) |
| 160 | o15·=·3 | 160 | o15·=·3 |
| 161 | We·verify·that·the·composition·of·T·with·itself·is·defined·by·linear·forms: | 161 | We·verify·that·the·composition·of·T·with·itself·is·defined·by·linear·forms: |
| 162 | i16·:·time·T2·=·T·*·T | 162 | i16·:·time·T2·=·T·*·T |
| 163 | ·--·used·0.0001 | 163 | ·--·used·0.00014931s·(cpu);·1.9707e-05s·(thread);·0s·(gc) |
| 164 | o16·=·--·rational·map·-- | 164 | o16·=·--·rational·map·-- |
| 165 | ·····················ZZ | 165 | ·····················ZZ |
| 166 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 166 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 167 | ···················65521··0···1···2···3 | 167 | ···················65521··0···1···2···3 |
| 168 | ·····················ZZ | 168 | ·····················ZZ |
| 169 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 169 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| 170 | ···················65521··0···1···2···3 | 170 | ···················65521··0···1···2···3 |
| 171 | ······defining·forms:·given·by·a·function | 171 | ······defining·forms:·given·by·a·function |
| 172 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) | 172 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3) |
| 173 | i17·:·time·projectiveDegrees(T2,2) | 173 | i17·:·time·projectiveDegrees(T2,2) |
| 174 | ·--·used· | 174 | ·--·used·4.00796s·(cpu);·2.53047s·(thread);·0s·(gc) |
| 175 | o17·=·1 | 175 | o17·=·1 |
| 176 | We·verify·that·the·composition·of·T·with·itself·leaves·a·random·point·fixed: | 176 | We·verify·that·the·composition·of·T·with·itself·leaves·a·random·point·fixed: |
| 177 | i18·:·p·=·apply(3,i->random(ZZ/65521))|{1} | 177 | i18·:·p·=·apply(3,i->random(ZZ/65521))|{1} |
| 178 | o18·=·{28963,·31975,·-30172,·1} | 178 | o18·=·{28963,·31975,·-30172,·1} |
| Offset 194, 15 lines modified | Offset 194, 15 lines modified | ||
| 194 | i20·:·T·q | 194 | i20·:·T·q |
| 195 | o20·=·{28963,·31975,·-30172,·1} | 195 | o20·=·{28963,·31975,·-30172,·1} |
| 196 | o20·:·List | 196 | o20·:·List |
| 197 | We·now·compute·the·concrete·rational·map·corresponding·to·T: | 197 | We·now·compute·the·concrete·rational·map·corresponding·to·T: |
| 198 | i21·:·time·f·=·rationalMap·T | 198 | i21·:·time·f·=·rationalMap·T |
| 199 | ·--·used· | 199 | ·--·used·3.53929s·(cpu);·2.34378s·(thread);·0s·(gc) |
| 200 | o21·=·--·rational·map·-- | 200 | o21·=·--·rational·map·-- |
| 201 | ·····················ZZ | 201 | ·····················ZZ |
| 202 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 202 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 203 | ···················65521··0···1···2···3 | 203 | ···················65521··0···1···2···3 |
| 204 | ·····················ZZ | 204 | ·····················ZZ |
| 205 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 205 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 129 | ·······················1·2····0·4 | 129 | ·······················1·2····0·4 |
| 130 | ·····················} | 130 | ·····················} |
| 131 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)</code></pre> | 131 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·psi·=·approximateInverseMap·phi | 134 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·psi·=·approximateInverseMap·phi |
| 135 | ·--·used·0. | 135 | ·--·used·0.241364s·(cpu);·0.204377s·(thread);·0s·(gc) |
| 136 | --·approximateInverseMap:·step·1·of·10 | 136 | --·approximateInverseMap:·step·1·of·10 |
| 137 | --·approximateInverseMap:·step·2·of·10 | 137 | --·approximateInverseMap:·step·2·of·10 |
| 138 | --·approximateInverseMap:·step·3·of·10 | 138 | --·approximateInverseMap:·step·3·of·10 |
| 139 | --·approximateInverseMap:·step·4·of·10 | 139 | --·approximateInverseMap:·step·4·of·10 |
| 140 | --·approximateInverseMap:·step·5·of·10 | 140 | --·approximateInverseMap:·step·5·of·10 |
| 141 | --·approximateInverseMap:·step·6·of·10 | 141 | --·approximateInverseMap:·step·6·of·10 |
| 142 | --·approximateInverseMap:·step·7·of·10 | 142 | --·approximateInverseMap:·step·7·of·10 |
| Offset 193, 15 lines modified | Offset 193, 15 lines modified | ||
| 193 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> | 193 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> |
| 194 | </td>··········</tr> | 194 | </td>··········</tr> |
| 195 | ··········<tr> | 195 | ··········<tr> |
| 196 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)</code></pre> | 196 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)</code></pre> |
| 197 | </td>··········</tr> | 197 | </td>··········</tr> |
| 198 | ··········<tr> | 198 | ··········<tr> |
| 199 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); | 199 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); |
| 200 | ·--·used·0.1 | 200 | ·--·used·0.197017s·(cpu);·0.150704s·(thread);·0s·(gc) |
| 201 | --·approximateInverseMap:·step·1·of·3 | 201 | --·approximateInverseMap:·step·1·of·3 |
| 202 | --·approximateInverseMap:·step·2·of·3 | 202 | --·approximateInverseMap:·step·2·of·3 |
| 203 | --·approximateInverseMap:·step·3·of·3 | 203 | --·approximateInverseMap:·step·3·of·3 |
| 204 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> | 204 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> |
| 205 | </td>··········</tr> | 205 | </td>··········</tr> |
| 206 | ··········<tr> | 206 | ··········<tr> |
| Offset 282, 15 lines modified | Offset 282, 15 lines modified | ||
| 282 | ·····················} | 282 | ·····················} |
| 283 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)</code></pre> | 283 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)</code></pre> |
| 284 | </td>··········</tr> | 284 | </td>··········</tr> |
| 285 | ··········<tr> | 285 | ··········<tr> |
| 286 | <td>··············<pre><code·class="language-macaulay2">i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time· | 286 | <td>··············<pre><code·class="language-macaulay2">i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time· |
| 287 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) | 287 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) |
| 288 | ·--·used·1. | 288 | ·--·used·1.93705s·(cpu);·1.66113s·(thread);·0s·(gc) |
| 289 | --·approximateInverseMap:·step·1·of·3 | 289 | --·approximateInverseMap:·step·1·of·3 |
| 290 | --·approximateInverseMap:·step·2·of·3 | 290 | --·approximateInverseMap:·step·2·of·3 |
| 291 | --·approximateInverseMap:·step·3·of·3 | 291 | --·approximateInverseMap:·step·3·of·3 |
| 292 | o8·=·--·rational·map·-- | 292 | o8·=·--·rational·map·-- |
| 293 | ································ZZ | 293 | ································ZZ |
| 294 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by | 294 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by |
| Offset 349, 15 lines modified | Offset 349, 15 lines modified | ||
| 349 | ·····phi·*·psi·==·1 | 349 | ·····phi·*·psi·==·1 |
| 350 | o9·=·false</code></pre> | 350 | o9·=·false</code></pre> |
| 351 | </td>··········</tr> | 351 | </td>··········</tr> |
| 352 | ··········<tr> | 352 | ··········<tr> |
| 353 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify | 353 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify |
| 354 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) | 354 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) |
| 355 | ·--·used·2. | 355 | ·--·used·2.89006s·(cpu);·2.51569s·(thread);·0s·(gc) |
| 356 | --·approximateInverseMap:·step·1·of·3 | 356 | --·approximateInverseMap:·step·1·of·3 |
| 357 | --·approximateInverseMap:·step·2·of·3 | 357 | --·approximateInverseMap:·step·2·of·3 |
| 358 | --·approximateInverseMap:·step·3·of·3 | 358 | --·approximateInverseMap:·step·3·of·3 |
| 359 | Certify:·output·certified! | 359 | Certify:·output·certified! |
| 360 | o10·=·--·rational·map·-- | 360 | o10·=·--·rational·map·-- |
| 361 | ·································ZZ | 361 | ·································ZZ |
| Offset 126, 15 lines modified | Offset 126, 15 lines modified | ||
| 126 | ······················x·x··-·x·x | 126 | ······················x·x··-·x·x |
| 127 | ·······················1·2····0·4 | 127 | ·······················1·2····0·4 |
| 128 | ·····················} | 128 | ·····················} |
| 129 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8) | 129 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8) |
| 130 | i3·:·time·psi·=·approximateInverseMap·phi | 130 | i3·:·time·psi·=·approximateInverseMap·phi |
| 131 | ·--·used·0. | 131 | ·--·used·0.241364s·(cpu);·0.204377s·(thread);·0s·(gc) |
| 132 | --·approximateInverseMap:·step·1·of·10 | 132 | --·approximateInverseMap:·step·1·of·10 |
| 133 | --·approximateInverseMap:·step·2·of·10 | 133 | --·approximateInverseMap:·step·2·of·10 |
| 134 | --·approximateInverseMap:·step·3·of·10 | 134 | --·approximateInverseMap:·step·3·of·10 |
| 135 | --·approximateInverseMap:·step·4·of·10 | 135 | --·approximateInverseMap:·step·4·of·10 |
| 136 | --·approximateInverseMap:·step·5·of·10 | 136 | --·approximateInverseMap:·step·5·of·10 |
| 137 | --·approximateInverseMap:·step·6·of·10 | 137 | --·approximateInverseMap:·step·6·of·10 |
| 138 | --·approximateInverseMap:·step·7·of·10 | 138 | --·approximateInverseMap:·step·7·of·10 |
| Offset 250, 15 lines modified | Offset 250, 15 lines modified | ||
| 250 | 0·6·····3·6······6······0·7······1·7······3·7······4·7······6·7······7······0·8 | 250 | 0·6·····3·6······6······0·7······1·7······3·7······4·7······6·7······7······0·8 |
| 251 | 1·8······2·8······3·8······4·8······5·8······6·8······7·8·····8 | 251 | 1·8······2·8······3·8······4·8······5·8······6·8······7·8·····8 |
| 252 | ·····················} | 252 | ·····················} |
| 253 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) | 253 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) |
| 254 | i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1) | 254 | i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1) |
| 255 | i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); | 255 | i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); |
| 256 | ·--·used·0.1 | 256 | ·--·used·0.197017s·(cpu);·0.150704s·(thread);·0s·(gc) |
| 257 | --·approximateInverseMap:·step·1·of·3 | 257 | --·approximateInverseMap:·step·1·of·3 |
| 258 | --·approximateInverseMap:·step·2·of·3 | 258 | --·approximateInverseMap:·step·2·of·3 |
| 259 | --·approximateInverseMap:·step·3·of·3 | 259 | --·approximateInverseMap:·step·3·of·3 |
| 260 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) | 260 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9) |
| 261 | i6·:·assert(psi·==·psi') | 261 | i6·:·assert(psi·==·psi') |
| 262 | A·more·complicated·example·is·the·following·(here·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8M_\x8a_\x8p·takes·a·lot·of | 262 | A·more·complicated·example·is·the·following·(here·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8M_\x8a_\x8p·takes·a·lot·of |
| Offset 416, 15 lines modified | Offset 416, 15 lines modified | ||
| 416 | 4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8 | 416 | 4·6······5·6······6······0·7······1·7······2·7·····3·7······4·7······5·7······6·7·····0·8······1·8······3·8·····4·8 |
| 417 | 5·8······6·8·····7·8 | 417 | 5·8······6·8·····7·8 |
| 418 | ·····················} | 418 | ·····················} |
| 419 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11) | 419 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11) |
| 420 | i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time | 420 | i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time |
| 421 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) | 421 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) |
| 422 | ·--·used·1. | 422 | ·--·used·1.93705s·(cpu);·1.66113s·(thread);·0s·(gc) |
| 423 | --·approximateInverseMap:·step·1·of·3 | 423 | --·approximateInverseMap:·step·1·of·3 |
| 424 | --·approximateInverseMap:·step·2·of·3 | 424 | --·approximateInverseMap:·step·2·of·3 |
| 425 | --·approximateInverseMap:·step·3·of·3 | 425 | --·approximateInverseMap:·step·3·of·3 |
| 426 | o8·=·--·rational·map·-- | 426 | o8·=·--·rational·map·-- |
| 427 | ································ZZ | 427 | ································ZZ |
| 428 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by | 428 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by |
| Offset 523, 15 lines modified | Offset 523, 15 lines modified | ||
| 523 | o8·:·RationalMap·(quadratic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8) | 523 | o8·:·RationalMap·(quadratic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8) |
| 524 | i9·:·--·but... | 524 | i9·:·--·but... |
| 525 | ·····phi·*·psi·==·1 | 525 | ·····phi·*·psi·==·1 |
| 526 | o9·=·false | 526 | o9·=·false |
| 527 | i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify | 527 | i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify |
| 528 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) | 528 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) |
| 529 | ·--·used·2. | 529 | ·--·used·2.89006s·(cpu);·2.51569s·(thread);·0s·(gc) |
| 530 | --·approximateInverseMap:·step·1·of·3 | 530 | --·approximateInverseMap:·step·1·of·3 |
| 531 | --·approximateInverseMap:·step·2·of·3 | 531 | --·approximateInverseMap:·step·2·of·3 |
| 532 | --·approximateInverseMap:·step·3·of·3 | 532 | --·approximateInverseMap:·step·3·of·3 |
| 533 | Certify:·output·certified! | 533 | Certify:·output·certified! |
| 534 | o10·=·--·rational·map·-- | 534 | o10·=·--·rational·map·-- |
| 535 | ·································ZZ | 535 | ·································ZZ |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | 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·646x·x··+·225x·x··-·1411x··+·1227x·x··-·1108x·x··+·1291x·x··-·59x·x··-·142x··+·586x·x··-·676x·x··+·655x·x··-·1476x·x··+·453x·x··-·1076x··-·1152x·x··+·1373x·x··-·1191x·x··-·416x·x··+·699x·x··+·317x·x··+·825x··-·1560x·x··-·488x·x··-·1035x·x··-·1561x·x··-·644x·x··-·1178x·x··-·1320x·x··+·158x··+·889x·x··+·1444x·x··-·1486x·x··-·1211x·x··+·1269x·x··-·1228x·x··+·568x·x··+·1591x·x··+·1207x·,·105x··-·538x·x··-·1222x··-·277x·x··+·716x·x··-·1067x··-·428x·x··+·154x·x··-·469x·x··+·77x··+·538x·x··-·179x·x··+·921x·x··-·223x·x··+·1093x··-·262x·x··+·1299x·x··+·631x·x··+·1486x·x··-·1280x·x··-·121x··-·50x·x··-·978x·x··-·694x·x··-·531x·x··+·505x·x··+·1412x·x··-·1061x··+·1202x·x··+·448x·x··-·187x·x··+·1276x·x··-·121x·x··+·1361x·x··+·697x·x··+·682x··+·1592x·x··+·705x·x··-·227x·x··-·7x·x··-·1423x·x··-·1446x·x··-·1578x·x··+·1511x·x··+·917x·,·1270x··-·391x·x··-·1116x··-·287x·x··+·653x·x··+·1643x··+·1623x·x··+·514x·x··-·14x·x··-·90x··+·1232x·x··-·1434x·x··+·1296x·x··+·1522x·x··+·136x··-·623x·x··-·607x·x··+·18x·x··+·896x·x··-·29x·x··+·1059x··-·1053x·x··+·1643x·x··+·1652x·x··-·1190x·x··-·1073x·x··+·1470x·x··-·944x··-·93x·x··-·187x·x··-·994x·x··-·1415x·x··-·229x·x··-·796x·x··+·1642x·x··+·1600x··-·344x·x··+·905x·x··+·1032x·x··-·538x·x··-·891x·x··+·1243x·x··+·1290x·x··+·490x·x··-·1148x·,·1613x··+·175x·x··-·1346x··-·1000x·x··-·1217x·x··-·729x··-·1296x·x··+·1456x·x··+·745x·x··+·539x··+·525x·x··-·811x·x··+·753x·x··+·1362x·x··+·1629x··-·840x·x··+·513x·x··+·429x·x··+·842x·x··+·1414x·x··-·308x··+·1415x·x··-·1461x·x··-·1135x·x··+·701x·x··+·766x·x··+·785x·x··+·1503x··+·147x·x··+·929x·x··-·1220x·x··-·853x·x··+·493x·x··+·226x·x··+·1416x·x··+·280x··-·7x·x··+·1632x·x··+·520x·x··+·1259x·x··+·157x·x··+·1596x·x··+·655x·x··-·42x·x··-·586x·}) | 91 | o4·=·map·(ringP8,·ringP14,·{-·95x··+·181x·x··+·1028x··-·1384x·x··-·1455x·x··+·559x··-·502x·x··+·1264x·x··-·162x·x··+·1209x··-·180x·x··-·504x·x··-·1168x·x··-·676x·x··+·501x··+·73x·x··+·1263x·x··+·1035x·x··+·844x·x··+·1593x·x··+·785x··+·982x·x··-·412x·x··+·1335x·x··+·1136x·x··+·826x·x··+·1078x·x··+·1158x··+·335x·x··-·982x·x··-·1479x·x··-·15x·x··+·1363x·x··+·1397x·x··-·575x·x··-·71x··+·1255x·x··-·1138x·x··-·1590x·x··+·604x·x··+·1182x·x··-·63x·x··-·1382x·x··-·1255x·x··-·613x·,·-·1444x··+·575x·x··+·767x··-·1495x·x··+·1631x·x··-·217x··-·294x·x··-·1511x·x··-·504x·x··-·1284x··-·1459x·x··+·152x·x··+·141x·x··-·10x·x··-·95x··+·1056x·x··+·654x·x··+·1397x·x··-·930x·x··+·578x·x··-·696x··+·759x·x··+·733x·x··+·505x·x··-·609x·x··+·526x·x··-·659x·x··+·846x··+·1253x·x··-·1519x·x··+·635x·x··+·576x·x··+·54x·x··-·1261x·x··-·822x·x··-·257x··-·986x·x··+·356x·x··-·1488x·x··-·1561x·x··-·850x·x··-·85x·x··-·1350x·x··-·783x·x··-·1335x·,·-·871x··+·1006x·x··-·1399x··-·1636x·x··-·699x·x··-·769x··-·307x·x··-·1645x·x··-·502x·x··-·719x··+·1405x·x··+·870x·x··-·1133x·x··+·425x·x··-·1203x··-·1601x·x··+·117x·x··-·382x·x··+·318x·x··-·117x·x··-·560x··+·1135x·x··+·1468x·x··+·869x·x··-·943x·x··-·335x·x··-·1218x·x··+·201x··-·11x·x··+·540x·x··-·710x·x··-·489x·x··+·1605x·x··+·1663x·x··-·423x·x··+·1246x··+·97x·x··-·644x·x··+·1655x·x··+·1219x·x··+·1476x·x··+·1355x·x··+·1594x·x··+·893x·x··+·1150x·,·-·143x··+·1240x·x··-·1042x··+·1649x·x··+·1024x·x··+·794x··+·1442x·x··-·1263x·x··+·537x·x··-·82x··-·734x·x··-·1569x·x··-·798x·x··-·366x·x··+·1289x··-·569x·x··-·254x·x··+·237x·x··-·1234x·x··-·807x·x··+·264x··-·202x·x··-·616x·x··+·44x·x··+·1465x·x··+·685x·x··+·1630x·x··-·406x··-·123x·x··-·4x·x··+·1583x·x··+·1235x·x··+·162x·x··+·1034x·x··-·1035x·x··+·737x··+·660x·x··+·1459x·x··-·359x·x··-·1291x·x··+·1638x·x··-·325x·x··-·631x·x··+·73x·x··-·1471x·,·-·1340x··+·31x·x··-·994x··-·880x·x··-·89x·x··+·574x··+·760x·x··-·1054x·x··+·772x·x··-·239x··-·443x·x··+·1240x·x··+·637x·x··-·1423x·x··+·320x··-·1363x·x··-·1139x·x··-·158x·x··-·325x·x··-·1578x·x··+·32x··+·695x·x··+·305x·x··+·1012x·x··+·1492x·x··+·1290x·x··+·1579x·x··-·342x··-·83x·x··-·104x·x··+·998x·x··-·92x·x··+·1554x·x··+·201x·x··-·237x·x··+·160x··-·228x·x··-·543x·x··-·1147x·x··-·376x·x··+·1313x·x··+·603x·x··+·106x·x··-·1361x·x··+·699x·,·-·228x··-·1510x·x··+·277x··-·4x·x··-·22x·x··-·1526x··+·234x·x··+·969x·x··+·1253x·x··-·1426x··-·1474x·x··+·947x·x··+·194x·x··-·316x·x··-·988x··-·1211x·x··+·1087x·x··+·536x·x··-·491x·x··+·870x·x··-·659x··+·1490x·x··-·469x·x··+·1190x·x··+·807x·x··+·650x·x··+·448x·x··-·1353x··-·218x·x··+·759x·x··-·253x·x··+·830x·x··-·1080x·x··-·143x·x··-·1313x·x··-·374x··-·180x·x··+·741x·x··+·742x·x··-·1254x·x··+·458x·x··-·345x·x··+·597x·x··+·1567x·x··-·31x·,·1120x··+·709x·x··-·1538x··-·1048x·x··-·162x·x··-·1518x··-·73x·x··+·380x·x··+·533x·x··-·286x··+·1374x·x··-·74x·x··-·22x·x··+·1535x·x··-·1071x··-·839x·x··-·560x·x··+·928x·x··+·335x·x··-·1008x·x··+·810x··-·448x·x··-·357x·x··-·107x·x··+·40x·x··+·784x·x··-·1423x·x··+·1276x··+·147x·x··+·443x·x··-·598x·x··-·1077x·x··-·1214x·x··+·322x·x··-·1408x·x··+·72x··-·63x·x··-·1513x·x··-·791x·x··+·11x·x··+·77x·x··+·836x·x··-·1100x·x··+·1637x·x··-·788x·,·1331x··+·318x·x··-·704x··+·51x·x··+·275x·x··+·1149x··+·1526x·x··+·768x·x··+·414x·x··-·782x··-·262x·x··+·686x·x··-·380x·x··+·1377x·x··+·1077x··+·1650x·x··-·1129x·x··-·508x·x··+·846x·x··+·1513x·x··+·460x··-·1626x·x··-·1024x·x··+·862x·x··+·1352x·x··-·188x·x··-·1382x·x··-·650x··+·55x·x··-·326x·x··+·1037x·x··+·705x·x··-·667x·x··+·1483x·x··+·1661x·x··-·1652x··-·1052x·x··-·692x·x··-·542x·x··+·162x·x··+·582x·x··-·1369x·x··+·934x·x··+·1392x·x··+·1227x·,·-·346x··+·1408x·x··-·1225x··-·1536x·x··-·1028x·x··-·985x··-·210x·x··-·1312x·x··+·915x·x··+·1633x··-·202x·x··-·1636x·x··-·1653x·x··-·480x·x··-·1260x··-·813x·x··-·1623x·x··-·1429x·x··+·1094x·x··-·747x·x··+·955x··+·898x·x··-·795x·x··-·35x·x··-·566x·x··+·1631x·x··-·324x·x··+·926x··-·132x·x··-·9x·x··-·1290x·x··-·543x·x··+·902x·x··+·735x·x··-·342x·x··-·400x··+·900x·x··-·463x·x··+·694x·x··-·1262x·x··-·1449x·x··-·448x·x··-·1402x·x··-·731x·x··-·996x·,·301x··+·166x·x··-·955x··-·739x·x··-·1199x·x··-·319x··+·1047x·x··-·532x·x··+·902x·x··+·1195x··-·663x·x··+·1215x·x··-·534x·x··-·332x·x··-·973x··+·772x·x··-·308x·x··+·315x·x··-·454x·x··-·483x·x··-·239x··-·1313x·x··-·419x·x··-·1340x·x··-·1388x·x··-·1340x·x··-·1665x·x··-·333x··-·465x·x··-·1084x·x··+·676x·x··-·1612x·x··-·288x·x··+·11x·x··-·1170x·x··-·189x··+·498x·x··-·889x·x··+·693x·x··+·1460x·x··-·473x·x··-·414x·x··-·122x·x··-·1659x·x··-·1421x·,·14x··-·1049x·x··+·1506x··+·1235x·x··+·642x·x··-·1034x··+·460x·x··+·150x·x··+·760x·x··-·1246x··-·1407x·x··+·1570x·x··+·1403x·x··-·1610x·x··-·431x··+·574x·x··+·893x·x··-·657x·x··+·417x·x··+·1362x·x··+·224x··+·268x·x··+·1097x·x··+·1132x·x··+·148x·x··+·1331x·x··-·77x·x··-·756x··+·228x·x··+·136x·x··-·1484x·x··-·1478x·x··-·13x·x··+·1620x·x··-·701x·x··-·769x··-·760x·x··-·492x·x··-·1077x·x··-·1249x·x··-·834x·x··-·395x·x··-·1358x·x··-·988x·x··+·113x·,·-·1634x··-·13x·x··+·805x··-·21x·x··-·1655x·x··+·1479x··-·1510x·x··-·646x·x··+·225x·x··-·1411x··+·1227x·x··-·1108x·x··+·1291x·x··-·59x·x··-·142x··+·586x·x··-·676x·x··+·655x·x··-·1476x·x··+·453x·x··-·1076x··-·1152x·x··+·1373x·x··-·1191x·x··-·416x·x··+·699x·x··+·317x·x··+·825x··-·1560x·x··-·488x·x··-·1035x·x··-·1561x·x··-·644x·x··-·1178x·x··-·1320x·x··+·158x··+·889x·x··+·1444x·x··-·1486x·x··-·1211x·x··+·1269x·x··-·1228x·x··+·568x·x··+·1591x·x··+·1207x·,·105x··-·538x·x··-·1222x··-·277x·x··+·716x·x··-·1067x··-·428x·x··+·154x·x··-·469x·x··+·77x··+·538x·x··-·179x·x··+·921x·x··-·223x·x··+·1093x··-·262x·x··+·1299x·x··+·631x·x··+·1486x·x··-·1280x·x··-·121x··-·50x·x··-·978x·x··-·694x·x··-·531x·x··+·505x·x··+·1412x·x··-·1061x··+·1202x·x··+·448x·x··-·187x·x··+·1276x·x··-·121x·x··+·1361x·x··+·697x·x··+·682x··+·1592x·x··+·705x·x··-·227x·x··-·7x·x··-·1423x·x··-·1446x·x··-·1578x·x··+·1511x·x··+·917x·,·1270x··-·391x·x··-·1116x··-·287x·x··+·653x·x··+·1643x··+·1623x·x··+·514x·x··-·14x·x··-·90x··+·1232x·x··-·1434x·x··+·1296x·x··+·1522x·x··+·136x··-·623x·x··-·607x·x··+·18x·x··+·896x·x··-·29x·x··+·1059x··-·1053x·x··+·1643x·x··+·1652x·x··-·1190x·x··-·1073x·x··+·1470x·x··-·944x··-·93x·x··-·187x·x··-·994x·x··-·1415x·x··-·229x·x··-·796x·x··+·1642x·x··+·1600x··-·344x·x··+·905x·x··+·1032x·x··-·538x·x··-·891x·x··+·1243x·x··+·1290x·x··+·490x·x··-·1148x·,·1613x··+·175x·x··-·1346x··-·1000x·x··-·1217x·x··-·729x··-·1296x·x··+·1456x·x··+·745x·x··+·539x··+·525x·x··-·811x·x··+·753x·x··+·1362x·x··+·1629x··-·840x·x··+·513x·x··+·429x·x··+·842x·x··+·1414x·x··-·308x··+·1415x·x··-·1461x·x··-·1135x·x··+·701x·x··+·766x·x··+·785x·x··+·1503x··+·147x·x··+·929x·x··-·1220x·x··-·853x·x··+·493x·x··+·226x·x··+·1416x·x··+·280x··-·7x·x··+·1632x·x··+·520x·x··+·1259x·x··+·157x·x··+·1596x·x··+·655x·x··-·42x·x··-·586x·}) 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| 92 | 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·····1·3·······2·3········3········0·4········1·4········2·4······3·4·······4·······0·5·······1·5·······2·5········3·5·······4·5········5········0·6········1·6········2·6·······3·6·······4·6·······5·6·······6········0·7·······1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8········2·8········3·8········4·8········5·8·······6·8········7·8········8······0·······0·1········1·······0·2·······1·2········2·······0·3·······1·3·······2·3······3·······0·4·······1·4·······2·4·······3·4········4·······0·5········1·5·······2·5········3·5········4·5·······5······0·6·······1·6·······2·6·······3·6·······4·6········5·6········6········0·7·······1·7·······2·7········3·7·······4·7········5·7·······6·7·······7········0·8·······1·8·······2·8·····3·8········4·8········5·8········6·8········7·8·······8·······0·······0·1········1·······0·2·······1·2········2········0·3·······1·3······2·3······3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5······2·5·······3·5······4·5········5········0·6········1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7········3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8·······4·8········5·8········6·8·······7·8········8·······0·······0·1········1········0·2········1·2·······2········0·3········1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6········1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7········2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2·8········3·8·······4·8········5·8·······6·8······7·8·······8 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·····1·3·······2·3········3········0·4········1·4········2·4······3·4·······4·······0·5·······1·5·······2·5········3·5·······4·5········5········0·6········1·6········2·6·······3·6·······4·6·······5·6·······6········0·7·······1·7········2·7········3·7·······4·7········5·7········6·7·······7·······0·8········1·8········2·8········3·8········4·8········5·8·······6·8········7·8········8······0·······0·1········1·······0·2·······1·2········2·······0·3·······1·3·······2·3······3·······0·4·······1·4·······2·4·······3·4········4·······0·5········1·5·······2·5········3·5········4·5·······5······0·6·······1·6·······2·6·······3·6·······4·6········5·6········6········0·7·······1·7·······2·7········3·7·······4·7········5·7·······6·7·······7········0·8·······1·8·······2·8·····3·8········4·8········5·8········6·8········7·8·······8·······0·······0·1········1·······0·2·······1·2········2········0·3·······1·3······2·3······3········0·4········1·4········2·4········3·4·······4·······0·5·······1·5······2·5·······3·5······4·5········5········0·6········1·6········2·6········3·6········4·6········5·6·······6······0·7·······1·7·······2·7········3·7·······4·7·······5·7········6·7········7·······0·8·······1·8········2·8·······3·8·······4·8········5·8········6·8·······7·8········8·······0·······0·1········1········0·2········1·2·······2········0·3········1·3·······2·3·······3·······0·4·······1·4·······2·4········3·4········4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6········1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7········2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2·8········3·8·······4·8········5·8·······6·8······7·8·······8 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| 93 | o4·:·RingMap·ringP8·<--·ringP14</code></pre> | 93 | o4·:·RingMap·ringP8·<--·ringP14</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degreeMap·phi | 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degreeMap·phi |
| 97 | ·--·used·0.08 | 97 | ·--·used·0.0889568s·(cpu);·0.0496064s·(thread);·0s·(gc) |
| 98 | o5·=·1</code></pre> | 98 | o5·=·1</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14· | 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a·general·subspace·of·P^14· |
| 102 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14) | 102 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14) |
| 103 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) | 103 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) |
| Offset 108, 15 lines modified | Offset 108, 15 lines modified | ||
| 108 | o6·=·map·(ringP8,·ringP8,·{-·780x··-·506x·x··+·1537x··-·132x·x··-·928x·x··+·386x··-·102x·x··+·422x·x··+·725x·x··-·1073x··-·905x·x··-·830x·x··+·1500x·x··+·276x·x··+·1533x··-·653x·x··+·1558x·x··+·939x·x··-·1432x·x··+·462x·x··-·329x··-·92x·x··+·661x·x··-·1298x·x··-·684x·x··+·70x·x··-·715x·x··+·1093x··+·581x·x··+·329x·x··+·454x·x··-·911x·x··-·84x·x··-·1452x·x··-·809x·x··+·1202x··+·1353x·x··+·1503x·x··+·482x·x··+·893x·x··-·643x·x··+·598x·x··+·110x·x··+·1064x·x··-·472x·,·-·522x··-·583x·x··+·1339x··+·1535x·x··-·1317x·x··+·1113x··-·169x·x··+·1440x·x··-·1657x·x··+·721x··+·40x·x··-·1576x·x··-·367x·x··+·257x·x··-·1454x··+·1612x·x··+·1529x·x··-·1068x·x··+·560x·x··-·1441x·x··+·608x··-·92x·x··-·1006x·x··+·285x·x··+·102x·x··-·397x·x··+·66x·x··-·643x··-·38x·x··+·1380x·x··+·1069x·x··-·426x·x··+·1147x·x··+·982x·x··+·10x·x··-·662x··+·16x·x··+·1561x·x··+·1597x·x··+·512x·x··+·1288x·x··-·1253x·x··+·1317x·x··+·1481x·x··-·354x·,·-·640x··-·1551x·x··+·469x··+·1482x·x··-·1593x·x··-·986x··+·471x·x··+·612x·x··+·1228x·x··+·1156x··-·731x·x··+·1503x·x··-·628x·x··+·674x·x··-·799x··+·1137x·x··+·844x·x··+·589x·x··-·666x·x··+·829x·x··-·1024x··-·170x·x··+·450x·x··+·1497x·x··+·1204x·x··-·907x·x··+·1621x·x··-·417x··+·1297x·x··+·1444x·x··+·4x·x··+·398x·x··+·996x·x··-·1031x·x··+·239x·x··+·303x··+·1215x·x··-·83x·x··+·1571x·x··-·1543x·x··-·925x·x··-·694x·x··+·151x·x··-·520x·x··+·880x·,·-·1210x··-·222x·x··+·185x··+·245x·x··+·1059x·x··-·322x··+·238x·x··+·962x·x··+·1260x·x··-·1581x··+·50x·x··+·1352x·x··-·1465x·x··+·1555x·x··+·1333x··+·1362x·x··+·1365x·x··+·1168x·x··-·1401x·x··+·149x·x··-·652x··+·1378x·x··-·557x·x··-·112x·x··+·26x·x··+·315x·x··+·111x·x··+·1592x··-·283x·x··-·1454x·x··+·907x·x··+·212x·x··+·400x·x··+·1049x·x··-·882x·x··-·1429x··-·183x·x··+·1571x·x··-·1286x·x··-·1179x·x··+·1319x·x··+·240x·x··-·1100x·x··+·1500x·x··-·348x·,·1051x··-·1325x·x··+·1354x··-·346x·x··-·1532x·x··-·466x··+·163x·x··-·659x·x··-·291x·x··+·966x··+·789x·x··+·393x·x··+·403x·x··-·1199x·x··-·570x··-·93x·x··-·492x·x··-·418x·x··+·713x·x··-·1323x·x··-·1384x··-·830x·x··-·54x·x··-·306x·x··+·709x·x··+·421x·x··-·954x·x··-·299x··+·1053x·x··-·1080x·x··+·686x·x··+·170x·x··-·1272x·x··-·1661x·x··+·1235x·x··+·1553x··-·1454x·x··-·1411x·x··-·1195x·x··-·962x·x··+·737x·x··-·390x·x··+·957x·x··+·1538x·x··+·1234x·,·-·509x··+·9x·x··-·1563x··-·710x·x··-·642x·x··+·541x··+·220x·x··-·1214x·x··-·16x·x··+·1008x··-·1088x·x··+·755x·x··-·886x·x··-·1433x·x··+·1154x··+·1627x·x··-·1547x·x··-·951x·x··+·866x·x··+·163x·x··-·1142x··-·668x·x··+·1361x·x··+·1324x·x··-·490x·x··+·282x·x··-·1133x·x··-·612x··+·805x·x··-·126x·x··+·1296x·x··-·973x·x··+·1271x·x··-·1646x·x··+·844x·x··+·1073x··-·1452x·x··-·1112x·x··-·141x·x··+·176x·x··-·1579x·x··-·78x·x··+·848x·x··-·1365x·x··+·711x·,·x··+·1543x·x··-·1076x··+·493x·x··-·526x·x··+·868x··-·582x·x··-·996x·x··+·206x·x··-·419x··+·1258x·x··-·391x·x··+·1002x·x··-·1539x·x··+·931x··-·1504x·x··+·810x·x··+·324x·x··+·1356x·x··+·313x·x··+·772x··+·299x·x··+·1186x·x··+·718x·x··+·407x·x··-·64x·x··-·828x·x··-·1393x··+·94x·x··-·290x·x··-·766x·x··+·950x·x··-·640x·x··+·265x·x··-·1640x·x··-·1403x··-·126x·x··+·891x·x··-·1519x·x··-·927x·x··-·1335x·x··-·1448x·x··-·x·x··-·1103x·x··-·1152x·,·821x··+·558x·x··-·1174x··-·168x·x··+·986x·x··+·790x··+·549x·x··+·817x·x··+·1396x·x··+·695x··+·1211x·x··+·878x·x··-·1061x·x··-·1244x·x··-·880x··+·1409x·x··-·567x·x··+·1240x·x··+·1126x·x··-·1262x·x··+·490x··+·1553x·x··+·1276x·x··+·805x·x··+·576x·x··-·1076x·x··+·1617x·x··-·495x··-·750x·x··-·277x·x··+·544x·x··+·1479x·x··-·784x·x··-·64x·x··-·1203x·x··+·405x··+·1013x·x··+·604x·x··+·1301x·x··+·1003x·x··+·235x·x··+·696x·x··+·939x·x··-·714x·x··-·879x·,·-·1452x··+·727x·x··-·1159x··+·449x·x··-·1169x·x··+·732x··+·575x·x··-·600x·x··+·924x·x··-·837x··+·1298x·x··-·860x·x··+·1010x·x··+·774x·x··+·319x··+·1087x·x··-·1120x·x··+·1439x·x··+·1175x·x··-·1648x·x··+·985x··-·1317x·x··-·878x·x··+·399x·x··-·1339x·x··+·70x·x··-·463x·x··+·470x··-·628x·x··-·907x·x··+·748x·x··+·98x·x··+·1150x·x··+·1140x·x··+·1308x·x··+·621x··+·369x·x··-·991x·x··-·1186x·x··+·61x·x··-·907x·x··-·681x·x··-·1528x·x··+·717x·x··+·854x·}) | 108 | o6·=·map·(ringP8,·ringP8,·{-·780x··-·506x·x··+·1537x··-·132x·x··-·928x·x··+·386x··-·102x·x··+·422x·x··+·725x·x··-·1073x··-·905x·x··-·830x·x··+·1500x·x··+·276x·x··+·1533x··-·653x·x··+·1558x·x··+·939x·x··-·1432x·x··+·462x·x··-·329x··-·92x·x··+·661x·x··-·1298x·x··-·684x·x··+·70x·x··-·715x·x··+·1093x··+·581x·x··+·329x·x··+·454x·x··-·911x·x··-·84x·x··-·1452x·x··-·809x·x··+·1202x··+·1353x·x··+·1503x·x··+·482x·x··+·893x·x··-·643x·x··+·598x·x··+·110x·x··+·1064x·x··-·472x·,·-·522x··-·583x·x··+·1339x··+·1535x·x··-·1317x·x··+·1113x··-·169x·x··+·1440x·x··-·1657x·x··+·721x··+·40x·x··-·1576x·x··-·367x·x··+·257x·x··-·1454x··+·1612x·x··+·1529x·x··-·1068x·x··+·560x·x··-·1441x·x··+·608x··-·92x·x··-·1006x·x··+·285x·x··+·102x·x··-·397x·x··+·66x·x··-·643x··-·38x·x··+·1380x·x··+·1069x·x··-·426x·x··+·1147x·x··+·982x·x··+·10x·x··-·662x··+·16x·x··+·1561x·x··+·1597x·x··+·512x·x··+·1288x·x··-·1253x·x··+·1317x·x··+·1481x·x··-·354x·,·-·640x··-·1551x·x··+·469x··+·1482x·x··-·1593x·x··-·986x··+·471x·x··+·612x·x··+·1228x·x··+·1156x··-·731x·x··+·1503x·x··-·628x·x··+·674x·x··-·799x··+·1137x·x··+·844x·x··+·589x·x··-·666x·x··+·829x·x··-·1024x··-·170x·x··+·450x·x··+·1497x·x··+·1204x·x··-·907x·x··+·1621x·x··-·417x··+·1297x·x··+·1444x·x··+·4x·x··+·398x·x··+·996x·x··-·1031x·x··+·239x·x··+·303x··+·1215x·x··-·83x·x··+·1571x·x··-·1543x·x··-·925x·x··-·694x·x··+·151x·x··-·520x·x··+·880x·,·-·1210x··-·222x·x··+·185x··+·245x·x··+·1059x·x··-·322x··+·238x·x··+·962x·x··+·1260x·x··-·1581x··+·50x·x··+·1352x·x··-·1465x·x··+·1555x·x··+·1333x··+·1362x·x··+·1365x·x··+·1168x·x··-·1401x·x··+·149x·x··-·652x··+·1378x·x··-·557x·x··-·112x·x··+·26x·x··+·315x·x··+·111x·x··+·1592x··-·283x·x··-·1454x·x··+·907x·x··+·212x·x··+·400x·x··+·1049x·x··-·882x·x··-·1429x··-·183x·x··+·1571x·x··-·1286x·x··-·1179x·x··+·1319x·x··+·240x·x··-·1100x·x··+·1500x·x··-·348x·,·1051x··-·1325x·x··+·1354x··-·346x·x··-·1532x·x··-·466x··+·163x·x··-·659x·x··-·291x·x··+·966x··+·789x·x··+·393x·x··+·403x·x··-·1199x·x··-·570x··-·93x·x··-·492x·x··-·418x·x··+·713x·x··-·1323x·x··-·1384x··-·830x·x··-·54x·x··-·306x·x··+·709x·x··+·421x·x··-·954x·x··-·299x··+·1053x·x··-·1080x·x··+·686x·x··+·170x·x··-·1272x·x··-·1661x·x··+·1235x·x··+·1553x··-·1454x·x··-·1411x·x··-·1195x·x··-·962x·x··+·737x·x··-·390x·x··+·957x·x··+·1538x·x··+·1234x·,·-·509x··+·9x·x··-·1563x··-·710x·x··-·642x·x··+·541x··+·220x·x··-·1214x·x··-·16x·x··+·1008x··-·1088x·x··+·755x·x··-·886x·x··-·1433x·x··+·1154x··+·1627x·x··-·1547x·x··-·951x·x··+·866x·x··+·163x·x··-·1142x··-·668x·x··+·1361x·x··+·1324x·x··-·490x·x··+·282x·x··-·1133x·x··-·612x··+·805x·x··-·126x·x··+·1296x·x··-·973x·x··+·1271x·x··-·1646x·x··+·844x·x··+·1073x··-·1452x·x··-·1112x·x··-·141x·x··+·176x·x··-·1579x·x··-·78x·x··+·848x·x··-·1365x·x··+·711x·,·x··+·1543x·x··-·1076x··+·493x·x··-·526x·x··+·868x··-·582x·x··-·996x·x··+·206x·x··-·419x··+·1258x·x··-·391x·x··+·1002x·x··-·1539x·x··+·931x··-·1504x·x··+·810x·x··+·324x·x··+·1356x·x··+·313x·x··+·772x··+·299x·x··+·1186x·x··+·718x·x··+·407x·x··-·64x·x··-·828x·x··-·1393x··+·94x·x··-·290x·x··-·766x·x··+·950x·x··-·640x·x··+·265x·x··-·1640x·x··-·1403x··-·126x·x··+·891x·x··-·1519x·x··-·927x·x··-·1335x·x··-·1448x·x··-·x·x··-·1103x·x··-·1152x·,·821x··+·558x·x··-·1174x··-·168x·x··+·986x·x··+·790x··+·549x·x··+·817x·x··+·1396x·x··+·695x··+·1211x·x··+·878x·x··-·1061x·x··-·1244x·x··-·880x··+·1409x·x··-·567x·x··+·1240x·x··+·1126x·x··-·1262x·x··+·490x··+·1553x·x··+·1276x·x··+·805x·x··+·576x·x··-·1076x·x··+·1617x·x··-·495x··-·750x·x··-·277x·x··+·544x·x··+·1479x·x··-·784x·x··-·64x·x··-·1203x·x··+·405x··+·1013x·x··+·604x·x··+·1301x·x··+·1003x·x··+·235x·x··+·696x·x··+·939x·x··-·714x·x··-·879x·,·-·1452x··+·727x·x··-·1159x··+·449x·x··-·1169x·x··+·732x··+·575x·x··-·600x·x··+·924x·x··-·837x··+·1298x·x··-·860x·x··+·1010x·x··+·774x·x··+·319x··+·1087x·x··-·1120x·x··+·1439x·x··+·1175x·x··-·1648x·x··+·985x··-·1317x·x··-·878x·x··+·399x·x··-·1339x·x··+·70x·x··-·463x·x··+·470x··-·628x·x··-·907x·x··+·748x·x··+·98x·x··+·1150x·x··+·1140x·x··+·1308x·x··+·621x··+·369x·x··-·991x·x··-·1186x·x··+·61x·x··-·907x·x··-·681x·x··-·1528x·x··+·717x·x··+·854x·}) 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|
| 110 | o6·:·RingMap·ringP8·<--·ringP8</code></pre> | 110 | o6·:·RingMap·ringP8·<--·ringP8</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·degreeMap·phi' | 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·degreeMap·phi' |
| 114 | ·--·used·0. | 114 | ·--·used·0.545321s·(cpu);·0.454568s·(thread);·0s·(gc) |
| 115 | o7·=·14</code></pre> | 115 | o7·=·14</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ········</table> | 117 | ········</table> |
| 118 | ······</div> | 118 | ······</div> |
| 119 | ······<div> | 119 | ······<div> |
| 120 | ········<h2>See·also</h2> | 120 | ········<h2>See·also</h2> |
| Offset 267, 15 lines modified | Offset 267, 15 lines modified | ||
| 267 | 4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6 | 267 | 4·······0·5·······1·5·······2·5·······3·5········4·5·······5········0·6 |
| 268 | 1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7 | 268 | 1·6········2·6·······3·6·······4·6·······5·6········6·······0·7·······1·7 |
| 269 | 2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2 | 269 | 2·7·······3·7·······4·7·······5·7········6·7·······7·····0·8········1·8·······2 |
| 270 | 8········3·8·······4·8········5·8·······6·8······7·8·······8 | 270 | 8········3·8·······4·8········5·8·······6·8······7·8·······8 |
| 271 | o4·:·RingMap·ringP8·<--·ringP14 | 271 | o4·:·RingMap·ringP8·<--·ringP14 |
| 272 | i5·:·time·degreeMap·phi | 272 | i5·:·time·degreeMap·phi |
| 273 | ·--·used·0.08 | 273 | ·--·used·0.0889568s·(cpu);·0.0496064s·(thread);·0s·(gc) |
| 274 | o5·=·1 | 274 | o5·=·1 |
| 275 | i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a | 275 | i6·:·--·Compose·phi:P^8--->P^14·with·a·linear·projection·P^14--->P^8·from·a |
| 276 | general·subspace·of·P^14 | 276 | general·subspace·of·P^14 |
| 277 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have | 277 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have |
| 278 | degree·equal·to·deg(G(1,5))=14) | 278 | degree·equal·to·deg(G(1,5))=14) |
| 279 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) | 279 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) |
| Offset 419, 15 lines modified | Offset 419, 15 lines modified | ||
| 419 | 0·5········1·5········2·5········3·5········4·5·······5········0·6·······1·6 | 419 | 0·5········1·5········2·5········3·5········4·5·······5········0·6·······1·6 |
| 420 | 2·6········3·6······4·6·······5·6·······6·······0·7·······1·7·······2·7······3 | 420 | 2·6········3·6······4·6·······5·6·······6·······0·7·······1·7·······2·7······3 |
| 421 | 7········4·7········5·7········6·7·······7·······0·8·······1·8········2·8 | 421 | 7········4·7········5·7········6·7·······7·······0·8·······1·8········2·8 |
| 422 | 3·8·······4·8·······5·8········6·8·······7·8·······8 | 422 | 3·8·······4·8·······5·8········6·8·······7·8·······8 |
| 423 | o6·:·RingMap·ringP8·<--·ringP8 | 423 | o6·:·RingMap·ringP8·<--·ringP8 |
| 424 | i7·:·time·degreeMap·phi' | 424 | i7·:·time·degreeMap·phi' |
| 425 | ·--·used·0. | 425 | ·--·used·0.545321s·(cpu);·0.454568s·(thread);·0s·(gc) |
| 426 | o7·=·14 | 426 | o7·=·14 |
| 427 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 427 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 428 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map | 428 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map |
| 429 | ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·projective·degrees·of·a·rational·map·between | 429 | ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·projective·degrees·of·a·rational·map·between |
| 430 | ······projective·varieties | 430 | ······projective·varieties |
| 431 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·d\x8de\x8eg\x8gr\x8re\x8ee\x8eM\x8Ma\x8ap\x8p:\x8:·*\x8**\x8**\x8**\x8**\x8* | 431 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·d\x8de\x8eg\x8gr\x8re\x8ee\x8eM\x8Ma\x8ap\x8p:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap(X,Dominant=>2); | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap(X,Dominant=>2); |
| 81 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> | 81 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) |
| 85 | ·--·used·0.000 | 85 | ·--·used·0.000196629s·(cpu);·0.000579297s·(thread);·0s·(gc)</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi; | 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi; |
| 89 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> | 89 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ········</table> | 91 | ········</table> |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | o2·:·Ideal·of·P6 | 20 | o2·:·Ideal·of·P6 |
| 21 | i3·:·Phi·=·rationalMap(X,Dominant=>2); | 21 | i3·:·Phi·=·rationalMap(X,Dominant=>2); |
| 22 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of | 22 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of |
| 23 | PP^9) | 23 | PP^9) |
| 24 | i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) | 24 | i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) |
| 25 | ·--·used·0.000 | 25 | ·--·used·0.000196629s·(cpu);·0.000579297s·(thread);·0s·(gc) |
| 26 | i5·:·Phi; | 26 | i5·:·Phi; |
| 27 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional | 27 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional |
| 28 | subvariety·of·PP^9) | 28 | subvariety·of·PP^9) |
| 29 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 30 | If·the·declaration·is·false,·nonsensical·answers·may·result. | 30 | If·the·declaration·is·false,·nonsensical·answers·may·result. |
| 31 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 31 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 113, 15 lines modified | Offset 113, 15 lines modified | ||
| 113 | ·························3····2·4 | 113 | ·························3····2·4 |
| 114 | ·····················} | 114 | ·····················} |
| 115 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 115 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(p1,p2)·=·graph·phi; | 118 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(p1,p2)·=·graph·phi; |
| 119 | ·--·used·0.2 | 119 | ·--·used·0.274214s·(cpu);·0.0495487s·(thread);·0s·(gc)</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·p1 | 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·p1 |
| 123 | o4·=·--·rational·map·-- | 123 | o4·=·--·rational·map·-- |
| 124 | ··································ZZ·································ZZ | 124 | ··································ZZ·································ZZ |
| 125 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by | 125 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by |
| Offset 260, 15 lines modified | Offset 260, 15 lines modified | ||
| 260 | o8·:·List</code></pre> | 260 | o8·:·List</code></pre> |
| 261 | </td>··········</tr> | 261 | </td>··········</tr> |
| 262 | ········</table> | 262 | ········</table> |
| 263 | ········<p>When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method·returns·all·the·projections.</p> | 263 | ········<p>When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method·returns·all·the·projections.</p> |
| 264 | ········<table·class="examples"> | 264 | ········<table·class="examples"> |
| 265 | ··········<tr> | 265 | ··········<tr> |
| 266 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·g·=·graph·p2; | 266 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·g·=·graph·p2; |
| 267 | ·--·used·0.2 | 267 | ·--·used·0.286291s·(cpu);·0.0657456s·(thread);·0s·(gc)</code></pre> |
| 268 | </td>··········</tr> | 268 | </td>··········</tr> |
| 269 | ··········<tr> | 269 | ··········<tr> |
| 270 | <td>··············<pre><code·class="language-macaulay2">i10·:·g_0; | 270 | <td>··············<pre><code·class="language-macaulay2">i10·:·g_0; |
| 271 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)</code></pre> | 271 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)</code></pre> |
| 272 | </td>··········</tr> | 272 | </td>··········</tr> |
| 273 | ··········<tr> | 273 | ··········<tr> |
| Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
| 51 | ······················-·x··+·x·x | 51 | ······················-·x··+·x·x |
| 52 | ·························3····2·4 | 52 | ·························3····2·4 |
| 53 | ·····················} | 53 | ·····················} |
| 54 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in | 54 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in |
| 55 | PP^5) | 55 | PP^5) |
| 56 | i3·:·time·(p1,p2)·=·graph·phi; | 56 | i3·:·time·(p1,p2)·=·graph·phi; |
| 57 | ·--·used·0.2 | 57 | ·--·used·0.274214s·(cpu);·0.0495487s·(thread);·0s·(gc) |
| 58 | i4·:·p1 | 58 | i4·:·p1 |
| 59 | o4·=·--·rational·map·-- | 59 | o4·=·--·rational·map·-- |
| 60 | ··································ZZ·································ZZ | 60 | ··································ZZ·································ZZ |
| 61 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y | 61 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y |
| 62 | ,·y·,·y·,·y·,·y·])·defined·by | 62 | ,·y·,·y·,·y·,·y·])·defined·by |
| 63 | ································190181··0···1···2···3···4··········190181··0 | 63 | ································190181··0···1···2···3···4··········190181··0 |
| Offset 193, 15 lines modified | Offset 193, 15 lines modified | ||
| 193 | o8·=·{51,·28,·14,·6,·2} | 193 | o8·=·{51,·28,·14,·6,·2} |
| 194 | o8·:·List | 194 | o8·:·List |
| 195 | When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method | 195 | When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method |
| 196 | returns·all·the·projections. | 196 | returns·all·the·projections. |
| 197 | i9·:·time·g·=·graph·p2; | 197 | i9·:·time·g·=·graph·p2; |
| 198 | ·--·used·0.2 | 198 | ·--·used·0.286291s·(cpu);·0.0657456s·(thread);·0s·(gc) |
| 199 | i10·:·g_0; | 199 | i10·:·g_0; |
| 200 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety | 200 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety |
| 201 | of·PP^4·x·PP^5·x·PP^5·to·PP^4) | 201 | of·PP^4·x·PP^5·x·PP^5·to·PP^4) |
| 202 | i11·:·g_1; | 202 | i11·:·g_1; |
| 203 | o11·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety | 203 | o11·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety |
| Offset 107, 15 lines modified | Offset 107, 15 lines modified | ||
| 107 | ·······················1····0·3 | 107 | ·······················1····0·3 |
| 108 | ·····················} | 108 | ·····················} |
| 109 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> | 109 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ideal·phi | 112 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ideal·phi |
| 113 | ·--·used·0.003 | 113 | ·--·used·0.00348825s·(cpu);·0.00327104s·(thread);·0s·(gc) |
| 114 | ·············2·····································2······················ | 114 | ·············2·····································2······················ |
| 115 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ | 115 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ |
| 116 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3·· | 116 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3·· |
| 117 | ·····------------------------------------------------------------------------ | 117 | ·····------------------------------------------------------------------------ |
| 118 | ············2 | 118 | ············2 |
| 119 | ·····x·x·,·x··-·x·x·) | 119 | ·····x·x·,·x··-·x·x·) |
| Offset 185, 15 lines modified | Offset 185, 15 lines modified | ||
| 185 | ·······················4 | 185 | ·······················4 |
| 186 | ·····················} | 186 | ·····················} |
| 187 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)</code></pre> | 187 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)</code></pre> |
| 188 | </td>··········</tr> | 188 | </td>··········</tr> |
| 189 | ··········<tr> | 189 | ··········<tr> |
| 190 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·phi' | 190 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·phi' |
| 191 | ·--·used·0.15 | 191 | ·--·used·0.157543s·(cpu);·0.089825s·(thread);·0s·(gc) |
| 192 | o6·=·ideal·1 | 192 | o6·=·ideal·1 |
| 193 | ············································································································QQ[x·..x·,·y·..y·] | 193 | ············································································································QQ[x·..x·,·y·..y·] |
| 194 | ················································································································0···5···0···4 | 194 | ················································································································0···5···0···4 |
| 195 | o6·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 195 | o6·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 196 | ·····································································································································································································2 | 196 | ·····································································································································································································2 |
| Offset 47, 15 lines modified | Offset 47, 15 lines modified | ||
| 47 | ·······················2 | 47 | ·······················2 |
| 48 | ······················x··-·x·x | 48 | ······················x··-·x·x |
| 49 | ·······················1····0·3 | 49 | ·······················1····0·3 |
| 50 | ·····················} | 50 | ·····················} |
| 51 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4) | 51 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4) |
| 52 | i3·:·time·ideal·phi | 52 | i3·:·time·ideal·phi |
| 53 | ·--·used·0.003 | 53 | ·--·used·0.00348825s·(cpu);·0.00327104s·(thread);·0s·(gc) |
| 54 | ·············2·····································2 | 54 | ·············2·····································2 |
| 55 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ | 55 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ |
| 56 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3 | 56 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3 |
| 57 | ·····------------------------------------------------------------------------ | 57 | ·····------------------------------------------------------------------------ |
| 58 | ············2 | 58 | ············2 |
| 59 | ·····x·x·,·x··-·x·x·) | 59 | ·····x·x·,·x··-·x·x·) |
| Offset 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ······················y | 122 | ······················y |
| 123 | ·······················4 | 123 | ·······················4 |
| 124 | ·····················} | 124 | ·····················} |
| 125 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of | 125 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of |
| 126 | PP^5·x·PP^4·to·PP^4) | 126 | PP^5·x·PP^4·to·PP^4) |
| 127 | i6·:·time·ideal·phi' | 127 | i6·:·time·ideal·phi' |
| 128 | ·--·used·0.15 | 128 | ·--·used·0.157543s·(cpu);·0.089825s·(thread);·0s·(gc) |
| 129 | o6·=·ideal·1 | 129 | o6·=·ideal·1 |
| 130 | QQ[x·..x·,·y·..y·] | 130 | QQ[x·..x·,·y·..y·] |
| 131 | 0···5···0···4 | 131 | 0···5···0···4 |
| Offset 154, 15 lines modified | Offset 154, 15 lines modified | ||
| 154 | ·······················2·4····1·5····0·6 | 154 | ·······················2·4····1·5····0·6 |
| 155 | ·····················} | 155 | ·····················} |
| 156 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)</code></pre> | 156 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·psi·=·inverseMap·phi | 159 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·psi·=·inverseMap·phi |
| 160 | ·--·used·0.1 | 160 | ·--·used·0.154207s·(cpu);·0.10972s·(thread);·0s·(gc) |
| 161 | o2·=·--·rational·map·-- | 161 | o2·=·--·rational·map·-- |
| 162 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) | 162 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 163 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 | 163 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 |
| 164 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) | 164 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 165 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 | 165 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 |
| 166 | ·····defining·forms:·{ | 166 | ·····defining·forms:·{ |
| Offset 246, 15 lines modified | Offset 246, 15 lines modified | ||
| 246 | ··············0···26·······0···26·····21·22····20·23····15·24····10·25····0·26···19·22····18·23····16·24····11·25····1·26···19·20····18·21····17·24····12·25····2·26···15·19····16·21····17·23····13·25····3·26···10·19····11·21····12·23····13·24····4·26···0·19····1·21····2·23····3·24····4·25···15·18····16·20····17·22····14·25····5·26···10·18····11·20····12·22····14·24····6·26···0·18····1·20····2·22····5·24····6·25···12·16····11·17····13·18····14·19····7·26···2·16····1·17····3·18····5·19····7·25···12·15····10·17····13·20····14·21····8·26···11·15····10·16····13·22····14·23····9·26···2·15····0·17····3·20····5·21····8·25···1·15····0·16····3·22····5·23····9·25···5·13····3·14····7·15····8·16····9·17···5·12····2·14····6·17····8·18····7·20···3·12····2·13····4·17····8·19····7·21···5·11····1·14····6·16····9·18····7·22···3·11····1·13····4·16····9·19····7·23···2·11····1·12····4·18····6·19····7·24···7·10····8·11····9·12····6·13····4·14···5·10····0·14····6·15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4·20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7····1·8····2·9 | 246 | ··············0···26·······0···26·····21·22····20·23····15·24····10·25····0·26···19·22····18·23····16·24····11·25····1·26···19·20····18·21····17·24····12·25····2·26···15·19····16·21····17·23····13·25····3·26···10·19····11·21····12·23····13·24····4·26···0·19····1·21····2·23····3·24····4·25···15·18····16·20····17·22····14·25····5·26···10·18····11·20····12·22····14·24····6·26···0·18····1·20····2·22····5·24····6·25···12·16····11·17····13·18····14·19····7·26···2·16····1·17····3·18····5·19····7·25···12·15····10·17····13·20····14·21····8·26···11·15····10·16····13·22····14·23····9·26···2·15····0·17····3·20····5·21····8·25···1·15····0·16····3·22····5·23····9·25···5·13····3·14····7·15····8·16····9·17···5·12····2·14····6·17····8·18····7·20···3·12····2·13····4·17····8·19····7·21···5·11····1·14····6·16····9·18····7·22···3·11····1·13····4·16····9·19····7·23···2·11····1·12····4·18····6·19····7·24···7·10····8·11····9·12····6·13····4·14···5·10····0·14····6·15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4·20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7····1·8····2·9 |
| 247 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 247 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 248 | ·················0···26··········0···26</code></pre> | 248 | ·················0···26··········0···26</code></pre> |
| 249 | </td>··········</tr> | 249 | </td>··········</tr> |
| 250 | ··········<tr> | 250 | ··········<tr> |
| 251 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi·=·inverseMap·phi | 251 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi·=·inverseMap·phi |
| 252 | ·--·used·0.2 | 252 | ·--·used·0.28098s·(cpu);·0.169417s·(thread);·0s·(gc) |
| 253 | o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··}) | 253 | o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w··,·w·w···-·w·w···+·w·w···+·w··w···-·w··w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···+·w·w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·-·w·w···-·w··w···+·w··w···+·w·w···-·w·w··,·w··w···-·w··w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w··w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w···-·w·w···+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w···+·w·w···-·w·w··,·-·w·w··+·w·w··+·w·w···-·w·w···+·w·w··,·w·w··-·w·w··-·w·w··+·w·w···-·w·w··}) |
| 254 | ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12 | 254 | ··············0···26·······0···26·······5·22····8·23····14·24····13·25····0·26·····5·18····8·19····14·20····10·25····1·26·····5·16····8·17····13·20····10·24····2·26·····5·15····14·17····13·19····10·23····3·26·····5·21····20·23····19·24····17·25····4·26·····8·15····14·16····13·18····10·22····6·26·····8·21····20·22····18·24····16·25····7·26···17·18····16·19····15·20····10·21····9·26·····13·21····17·22····16·23····15·24····11·26·····14·21····19·22····18·23····15·25····12·26···0·21····4·22····7·23····12·24····11·25·····4·18····7·19····12·20····1·21····9·25·····4·16····7·17····11·20····2·21····9·24·····4·15····12·17····11·19····3·21····9·23·····7·15····12·16····11·18····6·21····9·22···12·13····11·14····0·15····3·22····6·23···10·12····9·14····1·15····3·18····6·19···10·11····9·13····2·15····3·16····6·17···8·9····7·10····1·16····2·18····6·20···5·9····4·10····1·17····2·19····3·20···8·11····7·13····0·16····2·22····6·24···5·11····4·13····0·17····2·23····3·24···8·12····7·14····0·18····1·22····6·25···5·12····4·14····0·19····1·23····3·25···5·7····4·8····0·20····1·24····2·25·····5·6····3·8····0·10····1·13····2·14···4·6····3·7····0·9····1·11····2·12 |
| 255 | o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 255 | o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 256 | ·················0···26··········0···26</code></pre> | 256 | ·················0···26··········0···26</code></pre> |
| 257 | </td>··········</tr> | 257 | </td>··········</tr> |
| Offset 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | ······················w·w··-·w·w··+·w·w | 99 | ······················w·w··-·w·w··+·w·w |
| 100 | ·······················2·4····1·5····0·6 | 100 | ·······················2·4····1·5····0·6 |
| 101 | ·····················} | 101 | ·····················} |
| 102 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20) | 102 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20) |
| 103 | i2·:·time·psi·=·inverseMap·phi | 103 | i2·:·time·psi·=·inverseMap·phi |
| 104 | ·--·used·0.1 | 104 | ·--·used·0.154207s·(cpu);·0.10972s·(thread);·0s·(gc) |
| 105 | o2·=·--·rational·map·-- | 105 | o2·=·--·rational·map·-- |
| 106 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w | 106 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w |
| 107 | ,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) | 107 | ,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 108 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13 | 108 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13 |
| 109 | 14···15···16···17···18···19···20 | 109 | 14···15···16···17···18···19···20 |
| 110 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w | 110 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w |
| Offset 217, 15 lines modified | Offset 217, 15 lines modified | ||
| 217 | 15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4 | 217 | 15····9·20····8·22···3·10····0·13····4·15····9·21····8·23···2·10····0·12····4 |
| 218 | 20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7 | 218 | 20····6·21····8·24···1·10····0·11····4·22····6·23····9·24···4·5····3·6····0·7 |
| 219 | 1·8····2·9 | 219 | 1·8····2·9 |
| 220 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 220 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 221 | ·················0···26··········0···26 | 221 | ·················0···26··········0···26 |
| 222 | i5·:·time·psi·=·inverseMap·phi | 222 | i5·:·time·psi·=·inverseMap·phi |
| 223 | ·--·used·0.2 | 223 | ·--·used·0.28098s·(cpu);·0.169417s·(thread);·0s·(gc) |
| 224 | o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··, | 224 | o5·=·map·(QQ[w·..w··],·QQ[w·..w··],·{-·w·w···+·w·w···+·w··w···-·w··w···-·w·w··, |
| 225 | -·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···- | 225 | -·w·w···+·w·w···+·w··w···-·w··w···-·w·w··,·-·w·w···+·w·w···+·w··w···-·w··w···- |
| 226 | w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···- | 226 | w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···- |
| 227 | w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+ | 227 | w··w···-·w·w··,·-·w·w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w·w···-·w··w···+ |
| 228 | w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+ | 228 | w··w···-·w··w···-·w·w··,·w··w···-·w··w···+·w··w···-·w··w···-·w·w··,·-·w··w···+ |
| 229 | w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w | 229 | w··w···-·w··w···+·w··w···-·w··w··,·-·w··w···+·w··w···-·w··w···+·w··w···-·w··w |
| Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | ·························2800·0····6350400··0·1·····50803200··0·1·····33868800··0·1····181440··1····196000·0·2····381024000··0·1·2·····47628000··0·1·2····10160640··1·2····2268000·0·2····2126250·0·1·2····762048000··1·2····992250·0·2····31752000··1·2····529200·2····73500·0·3····28576800··0·1·3·····32659200··0·1·3·····6531840··1·3····15876000·0·2·3····21432600··0·1·2·3····137168640··1·2·3····158760000·0·2·3·····571536000··1·2·3····95256000·2·3····15876000·0·3····228614400··0·1·3·····65318400··1·3····190512000·0·2·3····95256000··1·2·3····31752000·2·3····352800·0·3····604800··1·3····31752000··2·3····15120·3····47628000·0·4····444528000··0·1·4····4267468800··0·1·4····152409600·1·4····714420000··0·2·4····16003008000··0·1·2·4····1524096000··1·2·4····95256000··0·2·4····533433600··1·2·4····211680·2·4····1000188000·0·3·4····2667168000··0·1·3·4·····457228800··1·3·4····240045120··0·2·3·4·····48009024000··1·2·3·4····14817600·2·3·4····4000752000··0·3·4····1524096000··1·3·4····2667168000··2·3·4····27216000··3·4····190512000·0·4····1778112000··0·1·4····304819200··1·4····47628000··0·2·4····1333584000··1·2·4····5292000··2·4····4000752000··0·3·4···71442000·1·3·4····1333584000··2·3·4····95256000··3·4····3969000·0·4···127008000·1·4····5292000··2·4····21168000·3·4···28000·4 | 102 | ·························2800·0····6350400··0·1·····50803200··0·1·····33868800··0·1····181440··1····196000·0·2····381024000··0·1·2·····47628000··0·1·2····10160640··1·2····2268000·0·2····2126250·0·1·2····762048000··1·2····992250·0·2····31752000··1·2····529200·2····73500·0·3····28576800··0·1·3·····32659200··0·1·3·····6531840··1·3····15876000·0·2·3····21432600··0·1·2·3····137168640··1·2·3····158760000·0·2·3·····571536000··1·2·3····95256000·2·3····15876000·0·3····228614400··0·1·3·····65318400··1·3····190512000·0·2·3····95256000··1·2·3····31752000·2·3····352800·0·3····604800··1·3····31752000··2·3····15120·3····47628000·0·4····444528000··0·1·4····4267468800··0·1·4····152409600·1·4····714420000··0·2·4····16003008000··0·1·2·4····1524096000··1·2·4····95256000··0·2·4····533433600··1·2·4····211680·2·4····1000188000·0·3·4····2667168000··0·1·3·4·····457228800··1·3·4····240045120··0·2·3·4·····48009024000··1·2·3·4····14817600·2·3·4····4000752000··0·3·4····1524096000··1·3·4····2667168000··2·3·4····27216000··3·4····190512000·0·4····1778112000··0·1·4····304819200··1·4····47628000··0·2·4····1333584000··1·2·4····5292000··2·4····4000752000··0·3·4···71442000·1·3·4····1333584000··2·3·4····95256000··3·4····3969000·0·4···127008000·1·4····5292000··2·4····21168000·3·4···28000·4 |
| 103 | ·····················} | 103 | ·····················} |
| 104 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)</code></pre> | 104 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·phi | 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·phi |
| 108 | ·--·used·0. | 108 | ·--·used·0.120667s·(cpu);·0.066183s·(thread);·0s·(gc) |
| 109 | o3·=·--·rational·map·-- | 109 | o3·=·--·rational·map·-- |
| 110 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 110 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 111 | ······················0···1···2···3···4 | 111 | ······················0···1···2···3···4 |
| 112 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 112 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 113 | ······················0···1···2···3···4 | 113 | ······················0···1···2···3···4 |
| 114 | ·····defining·forms:·{ | 114 | ·····defining·forms:·{ |
| Offset 282, 15 lines modified | Offset 282, 15 lines modified | ||
| 282 | 1333584000··1·2·4····5292000··2·4····4000752000··0·3·4···71442000·1·3·4 | 282 | 1333584000··1·2·4····5292000··2·4····4000752000··0·3·4···71442000·1·3·4 |
| 283 | 1333584000··2·3·4····95256000··3·4····3969000·0·4···127008000·1·4····5292000··2 | 283 | 1333584000··2·3·4····95256000··3·4····3969000·0·4···127008000·1·4····5292000··2 |
| 284 | 4····21168000·3·4···28000·4 | 284 | 4····21168000·3·4···28000·4 |
| 285 | ·····················} | 285 | ·····················} |
| 286 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4) | 286 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4) |
| 287 | i3·:·time·inverse·phi | 287 | i3·:·time·inverse·phi |
| 288 | ·--·used·0. | 288 | ·--·used·0.120667s·(cpu);·0.066183s·(thread);·0s·(gc) |
| 289 | o3·=·--·rational·map·-- | 289 | o3·=·--·rational·map·-- |
| 290 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 290 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 291 | ······················0···1···2···3···4 | 291 | ······················0···1···2···3···4 |
| 292 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 292 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 293 | ······················0···1···2···3···4 | 293 | ······················0···1···2···3···4 |
| 294 | ·····defining·forms:·{ | 294 | ·····defining·forms:·{ |
| Offset 122, 21 lines modified | Offset 122, 21 lines modified | ||
| 122 | ·························3····2·4 | 122 | ·························3····2·4 |
| 123 | ·····················} | 123 | ·····················} |
| 124 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 124 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isBirational·phi | 127 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isBirational·phi |
| 128 | ·--·used·0.0 | 128 | ·--·used·0.0937433s·(cpu);·0.0391452s·(thread);·0s·(gc) |
| 129 | o3·=·true</code></pre> | 129 | o3·=·true</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isBirational(phi,Certify=>true) | 132 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isBirational(phi,Certify=>true) |
| 133 | ·--·used·0.2 | 133 | ·--·used·0.283204s·(cpu);·0.0649912s·(thread);·0s·(gc) |
| 134 | Certify:·output·certified! | 134 | Certify:·output·certified! |
| 135 | o4·=·true</code></pre> | 135 | o4·=·true</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ········</table> | 137 | ········</table> |
| 138 | ······</div> | 138 | ······</div> |
| 139 | ······<div> | 139 | ······<div> |
| Offset 59, 19 lines modified | Offset 59, 19 lines modified | ||
| 59 | ······················-·t··+·t·t | 59 | ······················-·t··+·t·t |
| 60 | ·························3····2·4 | 60 | ·························3····2·4 |
| 61 | ·····················} | 61 | ·····················} |
| 62 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in | 62 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in |
| 63 | PP^5) | 63 | PP^5) |
| 64 | i3·:·time·isBirational·phi | 64 | i3·:·time·isBirational·phi |
| 65 | ·--·used·0.0 | 65 | ·--·used·0.0937433s·(cpu);·0.0391452s·(thread);·0s·(gc) |
| 66 | o3·=·true | 66 | o3·=·true |
| 67 | i4·:·time·isBirational(phi,Certify=>true) | 67 | i4·:·time·isBirational(phi,Certify=>true) |
| 68 | ·--·used·0.2 | 68 | ·--·used·0.283204s·(cpu);·0.0649912s·(thread);·0s·(gc) |
| 69 | Certify:·output·certified! | 69 | Certify:·output·certified! |
| 70 | o4·=·true | 70 | o4·=·true |
| 71 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 71 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 72 | ····*·_\x8i_\x8s_\x8D_\x8o_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·whether·a·rational·map·is·dominant | 72 | ····*·_\x8i_\x8s_\x8D_\x8o_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·whether·a·rational·map·is·dominant |
| 73 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sB\x8Bi\x8ir\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* | 73 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sB\x8Bi\x8ir\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 74 | ····*·isBirational(RationalMap) | 74 | ····*·isBirational(RationalMap) |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},{x_4..x_8}}; | 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7},{x_4..x_8}}; |
| 85 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)</code></pre> | 85 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isDominant(phi,Certify=>true) | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isDominant(phi,Certify=>true) |
| 89 | ·--·used· | 89 | ·--·used·2.0284s·(cpu);·1.8784s·(thread);·0s·(gc) |
| 90 | Certify:·output·certified! | 90 | Certify:·output·certified! |
| 91 | o3·=·true</code></pre> | 91 | o3·=·true</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·P7·=·ZZ/101[x_0..x_7];</code></pre> | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·P7·=·ZZ/101[x_0..x_7];</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·rationalMap(C,3,2); | 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·rationalMap(C,3,2); |
| 106 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)</code></pre> | 106 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDominant(phi,Certify=>true) | 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDominant(phi,Certify=>true) |
| 110 | ·--·used·2. | 110 | ·--·used·2.67717s·(cpu);·2.14012s·(thread);·0s·(gc) |
| 111 | Certify:·output·certified! | 111 | Certify:·output·certified! |
| 112 | o7·=·false</code></pre> | 112 | o7·=·false</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ········</table> | 114 | ········</table> |
| 115 | ······</div> | 115 | ······</div> |
| 116 | ······<div> | 116 | ······<div> |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | be·to·perform·the·command·kernel·map·phi·==·0. | 20 | be·to·perform·the·command·kernel·map·phi·==·0. |
| 21 | i1·:·P8·=·ZZ/101[x_0..x_8]; | 21 | i1·:·P8·=·ZZ/101[x_0..x_8]; |
| 22 | i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7}, | 22 | i2·:·phi·=·rationalMap·ideal·jacobian·ideal·det·matrix{{x_0..x_4},{x_1..x_5},{x_2..x_6},{x_3..x_7}, |
| 23 | {x_4..x_8}}; | 23 | {x_4..x_8}}; |
| 24 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8) | 24 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8) |
| 25 | i3·:·time·isDominant(phi,Certify=>true) | 25 | i3·:·time·isDominant(phi,Certify=>true) |
| 26 | ·--·used· | 26 | ·--·used·2.0284s·(cpu);·1.8784s·(thread);·0s·(gc) |
| 27 | Certify:·output·certified! | 27 | Certify:·output·certified! |
| 28 | o3·=·true | 28 | o3·=·true |
| 29 | i4·:·P7·=·ZZ/101[x_0..x_7]; | 29 | i4·:·P7·=·ZZ/101[x_0..x_7]; |
| 30 | i5·:·--·hyperelliptic·curve·of·genus·3 | 30 | i5·:·--·hyperelliptic·curve·of·genus·3 |
| 31 | ·····C·=·ideal(x_4*x_5+23*x_5^2-23*x_0*x_6-18*x_1*x_6+6*x_2*x_6+37*x_3*x_6+23*x_4*x_6- | 31 | ·····C·=·ideal(x_4*x_5+23*x_5^2-23*x_0*x_6-18*x_1*x_6+6*x_2*x_6+37*x_3*x_6+23*x_4*x_6- |
| 32 | 26*x_5*x_6+2*x_6^2-25*x_0*x_7+45*x_1*x_7+30*x_2*x_7-49*x_3*x_7-49*x_4*x_7+50*x_5*x_7,x_3*x_5- | 32 | 26*x_5*x_6+2*x_6^2-25*x_0*x_7+45*x_1*x_7+30*x_2*x_7-49*x_3*x_7-49*x_4*x_7+50*x_5*x_7,x_3*x_5- |
| Offset 65, 15 lines modified | Offset 65, 15 lines modified | ||
| 65 | 47*x_1*x_7-19*x_2*x_7+25*x_3*x_7+28*x_4*x_7+34*x_5*x_7); | 65 | 47*x_1*x_7-19*x_2*x_7+25*x_3*x_7+28*x_4*x_7+34*x_5*x_7); |
| 66 | o5·:·Ideal·of·P7 | 66 | o5·:·Ideal·of·P7 |
| 67 | i6·:·phi·=·rationalMap(C,3,2); | 67 | i6·:·phi·=·rationalMap(C,3,2); |
| 68 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7) | 68 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7) |
| 69 | i7·:·time·isDominant(phi,Certify=>true) | 69 | i7·:·time·isDominant(phi,Certify=>true) |
| 70 | ·--·used·2. | 70 | ·--·used·2.67717s·(cpu);·2.14012s·(thread);·0s·(gc) |
| 71 | Certify:·output·certified! | 71 | Certify:·output·certified! |
| 72 | o7·=·false | 72 | o7·=·false |
| 73 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 73 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 74 | ····*·_\x8i_\x8s_\x8B_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·rational·map·is·birational | 74 | ····*·_\x8i_\x8s_\x8B_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·rational·map·is·birational |
| 75 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sD\x8Do\x8om\x8mi\x8in\x8na\x8an\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 75 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sD\x8Do\x8om\x8mi\x8in\x8na\x8an\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 76 | ····*·isDominant(RationalMap) | 76 | ····*·isDominant(RationalMap) |
| Offset 87, 24 lines modified | Offset 87, 24 lines modified | ||
| 87 | ··············0···8·······0···11········0·3····2·4····3·4······0·5·····2·5····3·5····4·5······5·····0·6·····2·6····4·6······5·6·····6····4·7·····5·7·····6·7·····4·8······5·8·····6·8·····1·2·····1·5·····0·6·····1·6····4·6····5·6·····0·7····1·7·····2·7·····5·7·····6·7·····1·8·····7·8·······0·····0·2······0·4·····2·4····4······0·5····2·5·····4·5······0·6·····4·6····5·6····0·7·····2·7····4·7·····5·7·····6·7·····0·8·····4·8·····7·8···2·4····3·4····4·····2·5·····4·5······5·6·····6·····3·7·····4·7······5·7·····6·7····3·8····4·8······5·8····6·8······0·4····2·4·····2·5·····4·5·····0·6·····2·6····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···0·4····4·····1·5·····4·5····0·6····1·6·····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···2·3····4·····4·5····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8···1·3·····1·5····1·6····4·6·····5·6·····6····3·7······0·3····3·4····4·····0·5·····4·5····0·6····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8······0·2·····2····2·4····4····2·5·····4·5······0·6·····5·6·····2·7·····4·7······5·7·····6·7·····0·8·····2·8·····4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7···0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2·7·····0·8·····1·8·····5·8·····6·8·····7·8 | 87 | ··············0···8·······0···11········0·3····2·4····3·4······0·5·····2·5····3·5····4·5······5·····0·6·····2·6····4·6······5·6·····6····4·7·····5·7·····6·7·····4·8······5·8·····6·8·····1·2·····1·5·····0·6·····1·6····4·6····5·6·····0·7····1·7·····2·7·····5·7·····6·7·····1·8·····7·8·······0·····0·2······0·4·····2·4····4······0·5····2·5·····4·5······0·6·····4·6····5·6····0·7·····2·7····4·7·····5·7·····6·7·····0·8·····4·8·····7·8···2·4····3·4····4·····2·5·····4·5······5·6·····6·····3·7·····4·7······5·7·····6·7····3·8····4·8······5·8····6·8······0·4····2·4·····2·5·····4·5·····0·6·····2·6····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···0·4····4·····1·5·····4·5····0·6····1·6·····4·6····5·6····4·7·····5·7·····6·7····4·8·····5·8·····6·8···2·3····4·····4·5····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8···1·3·····1·5····1·6····4·6·····5·6·····6····3·7······0·3····3·4····4·····0·5·····4·5····0·6····4·6·····5·6·····6····3·7····4·7·····5·7·····6·7····4·8·····5·8·····6·8······0·2·····2····2·4····4····2·5·····4·5······0·6·····5·6·····2·7·····4·7······5·7·····6·7·····0·8·····2·8·····4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7···0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2·7·····0·8·····1·8·····5·8·····6·8·····7·8 |
| 88 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] | 88 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] |
| 89 | ·················0···8··········0···11</code></pre> | 89 | ·················0···8··········0···11</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·kernel(phi,1) | 92 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·kernel(phi,1) |
| 93 | ·--·used·0.01 | 93 | ·--·used·0.012553s·(cpu);·0.016148s·(thread);·0s·(gc) |
| 94 | o2·=·ideal·() | 94 | o2·=·ideal·() |
| 95 | o2·:·Ideal·of·QQ[y·..y··] | 95 | o2·:·Ideal·of·QQ[y·..y··] |
| 96 | ··················0···11</code></pre> | 96 | ··················0···11</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·kernel(phi,2) | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·kernel(phi,2) |
| 100 | ·--·used·0.3 | 100 | ·--·used·0.373972s·(cpu);·0.264096s·(thread);·0s·(gc) |
| 101 | ···························2················································ | 101 | ···························2················································ |
| 102 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- | 102 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- |
| 103 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6·· | 103 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6·· |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ··········································································· | 105 | ··········································································· |
| 106 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- | 106 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- |
| Offset 68, 22 lines modified | Offset 68, 22 lines modified | ||
| 68 | 4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7 | 68 | 4·8·····5·8·····6·8·····7·8······0·1····1·2····1·4·····0·6····1·6····4·6····0·7 |
| 69 | 0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2 | 69 | 0·2····1·2·····0·4····1·4······1·5····2·5·····4·5·····0·6·····1·6·····4·6·····2 |
| 70 | 7·····0·8·····1·8·····5·8·····6·8·····7·8 | 70 | 7·····0·8·····1·8·····5·8·····6·8·····7·8 |
| 71 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] | 71 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] |
| 72 | ·················0···8··········0···11 | 72 | ·················0···8··········0···11 |
| 73 | i2·:·time·kernel(phi,1) | 73 | i2·:·time·kernel(phi,1) |
| 74 | ·--·used·0.01 | 74 | ·--·used·0.012553s·(cpu);·0.016148s·(thread);·0s·(gc) |
| 75 | o2·=·ideal·() | 75 | o2·=·ideal·() |
| 76 | o2·:·Ideal·of·QQ[y·..y··] | 76 | o2·:·Ideal·of·QQ[y·..y··] |
| 77 | ··················0···11 | 77 | ··················0···11 |
| 78 | i3·:·time·kernel(phi,2) | 78 | i3·:·time·kernel(phi,2) |
| 79 | ·--·used·0.3 | 79 | ·--·used·0.373972s·(cpu);·0.264096s·(thread);·0s·(gc) |
| 80 | ···························2 | 80 | ···························2 |
| 81 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- | 81 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- |
| 82 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6 | 82 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6 |
| 83 | ·····------------------------------------------------------------------------ | 83 | ·····------------------------------------------------------------------------ |
| 84 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- | 84 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- |
| Offset 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | ·················ZZ | 101 | ·················ZZ |
| 102 | o2·:·Ideal·of·--------[x·..x·] | 102 | o2·:·Ideal·of·--------[x·..x·] |
| 103 | ··············10000019··0···9</code></pre> | 103 | ··············10000019··0···9</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·parametrize·L | 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·parametrize·L |
| 107 | ·--·used·0.00 | 107 | ·--·used·0.00396491s·(cpu);·0.0045012s·(thread);·0s·(gc) |
| 108 | o3·=·--·rational·map·-- | 108 | o3·=·--·rational·map·-- |
| 109 | ·····················ZZ | 109 | ·····················ZZ |
| 110 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) | 110 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) |
| 111 | ··················10000019··0···1···2···3···4···5 | 111 | ··················10000019··0···1···2···3···4···5 |
| 112 | ·····················ZZ | 112 | ·····················ZZ |
| 113 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 113 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 193, 15 lines modified | Offset 193, 15 lines modified | ||
| 193 | ·················ZZ | 193 | ·················ZZ |
| 194 | o4·:·Ideal·of·--------[x·..x·] | 194 | o4·:·Ideal·of·--------[x·..x·] |
| 195 | ··············10000019··0···9</code></pre> | 195 | ··············10000019··0···9</code></pre> |
| 196 | </td>··········</tr> | 196 | </td>··········</tr> |
| 197 | ··········<tr> | 197 | ··········<tr> |
| 198 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·parametrize·Q | 198 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·parametrize·Q |
| 199 | ·--·used·0.6 | 199 | ·--·used·0.646178s·(cpu);·0.360424s·(thread);·0s·(gc) |
| 200 | o5·=·--·rational·map·-- | 200 | o5·=·--·rational·map·-- |
| 201 | ·····················ZZ | 201 | ·····················ZZ |
| 202 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 202 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 203 | ··················10000019··0···1···2···3···4···5···6 | 203 | ··················10000019··0···1···2···3···4···5···6 |
| 204 | ·····················ZZ | 204 | ·····················ZZ |
| 205 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 205 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | ·····-·849671x··+·3034137x·) | 41 | ·····-·849671x··+·3034137x·) |
| 42 | ··············8···········9 | 42 | ··············8···········9 |
| 43 | ·················ZZ | 43 | ·················ZZ |
| 44 | o2·:·Ideal·of·--------[x·..x·] | 44 | o2·:·Ideal·of·--------[x·..x·] |
| 45 | ··············10000019··0···9 | 45 | ··············10000019··0···9 |
| 46 | i3·:·time·parametrize·L | 46 | i3·:·time·parametrize·L |
| 47 | ·--·used·0.00 | 47 | ·--·used·0.00396491s·(cpu);·0.0045012s·(thread);·0s·(gc) |
| 48 | o3·=·--·rational·map·-- | 48 | o3·=·--·rational·map·-- |
| 49 | ·····················ZZ | 49 | ·····················ZZ |
| 50 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) | 50 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) |
| 51 | ··················10000019··0···1···2···3···4···5 | 51 | ··················10000019··0···1···2···3···4···5 |
| 52 | ·····················ZZ | 52 | ·····················ZZ |
| 53 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 53 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | ·····1211601x·x··-·2168594x·x··-·1801762x·x··+·3022242x·x··+·3618789x·) | 137 | ·····1211601x·x··-·2168594x·x··-·1801762x·x··+·3022242x·x··+·3618789x·) |
| 138 | ·············5·9···········6·9···········7·9···········8·9···········9 | 138 | ·············5·9···········6·9···········7·9···········8·9···········9 |
| 139 | ·················ZZ | 139 | ·················ZZ |
| 140 | o4·:·Ideal·of·--------[x·..x·] | 140 | o4·:·Ideal·of·--------[x·..x·] |
| 141 | ··············10000019··0···9 | 141 | ··············10000019··0···9 |
| 142 | i5·:·time·parametrize·Q | 142 | i5·:·time·parametrize·Q |
| 143 | ·--·used·0.6 | 143 | ·--·used·0.646178s·(cpu);·0.360424s·(thread);·0s·(gc) |
| 144 | o5·=·--·rational·map·-- | 144 | o5·=·--·rational·map·-- |
| 145 | ·····················ZZ | 145 | ·····················ZZ |
| 146 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 146 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 147 | ··················10000019··0···1···2···3···4···5···6 | 147 | ··················10000019··0···1···2···3···4···5···6 |
| 148 | ·····················ZZ | 148 | ·····················ZZ |
| 149 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 149 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); |
| 78 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)</code></pre> | 78 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·p·=·point·source·f | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·p·=·point·source·f |
| 82 | ·--·used·0.1 | 82 | ·--·used·0.180833s·(cpu);·0.133539s·(thread);·0s·(gc) |
| 83 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ | 83 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ |
| 84 | ·············10········11···9·········11···8········11···7········11···6·· | 84 | ·············10········11···9·········11···8········11···7········11···6·· |
| 85 | ·····------------------------------------------------------------------------ | 85 | ·····------------------------------------------------------------------------ |
| 86 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- | 86 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- |
| 87 | ···········11···5········11···4········11···3·········11···2········11···1·· | 87 | ···········11···5········11···4········11···3·········11···2········11···1·· |
| 88 | ·····------------------------------------------------------------------------ | 88 | ·····------------------------------------------------------------------------ |
| Offset 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | ···························································33331··0···11 | 96 | ···························································33331··0···11 |
| 97 | o2·:·Ideal·of·------------------------------------------------------------------------------------------------------- | 97 | o2·:·Ideal·of·------------------------------------------------------------------------------------------------------- |
| 98 | ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) | 98 | ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) |
| 99 | ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7</code></pre> | 99 | ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11···3·4····1·6····0·8···2·4····1·5····0·7</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·==·f^*·f·p | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·==·f^*·f·p |
| 103 | ·--·used·0.1 | 103 | ·--·used·0.15898s·(cpu);·0.106391s·(thread);·0s·(gc) |
| 104 | o3·=·true</code></pre> | 104 | o3·=·true</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | ······</div> | 107 | ······</div> |
| 108 | ······<div> | 108 | ······<div> |
| 109 | ········<h2>See·also</h2> | 109 | ········<h2>See·also</h2> |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | documentation)·,·see·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8). | 20 | documentation)·,·see·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8). |
| 21 | Below·we·verify·the·birationality·of·a·rational·map. | 21 | Below·we·verify·the·birationality·of·a·rational·map. |
| 22 | i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); | 22 | i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); |
| 23 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to | 23 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to |
| 24 | PP^8) | 24 | PP^8) |
| 25 | i2·:·time·p·=·point·source·f | 25 | i2·:·time·p·=·point·source·f |
| 26 | ·--·used·0.1 | 26 | ·--·used·0.180833s·(cpu);·0.133539s·(thread);·0s·(gc) |
| 27 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ | 27 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ |
| 28 | ·············10········11···9·········11···8········11···7········11···6 | 28 | ·············10········11···9·········11···8········11···7········11···6 |
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- | 30 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- |
| 31 | ···········11···5········11···4········11···3·········11···2········11···1 | 31 | ···········11···5········11···4········11···3·········11···2········11···1 |
| 32 | ·····------------------------------------------------------------------------ | 32 | ·····------------------------------------------------------------------------ |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | o2·:·Ideal·of·----------------------------------------------------------------- | 41 | o2·:·Ideal·of·----------------------------------------------------------------- |
| 42 | -------------------------------------- | 42 | -------------------------------------- |
| 43 | ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y | 43 | ··············(y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y·y··-·y·y··+·y·y··,·y |
| 44 | y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) | 44 | y··-·y·y··+·y·y·,·y·y··-·y·y··+·y·y·) |
| 45 | ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11 | 45 | ················6·7····5·8····4·11···3·7····2·8····1·11···3·5····2·6····0·11 |
| 46 | 3·4····1·6····0·8···2·4····1·5····0·7 | 46 | 3·4····1·6····0·8···2·4····1·5····0·7 |
| 47 | i3·:·time·p·==·f^*·f·p | 47 | i3·:·time·p·==·f^*·f·p |
| 48 | ·--·used·0.1 | 48 | ·--·used·0.15898s·(cpu);·0.106391s·(thread);·0s·(gc) |
| 49 | o3·=·true | 49 | o3·=·true |
| 50 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 50 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 51 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·--·Pick·a·random·K·rational·point·on·the·scheme·X | 51 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·--·Pick·a·random·K·rational·point·on·the·scheme·X |
| 52 | ······defined·by·I | 52 | ······defined·by·I |
| 53 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 53 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 54 | ····*·point(PolynomialRing) | 54 | ····*·point(PolynomialRing) |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ·····················0···4··············0···5·······1····0·2·····1·2····0·3·····2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4 | 90 | ·····················0···4··············0···5·······1····0·2·····1·2····0·3·····2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4 |
| 91 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] | 91 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] |
| 92 | ························0···4·················0···5</code></pre> | 92 | ························0···4·················0···5</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·projectiveDegrees(phi,Certify=>true) | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·projectiveDegrees(phi,Certify=>true) |
| 96 | ·--·used·0. | 96 | ·--·used·0.165802s·(cpu);·0.0280862s·(thread);·0s·(gc) |
| 97 | Certify:·output·certified! | 97 | Certify:·output·certified! |
| 98 | o3·=·{1,·2,·4,·4,·2} | 98 | o3·=·{1,·2,·4,·4,·2} |
| 99 | o3·:·List</code></pre> | 99 | o3·:·List</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | ·························0···5 | 114 | ·························0···5 |
| 115 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] | 115 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] |
| 116 | ·············x·x··-·x·x··+·x·x·················0···4 | 116 | ·············x·x··-·x·x··+·x·x·················0···4 |
| 117 | ··············2·3····1·4····0·5</code></pre> | 117 | ··············2·3····1·4····0·5</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,Certify=>true) | 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,Certify=>true) |
| 121 | ·--·used·0.24 | 121 | ·--·used·0.241661s·(cpu);·0.0328156s·(thread);·0s·(gc) |
| 122 | Certify:·output·certified! | 122 | Certify:·output·certified! |
| 123 | o5·=·{2,·4,·4,·2,·1} | 123 | o5·=·{2,·4,·4,·2,·1} |
| 124 | o5·:·List</code></pre> | 124 | o5·:·List</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ········</table> | 126 | ········</table> |
| Offset 137, 23 lines modified | Offset 137, 23 lines modified | ||
| 137 | ···············ZZ·················ZZ | 137 | ···············ZZ·················ZZ |
| 138 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] | 138 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] |
| 139 | ·············300007··0···6······300007··0···6</code></pre> | 139 | ·············300007··0···6······300007··0···6</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·projectiveDegrees·phi | 142 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·projectiveDegrees·phi |
| 143 | ·--·used·0.00 | 143 | ·--·used·0.000775454s·(cpu);·5.0575e-05s·(thread);·0s·(gc) |
| 144 | o7·=·{1,·2,·4,·8,·8,·4,·1} | 144 | o7·=·{1,·2,·4,·8,·8,·4,·1} |
| 145 | o7·:·List</code></pre> | 145 | o7·:·List</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·projectiveDegrees(phi,NumDegrees=>1) | 148 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·projectiveDegrees(phi,NumDegrees=>1) |
| 149 | ·--·used· | 149 | ·--·used·9.9096e-05s·(cpu);·2.149e-05s·(thread);·0s·(gc) |
| 150 | o8·=·{4,·1} | 150 | o8·=·{4,·1} |
| 151 | o8·:·List</code></pre> | 151 | o8·:·List</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ········</table> | 153 | ········</table> |
| 154 | ········<p>Another·way·to·use·this·method·is·by·passing·an·integer·<span·class="tt">i</span>·as·second·argument.·However,·this·is·equivalent·to·<span·class="tt">first·projectiveDegrees(phi,NumDegrees=>i)</span>·and·generally·it·is·not·faster.</p> | 154 | ········<p>Another·way·to·use·this·method·is·by·passing·an·integer·<span·class="tt">i</span>·as·second·argument.·However,·this·is·equivalent·to·<span·class="tt">first·projectiveDegrees(phi,NumDegrees=>i)</span>·and·generally·it·is·not·faster.</p> |
| Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
| 53 | t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a}) | 53 | t··+·t·t·,·-·t·t··+·t·t·,·-·t·t··+·t·t·,·-·t··+·t·t·,·a}) |
| 54 | ·····················0···4··············0···5·······1····0·2·····1·2····0·3 | 54 | ·····················0···4··············0···5·······1····0·2·····1·2····0·3 |
| 55 | 2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4 | 55 | 2····1·3·····1·3····0·4·····2·3····1·4·····3····2·4 |
| 56 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] | 56 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] |
| 57 | ························0···4·················0···5 | 57 | ························0···4·················0···5 |
| 58 | i3·:·time·projectiveDegrees(phi,Certify=>true) | 58 | i3·:·time·projectiveDegrees(phi,Certify=>true) |
| 59 | ·--·used·0. | 59 | ·--·used·0.165802s·(cpu);·0.0280862s·(thread);·0s·(gc) |
| 60 | Certify:·output·certified! | 60 | Certify:·output·certified! |
| 61 | o3·=·{1,·2,·4,·4,·2} | 61 | o3·=·{1,·2,·4,·4,·2} |
| 62 | o3·:·List | 62 | o3·:·List |
| 63 | i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity)) | 63 | i4·:·psi=inverseMap(toMap(phi,Dominant=>infinity)) |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | ··············GF·109561[x·..x·] | 76 | ··············GF·109561[x·..x·] |
| 77 | ·························0···5 | 77 | ·························0···5 |
| 78 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] | 78 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] |
| 79 | ·············x·x··-·x·x··+·x·x·················0···4 | 79 | ·············x·x··-·x·x··+·x·x·················0···4 |
| 80 | ··············2·3····1·4····0·5 | 80 | ··············2·3····1·4····0·5 |
| 81 | i5·:·time·projectiveDegrees(psi,Certify=>true) | 81 | i5·:·time·projectiveDegrees(psi,Certify=>true) |
| 82 | ·--·used·0.24 | 82 | ·--·used·0.241661s·(cpu);·0.0328156s·(thread);·0s·(gc) |
| 83 | Certify:·output·certified! | 83 | Certify:·output·certified! |
| 84 | o5·=·{2,·4,·4,·2,·1} | 84 | o5·=·{2,·4,·4,·2,·1} |
| 85 | o5·:·List | 85 | o5·:·List |
| 86 | i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a | 86 | i6·:·--·Cremona·transformation·of·P^6·defined·by·the·quadrics·through·a |
| 87 | rational·octic·surface | 87 | rational·octic·surface |
| Offset 120, 21 lines modified | Offset 120, 21 lines modified | ||
| 120 | 4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6 | 120 | 4·5·········5·········0·6·········1·6··········2·6··········3·6·········4·6 |
| 121 | 5·6 | 121 | 5·6 |
| 122 | ···············ZZ·················ZZ | 122 | ···············ZZ·················ZZ |
| 123 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] | 123 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] |
| 124 | ·············300007··0···6······300007··0···6 | 124 | ·············300007··0···6······300007··0···6 |
| 125 | i7·:·time·projectiveDegrees·phi | 125 | i7·:·time·projectiveDegrees·phi |
| 126 | ·--·used·0.00 | 126 | ·--·used·0.000775454s·(cpu);·5.0575e-05s·(thread);·0s·(gc) |
| 127 | o7·=·{1,·2,·4,·8,·8,·4,·1} | 127 | o7·=·{1,·2,·4,·8,·8,·4,·1} |
| 128 | o7·:·List | 128 | o7·:·List |
| 129 | i8·:·time·projectiveDegrees(phi,NumDegrees=>1) | 129 | i8·:·time·projectiveDegrees(phi,NumDegrees=>1) |
| 130 | ·--·used· | 130 | ·--·used·9.9096e-05s·(cpu);·2.149e-05s·(thread);·0s·(gc) |
| 131 | o8·=·{4,·1} | 131 | o8·=·{4,·1} |
| 132 | o8·:·List | 132 | o8·:·List |
| 133 | Another·way·to·use·this·method·is·by·passing·an·integer·i·as·second·argument. | 133 | Another·way·to·use·this·method·is·by·passing·an·integer·i·as·second·argument. |
| 134 | However,·this·is·equivalent·to·first·projectiveDegrees(phi,NumDegrees=>i)·and | 134 | However,·this·is·equivalent·to·first·projectiveDegrees(phi,NumDegrees=>i)·and |
| 135 | generally·it·is·not·faster. | 135 | generally·it·is·not·faster. |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ················ZZ | 90 | ················ZZ |
| 91 | o2·:·Ideal·of·-----[x·..x·] | 91 | o2·:·Ideal·of·-----[x·..x·] |
| 92 | ··············33331··0···6</code></pre> | 92 | ··············33331··0···6</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·phi·=·rationalMap(V,3,2) | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·phi·=·rationalMap(V,3,2) |
| 96 | ·--·used·0.0 | 96 | ·--·used·0.0860963s·(cpu);·0.0860586s·(thread);·0s·(gc) |
| 97 | o3·=·--·rational·map·-- | 97 | o3·=·--·rational·map·-- |
| 98 | ····················ZZ | 98 | ····················ZZ |
| 99 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 99 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 100 | ··················33331··0···1···2···3···4···5···6 | 100 | ··················33331··0···1···2···3···4···5···6 |
| 101 | ····················ZZ | 101 | ····················ZZ |
| 102 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··]) | 102 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··]) |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3- | 35 | i1·:·ZZ/33331[x_0..x_6];·V·=·ideal(x_4^2-x_3*x_5,x_2*x_4-x_1*x_5,x_2*x_3- |
| 36 | x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6); | 36 | x_1*x_4,x_2^2-x_0*x_5,x_1*x_2-x_0*x_4,x_1^2-x_0*x_3,x_6); |
| 37 | ················ZZ | 37 | ················ZZ |
| 38 | o2·:·Ideal·of·-----[x·..x·] | 38 | o2·:·Ideal·of·-----[x·..x·] |
| 39 | ··············33331··0···6 | 39 | ··············33331··0···6 |
| 40 | i3·:·time·phi·=·rationalMap(V,3,2) | 40 | i3·:·time·phi·=·rationalMap(V,3,2) |
| 41 | ·--·used·0.0 | 41 | ·--·used·0.0860963s·(cpu);·0.0860586s·(thread);·0s·(gc) |
| 42 | o3·=·--·rational·map·-- | 42 | o3·=·--·rational·map·-- |
| 43 | ····················ZZ | 43 | ····················ZZ |
| 44 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 44 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 45 | ··················33331··0···1···2···3···4···5···6 | 45 | ··················33331··0···1···2···3···4···5···6 |
| 46 | ····················ZZ | 46 | ····················ZZ |
| 47 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··, | 47 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··, |
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| 104 | o4·:·Ideal·of·X</code></pre> | 104 | o4·:·Ideal·of·X</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi·=·rationalMap·D | 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi·=·rationalMap·D |
| 111 | ·--·used·0.0 | 111 | ·--·used·0.031973s·(cpu);·0.0319217s·(thread);·0s·(gc) |
| 112 | o6·=·--·rational·map·-- | 112 | o6·=·--·rational·map·-- |
| 113 | ··································ZZ | 113 | ··································ZZ |
| 114 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by | 114 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by |
| 115 | ································65521··0···1···2···3···4···5 | 115 | ································65521··0···1···2···3···4···5 |
| 116 | ·············{ | 116 | ·············{ |
| 117 | ·················2··················2 | 117 | ·················2··················2 |
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| 210 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 | 210 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 |
| 211 | ·····················} | 211 | ·····················} |
| 212 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)</code></pre> | 212 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ··········<tr> | 214 | ··········<tr> |
| 215 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·?·image(phi,"F4") | 215 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·?·image(phi,"F4") |
| 216 | ·--·used·0. | 216 | ·--·used·0.85525s·(cpu);·0.520579s·(thread);·0s·(gc) |
| 217 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 | 217 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 |
| 218 | ·····hypersurfaces·of·degree·2</code></pre> | 218 | ·····hypersurfaces·of·degree·2</code></pre> |
| 219 | </td>··········</tr> | 219 | </td>··········</tr> |
| 220 | ········</table> | 220 | ········</table> |
| 221 | ········<p>See·also·the·package·<a·href="http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.16/share/doc/Macaulay2/Divisor/html/index.html">Divisor</a>,·which·provides·general·tools·for·working·with·divisors.</p> | 221 | ········<p>See·also·the·package·<a·href="http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.16/share/doc/Macaulay2/Divisor/html/index.html">Divisor</a>,·which·provides·general·tools·for·working·with·divisors.</p> |
| 222 | ······</div> | 222 | ······</div> |
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| 41 | o4·=·ideal(-·32646x··-·28377x··+·26433x··-·29566x··+·3783x··+·26696x·) | 41 | o4·=·ideal(-·32646x··-·28377x··+·26433x··-·29566x··+·3783x··+·26696x·) |
| 42 | ···················0·········1·········2·········3········4·········5 | 42 | ···················0·········1·········2·········3········4·········5 |
| 43 | o4·:·Ideal·of·X | 43 | o4·:·Ideal·of·X |
| 44 | i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1}; | 44 | i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1}; |
| 45 | i6·:·time·phi·=·rationalMap·D | 45 | i6·:·time·phi·=·rationalMap·D |
| 46 | ·--·used·0.0 | 46 | ·--·used·0.031973s·(cpu);·0.0319217s·(thread);·0s·(gc) |
| 47 | o6·=·--·rational·map·-- | 47 | o6·=·--·rational·map·-- |
| 48 | ··································ZZ | 48 | ··································ZZ |
| 49 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by | 49 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by |
| 50 | ································65521··0···1···2···3···4···5 | 50 | ································65521··0···1···2···3···4···5 |
| 51 | ·············{ | 51 | ·············{ |
| 52 | ·················2··················2 | 52 | ·················2··················2 |
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| 170 | ··················································2·························2 | 170 | ··················································2·························2 |
| 171 | ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x | 171 | ······················x·x·x··+·x·x·x··+·x·x·x··+·x·x··+·x·x·x··-·2x·x·x··+·x·x |
| 172 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 | 172 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 |
| 173 | ·····················} | 173 | ·····················} |
| 174 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20) | 174 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20) |
| 175 | i7·:·time·?·image(phi,"F4") | 175 | i7·:·time·?·image(phi,"F4") |
| 176 | ·--·used·0. | 176 | ·--·used·0.85525s·(cpu);·0.520579s·(thread);·0s·(gc) |
| 177 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 | 177 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 |
| 178 | ·····hypersurfaces·of·degree·2 | 178 | ·····hypersurfaces·of·degree·2 |
| 179 | See·also·the·package·_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r,·which·provides·general·tools·for·working·with | 179 | See·also·the·package·_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r,·which·provides·general·tools·for·working·with |
| 180 | divisors. | 180 | divisors. |
| 181 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 181 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 182 | ····*·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·makes·a·rational·map | 182 | ····*·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·makes·a·rational·map |
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| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 73 | ········<p>A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is·smooth·and·irreducible.·To·ensure·this·condition,·the·field·<span·class="tt">K</span>·must·be·large·enough·but·no·check·is·made.</p> | 73 | ········<p>A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is·smooth·and·irreducible.·To·ensure·this·condition,·the·field·<span·class="tt">K</span>·must·be·large·enough·but·no·check·is·made.</p> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) |
| 77 | ·--·used·0. | 77 | ·--·used·0.936673s·(cpu);·0.846677s·(thread);·0s·(gc) |
| 78 | o1·=·(rational·map·defined·by·forms·of·degree·3, | 78 | o1·=·(rational·map·defined·by·forms·of·degree·3, |
| 79 | ······source·variety:·PP^3······················ | 79 | ······source·variety:·PP^3······················ |
| 80 | ······target·variety:·PP^3······················ | 80 | ······target·variety:·PP^3······················ |
| 81 | ······dominance:·true··························· | 81 | ······dominance:·true··························· |
| 82 | ······birationality:·true······················· | 82 | ······birationality:·true······················· |
| 83 | ······projective·degrees:·{1,·3,·3,·1}·········· | 83 | ······projective·degrees:·{1,·3,·3,·1}·········· |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | ············K,·according·to·the·classification·given·in·Table·1·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l | 17 | ············K,·according·to·the·classification·given·in·Table·1·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l |
| 18 | ············_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8C_\x8r_\x8e_\x8m_\x8o_\x8n_\x8a_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8P_\x86_\x8·_\x8a_\x8n_\x8d_\x8·_\x8P_\x87. | 18 | ············_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8C_\x8r_\x8e_\x8m_\x8o_\x8n_\x8a_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8P_\x86_\x8·_\x8a_\x8n_\x8d_\x8·_\x8P_\x87. |
| 19 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 19 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 20 | A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is | 20 | A·Cremona·transformation·is·said·to·be·special·if·the·base·locus·scheme·is |
| 21 | smooth·and·irreducible.·To·ensure·this·condition,·the·field·K·must·be·large | 21 | smooth·and·irreducible.·To·ensure·this·condition,·the·field·K·must·be·large |
| 22 | enough·but·no·check·is·made. | 22 | enough·but·no·check·is·made. |
| 23 | i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) | 23 | i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) |
| 24 | ·--·used·0. | 24 | ·--·used·0.936673s·(cpu);·0.846677s·(thread);·0s·(gc) |
| 25 | o1·=·(rational·map·defined·by·forms·of·degree·3, | 25 | o1·=·(rational·map·defined·by·forms·of·degree·3, |
| 26 | ······source·variety:·PP^3 | 26 | ······source·variety:·PP^3 |
| 27 | ······target·variety:·PP^3 | 27 | ······target·variety:·PP^3 |
| 28 | ······dominance:·true | 28 | ······dominance:·true |
| 29 | ······birationality:·true | 29 | ······birationality:·true |
| 30 | ······projective·degrees:·{1,·3,·3,·1} | 30 | ······projective·degrees:·{1,·3,·3,·1} |
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| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 73 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> | 73 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialCubicTransformation·9 | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialCubicTransformation·9 |
| 77 | ·--·used·0.0 | 77 | ·--·used·0.0728556s·(cpu);·0.0727528s·(thread);·0s·(gc) |
| 78 | o1·=·--·rational·map·-- | 78 | o1·=·--·rational·map·-- |
| 79 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 79 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 80 | ······················0···1···2···3···4···5···6 | 80 | ······················0···1···2···3···4···5···6 |
| 81 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by | 81 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by |
| 82 | ····································0···1···2···3···4···5···6···7···8···9 | 82 | ····································0···1···2···3···4···5···6···7···8···9 |
| 83 | ·············{ | 83 | ·············{ |
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| 136 | ························0·1······0·1······1······0·2······0·1·2······1·2······0·2······1·2·····2·····0·3······0·1·3······1·3······0·2·3······1·2·3······2·3······0·3······1·3······2·3······3·····0·4·····0·1·4······1·4······0·2·4·····1·2·4·····2·4·····0·3·4······1·3·4······2·3·4······3·4·····0·4·····1·4·····2·4·····3·4····4······0·5······0·1·5······1·5·····0·2·5······1·2·5·····2·5······0·3·5······1·3·5······2·3·5······3·5······0·4·5·····1·4·5·····2·4·5·····3·4·5·····4·5·····0·5······1·5·····2·5······3·5····4·5·····5·····0·6·····0·1·6······1·6······0·2·6······1·2·6·····2·6······1·3·6······2·3·6······3·6····0·4·6·····1·4·6·····2·4·6·····3·4·6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6······1·6·····2·6······3·6·····4·6·····5·6 | 136 | ························0·1······0·1······1······0·2······0·1·2······1·2······0·2······1·2·····2·····0·3······0·1·3······1·3······0·2·3······1·2·3······2·3······0·3······1·3······2·3······3·····0·4·····0·1·4······1·4······0·2·4·····1·2·4·····2·4·····0·3·4······1·3·4······2·3·4······3·4·····0·4·····1·4·····2·4·····3·4····4······0·5······0·1·5······1·5·····0·2·5······1·2·5·····2·5······0·3·5······1·3·5······2·3·5······3·5······0·4·5·····1·4·5·····2·4·5·····3·4·5·····4·5·····0·5······1·5·····2·5······3·5····4·5·····5·····0·6·····0·1·6······1·6······0·2·6······1·2·6·····2·6······1·3·6······2·3·6······3·6····0·4·6·····1·4·6·····2·4·6·····3·4·6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6······1·6·····2·6······3·6·····4·6·····5·6 |
| 137 | ·····················} | 137 | ·····················} |
| 138 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> | 138 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo | 141 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo |
| 142 | ·--·used·0.01 | 142 | ·--·used·0.0147798s·(cpu);·0.0149229s·(thread);·0s·(gc) |
| 143 | o2·=·rational·map·defined·by·forms·of·degree·3 | 143 | o2·=·rational·map·defined·by·forms·of·degree·3 |
| 144 | ·····source·variety:·PP^6 | 144 | ·····source·variety:·PP^6 |
| 145 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 | 145 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 |
| 146 | ·····dominance:·true | 146 | ·····dominance:·true |
| 147 | ·····birationality:·true | 147 | ·····birationality:·true |
| 148 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} | 148 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·cubic·birational | 16 | ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·cubic·birational |
| 17 | ············transformation·over·K,·according·to·the·classification·given·in | 17 | ············transformation·over·K,·according·to·the·classification·given·in |
| 18 | ············Table·2·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e | 18 | ············Table·2·of·_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8c_\x8u_\x8b_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e |
| 19 | ············_\x8s_\x8p_\x8a_\x8c_\x8e_\x8s. | 19 | ············_\x8s_\x8p_\x8a_\x8c_\x8e_\x8s. |
| 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 21 | The·field·K·is·required·to·be·large·enough. | 21 | The·field·K·is·required·to·be·large·enough. |
| 22 | i1·:·time·specialCubicTransformation·9 | 22 | i1·:·time·specialCubicTransformation·9 |
| 23 | ·--·used·0.0 | 23 | ·--·used·0.0728556s·(cpu);·0.0727528s·(thread);·0s·(gc) |
| 24 | o1·=·--·rational·map·-- | 24 | o1·=·--·rational·map·-- |
| 25 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 25 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 26 | ······················0···1···2···3···4···5···6 | 26 | ······················0···1···2···3···4···5···6 |
| 27 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 27 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 28 | defined·by | 28 | defined·by |
| 29 | ····································0···1···2···3···4···5···6···7···8···9 | 29 | ····································0···1···2···3···4···5···6···7···8···9 |
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| 324 | 6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6 | 324 | 6·····4·6······0·5·6······1·5·6·····2·5·6······3·5·6······4·5·6·····5·6·····0·6 |
| 325 | 1·6·····2·6······3·6·····4·6·····5·6 | 325 | 1·6·····2·6······3·6·····4·6·····5·6 |
| 326 | ·····················} | 326 | ·····················} |
| 327 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of | 327 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of |
| 328 | PP^9) | 328 | PP^9) |
| 329 | i2·:·time·describe·oo | 329 | i2·:·time·describe·oo |
| 330 | ·--·used·0.01 | 330 | ·--·used·0.0147798s·(cpu);·0.0149229s·(thread);·0s·(gc) |
| 331 | o2·=·rational·map·defined·by·forms·of·degree·3 | 331 | o2·=·rational·map·defined·by·forms·of·degree·3 |
| 332 | ·····source·variety:·PP^6 | 332 | ·····source·variety:·PP^6 |
| 333 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 | 333 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 |
| 334 | ·····dominance:·true | 334 | ·····dominance:·true |
| 335 | ·····birationality:·true | 335 | ·····birationality:·true |
| 336 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} | 336 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} |
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| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 73 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> | 73 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialQuadraticTransformation·4 | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialQuadraticTransformation·4 |
| 77 | ·--·used·0.05 | 77 | ·--·used·0.0595821s·(cpu);·0.0593365s·(thread);·0s·(gc) |
| 78 | o1·=·--·rational·map·-- | 78 | o1·=·--·rational·map·-- |
| 79 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 79 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 80 | ······················0···1···2···3···4···5···6···7···8 | 80 | ······················0···1···2···3···4···5···6···7···8 |
| 81 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by | 81 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by |
| 82 | ····································0···1···2···3···4···5···6···7···8···9 | 82 | ····································0···1···2···3···4···5···6···7···8···9 |
| 83 | ·············{ | 83 | ·············{ |
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| 124 | ·······················0·1····0·4····3·6····4·6····6····5·7 | 124 | ·······················0·1····0·4····3·6····4·6····6····5·7 |
| 125 | ·····················} | 125 | ·····················} |
| 126 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> | 126 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo | 129 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo |
| 130 | ·--·used·0.00 | 130 | ·--·used·0.00329983s·(cpu);·0.00575038s·(thread);·0s·(gc) |
| 131 | o2·=·rational·map·defined·by·forms·of·degree·2 | 131 | o2·=·rational·map·defined·by·forms·of·degree·2 |
| 132 | ·····source·variety:·PP^8 | 132 | ·····source·variety:·PP^8 |
| 133 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 | 133 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 |
| 134 | ·····dominance:·true | 134 | ·····dominance:·true |
| 135 | ·····birationality:·true | 135 | ·····birationality:·true |
| 136 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} | 136 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·quadratic·birational | 16 | ··········o·a·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p,·an·example·of·special·quadratic·birational |
| 17 | ············transformation·over·K,·according·to·the·classification·given·in | 17 | ············transformation·over·K,·according·to·the·classification·given·in |
| 18 | ············Table·1·of·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s_\x8·_\x8o_\x8f_\x8·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8a_\x8t_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s | 18 | ············Table·1·of·_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e_\x8s_\x8·_\x8o_\x8f_\x8·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8a_\x8t_\x8i_\x8c_\x8·_\x8b_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8t_\x8r_\x8a_\x8n_\x8s_\x8f_\x8o_\x8r_\x8m_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s |
| 19 | ············_\x8i_\x8n_\x8t_\x8o_\x8·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8t_\x8e_\x8·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8i_\x8c_\x8s. | 19 | ············_\x8i_\x8n_\x8t_\x8o_\x8·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8t_\x8e_\x8·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8o_\x8f_\x8·_\x8q_\x8u_\x8a_\x8d_\x8r_\x8i_\x8c_\x8s. |
| 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 21 | The·field·K·is·required·to·be·large·enough. | 21 | The·field·K·is·required·to·be·large·enough. |
| 22 | i1·:·time·specialQuadraticTransformation·4 | 22 | i1·:·time·specialQuadraticTransformation·4 |
| 23 | ·--·used·0.05 | 23 | ·--·used·0.0595821s·(cpu);·0.0593365s·(thread);·0s·(gc) |
| 24 | o1·=·--·rational·map·-- | 24 | o1·=·--·rational·map·-- |
| 25 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 25 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 26 | ······················0···1···2···3···4···5···6···7···8 | 26 | ······················0···1···2···3···4···5···6···7···8 |
| 27 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·]) | 27 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·]) |
| 28 | defined·by | 28 | defined·by |
| 29 | ····································0···1···2···3···4···5···6···7···8···9 | 29 | ····································0···1···2···3···4···5···6···7···8···9 |
| Offset 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | ···················································2 | 79 | ···················································2 |
| 80 | ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x | 80 | ······················x·x··-·x·x··+·x·x··-·x·x··-·x··-·x·x |
| 81 | ·······················0·1····0·4····3·6····4·6····6····5·7 | 81 | ·······················0·1····0·4····3·6····4·6····6····5·7 |
| 82 | ·····················} | 82 | ·····················} |
| 83 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9) | 83 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9) |
| 84 | i2·:·time·describe·oo | 84 | i2·:·time·describe·oo |
| 85 | ·--·used·0.00 | 85 | ·--·used·0.00329983s·(cpu);·0.00575038s·(thread);·0s·(gc) |
| 86 | o2·=·rational·map·defined·by·forms·of·degree·2 | 86 | o2·=·rational·map·defined·by·forms·of·degree·2 |
| 87 | ·····source·variety:·PP^8 | 87 | ·····source·variety:·PP^8 |
| 88 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 | 88 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 |
| 89 | ·····dominance:·true | 89 | ·····dominance:·true |
| 90 | ·····birationality:·true | 90 | ·····birationality:·true |
| 91 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} | 91 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} |
| Offset 82, 36 lines modified | Offset 82, 36 lines modified | ||
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·#str | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·#str |
| 84 | o3·=·6927</code></pre> | 84 | o3·=·6927</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi'·=·value·str; | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi'·=·value·str; |
| 88 | ·--·used·0.0 | 88 | ·--·used·0.0880272s·(cpu);·0.0403649s·(thread);·0s·(gc) |
| 89 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)</code></pre> | 89 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·phi' | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·phi' |
| 93 | ·--·used·0.00 | 93 | ·--·used·0.00223309s·(cpu);·0.00564086s·(thread);·0s·(gc) |
| 94 | o5·=·rational·map·defined·by·forms·of·degree·3 | 94 | o5·=·rational·map·defined·by·forms·of·degree·3 |
| 95 | ·····source·variety:·PP^3 | 95 | ·····source·variety:·PP^3 |
| 96 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 | 96 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 97 | ·····dominance:·true | 97 | ·····dominance:·true |
| 98 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 98 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 99 | ·····projective·degrees:·{1,·3,·4,·2} | 99 | ·····projective·degrees:·{1,·3,·4,·2} |
| 100 | ·····number·of·minimal·representatives:·1 | 100 | ·····number·of·minimal·representatives:·1 |
| 101 | ·····dimension·base·locus:·1 | 101 | ·····dimension·base·locus:·1 |
| 102 | ·····degree·base·locus:·5 | 102 | ·····degree·base·locus:·5 |
| 103 | ·····coefficient·ring:·ZZ/33331</code></pre> | 103 | ·····coefficient·ring:·ZZ/33331</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·inverse·phi' | 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·inverse·phi' |
| 107 | ·--·used·0.00 | 107 | ·--·used·0.00418856s·(cpu);·0.00490979s·(thread);·0s·(gc) |
| 108 | o6·=·rational·map·defined·by·forms·of·degree·2 | 108 | o6·=·rational·map·defined·by·forms·of·degree·2 |
| 109 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 | 109 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 110 | ·····target·variety:·PP^3 | 110 | ·····target·variety:·PP^3 |
| 111 | ·····dominance:·true | 111 | ·····dominance:·true |
| 112 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 112 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 113 | ·····projective·degrees:·{2,·4,·3,·1} | 113 | ·····projective·degrees:·{2,·4,·3,·1} |
| Offset 20, 32 lines modified | Offset 20, 32 lines modified | ||
| 20 | o1·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4) | 20 | o1·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4) |
| 21 | i2·:·str·=·toExternalString·phi; | 21 | i2·:·str·=·toExternalString·phi; |
| 22 | i3·:·#str | 22 | i3·:·#str |
| 23 | o3·=·6927 | 23 | o3·=·6927 |
| 24 | i4·:·time·phi'·=·value·str; | 24 | i4·:·time·phi'·=·value·str; |
| 25 | ·--·used·0.0 | 25 | ·--·used·0.0880272s·(cpu);·0.0403649s·(thread);·0s·(gc) |
| 26 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4) | 26 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4) |
| 27 | i5·:·time·describe·phi' | 27 | i5·:·time·describe·phi' |
| 28 | ·--·used·0.00 | 28 | ·--·used·0.00223309s·(cpu);·0.00564086s·(thread);·0s·(gc) |
| 29 | o5·=·rational·map·defined·by·forms·of·degree·3 | 29 | o5·=·rational·map·defined·by·forms·of·degree·3 |
| 30 | ·····source·variety:·PP^3 | 30 | ·····source·variety:·PP^3 |
| 31 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 | 31 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 32 | ·····dominance:·true | 32 | ·····dominance:·true |
| 33 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 33 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 34 | ·····projective·degrees:·{1,·3,·4,·2} | 34 | ·····projective·degrees:·{1,·3,·4,·2} |
| 35 | ·····number·of·minimal·representatives:·1 | 35 | ·····number·of·minimal·representatives:·1 |
| 36 | ·····dimension·base·locus:·1 | 36 | ·····dimension·base·locus:·1 |
| 37 | ·····degree·base·locus:·5 | 37 | ·····degree·base·locus:·5 |
| 38 | ·····coefficient·ring:·ZZ/33331 | 38 | ·····coefficient·ring:·ZZ/33331 |
| 39 | i6·:·time·describe·inverse·phi' | 39 | i6·:·time·describe·inverse·phi' |
| 40 | ·--·used·0.00 | 40 | ·--·used·0.00418856s·(cpu);·0.00490979s·(thread);·0s·(gc) |
| 41 | o6·=·rational·map·defined·by·forms·of·degree·2 | 41 | o6·=·rational·map·defined·by·forms·of·degree·2 |
| 42 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 | 42 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 43 | ·····target·variety:·PP^3 | 43 | ·····target·variety:·PP^3 |
| 44 | ·····dominance:·true | 44 | ·····dominance:·true |
| 45 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 45 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 46 | ·····projective·degrees:·{2,·4,·3,·1} | 46 | ·····projective·degrees:·{2,·4,·3,·1} |
| Offset 48, 63 lines modified | Offset 48, 63 lines modified | ||
| 48 | ········<p>Below·is·an·example·using·the·methods·provided·by·this·package,·dealing·with·a·birational·transformation·$\Phi:\mathbb{P}^6·\dashrightarrow·\mathbb{G}(2,4)\subset\mathbb{P}^9$·of·bidegree·$(3,3)$.</p> | 48 | ········<p>Below·is·an·example·using·the·methods·provided·by·this·package,·dealing·with·a·birational·transformation·$\Phi:\mathbb{P}^6·\dashrightarrow·\mathbb{G}(2,4)\subset\mathbb{P}^9$·of·bidegree·$(3,3)$.</p> |
| 49 | ········<table·class="examples"> | 49 | ········<table·class="examples"> |
| 50 | ··········<tr> | 50 | ··········<tr> |
| 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·ZZ/300007[t_0..t_6];</code></pre> | 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·ZZ/300007[t_0..t_6];</code></pre> |
| 52 | </td>··········</tr> | 52 | </td>··········</tr> |
| 53 | ··········<tr> | 53 | ··········<tr> |
| 54 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) | 54 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) |
| 55 | ·--·used·0.0040 | 55 | ·--·used·0.00401078s·(cpu);·0.00373695s·(thread);·0s·(gc) |
| 56 | ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 | 56 | ············ZZ··············ZZ················3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 |
| 57 | o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) | 57 | o2·=·map·(------[t·..t·],·------[x·..x·],·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) |
| 58 | ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 | 58 | ··········300007··0···6···300007··0···9·······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 |
| 59 | ···············ZZ·················ZZ | 59 | ···············ZZ·················ZZ |
| 60 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] | 60 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] |
| 61 | ·············300007··0···6······300007··0···9</code></pre> | 61 | ·············300007··0···6······300007··0···9</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·J·=·kernel(phi,2) | 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·J·=·kernel(phi,2) |
| 65 | ·--·used·0.03 | 65 | ·--·used·0.0362442s·(cpu);·0.037683s·(thread);·0s·(gc) |
| 66 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x· | 66 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x· |
| 67 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 | 67 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 |
| 68 | ·····------------------------------------------------------------------------ | 68 | ·····------------------------------------------------------------------------ |
| 69 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 69 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 70 | ········1·6····0·8···2·4····1·5····0·7 | 70 | ········1·6····0·8···2·4····1·5····0·7 |
| 71 | ················ZZ | 71 | ················ZZ |
| 72 | o3·:·Ideal·of·------[x·..x·] | 72 | o3·:·Ideal·of·------[x·..x·] |
| 73 | ··············300007··0···9</code></pre> | 73 | ··············300007··0···9</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degreeMap·phi | 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degreeMap·phi |
| 77 | ·--·used·0.0 | 77 | ·--·used·0.0812392s·(cpu);·0.0356259s·(thread);·0s·(gc) |
| 78 | o4·=·1</code></pre> | 78 | o4·=·1</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees·phi | 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees·phi |
| 82 | ·--·used·0.3 | 82 | ·--·used·0.375054s·(cpu);·0.339625s·(thread);·0s·(gc) |
| 83 | o5·=·{1,·3,·9,·17,·21,·15,·5} | 83 | o5·=·{1,·3,·9,·17,·21,·15,·5} |
| 84 | o5·:·List</code></pre> | 84 | o5·:·List</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·projectiveDegrees(phi,NumDegrees=>0) | 87 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·projectiveDegrees(phi,NumDegrees=>0) |
| 88 | ·--·used·0.0 | 88 | ·--·used·0.0627803s·(cpu);·0.0626703s·(thread);·0s·(gc) |
| 89 | o6·=·{5} | 89 | o6·=·{5} |
| 90 | o6·:·List</code></pre> | 90 | o6·:·List</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·phi·=·toMap(phi,Dominant=>J) | 93 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·phi·=·toMap(phi,Dominant=>J) |
| 94 | ·--·used·0.000 | 94 | ·--·used·0.000242715s·(cpu);·0.00237005s·(thread);·0s·(gc) |
| 95 | ·······································································ZZ | 95 | ·······································································ZZ |
| 96 | ·····································································------[x·..x·] | 96 | ·····································································------[x·..x·] |
| 97 | ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 | 97 | ············ZZ·······················································300007··0···9··················································3················2····2················2········2······················2··················2····2·················2·······················3················2····2················2·································2···························2····2··································2········2······················2··················2························2·························2····2·················2·······················3················2····2 |
| 98 | o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) | 98 | o7·=·map·(------[t·..t·],·----------------------------------------------------------------------------------------------------,·{-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t·t··+·t·t··+·t·t··-·t·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t·t··-·t·t··+·t·t·t·,·-·t·t··+·t·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t·t··+·t·t··+·t·t·t··-·t·t··-·t·t·t··+·t·t·t·,·-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t·}) |
| 99 | ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 | 99 | ··········300007··0···6···(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)······2·····1·2·3····0·3····1·4····0·2·4·····2·3····1·3····1·2·4····0·3·4····1·5····0·2·5·····2·3····2·4····1·3·4····0·4····1·2·5····0·3·5·····3·····2·3·4····1·4····2·5····1·3·5·····2·4····1·3·4····1·2·5····0·3·5····1·6····0·2·6·····2·3·4····1·4····2·5····0·4·5····1·2·6····0·3·6·····3·4····2·4····2·3·5····1·4·5····2·6····1·3·6·····2·4····2·3·5····1·4·5····0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4·····3·4·5····2·5····3·6····2·4·6 |
| 100 | ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 100 | ····························6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | ···············ZZ··························································300007··0···9 | 114 | ···············ZZ··························································300007··0···9 |
| 115 | o7·:·RingMap·------[t·..t·]·<--·---------------------------------------------------------------------------------------------------- | 115 | o7·:·RingMap·------[t·..t·]·<--·---------------------------------------------------------------------------------------------------- |
| 116 | ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 116 | ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 117 | ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre> | 117 | ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·psi·=·inverseMap·phi | 120 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·psi·=·inverseMap·phi |
| 121 | ·--·used·0.37 | 121 | ·--·used·0.437051s·(cpu);·0.384559s·(thread);·0s·(gc) |
| 122 | ·······················································ZZ | 122 | ·······················································ZZ |
| 123 | ·····················································------[x·..x·] | 123 | ·····················································------[x·..x·] |
| 124 | ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2 | 124 | ·····················································300007··0···9················································ZZ··············3················2···············2····2························2··························2·····2········2·······························2···································2···············2·············2·······················3·················································2·················2····2··································2····2·················2·················································3·························2······2····2······2··············································2 |
| 125 | o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·}) | 125 | o8·=·map·(----------------------------------------------------------------------------------------------------,·------[t·..t·],·{x··-·2x·x·x··+·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x·x··-·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··-·2x·x·,·x·x··-·x·x··-·x·x·x··+·x·x·x··+·x·x·x··+·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x·x··-·x·x·x··+·x·x··-·x·x·x··+·x·x··-·x·x·x··-·x·x·x·,·x··-·x·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x·,·x·x··-·x·x·x··+·x·x··+·x·x··-·x·x·x··-·x·x·x··-·x·x·x·,·x·x··-·x·x··-·x·x·x··+·x·x··+·x·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··+·x·x·x·,·x··-·2x·x·x··-·x·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·x··-·2x·x·x··-·x·x·x··-·x·x·x··-·2x·x·}) |
| 126 | ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9 | 126 | ··········(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)··300007··0···6·····2·····1·2·3····0·3····1·2·5····0·5····1·6····0·2·6····0·4·6····1·7·····0·2·7····0·4·7·····0·9···2·3····1·3····1·2·6····0·3·6····0·5·6····1·8·····0·2·8····0·4·8····0·1·9···2·3····1·3·6····0·6····0·3·8····1·9····0·2·9····0·4·9···3····1·3·8····0·6·8····1·2·9·····0·3·9····0·5·9···3·6····2·3·8····0·8····2·9····1·3·9····0·6·9····0·7·9···3·6····3·8····2·6·8····1·8····2·3·9····2·5·9·····1·6·9····1·7·9····0·8·9···6·····3·6·8····5·6·8····2·8····4·8····3·9····5·9····2·6·9·····4·6·9····2·7·9····4·7·9·····0·9 |
| 127 | ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 127 | ············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| Offset 132, 38 lines modified | Offset 132, 38 lines modified | ||
| 132 | ························································300007··0···9···················································ZZ | 132 | ························································300007··0···9···················································ZZ |
| 133 | o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·] | 133 | o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·] |
| 134 | ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6 | 134 | ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6 |
| 135 | ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre> | 135 | ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isInverseMap(phi,psi) | 138 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isInverseMap(phi,psi) |
| 139 | ·--·used·0.00 | 139 | ·--·used·0.00737805s·(cpu);·0.00798491s·(thread);·0s·(gc) |
| 140 | o9·=·true</code></pre> | 140 | o9·=·true</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·degreeMap·psi | 143 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·degreeMap·psi |
| 144 | ·--·used·0.18 | 144 | ·--·used·0.218521s·(cpu);·0.16695s·(thread);·0s·(gc) |
| 145 | o10·=·1</code></pre> | 145 | o10·=·1</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·projectiveDegrees·psi | 148 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·projectiveDegrees·psi |
| 149 | ·--·used· | 149 | ·--·used·5.11597s·(cpu);·4.7932s·(thread);·0s·(gc) |
| 150 | o11·=·{5,·15,·21,·17,·9,·3,·1} | 150 | o11·=·{5,·15,·21,·17,·9,·3,·1} |
| 151 | o11·:·List</code></pre> | 151 | o11·:·List</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ········</table> | 153 | ········</table> |
| 154 | ········<p>We·repeat·the·example·using·the·type·<a·title="the·class·of·all·rational·maps·between·absolutely·irreducible·projective·varieties·over·a·field"·href="___Rational__Map.html">RationalMap</a>·and·using·deterministic·methods.</p> | 154 | ········<p>We·repeat·the·example·using·the·type·<a·title="the·class·of·all·rational·maps·between·absolutely·irreducible·projective·varieties·over·a·field"·href="___Rational__Map.html">RationalMap</a>·and·using·deterministic·methods.</p> |
| 155 | ········<table·class="examples"> | 155 | ········<table·class="examples"> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) | 157 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) |
| 158 | ·--·used·0.00 | 158 | ·--·used·0.000742082s·(cpu);·0.00252711s·(thread);·0s·(gc) |
| 159 | o12·=·--·rational·map·-- | 159 | o12·=·--·rational·map·-- |
| 160 | ·····················ZZ | 160 | ·····················ZZ |
| 161 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 161 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 162 | ···················300007··0···1···2···3···4···5···6 | 162 | ···················300007··0···1···2···3···4···5···6 |
| 163 | ·····················ZZ | 163 | ·····················ZZ |
| 164 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 164 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 210, 15 lines modified | Offset 210, 15 lines modified | ||
| 210 | ··························4·····3·4·5····2·5····3·6····2·4·6 | 210 | ··························4·····3·4·5····2·5····3·6····2·4·6 |
| 211 | ······················} | 211 | ······················} |
| 212 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)</code></pre> | 212 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ··········<tr> | 214 | ··········<tr> |
| 215 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·phi·=·rationalMap(phi,Dominant=>2) | 215 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·phi·=·rationalMap(phi,Dominant=>2) |
| 216 | ·--·used·0.1 | 216 | ·--·used·0.131657s·(cpu);·0.0892685s·(thread);·0s·(gc) |
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| Offset 25, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | map)·from·a·list·of·$m+1$·homogeneous·elements·of·the·same·degree·in·$K | 25 | map)·from·a·list·of·$m+1$·homogeneous·elements·of·the·same·degree·in·$K |
| 26 | [x_0,...,x_n]/I$. | 26 | [x_0,...,x_n]/I$. |
| 27 | Below·is·an·example·using·the·methods·provided·by·this·package,·dealing·with·a | 27 | Below·is·an·example·using·the·methods·provided·by·this·package,·dealing·with·a |
| 28 | birational·transformation·$\Phi:\mathbb{P}^6·\dashrightarrow·\mathbb{G} | 28 | birational·transformation·$\Phi:\mathbb{P}^6·\dashrightarrow·\mathbb{G} |
| 29 | (2,4)\subset\mathbb{P}^9$·of·bidegree·$(3,3)$. | 29 | (2,4)\subset\mathbb{P}^9$·of·bidegree·$(3,3)$. |
| 30 | i1·:·ZZ/300007[t_0..t_6]; | 30 | i1·:·ZZ/300007[t_0..t_6]; |
| 31 | i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) | 31 | i2·:·time·phi·=·toMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) |
| 32 | ·--·used·0.0040 | 32 | ·--·used·0.00401078s·(cpu);·0.00373695s·(thread);·0s·(gc) |
| 33 | ············ZZ··············ZZ················3················2····2 | 33 | ············ZZ··············ZZ················3················2····2 |
| 34 | 2········2······················2··················2····2·················2 | 34 | 2········2······················2··················2····2·················2 |
| 35 | 3················2····2················2·································2 | 35 | 3················2····2················2·································2 |
| 36 | 2····2··································2········2······················2 | 36 | 2····2··································2········2······················2 |
| 37 | 2························2·························2····2·················2 | 37 | 2························2·························2····2·················2 |
| 38 | 3················2····2 | 38 | 3················2····2 |
| Offset 52, 43 lines modified | Offset 52, 43 lines modified | ||
| 52 | 0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4 | 52 | 0·5····1·3·6····0·4·6·····3·4····3·5····2·4·5····1·5····2·3·6····1·4·6·····4 |
| 53 | 3·4·5····2·5····3·6····2·4·6 | 53 | 3·4·5····2·5····3·6····2·4·6 |
| 54 | ···············ZZ·················ZZ | 54 | ···············ZZ·················ZZ |
| 55 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] | 55 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] |
| 56 | ·············300007··0···6······300007··0···9 | 56 | ·············300007··0···6······300007··0···9 |
| 57 | i3·:·time·J·=·kernel(phi,2) | 57 | i3·:·time·J·=·kernel(phi,2) |
| 58 | ·--·used·0.03 | 58 | ·--·used·0.0362442s·(cpu);·0.037683s·(thread);·0s·(gc) |
| 59 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x | 59 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x |
| 60 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 | 60 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 |
| 61 | ·····------------------------------------------------------------------------ | 61 | ·····------------------------------------------------------------------------ |
| 62 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 62 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 63 | ········1·6····0·8···2·4····1·5····0·7 | 63 | ········1·6····0·8···2·4····1·5····0·7 |
| 64 | ················ZZ | 64 | ················ZZ |
| 65 | o3·:·Ideal·of·------[x·..x·] | 65 | o3·:·Ideal·of·------[x·..x·] |
| 66 | ··············300007··0···9 | 66 | ··············300007··0···9 |
| 67 | i4·:·time·degreeMap·phi | 67 | i4·:·time·degreeMap·phi |
| 68 | ·--·used·0.0 | 68 | ·--·used·0.0812392s·(cpu);·0.0356259s·(thread);·0s·(gc) |
| 69 | o4·=·1 | 69 | o4·=·1 |
| 70 | i5·:·time·projectiveDegrees·phi | 70 | i5·:·time·projectiveDegrees·phi |
| 71 | ·--·used·0.3 | 71 | ·--·used·0.375054s·(cpu);·0.339625s·(thread);·0s·(gc) |
| 72 | o5·=·{1,·3,·9,·17,·21,·15,·5} | 72 | o5·=·{1,·3,·9,·17,·21,·15,·5} |
| 73 | o5·:·List | 73 | o5·:·List |
| 74 | i6·:·time·projectiveDegrees(phi,NumDegrees=>0) | 74 | i6·:·time·projectiveDegrees(phi,NumDegrees=>0) |
| 75 | ·--·used·0.0 | 75 | ·--·used·0.0627803s·(cpu);·0.0626703s·(thread);·0s·(gc) |
| 76 | o6·=·{5} | 76 | o6·=·{5} |
| 77 | o6·:·List | 77 | o6·:·List |
| 78 | i7·:·time·phi·=·toMap(phi,Dominant=>J) | 78 | i7·:·time·phi·=·toMap(phi,Dominant=>J) |
| 79 | ·--·used·0.000 | 79 | ·--·used·0.000242715s·(cpu);·0.00237005s·(thread);·0s·(gc) |
| 80 | ·······································································ZZ | 80 | ·······································································ZZ |
| 81 | ·····································································------[x | 81 | ·····································································------[x |
| 82 | ..x·] | 82 | ..x·] |
| 83 | ············ZZ·······················································300007··0 | 83 | ············ZZ·······················································300007··0 |
| 84 | 9··················································3················2····2 | 84 | 9··················································3················2····2 |
| 85 | 2········2······················2··················2····2·················2 | 85 | 2········2······················2··················2····2·················2 |
| Offset 123, 15 lines modified | Offset 123, 15 lines modified | ||
| 123 | o7·:·RingMap·------[t·..t·]·<--·----------------------------------------------- | 123 | o7·:·RingMap·------[t·..t·]·<--·----------------------------------------------- |
| 124 | ----------------------------------------------------- | 124 | ----------------------------------------------------- |
| 125 | ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··- | 125 | ·············300007··0···6······(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··- |
| 126 | x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 126 | x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 127 | ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5 | 127 | ··································6·7····5·8····4·9···3·7····2·8····1·9···3·5 |
| 128 | 2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 | 128 | 2·6····0·9···3·4····1·6····0·8···2·4····1·5····0·7 |
| 129 | i8·:·time·psi·=·inverseMap·phi | 129 | i8·:·time·psi·=·inverseMap·phi |
| 130 | ·--·used·0.37 | 130 | ·--·used·0.437051s·(cpu);·0.384559s·(thread);·0s·(gc) |
| 131 | ·······················································ZZ | 131 | ·······················································ZZ |
| 132 | ·····················································------[x·..x·] | 132 | ·····················································------[x·..x·] |
| 133 | ·····················································300007··0···9 | 133 | ·····················································300007··0···9 |
| 134 | ZZ··············3················2···············2····2 | 134 | ZZ··············3················2···············2····2 |
| 135 | 2··························2·····2········2·······························2 | 135 | 2··························2·····2········2·······························2 |
| 136 | 2···············2·············2·······················3 | 136 | 2···············2·············2·······················3 |
| Offset 164, 31 lines modified | Offset 164, 31 lines modified | ||
| 164 | o8·:·RingMap·------------------------------------------------------------------ | 164 | o8·:·RingMap·------------------------------------------------------------------ |
| 165 | ----------------------------------·<--·------[t·..t·] | 165 | ----------------------------------·<--·------[t·..t·] |
| 166 | ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x | 166 | ·············(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x |
| 167 | -·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6 | 167 | -·x·x··+·x·x·,·x·x··-·x·x··+·x·x·)·····300007··0···6 |
| 168 | ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 | 168 | ···············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 |
| 169 | 1·6····0·8···2·4····1·5····0·7 | 169 | 1·6····0·8···2·4····1·5····0·7 |
| 170 | i9·:·time·isInverseMap(phi,psi) | 170 | i9·:·time·isInverseMap(phi,psi) |
| 171 | ·--·used·0.00 | 171 | ·--·used·0.00737805s·(cpu);·0.00798491s·(thread);·0s·(gc) |
| 172 | o9·=·true | 172 | o9·=·true |
| 173 | i10·:·time·degreeMap·psi | 173 | i10·:·time·degreeMap·psi |
| 174 | ·--·used·0.18 | 174 | ·--·used·0.218521s·(cpu);·0.16695s·(thread);·0s·(gc) |
| 175 | o10·=·1 | 175 | o10·=·1 |
| 176 | i11·:·time·projectiveDegrees·psi | 176 | i11·:·time·projectiveDegrees·psi |
| 177 | ·--·used· | 177 | ·--·used·5.11597s·(cpu);·4.7932s·(thread);·0s·(gc) |
| 178 | o11·=·{5,·15,·21,·17,·9,·3,·1} | 178 | o11·=·{5,·15,·21,·17,·9,·3,·1} |
| 179 | o11·:·List | 179 | o11·:·List |
| 180 | We·repeat·the·example·using·the·type·_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·and·using·deterministic | 180 | We·repeat·the·example·using·the·type·_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·and·using·deterministic |
| 181 | methods. | 181 | methods. |
| 182 | i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) | 182 | i12·:·time·phi·=·rationalMap·minors(3,matrix{{t_0..t_4},{t_1..t_5},{t_2..t_6}}) |
| 183 | ·--·used·0.00 | 183 | ·--·used·0.000742082s·(cpu);·0.00252711s·(thread);·0s·(gc) |
| 184 | o12·=·--·rational·map·-- | 184 | o12·=·--·rational·map·-- |
| 185 | ·····················ZZ | 185 | ·····················ZZ |
| 186 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 186 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 187 | ···················300007··0···1···2···3···4···5···6 | 187 | ···················300007··0···1···2···3···4···5···6 |
| 188 | ·····················ZZ | 188 | ·····················ZZ |
| 189 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 189 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 233, 15 lines modified | Offset 233, 15 lines modified | ||
| 233 | ··························3················2····2 | 233 | ··························3················2····2 |
| 234 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t | 234 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t |
| 235 | ··························4·····3·4·5····2·5····3·6····2·4·6 | 235 | ··························4·····3·4·5····2·5····3·6····2·4·6 |
| 236 | ······················} | 236 | ······················} |
| 237 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9) | 237 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9) |
| 238 | i13·:·time·phi·=·rationalMap(phi,Dominant=>2) | 238 | i13·:·time·phi·=·rationalMap(phi,Dominant=>2) |
| 239 | ·--·used·0.1 | 239 | ·--·used·0.131657s·(cpu);·0.0892685s·(thread);·0s·(gc) |
| 240 | o13·=·--·rational·map·-- | 240 | o13·=·--·rational·map·-- |
| 241 | ·····················ZZ | 241 | ·····················ZZ |
| 242 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 242 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 243 | ···················300007··0···1···2···3···4···5···6 | 243 | ···················300007··0···1···2···3···4···5···6 |
| 244 | ···································ZZ | 244 | ···································ZZ |
| 245 | ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x | 245 | ······target:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x |
| Offset 304, 15 lines modified | Offset 304, 15 lines modified | ||
| 304 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t | 304 | ·······················-·t··+·2t·t·t··-·t·t··-·t·t··+·t·t·t |
| 305 | ··························4·····3·4·5····2·5····3·6····2·4·6 | 305 | ··························4·····3·4·5····2·5····3·6····2·4·6 |
| 306 | ······················} | 306 | ······················} |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=10 | 7 | #:len=10 |
| 8 | Q3ljbG90b21pYw== | 8 | Q3ljbG90b21pYw== |
| 9 | #:len=478 | 9 | #:len=478 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY3ljbG90b21pYyBmaWVsZHMiLCBEZXNj | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY3ljbG90b21pYyBmaWVsZHMiLCBEZXNj |
| 11 | cmlwdGlvbiA9PiAoRU17IkN5Y2xvdG9taWMifSwiIGlzIGEgcGFja2FnZSBmb3IgY3ljbG90b21p | 11 | cmlwdGlvbiA9PiAoRU17IkN5Y2xvdG9taWMifSwiIGlzIGEgcGFja2FnZSBmb3IgY3ljbG90b21p |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | c291cmNlKERHQWxnZWJyYU1hcCk= | 8 | c291cmNlKERHQWxnZWJyYU1hcCk= |
| 9 | #:len=659 | 9 | #:len=659 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3V0cHV0cyB0aGUgc291cmNlIG9mIGEg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3V0cHV0cyB0aGUgc291cmNlIG9mIGEg |
| 11 | REdBbGdlYnJhTWFwIiwgImxpbmVudW0iID0+IDMxMDQsIElucHV0cyA9PiB7U1BBTntUVHsicGhp | 11 | REdBbGdlYnJhTWFwIiwgImxpbmVudW0iID0+IDMxMDQsIElucHV0cyA9PiB7U1BBTntUVHsicGhp |
| Offset 155, 15 lines modified | Offset 155, 15 lines modified | ||
| 155 | ··································2·····2·····2·······2·2·····2·2······2·2······2·2·····2·2········2·2·······2·2········2·······2·······2 | 155 | ··································2·····2·····2·······2·2·····2·2······2·2······2·2·····2·2········2·2·······2·2········2·······2·······2 |
| 156 | ·······Differential·=>·{a,·b,·c,·a·T·,·b·T·,·c·T·,·a*b·c·T·,·b·c·T·,·-a·b·T·,·-a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·} | 156 | ·······Differential·=>·{a,·b,·c,·a·T·,·b·T·,·c·T·,·a*b·c·T·,·b·c·T·,·-a·b·T·,·-a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·} |
| 157 | ····································1·····2·····3·········1·······4········6········5·······3·4········3·5·······2·4······1·7·····3·7·····2·7 | 157 | ····································1·····2·····3·········1·······4········6········5·······3·4········3·5·······2·4······1·7·····3·7·····2·7 |
| 158 | o16·:·DGAlgebra | 158 | o16·:·DGAlgebra |
| 159 | i17·:·HHg·=·HH·g | 159 | i17·:·HHg·=·HH·g |
| 160 | ·--·used·0.5 | 160 | ·--·used·0.54213s·(cpu);·0.0704357s·(thread);·0s·(gc) |
| 161 | Finding·easy·relations···········:· | 161 | Finding·easy·relations···········:· |
| 162 | ··························ZZ | 162 | ··························ZZ |
| 163 | ·························---[a..c] | 163 | ·························---[a..c] |
| 164 | ············ZZ···········101 | 164 | ············ZZ···········101 |
| 165 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 165 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 166 | ···········101··1···2···········3···1·····1 | 166 | ···········101··1···2···········3···1·····1 |
| 167 | ························(c,·b,·a·) | 167 | ························(c,·b,·a·) |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | ······Underlying·algebra·=>·R[S·..S·] | 30 | ······Underlying·algebra·=>·R[S·..S·] |
| 31 | ·······························1···4 | 31 | ·······························1···4 |
| 32 | ······Differential·=>·{a,·b,·c,·d} | 32 | ······Differential·=>·{a,·b,·c,·d} |
| 33 | o4·:·DGAlgebra | 33 | o4·:·DGAlgebra |
| 34 | i5·:·HB·=·HH·B | 34 | i5·:·HB·=·HH·B |
| 35 | ·--·used·0.6 | 35 | ·--·used·0.6029s·(cpu);·0.0718555s·(thread);·0s·(gc) |
| 36 | Finding·easy·relations···········:· | 36 | Finding·easy·relations···········:· |
| 37 | o5·=·HB | 37 | o5·=·HB |
| 38 | o5·:·PolynomialRing,·4·skew·commutative·variable(s) | 38 | o5·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 39 | i6·:·describe·HB | 39 | i6·:·describe·HB |
| Offset 68, 15 lines modified | Offset 68, 15 lines modified | ||
| 68 | ····································2 | 68 | ····································2 |
| 69 | ······Differential·=>·{a,·b,·c,·d,·a·T·} | 69 | ······Differential·=>·{a,·b,·c,·d,·a·T·} |
| 70 | ······································1 | 70 | ······································1 |
| 71 | o9·:·DGAlgebra | 71 | o9·:·DGAlgebra |
| 72 | i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) | 72 | i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) |
| 73 | ·--·used· | 73 | ·--·used·0.953487s·(cpu);·0.17287s·(thread);·0s·(gc) |
| 74 | Finding·easy·relations···········:· | 74 | Finding·easy·relations···········:· |
| 75 | ·······ZZ | 75 | ·······ZZ |
| 76 | o10·=·---[X·..X·] | 76 | o10·=·---[X·..X·] |
| 77 | ······101··1···3 | 77 | ······101··1···3 |
| 78 | o10·:·PolynomialRing,·3·skew·commutative·variable(s) | 78 | o10·:·PolynomialRing,·3·skew·commutative·variable(s) |
| Offset 55, 15 lines modified | Offset 55, 15 lines modified | ||
| 55 | ···············{2}·|·0·| | 55 | ···············{2}·|·0·| |
| 56 | ···············{2}·|·0·| | 56 | ···············{2}·|·0·| |
| 57 | ···············{2}·|·1·| | 57 | ···············{2}·|·1·| |
| 58 | o6·:·ChainComplexMap | 58 | o6·:·ChainComplexMap |
| 59 | i7·:·HHg·=·HH·g | 59 | i7·:·HHg·=·HH·g |
| 60 | ·--·used·0.5 | 60 | ·--·used·0.541556s·(cpu);·0.081186s·(thread);·0s·(gc) |
| 61 | Finding·easy·relations···········:· | 61 | Finding·easy·relations···········:· |
| 62 | ·························ZZ | 62 | ·························ZZ |
| 63 | ························---[a..c] | 63 | ························---[a..c] |
| 64 | ···········ZZ···········101 | 64 | ···········ZZ···········101 |
| 65 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 65 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 66 | ··········101··1···2···········3···1·····1 | 66 | ··········101··1···2···········3···1·····1 |
| 67 | ·······················(c,·b,·a·) | 67 | ·······················(c,·b,·a·) |
| Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
| 61 | ··················{9}·|·0·0·0·0·0·0·0·0·0·0·0·0·d·c·b·a·|················ | 61 | ··················{9}·|·0·0·0·0·0·0·0·0·0·0·0·0·d·c·b·a·|················ |
| 62 | ·····4·:·cokernel·{12}·|·d·c·b·a·|······································· | 62 | ·····4·:·cokernel·{12}·|·d·c·b·a·|······································· |
| 63 | o6·:·GradedModule | 63 | o6·:·GradedModule |
| 64 | i7·:·HKR·=·HH·KR | 64 | i7·:·HKR·=·HH·KR |
| 65 | ·--·used·0. | 65 | ·--·used·0.584578s·(cpu);·0.0932149s·(thread);·0s·(gc) |
| 66 | Finding·easy·relations···········:· | 66 | Finding·easy·relations···········:· |
| 67 | o7·=·HKR | 67 | o7·=·HKR |
| 68 | o7·:·PolynomialRing,·4·skew·commutative·variable(s) | 68 | o7·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 69 | i8·:·ideal·HKR | 69 | i8·:·ideal·HKR |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2-c^2*d^2} | 80 | i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2-c^2*d^2} |
| 81 | o9·=·R' | 81 | o9·=·R' |
| 82 | o9·:·QuotientRing | 82 | o9·:·QuotientRing |
| 83 | i10·:·HKR'·=·HH·koszulComplexDGA·R' | 83 | i10·:·HKR'·=·HH·koszulComplexDGA·R' |
| 84 | ·--·used·2. | 84 | ·--·used·2.43948s·(cpu);·0.740714s·(thread);·0s·(gc) |
| 85 | Finding·easy·relations···········:· | 85 | Finding·easy·relations···········:· |
| 86 | o10·=·HKR' | 86 | o10·=·HKR' |
| 87 | o10·:·QuotientRing | 87 | o10·:·QuotientRing |
| 88 | i11·:·numgens·HKR' | 88 | i11·:·numgens·HKR' |
| Offset 18, 15 lines modified | Offset 18, 15 lines modified | ||
| 18 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 18 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 19 | o3·=·{1,·4,·6,·4,·1} | 19 | o3·=·{1,·4,·6,·4,·1} |
| 20 | o3·:·List | 20 | o3·:·List |
| 21 | i4·:·HA·=·homologyAlgebra(A) | 21 | i4·:·HA·=·homologyAlgebra(A) |
| 22 | ·--·used· | 22 | ·--·used·1.76325s·(cpu);·0.255884s·(thread);·0s·(gc) |
| 23 | Finding·easy·relations···········:· | 23 | Finding·easy·relations···········:· |
| 24 | o4·=·HA | 24 | o4·=·HA |
| 25 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) | 25 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 26 | i5·:·numgens·HA | 26 | i5·:·numgens·HA |
| Offset 18, 15 lines modified | Offset 18, 15 lines modified | ||
| 18 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 18 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 19 | o3·=·{1,·4,·6,·4,·1} | 19 | o3·=·{1,·4,·6,·4,·1} |
| 20 | o3·:·List | 20 | o3·:·List |
| 21 | i4·:·HA·=·homologyAlgebra(A) | 21 | i4·:·HA·=·homologyAlgebra(A) |
| 22 | ·--·used·0. | 22 | ·--·used·0.536262s·(cpu);·0.0720261s·(thread);·0s·(gc) |
| 23 | Finding·easy·relations···········:· | 23 | Finding·easy·relations···········:· |
| 24 | o4·=·HA | 24 | o4·=·HA |
| 25 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) | 25 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 26 | i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3} | 26 | i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3} |
| Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
| 46 | i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 46 | i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 47 | o7·=·{1,·5,·10,·10,·4} | 47 | o7·=·{1,·5,·10,·10,·4} |
| 48 | o7·:·List | 48 | o7·:·List |
| 49 | i8·:·HA·=·homologyAlgebra(A) | 49 | i8·:·HA·=·homologyAlgebra(A) |
| 50 | ·--·used· | 50 | ·--·used·1.83319s·(cpu);·0.327293s·(thread);·0s·(gc) |
| 51 | Finding·easy·relations···········:· | 51 | Finding·easy·relations···········:· |
| 52 | o8·=·HA | 52 | o8·=·HA |
| 53 | o8·:·QuotientRing | 53 | o8·:·QuotientRing |
| 54 | i9·:·numgens·HA | 54 | i9·:·numgens·HA |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 114 | i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 115 | o15·=·{1,·7,·7,·1} | 115 | o15·=·{1,·7,·7,·1} |
| 116 | o15·:·List | 116 | o15·:·List |
| 117 | i16·:·HA·=·homologyAlgebra(A) | 117 | i16·:·HA·=·homologyAlgebra(A) |
| 118 | ·--·used·1. | 118 | ·--·used·1.07198s·(cpu);·0.142094s·(thread);·0s·(gc) |
| 119 | Finding·easy·relations···········:· | 119 | Finding·easy·relations···········:· |
| 120 | o16·=·HA | 120 | o16·=·HA |
| 121 | o16·:·QuotientRing | 121 | o16·:·QuotientRing |
| 122 | i17·:·R·=·ZZ/101[a,b,c,d] | 122 | i17·:·R·=·ZZ/101[a,b,c,d] |
| Offset 151, 14 lines modified | Offset 151, 14 lines modified | ||
| 151 | ·······Underlying·algebra·=>·S[T·..T·] | 151 | ·······Underlying·algebra·=>·S[T·..T·] |
| 152 | ································1···4 | 152 | ································1···4 |
| 153 | ·······Differential·=>·{a,·b,·c,·d} | 153 | ·······Differential·=>·{a,·b,·c,·d} |
| 154 | o20·:·DGAlgebra | 154 | o20·:·DGAlgebra |
| 155 | i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) | 155 | i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) |
| 156 | ·--·used·0. | 156 | ·--·used·0.532791s·(cpu);·0.0788856s·(thread);·0s·(gc) |
| 157 | Finding·easy·relations···········:· | 157 | Finding·easy·relations···········:· |
| 158 | o21·=·HB | 158 | o21·=·HB |
| 159 | o21·:·PolynomialRing,·4·skew·commutative·variable(s) | 159 | o21·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 160 | i22·:· | 160 | i22·:· |
| Offset 43, 15 lines modified | Offset 43, 15 lines modified | ||
| 43 | o6·=·y·T | 43 | o6·=·y·T |
| 44 | ········2 | 44 | ········2 |
| 45 | o6·:·R[T·..T·] | 45 | o6·:·R[T·..T·] |
| 46 | ········1···3 | 46 | ········1···3 |
| 47 | i7·:·H·=·HH(KR) | 47 | i7·:·H·=·HH(KR) |
| 48 | ·--·used·0.5 | 48 | ·--·used·0.523988s·(cpu);·0.0823843s·(thread);·0s·(gc) |
| 49 | Finding·easy·relations···········:· | 49 | Finding·easy·relations···········:· |
| 50 | o7·=·H | 50 | o7·=·H |
| 51 | o7·:·PolynomialRing,·3·skew·commutative·variable(s) | 51 | o7·:·PolynomialRing,·3·skew·commutative·variable(s) |
| 52 | i8·:·homologyClass(KR,z1*z2) | 52 | i8·:·homologyClass(KR,z1*z2) |
| Offset 34, 15 lines modified | Offset 34, 15 lines modified | ||
| 34 | o5·=·R··<--·R··<--·R··<--·R··<--·R | 34 | o5·=·R··<--·R··<--·R··<--·R··<--·R |
| 35 | ·································· | 35 | ·································· |
| 36 | ·····0······1······2······3······4 | 36 | ·····0······1······2······3······4 |
| 37 | o5·:·ChainComplex | 37 | o5·:·ChainComplex |
| 38 | i6·:·HKR·=·HH(KR) | 38 | i6·:·HKR·=·HH(KR) |
| 39 | ·--·used·1.3 | 39 | ·--·used·1.37771s·(cpu);·0.253982s·(thread);·0s·(gc) |
| 40 | Finding·easy·relations···········:· | 40 | Finding·easy·relations···········:· |
| 41 | o6·=·HKR | 41 | o6·=·HKR |
| 42 | o6·:·QuotientRing | 42 | o6·:·QuotientRing |
| 43 | i7·:·degList·=·first·entries·vars·Q·/·degree·/·first | 43 | i7·:·degList·=·first·entries·vars·Q·/·degree·/·first |
| Offset 68, 15 lines modified | Offset 68, 15 lines modified | ||
| 68 | ···············2 | 68 | ···············2 |
| 69 | o9·=·(true,·x·y·T·T·T··-·x·x·y·T·T·T·) | 69 | o9·=·(true,·x·y·T·T·T··-·x·x·y·T·T·T·) |
| 70 | ·············2·2·1·2·3····1·2·2·2·3·4 | 70 | ·············2·2·1·2·3····1·2·2·2·3·4 |
| 71 | o9·:·Sequence | 71 | o9·:·Sequence |
| 72 | i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) | 72 | i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) |
| 73 | ·--·used·2. | 73 | ·--·used·2.54893s·(cpu);·0.780215s·(thread);·0s·(gc) |
| 74 | Finding·easy·relations···········:· | 74 | Finding·easy·relations···········:· |
| 75 | ·············2 | 75 | ·············2 |
| 76 | o10·=·x·x·y·z·T·T·T·T | 76 | o10·=·x·x·y·z·T·T·T·T |
| 77 | ·······1·2·2···2·3·4·5 | 77 | ·······1·2·2···2·3·4·5 |
| 78 | o10·:·R[T·..T·] | 78 | o10·:·R[T·..T·] |
| 79 | ·········1···5 | 79 | ·········1···5 |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | ·······························1···4 | 27 | ·······························1···4 |
| 28 | ······Differential·=>·{t·,·t·,·t·,·t·} | 28 | ······Differential·=>·{t·,·t·,·t·,·t·} |
| 29 | ························1···2···3···4 | 29 | ························1···2···3···4 |
| 30 | o4·:·DGAlgebra | 30 | o4·:·DGAlgebra |
| 31 | i5·:·H·=·HH(KR) | 31 | i5·:·H·=·HH(KR) |
| 32 | ·--·used· | 32 | ·--·used·1.83569s·(cpu);·0.353695s·(thread);·0s·(gc) |
| 33 | Finding·easy·relations···········:· | 33 | Finding·easy·relations···········:· |
| 34 | o5·=·H | 34 | o5·=·H |
| 35 | o5·:·QuotientRing | 35 | o5·:·QuotientRing |
| 36 | i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); | 36 | i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3} | 11 | i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3} |
| 12 | o3·=·S | 12 | o3·=·S |
| 13 | o3·:·QuotientRing | 13 | o3·:·QuotientRing |
| 14 | i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) | 14 | i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) |
| 15 | ·--·used· | 15 | ·--·used·2.59494s·(cpu);·0.694479s·(thread);·0s·(gc) |
| 16 | Finding·easy·relations···········:· | 16 | Finding·easy·relations···········:· |
| 17 | o4·=·HB | 17 | o4·=·HB |
| 18 | o4·:·QuotientRing | 18 | o4·:·QuotientRing |
| 19 | i5·:·numgens·HB | 19 | i5·:·numgens·HB |
| Offset 249, 15 lines modified | Offset 249, 15 lines modified | ||
| 249 | ········</table> | 249 | ········</table> |
| 250 | ········<div> | 250 | ········<div> |
| 251 | ··········<p>One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.</p> | 251 | ··········<p>One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.</p> |
| 252 | ········</div> | 252 | ········</div> |
| 253 | ········<table·class="examples"> | 253 | ········<table·class="examples"> |
| 254 | ··········<tr> | 254 | ··········<tr> |
| 255 | <td>··············<pre><code·class="language-macaulay2">i17·:·HHg·=·HH·g | 255 | <td>··············<pre><code·class="language-macaulay2">i17·:·HHg·=·HH·g |
| 256 | ·--·used·0.5 | 256 | ·--·used·0.54213s·(cpu);·0.0704357s·(thread);·0s·(gc) |
| 257 | Finding·easy·relations···········:· | 257 | Finding·easy·relations···········:· |
| 258 | ··························ZZ | 258 | ··························ZZ |
| 259 | ·························---[a..c] | 259 | ·························---[a..c] |
| 260 | ············ZZ···········101 | 260 | ············ZZ···········101 |
| 261 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 261 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 262 | ···········101··1···2···········3···1·····1 | 262 | ···········101··1···2···········3···1·····1 |
| 263 | ························(c,·b,·a·) | 263 | ························(c,·b,·a·) |
| Offset 210, 15 lines modified | Offset 210, 15 lines modified | ||
| 210 | a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·} | 210 | a·c·T·,·b·c·T·T·,·-a·c·T·T·,·b·c·T·T·,·-a·T·T·,·c·T·T·,·b·T·T·} |
| 211 | ····································1·····2·····3·········1·······4········6 | 211 | ····································1·····2·····3·········1·······4········6 |
| 212 | 5·······3·4········3·5·······2·4······1·7·····3·7·····2·7 | 212 | 5·······3·4········3·5·······2·4······1·7·····3·7·····2·7 |
| 213 | o16·:·DGAlgebra | 213 | o16·:·DGAlgebra |
| 214 | One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map. | 214 | One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map. |
| 215 | i17·:·HHg·=·HH·g | 215 | i17·:·HHg·=·HH·g |
| 216 | ·--·used·0.5 | 216 | ·--·used·0.54213s·(cpu);·0.0704357s·(thread);·0s·(gc) |
| 217 | Finding·easy·relations···········: | 217 | Finding·easy·relations···········: |
| 218 | ··························ZZ | 218 | ··························ZZ |
| 219 | ·························---[a..c] | 219 | ·························---[a..c] |
| 220 | ············ZZ···········101 | 220 | ············ZZ···········101 |
| 221 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 221 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 222 | ···········101··1···2···········3···1·····1 | 222 | ···········101··1···2···········3···1·····1 |
| 223 | ························(c,·b,·a·) | 223 | ························(c,·b,·a·) |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | ········</table> | 97 | ········</table> |
| 98 | ········<div> | 98 | ········<div> |
| 99 | ··········<p>One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)·command.</p> | 99 | ··········<p>One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)·command.</p> |
| 100 | ········</div> | 100 | ········</div> |
| 101 | ········<table·class="examples"> | 101 | ········<table·class="examples"> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·HB·=·HH·B | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·HB·=·HH·B |
| 104 | ·--·used·0.6 | 104 | ·--·used·0.6029s·(cpu);·0.0718555s·(thread);·0s·(gc) |
| 105 | Finding·easy·relations···········:· | 105 | Finding·easy·relations···········:· |
| 106 | o5·=·HB | 106 | o5·=·HB |
| 107 | o5·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 107 | o5·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·HB | 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·HB |
| Offset 148, 15 lines modified | Offset 148, 15 lines modified | ||
| 148 | ······Differential·=>·{a,·b,·c,·d,·a·T·} | 148 | ······Differential·=>·{a,·b,·c,·d,·a·T·} |
| 149 | ······································1 | 149 | ······································1 |
| 150 | o9·:·DGAlgebra</code></pre> | 150 | o9·:·DGAlgebra</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| 152 | ··········<tr> | 152 | ··········<tr> |
| 153 | <td>··············<pre><code·class="language-macaulay2">i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) | 153 | <td>··············<pre><code·class="language-macaulay2">i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) |
| 154 | ·--·used· | 154 | ·--·used·0.953487s·(cpu);·0.17287s·(thread);·0s·(gc) |
| 155 | Finding·easy·relations···········:· | 155 | Finding·easy·relations···········:· |
| 156 | ·······ZZ | 156 | ·······ZZ |
| 157 | o10·=·---[X·..X·] | 157 | o10·=·---[X·..X·] |
| 158 | ······101··1···3 | 158 | ······101··1···3 |
| 159 | o10·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> | 159 | o10·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| Offset 42, 15 lines modified | Offset 42, 15 lines modified | ||
| 42 | ·······························1···4 | 42 | ·······························1···4 |
| 43 | ······Differential·=>·{a,·b,·c,·d} | 43 | ······Differential·=>·{a,·b,·c,·d} |
| 44 | o4·:·DGAlgebra | 44 | o4·:·DGAlgebra |
| 45 | One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH) | 45 | One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH) |
| 46 | command. | 46 | command. |
| 47 | i5·:·HB·=·HH·B | 47 | i5·:·HB·=·HH·B |
| 48 | ·--·used·0.6 | 48 | ·--·used·0.6029s·(cpu);·0.0718555s·(thread);·0s·(gc) |
| 49 | Finding·easy·relations···········: | 49 | Finding·easy·relations···········: |
| 50 | o5·=·HB | 50 | o5·=·HB |
| 51 | o5·:·PolynomialRing,·4·skew·commutative·variable(s) | 51 | o5·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 52 | i6·:·describe·HB | 52 | i6·:·describe·HB |
| 53 | ······ZZ | 53 | ······ZZ |
| Offset 86, 15 lines modified | Offset 86, 15 lines modified | ||
| 86 | ·······························1···5 | 86 | ·······························1···5 |
| 87 | ····································2 | 87 | ····································2 |
| 88 | ······Differential·=>·{a,·b,·c,·d,·a·T·} | 88 | ······Differential·=>·{a,·b,·c,·d,·a·T·} |
| 89 | ······································1 | 89 | ······································1 |
| 90 | o9·:·DGAlgebra | 90 | o9·:·DGAlgebra |
| 91 | i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) | 91 | i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) |
| 92 | ·--·used· | 92 | ·--·used·0.953487s·(cpu);·0.17287s·(thread);·0s·(gc) |
| 93 | Finding·easy·relations···········: | 93 | Finding·easy·relations···········: |
| 94 | ·······ZZ | 94 | ·······ZZ |
| 95 | o10·=·---[X·..X·] | 95 | o10·=·---[X·..X·] |
| 96 | ······101··1···3 | 96 | ······101··1···3 |
| 97 | o10·:·PolynomialRing,·3·skew·commutative·variable(s) | 97 | o10·:·PolynomialRing,·3·skew·commutative·variable(s) |
| 98 | i11·:·C·=·killCycles(B) | 98 | i11·:·C·=·killCycles(B) |
| Offset 132, 15 lines modified | Offset 132, 15 lines modified | ||
| 132 | ···············{2}·|·0·| | 132 | ···············{2}·|·0·| |
| 133 | ···············{2}·|·1·| | 133 | ···············{2}·|·1·| |
| 134 | o6·:·ChainComplexMap</code></pre> | 134 | o6·:·ChainComplexMap</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i7·:·HHg·=·HH·g | 137 | <td>··············<pre><code·class="language-macaulay2">i7·:·HHg·=·HH·g |
| 138 | ·--·used·0.5 | 138 | ·--·used·0.541556s·(cpu);·0.081186s·(thread);·0s·(gc) |
| 139 | Finding·easy·relations···········:· | 139 | Finding·easy·relations···········:· |
| 140 | ·························ZZ | 140 | ·························ZZ |
| 141 | ························---[a..c] | 141 | ························---[a..c] |
| 142 | ···········ZZ···········101 | 142 | ···········ZZ···········101 |
| 143 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 143 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 144 | ··········101··1···2···········3···1·····1 | 144 | ··········101··1···2···········3···1·····1 |
| 145 | ·······················(c,·b,·a·) | 145 | ·······················(c,·b,·a·) |
| Offset 63, 15 lines modified | Offset 63, 15 lines modified | ||
| 63 | ·····2·:·R··<-------------·R··:·2 | 63 | ·····2·:·R··<-------------·R··:·2 |
| 64 | ···············{2}·|·0·| | 64 | ···············{2}·|·0·| |
| 65 | ···············{2}·|·0·| | 65 | ···············{2}·|·0·| |
| 66 | ···············{2}·|·1·| | 66 | ···············{2}·|·1·| |
| 67 | o6·:·ChainComplexMap | 67 | o6·:·ChainComplexMap |
| 68 | i7·:·HHg·=·HH·g | 68 | i7·:·HHg·=·HH·g |
| 69 | ·--·used·0.5 | 69 | ·--·used·0.541556s·(cpu);·0.081186s·(thread);·0s·(gc) |
| 70 | Finding·easy·relations···········: | 70 | Finding·easy·relations···········: |
| 71 | ·························ZZ | 71 | ·························ZZ |
| 72 | ························---[a..c] | 72 | ························---[a..c] |
| 73 | ···········ZZ···········101 | 73 | ···········ZZ···········101 |
| 74 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 74 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 75 | ··········101··1···2···········3···1·····1 | 75 | ··········101··1···2···········3···1·····1 |
| 76 | ·······················(c,·b,·a·) | 76 | ·······················(c,·b,·a·) |
| Offset 130, 15 lines modified | Offset 130, 15 lines modified | ||
| 130 | ········</table> | 130 | ········</table> |
| 131 | ········<div> | 131 | ········<div> |
| 132 | ··········<p>Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra.··One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH·(all·commands·work).··This·algebra·structure·can·detect·whether·or·not·the·ring·is·a·complete·intersection·or·Gorenstein.</p> | 132 | ··········<p>Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra.··One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH·(all·commands·work).··This·algebra·structure·can·detect·whether·or·not·the·ring·is·a·complete·intersection·or·Gorenstein.</p> |
| 133 | ········</div> | 133 | ········</div> |
| 134 | ········<table·class="examples"> | 134 | ········<table·class="examples"> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i7·:·HKR·=·HH·KR | 136 | <td>··············<pre><code·class="language-macaulay2">i7·:·HKR·=·HH·KR |
| 137 | ·--·used·0. | 137 | ·--·used·0.584578s·(cpu);·0.0932149s·(thread);·0s·(gc) |
| 138 | Finding·easy·relations···········:· | 138 | Finding·easy·relations···········:· |
| 139 | o7·=·HKR | 139 | o7·=·HKR |
| 140 | o7·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 140 | o7·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i8·:·ideal·HKR | 143 | <td>··············<pre><code·class="language-macaulay2">i8·:·ideal·HKR |
| Offset 152, 15 lines modified | Offset 152, 15 lines modified | ||
| 152 | o9·=·R' | 152 | o9·=·R' |
| 153 | o9·:·QuotientRing</code></pre> | 153 | o9·:·QuotientRing</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i10·:·HKR'·=·HH·koszulComplexDGA·R' | 156 | <td>··············<pre><code·class="language-macaulay2">i10·:·HKR'·=·HH·koszulComplexDGA·R' |
| 157 | ·--·used·2. | 157 | ·--·used·2.43948s·(cpu);·0.740714s·(thread);·0s·(gc) |
| 158 | Finding·easy·relations···········:· | 158 | Finding·easy·relations···········:· |
| 159 | o10·=·HKR' | 159 | o10·=·HKR' |
| 160 | o10·:·QuotientRing</code></pre> | 160 | o10·:·QuotientRing</code></pre> |
| 161 | </td>··········</tr> | 161 | </td>··········</tr> |
| 162 | ··········<tr> | 162 | ··········<tr> |
| 163 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·HKR' | 163 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·HKR' |
| Offset 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | o6·:·GradedModule | 75 | o6·:·GradedModule |
| 76 | Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra. | 76 | Since·the·Koszul·complex·is·a·DG·algebra,·its·homology·is·itself·an·algebra. |
| 77 | One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH | 77 | One·can·obtain·this·algebra·using·the·command·homology,·homologyAlgebra,·or·HH |
| 78 | (all·commands·work).·This·algebra·structure·can·detect·whether·or·not·the·ring | 78 | (all·commands·work).·This·algebra·structure·can·detect·whether·or·not·the·ring |
| 79 | is·a·complete·intersection·or·Gorenstein. | 79 | is·a·complete·intersection·or·Gorenstein. |
| 80 | i7·:·HKR·=·HH·KR | 80 | i7·:·HKR·=·HH·KR |
| 81 | ·--·used·0. | 81 | ·--·used·0.584578s·(cpu);·0.0932149s·(thread);·0s·(gc) |
| 82 | Finding·easy·relations···········: | 82 | Finding·easy·relations···········: |
| 83 | o7·=·HKR | 83 | o7·=·HKR |
| 84 | o7·:·PolynomialRing,·4·skew·commutative·variable(s) | 84 | o7·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 85 | i8·:·ideal·HKR | 85 | i8·:·ideal·HKR |
| 86 | o8·=·ideal·() | 86 | o8·=·ideal·() |
| Offset 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2- | 92 | i9·:·R'·=·ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3,a*c,a*d,b*c,b*d,a^2*b^2- |
| 93 | c^2*d^2} | 93 | c^2*d^2} |
| 94 | o9·=·R' | 94 | o9·=·R' |
| 95 | o9·:·QuotientRing | 95 | o9·:·QuotientRing |
| 96 | i10·:·HKR'·=·HH·koszulComplexDGA·R' | 96 | i10·:·HKR'·=·HH·koszulComplexDGA·R' |
| 97 | ·--·used·2. | 97 | ·--·used·2.43948s·(cpu);·0.740714s·(thread);·0s·(gc) |
| 98 | Finding·easy·relations···········: | 98 | Finding·easy·relations···········: |
| 99 | o10·=·HKR' | 99 | o10·=·HKR' |
| 100 | o10·:·QuotientRing | 100 | o10·:·QuotientRing |
| 101 | i11·:·numgens·HKR' | 101 | i11·:·numgens·HKR' |
| 102 | o11·=·34 | 102 | o11·=·34 |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | o3·=·{1,·4,·6,·4,·1} | 78 | o3·=·{1,·4,·6,·4,·1} |
| 79 | o3·:·List</code></pre> | 79 | o3·:·List</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) | 82 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) |
| 83 | ·--·used· | 83 | ·--·used·1.76325s·(cpu);·0.255884s·(thread);·0s·(gc) |
| 84 | Finding·easy·relations···········:· | 84 | Finding·easy·relations···········:· |
| 85 | o4·=·HA | 85 | o4·=·HA |
| 86 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 86 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·numgens·HA | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·numgens·HA |
| Offset 24, 15 lines modified | Offset 24, 15 lines modified | ||
| 24 | o2·:·DGAlgebra | 24 | o2·:·DGAlgebra |
| 25 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 25 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 26 | o3·=·{1,·4,·6,·4,·1} | 26 | o3·=·{1,·4,·6,·4,·1} |
| 27 | o3·:·List | 27 | o3·:·List |
| 28 | i4·:·HA·=·homologyAlgebra(A) | 28 | i4·:·HA·=·homologyAlgebra(A) |
| 29 | ·--·used· | 29 | ·--·used·1.76325s·(cpu);·0.255884s·(thread);·0s·(gc) |
| 30 | Finding·easy·relations···········: | 30 | Finding·easy·relations···········: |
| 31 | o4·=·HA | 31 | o4·=·HA |
| 32 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) | 32 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 33 | i5·:·numgens·HA | 33 | i5·:·numgens·HA |
| 34 | o5·=·4 | 34 | o5·=·4 |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | o3·=·{1,·4,·6,·4,·1} | 100 | o3·=·{1,·4,·6,·4,·1} |
| 101 | o3·:·List</code></pre> | 101 | o3·:·List</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) | 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) |
| 105 | ·--·used·0. | 105 | ·--·used·0.536262s·(cpu);·0.0720261s·(thread);·0s·(gc) |
| 106 | Finding·easy·relations···········:· | 106 | Finding·easy·relations···········:· |
| 107 | o4·=·HA | 107 | o4·=·HA |
| 108 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 108 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ········</table> | 110 | ········</table> |
| 111 | ········<div> | 111 | ········<div> |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | o7·=·{1,·5,·10,·10,·4} | 137 | o7·=·{1,·5,·10,·10,·4} |
| 138 | o7·:·List</code></pre> | 138 | o7·:·List</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i8·:·HA·=·homologyAlgebra(A) | 141 | <td>··············<pre><code·class="language-macaulay2">i8·:·HA·=·homologyAlgebra(A) |
| 142 | ·--·used· | 142 | ·--·used·1.83319s·(cpu);·0.327293s·(thread);·0s·(gc) |
| 143 | Finding·easy·relations···········:· | 143 | Finding·easy·relations···········:· |
| 144 | o8·=·HA | 144 | o8·=·HA |
| 145 | o8·:·QuotientRing</code></pre> | 145 | o8·:·QuotientRing</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i9·:·numgens·HA | 148 | <td>··············<pre><code·class="language-macaulay2">i9·:·numgens·HA |
| Offset 215, 15 lines modified | Offset 215, 15 lines modified | ||
| 215 | o15·=·{1,·7,·7,·1} | 215 | o15·=·{1,·7,·7,·1} |
| 216 | o15·:·List</code></pre> | 216 | o15·:·List</code></pre> |
| 217 | </td>··········</tr> | 217 | </td>··········</tr> |
| 218 | ··········<tr> | 218 | ··········<tr> |
| 219 | <td>··············<pre><code·class="language-macaulay2">i16·:·HA·=·homologyAlgebra(A) | 219 | <td>··············<pre><code·class="language-macaulay2">i16·:·HA·=·homologyAlgebra(A) |
| 220 | ·--·used·1. | 220 | ·--·used·1.07198s·(cpu);·0.142094s·(thread);·0s·(gc) |
| 221 | Finding·easy·relations···········:· | 221 | Finding·easy·relations···········:· |
| 222 | o16·=·HA | 222 | o16·=·HA |
| 223 | o16·:·QuotientRing</code></pre> | 223 | o16·:·QuotientRing</code></pre> |
| 224 | </td>··········</tr> | 224 | </td>··········</tr> |
| 225 | ········</table> | 225 | ········</table> |
| 226 | ········<div> | 226 | ········<div> |
| Offset 265, 15 lines modified | Offset 265, 15 lines modified | ||
| 265 | ································1···4 | 265 | ································1···4 |
| 266 | ·······Differential·=>·{a,·b,·c,·d} | 266 | ·······Differential·=>·{a,·b,·c,·d} |
| 267 | o20·:·DGAlgebra</code></pre> | 267 | o20·:·DGAlgebra</code></pre> |
| 268 | </td>··········</tr> | 268 | </td>··········</tr> |
| 269 | ··········<tr> | 269 | ··········<tr> |
| 270 | <td>··············<pre><code·class="language-macaulay2">i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) | 270 | <td>··············<pre><code·class="language-macaulay2">i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) |
| 271 | ·--·used·0. | 271 | ·--·used·0.532791s·(cpu);·0.0788856s·(thread);·0s·(gc) |
| 272 | Finding·easy·relations···········:· | 272 | Finding·easy·relations···········:· |
| 273 | o21·=·HB | 273 | o21·=·HB |
| 274 | o21·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 274 | o21·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 275 | </td>··········</tr> | 275 | </td>··········</tr> |
| 276 | ········</table> | 276 | ········</table> |
| 277 | ······</div> | 277 | ······</div> |
| Offset 34, 15 lines modified | Offset 34, 15 lines modified | ||
| 34 | o2·:·DGAlgebra | 34 | o2·:·DGAlgebra |
| 35 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 35 | i3·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 36 | o3·=·{1,·4,·6,·4,·1} | 36 | o3·=·{1,·4,·6,·4,·1} |
| 37 | o3·:·List | 37 | o3·:·List |
| 38 | i4·:·HA·=·homologyAlgebra(A) | 38 | i4·:·HA·=·homologyAlgebra(A) |
| 39 | ·--·used·0. | 39 | ·--·used·0.536262s·(cpu);·0.0720261s·(thread);·0s·(gc) |
| 40 | Finding·easy·relations···········: | 40 | Finding·easy·relations···········: |
| 41 | o4·=·HA | 41 | o4·=·HA |
| 42 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) | 42 | o4·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 43 | Note·that·HA·is·a·graded·commutative·polynomial·ring·(i.e.·an·exterior·algebra) | 43 | Note·that·HA·is·a·graded·commutative·polynomial·ring·(i.e.·an·exterior·algebra) |
| 44 | since·R·is·a·complete·intersection. | 44 | since·R·is·a·complete·intersection. |
| 45 | i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3} | 45 | i5·:·R·=·ZZ/101[a,b,c,d]/ideal{a^4,b^4,c^4,d^4,a^3*b^3*c^3*d^3} |
| Offset 60, 15 lines modified | Offset 60, 15 lines modified | ||
| 60 | o6·:·DGAlgebra | 60 | o6·:·DGAlgebra |
| 61 | i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 61 | i7·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 62 | o7·=·{1,·5,·10,·10,·4} | 62 | o7·=·{1,·5,·10,·10,·4} |
| 63 | o7·:·List | 63 | o7·:·List |
| 64 | i8·:·HA·=·homologyAlgebra(A) | 64 | i8·:·HA·=·homologyAlgebra(A) |
| 65 | ·--·used· | 65 | ·--·used·1.83319s·(cpu);·0.327293s·(thread);·0s·(gc) |
| 66 | Finding·easy·relations···········: | 66 | Finding·easy·relations···········: |
| 67 | o8·=·HA | 67 | o8·=·HA |
| 68 | o8·:·QuotientRing | 68 | o8·:·QuotientRing |
| 69 | i9·:·numgens·HA | 69 | i9·:·numgens·HA |
| 70 | o9·=·19 | 70 | o9·=·19 |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | o14·:·DGAlgebra | 121 | o14·:·DGAlgebra |
| 122 | i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) | 122 | i15·:·apply(maxDegree·A·+·1,·i·->·numgens·prune·homology(i,A)) |
| 123 | o15·=·{1,·7,·7,·1} | 123 | o15·=·{1,·7,·7,·1} |
| 124 | o15·:·List | 124 | o15·:·List |
| 125 | i16·:·HA·=·homologyAlgebra(A) | 125 | i16·:·HA·=·homologyAlgebra(A) |
| 126 | ·--·used·1. | 126 | ·--·used·1.07198s·(cpu);·0.142094s·(thread);·0s·(gc) |
| 127 | Finding·easy·relations···········: | 127 | Finding·easy·relations···········: |
| 128 | o16·=·HA | 128 | o16·=·HA |
| 129 | o16·:·QuotientRing | 129 | o16·:·QuotientRing |
| 130 | One·can·check·that·HA·has·Poincare·duality·since·R·is·Gorenstein. | 130 | One·can·check·that·HA·has·Poincare·duality·since·R·is·Gorenstein. |
| 131 | If·your·DGAlgebra·has·generators·in·even·degrees,·then·one·must·specify·the | 131 | If·your·DGAlgebra·has·generators·in·even·degrees,·then·one·must·specify·the |
| 132 | options·GenDegreeLimit·and·RelDegreeLimit. | 132 | options·GenDegreeLimit·and·RelDegreeLimit. |
| Offset 156, 15 lines modified | Offset 156, 15 lines modified | ||
| 156 | o20·=·{Ring·=>·S······················} | 156 | o20·=·{Ring·=>·S······················} |
| 157 | ·······Underlying·algebra·=>·S[T·..T·] | 157 | ·······Underlying·algebra·=>·S[T·..T·] |
| 158 | ································1···4 | 158 | ································1···4 |
| 159 | ·······Differential·=>·{a,·b,·c,·d} | 159 | ·······Differential·=>·{a,·b,·c,·d} |
| 160 | o20·:·DGAlgebra | 160 | o20·:·DGAlgebra |
| 161 | i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) | 161 | i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) |
| 162 | ·--·used·0. | 162 | ·--·used·0.532791s·(cpu);·0.0788856s·(thread);·0s·(gc) |
| 163 | Finding·easy·relations···········: | 163 | Finding·easy·relations···········: |
| 164 | o21·=·HB | 164 | o21·=·HB |
| 165 | o21·:·PolynomialRing,·4·skew·commutative·variable(s) | 165 | o21·:·PolynomialRing,·4·skew·commutative·variable(s) |
| 166 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ho\x8om\x8mo\x8ol\x8lo\x8og\x8gy\x8yA\x8Al\x8lg\x8ge\x8eb\x8br\x8ra\x8a:\x8:·*\x8**\x8**\x8**\x8**\x8* | 166 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ho\x8om\x8mo\x8ol\x8lo\x8og\x8gy\x8yA\x8Al\x8lg\x8ge\x8eb\x8br\x8ra\x8a:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 167 | ····*·homologyAlgebra(DGAlgebra) | 167 | ····*·homologyAlgebra(DGAlgebra) |
| 168 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 168 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 123, 15 lines modified | Offset 123, 15 lines modified | ||
| 123 | ········2 | 123 | ········2 |
| 124 | o6·:·R[T·..T·] | 124 | o6·:·R[T·..T·] |
| 125 | ········1···3</code></pre> | 125 | ········1···3</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i7·:·H·=·HH(KR) | 128 | <td>··············<pre><code·class="language-macaulay2">i7·:·H·=·HH(KR) |
| 129 | ·--·used·0.5 | 129 | ·--·used·0.523988s·(cpu);·0.0823843s·(thread);·0s·(gc) |
| 130 | Finding·easy·relations···········:· | 130 | Finding·easy·relations···········:· |
| 131 | o7·=·H | 131 | o7·=·H |
| 132 | o7·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> | 132 | o7·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·homologyClass(KR,z1*z2) | 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·homologyClass(KR,z1*z2) |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | ······2 | 54 | ······2 |
| 55 | o6·=·y·T | 55 | o6·=·y·T |
| 56 | ········2 | 56 | ········2 |
| 57 | o6·:·R[T·..T·] | 57 | o6·:·R[T·..T·] |
| 58 | ········1···3 | 58 | ········1···3 |
| 59 | i7·:·H·=·HH(KR) | 59 | i7·:·H·=·HH(KR) |
| 60 | ·--·used·0.5 | 60 | ·--·used·0.523988s·(cpu);·0.0823843s·(thread);·0s·(gc) |
| 61 | Finding·easy·relations···········: | 61 | Finding·easy·relations···········: |
| 62 | o7·=·H | 62 | o7·=·H |
| 63 | o7·:·PolynomialRing,·3·skew·commutative·variable(s) | 63 | o7·:·PolynomialRing,·3·skew·commutative·variable(s) |
| 64 | i8·:·homologyClass(KR,z1*z2) | 64 | i8·:·homologyClass(KR,z1*z2) |
| 65 | o8·=·X·X | 65 | o8·=·X·X |
| Offset 119, 15 lines modified | Offset 119, 15 lines modified | ||
| 119 | ·································· | 119 | ·································· |
| 120 | ·····0······1······2······3······4 | 120 | ·····0······1······2······3······4 |
| 121 | o5·:·ChainComplex</code></pre> | 121 | o5·:·ChainComplex</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·HKR·=·HH(KR) | 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·HKR·=·HH(KR) |
| 125 | ·--·used·1.3 | 125 | ·--·used·1.37771s·(cpu);·0.253982s·(thread);·0s·(gc) |
| 126 | Finding·easy·relations···········:· | 126 | Finding·easy·relations···········:· |
| 127 | o6·=·HKR | 127 | o6·=·HKR |
| 128 | o6·:·QuotientRing</code></pre> | 128 | o6·:·QuotientRing</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ········</table> | 130 | ········</table> |
| 131 | ········<div> | 131 | ········<div> |
| Offset 55, 15 lines modified | Offset 55, 15 lines modified | ||
| 55 | ······1······4······6······4······1 | 55 | ······1······4······6······4······1 |
| 56 | o5·=·R··<--·R··<--·R··<--·R··<--·R | 56 | o5·=·R··<--·R··<--·R··<--·R··<--·R |
| 57 | ·····0······1······2······3······4 | 57 | ·····0······1······2······3······4 |
| 58 | o5·:·ChainComplex | 58 | o5·:·ChainComplex |
| 59 | i6·:·HKR·=·HH(KR) | 59 | i6·:·HKR·=·HH(KR) |
| 60 | ·--·used·1.3 | 60 | ·--·used·1.37771s·(cpu);·0.253982s·(thread);·0s·(gc) |
| 61 | Finding·easy·relations···········: | 61 | Finding·easy·relations···········: |
| 62 | o6·=·HKR | 62 | o6·=·HKR |
| 63 | o6·:·QuotientRing | 63 | o6·:·QuotientRing |
| 64 | The·following·is·the·graded·canonical·module·of·R: | 64 | The·following·is·the·graded·canonical·module·of·R: |
| 65 | i7·:·degList·=·first·entries·vars·Q·/·degree·/·first | 65 | i7·:·degList·=·first·entries·vars·Q·/·degree·/·first |
| Offset 176, 15 lines modified | Offset 176, 15 lines modified | ||
| 176 | ········</div> | 176 | ········</div> |
| 177 | ········<div> | 177 | ········<div> |
| 178 | ··········<p>Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey·triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the·homology·class·of·lift12*z3·+·z1*lift23.··To·see·this,·we·compute·and·check:</p> | 178 | ··········<p>Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey·triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the·homology·class·of·lift12*z3·+·z1*lift23.··To·see·this,·we·compute·and·check:</p> |
| 179 | ········</div> | 179 | ········</div> |
| 180 | ········<table·class="examples"> | 180 | ········<table·class="examples"> |
| 181 | ··········<tr> | 181 | ··········<tr> |
| 182 | <td>··············<pre><code·class="language-macaulay2">i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) | 182 | <td>··············<pre><code·class="language-macaulay2">i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) |
| 183 | ·--·used·2. | 183 | ·--·used·2.54893s·(cpu);·0.780215s·(thread);·0s·(gc) |
| 184 | Finding·easy·relations···········:· | 184 | Finding·easy·relations···········:· |
| 185 | ·············2 | 185 | ·············2 |
| 186 | o10·=·x·x·y·z·T·T·T·T | 186 | o10·=·x·x·y·z·T·T·T·T |
| 187 | ·······1·2·2···2·3·4·5 | 187 | ·······1·2·2···2·3·4·5 |
| 188 | o10·:·R[T·..T·] | 188 | o10·:·R[T·..T·] |
| 189 | ·········1···5</code></pre> | 189 | ·········1···5</code></pre> |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | Note·that·the·first·return·value·of·_\x8g_\x8e_\x8t_\x8B_\x8o_\x8u_\x8n_\x8d_\x8a_\x8r_\x8y_\x8P_\x8r_\x8e_\x8i_\x8m_\x8a_\x8g_\x8e·indicates·that·the | 91 | Note·that·the·first·return·value·of·_\x8g_\x8e_\x8t_\x8B_\x8o_\x8u_\x8n_\x8d_\x8a_\x8r_\x8y_\x8P_\x8r_\x8e_\x8i_\x8m_\x8a_\x8g_\x8e·indicates·that·the |
| 92 | inputs·are·indeed·boundaries,·and·the·second·value·is·the·lift·of·the·boundary | 92 | inputs·are·indeed·boundaries,·and·the·second·value·is·the·lift·of·the·boundary |
| 93 | along·the·differential. | 93 | along·the·differential. |
| 94 | Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey | 94 | Given·cycles·z1,z2,z3·such·that·z1*z2·and·z2*z3·are·boundaries,·the·Massey |
| 95 | triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the | 95 | triple·product·of·the·homology·classes·represented·by·z1,z2·and·z3·is·the |
| 96 | homology·class·of·lift12*z3·+·z1*lift23.·To·see·this,·we·compute·and·check: | 96 | homology·class·of·lift12*z3·+·z1*lift23.·To·see·this,·we·compute·and·check: |
| 97 | i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) | 97 | i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) |
| 98 | ·--·used·2. | 98 | ·--·used·2.54893s·(cpu);·0.780215s·(thread);·0s·(gc) |
| 99 | Finding·easy·relations···········: | 99 | Finding·easy·relations···········: |
| 100 | ·············2 | 100 | ·············2 |
| 101 | o10·=·x·x·y·z·T·T·T·T | 101 | o10·=·x·x·y·z·T·T·T·T |
| 102 | ·······1·2·2···2·3·4·5 | 102 | ·······1·2·2···2·3·4·5 |
| 103 | o10·:·R[T·..T·] | 103 | o10·:·R[T·..T·] |
| 104 | ·········1···5 | 104 | ·········1···5 |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | ······Differential·=>·{t·,·t·,·t·,·t·} | 114 | ······Differential·=>·{t·,·t·,·t·,·t·} |
| 115 | ························1···2···3···4 | 115 | ························1···2···3···4 |
| 116 | o4·:·DGAlgebra</code></pre> | 116 | o4·:·DGAlgebra</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·H·=·HH(KR) | 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·H·=·HH(KR) |
| 120 | ·--·used· | 120 | ·--·used·1.83569s·(cpu);·0.353695s·(thread);·0s·(gc) |
| 121 | Finding·easy·relations···········:· | 121 | Finding·easy·relations···········:· |
| 122 | o5·=·H | 122 | o5·=·H |
| 123 | o5·:·QuotientRing</code></pre> | 123 | o5·:·QuotientRing</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); | 126 | <td>··············<pre><code·class="language-macaulay2">i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); |
| Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
| 50 | ······Underlying·algebra·=>·R[T·..T·] | 50 | ······Underlying·algebra·=>·R[T·..T·] |
| 51 | ·······························1···4 | 51 | ·······························1···4 |
| 52 | ······Differential·=>·{t·,·t·,·t·,·t·} | 52 | ······Differential·=>·{t·,·t·,·t·,·t·} |
| 53 | ························1···2···3···4 | 53 | ························1···2···3···4 |
| 54 | o4·:·DGAlgebra | 54 | o4·:·DGAlgebra |
| 55 | i5·:·H·=·HH(KR) | 55 | i5·:·H·=·HH(KR) |
| 56 | ·--·used· | 56 | ·--·used·1.83569s·(cpu);·0.353695s·(thread);·0s·(gc) |
| 57 | Finding·easy·relations···········: | 57 | Finding·easy·relations···········: |
| 58 | o5·=·H | 58 | o5·=·H |
| 59 | o5·:·QuotientRing | 59 | o5·:·QuotientRing |
| 60 | i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); | 60 | i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); |
| 61 | ··············5·······343 | 61 | ··············5·······343 |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | o3·=·S | 95 | o3·=·S |
| 96 | o3·:·QuotientRing</code></pre> | 96 | o3·:·QuotientRing</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) | 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) |
| 100 | ·--·used· | 100 | ·--·used·2.59494s·(cpu);·0.694479s·(thread);·0s·(gc) |
| 101 | Finding·easy·relations···········:· | 101 | Finding·easy·relations···········:· |
| 102 | o4·=·HB | 102 | o4·=·HB |
| 103 | o4·:·QuotientRing</code></pre> | 103 | o4·:·QuotientRing</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·numgens·HB | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·numgens·HB |
| Offset 28, 15 lines modified | Offset 28, 15 lines modified | ||
| 28 | i2·:·M·=·coker·matrix·{{a^3*b^3*c^3*d^3}}; | 28 | i2·:·M·=·coker·matrix·{{a^3*b^3*c^3*d^3}}; |
| 29 | i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3} | 29 | i3·:·S·=·R/ideal{a^3*b^3*c^3*d^3} |
| 30 | o3·=·S | 30 | o3·=·S |
| 31 | o3·:·QuotientRing | 31 | o3·:·QuotientRing |
| 32 | i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) | 32 | i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) |
| 33 | ·--·used· | 33 | ·--·used·2.59494s·(cpu);·0.694479s·(thread);·0s·(gc) |
| 34 | Finding·easy·relations···········: | 34 | Finding·easy·relations···········: |
| 35 | o4·=·HB | 35 | o4·=·HB |
| 36 | o4·:·QuotientRing | 36 | o4·:·QuotientRing |
| 37 | i5·:·numgens·HB | 37 | i5·:·numgens·HB |
| 38 | o5·=·35 | 38 | o5·=·35 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 8 | U2VlZA== | 8 | U2VlZA== |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 6 | #·End·of·header | 6 | #·End·of·header |
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| 9 | #:len=367 | 9 | #:len=367 |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=10 | 7 | #:len=10 |
| 8 | bGluZWFyQ29tYg== | 8 | bGluZWFyQ29tYg== |
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| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZ2VuZXJpYyBsaW5lYXIgY29tYmluYXRp | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZ2VuZXJpYyBsaW5lYXIgY29tYmluYXRp |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=19 | 7 | #:len=19 |
| 8 | Zmxvb3IoUldlaWxEaXZpc29yKQ== | 8 | Zmxvb3IoUldlaWxEaXZpc29yKQ== |
| 9 | #:len=260 | 9 | #:len=260 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU1Nywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU1Nywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZmxvb3IsUldlaWxEaXZpc29yKSwiZmxvb3IoUldl | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZmxvb3IsUldlaWxEaXZpc29yKSwiZmxvb3IoUldl |
| Offset 64, 30 lines modified | Offset 64, 30 lines modified | ||
| 64 | o12·:·RWeilDivisor·on·R | 64 | o12·:·RWeilDivisor·on·R |
| 65 | i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z); | 65 | i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z); |
| 66 | i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)}) | 66 | i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)}) |
| 67 | o14·=· | 67 | o14·=·3*Div(x,·z)·+·0*Div(y,·z)·+·-Div(x-y,·x-z) |
| 68 | o14·:·WeilDivisor·on·R | 68 | o14·:·WeilDivisor·on·R |
| 69 | i15·:·-D | 69 | i15·:·-D |
| 70 | o15·=·Div(x | 70 | o15·=·-3*Div(x,·z)·+·Div(x-y,·x-z) |
| 71 | o15·:·WeilDivisor·on·R | 71 | o15·:·WeilDivisor·on·R |
| 72 | i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)}) | 72 | i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)}) |
| 73 | o16·=· | 73 | o16·=·3/2*Div(x,·z)·+·-2/3*Div(y,·z) |
| 74 | o16·:·WeilDivisor·on·R | 74 | o16·:·WeilDivisor·on·R |
| 75 | i17·:·-E | 75 | i17·:·-E |
| 76 | o17·=· | 76 | o17·=·-3/2*Div(x,·z)·+·2/3*Div(y,·z) |
| 77 | o17·:·WeilDivisor·on·R | 77 | o17·:·WeilDivisor·on·R |
| 78 | i18·:· | 78 | i18·:· |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ······························2 | 90 | ······························2 |
| 91 | o15·:·R-module,·submodule·of·R | 91 | o15·:·R-module,·submodule·of·R |
| 92 | i16·:·R·=·ZZ/11[x,y]; | 92 | i16·:·R·=·ZZ/11[x,y]; |
| 93 | i17·:·D·=·divisor(x*y/(x+y)) | 93 | i17·:·D·=·divisor(x*y/(x+y)) |
| 94 | o17·=· | 94 | o17·=·Div(x)·+·Div(y)·+·-Div(x+y) |
| 95 | o17·:·WeilDivisor·on·R | 95 | o17·:·WeilDivisor·on·R |
| 96 | i18·:·divisor(OO(D)) | 96 | i18·:·divisor(OO(D)) |
| 97 | o18·=·0,·the·zero·divisor | 97 | o18·=·0,·the·zero·divisor |
| Offset 1, 17 lines modified | Offset 1, 17 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·2803818461661759459 | 1 | --·-*-·M2-comint·-*-·hash:·2803818461661759459 |
| 2 | i1·:·R·=·QQ[x,y,z]; | 2 | i1·:·R·=·QQ[x,y,z]; |
| 3 | i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) | 3 | i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) |
| 4 | o2·=·Div( | 4 | o2·=·0*Div(y)·+·-2*Div(z)·+·Div(x) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·cleanSupport(D) | 6 | i3·:·cleanSupport(D) |
| 7 | o3·=·Div( | 7 | o3·=·-2*Div(z)·+·Div(x) |
| 8 | o3·:·WeilDivisor·on·R | 8 | o3·:·WeilDivisor·on·R |
| 9 | i4·:· | 9 | i4·:· |
| Offset 60, 29 lines modified | Offset 60, 29 lines modified | ||
| 60 | o14·=·3*Div(xz2,·xyz,·xy2,·x2z,·x2y,·x3) | 60 | o14·=·3*Div(xz2,·xyz,·xy2,·x2z,·x2y,·x3) |
| 61 | o14·:·WeilDivisor·on·A | 61 | o14·:·WeilDivisor·on·A |
| 62 | i15·:·E·=·divisor(y2z) | 62 | i15·:·E·=·divisor(y2z) |
| 63 | o15·=·Div(z | 63 | o15·=·2*Div(yz2,·y2z,·y3,·xyz,·xy2,·x2y)·+·Div(z3,·yz2,·y2z,·xz2,·xyz,·x2z) |
| 64 | o15·:·WeilDivisor·on·A | 64 | o15·:·WeilDivisor·on·A |
| 65 | i16·:·R·=·ZZ/7[x,y]; | 65 | i16·:·R·=·ZZ/7[x,y]; |
| 66 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) | 66 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) |
| 67 | o17·=·2*Div(x | 67 | o17·=·-1/2*Div(-x^3+y^2)·+·2*Div(x) |
| 68 | o17·:·QWeilDivisor·on·R | 68 | o17·:·QWeilDivisor·on·R |
| 69 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) | 69 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) |
| 70 | o18·=·2*Div(x | 70 | o18·=·-1/2*Div(-x^3+y^2)·+·2*Div(x) |
| 71 | o18·:·QWeilDivisor·on·R | 71 | o18·:·QWeilDivisor·on·R |
| 72 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); | 72 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); |
| 73 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)},·CoefficientType=>RR) | 73 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)},·CoefficientType=>RR) |
| Offset 44, 51 lines modified | Offset 44, 51 lines modified | ||
| 44 | i10·:·J·=·m^9; | 44 | i10·:·J·=·m^9; |
| 45 | o10·:·Ideal·of·R | 45 | o10·:·Ideal·of·R |
| 46 | i11·:·M·=·J*R^1; | 46 | i11·:·M·=·J*R^1; |
| 47 | i12·:·time·dualize(J,·Strategy=>IdealStrategy); | 47 | i12·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 48 | ·--·used·0.0 | 48 | ·--·used·0.043356s·(cpu);·0.0424366s·(thread);·0s·(gc) |
| 49 | o12·:·Ideal·of·R | 49 | o12·:·Ideal·of·R |
| 50 | i13·:·time·dualize(J,·Strategy=>ModuleStrategy); | 50 | i13·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 51 | ·--·used·0. | 51 | ·--·used·0.473821s·(cpu);·0.475756s·(thread);·0s·(gc) |
| 52 | o13·:·Ideal·of·R | 52 | o13·:·Ideal·of·R |
| 53 | i14·:·time·dualize(M,·Strategy=>IdealStrategy); | 53 | i14·:·time·dualize(M,·Strategy=>IdealStrategy); |
| 54 | ·--·used·0. | 54 | ·--·used·0.562077s·(cpu);·0.517849s·(thread);·0s·(gc) |
| 55 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); | 55 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); |
| 56 | ·--·used·0.001 | 56 | ·--·used·0.00132728s·(cpu);·0.00270744s·(thread);·0s·(gc) |
| 57 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); | 57 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); |
| 58 | ·--·used· | 58 | ·--·used·0.00242478s·(cpu);·0.00241584s·(thread);·0s·(gc) |
| 59 | o16·:·Ideal·of·R | 59 | o16·:·Ideal·of·R |
| 60 | i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v); | 60 | i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v); |
| 61 | i18·:·I·=·ideal(x,u); | 61 | i18·:·I·=·ideal(x,u); |
| 62 | o18·:·Ideal·of·R | 62 | o18·:·Ideal·of·R |
| 63 | i19·:·J·=·I^15; | 63 | i19·:·J·=·I^15; |
| 64 | o19·:·Ideal·of·R | 64 | o19·:·Ideal·of·R |
| 65 | i20·:·time·dualize(J,·Strategy=>IdealStrategy); | 65 | i20·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 66 | ·--·used·0.1 | 66 | ·--·used·0.134665s·(cpu);·0.096899s·(thread);·0s·(gc) |
| 67 | o20·:·Ideal·of·R | 67 | o20·:·Ideal·of·R |
| 68 | i21·:·time·dualize(J,·Strategy=>ModuleStrategy); | 68 | i21·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 69 | ·--·used·0.0029 | 69 | ·--·used·0.0029858s·(cpu);·0.00544469s·(thread);·0s·(gc) |
| 70 | o21·:·Ideal·of·R | 70 | o21·:·Ideal·of·R |
| 71 | i22·:·R·=·QQ[x,y]/ideal(x*y); | 71 | i22·:·R·=·QQ[x,y]/ideal(x*y); |
| 72 | i23·:·J·=·ideal(x,y); | 72 | i23·:·J·=·ideal(x,y); |
| Offset 1, 23 lines modified | Offset 1, 23 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·6816075660530398278 | 1 | --·-*-·M2-comint·-*-·hash:·6816075660530398278 |
| 2 | i1·:·R·=·QQ[x,·y,·z]; | 2 | i1·:·R·=·QQ[x,·y,·z]; |
| 3 | i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) | 3 | i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) |
| 4 | o2·=· | 4 | o2·=·2*Div(y)·+·0*Div(x^2+z)·+·-8*Div(x) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·getPrimeDivisors(·D·) | 6 | i3·:·getPrimeDivisors(·D·) |
| 7 | o3·=·{Div( | 7 | o3·=·{Div(y),·Div(x^2+z),·Div(x)} |
| 8 | o3·:·List | 8 | o3·:·List |
| 9 | i4·:·getPrimeDivisors(·cleanSupport·D·) | 9 | i4·:·getPrimeDivisors(·cleanSupport·D·) |
| 10 | o4·=·{Div( | 10 | o4·=·{Div(y),·Div(x)} |
| 11 | o4·:·List | 11 | o4·:·List |
| 12 | i5·:· | 12 | i5·:· |
| Offset 1, 20 lines modified | Offset 1, 20 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·13719144060491348416 | 1 | --·-*-·M2-comint·-*-·hash:·13719144060491348416 |
| 2 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); | 2 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); |
| 3 | i2·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) | 3 | i2·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) |
| 4 | o2·=·Div( | 4 | o2·=·2*Div(y,·z)·+·Div(x,·z) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 6 | i3·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 7 | o3·=· | 7 | o3·=·1/2*Div(y,·z)·+·3/4*Div(x,·z) |
| 8 | o3·:·QWeilDivisor·on·R | 8 | o3·:·QWeilDivisor·on·R |
| 9 | i4·:·isQCartier(10,·D1) | 9 | i4·:·isQCartier(10,·D1) |
| 10 | o4·=·2 | 10 | o4·=·2 |
| Offset 44, 21 lines modified | Offset 44, 21 lines modified | ||
| 44 | o10·=·0 | 44 | o10·=·0 |
| 45 | i11·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); | 45 | i11·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); |
| 46 | i12·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) | 46 | i12·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) |
| 47 | o12·=· | 47 | o12·=·Div(x,·z)·+·2*Div(y,·z) |
| 48 | o12·:·WeilDivisor·on·R | 48 | o12·:·WeilDivisor·on·R |
| 49 | i13·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 49 | i13·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 50 | o13·=· | 50 | o13·=·3/4*Div(x,·z)·+·1/2*Div(y,·z) |
| 51 | o13·:·QWeilDivisor·on·R | 51 | o13·:·QWeilDivisor·on·R |
| 52 | i14·:·isQCartier(10,·D1,·IsGraded·=>·true) | 52 | i14·:·isQCartier(10,·D1,·IsGraded·=>·true) |
| 53 | o14·=·1 | 53 | o14·=·1 |
| Offset 1, 20 lines modified | Offset 1, 20 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·13920959388108803216 | 1 | --·-*-·M2-comint·-*-·hash:·13920959388108803216 |
| 2 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); | 2 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); |
| 3 | i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 3 | i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 4 | o2·=· | 4 | o2·=·3/4*Div(y,·z)·+·1/2*Div(x,·z) |
| 5 | o2·:·QWeilDivisor·on·R | 5 | o2·:·QWeilDivisor·on·R |
| 6 | i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 6 | i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 7 | o3·=· | 7 | o3·=·3/4*Div(y,·z)·+·5/2*Div(x,·z) |
| 8 | o3·:·QWeilDivisor·on·R | 8 | o3·:·QWeilDivisor·on·R |
| 9 | i4·:·isQLinearEquivalent(10,·D,·E) | 9 | i4·:·isQLinearEquivalent(10,·D,·E) |
| 10 | o4·=·true | 10 | o4·=·true |
| Offset 36, 21 lines modified | Offset 36, 21 lines modified | ||
| 36 | o9·=·true | 36 | o9·=·true |
| 37 | i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); | 37 | i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); |
| 38 | i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 38 | i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 39 | o11·=· | 39 | o11·=·1/2*Div(x,·z)·+·3/4*Div(y,·z) |
| 40 | o11·:·QWeilDivisor·on·R | 40 | o11·:·QWeilDivisor·on·R |
| 41 | i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 41 | i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 42 | o12·=· | 42 | o12·=·-1/4*Div(x,·z)·+·3/2*Div(y,·z) |
| 43 | o12·:·QWeilDivisor·on·R | 43 | o12·:·QWeilDivisor·on·R |
| 44 | i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true) | 44 | i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true) |
| 45 | o13·=·true | 45 | o13·=·true |
| Offset 103, 104 lines modified | Offset 103, 104 lines modified | ||
| 103 | o21·:·Ideal·of·R | 103 | o21·:·Ideal·of·R |
| 104 | i22·:·J·=·I^21; | 104 | i22·:·J·=·I^21; |
| 105 | o22·:·Ideal·of·R | 105 | o22·:·Ideal·of·R |
| 106 | i23·:·time·reflexify(J); | 106 | i23·:·time·reflexify(J); |
| 107 | ·--·used·0. | 107 | ·--·used·0.214073s·(cpu);·0.165499s·(thread);·0s·(gc) |
| 108 | o23·:·Ideal·of·R | 108 | o23·:·Ideal·of·R |
| 109 | i24·:·time·reflexify(J*R^1); | 109 | i24·:·time·reflexify(J*R^1); |
| 110 | ·--·used·0. | 110 | ·--·used·0.377369s·(cpu);·0.336166s·(thread);·0s·(gc) |
| 111 | i25·:·R·=·ZZ/13[x,y,z]/ideal(x^3·+·y^3-z^11*x*y); | 111 | i25·:·R·=·ZZ/13[x,y,z]/ideal(x^3·+·y^3-z^11*x*y); |
| 112 | i26·:·I·=·ideal(x-4*y,·z); | 112 | i26·:·I·=·ideal(x-4*y,·z); |
| 113 | o26·:·Ideal·of·R | 113 | o26·:·Ideal·of·R |
| 114 | i27·:·J·=·I^20; | 114 | i27·:·J·=·I^20; |
| 115 | o27·:·Ideal·of·R | 115 | o27·:·Ideal·of·R |
| 116 | i28·:·M·=·J*R^1; | 116 | i28·:·M·=·J*R^1; |
| 117 | i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) | 117 | i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 118 | ·--·used·0. | 118 | ·--·used·0.205755s·(cpu);·0.122281s·(thread);·0s·(gc) |
| 119 | ··············2············2·····9·······9···11 | 119 | ··············2············2·····9·······9···11 |
| 120 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 120 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 121 | o29·:·Ideal·of·R | 121 | o29·:·Ideal·of·R |
| 122 | i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 122 | i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 123 | ·--·used· | 123 | ·--·used·5.31101s·(cpu);·4.22567s·(thread);·0s·(gc) |
| 124 | ··············2············2·····9·······9···11 | 124 | ··············2············2·····9·······9···11 |
| 125 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 125 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 126 | o30·:·Ideal·of·R | 126 | o30·:·Ideal·of·R |
| 127 | i31·:·J1·==·J2 | 127 | i31·:·J1·==·J2 |
| 128 | o31·=·true | 128 | o31·=·true |
| 129 | i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 129 | i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 130 | ·--·used· | 130 | ·--·used·5.39384s·(cpu);·4.32502s·(thread);·0s·(gc) |
| 131 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 131 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 132 | ·--·used·0. | 132 | ·--·used·0.586407s·(cpu);·0.44375s·(thread);·0s·(gc) |
| 133 | i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v); | 133 | i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v); |
| 134 | i35·:·I·=·ideal(x,u); | 134 | i35·:·I·=·ideal(x,u); |
| 135 | o35·:·Ideal·of·R | 135 | o35·:·Ideal·of·R |
| 136 | i36·:·J·=·I^20; | 136 | i36·:·J·=·I^20; |
| 137 | o36·:·Ideal·of·R | 137 | o36·:·Ideal·of·R |
| 138 | i37·:·M·=·I^20*R^1; | 138 | i37·:·M·=·I^20*R^1; |
| 139 | i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) | 139 | i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 140 | ·--·used·0. | 140 | ·--·used·0.853554s·(cpu);·0.318374s·(thread);·0s·(gc) |
| 141 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· | 141 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· |
| 142 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 142 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 143 | ······----------------------------------------------------------------------- | 143 | ······----------------------------------------------------------------------- |
| 144 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· | 144 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· |
| 145 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 145 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 146 | ······----------------------------------------------------------------------- | 146 | ······----------------------------------------------------------------------- |
| 147 | ·······19····20 | 147 | ·······19····20 |
| 148 | ······x··u,·x··) | 148 | ······x··u,·x··) |
| 149 | o38·:·Ideal·of·R | 149 | o38·:·Ideal·of·R |
| 150 | i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 150 | i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 151 | ·--·used·0.012 | 151 | ·--·used·0.0129902s·(cpu);·0.0138033s·(thread);·0s·(gc) |
| 152 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· | 152 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· |
| 153 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 153 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 154 | ······----------------------------------------------------------------------- | 154 | ······----------------------------------------------------------------------- |
| 155 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· | 155 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· |
| 156 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 156 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 157 | ······----------------------------------------------------------------------- | 157 | ······----------------------------------------------------------------------- |
| 158 | ·······19····20 | 158 | ·······19····20 |
| 159 | ······x··u,·x··) | 159 | ······x··u,·x··) |
| 160 | o39·:·Ideal·of·R | 160 | o39·:·Ideal·of·R |
| 161 | i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 161 | i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 162 | ·--·used·0. | 162 | ·--·used·0.203497s·(cpu);·0.0676861s·(thread);·0s·(gc) |
| 163 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 163 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 164 | ·--·used·0.00 | 164 | ·--·used·0.0037396s·(cpu);·0.00578348s·(thread);·0s·(gc) |
| 165 | i42·:·R·=·QQ[x,y]/ideal(x*y); | 165 | i42·:·R·=·QQ[x,y]/ideal(x*y); |
| 166 | i43·:·I·=·ideal(x,y); | 166 | i43·:·I·=·ideal(x,y); |
| 167 | o43·:·Ideal·of·R | 167 | o43·:·Ideal·of·R |
| Offset 23, 44 lines modified | Offset 23, 44 lines modified | ||
| 23 | i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); | 23 | i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); |
| 24 | i6·:·I·=·ideal(x-z,y-2*z); | 24 | i6·:·I·=·ideal(x-z,y-2*z); |
| 25 | o6·:·Ideal·of·R | 25 | o6·:·Ideal·of·R |
| 26 | i7·:·time·J20a·=·reflexivePower(20,·I); | 26 | i7·:·time·J20a·=·reflexivePower(20,·I); |
| 27 | ·--·used·0.0 | 27 | ·--·used·0.08295s·(cpu);·0.0393105s·(thread);·0s·(gc) |
| 28 | o7·:·Ideal·of·R | 28 | o7·:·Ideal·of·R |
| 29 | i8·:·I20·=·I^20; | 29 | i8·:·I20·=·I^20; |
| 30 | o8·:·Ideal·of·R | 30 | o8·:·Ideal·of·R |
| 31 | i9·:·time·J20b·=·reflexify(I20); | 31 | i9·:·time·J20b·=·reflexify(I20); |
| 32 | ·--·used·0. | 32 | ·--·used·0.126397s·(cpu);·0.127436s·(thread);·0s·(gc) |
| 33 | o9·:·Ideal·of·R | 33 | o9·:·Ideal·of·R |
| 34 | i10·:·J20a·==·J20b | 34 | i10·:·J20a·==·J20b |
| 35 | o10·=·true | 35 | o10·=·true |
| 36 | i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); | 36 | i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); |
| 37 | i12·:·I·=·ideal(x-z,y-2*z); | 37 | i12·:·I·=·ideal(x-z,y-2*z); |
| 38 | o12·:·Ideal·of·R | 38 | o12·:·Ideal·of·R |
| 39 | i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); | 39 | i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); |
| 40 | ·--·used·0.0 | 40 | ·--·used·0.0332655s·(cpu);·0.0338725s·(thread);·0s·(gc) |
| 41 | o13·:·Ideal·of·R | 41 | o13·:·Ideal·of·R |
| 42 | i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); | 42 | i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); |
| 43 | ·--·used·0. | 43 | ·--·used·0.137002s·(cpu);·0.0911039s·(thread);·0s·(gc) |
| 44 | o14·:·Ideal·of·R | 44 | o14·:·Ideal·of·R |
| 45 | i15·:·J1·==·J2 | 45 | i15·:·J1·==·J2 |
| 46 | o15·=·true | 46 | o15·=·true |
| Offset 165, 36 lines modified | Offset 165, 36 lines modified | ||
| 165 | ········<table·class="examples"> | 165 | ········<table·class="examples"> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);</code></pre> | 167 | <td>··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z);</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)}) | 170 | <td>··············<pre><code·class="language-macaulay2">i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)}) |
| 171 | o14·=· | 171 | o14·=·3*Div(x,·z)·+·0*Div(y,·z)·+·-Div(x-y,·x-z) |
| 172 | o14·:·WeilDivisor·on·R</code></pre> | 172 | o14·:·WeilDivisor·on·R</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i15·:·-D | 175 | <td>··············<pre><code·class="language-macaulay2">i15·:·-D |
| 176 | o15·=·Div(x | 176 | o15·=·-3*Div(x,·z)·+·Div(x-y,·x-z) |
| 177 | o15·:·WeilDivisor·on·R</code></pre> | 177 | o15·:·WeilDivisor·on·R</code></pre> |
| 178 | </td>··········</tr> | 178 | </td>··········</tr> |
| 179 | ··········<tr> | 179 | ··········<tr> |
| 180 | <td>··············<pre><code·class="language-macaulay2">i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)}) | 180 | <td>··············<pre><code·class="language-macaulay2">i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)}) |
| 181 | o16·=· | 181 | o16·=·3/2*Div(x,·z)·+·-2/3*Div(y,·z) |
| 182 | o16·:·WeilDivisor·on·R</code></pre> | 182 | o16·:·WeilDivisor·on·R</code></pre> |
| 183 | </td>··········</tr> | 183 | </td>··········</tr> |
| 184 | ··········<tr> | 184 | ··········<tr> |
| 185 | <td>··············<pre><code·class="language-macaulay2">i17·:·-E | 185 | <td>··············<pre><code·class="language-macaulay2">i17·:·-E |
| 186 | o17·=· | 186 | o17·=·-3/2*Div(x,·z)·+·2/3*Div(y,·z) |
| 187 | o17·:·WeilDivisor·on·R</code></pre> | 187 | o17·:·WeilDivisor·on·R</code></pre> |
| 188 | </td>··········</tr> | 188 | </td>··········</tr> |
| 189 | ········</table> | 189 | ········</table> |
| 190 | ······</div> | 190 | ······</div> |
| 191 | ······<div·class="waystouse"> | 191 | ······<div·class="waystouse"> |
| 192 | ········<h2>Ways·to·use·this·method:</h2> | 192 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 71, 28 lines modified | Offset 71, 28 lines modified | ||
| 71 | o12·=·-Div(y)·+·2.75*Div(x) | 71 | o12·=·-Div(y)·+·2.75*Div(x) |
| 72 | o12·:·RWeilDivisor·on·R | 72 | o12·:·RWeilDivisor·on·R |
| 73 | Finally,·we·can·negate·a·divisor. | 73 | Finally,·we·can·negate·a·divisor. |
| 74 | i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z); | 74 | i13·:·R·=·ZZ/3[x,y,z]/ideal(x^2-y*z); |
| 75 | i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)}) | 75 | i14·:·D·=·divisor({3,·0,·-1},·{ideal(x,z),·ideal(y,z),·ideal(x-y,·x-z)}) |
| 76 | o14·=· | 76 | o14·=·3*Div(x,·z)·+·0*Div(y,·z)·+·-Div(x-y,·x-z) |
| 77 | o14·:·WeilDivisor·on·R | 77 | o14·:·WeilDivisor·on·R |
| 78 | i15·:·-D | 78 | i15·:·-D |
| 79 | o15·=·Div(x | 79 | o15·=·-3*Div(x,·z)·+·Div(x-y,·x-z) |
| 80 | o15·:·WeilDivisor·on·R | 80 | o15·:·WeilDivisor·on·R |
| 81 | i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)}) | 81 | i16·:·E·=·divisor({3/2,·-2/3},·{ideal(x,·z),·ideal(y,·z)}) |
| 82 | o16·=· | 82 | o16·=·3/2*Div(x,·z)·+·-2/3*Div(y,·z) |
| 83 | o16·:·WeilDivisor·on·R | 83 | o16·:·WeilDivisor·on·R |
| 84 | i17·:·-E | 84 | i17·:·-E |
| 85 | o17·=· | 85 | o17·=·-3/2*Div(x,·z)·+·2/3*Div(y,·z) |
| 86 | o17·:·WeilDivisor·on·R | 86 | o17·:·WeilDivisor·on·R |
| 87 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 87 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 88 | ····*·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8·_\x8+_\x8·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·add·or·subtract·two·divisors,·or·negate·a | 88 | ····*·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8·_\x8+_\x8·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·add·or·subtract·two·divisors,·or·negate·a |
| 89 | ······divisor | 89 | ······divisor |
| Offset 195, 15 lines modified | Offset 195, 15 lines modified | ||
| 195 | ········<table·class="examples"> | 195 | ········<table·class="examples"> |
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/11[x,y];</code></pre> | 197 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/11[x,y];</code></pre> |
| 198 | </td>··········</tr> | 198 | </td>··········</tr> |
| 199 | ··········<tr> | 199 | ··········<tr> |
| 200 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor(x*y/(x+y)) | 200 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor(x*y/(x+y)) |
| 201 | o17·=· | 201 | o17·=·Div(x)·+·Div(y)·+·-Div(x+y) |
| 202 | o17·:·WeilDivisor·on·R</code></pre> | 202 | o17·:·WeilDivisor·on·R</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i18·:·divisor(OO(D)) | 205 | <td>··············<pre><code·class="language-macaulay2">i18·:·divisor(OO(D)) |
| 206 | o18·=·0,·the·zero·divisor | 206 | o18·=·0,·the·zero·divisor |
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| 101 | Note·that·you·can·call·the·divisor·constructor·on·the·module·you·construct,·but | 101 | Note·that·you·can·call·the·divisor·constructor·on·the·module·you·construct,·but |
| 102 | it·will·only·produce·a·divisor·up·to·linear·equivalence·(which·can·mean | 102 | it·will·only·produce·a·divisor·up·to·linear·equivalence·(which·can·mean |
| 103 | different·things·depending·on·whether·or·not·you·are·keeping·track·of·the | 103 | different·things·depending·on·whether·or·not·you·are·keeping·track·of·the |
| 104 | grading). | 104 | grading). |
| 105 | i16·:·R·=·ZZ/11[x,y]; | 105 | i16·:·R·=·ZZ/11[x,y]; |
| 106 | i17·:·D·=·divisor(x*y/(x+y)) | 106 | i17·:·D·=·divisor(x*y/(x+y)) |
| 107 | o17·=· | 107 | o17·=·Div(x)·+·Div(y)·+·-Div(x+y) |
| 108 | o17·:·WeilDivisor·on·R | 108 | o17·:·WeilDivisor·on·R |
| 109 | i18·:·divisor(OO(D)) | 109 | i18·:·divisor(OO(D)) |
| 110 | o18·=·0,·the·zero·divisor | 110 | o18·=·0,·the·zero·divisor |
| 111 | o18·:·WeilDivisor·on·R | 111 | o18·:·WeilDivisor·on·R |
| Offset 73, 22 lines modified | Offset 73, 22 lines modified | ||
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) |
| 79 | o2·=·Div( | 79 | o2·=·0*Div(y)·+·-2*Div(z)·+·Div(x) |
| 80 | o2·:·WeilDivisor·on·R</code></pre> | 80 | o2·:·WeilDivisor·on·R</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·cleanSupport(D) | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·cleanSupport(D) |
| 84 | o3·=·Div( | 84 | o3·=·-2*Div(z)·+·Div(x) |
| 85 | o3·:·WeilDivisor·on·R</code></pre> | 85 | o3·:·WeilDivisor·on·R</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ········</table> | 87 | ········</table> |
| 88 | ······</div> | 88 | ······</div> |
| 89 | ······<div·class="waystouse"> | 89 | ······<div·class="waystouse"> |
| 90 | ········<h2>Ways·to·use·<span·class="tt">cleanSupport</span>:</h2> | 90 | ········<h2>Ways·to·use·<span·class="tt">cleanSupport</span>:</h2> |
| Offset 14, 19 lines modified | Offset 14, 19 lines modified | ||
| 14 | ··········o·an·instance·of·the·type·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r, | 14 | ··········o·an·instance·of·the·type·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r, |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | This·function·returns·a·divisor·where·all·entries·with·coefficient·zero·are | 16 | This·function·returns·a·divisor·where·all·entries·with·coefficient·zero·are |
| 17 | removed. | 17 | removed. |
| 18 | i1·:·R·=·QQ[x,y,z]; | 18 | i1·:·R·=·QQ[x,y,z]; |
| 19 | i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) | 19 | i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) |
| 20 | o2·=·Div( | 20 | o2·=·0*Div(y)·+·-2*Div(z)·+·Div(x) |
| 21 | o2·:·WeilDivisor·on·R | 21 | o2·:·WeilDivisor·on·R |
| 22 | i3·:·cleanSupport(D) | 22 | i3·:·cleanSupport(D) |
| 23 | o3·=·Div( | 23 | o3·=·-2*Div(z)·+·Div(x) |
| 24 | o3·:·WeilDivisor·on·R | 24 | o3·:·WeilDivisor·on·R |
| 25 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8cl\x8le\x8ea\x8an\x8nS\x8Su\x8up\x8pp\x8po\x8or\x8rt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8cl\x8le\x8ea\x8an\x8nS\x8Su\x8up\x8pp\x8po\x8or\x8rt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·cleanSupport(BasicDivisor) | 26 | ····*·cleanSupport(BasicDivisor) |
| 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 28 | The·object·_\x8c_\x8l_\x8e_\x8a_\x8n_\x8S_\x8u_\x8p_\x8p_\x8o_\x8r_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 28 | The·object·_\x8c_\x8l_\x8e_\x8a_\x8n_\x8S_\x8u_\x8p_\x8p_\x8o_\x8r_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 187, 37 lines modified | Offset 187, 37 lines modified | ||
| 187 | o14·=·3*Div(xz2,·xyz,·xy2,·x2z,·x2y,·x3) | 187 | o14·=·3*Div(xz2,·xyz,·xy2,·x2z,·x2y,·x3) |
| 188 | o14·:·WeilDivisor·on·A</code></pre> | 188 | o14·:·WeilDivisor·on·A</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i15·:·E·=·divisor(y2z) | 191 | <td>··············<pre><code·class="language-macaulay2">i15·:·E·=·divisor(y2z) |
| 192 | o15·=·Div(z | 192 | o15·=·2*Div(yz2,·y2z,·y3,·xyz,·xy2,·x2y)·+·Div(z3,·yz2,·y2z,·xz2,·xyz,·x2z) |
| 193 | o15·:·WeilDivisor·on·A</code></pre> | 193 | o15·:·WeilDivisor·on·A</code></pre> |
| 194 | </td>··········</tr> | 194 | </td>··········</tr> |
| 195 | ········</table> | 195 | ········</table> |
| 196 | ········<div> | 196 | ········<div> |
| 197 | ··········<p>We·can·construct·a·Q-divisor·as·well.··Here·are·two·ways·to·do·it·(we·work·in·$A^2$·this·time).</p> | 197 | ··········<p>We·can·construct·a·Q-divisor·as·well.··Here·are·two·ways·to·do·it·(we·work·in·$A^2$·this·time).</p> |
| 198 | ········</div> | 198 | ········</div> |
| 199 | ········<table·class="examples"> | 199 | ········<table·class="examples"> |
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/7[x,y];</code></pre> | 201 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/7[x,y];</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) | 204 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) |
| 205 | o17·=·2*Div(x | 205 | o17·=·-1/2*Div(-x^3+y^2)·+·2*Div(x) |
| 206 | o17·:·QWeilDivisor·on·R</code></pre> | 206 | o17·:·QWeilDivisor·on·R</code></pre> |
| 207 | </td>··········</tr> | 207 | </td>··········</tr> |
| 208 | ··········<tr> | 208 | ··········<tr> |
| 209 | <td>··············<pre><code·class="language-macaulay2">i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) | 209 | <td>··············<pre><code·class="language-macaulay2">i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) |
| 210 | o18·=·2*Div(x | 210 | o18·=·-1/2*Div(-x^3+y^2)·+·2*Div(x) |
| 211 | o18·:·QWeilDivisor·on·R</code></pre> | 211 | o18·:·QWeilDivisor·on·R</code></pre> |
| 212 | </td>··········</tr> | 212 | </td>··········</tr> |
| 213 | ········</table> | 213 | ········</table> |
| 214 | ········<div> | 214 | ········<div> |
| 215 | ··········<p>Or·an·R-divisor.··This·time·we·work·in·the·cone·over·$P^1·\times·P^1$.</p> | 215 | ··········<p>Or·an·R-divisor.··This·time·we·work·in·the·cone·over·$P^1·\times·P^1$.</p> |
| 216 | ········</div> | 216 | ········</div> |
| Offset 96, 28 lines modified | Offset 96, 28 lines modified | ||
| 96 | i14·:·D·=·divisor(x3) | 96 | i14·:·D·=·divisor(x3) |
| 97 | o14·=·3*Div(xz2,·xyz,·xy2,·x2z,·x2y,·x3) | 97 | o14·=·3*Div(xz2,·xyz,·xy2,·x2z,·x2y,·x3) |
| 98 | o14·:·WeilDivisor·on·A | 98 | o14·:·WeilDivisor·on·A |
| 99 | i15·:·E·=·divisor(y2z) | 99 | i15·:·E·=·divisor(y2z) |
| 100 | o15·=·Div(z | 100 | o15·=·2*Div(yz2,·y2z,·y3,·xyz,·xy2,·x2y)·+·Div(z3,·yz2,·y2z,·xz2,·xyz,·x2z) |
| 101 | o15·:·WeilDivisor·on·A | 101 | o15·:·WeilDivisor·on·A |
| 102 | We·can·construct·a·Q-divisor·as·well.·Here·are·two·ways·to·do·it·(we·work·in | 102 | We·can·construct·a·Q-divisor·as·well.·Here·are·two·ways·to·do·it·(we·work·in |
| 103 | $A^2$·this·time). | 103 | $A^2$·this·time). |
| 104 | i16·:·R·=·ZZ/7[x,y]; | 104 | i16·:·R·=·ZZ/7[x,y]; |
| 105 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) | 105 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) |
| 106 | o17·=·2*Div(x | 106 | o17·=·-1/2*Div(-x^3+y^2)·+·2*Div(x) |
| 107 | o17·:·QWeilDivisor·on·R | 107 | o17·:·QWeilDivisor·on·R |
| 108 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) | 108 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) |
| 109 | o18·=·2*Div(x | 109 | o18·=·-1/2*Div(-x^3+y^2)·+·2*Div(x) |
| 110 | o18·:·QWeilDivisor·on·R | 110 | o18·:·QWeilDivisor·on·R |
| 111 | Or·an·R-divisor.·This·time·we·work·in·the·cone·over·$P^1·\times·P^1$. | 111 | Or·an·R-divisor.·This·time·we·work·in·the·cone·over·$P^1·\times·P^1$. |
| 112 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); | 112 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); |
| 113 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)}, | 113 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)}, |
| 114 | CoefficientType=>RR) | 114 | CoefficientType=>RR) |
| Offset 145, 35 lines modified | Offset 145, 35 lines modified | ||
| 145 | o10·:·Ideal·of·R</code></pre> | 145 | o10·:·Ideal·of·R</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i11·:·M·=·J*R^1;</code></pre> | 148 | <td>··············<pre><code·class="language-macaulay2">i11·:·M·=·J*R^1;</code></pre> |
| 149 | </td>··········</tr> | 149 | </td>··········</tr> |
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·dualize(J,·Strategy=>IdealStrategy); | 151 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 152 | ·--·used·0.0 | 152 | ·--·used·0.043356s·(cpu);·0.0424366s·(thread);·0s·(gc) |
| 153 | o12·:·Ideal·of·R</code></pre> | 153 | o12·:·Ideal·of·R</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·dualize(J,·Strategy=>ModuleStrategy); | 156 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 157 | ·--·used·0. | 157 | ·--·used·0.473821s·(cpu);·0.475756s·(thread);·0s·(gc) |
| 158 | o13·:·Ideal·of·R</code></pre> | 158 | o13·:·Ideal·of·R</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ··········<tr> | 160 | ··········<tr> |
| 161 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·dualize(M,·Strategy=>IdealStrategy); | 161 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·dualize(M,·Strategy=>IdealStrategy); |
| 162 | ·--·used·0. | 162 | ·--·used·0.562077s·(cpu);·0.517849s·(thread);·0s·(gc)</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·dualize(M,·Strategy=>ModuleStrategy); | 165 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·dualize(M,·Strategy=>ModuleStrategy); |
| 166 | ·--·used·0.001 | 166 | ·--·used·0.00132728s·(cpu);·0.00270744s·(thread);·0s·(gc)</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); | 169 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); |
| 170 | ·--·used· | 170 | ·--·used·0.00242478s·(cpu);·0.00241584s·(thread);·0s·(gc) |
| 171 | o16·:·Ideal·of·R</code></pre> | 171 | o16·:·Ideal·of·R</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ········</table> | 173 | ········</table> |
| 174 | ········<div> | 174 | ········<div> |
| 175 | ··········<p>For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.</p> | 175 | ··········<p>For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.</p> |
| 176 | ········</div> | 176 | ········</div> |
| Offset 189, 21 lines modified | Offset 189, 21 lines modified | ||
| 189 | ··········<tr> | 189 | ··········<tr> |
| 190 | <td>··············<pre><code·class="language-macaulay2">i19·:·J·=·I^15; | 190 | <td>··············<pre><code·class="language-macaulay2">i19·:·J·=·I^15; |
| 191 | o19·:·Ideal·of·R</code></pre> | 191 | o19·:·Ideal·of·R</code></pre> |
| 192 | </td>··········</tr> | 192 | </td>··········</tr> |
| 193 | ··········<tr> | 193 | ··········<tr> |
| 194 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·dualize(J,·Strategy=>IdealStrategy); | 194 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 195 | ·--·used·0.1 | 195 | ·--·used·0.134665s·(cpu);·0.096899s·(thread);·0s·(gc) |
| 196 | o20·:·Ideal·of·R</code></pre> | 196 | o20·:·Ideal·of·R</code></pre> |
| 197 | </td>··········</tr> | 197 | </td>··········</tr> |
| 198 | ··········<tr> | 198 | ··········<tr> |
| 199 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·dualize(J,·Strategy=>ModuleStrategy); | 199 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 200 | ·--·used·0.0029 | 200 | ·--·used·0.0029858s·(cpu);·0.00544469s·(thread);·0s·(gc) |
| 201 | o21·:·Ideal·of·R</code></pre> | 201 | o21·:·Ideal·of·R</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ········</table> | 203 | ········</table> |
| 204 | ········<div> | 204 | ········<div> |
| 205 | ··········<p><span·class="tt">KnownDomain</span>·is·an·option·for·<span·class="tt">dualize</span>.··If·it·is·<span·class="tt">false</span>·(default·is·<span·class="tt">true</span>),·then·the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then·it·will·revert·to·<span·class="tt">ModuleStrategy</span>.··If·<span·class="tt">KnownDomain</span>·is·set·to·<span·class="tt">true</span>·for·a·non-domain,·then·the·function·can·return·an·incorrect·answer.</p> | 205 | ··········<p><span·class="tt">KnownDomain</span>·is·an·option·for·<span·class="tt">dualize</span>.··If·it·is·<span·class="tt">false</span>·(default·is·<span·class="tt">true</span>),·then·the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then·it·will·revert·to·<span·class="tt">ModuleStrategy</span>.··If·<span·class="tt">KnownDomain</span>·is·set·to·<span·class="tt">true</span>·for·a·non-domain,·then·the·function·can·return·an·incorrect·answer.</p> |
| 206 | ········</div> | 206 | ········</div> |
| Offset 61, 43 lines modified | Offset 61, 43 lines modified | ||
| 61 | o9·:·Ideal·of·R | 61 | o9·:·Ideal·of·R |
| 62 | i10·:·J·=·m^9; | 62 | i10·:·J·=·m^9; |
| 63 | o10·:·Ideal·of·R | 63 | o10·:·Ideal·of·R |
| 64 | i11·:·M·=·J*R^1; | 64 | i11·:·M·=·J*R^1; |
| 65 | i12·:·time·dualize(J,·Strategy=>IdealStrategy); | 65 | i12·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 66 | ·--·used·0.0 | 66 | ·--·used·0.043356s·(cpu);·0.0424366s·(thread);·0s·(gc) |
| 67 | o12·:·Ideal·of·R | 67 | o12·:·Ideal·of·R |
| 68 | i13·:·time·dualize(J,·Strategy=>ModuleStrategy); | 68 | i13·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 69 | ·--·used·0. | 69 | ·--·used·0.473821s·(cpu);·0.475756s·(thread);·0s·(gc) |
| 70 | o13·:·Ideal·of·R | 70 | o13·:·Ideal·of·R |
| 71 | i14·:·time·dualize(M,·Strategy=>IdealStrategy); | 71 | i14·:·time·dualize(M,·Strategy=>IdealStrategy); |
| 72 | ·--·used·0. | 72 | ·--·used·0.562077s·(cpu);·0.517849s·(thread);·0s·(gc) |
| 73 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); | 73 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); |
| 74 | ·--·used·0.001 | 74 | ·--·used·0.00132728s·(cpu);·0.00270744s·(thread);·0s·(gc) |
| 75 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); | 75 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); |
| 76 | ·--·used· | 76 | ·--·used·0.00242478s·(cpu);·0.00241584s·(thread);·0s·(gc) |
| 77 | o16·:·Ideal·of·R | 77 | o16·:·Ideal·of·R |
| 78 | For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster. | 78 | For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster. |
| 79 | i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v); | 79 | i17·:·R·=·ZZ/7[x,y,u,v]/ideal(x*y-u*v); |
| 80 | i18·:·I·=·ideal(x,u); | 80 | i18·:·I·=·ideal(x,u); |
| 81 | o18·:·Ideal·of·R | 81 | o18·:·Ideal·of·R |
| 82 | i19·:·J·=·I^15; | 82 | i19·:·J·=·I^15; |
| 83 | o19·:·Ideal·of·R | 83 | o19·:·Ideal·of·R |
| 84 | i20·:·time·dualize(J,·Strategy=>IdealStrategy); | 84 | i20·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 85 | ·--·used·0.1 | 85 | ·--·used·0.134665s·(cpu);·0.096899s·(thread);·0s·(gc) |
| 86 | o20·:·Ideal·of·R | 86 | o20·:·Ideal·of·R |
| 87 | i21·:·time·dualize(J,·Strategy=>ModuleStrategy); | 87 | i21·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 88 | ·--·used·0.0029 | 88 | ·--·used·0.0029858s·(cpu);·0.00544469s·(thread);·0s·(gc) |
| 89 | o21·:·Ideal·of·R | 89 | o21·:·Ideal·of·R |
| 90 | KnownDomain·is·an·option·for·dualize.·If·it·is·false·(default·is·true),·then | 90 | KnownDomain·is·an·option·for·dualize.·If·it·is·false·(default·is·true),·then |
| 91 | the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then | 91 | the·computer·will·first·check·whether·the·ring·is·a·domain,·if·it·is·not·then |
| 92 | it·will·revert·to·ModuleStrategy.·If·KnownDomain·is·set·to·true·for·a·non- | 92 | it·will·revert·to·ModuleStrategy.·If·KnownDomain·is·set·to·true·for·a·non- |
| 93 | domain,·then·the·function·can·return·an·incorrect·answer. | 93 | domain,·then·the·function·can·return·an·incorrect·answer. |
| 94 | i22·:·R·=·QQ[x,y]/ideal(x*y); | 94 | i22·:·R·=·QQ[x,y]/ideal(x*y); |
| Offset 73, 29 lines modified | Offset 73, 29 lines modified | ||
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre> | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) |
| 79 | o2·=· | 79 | o2·=·2*Div(y)·+·0*Div(x^2+z)·+·-8*Div(x) |
| 80 | o2·:·WeilDivisor·on·R</code></pre> | 80 | o2·:·WeilDivisor·on·R</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·getPrimeDivisors(·D·) | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·getPrimeDivisors(·D·) |
| 84 | o3·=·{Div( | 84 | o3·=·{Div(y),·Div(x^2+z),·Div(x)} |
| 85 | o3·:·List</code></pre> | 85 | o3·:·List</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·getPrimeDivisors(·cleanSupport·D·) | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·getPrimeDivisors(·cleanSupport·D·) |
| 89 | o4·=·{Div( | 89 | o4·=·{Div(y),·Div(x)} |
| 90 | o4·:·List</code></pre> | 90 | o4·:·List</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ········</table> | 92 | ········</table> |
| 93 | ······</div> | 93 | ······</div> |
| 94 | ······<div·class="waystouse"> | 94 | ······<div·class="waystouse"> |
| 95 | ········<h2>Ways·to·use·<span·class="tt">getPrimeDivisors</span>:</h2> | 95 | ········<h2>Ways·to·use·<span·class="tt">getPrimeDivisors</span>:</h2> |
| Offset 15, 24 lines modified | Offset 15, 24 lines modified | ||
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | This·function·returns·the·list·of·prime·divisors·of·a·given·divisor.·The·prime | 16 | This·function·returns·the·list·of·prime·divisors·of·a·given·divisor.·The·prime |
| 17 | divisors·are·all·of·the·class·WeilDivisor.·If·you·do·not·call·cleanSupport,·you | 17 | divisors·are·all·of·the·class·WeilDivisor.·If·you·do·not·call·cleanSupport,·you |
| 18 | may·obtain·divisors·with·zero·coefficients. | 18 | may·obtain·divisors·with·zero·coefficients. |
| 19 | i1·:·R·=·QQ[x,·y,·z]; | 19 | i1·:·R·=·QQ[x,·y,·z]; |
| 20 | i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) | 20 | i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) |
| 21 | o2·=· | 21 | o2·=·2*Div(y)·+·0*Div(x^2+z)·+·-8*Div(x) |
| 22 | o2·:·WeilDivisor·on·R | 22 | o2·:·WeilDivisor·on·R |
| 23 | i3·:·getPrimeDivisors(·D·) | 23 | i3·:·getPrimeDivisors(·D·) |
| 24 | o3·=·{Div( | 24 | o3·=·{Div(y),·Div(x^2+z),·Div(x)} |
| 25 | o3·:·List | 25 | o3·:·List |
| 26 | i4·:·getPrimeDivisors(·cleanSupport·D·) | 26 | i4·:·getPrimeDivisors(·cleanSupport·D·) |
| 27 | o4·=·{Div( | 27 | o4·=·{Div(y),·Div(x)} |
| 28 | o4·:·List | 28 | o4·:·List |
| 29 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8tP\x8Pr\x8ri\x8im\x8me\x8eD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8rs\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8tP\x8Pr\x8ri\x8im\x8me\x8eD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8rs\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 30 | ····*·getPrimeDivisors(BasicDivisor) | 30 | ····*·getPrimeDivisors(BasicDivisor) |
| 31 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 31 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 32 | The·object·_\x8g_\x8e_\x8t_\x8P_\x8r_\x8i_\x8m_\x8e_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 32 | The·object·_\x8g_\x8e_\x8t_\x8P_\x8r_\x8i_\x8m_\x8e_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 84, 22 lines modified | Offset 84, 22 lines modified | ||
| 84 | ········<table·class="examples"> | 84 | ········<table·class="examples"> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·);</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·);</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) | 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) |
| 90 | o2·=·Div( | 90 | o2·=·2*Div(y,·z)·+·Div(x,·z) |
| 91 | o2·:·WeilDivisor·on·R</code></pre> | 91 | o2·:·WeilDivisor·on·R</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 95 | o3·=· | 95 | o3·=·1/2*Div(y,·z)·+·3/4*Div(x,·z) |
| 96 | o3·:·QWeilDivisor·on·R</code></pre> | 96 | o3·:·QWeilDivisor·on·R</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·isQCartier(10,·D1) | 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·isQCartier(10,·D1) |
| 100 | o4·=·2</code></pre> | 100 | o4·=·2</code></pre> |
| Offset 145, 22 lines modified | Offset 145, 22 lines modified | ||
| 145 | ········<table·class="examples"> | 145 | ········<table·class="examples"> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i11·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·);</code></pre> | 147 | <td>··············<pre><code·class="language-macaulay2">i11·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·);</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i12·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) | 150 | <td>··············<pre><code·class="language-macaulay2">i12·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) |
| 151 | o12·=· | 151 | o12·=·Div(x,·z)·+·2*Div(y,·z) |
| 152 | o12·:·WeilDivisor·on·R</code></pre> | 152 | o12·:·WeilDivisor·on·R</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 156 | o13·=· | 156 | o13·=·3/4*Div(x,·z)·+·1/2*Div(y,·z) |
| 157 | o13·:·QWeilDivisor·on·R</code></pre> | 157 | o13·:·QWeilDivisor·on·R</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i14·:·isQCartier(10,·D1,·IsGraded·=>·true) | 160 | <td>··············<pre><code·class="language-macaulay2">i14·:·isQCartier(10,·D1,·IsGraded·=>·true) |
| 161 | o14·=·1</code></pre> | 161 | o14·=·1</code></pre> |
| Offset 22, 21 lines modified | Offset 22, 21 lines modified | ||
| 22 | Check·whether·$m$·times·a·Weil·or·Q-divisor·$D$·is·Cartier·for·each·$m$·from·1 | 22 | Check·whether·$m$·times·a·Weil·or·Q-divisor·$D$·is·Cartier·for·each·$m$·from·1 |
| 23 | to·a·fixed·positive·integer·n1·(if·the·divisor·is·a·QWeilDivisor,·it·can·search | 23 | to·a·fixed·positive·integer·n1·(if·the·divisor·is·a·QWeilDivisor,·it·can·search |
| 24 | slightly·higher·than·n1).·If·m·*·D1·is·Cartier,·it·returns·m.·If·it·fails·to | 24 | slightly·higher·than·n1).·If·m·*·D1·is·Cartier,·it·returns·m.·If·it·fails·to |
| 25 | find·an·m,·it·returns·0. | 25 | find·an·m,·it·returns·0. |
| 26 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); | 26 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); |
| 27 | i2·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) | 27 | i2·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) |
| 28 | o2·=·Div( | 28 | o2·=·2*Div(y,·z)·+·Div(x,·z) |
| 29 | o2·:·WeilDivisor·on·R | 29 | o2·:·WeilDivisor·on·R |
| 30 | i3·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=> | 30 | i3·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=> |
| 31 | QQ) | 31 | QQ) |
| 32 | o3·=· | 32 | o3·=·1/2*Div(y,·z)·+·3/4*Div(x,·z) |
| 33 | o3·:·QWeilDivisor·on·R | 33 | o3·:·QWeilDivisor·on·R |
| 34 | i4·:·isQCartier(10,·D1) | 34 | i4·:·isQCartier(10,·D1) |
| 35 | o4·=·2 | 35 | o4·=·2 |
| 36 | i5·:·isQCartier(10,·D2) | 36 | i5·:·isQCartier(10,·D2) |
| Offset 60, 21 lines modified | Offset 60, 21 lines modified | ||
| 60 | o10·=·0 | 60 | o10·=·0 |
| 61 | If·the·option·IsGraded·is·set·to·true·(by·default·it·is·false),·then·it·treats | 61 | If·the·option·IsGraded·is·set·to·true·(by·default·it·is·false),·then·it·treats |
| 62 | the·divisor·as·a·divisor·on·the·$Proj$·of·their·ambient·ring. | 62 | the·divisor·as·a·divisor·on·the·$Proj$·of·their·ambient·ring. |
| 63 | i11·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); | 63 | i11·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); |
| 64 | i12·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) | 64 | i12·:·D1·=·divisor({1,·2},·{ideal(x,·z),·ideal(y,·z)}) |
| 65 | o12·=· | 65 | o12·=·Div(x,·z)·+·2*Div(y,·z) |
| 66 | o12·:·WeilDivisor·on·R | 66 | o12·:·WeilDivisor·on·R |
| 67 | i13·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=> | 67 | i13·:·D2·=·divisor({1/2,·3/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=> |
| 68 | QQ) | 68 | QQ) |
| 69 | o13·=· | 69 | o13·=·3/4*Div(x,·z)·+·1/2*Div(y,·z) |
| 70 | o13·:·QWeilDivisor·on·R | 70 | o13·:·QWeilDivisor·on·R |
| 71 | i14·:·isQCartier(10,·D1,·IsGraded·=>·true) | 71 | i14·:·isQCartier(10,·D1,·IsGraded·=>·true) |
| 72 | o14·=·1 | 72 | o14·=·1 |
| 73 | i15·:·isQCartier(10,·D2,·IsGraded·=>·true) | 73 | i15·:·isQCartier(10,·D2,·IsGraded·=>·true) |
| Offset 83, 22 lines modified | Offset 83, 22 lines modified | ||
| 83 | ········<table·class="examples"> | 83 | ········<table·class="examples"> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre> | 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 89 | o2·=· | 89 | o2·=·3/4*Div(y,·z)·+·1/2*Div(x,·z) |
| 90 | o2·:·QWeilDivisor·on·R</code></pre> | 90 | o2·:·QWeilDivisor·on·R</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 94 | o3·=· | 94 | o3·=·3/4*Div(y,·z)·+·5/2*Div(x,·z) |
| 95 | o3·:·QWeilDivisor·on·R</code></pre> | 95 | o3·:·QWeilDivisor·on·R</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·isQLinearEquivalent(10,·D,·E) | 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·isQLinearEquivalent(10,·D,·E) |
| 99 | o4·=·true</code></pre> | 99 | o4·=·true</code></pre> |
| Offset 138, 22 lines modified | Offset 138, 22 lines modified | ||
| 138 | ········<table·class="examples"> | 138 | ········<table·class="examples"> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre> | 140 | <td>··············<pre><code·class="language-macaulay2">i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2);</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 143 | <td>··············<pre><code·class="language-macaulay2">i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 144 | o11·=· | 144 | o11·=·1/2*Div(x,·z)·+·3/4*Div(y,·z) |
| 145 | o11·:·QWeilDivisor·on·R</code></pre> | 145 | o11·:·QWeilDivisor·on·R</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 148 | <td>··············<pre><code·class="language-macaulay2">i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 149 | o12·=· | 149 | o12·=·-1/4*Div(x,·z)·+·3/2*Div(y,·z) |
| 150 | o12·:·QWeilDivisor·on·R</code></pre> | 150 | o12·:·QWeilDivisor·on·R</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| 152 | ··········<tr> | 152 | ··········<tr> |
| 153 | <td>··············<pre><code·class="language-macaulay2">i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true) | 153 | <td>··············<pre><code·class="language-macaulay2">i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true) |
| 154 | o13·=·true</code></pre> | 154 | o13·=·true</code></pre> |
| Offset 20, 20 lines modified | Offset 20, 20 lines modified | ||
| 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 21 | Given·two·rational·divisors,·this·method·returns·true·if·they·linearly | 21 | Given·two·rational·divisors,·this·method·returns·true·if·they·linearly |
| 22 | equivalent·after·clearing·denominators·or·if·some·further·multiple·up·to·n | 22 | equivalent·after·clearing·denominators·or·if·some·further·multiple·up·to·n |
| 23 | makes·them·linearly·equivalent.·Otherwise·it·returns·false. | 23 | makes·them·linearly·equivalent.·Otherwise·it·returns·false. |
| 24 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); | 24 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); |
| 25 | i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 25 | i2·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 26 | o2·=· | 26 | o2·=·3/4*Div(y,·z)·+·1/2*Div(x,·z) |
| 27 | o2·:·QWeilDivisor·on·R | 27 | o2·:·QWeilDivisor·on·R |
| 28 | i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) | 28 | i3·:·E·=·divisor({3/4,·5/2},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=>·QQ) |
| 29 | o3·=· | 29 | o3·=·3/4*Div(y,·z)·+·5/2*Div(x,·z) |
| 30 | o3·:·QWeilDivisor·on·R | 30 | o3·:·QWeilDivisor·on·R |
| 31 | i4·:·isQLinearEquivalent(10,·D,·E) | 31 | i4·:·isQLinearEquivalent(10,·D,·E) |
| 32 | o4·=·true | 32 | o4·=·true |
| 33 | In·the·above·ring,·every·pair·of·divisors·is·Q-linearly·equivalent·because·the | 33 | In·the·above·ring,·every·pair·of·divisors·is·Q-linearly·equivalent·because·the |
| 34 | Weil·divisor·class·group·is·isomorphic·to·Z/2.·However,·if·we·don't·set·n·high | 34 | Weil·divisor·class·group·is·isomorphic·to·Z/2.·However,·if·we·don't·set·n·high |
| Offset 53, 21 lines modified | Offset 53, 21 lines modified | ||
| 53 | o9·=·true | 53 | o9·=·true |
| 54 | If·IsGraded=>true·(the·default·is·false),·then·it·treats·the·divisors·as·if | 54 | If·IsGraded=>true·(the·default·is·false),·then·it·treats·the·divisors·as·if |
| 55 | they·are·divisors·on·the·$Proj$·of·their·ambient·ring. | 55 | they·are·divisors·on·the·$Proj$·of·their·ambient·ring. |
| 56 | i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); | 56 | i10·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2); |
| 57 | i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=> | 57 | i11·:·D·=·divisor({1/2,·3/4},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=> |
| 58 | QQ) | 58 | QQ) |
| 59 | o11·=· | 59 | o11·=·1/2*Div(x,·z)·+·3/4*Div(y,·z) |
| 60 | o11·:·QWeilDivisor·on·R | 60 | o11·:·QWeilDivisor·on·R |
| 61 | i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=> | 61 | i12·:·E·=·divisor({3/2,·-1/4},·{ideal(y,·z),·ideal(x,·z)},·CoefficientType·=> |
| 62 | QQ) | 62 | QQ) |
| 63 | o12·=· | 63 | o12·=·-1/4*Div(x,·z)·+·3/2*Div(y,·z) |
| 64 | o12·:·QWeilDivisor·on·R | 64 | o12·:·QWeilDivisor·on·R |
| 65 | i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true) | 65 | i13·:·isQLinearEquivalent(10,·D,·E,·IsGraded·=>·true) |
| 66 | o13·=·true | 66 | o13·=·true |
| 67 | i14·:·isQLinearEquivalent(10,·3*D,·E,·IsGraded·=>·true) | 67 | i14·:·isQLinearEquivalent(10,·3*D,·E,·IsGraded·=>·true) |
| Offset 229, 21 lines modified | Offset 229, 21 lines modified | ||
| 229 | ··········<tr> | 229 | ··········<tr> |
| 230 | <td>··············<pre><code·class="language-macaulay2">i22·:·J·=·I^21; | 230 | <td>··············<pre><code·class="language-macaulay2">i22·:·J·=·I^21; |
| 231 | o22·:·Ideal·of·R</code></pre> | 231 | o22·:·Ideal·of·R</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| 233 | ··········<tr> | 233 | ··········<tr> |
| 234 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·reflexify(J); | 234 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·reflexify(J); |
| 235 | ·--·used·0. | 235 | ·--·used·0.214073s·(cpu);·0.165499s·(thread);·0s·(gc) |
| 236 | o23·:·Ideal·of·R</code></pre> | 236 | o23·:·Ideal·of·R</code></pre> |
| 237 | </td>··········</tr> | 237 | </td>··········</tr> |
| 238 | ··········<tr> | 238 | ··········<tr> |
| 239 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·reflexify(J*R^1); | 239 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·reflexify(J*R^1); |
| 240 | ·--·used·0. | 240 | ·--·used·0.377369s·(cpu);·0.336166s·(thread);·0s·(gc)</code></pre> |
| 241 | </td>··········</tr> | 241 | </td>··········</tr> |
| 242 | ········</table> | 242 | ········</table> |
| 243 | ········<div> | 243 | ········<div> |
| 244 | ··········<p>Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at·least·if·the·module·embeds·as·an·ideal).</p> | 244 | ··········<p>Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at·least·if·the·module·embeds·as·an·ideal).</p> |
| 245 | ········</div> | 245 | ········</div> |
| 246 | ········<div> | 246 | ········<div> |
| 247 | ··········<p><span·class="tt">IdealStrategy</span>.··In·the·case·that·$R$·is·a·domain,·and·our·module·is·isomorphic·to·an·ideal·$I$,·then·one·can·compute·the·reflexification·by·computing·colons.</p> | 247 | ··········<p><span·class="tt">IdealStrategy</span>.··In·the·case·that·$R$·is·a·domain,·and·our·module·is·isomorphic·to·an·ideal·$I$,·then·one·can·compute·the·reflexification·by·computing·colons.</p> |
| Offset 269, 42 lines modified | Offset 269, 42 lines modified | ||
| 269 | o27·:·Ideal·of·R</code></pre> | 269 | o27·:·Ideal·of·R</code></pre> |
| 270 | </td>··········</tr> | 270 | </td>··········</tr> |
| 271 | ··········<tr> | 271 | ··········<tr> |
| 272 | <td>··············<pre><code·class="language-macaulay2">i28·:·M·=·J*R^1;</code></pre> | 272 | <td>··············<pre><code·class="language-macaulay2">i28·:·M·=·J*R^1;</code></pre> |
| 273 | </td>··········</tr> | 273 | </td>··········</tr> |
| 274 | ··········<tr> | 274 | ··········<tr> |
| 275 | <td>··············<pre><code·class="language-macaulay2">i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) | 275 | <td>··············<pre><code·class="language-macaulay2">i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 276 | ·--·used·0. | 276 | ·--·used·0.205755s·(cpu);·0.122281s·(thread);·0s·(gc) |
| 277 | ··············2············2·····9·······9···11 | 277 | ··············2············2·····9·······9···11 |
| 278 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 278 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 279 | o29·:·Ideal·of·R</code></pre> | 279 | o29·:·Ideal·of·R</code></pre> |
| 280 | </td>··········</tr> | 280 | </td>··········</tr> |
| 281 | ··········<tr> | 281 | ··········<tr> |
| 282 | <td>··············<pre><code·class="language-macaulay2">i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 282 | <td>··············<pre><code·class="language-macaulay2">i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 283 | ·--·used· | 283 | ·--·used·5.31101s·(cpu);·4.22567s·(thread);·0s·(gc) |
| 284 | ··············2············2·····9·······9···11 | 284 | ··············2············2·····9·······9···11 |
| 285 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 285 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 286 | o30·:·Ideal·of·R</code></pre> | 286 | o30·:·Ideal·of·R</code></pre> |
| 287 | </td>··········</tr> | 287 | </td>··········</tr> |
| 288 | ··········<tr> | 288 | ··········<tr> |
| 289 | <td>··············<pre><code·class="language-macaulay2">i31·:·J1·==·J2 | 289 | <td>··············<pre><code·class="language-macaulay2">i31·:·J1·==·J2 |
| 290 | o31·=·true</code></pre> | 290 | o31·=·true</code></pre> |
| 291 | </td>··········</tr> | 291 | </td>··········</tr> |
| 292 | ··········<tr> | 292 | ··········<tr> |
| 293 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 293 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 294 | ·--·used· | 294 | ·--·used·5.39384s·(cpu);·4.32502s·(thread);·0s·(gc)</code></pre> |
| 295 | </td>··········</tr> | 295 | </td>··········</tr> |
| 296 | ··········<tr> | 296 | ··········<tr> |
| 297 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 297 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 298 | ·--·used·0. | 298 | ·--·used·0.586407s·(cpu);·0.44375s·(thread);·0s·(gc)</code></pre> |
| 299 | </td>··········</tr> | 299 | </td>··········</tr> |
| 300 | ········</table> | 300 | ········</table> |
| 301 | ········<div> | 301 | ········<div> |
| 302 | ··········<p>However,·sometimes·<span·class="tt">ModuleStrategy</span>·is·faster,·especially·for·Monomial·ideals.</p> | 302 | ··········<p>However,·sometimes·<span·class="tt">ModuleStrategy</span>·is·faster,·especially·for·Monomial·ideals.</p> |
| 303 | ········</div> | 303 | ········</div> |
| 304 | ········<table·class="examples"> | 304 | ········<table·class="examples"> |
| 305 | ··········<tr> | 305 | ··········<tr> |
| Offset 321, 49 lines modified | Offset 321, 49 lines modified | ||
| 321 | o36·:·Ideal·of·R</code></pre> | 321 | o36·:·Ideal·of·R</code></pre> |
| 322 | </td>··········</tr> | 322 | </td>··········</tr> |
| 323 | ··········<tr> | 323 | ··········<tr> |
| 324 | <td>··············<pre><code·class="language-macaulay2">i37·:·M·=·I^20*R^1;</code></pre> | 324 | <td>··············<pre><code·class="language-macaulay2">i37·:·M·=·I^20*R^1;</code></pre> |
| 325 | </td>··········</tr> | 325 | </td>··········</tr> |
| 326 | ··········<tr> | 326 | ··········<tr> |
| 327 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) | 327 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 328 | ·--·used·0. | 328 | ·--·used·0.853554s·(cpu);·0.318374s·(thread);·0s·(gc) |
| 329 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· | 329 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· |
| 330 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 330 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 331 | ······----------------------------------------------------------------------- | 331 | ······----------------------------------------------------------------------- |
| 332 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· | 332 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· |
| 333 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 333 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 334 | ······----------------------------------------------------------------------- | 334 | ······----------------------------------------------------------------------- |
| 335 | ·······19····20 | 335 | ·······19····20 |
| 336 | ······x··u,·x··) | 336 | ······x··u,·x··) |
| 337 | o38·:·Ideal·of·R</code></pre> | 337 | o38·:·Ideal·of·R</code></pre> |
| 338 | </td>··········</tr> | 338 | </td>··········</tr> |
| 339 | ··········<tr> | 339 | ··········<tr> |
| 340 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 340 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 341 | ·--·used·0.012 | 341 | ·--·used·0.0129902s·(cpu);·0.0138033s·(thread);·0s·(gc) |
| 342 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· | 342 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· |
| 343 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 343 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 344 | ······----------------------------------------------------------------------- | 344 | ······----------------------------------------------------------------------- |
| 345 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· | 345 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· |
| 346 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 346 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 347 | ······----------------------------------------------------------------------- | 347 | ······----------------------------------------------------------------------- |
| 348 | ·······19····20 | 348 | ·······19····20 |
| 349 | ······x··u,·x··) | 349 | ······x··u,·x··) |
| 350 | o39·:·Ideal·of·R</code></pre> | 350 | o39·:·Ideal·of·R</code></pre> |
| 351 | </td>··········</tr> | 351 | </td>··········</tr> |
| 352 | ··········<tr> | 352 | ··········<tr> |
| 353 | <td>··············<pre><code·class="language-macaulay2">i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 353 | <td>··············<pre><code·class="language-macaulay2">i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 354 | ·--·used·0. | 354 | ·--·used·0.203497s·(cpu);·0.0676861s·(thread);·0s·(gc)</code></pre> |
| 355 | </td>··········</tr> | 355 | </td>··········</tr> |
| 356 | ··········<tr> | 356 | ··········<tr> |
| 357 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 357 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 358 | ·--·used·0.00 | 358 | ·--·used·0.0037396s·(cpu);·0.00578348s·(thread);·0s·(gc)</code></pre> |
| 359 | </td>··········</tr> | 359 | </td>··········</tr> |
| 360 | ········</table> | 360 | ········</table> |
| 361 | ········<div> | 361 | ········<div> |
| 362 | ··········<p>For·ideals,·if·<span·class="tt">KnownDomain</span>·is·false·(default·value·is·<span·class="tt">true</span>),·then·the·function·will·check·whether·it·is·a·domain.··If·it·is·a·domain·(or·assumed·to·be·a·domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if·not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially·reflexifying·it·as·a·module.</p> | 362 | ··········<p>For·ideals,·if·<span·class="tt">KnownDomain</span>·is·false·(default·value·is·<span·class="tt">true</span>),·then·the·function·will·check·whether·it·is·a·domain.··If·it·is·a·domain·(or·assumed·to·be·a·domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if·not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially·reflexifying·it·as·a·module.</p> |
| 363 | ········</div> | 363 | ········</div> |
| 364 | ········<div> | 364 | ········<div> |
| 365 | ··········<p>Consider·the·following·example·showing·the·importance·of·making·the·correct·assumption·about·the·ring·being·a·domain.</p> | 365 | ··········<p>Consider·the·following·example·showing·the·importance·of·making·the·correct·assumption·about·the·ring·being·a·domain.</p> |
| Offset 115, 19 lines modified | Offset 115, 19 lines modified | ||
| 115 | i21·:·I·=·ideal(x-z,y-2*z); | 115 | i21·:·I·=·ideal(x-z,y-2*z); |
| 116 | o21·:·Ideal·of·R | 116 | o21·:·Ideal·of·R |
| 117 | i22·:·J·=·I^21; | 117 | i22·:·J·=·I^21; |
| 118 | o22·:·Ideal·of·R | 118 | o22·:·Ideal·of·R |
| 119 | i23·:·time·reflexify(J); | 119 | i23·:·time·reflexify(J); |
| 120 | ·--·used·0. | 120 | ·--·used·0.214073s·(cpu);·0.165499s·(thread);·0s·(gc) |
| 121 | o23·:·Ideal·of·R | 121 | o23·:·Ideal·of·R |
| 122 | i24·:·time·reflexify(J*R^1); | 122 | i24·:·time·reflexify(J*R^1); |
| 123 | ·--·used·0. | 123 | ·--·used·0.377369s·(cpu);·0.336166s·(thread);·0s·(gc) |
| 124 | Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at | 124 | Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at |
| 125 | least·if·the·module·embeds·as·an·ideal). | 125 | least·if·the·module·embeds·as·an·ideal). |
| 126 | IdealStrategy.·In·the·case·that·$R$·is·a·domain,·and·our·module·is·isomorphic | 126 | IdealStrategy.·In·the·case·that·$R$·is·a·domain,·and·our·module·is·isomorphic |
| 127 | to·an·ideal·$I$,·then·one·can·compute·the·reflexification·by·computing·colons. | 127 | to·an·ideal·$I$,·then·one·can·compute·the·reflexification·by·computing·colons. |
| 128 | ModuleStrategy.·This·computes·the·reflexification·simply·by·computing·$Hom$ | 128 | ModuleStrategy.·This·computes·the·reflexification·simply·by·computing·$Hom$ |
| 129 | twice. | 129 | twice. |
| 130 | ModuleStrategy·is·the·default·strategy·for·modules,·IdealStrategy·is·the | 130 | ModuleStrategy·is·the·default·strategy·for·modules,·IdealStrategy·is·the |
| Offset 140, 73 lines modified | Offset 140, 73 lines modified | ||
| 140 | o26·:·Ideal·of·R | 140 | o26·:·Ideal·of·R |
| 141 | i27·:·J·=·I^20; | 141 | i27·:·J·=·I^20; |
| 142 | o27·:·Ideal·of·R | 142 | o27·:·Ideal·of·R |
| 143 | i28·:·M·=·J*R^1; | 143 | i28·:·M·=·J*R^1; |
| 144 | i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) | 144 | i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 145 | ·--·used·0. | 145 | ·--·used·0.205755s·(cpu);·0.122281s·(thread);·0s·(gc) |
| 146 | ··············2············2·····9·······9···11 | 146 | ··············2············2·····9·······9···11 |
| 147 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 147 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 148 | o29·:·Ideal·of·R | 148 | o29·:·Ideal·of·R |
| 149 | i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 149 | i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 150 | ·--·used· | 150 | ·--·used·5.31101s·(cpu);·4.22567s·(thread);·0s·(gc) |
| 151 | ··············2············2·····9·······9···11 | 151 | ··············2············2·····9·······9···11 |
| 152 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 152 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 153 | o30·:·Ideal·of·R | 153 | o30·:·Ideal·of·R |
| 154 | i31·:·J1·==·J2 | 154 | i31·:·J1·==·J2 |
| 155 | o31·=·true | 155 | o31·=·true |
| 156 | i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 156 | i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 157 | ·--·used· | 157 | ·--·used·5.39384s·(cpu);·4.32502s·(thread);·0s·(gc) |
| 158 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 158 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 159 | ·--·used·0. | 159 | ·--·used·0.586407s·(cpu);·0.44375s·(thread);·0s·(gc) |
| 160 | However,·sometimes·ModuleStrategy·is·faster,·especially·for·Monomial·ideals. | 160 | However,·sometimes·ModuleStrategy·is·faster,·especially·for·Monomial·ideals. |
| 161 | i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v); | 161 | i34·:·R·=·QQ[x,y,u,v]/ideal(x*y-u*v); |
| 162 | i35·:·I·=·ideal(x,u); | 162 | i35·:·I·=·ideal(x,u); |
| 163 | o35·:·Ideal·of·R | 163 | o35·:·Ideal·of·R |
| 164 | i36·:·J·=·I^20; | 164 | i36·:·J·=·I^20; |
| 165 | o36·:·Ideal·of·R | 165 | o36·:·Ideal·of·R |
| 166 | i37·:·M·=·I^20*R^1; | 166 | i37·:·M·=·I^20*R^1; |
| 167 | i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) | 167 | i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 168 | ·--·used·0. | 168 | ·--·used·0.853554s·(cpu);·0.318374s·(thread);·0s·(gc) |
| 169 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12 | 169 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12 |
| 170 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 170 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 171 | ······----------------------------------------------------------------------- | 171 | ······----------------------------------------------------------------------- |
| 172 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2 | 172 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2 |
| 173 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 173 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 174 | ······----------------------------------------------------------------------- | 174 | ······----------------------------------------------------------------------- |
| 175 | ·······19····20 | 175 | ·······19····20 |
| 176 | ······x··u,·x··) | 176 | ······x··u,·x··) |
| 177 | o38·:·Ideal·of·R | 177 | o38·:·Ideal·of·R |
| 178 | i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 178 | i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 179 | ·--·used·0.012 | 179 | ·--·used·0.0129902s·(cpu);·0.0138033s·(thread);·0s·(gc) |
| 180 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12 | 180 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12 |
| 181 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 181 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 182 | ······----------------------------------------------------------------------- | 182 | ······----------------------------------------------------------------------- |
| 183 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2 | 183 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2 |
| 184 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 184 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 185 | ······----------------------------------------------------------------------- | 185 | ······----------------------------------------------------------------------- |
| 186 | ·······19····20 | 186 | ·······19····20 |
| 187 | ······x··u,·x··) | 187 | ······x··u,·x··) |
| 188 | o39·:·Ideal·of·R | 188 | o39·:·Ideal·of·R |
| 189 | i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 189 | i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 190 | ·--·used·0. | 190 | ·--·used·0.203497s·(cpu);·0.0676861s·(thread);·0s·(gc) |
| 191 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 191 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 192 | ·--·used·0.00 | 192 | ·--·used·0.0037396s·(cpu);·0.00578348s·(thread);·0s·(gc) |
| 193 | For·ideals,·if·KnownDomain·is·false·(default·value·is·true),·then·the·function | 193 | For·ideals,·if·KnownDomain·is·false·(default·value·is·true),·then·the·function |
| 194 | will·check·whether·it·is·a·domain.·If·it·is·a·domain·(or·assumed·to·be·a | 194 | will·check·whether·it·is·a·domain.·If·it·is·a·domain·(or·assumed·to·be·a |
| 195 | domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if | 195 | domain),·it·will·reflexify·using·a·strategy·which·can·speed·up·computation,·if |
| 196 | not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially | 196 | not·it·will·compute·using·a·sometimes·slower·method·which·is·essentially |
| 197 | reflexifying·it·as·a·module. | 197 | reflexifying·it·as·a·module. |
| 198 | Consider·the·following·example·showing·the·importance·of·making·the·correct | 198 | Consider·the·following·example·showing·the·importance·of·making·the·correct |
| 199 | assumption·about·the·ring·being·a·domain. | 199 | assumption·about·the·ring·being·a·domain. |
| Offset 114, 26 lines modified | Offset 114, 26 lines modified | ||
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal(x-z,y-2*z); | 115 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal(x-z,y-2*z); |
| 116 | o6·:·Ideal·of·R</code></pre> | 116 | o6·:·Ideal·of·R</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·J20a·=·reflexivePower(20,·I); | 119 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·J20a·=·reflexivePower(20,·I); |
| 120 | ·--·used·0.0 | 120 | ·--·used·0.08295s·(cpu);·0.0393105s·(thread);·0s·(gc) |
| 121 | o7·:·Ideal·of·R</code></pre> | 121 | o7·:·Ideal·of·R</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i8·:·I20·=·I^20; | 124 | <td>··············<pre><code·class="language-macaulay2">i8·:·I20·=·I^20; |
| 125 | o8·:·Ideal·of·R</code></pre> | 125 | o8·:·Ideal·of·R</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J20b·=·reflexify(I20); | 128 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J20b·=·reflexify(I20); |
| 129 | ·--·used·0. | 129 | ·--·used·0.126397s·(cpu);·0.127436s·(thread);·0s·(gc) |
| 130 | o9·:·Ideal·of·R</code></pre> | 130 | o9·:·Ideal·of·R</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·J20a·==·J20b | 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·J20a·==·J20b |
| 134 | o10·=·true</code></pre> | 134 | o10·=·true</code></pre> |
| Offset 149, 21 lines modified | Offset 149, 21 lines modified | ||
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal(x-z,y-2*z); | 150 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal(x-z,y-2*z); |
| 151 | o12·:·Ideal·of·R</code></pre> | 151 | o12·:·Ideal·of·R</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); | 154 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); |
| 155 | ·--·used·0.0 | 155 | ·--·used·0.0332655s·(cpu);·0.0338725s·(thread);·0s·(gc) |
| 156 | o13·:·Ideal·of·R</code></pre> | 156 | o13·:·Ideal·of·R</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); | 159 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); |
| 160 | ·--·used·0. | 160 | ·--·used·0.137002s·(cpu);·0.0911039s·(thread);·0s·(gc) |
| 161 | o14·:·Ideal·of·R</code></pre> | 161 | o14·:·Ideal·of·R</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i15·:·J1·==·J2 | 164 | <td>··············<pre><code·class="language-macaulay2">i15·:·J1·==·J2 |
| 165 | o15·=·true</code></pre> | 165 | o15·=·true</code></pre> |
| Offset 41, 39 lines modified | Offset 41, 39 lines modified | ||
| 41 | of·the·generators·of·$I$.·Consider·the·example·of·a·cone·over·a·point·on·an | 41 | of·the·generators·of·$I$.·Consider·the·example·of·a·cone·over·a·point·on·an |
| 42 | elliptic·curve. | 42 | elliptic·curve. |
| 43 | i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); | 43 | i5·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); |
| 44 | i6·:·I·=·ideal(x-z,y-2*z); | 44 | i6·:·I·=·ideal(x-z,y-2*z); |
| 45 | o6·:·Ideal·of·R | 45 | o6·:·Ideal·of·R |
| 46 | i7·:·time·J20a·=·reflexivePower(20,·I); | 46 | i7·:·time·J20a·=·reflexivePower(20,·I); |
| 47 | ·--·used·0.0 | 47 | ·--·used·0.08295s·(cpu);·0.0393105s·(thread);·0s·(gc) |
| 48 | o7·:·Ideal·of·R | 48 | o7·:·Ideal·of·R |
| 49 | i8·:·I20·=·I^20; | 49 | i8·:·I20·=·I^20; |
| 50 | o8·:·Ideal·of·R | 50 | o8·:·Ideal·of·R |
| 51 | i9·:·time·J20b·=·reflexify(I20); | 51 | i9·:·time·J20b·=·reflexify(I20); |
| 52 | ·--·used·0. | 52 | ·--·used·0.126397s·(cpu);·0.127436s·(thread);·0s·(gc) |
| 53 | o9·:·Ideal·of·R | 53 | o9·:·Ideal·of·R |
| 54 | i10·:·J20a·==·J20b | 54 | i10·:·J20a·==·J20b |
| 55 | o10·=·true | 55 | o10·=·true |
| 56 | This·passes·the·Strategy·option·to·a·reflexify·call.·Valid·options·are | 56 | This·passes·the·Strategy·option·to·a·reflexify·call.·Valid·options·are |
| 57 | IdealStrategy·and·ModuleStrategy. | 57 | IdealStrategy·and·ModuleStrategy. |
| 58 | i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); | 58 | i11·:·R·=·QQ[x,y,z]/ideal(-y^2*z·+x^3·+·x^2*z·+·x*z^2+z^3); |
| 59 | i12·:·I·=·ideal(x-z,y-2*z); | 59 | i12·:·I·=·ideal(x-z,y-2*z); |
| 60 | o12·:·Ideal·of·R | 60 | o12·:·Ideal·of·R |
| 61 | i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); | 61 | i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); |
| 62 | ·--·used·0.0 | 62 | ·--·used·0.0332655s·(cpu);·0.0338725s·(thread);·0s·(gc) |
| 63 | o13·:·Ideal·of·R | 63 | o13·:·Ideal·of·R |
| 64 | i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); | 64 | i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); |
| 65 | ·--·used·0. | 65 | ·--·used·0.137002s·(cpu);·0.0911039s·(thread);·0s·(gc) |
| 66 | o14·:·Ideal·of·R | 66 | o14·:·Ideal·of·R |
| 67 | i15·:·J1·==·J2 | 67 | i15·:·J1·==·J2 |
| 68 | o15·=·true | 68 | o15·=·true |
| 69 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 69 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 70 | ····*·_\x8r_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8f_\x8y·--·calculate·the·double·dual·of·an·ideal·or·module·Hom(Hom(M, | 70 | ····*·_\x8r_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8f_\x8y·--·calculate·the·double·dual·of·an·ideal·or·module·Hom(Hom(M, |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | RG1vZHVsZXM= | 8 | RG1vZHVsZXM= |
| 9 | #:len=758 | 9 | #:len=758 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRC1tb2R1bGVzIHBhY2thZ2UgY29sbGVj | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRC1tb2R1bGVzIHBhY2thZ2UgY29sbGVj |
| 11 | dGlvbiIsICJsaW5lbnVtIiA9PiAxNDIsICJmaWxlbmFtZSIgPT4gIkRtb2R1bGVzLm0yIiwgRGVz | 11 | dGlvbiIsICJsaW5lbnVtIiA9PiAxNDIsICJmaWxlbmFtZSIgPT4gIkRtb2R1bGVzLm0yIiwgRGVz |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=9 | 7 | #:len=9 |
| 8 | VHJhbnNwb3Nl | 8 | VHJhbnNwb3Nl |
| 9 | #:len=1366 | 9 | #:len=1366 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVHJhbnNwb3NlID0+IGZhbHNlLCBkZWZh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVHJhbnNwb3NlID0+IGZhbHNlLCBkZWZh |
| 11 | dWx0IG9wdGlvbiBmb3IgcGljdHVyZSIsICJsaW5lbnVtIiA9PiAxMzUwLCBJbnB1dHMgPT4ge1NQ | 11 | dWx0IG9wdGlvbiBmb3IgcGljdHVyZSIsICJsaW5lbnVtIiA9PiAxMzUwLCBJbnB1dHMgPT4ge1NQ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=15 | 7 | #:len=15 |
| 8 | Y29tcGxlbWVudEdyYXBo | 8 | Y29tcGxlbWVudEdyYXBo |
| 9 | #:len=2011 | 9 | #:len=2011 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgY29tcGxlbWVudCBv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgY29tcGxlbWVudCBv |
| 11 | ZiBhIGdyYXBoIG9yIGh5cGVyZ3JhcGgiLCAibGluZW51bSIgPT4gMjA4MCwgSW5wdXRzID0+IHtT | 11 | ZiBhIGdyYXBoIG9yIGh5cGVyZ3JhcGgiLCAibGluZW51bSIgPT4gMjA4MCwgSW5wdXRzID0+IHtT |
| Offset 2, 15 lines modified | Offset 2, 15 lines modified | ||
| 2 | i1·:·R·=·QQ[a,b,c,d,e]; | 2 | i1·:·R·=·QQ[a,b,c,d,e]; |
| 3 | i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle | 3 | i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle |
| 4 | i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle | 4 | i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle |
| 5 | o3·=·Graph{"edges"·=>·{{a,· | 5 | o3·=·Graph{"edges"·=>·{{a,·d},·{a,·c},·{b,·e},·{b,·d},·{c,·e}}} |
| 6 | ···········"ring"·=>·R | 6 | ···········"ring"·=>·R |
| 7 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 7 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 8 | o3·:·Graph | 8 | o3·:·Graph |
| 9 | i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph | 9 | i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph |
| Offset 14, 15 lines modified | Offset 14, 15 lines modified | ||
| 14 | o3·=·{{a,·b},·{d,·e}} | 14 | o3·=·{{a,·b},·{d,·e}} |
| 15 | o3·:·List | 15 | o3·:·List |
| 16 | i4·:·gprime·=·deleteEdges·(g,T) | 16 | i4·:·gprime·=·deleteEdges·(g,T) |
| 17 | o4·=·HyperGraph{"edges"·=>·{{ | 17 | o4·=·HyperGraph{"edges"·=>·{{c,·d},·{b,·c},·{a,·e}}} |
| 18 | ················"ring"·=>·S | 18 | ················"ring"·=>·S |
| 19 | ················"vertices"·=>·{a,·b,·c,·d,·e} | 19 | ················"vertices"·=>·{a,·b,·c,·d,·e} |
| 20 | o4·:·HyperGraph | 20 | o4·:·HyperGraph |
| 21 | i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} | 21 | i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} |
| Offset 3, 27 lines modified | Offset 3, 19 lines modified | ||
| 3 | i1·:·R·=·QQ[x_1..x_5]; | 3 | i1·:·R·=·QQ[x_1..x_5]; |
| 4 | i2·:·randomHyperGraph(R,{3,2,4}) | 4 | i2·:·randomHyperGraph(R,{3,2,4}) |
| 5 | i3·:·randomHyperGraph(R,{3,2,4}) | 5 | i3·:·randomHyperGraph(R,{3,2,4}) |
| 6 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | 6 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} |
| 7 | ······························ | 7 | ······························1···3···5·····4···5·····1···2···3···4 |
| 8 | ················"ring"·=>·R | 8 | ················"ring"·=>·R |
| 9 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | 9 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} |
| 10 | ································1···2···3···4···5 | 10 | ································1···2···3···4···5 |
| 11 | o3·:·HyperGraph | 11 | o3·:·HyperGraph |
| 12 | i4·:·randomHyperGraph(R,{3,2,4}) | 12 | i4·:·randomHyperGraph(R,{3,2,4}) |
| 13 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | ||
| 14 | ······························1···3···4·····1···2·····2···3···4···5 | ||
| 15 | ················"ring"·=>·R | ||
| 16 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | ||
| 17 | ································1···2···3···4···5 | ||
| 18 | o4·:·HyperGraph | ||
| 19 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached | 13 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached |
| 20 | i6·:· | 14 | i6·:· |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle</code></pre> | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle | 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle |
| 87 | o3·=·Graph{"edges"·=>·{{a,· | 87 | o3·=·Graph{"edges"·=>·{{a,·d},·{a,·c},·{b,·e},·{b,·d},·{c,·e}}} |
| 88 | ···········"ring"·=>·R | 88 | ···········"ring"·=>·R |
| 89 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 89 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 90 | o3·:·Graph</code></pre> | 90 | o3·:·Graph</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph |
| Offset 23, 15 lines modified | Offset 23, 15 lines modified | ||
| 23 | When·applied·to·a·graph,·complementGraph·returns·the·graph·whose·edge·set·is | 23 | When·applied·to·a·graph,·complementGraph·returns·the·graph·whose·edge·set·is |
| 24 | the·set·of·edges·not·in·G.·When·applied·to·a·hypergraph,·the·edge·set·is·found | 24 | the·set·of·edges·not·in·G.·When·applied·to·a·hypergraph,·the·edge·set·is·found |
| 25 | by·taking·the·complement·of·each·edge·of·H·in·the·vertex·set. | 25 | by·taking·the·complement·of·each·edge·of·H·in·the·vertex·set. |
| 26 | i1·:·R·=·QQ[a,b,c,d,e]; | 26 | i1·:·R·=·QQ[a,b,c,d,e]; |
| 27 | i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle | 27 | i2·:·c5·=·graph·{a*b,b*c,c*d,d*e,e*a};·--·graph·of·the·5-cycle |
| 28 | i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle | 28 | i3·:·complementGraph·c5·--·the·graph·complement·of·the·5-cycle |
| 29 | o3·=·Graph{"edges"·=>·{{a,· | 29 | o3·=·Graph{"edges"·=>·{{a,·d},·{a,·c},·{b,·e},·{b,·d},·{c,·e}}} |
| 30 | ···········"ring"·=>·R | 30 | ···········"ring"·=>·R |
| 31 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 31 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 32 | o3·:·Graph | 32 | o3·:·Graph |
| 33 | i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph | 33 | i4·:·c5hypergraph·=·hyperGraph·c5·--·the·5-cycle,·but·viewed·as·a·hypergraph |
| 34 | o4·=·HyperGraph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}} | 34 | o4·=·HyperGraph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}} |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | o3·=·{{a,·b},·{d,·e}} | 91 | o3·=·{{a,·b},·{d,·e}} |
| 92 | o3·:·List</code></pre> | 92 | o3·:·List</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·gprime·=·deleteEdges·(g,T) | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·gprime·=·deleteEdges·(g,T) |
| 96 | o4·=·HyperGraph{"edges"·=>·{{ | 96 | o4·=·HyperGraph{"edges"·=>·{{c,·d},·{b,·c},·{a,·e}}} |
| 97 | ················"ring"·=>·S | 97 | ················"ring"·=>·S |
| 98 | ················"vertices"·=>·{a,·b,·c,·d,·e} | 98 | ················"vertices"·=>·{a,·b,·c,·d,·e} |
| 99 | o4·:·HyperGraph</code></pre> | 99 | o4·:·HyperGraph</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} | 102 | <td>··············<pre><code·class="language-macaulay2">i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | i3·:·T·=·{{a,b},{d,e}} | 27 | i3·:·T·=·{{a,b},{d,e}} |
| 28 | o3·=·{{a,·b},·{d,·e}} | 28 | o3·=·{{a,·b},·{d,·e}} |
| 29 | o3·:·List | 29 | o3·:·List |
| 30 | i4·:·gprime·=·deleteEdges·(g,T) | 30 | i4·:·gprime·=·deleteEdges·(g,T) |
| 31 | o4·=·HyperGraph{"edges"·=>·{{ | 31 | o4·=·HyperGraph{"edges"·=>·{{c,·d},·{b,·c},·{a,·e}}} |
| 32 | ················"ring"·=>·S | 32 | ················"ring"·=>·S |
| 33 | ················"vertices"·=>·{a,·b,·c,·d,·e} | 33 | ················"vertices"·=>·{a,·b,·c,·d,·e} |
| 34 | o4·:·HyperGraph | 34 | o4·:·HyperGraph |
| 35 | i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} | 35 | i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} |
| 36 | o5·=·HyperGraph{"edges"·=>·{{a,·b,·c},·{a,·e},·{c,·d,·e}}} | 36 | o5·=·HyperGraph{"edges"·=>·{{a,·b,·c},·{a,·e},·{c,·d,·e}}} |
| Offset 87, 31 lines modified | Offset 87, 23 lines modified | ||
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·randomHyperGraph(R,{3,2,4})</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·randomHyperGraph(R,{3,2,4})</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·randomHyperGraph(R,{3,2,4}) | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·randomHyperGraph(R,{3,2,4}) |
| 92 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | 92 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} |
| 93 | ······························ | 93 | ······························1···3···5·····4···5·····1···2···3···4 |
| 94 | ················"ring"·=>·R | 94 | ················"ring"·=>·R |
| 95 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | 95 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} |
| 96 | ································1···2···3···4···5 | 96 | ································1···2···3···4···5 |
| 97 | o3·:·HyperGraph</code></pre> | 97 | o3·:·HyperGraph</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomHyperGraph(R,{3,2,4}) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomHyperGraph(R,{3,2,4})</code></pre> |
| 101 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | ||
| 102 | ······························1···3···4·····1···2·····2···3···4···5 | ||
| 103 | ················"ring"·=>·R | ||
| 104 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | ||
| 105 | ································1···2···3···4···5 | ||
| 106 | o4·:·HyperGraph</code></pre> | ||
| 107 | </td>··········</tr> | 101 | </td>··········</tr> |
| 108 | ··········<tr> | 102 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached</code></pre> | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached</code></pre> |
| 110 | </td>··········</tr> | 104 | </td>··········</tr> |
| 111 | ········</table> | 105 | ········</table> |
| 112 | ········<div> | 106 | ········<div> |
| 113 | ··········<p>The·<span·class="tt">randomHyperGraph</span>·method·will·return·null·immediately·if·the·sizes·of·the·edges·fail·to·pass·the·LYM-inequality:·$1/(n·choose·D_1)·+·1/(n·choose·D_2)·+·...·+·1/(n·choose·D_m)·\leq·1$·where·$n$·is·the·number·of·variables·in·<span·class="tt">R</span>·and·$m$·is·the·length·of·<span·class="tt">D</span>.·Note·that·even·if·<span·class="tt">D</span>·passes·this·inequality,·it·is·not·necessarily·true·that·there·is·some·hypergraph·with·edge·sizes·given·by·<span·class="tt">D</span>.·See·D.·Lubell's·"A·short·proof·of·Sperner's·lemma,"·J.·Combin.·Theory,·1:299·(1966).</p> | 107 | ··········<p>The·<span·class="tt">randomHyperGraph</span>·method·will·return·null·immediately·if·the·sizes·of·the·edges·fail·to·pass·the·LYM-inequality:·$1/(n·choose·D_1)·+·1/(n·choose·D_2)·+·...·+·1/(n·choose·D_m)·\leq·1$·where·$n$·is·the·number·of·variables·in·<span·class="tt">R</span>·and·$m$·is·the·length·of·<span·class="tt">D</span>.·Note·that·even·if·<span·class="tt">D</span>·passes·this·inequality,·it·is·not·necessarily·true·that·there·is·some·hypergraph·with·edge·sizes·given·by·<span·class="tt">D</span>.·See·D.·Lubell's·"A·short·proof·of·Sperner's·lemma,"·J.·Combin.·Theory,·1:299·(1966).</p> |
| Offset 26, 29 lines modified | Offset 26, 21 lines modified | ||
| 26 | _\x8T_\x8i_\x8m_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t).·The·method·will·return·null·if·it·cannot·find·a·hypergraph·within | 26 | _\x8T_\x8i_\x8m_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t).·The·method·will·return·null·if·it·cannot·find·a·hypergraph·within |
| 27 | the·branch·and·time·limits. | 27 | the·branch·and·time·limits. |
| 28 | i1·:·R·=·QQ[x_1..x_5]; | 28 | i1·:·R·=·QQ[x_1..x_5]; |
| 29 | i2·:·randomHyperGraph(R,{3,2,4}) | 29 | i2·:·randomHyperGraph(R,{3,2,4}) |
| 30 | i3·:·randomHyperGraph(R,{3,2,4}) | 30 | i3·:·randomHyperGraph(R,{3,2,4}) |
| 31 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | 31 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} |
| 32 | ······························ | 32 | ······························1···3···5·····4···5·····1···2···3···4 |
| 33 | ················"ring"·=>·R | 33 | ················"ring"·=>·R |
| 34 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | 34 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} |
| 35 | ································1···2···3···4···5 | 35 | ································1···2···3···4···5 |
| 36 | o3·:·HyperGraph | 36 | o3·:·HyperGraph |
| 37 | i4·:·randomHyperGraph(R,{3,2,4}) | 37 | i4·:·randomHyperGraph(R,{3,2,4}) |
| 38 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | ||
| 39 | ······························1···3···4·····1···2·····2···3···4···5 | ||
| 40 | ················"ring"·=>·R | ||
| 41 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | ||
| 42 | ································1···2···3···4···5 | ||
| 43 | o4·:·HyperGraph | ||
| 44 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch | 38 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch |
| 45 | limit·reached | 39 | limit·reached |
| 46 | The·randomHyperGraph·method·will·return·null·immediately·if·the·sizes·of·the | 40 | The·randomHyperGraph·method·will·return·null·immediately·if·the·sizes·of·the |
| 47 | edges·fail·to·pass·the·LYM-inequality:·$1/(n·choose·D_1)·+·1/(n·choose·D_2)·+ | 41 | edges·fail·to·pass·the·LYM-inequality:·$1/(n·choose·D_1)·+·1/(n·choose·D_2)·+ |
| 48 | ...·+·1/(n·choose·D_m)·\leq·1$·where·$n$·is·the·number·of·variables·in·R·and | 42 | ...·+·1/(n·choose·D_m)·\leq·1$·where·$n$·is·the·number·of·variables·in·R·and |
| 49 | $m$·is·the·length·of·D.·Note·that·even·if·D·passes·this·inequality,·it·is·not | 43 | $m$·is·the·length·of·D.·Note·that·even·if·D·passes·this·inequality,·it·is·not |
| 50 | necessarily·true·that·there·is·some·hypergraph·with·edge·sizes·given·by·D.·See | 44 | necessarily·true·that·there·is·some·hypergraph·with·edge·sizes·given·by·D.·See |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=19 | 7 | #:len=19 |
| 8 | emVyb0RpbVNvbHZlKElkZWFsKQ== | 8 | emVyb0RpbVNvbHZlKElkZWFsKQ== |
| 9 | #:len=254 | 9 | #:len=254 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc3LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc3LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh6ZXJvRGltU29sdmUsSWRlYWwpLCJ6ZXJvRGltU29s | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh6ZXJvRGltU29sdmUsSWRlYWwpLCJ6ZXJvRGltU29s |
| Offset 15, 14 lines modified | Offset 15, 14 lines modified | ||
| 15 | ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+ | 15 | ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+ |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) | 17 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) |
| 18 | o2·:·Ideal·of·QQ[a..f] | 18 | o2·:·Ideal·of·QQ[a..f] |
| 19 | i3·:·elapsedTime·sols·=·zeroDimSolve·I; | 19 | i3·:·elapsedTime·sols·=·zeroDimSolve·I; |
| 20 | ·--·. | 20 | ·--·.438051s·elapsed |
| 21 | i4·:·#sols·--·156·solutions | 21 | i4·:·#sols·--·156·solutions |
| 22 | o4·=·156 | 22 | o4·=·156 |
| 23 | i5·:· | 23 | i5·:· |
| Offset 68, 15 lines modified | Offset 68, 15 lines modified | ||
| 68 | ·····------------------------------------------------------------------------ | 68 | ·····------------------------------------------------------------------------ |
| 69 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) | 69 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) |
| 70 | o2·:·Ideal·of·QQ[a..f]</code></pre> | 70 | o2·:·Ideal·of·QQ[a..f]</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·sols·=·zeroDimSolve·I; | 73 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·sols·=·zeroDimSolve·I; |
| 74 | ·--·. | 74 | ·--·.438051s·elapsed</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·#sols·--·156·solutions | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·#sols·--·156·solutions |
| 78 | o4·=·156</code></pre> | 78 | o4·=·156</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ········</table> | 80 | ········</table> |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+ | 30 | ·····a*b*e*f·+·a*d*e*f·+·c*d*e*f,·a*b*c*d*e·+·a*b*c*d*f·+·a*b*c*e*f·+ |
| 31 | ·····------------------------------------------------------------------------ | 31 | ·····------------------------------------------------------------------------ |
| 32 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) | 32 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) |
| 33 | o2·:·Ideal·of·QQ[a..f] | 33 | o2·:·Ideal·of·QQ[a..f] |
| 34 | i3·:·elapsedTime·sols·=·zeroDimSolve·I; | 34 | i3·:·elapsedTime·sols·=·zeroDimSolve·I; |
| 35 | ·--·. | 35 | ·--·.438051s·elapsed |
| 36 | i4·:·#sols·--·156·solutions | 36 | i4·:·#sols·--·156·solutions |
| 37 | o4·=·156 | 37 | o4·=·156 |
| 38 | The·authors·would·like·to·acknowledge·the·June·2020·Macaulay2·workshop·held | 38 | The·authors·would·like·to·acknowledge·the·June·2020·Macaulay2·workshop·held |
| 39 | virtually·at·Warwick,·where·this·package·was·first·developed. | 39 | virtually·at·Warwick,·where·this·package·was·first·developed. |
| 40 | R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s: | 40 | R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s: |
| 41 | ····*·[1]·Sturmfels,·Bernd.·Solving·systems·of·polynomial·equations.·No.·97. | 41 | ····*·[1]·Sturmfels,·Bernd.·Solving·systems·of·polynomial·equations.·No.·97. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | ZWxpbWluYXRlKElkZWFsLExpc3Qp | 8 | ZWxpbWluYXRlKElkZWFsLExpc3Qp |
| 9 | #:len=200 | 9 | #:len=200 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgxLCAidW5kb2N1bWVudGVkIiA9PiB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgxLCAidW5kb2N1bWVudGVkIiA9PiB0 |
| 11 | cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhlbGltaW5h | 11 | cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhlbGltaW5h |
| Offset 17, 23 lines modified | Offset 17, 23 lines modified | ||
| 17 | ······2 | 17 | ······2 |
| 18 | o3·=·x··+·x*c·+·d | 18 | o3·=·x··+·x*c·+·d |
| 19 | o3·:·R | 19 | o3·:·R |
| 20 | i4·:·time·eliminate(x,ideal(f,g)) | 20 | i4·:·time·eliminate(x,ideal(f,g)) |
| 21 | ·--·used·0.00 | 21 | ·--·used·0.00296003s·(cpu);·0.00297663s·(thread);·0s·(gc) |
| 22 | ······················2····2·············2···········2 | 22 | ······················2····2·············2···········2 |
| 23 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 23 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 24 | o4·:·Ideal·of·R | 24 | o4·:·Ideal·of·R |
| 25 | i5·:·time·ideal·resultant(f,g,x) | 25 | i5·:·time·ideal·resultant(f,g,x) |
| 26 | ·--·used·0.00 | 26 | ·--·used·0.00131102s·(cpu);·0.00158347s·(thread);·0s·(gc) |
| 27 | ························2····2·············2···········2 | 27 | ························2····2·············2···········2 |
| 28 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 28 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 29 | o5·:·Ideal·of·R | 29 | o5·:·Ideal·of·R |
| 30 | i6·:·sylvesterMatrix(f,g,x) | 30 | i6·:·sylvesterMatrix(f,g,x) |
| Offset 17, 23 lines modified | Offset 17, 23 lines modified | ||
| 17 | ······2 | 17 | ······2 |
| 18 | o3·=·x··+·x*c·+·d | 18 | o3·=·x··+·x*c·+·d |
| 19 | o3·:·R | 19 | o3·:·R |
| 20 | i4·:·time·eliminate(x,ideal(f,g)) | 20 | i4·:·time·eliminate(x,ideal(f,g)) |
| 21 | ·--·used·0.00400 | 21 | ·--·used·0.00400714s·(cpu);·0.00242269s·(thread);·0s·(gc) |
| 22 | ······················2····2·············2···········2 | 22 | ······················2····2·············2···········2 |
| 23 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 23 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 24 | o4·:·Ideal·of·R | 24 | o4·:·Ideal·of·R |
| 25 | i5·:·time·ideal·resultant(f,g,x) | 25 | i5·:·time·ideal·resultant(f,g,x) |
| 26 | ·--·used·0.0002 | 26 | ·--·used·0.000284193s·(cpu);·0.00128201s·(thread);·0s·(gc) |
| 27 | ························2····2·············2···········2 | 27 | ························2····2·············2···········2 |
| 28 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 28 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 29 | o5·:·Ideal·of·R | 29 | o5·:·Ideal·of·R |
| 30 | i6·:·sylvesterMatrix(f,g,x) | 30 | i6·:·sylvesterMatrix(f,g,x) |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | ······8····5 | 17 | ······8····5 |
| 18 | o3·=·x··+·x··+·x*c·+·d | 18 | o3·=·x··+·x··+·x*c·+·d |
| 19 | o3·:·R | 19 | o3·:·R |
| 20 | i4·:·time·eliminate(ideal(f,g),x) | 20 | i4·:·time·eliminate(ideal(f,g),x) |
| 21 | ·--·used·1.1 | 21 | ·--·used·1.41361s·(cpu);·1.26975s·(thread);·0s·(gc) |
| 22 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 22 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 23 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 23 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 24 | ·····------------------------------------------------------------------------ | 24 | ·····------------------------------------------------------------------------ |
| 25 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 25 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 26 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 26 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| Offset 73, 15 lines modified | Offset 73, 15 lines modified | ||
| 73 | ·····------------------------------------------------------------------------ | 73 | ·····------------------------------------------------------------------------ |
| 74 | ···············3··········4········4 | 74 | ···············3··········4········4 |
| 75 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 75 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 76 | o4·:·Ideal·of·R | 76 | o4·:·Ideal·of·R |
| 77 | i5·:·time·ideal·resultant(f,g,x) | 77 | i5·:·time·ideal·resultant(f,g,x) |
| 78 | ·--·used·0.01 | 78 | ·--·used·0.0194731s·(cpu);·0.0161257s·(thread);·0s·(gc) |
| 79 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 79 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 80 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 80 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 81 | ·····------------------------------------------------------------------------ | 81 | ·····------------------------------------------------------------------------ |
| 82 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 82 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 83 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 83 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 84 | ·····------------------------------------------------------------------------ | 84 | ·····------------------------------------------------------------------------ |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | ······8····5 | 19 | ······8····5 |
| 20 | o4·=·x··+·x··+·x*c·+·d | 20 | o4·=·x··+·x··+·x*c·+·d |
| 21 | o4·:·R | 21 | o4·:·R |
| 22 | i5·:·time·eliminate(ideal(f,g),x) | 22 | i5·:·time·eliminate(ideal(f,g),x) |
| 23 | ·--·used·1.18 | 23 | ·--·used·1.41872s·(cpu);·1.2782s·(thread);·0s·(gc) |
| 24 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 24 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 25 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 25 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 26 | ·····------------------------------------------------------------------------ | 26 | ·····------------------------------------------------------------------------ |
| 27 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 27 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 28 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 28 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| Offset 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | ·····------------------------------------------------------------------------ | 75 | ·····------------------------------------------------------------------------ |
| 76 | ···············3··········4········4 | 76 | ···············3··········4········4 |
| 77 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 77 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 78 | o5·:·Ideal·of·R | 78 | o5·:·Ideal·of·R |
| 79 | i6·:·time·ideal·resultant(f,g,x) | 79 | i6·:·time·ideal·resultant(f,g,x) |
| 80 | ·--·used·0.01 | 80 | ·--·used·0.0114181s·(cpu);·0.0130411s·(thread);·0s·(gc) |
| 81 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 81 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 82 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 82 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 83 | ·····------------------------------------------------------------------------ | 83 | ·····------------------------------------------------------------------------ |
| 84 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 84 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 85 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 85 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| Offset 100, 24 lines modified | Offset 100, 24 lines modified | ||
| 100 | ······2 | 100 | ······2 |
| 101 | o3·=·x··+·x*c·+·d | 101 | o3·=·x··+·x*c·+·d |
| 102 | o3·:·R</code></pre> | 102 | o3·:·R</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) |
| 106 | ·--·used·0.00 | 106 | ·--·used·0.00296003s·(cpu);·0.00297663s·(thread);·0s·(gc) |
| 107 | ······················2····2·············2···········2 | 107 | ······················2····2·············2···········2 |
| 108 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 108 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 109 | o4·:·Ideal·of·R</code></pre> | 109 | o4·:·Ideal·of·R</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) | 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) |
| 113 | ·--·used·0.00 | 113 | ·--·used·0.00131102s·(cpu);·0.00158347s·(thread);·0s·(gc) |
| 114 | ························2····2·············2···········2 | 114 | ························2····2·············2···········2 |
| 115 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 115 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 116 | o5·:·Ideal·of·R</code></pre> | 116 | o5·:·Ideal·of·R</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| Offset 30, 22 lines modified | Offset 30, 22 lines modified | ||
| 30 | i3·:·g·=·x^2+c*x+d | 30 | i3·:·g·=·x^2+c*x+d |
| 31 | ······2 | 31 | ······2 |
| 32 | o3·=·x··+·x*c·+·d | 32 | o3·=·x··+·x*c·+·d |
| 33 | o3·:·R | 33 | o3·:·R |
| 34 | i4·:·time·eliminate(x,ideal(f,g)) | 34 | i4·:·time·eliminate(x,ideal(f,g)) |
| 35 | ·--·used·0.00 | 35 | ·--·used·0.00296003s·(cpu);·0.00297663s·(thread);·0s·(gc) |
| 36 | ······················2····2·············2···········2 | 36 | ······················2····2·············2···········2 |
| 37 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 37 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 38 | o4·:·Ideal·of·R | 38 | o4·:·Ideal·of·R |
| 39 | i5·:·time·ideal·resultant(f,g,x) | 39 | i5·:·time·ideal·resultant(f,g,x) |
| 40 | ·--·used·0.00 | 40 | ·--·used·0.00131102s·(cpu);·0.00158347s·(thread);·0s·(gc) |
| 41 | ························2····2·············2···········2 | 41 | ························2····2·············2···········2 |
| 42 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 42 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 43 | o5·:·Ideal·of·R | 43 | o5·:·Ideal·of·R |
| 44 | i6·:·sylvesterMatrix(f,g,x) | 44 | i6·:·sylvesterMatrix(f,g,x) |
| Offset 91, 24 lines modified | Offset 91, 24 lines modified | ||
| 91 | ······2 | 91 | ······2 |
| 92 | o3·=·x··+·x*c·+·d | 92 | o3·=·x··+·x*c·+·d |
| 93 | o3·:·R</code></pre> | 93 | o3·:·R</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) |
| 97 | ·--·used·0.00400 | 97 | ·--·used·0.00400714s·(cpu);·0.00242269s·(thread);·0s·(gc) |
| 98 | ······················2····2·············2···········2 | 98 | ······················2····2·············2···········2 |
| 99 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 99 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 100 | o4·:·Ideal·of·R</code></pre> | 100 | o4·:·Ideal·of·R</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) |
| 104 | ·--·used·0.0002 | 104 | ·--·used·0.000284193s·(cpu);·0.00128201s·(thread);·0s·(gc) |
| 105 | ························2····2·············2···········2 | 105 | ························2····2·············2···········2 |
| 106 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 106 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 107 | o5·:·Ideal·of·R</code></pre> | 107 | o5·:·Ideal·of·R</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| Offset 31, 22 lines modified | Offset 31, 22 lines modified | ||
| 31 | i3·:·g·=·x^2+c*x+d | 31 | i3·:·g·=·x^2+c*x+d |
| 32 | ······2 | 32 | ······2 |
| 33 | o3·=·x··+·x*c·+·d | 33 | o3·=·x··+·x*c·+·d |
| 34 | o3·:·R | 34 | o3·:·R |
| 35 | i4·:·time·eliminate(x,ideal(f,g)) | 35 | i4·:·time·eliminate(x,ideal(f,g)) |
| 36 | ·--·used·0.00400 | 36 | ·--·used·0.00400714s·(cpu);·0.00242269s·(thread);·0s·(gc) |
| 37 | ······················2····2·············2···········2 | 37 | ······················2····2·············2···········2 |
| 38 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 38 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 39 | o4·:·Ideal·of·R | 39 | o4·:·Ideal·of·R |
| 40 | i5·:·time·ideal·resultant(f,g,x) | 40 | i5·:·time·ideal·resultant(f,g,x) |
| 41 | ·--·used·0.0002 | 41 | ·--·used·0.000284193s·(cpu);·0.00128201s·(thread);·0s·(gc) |
| 42 | ························2····2·············2···········2 | 42 | ························2····2·············2···········2 |
| 43 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 43 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 44 | o5·:·Ideal·of·R | 44 | o5·:·Ideal·of·R |
| 45 | i6·:·sylvesterMatrix(f,g,x) | 45 | i6·:·sylvesterMatrix(f,g,x) |
| Offset 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | ······8····5 | 103 | ······8····5 |
| 104 | o3·=·x··+·x··+·x*c·+·d | 104 | o3·=·x··+·x··+·x*c·+·d |
| 105 | o3·:·R</code></pre> | 105 | o3·:·R</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(ideal(f,g),x) | 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(ideal(f,g),x) |
| 109 | ·--·used·1.1 | 109 | ·--·used·1.41361s·(cpu);·1.26975s·(thread);·0s·(gc) |
| 110 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 110 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 111 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 111 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 112 | ·····------------------------------------------------------------------------ | 112 | ·····------------------------------------------------------------------------ |
| 113 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 113 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 114 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 114 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 115 | ·····------------------------------------------------------------------------ | 115 | ·····------------------------------------------------------------------------ |
| Offset 160, 15 lines modified | Offset 160, 15 lines modified | ||
| 160 | ···············3··········4········4 | 160 | ···············3··········4········4 |
| 161 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 161 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 162 | o4·:·Ideal·of·R</code></pre> | 162 | o4·:·Ideal·of·R</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) | 165 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) |
| 166 | ·--·used·0.01 | 166 | ·--·used·0.0194731s·(cpu);·0.0161257s·(thread);·0s·(gc) |
| 167 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 167 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 168 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 168 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 169 | ·····------------------------------------------------------------------------ | 169 | ·····------------------------------------------------------------------------ |
| 170 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 170 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 171 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 171 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 172 | ·····------------------------------------------------------------------------ | 172 | ·····------------------------------------------------------------------------ |
| Offset 36, 15 lines modified | Offset 36, 15 lines modified | ||
| 36 | i3·:·g·=·x^8+x^5+c*x+d | 36 | i3·:·g·=·x^8+x^5+c*x+d |
| 37 | ······8····5 | 37 | ······8····5 |
| 38 | o3·=·x··+·x··+·x*c·+·d | 38 | o3·=·x··+·x··+·x*c·+·d |
| 39 | o3·:·R | 39 | o3·:·R |
| 40 | i4·:·time·eliminate(ideal(f,g),x) | 40 | i4·:·time·eliminate(ideal(f,g),x) |
| 41 | ·--·used·1.1 | 41 | ·--·used·1.41361s·(cpu);·1.26975s·(thread);·0s·(gc) |
| 42 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 | 42 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 |
| 43 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 43 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 44 | ·····------------------------------------------------------------------------ | 44 | ·····------------------------------------------------------------------------ |
| 45 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 | 45 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 |
| 46 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 46 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 47 | ·····------------------------------------------------------------------------ | 47 | ·····------------------------------------------------------------------------ |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d | 91 | ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d |
| 92 | ·····------------------------------------------------------------------------ | 92 | ·····------------------------------------------------------------------------ |
| 93 | ···············3··········4········4 | 93 | ···············3··········4········4 |
| 94 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 94 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 95 | o4·:·Ideal·of·R | 95 | o4·:·Ideal·of·R |
| 96 | i5·:·time·ideal·resultant(f,g,x) | 96 | i5·:·time·ideal·resultant(f,g,x) |
| 97 | ·--·used·0.01 | 97 | ·--·used·0.0194731s·(cpu);·0.0161257s·(thread);·0s·(gc) |
| 98 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 | 98 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 |
| 99 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 99 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 | 101 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 |
| 102 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 102 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 103 | ·····------------------------------------------------------------------------ | 103 | ·····------------------------------------------------------------------------ |
| Offset 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | ······8····5 | 98 | ······8····5 |
| 99 | o4·=·x··+·x··+·x*c·+·d | 99 | o4·=·x··+·x··+·x*c·+·d |
| 100 | o4·:·R</code></pre> | 100 | o4·:·R</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·eliminate(ideal(f,g),x) | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·eliminate(ideal(f,g),x) |
| 104 | ·--·used·1.18 | 104 | ·--·used·1.41872s·(cpu);·1.2782s·(thread);·0s·(gc) |
| 105 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 105 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 106 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 106 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 107 | ·····------------------------------------------------------------------------ | 107 | ·····------------------------------------------------------------------------ |
| 108 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 108 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 109 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 109 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| Offset 155, 15 lines modified | Offset 155, 15 lines modified | ||
| 155 | ···············3··········4········4 | 155 | ···············3··········4········4 |
| 156 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 156 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 157 | o5·:·Ideal·of·R</code></pre> | 157 | o5·:·Ideal·of·R</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·resultant(f,g,x) | 160 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·resultant(f,g,x) |
| 161 | ·--·used·0.01 | 161 | ·--·used·0.0114181s·(cpu);·0.0130411s·(thread);·0s·(gc) |
| 162 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 162 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 163 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 163 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 164 | ·····------------------------------------------------------------------------ | 164 | ·····------------------------------------------------------------------------ |
| 165 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 165 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 166 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 166 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 167 | ·····------------------------------------------------------------------------ | 167 | ·····------------------------------------------------------------------------ |
| Offset 31, 15 lines modified | Offset 31, 15 lines modified | ||
| 31 | i4·:·g·=·x^8+x^5+c*x+d | 31 | i4·:·g·=·x^8+x^5+c*x+d |
| 32 | ······8····5 | 32 | ······8····5 |
| 33 | o4·=·x··+·x··+·x*c·+·d | 33 | o4·=·x··+·x··+·x*c·+·d |
| 34 | o4·:·R | 34 | o4·:·R |
| 35 | i5·:·time·eliminate(ideal(f,g),x) | 35 | i5·:·time·eliminate(ideal(f,g),x) |
| 36 | ·--·used·1.18 | 36 | ·--·used·1.41872s·(cpu);·1.2782s·(thread);·0s·(gc) |
| 37 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 | 37 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 |
| 38 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 38 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 | 40 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 |
| 41 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 41 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| Offset 86, 15 lines modified | Offset 86, 15 lines modified | ||
| 86 | ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d | 86 | ·····+·792a*b·c*d·-·1512a*b*c·d·+·648a*c·d·-·360a·b*d··+·648a·c*d··-·504b·d |
| 87 | ·····------------------------------------------------------------------------ | 87 | ·····------------------------------------------------------------------------ |
| 88 | ···············3··········4········4 | 88 | ···············3··········4········4 |
| 89 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 89 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 90 | o5·:·Ideal·of·R | 90 | o5·:·Ideal·of·R |
| 91 | i6·:·time·ideal·resultant(f,g,x) | 91 | i6·:·time·ideal·resultant(f,g,x) |
| 92 | ·--·used·0.01 | 92 | ·--·used·0.0114181s·(cpu);·0.0130411s·(thread);·0s·(gc) |
| 93 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 | 93 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2 |
| 94 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 94 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 95 | ·····------------------------------------------------------------------------ | 95 | ·····------------------------------------------------------------------------ |
| 96 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 | 96 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7 |
| 97 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 97 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 98 | ·····------------------------------------------------------------------------ | 98 | ·····------------------------------------------------------------------------ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | bWF4Q29sKE1hdHJpeCk= | 8 | bWF4Q29sKE1hdHJpeCk= |
| 9 | #:len=257 | 9 | #:len=257 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEyMCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEyMCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobWF4Q29sLE1hdHJpeCksIm1heENvbChNYXRyaXgp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobWF4Q29sLE1hdHJpeCksIm1heENvbChNYXRyaXgp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | RWxsUG9pbnRXID09IEVsbFBvaW50Vw== | 8 | RWxsUG9pbnRXID09IEVsbFBvaW50Vw== |
| 9 | #:len=300 | 9 | #:len=300 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzQ3LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzQ3LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzeW1ib2wgPT0sRWxsUG9pbnRXLEVsbFBvaW50Vyks | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzeW1ib2wgPT0sRWxsUG9pbnRXLEVsbFBvaW50Vyks |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=17 | 7 | #:len=17 |
| 8 | RWxsaXB0aWNJbnRlZ3JhbHM= | 8 | RWxsaXB0aWNJbnRlZ3JhbHM= |
| 9 | #:len=584 | 9 | #:len=584 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=11 | 7 | #:len=11 |
| 8 | RW5naW5lVGVzdHM= | 8 | RW5naW5lVGVzdHM= |
| 9 | #:len=327 | 9 | #:len=327 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSB0ZXN0IHN1aXRlIGZvciB0aGUgTWFj | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSB0ZXN0IHN1aXRlIGZvciB0aGUgTWFj |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=17 | 7 | #:len=17 |
| 8 | RW51bWVyYXRpb25DdXJ2ZXM= | 8 | RW51bWVyYXRpb25DdXJ2ZXM= |
| 9 | #:len=747 | 9 | #:len=747 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRW51bWVyYXRpb24gb2YgcmF0aW9uYWwg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRW51bWVyYXRpb24gb2YgcmF0aW9uYWwg |
| 11 | Y3VydmVzIHZpYSB0b3J1cyBhY3Rpb25zIiwgRGVzY3JpcHRpb24gPT4gMTooRElWe1BBUkF7IiJ9 | 11 | Y3VydmVzIHZpYSB0b3J1cyBhY3Rpb25zIiwgRGVzY3JpcHRpb24gPT4gMTooRElWe1BBUkF7IiJ9 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1331975673177 | 1 | --·-*-·M2-comint·-*-·hash:·1331975673177 |
| 2 | i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) | 2 | i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) |
| 3 | ·--·used·0.0 | 3 | ·--·used·0.0315741s·(cpu);·0.0283798s·(thread);·0s·(gc) |
| 4 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 4 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 5 | ·····------------------------------------------------------------------------ | 5 | ·····------------------------------------------------------------------------ |
| 6 | ·····289139638632755625,·520764738758073845321} | 6 | ·····289139638632755625,·520764738758073845321} |
| 7 | o1·:·List | 7 | o1·:·List |
| Offset 37, 83 lines modified | Offset 37, 83 lines modified | ||
| 37 | i6·:·rationalCurve(2)·-·rationalCurve(1)/8 | 37 | i6·:·rationalCurve(2)·-·rationalCurve(1)/8 |
| 38 | o6·=·609250 | 38 | o6·=·609250 |
| 39 | o6·:·QQ | 39 | o6·:·QQ |
| 40 | i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 | 40 | i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 |
| 41 | ·--·used·0.2 | 41 | ·--·used·0.267587s·(cpu);·0.238357s·(thread);·0s·(gc) |
| 42 | o7·=·{609250,·92288,·52812,·22428,·9728} | 42 | o7·=·{609250,·92288,·52812,·22428,·9728} |
| 43 | o7·:·List | 43 | o7·:·List |
| 44 | i8·:·time·rationalCurve(3) | 44 | i8·:·time·rationalCurve(3) |
| 45 | ·--·used·0. | 45 | ·--·used·0.100373s·(cpu);·0.102417s·(thread);·0s·(gc) |
| 46 | ·····8564575000 | 46 | ·····8564575000 |
| 47 | o8·=·---------- | 47 | o8·=·---------- |
| 48 | ·········27 | 48 | ·········27 |
| 49 | o8·:·QQ | 49 | o8·:·QQ |
| 50 | i9·:·time·for·D·in·T·list·rationalCurve(3,D) | 50 | i9·:·time·for·D·in·T·list·rationalCurve(3,D) |
| 51 | ·--·used· | 51 | ·--·used·4.03565s·(cpu);·3.59501s·(thread);·0s·(gc) |
| 52 | ······8564575000··422690816···········4834592··11239424 | 52 | ······8564575000··422690816···········4834592··11239424 |
| 53 | o9·=·{----------,·---------,·6424365,·-------,·--------} | 53 | o9·=·{----------,·---------,·6424365,·-------,·--------} |
| 54 | ··········27··········27·················3········27 | 54 | ··········27··········27·················3········27 |
| 55 | o9·:·List | 55 | o9·:·List |
| 56 | i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 | 56 | i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 |
| 57 | ·--·used·0. | 57 | ·--·used·0.107031s·(cpu);·0.108864s·(thread);·0s·(gc) |
| 58 | o10·=·317206375 | 58 | o10·=·317206375 |
| 59 | o10·:·QQ | 59 | o10·:·QQ |
| 60 | i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 | 60 | i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 |
| 61 | ·--·used· | 61 | ·--·used·4.01766s·(cpu);·3.6294s·(thread);·0s·(gc) |
| 62 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} | 62 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} |
| 63 | o11·:·List | 63 | o11·:·List |
| 64 | i12·:·time·rationalCurve(4) | 64 | i12·:·time·rationalCurve(4) |
| 65 | ·--·used·1. | 65 | ·--·used·1.32473s·(cpu);·1.15257s·(thread);·0s·(gc) |
| 66 | ······15517926796875 | 66 | ······15517926796875 |
| 67 | o12·=·-------------- | 67 | o12·=·-------------- |
| 68 | ············64 | 68 | ············64 |
| 69 | o12·:·QQ | 69 | o12·:·QQ |
| 70 | i13·:·time·rationalCurve(4,{4,2}) | 70 | i13·:·time·rationalCurve(4,{4,2}) |
| 71 | ·--·used· | 71 | ·--·used·5.84756s·(cpu);·4.82931s·(thread);·0s·(gc) |
| 72 | o13·=·3883914084 | 72 | o13·=·3883914084 |
| 73 | o13·:·QQ | 73 | o13·:·QQ |
| 74 | i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 | 74 | i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 |
| 75 | ·--·used·1. | 75 | ·--·used·1.29268s·(cpu);·1.16955s·(thread);·0s·(gc) |
| 76 | o14·=·242467530000 | 76 | o14·=·242467530000 |
| 77 | o14·:·QQ | 77 | o14·:·QQ |
| 78 | i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 | 78 | i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 |
| 79 | ·--·used· | 79 | ·--·used·5.85651s·(cpu);·4.85361s·(thread);·0s·(gc) |
| 80 | o15·=·3883902528 | 80 | o15·=·3883902528 |
| 81 | o15·:·QQ | 81 | o15·:·QQ |
| 82 | i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 | 82 | i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 |
| 83 | ·--·used· | 83 | ·--·used·5.59437s·(cpu);·4.69938s·(thread);·0s·(gc) |
| 84 | o16·=·1139448384 | 84 | o16·=·1139448384 |
| 85 | o16·:·QQ | 85 | o16·:·QQ |
| 86 | i17·:· | 86 | i17·:· |
| Offset 70, 15 lines modified | Offset 70, 15 lines modified | ||
| 70 | ········<div> | 70 | ········<div> |
| 71 | ··········<p>Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in·\mathbb·P^n.</p> | 71 | ··········<p>Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in·\mathbb·P^n.</p> |
| 72 | ··········<p></p> | 72 | ··········<p></p> |
| 73 | ········</div> | 73 | ········</div> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) |
| 77 | ·--·used·0.0 | 77 | ·--·used·0.0315741s·(cpu);·0.0283798s·(thread);·0s·(gc) |
| 78 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 78 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 79 | ·····------------------------------------------------------------------------ | 79 | ·····------------------------------------------------------------------------ |
| 80 | ·····289139638632755625,·520764738758073845321} | 80 | ·····289139638632755625,·520764738758073845321} |
| 81 | o1·:·List</code></pre> | 81 | o1·:·List</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| Offset 12, 15 lines modified | Offset 12, 15 lines modified | ||
| 12 | ····*·Outputs: | 12 | ····*·Outputs: |
| 13 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·number·of·lines·on·a·general·hypersurface·of·degree | 13 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·number·of·lines·on·a·general·hypersurface·of·degree |
| 14 | ············2n·-·3·in·\mathbb·P^n | 14 | ············2n·-·3·in·\mathbb·P^n |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in | 16 | Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in |
| 17 | \mathbb·P^n. | 17 | \mathbb·P^n. |
| 18 | i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) | 18 | i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) |
| 19 | ·--·used·0.0 | 19 | ·--·used·0.0315741s·(cpu);·0.0283798s·(thread);·0s·(gc) |
| 20 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 20 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 21 | ·····------------------------------------------------------------------------ | 21 | ·····------------------------------------------------------------------------ |
| 22 | ·····289139638632755625,·520764738758073845321} | 22 | ·····289139638632755625,·520764738758073845321} |
| 23 | o1·:·List | 23 | o1·:·List |
| 24 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·l\x8li\x8in\x8ne\x8es\x8sH\x8Hy\x8yp\x8pe\x8er\x8rs\x8su\x8ur\x8rf\x8fa\x8ac\x8ce\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·l\x8li\x8in\x8ne\x8es\x8sH\x8Hy\x8yp\x8pe\x8er\x8rs\x8su\x8ur\x8rf\x8fa\x8ac\x8ce\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 140, 39 lines modified | Offset 140, 39 lines modified | ||
| 140 | ········<div> | 140 | ········<div> |
| 141 | ··········<p>The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> | 141 | ··········<p>The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> |
| 142 | ··········<p></p> | 142 | ··········<p></p> |
| 143 | ········</div> | 143 | ········</div> |
| 144 | ········<table·class="examples"> | 144 | ········<table·class="examples"> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 | 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 |
| 147 | ·--·used·0.2 | 147 | ·--·used·0.267587s·(cpu);·0.238357s·(thread);·0s·(gc) |
| 148 | o7·=·{609250,·92288,·52812,·22428,·9728} | 148 | o7·=·{609250,·92288,·52812,·22428,·9728} |
| 149 | o7·:·List</code></pre> | 149 | o7·:·List</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ········</table> | 151 | ········</table> |
| 152 | ········<div> | 152 | ········<div> |
| 153 | ··········<p>For·rational·curves·of·degree·3:</p> | 153 | ··········<p>For·rational·curves·of·degree·3:</p> |
| 154 | ··········<p></p> | 154 | ··········<p></p> |
| 155 | ········</div> | 155 | ········</div> |
| 156 | ········<table·class="examples"> | 156 | ········<table·class="examples"> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·rationalCurve(3) | 158 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·rationalCurve(3) |
| 159 | ·--·used·0. | 159 | ·--·used·0.100373s·(cpu);·0.102417s·(thread);·0s·(gc) |
| 160 | ·····8564575000 | 160 | ·····8564575000 |
| 161 | o8·=·---------- | 161 | o8·=·---------- |
| 162 | ·········27 | 162 | ·········27 |
| 163 | o8·:·QQ</code></pre> | 163 | o8·:·QQ</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·for·D·in·T·list·rationalCurve(3,D) | 166 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·for·D·in·T·list·rationalCurve(3,D) |
| 167 | ·--·used· | 167 | ·--·used·4.03565s·(cpu);·3.59501s·(thread);·0s·(gc) |
| 168 | ······8564575000··422690816···········4834592··11239424 | 168 | ······8564575000··422690816···········4834592··11239424 |
| 169 | o9·=·{----------,·---------,·6424365,·-------,·--------} | 169 | o9·=·{----------,·---------,·6424365,·-------,·--------} |
| 170 | ··········27··········27·················3········27 | 170 | ··········27··········27·················3········27 |
| 171 | o9·:·List</code></pre> | 171 | o9·:·List</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| Offset 180, 89 lines modified | Offset 180, 89 lines modified | ||
| 180 | ········<div> | 180 | ········<div> |
| 181 | ··········<p>The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> | 181 | ··········<p>The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> |
| 182 | ··········<p></p> | 182 | ··········<p></p> |
| 183 | ········</div> | 183 | ········</div> |
| 184 | ········<table·class="examples"> | 184 | ········<table·class="examples"> |
| 185 | ··········<tr> | 185 | ··········<tr> |
| 186 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 | 186 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 |
| 187 | ·--·used·0. | 187 | ·--·used·0.107031s·(cpu);·0.108864s·(thread);·0s·(gc) |
| 188 | o10·=·317206375 | 188 | o10·=·317206375 |
| 189 | o10·:·QQ</code></pre> | 189 | o10·:·QQ</code></pre> |
| 190 | </td>··········</tr> | 190 | </td>··········</tr> |
| 191 | ········</table> | 191 | ········</table> |
| 192 | ········<div> | 192 | ········<div> |
| 193 | ··········<p>The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> | 193 | ··········<p>The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> |
| 194 | ··········<p></p> | 194 | ··········<p></p> |
| 195 | ········</div> | 195 | ········</div> |
| 196 | ········<table·class="examples"> | 196 | ········<table·class="examples"> |
| 197 | ··········<tr> | 197 | ··········<tr> |
| 198 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 | 198 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 |
| 199 | ·--·used· | 199 | ·--·used·4.01766s·(cpu);·3.6294s·(thread);·0s·(gc) |
| 200 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} | 200 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} |
| 201 | o11·:·List</code></pre> | 201 | o11·:·List</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ········</table> | 203 | ········</table> |
| 204 | ········<div> | 204 | ········<div> |
| 205 | ··········<p>For·rational·curves·of·degree·4:</p> | 205 | ··········<p>For·rational·curves·of·degree·4:</p> |
| 206 | ··········<p></p> | 206 | ··········<p></p> |
| 207 | ········</div> | 207 | ········</div> |
| 208 | ········<table·class="examples"> | 208 | ········<table·class="examples"> |
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·rationalCurve(4) | 210 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·rationalCurve(4) |
| 211 | ·--·used·1. | 211 | ·--·used·1.32473s·(cpu);·1.15257s·(thread);·0s·(gc) |
| 212 | ······15517926796875 | 212 | ······15517926796875 |
| 213 | o12·=·-------------- | 213 | o12·=·-------------- |
| 214 | ············64 | 214 | ············64 |
| 215 | o12·:·QQ</code></pre> | 215 | o12·:·QQ</code></pre> |
| 216 | </td>··········</tr> | 216 | </td>··········</tr> |
| 217 | ··········<tr> | 217 | ··········<tr> |
| 218 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·rationalCurve(4,{4,2}) | 218 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·rationalCurve(4,{4,2}) |
| 219 | ·--·used· | 219 | ·--·used·5.84756s·(cpu);·4.82931s·(thread);·0s·(gc) |
| 220 | o13·=·3883914084 | 220 | o13·=·3883914084 |
| 221 | o13·:·QQ</code></pre> | 221 | o13·:·QQ</code></pre> |
| 222 | </td>··········</tr> | 222 | </td>··········</tr> |
| 223 | ········</table> | 223 | ········</table> |
| 224 | ········<div> | 224 | ········<div> |
| 225 | ··········<p>The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> | 225 | ··········<p>The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> |
| 226 | ··········<p></p> | 226 | ··········<p></p> |
| 227 | ········</div> | 227 | ········</div> |
| 228 | ········<table·class="examples"> | 228 | ········<table·class="examples"> |
| 229 | ··········<tr> | 229 | ··········<tr> |
| 230 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 | 230 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 |
| 231 | ·--·used·1. | 231 | ·--·used·1.29268s·(cpu);·1.16955s·(thread);·0s·(gc) |
| 232 | o14·=·242467530000 | 232 | o14·=·242467530000 |
| 233 | o14·:·QQ</code></pre> | 233 | o14·:·QQ</code></pre> |
| 234 | </td>··········</tr> | 234 | </td>··········</tr> |
| 235 | ········</table> | 235 | ········</table> |
| 236 | ········<div> | 236 | ········<div> |
| 237 | ··········<p>The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of·types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows:</p> | 237 | ··········<p>The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of·types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows:</p> |
| 238 | ··········<p></p> | 238 | ··········<p></p> |
| 239 | ········</div> | 239 | ········</div> |
| 240 | ········<table·class="examples"> | 240 | ········<table·class="examples"> |
| 241 | ··········<tr> | 241 | ··········<tr> |
| 242 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 | 242 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 |
| 243 | ·--·used· | 243 | ·--·used·5.85651s·(cpu);·4.85361s·(thread);·0s·(gc) |
| 244 | o15·=·3883902528 | 244 | o15·=·3883902528 |
| 245 | o15·:·QQ</code></pre> | 245 | o15·:·QQ</code></pre> |
| 246 | </td>··········</tr> | 246 | </td>··········</tr> |
| 247 | ··········<tr> | 247 | ··········<tr> |
| 248 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 | 248 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 |
| 249 | ·--·used· | 249 | ·--·used·5.59437s·(cpu);·4.69938s·(thread);·0s·(gc) |
| 250 | o16·=·1139448384 | 250 | o16·=·1139448384 |
| 251 | o16·:·QQ</code></pre> | 251 | o16·:·QQ</code></pre> |
| 252 | </td>··········</tr> | 252 | </td>··········</tr> |
| Max diff block lines reached; 14/4777 bytes (0.29%) of diff not shown. | |||
| Offset 60, 85 lines modified | Offset 60, 85 lines modified | ||
| 60 | o6·=·609250 | 60 | o6·=·609250 |
| 61 | o6·:·QQ | 61 | o6·:·QQ |
| 62 | The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds | 62 | The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds |
| 63 | can·be·computed·as·follows: | 63 | can·be·computed·as·follows: |
| 64 | i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 | 64 | i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 |
| 65 | ·--·used·0.2 | 65 | ·--·used·0.267587s·(cpu);·0.238357s·(thread);·0s·(gc) |
| 66 | o7·=·{609250,·92288,·52812,·22428,·9728} | 66 | o7·=·{609250,·92288,·52812,·22428,·9728} |
| 67 | o7·:·List | 67 | o7·:·List |
| 68 | For·rational·curves·of·degree·3: | 68 | For·rational·curves·of·degree·3: |
| 69 | i8·:·time·rationalCurve(3) | 69 | i8·:·time·rationalCurve(3) |
| 70 | ·--·used·0. | 70 | ·--·used·0.100373s·(cpu);·0.102417s·(thread);·0s·(gc) |
| 71 | ·····8564575000 | 71 | ·····8564575000 |
| 72 | o8·=·---------- | 72 | o8·=·---------- |
| 73 | ·········27 | 73 | ·········27 |
| 74 | o8·:·QQ | 74 | o8·:·QQ |
| 75 | i9·:·time·for·D·in·T·list·rationalCurve(3,D) | 75 | i9·:·time·for·D·in·T·list·rationalCurve(3,D) |
| 76 | ·--·used· | 76 | ·--·used·4.03565s·(cpu);·3.59501s·(thread);·0s·(gc) |
| 77 | ······8564575000··422690816···········4834592··11239424 | 77 | ······8564575000··422690816···········4834592··11239424 |
| 78 | o9·=·{----------,·---------,·6424365,·-------,·--------} | 78 | o9·=·{----------,·---------,·6424365,·-------,·--------} |
| 79 | ··········27··········27·················3········27 | 79 | ··········27··········27·················3········27 |
| 80 | o9·:·List | 80 | o9·:·List |
| 81 | The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be | 81 | The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be |
| 82 | computed·as·follows: | 82 | computed·as·follows: |
| 83 | i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 | 83 | i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 |
| 84 | ·--·used·0. | 84 | ·--·used·0.107031s·(cpu);·0.108864s·(thread);·0s·(gc) |
| 85 | o10·=·317206375 | 85 | o10·=·317206375 |
| 86 | o10·:·QQ | 86 | o10·:·QQ |
| 87 | The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection | 87 | The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection |
| 88 | Calabi-Yau·threefolds·can·be·computed·as·follows: | 88 | Calabi-Yau·threefolds·can·be·computed·as·follows: |
| 89 | i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 | 89 | i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 |
| 90 | ·--·used· | 90 | ·--·used·4.01766s·(cpu);·3.6294s·(thread);·0s·(gc) |
| 91 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} | 91 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} |
| 92 | o11·:·List | 92 | o11·:·List |
| 93 | For·rational·curves·of·degree·4: | 93 | For·rational·curves·of·degree·4: |
| 94 | i12·:·time·rationalCurve(4) | 94 | i12·:·time·rationalCurve(4) |
| 95 | ·--·used·1. | 95 | ·--·used·1.32473s·(cpu);·1.15257s·(thread);·0s·(gc) |
| 96 | ······15517926796875 | 96 | ······15517926796875 |
| 97 | o12·=·-------------- | 97 | o12·=·-------------- |
| 98 | ············64 | 98 | ············64 |
| 99 | o12·:·QQ | 99 | o12·:·QQ |
| 100 | i13·:·time·rationalCurve(4,{4,2}) | 100 | i13·:·time·rationalCurve(4,{4,2}) |
| 101 | ·--·used· | 101 | ·--·used·5.84756s·(cpu);·4.82931s·(thread);·0s·(gc) |
| 102 | o13·=·3883914084 | 102 | o13·=·3883914084 |
| 103 | o13·:·QQ | 103 | o13·:·QQ |
| 104 | The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be | 104 | The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be |
| 105 | computed·as·follows: | 105 | computed·as·follows: |
| 106 | i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 | 106 | i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 |
| 107 | ·--·used·1. | 107 | ·--·used·1.29268s·(cpu);·1.16955s·(thread);·0s·(gc) |
| 108 | o14·=·242467530000 | 108 | o14·=·242467530000 |
| 109 | o14·:·QQ | 109 | o14·:·QQ |
| 110 | The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of | 110 | The·numbers·of·rational·curves·of·degree·4·on·general·complete·intersections·of |
| 111 | types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows: | 111 | types·(4,2)·and·(3,3)·in·\mathbb·P^5·can·be·computed·as·follows: |
| 112 | i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 | 112 | i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 |
| 113 | ·--·used· | 113 | ·--·used·5.85651s·(cpu);·4.85361s·(thread);·0s·(gc) |
| 114 | o15·=·3883902528 | 114 | o15·=·3883902528 |
| 115 | o15·:·QQ | 115 | o15·:·QQ |
| 116 | i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 | 116 | i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 |
| 117 | ·--·used· | 117 | ·--·used·5.59437s·(cpu);·4.69938s·(thread);·0s·(gc) |
| 118 | o16·=·1139448384 | 118 | o16·=·1139448384 |
| 119 | o16·:·QQ | 119 | o16·:·QQ |
| 120 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lC\x8Cu\x8ur\x8rv\x8ve\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8* | 120 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lC\x8Cu\x8ur\x8rv\x8ve\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 121 | ····*·rationalCurve(ZZ) | 121 | ····*·rationalCurve(ZZ) |
| 122 | ····*·rationalCurve(ZZ,List) | 122 | ····*·rationalCurve(ZZ,List) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=33 | 7 | #:len=33 |
| 8 | YnVpbGRFTW9ub21pYWxNYXAoUmluZyxSaW5nLExpc3Qp | 8 | YnVpbGRFTW9ub21pYWxNYXAoUmluZyxSaW5nLExpc3Qp |
| 9 | #:len=299 | 9 | #:len=299 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIzNiwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIzNiwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYnVpbGRFTW9ub21pYWxNYXAsUmluZyxSaW5nLExp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYnVpbGRFTW9ub21pYWxNYXAsUmluZyxSaW5nLExp |
| Offset 10, 34 lines modified | Offset 10, 34 lines modified | ||
| 10 | o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·}) | 10 | o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·}) |
| 11 | ··················1···1·0···1·0···0 | 11 | ··················1···1·0···1·0···0 |
| 12 | o3·:·RingMap·R·<--·S | 12 | o3·:·RingMap·R·<--·S |
| 13 | i4·:·G·=·egbToric(m,·OutFile=>stdio) | 13 | i4·:·G·=·egbToric(m,·OutFile=>stdio) |
| 14 | 3 | 14 | 3 |
| 15 | ·····--·used·.00289959·seconds | ||
| 15 | ·····--·used·.0018 | 16 | ·····--·used·.000312887·seconds |
| 16 | ·····--·used·0·seconds | ||
| 17 | (9,·9) | 17 | (9,·9) |
| 18 | new·stuff·found | 18 | new·stuff·found |
| 19 | 4 | 19 | 4 |
| 20 | ·····--·used·.00 | 20 | ·····--·used·.0035407·seconds |
| 21 | ·····--·used·.0042 | 21 | ·····--·used·.00242248·seconds |
| 22 | (16,·26) | 22 | (16,·26) |
| 23 | new·stuff·found | 23 | new·stuff·found |
| 24 | 5 | 24 | 5 |
| 25 | ·····--·used·.00 | 25 | ·····--·used·.00581786·seconds |
| 26 | ·····--·used·.019 | 26 | ·····--·used·.0197886·seconds |
| 27 | (25,·60) | 27 | (25,·60) |
| 28 | 6 | 28 | 6 |
| 29 | ·····--·used·.01 | 29 | ·····--·used·.0168251·seconds |
| 30 | ·····--·used·.1 | 30 | ·····--·used·.177564·seconds |
| 31 | (36,·120) | 31 | (36,·120) |
| 32 | 7 | 32 | 7 |
| 33 | ·····--·used·.0270603·seconds | ||
| 34 | ·····--·used·. | 33 | ·····--·used·.0345264·seconds |
| 34 | ·····--·used·.70872·seconds | ||
| 35 | (49,·217) | 35 | (49,·217) |
| 36 | ···································2 | 36 | ···································2 |
| 37 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ | 37 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ |
| 38 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0·· | 38 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0·· |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ | 40 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ |
| Offset 96, 34 lines modified | Offset 96, 34 lines modified | ||
| 96 | ··················1···1·0···1·0···0 | 96 | ··················1···1·0···1·0···0 |
| 97 | o3·:·RingMap·R·<--·S</code></pre> | 97 | o3·:·RingMap·R·<--·S</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·egbToric(m,·OutFile=>stdio) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·egbToric(m,·OutFile=>stdio) |
| 101 | 3 | 101 | 3 |
| 102 | ·····--·used·.00289959·seconds | ||
| 102 | ·····--·used·.0018 | 103 | ·····--·used·.000312887·seconds |
| 103 | ·····--·used·0·seconds | ||
| 104 | (9,·9) | 104 | (9,·9) |
| 105 | new·stuff·found | 105 | new·stuff·found |
| 106 | 4 | 106 | 4 |
| 107 | ·····--·used·.00 | 107 | ·····--·used·.0035407·seconds |
| 108 | ·····--·used·.0042 | 108 | ·····--·used·.00242248·seconds |
| 109 | (16,·26) | 109 | (16,·26) |
| 110 | new·stuff·found | 110 | new·stuff·found |
| 111 | 5 | 111 | 5 |
| 112 | ·····--·used·.00 | 112 | ·····--·used·.00581786·seconds |
| 113 | ·····--·used·.019 | 113 | ·····--·used·.0197886·seconds |
| 114 | (25,·60) | 114 | (25,·60) |
| 115 | 6 | 115 | 6 |
| 116 | ·····--·used·.01 | 116 | ·····--·used·.0168251·seconds |
| 117 | ·····--·used·.1 | 117 | ·····--·used·.177564·seconds |
| 118 | (36,·120) | 118 | (36,·120) |
| 119 | 7 | 119 | 7 |
| 120 | ·····--·used·.0270603·seconds | ||
| 121 | ·····--·used·. | 120 | ·····--·used·.0345264·seconds |
| 121 | ·····--·used·.70872·seconds | ||
| 122 | (49,·217) | 122 | (49,·217) |
| 123 | ···································2 | 123 | ···································2 |
| 124 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ | 124 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ |
| 125 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0·· | 125 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0·· |
| 126 | ·····------------------------------------------------------------------------ | 126 | ·····------------------------------------------------------------------------ |
| 127 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ | 127 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ |
| Offset 34, 34 lines modified | Offset 34, 34 lines modified | ||
| 34 | ··················2···············2 | 34 | ··················2···············2 |
| 35 | o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·}) | 35 | o3·=·map·(R,·S,·{x·,·x·x·,·x·x·,·x·}) |
| 36 | ··················1···1·0···1·0···0 | 36 | ··················1···1·0···1·0···0 |
| 37 | o3·:·RingMap·R·<--·S | 37 | o3·:·RingMap·R·<--·S |
| 38 | i4·:·G·=·egbToric(m,·OutFile=>stdio) | 38 | i4·:·G·=·egbToric(m,·OutFile=>stdio) |
| 39 | 3 | 39 | 3 |
| 40 | ·····--·used·.00289959·seconds | ||
| 40 | ·····--·used·.0018 | 41 | ·····--·used·.000312887·seconds |
| 41 | ·····--·used·0·seconds | ||
| 42 | (9,·9) | 42 | (9,·9) |
| 43 | new·stuff·found | 43 | new·stuff·found |
| 44 | 4 | 44 | 4 |
| 45 | ·····--·used·.00 | 45 | ·····--·used·.0035407·seconds |
| 46 | ·····--·used·.0042 | 46 | ·····--·used·.00242248·seconds |
| 47 | (16,·26) | 47 | (16,·26) |
| 48 | new·stuff·found | 48 | new·stuff·found |
| 49 | 5 | 49 | 5 |
| 50 | ·····--·used·.00 | 50 | ·····--·used·.00581786·seconds |
| 51 | ·····--·used·.019 | 51 | ·····--·used·.0197886·seconds |
| 52 | (25,·60) | 52 | (25,·60) |
| 53 | 6 | 53 | 6 |
| 54 | ·····--·used·.01 | 54 | ·····--·used·.0168251·seconds |
| 55 | ·····--·used·.1 | 55 | ·····--·used·.177564·seconds |
| 56 | (36,·120) | 56 | (36,·120) |
| 57 | 7 | 57 | 7 |
| 58 | ·····--·used·.0270603·seconds | ||
| 59 | ·····--·used·. | 58 | ·····--·used·.0345264·seconds |
| 59 | ·····--·used·.70872·seconds | ||
| 60 | (49,·217) | 60 | (49,·217) |
| 61 | ···································2 | 61 | ···································2 |
| 62 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ | 62 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ |
| 63 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0 | 63 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0 |
| 64 | ·····------------------------------------------------------------------------ | 64 | ·····------------------------------------------------------------------------ |
| 65 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ | 65 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=5 | 7 | #:len=5 |
| 8 | aGVhcnQ= | 8 | aGVhcnQ= |
| 9 | #:len=1516 | 9 | #:len=1516 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gOC1kaW1lbnNpb25hbCBlY29ub21p | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gOC1kaW1lbnNpb25hbCBlY29ub21p |
| 11 | Y3MgcHJvYmxlbSIsICJsaW5lbnVtIiA9PiA0OCwgSW5wdXRzID0+IHtTUEFOe1RUeyJrayJ9LCIs | 11 | Y3MgcHJvYmxlbSIsICJsaW5lbnVtIiA9PiA0OCwgSW5wdXRzID0+IHtTUEFOe1RUeyJrayJ9LCIs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=28 | 7 | #:len=28 |
| 8 | c29sdmVNYWNhdWxheUV4cGFuc2lvbihMaXN0KQ== | 8 | c29sdmVNYWNhdWxheUV4cGFuc2lvbihMaXN0KQ== |
| 9 | #:len=301 | 9 | #:len=301 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDMxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDMxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzb2x2ZU1hY2F1bGF5RXhwYW5zaW9uLExpc3QpLCJz | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzb2x2ZU1hY2F1bGF5RXhwYW5zaW9uLExpc3QpLCJz |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=26 | 7 | #:len=26 |
| 8 | YWxtb3N0U3RhYmxlTW9kdWxlKE1vZHVsZSk= | 8 | YWxtb3N0U3RhYmxlTW9kdWxlKE1vZHVsZSk= |
| 9 | #:len=292 | 9 | #:len=292 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODAyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODAyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbG1vc3RTdGFibGVNb2R1bGUsTW9kdWxlKSwiYWxt | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbG1vc3RTdGFibGVNb2R1bGUsTW9kdWxlKSwiYWxt |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | ZmdsbShJZGVhbCxSaW5nKQ== | 8 | ZmdsbShJZGVhbCxSaW5nKQ== |
| 9 | #:len=211 | 9 | #:len=211 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzk2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzk2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmZ2xtLElkZWFsLFJpbmcpLCJmZ2xtKElkZWFsLFJp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmZ2xtLElkZWFsLFJpbmcpLCJmZ2xtKElkZWFsLFJp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=26 | 7 | #:len=26 |
| 8 | cmVjdXJzaXZlTWlub3JzKFpaLE1hdHJpeCk= | 8 | cmVjdXJzaXZlTWlub3JzKFpaLE1hdHJpeCk= |
| 9 | #:len=272 | 9 | #:len=272 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjAyOCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjAyOCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmVjdXJzaXZlTWlub3JzLFpaLE1hdHJpeCksInJl | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmVjdXJzaXZlTWlub3JzLFpaLE1hdHJpeCksInJl |
| Offset 462, 50 lines modified | Offset 462, 50 lines modified | ||
| 462 | ···············3·2·4·····3·6 | 462 | ···············3·2·4·····3·6 |
| 463 | o27·=·ideal(12x·x·x··-·4x·x·) | 463 | o27·=·ideal(12x·x·x··-·4x·x·) |
| 464 | ···············3·7·9·····3·9 | 464 | ···············3·7·9·····3·9 |
| 465 | o27·:·Ideal·of·S | 465 | o27·:·Ideal·of·S |
| 466 | i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) | 466 | i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) |
| 467 | ·--·used·0. | 467 | ·--·used·0.119366s·(cpu);·0.119073s·(thread);·0s·(gc) |
| 468 | o28·=·2 | 468 | o28·=·2 |
| 469 | i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) | 469 | i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) |
| 470 | ·--·used·0.2 | 470 | ·--·used·0.263386s·(cpu);·0.177442s·(thread);·0s·(gc) |
| 471 | o29·=·3 | 471 | o29·=·3 |
| 472 | i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) | 472 | i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) |
| 473 | ·--·used·0. | 473 | ·--·used·0.357944s·(cpu);·0.280249s·(thread);·0s·(gc) |
| 474 | o30·=·1 | 474 | o30·=·1 |
| 475 | i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) | 475 | i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) |
| 476 | ·--·used·0.2 | 476 | ·--·used·0.277491s·(cpu);·0.184436s·(thread);·0s·(gc) |
| 477 | o31·=·2 | 477 | o31·=·2 |
| 478 | i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) | 478 | i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) |
| 479 | ·--·used·0.2 | 479 | ·--·used·0.266849s·(cpu);·0.176592s·(thread);·0s·(gc) |
| 480 | o32·=·3 | 480 | o32·=·3 |
| 481 | i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm)) | 481 | i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm)) |
| 482 | ·--·used·0.2 | 482 | ·--·used·0.267642s·(cpu);·0.178649s·(thread);·0s·(gc) |
| 483 | o33·=·3 | 483 | o33·=·3 |
| 484 | i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) | 484 | i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) |
| 485 | ·--·used·0.2 | 485 | ·--·used·0.256235s·(cpu);·0.167778s·(thread);·0s·(gc) |
| 486 | o34·=·3 | 486 | o34·=·3 |
| 487 | i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) | 487 | i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) |
| 488 | ·--·used· | 488 | ·--·used·10.9639s·(cpu);·7.55967s·(thread);·0s·(gc) |
| 489 | o35·=·1 | 489 | o35·=·1 |
| 490 | i36·:·peek·StrategyDefault | 490 | i36·:·peek·StrategyDefault |
| 491 | o36·=·OptionTable{GRevLexLargest·=>·0······} | 491 | o36·=·OptionTable{GRevLexLargest·=>·0······} |
| 492 | ··················GRevLexSmallest·=>·16 | 492 | ··················GRevLexSmallest·=>·16 |
| Offset 514, 15 lines modified | Offset 514, 15 lines modified | ||
| 514 | ··················LexSmallest·=>·16 | 514 | ··················LexSmallest·=>·16 |
| 515 | ··················LexSmallestTerm·=>·16 | 515 | ··················LexSmallestTerm·=>·16 |
| 516 | ··················Points·=>·0 | 516 | ··················Points·=>·0 |
| 517 | ··················Random·=>·16 | 517 | ··················Random·=>·16 |
| 518 | ··················RandomNonzero·=>·16 | 518 | ··················RandomNonzero·=>·16 |
| 519 | i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true); | 519 | i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true); |
| 520 | ·--·used·0. | 520 | ·--·used·0.457038s·(cpu);·0.329306s·(thread);·0s·(gc) |
| 521 | internalChooseMinor:·Choosing·Random | 521 | internalChooseMinor:·Choosing·Random |
| 522 | internalChooseMinor:·Choosing·LexSmallest | 522 | internalChooseMinor:·Choosing·LexSmallest |
| 523 | internalChooseMinor:·Choosing·Random | 523 | internalChooseMinor:·Choosing·Random |
| 524 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 524 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 525 | internalChooseMinor:·Choosing·RandomNonZero | 525 | internalChooseMinor:·Choosing·RandomNonZero |
| 526 | internalChooseMinor:·Choosing·RandomNonZero | 526 | internalChooseMinor:·Choosing·RandomNonZero |
| 527 | internalChooseMinor:·Choosing·LexSmallest | 527 | internalChooseMinor:·Choosing·LexSmallest |
| Offset 582, 15 lines modified | Offset 582, 15 lines modified | ||
| 582 | i41·:·ptsStratGeometric·=·new·OptionTable·from·(options·chooseGoodMinors)#PointOptions; | 582 | i41·:·ptsStratGeometric·=·new·OptionTable·from·(options·chooseGoodMinors)#PointOptions; |
| 583 | i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value | 583 | i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value |
| 584 | o42·=·true | 584 | o42·=·true |
| 585 | i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric)) | 585 | i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric)) |
| 586 | ·--·used·0. | 586 | ·--·used·0.723809s·(cpu);·0.47833s·(thread);·0s·(gc) |
| 587 | o43·=·2 | 587 | o43·=·2 |
| 588 | i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value | 588 | i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value |
| 589 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} | 589 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} |
| 590 | ··················DimensionFunction·=>·dim | 590 | ··················DimensionFunction·=>·dim |
| Offset 605, 47 lines modified | Offset 605, 47 lines modified | ||
| 605 | o44·:·OptionTable | 605 | o44·:·OptionTable |
| 606 | i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value | 606 | i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value |
| 607 | o45·=·false | 607 | o45·=·false |
| 608 | i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational)) | 608 | i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational)) |
| 609 | ·--·used·0. | 609 | ·--·used·0.631258s·(cpu);·0.433472s·(thread);·0s·(gc) |
| 610 | o46·=·2 | 610 | o46·=·2 |
| 611 | i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault) | 611 | i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault) |
| 612 | ·--·used·3. | 612 | ·--·used·3.91007s·(cpu);·3.14554s·(thread);·0s·(gc) |
| 613 | i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom) | 613 | i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom) |
| 614 | ·--·used·0. | 614 | ·--·used·0.884992s·(cpu);·0.645128s·(thread);·0s·(gc) |
| 615 | o48·=·true | 615 | o48·=·true |
| 616 | i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) | 616 | i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) |
| 617 | ·--·used· | 617 | ·--·used·3.05851s·(cpu);·2.67863s·(thread);·0s·(gc) |
| 618 | i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest) | 618 | i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest) |
| 619 | ·--·used· | 619 | ·--·used·3.03217s·(cpu);·2.06215s·(thread);·0s·(gc) |
| 620 | i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallestTerm) | 620 | i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallestTerm) |
| 621 | ·--·used·0. | 621 | ·--·used·0.948219s·(cpu);·0.73611s·(thread);·0s·(gc) |
| 622 | o51·=·true | 622 | o51·=·true |
| 623 | i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallest) | 623 | i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallest) |
| 624 | ·--·used· | 624 | ·--·used·3.18284s·(cpu);·2.14484s·(thread);·0s·(gc) |
| 625 | i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallestTerm) | 625 | i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>GRevLexSmallestTerm) |
| 626 | ·--·used·3.1 | 626 | ·--·used·3.61743s·(cpu);·2.52589s·(thread);·0s·(gc) |
| 627 | i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points) | 627 | i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points) |
| 628 | ·--·used· | 628 | ·--·used·12.297s·(cpu);·8.1522s·(thread);·0s·(gc) |
| 629 | o54·=·true | 629 | o54·=·true |
| 630 | i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultWithPoints) | 630 | i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultWithPoints) |
| 631 | ·--·used· | 631 | ·--·used·9.1619s·(cpu);·6.00415s·(thread);·0s·(gc) |
| Max diff block lines reached; 10/5301 bytes (0.19%) of diff not shown. | |||
| Offset 7, 20 lines modified | Offset 7, 20 lines modified | ||
| 7 | o2·:·Ideal·of·S | 7 | o2·:·Ideal·of·S |
| 8 | i3·:·dim·(S/J) | 8 | i3·:·dim·(S/J) |
| 9 | o3·=·4 | 9 | o3·=·4 |
| 10 | i4·:·time·regularInCodimension(1,·S/J) | 10 | i4·:·time·regularInCodimension(1,·S/J) |
| 11 | ·--·used·0. | 11 | ·--·used·0.780357s·(cpu);·0.555781s·(thread);·0s·(gc) |
| 12 | o4·=·true | 12 | o4·=·true |
| 13 | i5·:·time·regularInCodimension(2,·S/J) | 13 | i5·:·time·regularInCodimension(2,·S/J) |
| 14 | ·--·used· | 14 | ·--·used·8.80657s·(cpu);·6.74172s·(thread);·0s·(gc) |
| 15 | i6·:·time·regularInCodimension(1,·S/J,·Verbose=>true) | 15 | i6·:·time·regularInCodimension(1,·S/J,·Verbose=>true) |
| 16 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·452.908·of·them. | 16 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·452.908·of·them. |
| 17 | regularInCodimension:·About·to·enter·loop | 17 | regularInCodimension:·About·to·enter·loop |
| 18 | internalChooseMinor:·Choosing·LexSmallestTerm | 18 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 19 | internalChooseMinor:·Choosing·Random | 19 | internalChooseMinor:·Choosing·Random |
| 20 | internalChooseMinor:·Choosing·GRevLexSmallest | 20 | internalChooseMinor:·Choosing·GRevLexSmallest |
| Offset 87, 21 lines modified | Offset 87, 21 lines modified | ||
| 87 | internalChooseMinor:·Choosing·LexSmallest | 87 | internalChooseMinor:·Choosing·LexSmallest |
| 88 | internalChooseMinor:·Choosing·LexSmallestTerm | 88 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 89 | internalChooseMinor:·Choosing·LexSmallest | 89 | internalChooseMinor:·Choosing·LexSmallest |
| 90 | internalChooseMinor:·Choosing·Random | 90 | internalChooseMinor:·Choosing·Random |
| 91 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39 | 91 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39 |
| 92 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast | 92 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast |
| 93 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 | 93 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 |
| 94 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used· | 94 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.10381s·(cpu);·0.81332s·(thread);·0s·(gc) |
| 95 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 | 95 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 |
| 96 | o6·=·true | 96 | o6·=·true |
| 97 | i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) | 97 | i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) |
| 98 | ·--·used·0.13 | 98 | ·--·used·0.135019s·(cpu);·0.103851s·(thread);·0s·(gc) |
| 99 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 99 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 100 | regularInCodimension:·About·to·enter·loop | 100 | regularInCodimension:·About·to·enter·loop |
| 101 | internalChooseMinor:·Choosing·Random | 101 | internalChooseMinor:·Choosing·Random |
| 102 | internalChooseMinor:·Choosing·RandomNonZero | 102 | internalChooseMinor:·Choosing·RandomNonZero |
| 103 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 103 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 104 | internalChooseMinor:·Choosing·Random | 104 | internalChooseMinor:·Choosing·Random |
| 105 | internalChooseMinor:·Choosing·Random | 105 | internalChooseMinor:·Choosing·Random |
| Offset 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | internalChooseMinor:·Choosing·LexSmallest | 115 | internalChooseMinor:·Choosing·LexSmallest |
| 116 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10 | 116 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10 |
| 117 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 117 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 118 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 | 118 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 |
| 119 | regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3 | 119 | regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3 |
| 120 | i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true) | 120 | i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true) |
| 121 | ·--·used·0.11 | 121 | ·--·used·0.116705s·(cpu);·0.0869311s·(thread);·0s·(gc) |
| 122 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 122 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 123 | regularInCodimension:·About·to·enter·loop | 123 | regularInCodimension:·About·to·enter·loop |
| 124 | internalChooseMinor:·Choosing·Random | 124 | internalChooseMinor:·Choosing·Random |
| 125 | internalChooseMinor:·Choosing·Random | 125 | internalChooseMinor:·Choosing·Random |
| 126 | internalChooseMinor:·Choosing·Random | 126 | internalChooseMinor:·Choosing·Random |
| 127 | internalChooseMinor:·Choosing·Random | 127 | internalChooseMinor:·Choosing·Random |
| 128 | internalChooseMinor:·Choosing·Random | 128 | internalChooseMinor:·Choosing·Random |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | internalChooseMinor:·Choosing·Random | 137 | internalChooseMinor:·Choosing·Random |
| 138 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10 | 138 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10 |
| 139 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 139 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 140 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 | 140 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 |
| 141 | regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3 | 141 | regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3 |
| 142 | i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true) | 142 | i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true) |
| 143 | ·--·used·0. | 143 | ·--·used·0.509394s·(cpu);·0.401631s·(thread);·0s·(gc) |
| 144 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 144 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 145 | regularInCodimension:·About·to·enter·loop | 145 | regularInCodimension:·About·to·enter·loop |
| 146 | internalChooseMinor:·Choosing·RandomNonZero | 146 | internalChooseMinor:·Choosing·RandomNonZero |
| 147 | internalChooseMinor:·Choosing·Random | 147 | internalChooseMinor:·Choosing·Random |
| 148 | internalChooseMinor:·Choosing·LexSmallest | 148 | internalChooseMinor:·Choosing·LexSmallest |
| 149 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3 | 149 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3 |
| 150 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 150 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| Offset 165, 15 lines modified | Offset 165, 15 lines modified | ||
| 165 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 165 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 166 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10 | 166 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·10,·and·computed·=·10 |
| 167 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 167 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 168 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 | 168 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 |
| 169 | regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3 | 169 | regularInCodimension:··Loop·completed,·submatrices·considered·=·10,·and·computed·=·10.··singular·locus·dimension·appears·to·be·=·3 |
| 170 | i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) | 170 | i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) |
| 171 | ·--·used·0. | 171 | ·--·used·0.607128s·(cpu);·0.447729s·(thread);·0s·(gc) |
| 172 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. | 172 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. |
| 173 | regularInCodimension:·About·to·enter·loop | 173 | regularInCodimension:·About·to·enter·loop |
| 174 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 174 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 175 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 175 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 176 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2 | 176 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2 |
| 177 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 177 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 178 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·4 | 178 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·4 |
| Offset 214, 15 lines modified | Offset 214, 15 lines modified | ||
| 214 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 214 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 215 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·25,·and·computed·=·23 | 215 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·25,·and·computed·=·23 |
| 216 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 216 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 217 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 | 217 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·3 |
| 218 | regularInCodimension:··Loop·completed,·submatrices·considered·=·25,·and·computed·=·23.··singular·locus·dimension·appears·to·be·=·3 | 218 | regularInCodimension:··Loop·completed,·submatrices·considered·=·25,·and·computed·=·23.··singular·locus·dimension·appears·to·be·=·3 |
| 219 | i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true) | 219 | i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true) |
| 220 | ·--·used·0. | 220 | ·--·used·0.40985s·(cpu);·0.278299s·(thread);·0s·(gc) |
| 221 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. | 221 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. |
| 222 | regularInCodimension:·About·to·enter·loop | 222 | regularInCodimension:·About·to·enter·loop |
| 223 | internalChooseMinor:·Choosing·GRevLexSmallest | 223 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 224 | internalChooseMinor:·Choosing·LexSmallest | 224 | internalChooseMinor:·Choosing·LexSmallest |
| 225 | internalChooseMinor:·Choosing·RandomNonZero | 225 | internalChooseMinor:·Choosing·RandomNonZero |
| 226 | internalChooseMinor:·Choosing·RandomNonZero | 226 | internalChooseMinor:·Choosing·RandomNonZero |
| 227 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 227 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 1, 13 lines modified | Offset 1, 13 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·5509279875405941999 | 1 | --·-*-·M2-comint·-*-·hash:·5509279875405941999 |
| 2 | i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2); | 2 | i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2); |
| 3 | i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) | 3 | i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) |
| 4 | ·--·1. | 4 | ·--·1.61954s·elapsed |
| 5 | o2·=·true | 5 | o2·=·true |
| 6 | i3·:·peek·StrategyDefault | 6 | i3·:·peek·StrategyDefault |
| 7 | o3·=·OptionTable{GRevLexLargest·=>·0······} | 7 | o3·=·OptionTable{GRevLexLargest·=>·0······} |
| 8 | ·················GRevLexSmallest·=>·16 | 8 | ·················GRevLexSmallest·=>·16 |
| Offset 16, 12 lines modified | Offset 16, 12 lines modified | ||
| 16 | ·················LexSmallest·=>·16 | 16 | ·················LexSmallest·=>·16 |
| 17 | ·················LexSmallestTerm·=>·16 | 17 | ·················LexSmallestTerm·=>·16 |
| 18 | ·················Points·=>·0 | 18 | ·················Points·=>·0 |
| 19 | ·················Random·=>·16 | 19 | ·················Random·=>·16 |
| 20 | ·················RandomNonzero·=>·16 | 20 | ·················RandomNonzero·=>·16 |
| 21 | i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) | 21 | i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) |
| 22 | ·--·1. | 22 | ·--·1.01929s·elapsed |
| 23 | o4·=·true | 23 | o4·=·true |
| 24 | i5·:· | 24 | i5·:· |
| Offset 16, 29 lines modified | Offset 16, 29 lines modified | ||
| 16 | i5·:·r·=·rank·myDiff; | 16 | i5·:·r·=·rank·myDiff; |
| 17 | i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); | 17 | i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); |
| 18 | o6·:·Ideal·of·R | 18 | o6·:·Ideal·of·R |
| 19 | i7·:·time·isCodimAtLeast(3,·J) | 19 | i7·:·time·isCodimAtLeast(3,·J) |
| 20 | ·--·used· | 20 | ·--·used·7.2586e-05s·(cpu);·0.00234213s·(thread);·0s·(gc) |
| 21 | o7·=·true | 21 | o7·=·true |
| 22 | i8·:·I·=·ideal(x_2^8*x_10^3-3*x_1*x_2^7*x_10^2*x_11+3*x_1^2*x_2^6*x_10*x_11^2-x_1^3*x_2^5*x_11^3,x_5^5*x_6^3*x_11^3-3*x_5^6*x_6^2*x_11^2*x_12+3*x_5^7*x_6*x_11*x_12^2-x_5^8*x_12^3,x_1^5*x_2^3*x_4^3-3*x_1^6*x_2^2*x_4^2*x_5+3*x_1^7*x_2*x_4*x_5^2-x_1^8*x_5^3,x_6^8*x_11^3-3*x_5*x_6^7*x_11^2*x_12+3*x_5^2*x_6^6*x_11*x_12^2-x_5^3*x_6^5*x_12^3,x_8^3*x_10^8-3*x_7*x_8^2*x_10^7*x_11+3*x_7^2*x_8*x_10^6*x_11^2-x_7^3*x_10^5*x_11^3,x_2^8*x_4^3-3*x_1*x_2^7*x_4^2*x_5+3*x_1^2*x_2^6*x_4*x_5^2-x_1^3*x_2^5*x_5^3,-x_6^3*x_11^8+3*x_5*x_6^2*x_11^7*x_12-3*x_5^2*x_6*x_11^6*x_12^2+x_5^3*x_11^5*x_12^3,-x_6^3*x_7^3*x_9^5+3*x_4*x_6^2*x_7^2*x_9^6-3*x_4^2*x_6*x_7*x_9^7+x_4^3*x_9^8,x_8^8*x_10^3-3*x_7*x_8^7*x_10^2*x_11+3*x_7^2*x_8^6*x_10*x_11^2-x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3-3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3); | 22 | i8·:·I·=·ideal(x_2^8*x_10^3-3*x_1*x_2^7*x_10^2*x_11+3*x_1^2*x_2^6*x_10*x_11^2-x_1^3*x_2^5*x_11^3,x_5^5*x_6^3*x_11^3-3*x_5^6*x_6^2*x_11^2*x_12+3*x_5^7*x_6*x_11*x_12^2-x_5^8*x_12^3,x_1^5*x_2^3*x_4^3-3*x_1^6*x_2^2*x_4^2*x_5+3*x_1^7*x_2*x_4*x_5^2-x_1^8*x_5^3,x_6^8*x_11^3-3*x_5*x_6^7*x_11^2*x_12+3*x_5^2*x_6^6*x_11*x_12^2-x_5^3*x_6^5*x_12^3,x_8^3*x_10^8-3*x_7*x_8^2*x_10^7*x_11+3*x_7^2*x_8*x_10^6*x_11^2-x_7^3*x_10^5*x_11^3,x_2^8*x_4^3-3*x_1*x_2^7*x_4^2*x_5+3*x_1^2*x_2^6*x_4*x_5^2-x_1^3*x_2^5*x_5^3,-x_6^3*x_11^8+3*x_5*x_6^2*x_11^7*x_12-3*x_5^2*x_6*x_11^6*x_12^2+x_5^3*x_11^5*x_12^3,-x_6^3*x_7^3*x_9^5+3*x_4*x_6^2*x_7^2*x_9^6-3*x_4^2*x_6*x_7*x_9^7+x_4^3*x_9^8,x_8^8*x_10^3-3*x_7*x_8^7*x_10^2*x_11+3*x_7^2*x_8^6*x_10*x_11^2-x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3-3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3); |
| 23 | ···············ZZ | 23 | ···············ZZ |
| 24 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] | 24 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] |
| 25 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7 | 25 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7 |
| 26 | i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) | 26 | i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) |
| 27 | ·--·used·0.001 | 27 | ·--·used·0.00172631s·(cpu);·0.00220457s·(thread);·0s·(gc) |
| 28 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. | 28 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. |
| 29 | o9·=·true | 29 | o9·=·true |
| 30 | i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) | 30 | i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) |
| 31 | ·--·used·0.00 | 31 | ·--·used·0.00109681s·(cpu);·0.00213519s·(thread);·0s·(gc) |
| 32 | o10·=·true | 32 | o10·=·true |
| 33 | i11·:· | 33 | i11·:· |
| Offset 7, 17 lines modified | Offset 7, 17 lines modified | ||
| 7 | o2·:·Ideal·of·R | 7 | o2·:·Ideal·of·R |
| 8 | i3·:·pdim(module·I) | 8 | i3·:·pdim(module·I) |
| 9 | o3·=·2 | 9 | o3·=·2 |
| 10 | i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) | 10 | i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) |
| 11 | ·--·used·0. | 11 | ·--·used·0.248911s·(cpu);·0.17183s·(thread);·0s·(gc) |
| 12 | o4·=·1 | 12 | o4·=·1 |
| 13 | i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) | 13 | i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) |
| 14 | ·--·used·0.01 | 14 | ·--·used·0.0156454s·(cpu);·0.0163892s·(thread);·0s·(gc) |
| 15 | o5·=·1 | 15 | o5·=·1 |
| 16 | i6·:· | 16 | i6·:· |
| Offset 4, 20 lines modified | Offset 4, 20 lines modified | ||
| 4 | i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); | 4 | i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); |
| 5 | ·············6······7 | 5 | ·············6······7 |
| 6 | o2·:·Matrix·R··<--·R | 6 | o2·:·Matrix·R··<--·R |
| 7 | i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); | 7 | i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); |
| 8 | ·--·used·0. | 8 | ·--·used·0.416259s·(cpu);·0.417722s·(thread);·0s·(gc) |
| 9 | o3·:·Ideal·of·R | 9 | o3·:·Ideal·of·R |
| 10 | i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); | 10 | i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); |
| 11 | ·--·used·1. | 11 | ·--·used·1.18853s·(cpu);·1.07841s·(thread);·0s·(gc) |
| 12 | o4·:·Ideal·of·R | 12 | o4·:·Ideal·of·R |
| 13 | i5·:·I1·==·I2 | 13 | i5·:·I1·==·I2 |
| 14 | o5·=·true | 14 | o5·=·true |
| Offset 17, 44 lines modified | Offset 17, 44 lines modified | ||
| 17 | i6·:·S·=·T/I; | 17 | i6·:·S·=·T/I; |
| 18 | i7·:·dim·S | 18 | i7·:·dim·S |
| 19 | o7·=·3 | 19 | o7·=·3 |
| 20 | i8·:·time·regularInCodimension(1,·S) | 20 | i8·:·time·regularInCodimension(1,·S) |
| 21 | ·--·used·1. | 21 | ·--·used·1.53488s·(cpu);·1.24176s·(thread);·0s·(gc) |
| 22 | o8·=·true | 22 | o8·=·true |
| 23 | i9·:·time·regularInCodimension(2,·S) | 23 | i9·:·time·regularInCodimension(2,·S) |
| 24 | ·--·used· | 24 | ·--·used·6.05837s·(cpu);·4.79633s·(thread);·0s·(gc) |
| 25 | i10·:·R·=·QQ[c,·f,·g,·h]/ideal(g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3-f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h-c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c); | 25 | i10·:·R·=·QQ[c,·f,·g,·h]/ideal(g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3-f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h-c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c); |
| 26 | i11·:·dim(R) | 26 | i11·:·dim(R) |
| 27 | o11·=·2 | 27 | o11·=·2 |
| 28 | i12·:·time·(dim·singularLocus·(R)) | 28 | i12·:·time·(dim·singularLocus·(R)) |
| 29 | ·--·used·0.01 | 29 | ·--·used·0.0147108s·(cpu);·0.0160957s·(thread);·0s·(gc) |
| 30 | o12·=·-1 | 30 | o12·=·-1 |
| 31 | i13·:·time·regularInCodimension(2,·R) | 31 | i13·:·time·regularInCodimension(2,·R) |
| 32 | ·--·used·0. | 32 | ·--·used·0.409309s·(cpu);·0.295977s·(thread);·0s·(gc) |
| 33 | o13·=·true | 33 | o13·=·true |
| 34 | i14·:·time·regularInCodimension(2,·R) | 34 | i14·:·time·regularInCodimension(2,·R) |
| 35 | ·--·used·0. | 35 | ·--·used·0.741773s·(cpu);·0.531034s·(thread);·0s·(gc) |
| 36 | o14·=·true | 36 | o14·=·true |
| 37 | i15·:·time·regularInCodimension(2,·R) | 37 | i15·:·time·regularInCodimension(2,·R) |
| 38 | ·--·used·0.2 | 38 | ·--·used·0.26943s·(cpu);·0.189476s·(thread);·0s·(gc) |
| 39 | o15·=·true | 39 | o15·=·true |
| 40 | i16·:·time·regularInCodimension(2,·S,·Verbose=>true) | 40 | i16·:·time·regularInCodimension(2,·S,·Verbose=>true) |
| 41 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·327.599·of·them. | 41 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·327.599·of·them. |
| 42 | regularInCodimension:·About·to·enter·loop | 42 | regularInCodimension:·About·to·enter·loop |
| 43 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 43 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 386, 15 lines modified | Offset 386, 15 lines modified | ||
| 386 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 386 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 387 | internalChooseMinor:·Choosing·RandomNonZero | 387 | internalChooseMinor:·Choosing·RandomNonZero |
| 388 | internalChooseMinor:·Choosing·LexSmallest | 388 | internalChooseMinor:·Choosing·LexSmallest |
| 389 | internalChooseMinor:·Choosing·Random | 389 | internalChooseMinor:·Choosing·Random |
| 390 | internalChooseMinor:·Choosing·Random | 390 | internalChooseMinor:·Choosing·Random |
| 391 | internalChooseMinor:·Choosing·LexSmallestTerm | 391 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 392 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 392 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 393 | internalChooseMinor:·Choosing·--·used· | 393 | internalChooseMinor:·Choosing·--·used·5.57679s·(cpu);·4.40399s·(thread);·0s·(gc) |
| 394 | ·LexSmallestTerm | 394 | ·LexSmallestTerm |
| 395 | internalChooseMinor:·Choosing·Random | 395 | internalChooseMinor:·Choosing·Random |
| 396 | internalChooseMinor:·Choosing·Random | 396 | internalChooseMinor:·Choosing·Random |
| 397 | internalChooseMinor:·Choosing·GRevLexSmallest | 397 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 398 | internalChooseMinor:·Choosing·RandomNonZero | 398 | internalChooseMinor:·Choosing·RandomNonZero |
| 399 | internalChooseMinor:·Choosing·GRevLexSmallest | 399 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 400 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 400 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 430, 15 lines modified | Offset 430, 15 lines modified | ||
| 430 | internalChooseMinor:·Choosing·Random | 430 | internalChooseMinor:·Choosing·Random |
| 431 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·328,·and·computed·=·186 | 431 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·328,·and·computed·=·186 |
| 432 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 432 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 433 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·1 | 433 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·1 |
| 434 | regularInCodimension:··Loop·completed,·submatrices·considered·=·328,·and·computed·=·186.··singular·locus·dimension·appears·to·be·=·1 | 434 | regularInCodimension:··Loop·completed,·submatrices·considered·=·328,·and·computed·=·186.··singular·locus·dimension·appears·to·be·=·1 |
| 435 | i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) | 435 | i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) |
| 436 | ·--·used· | 436 | ·--·used·1.2407s·(cpu);·1.04568s·(thread);·0s·(gc) |
| 437 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them. | 437 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them. |
| 438 | regularInCodimension:·About·to·enter·loop | 438 | regularInCodimension:·About·to·enter·loop |
| 439 | internalChooseMinor:·Choosing·Random | 439 | internalChooseMinor:·Choosing·Random |
| 440 | internalChooseMinor:·Choosing·Random | 440 | internalChooseMinor:·Choosing·Random |
| 441 | internalChooseMinor:·Choosing·RandomNonZero | 441 | internalChooseMinor:·Choosing·RandomNonZero |
| 442 | internalChooseMinor:·Choosing·LexSmallestTerm | 442 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 443 | internalChooseMinor:·Choosing·RandomNonZero | 443 | internalChooseMinor:·Choosing·RandomNonZero |
| Offset 490, 59 lines modified | Offset 490, 59 lines modified | ||
| 490 | i18·:·StrategyCurrent#Random·=·0; | 490 | i18·:·StrategyCurrent#Random·=·0; |
| 491 | i19·:·StrategyCurrent#LexSmallest·=·100; | 491 | i19·:·StrategyCurrent#LexSmallest·=·100; |
| 492 | i20·:·StrategyCurrent#LexSmallestTerm·=·0; | 492 | i20·:·StrategyCurrent#LexSmallestTerm·=·0; |
| 493 | i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 493 | i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 494 | ·--·used·0. | 494 | ·--·used·0.12559s·(cpu);·0.0833173s·(thread);·0s·(gc) |
| 495 | o21·=·true | 495 | o21·=·true |
| 496 | i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 496 | i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 497 | ·--·used·0.1 | 497 | ·--·used·0.183571s·(cpu);·0.138521s·(thread);·0s·(gc) |
| 498 | o22·=·true | 498 | o22·=·true |
| 499 | i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 499 | i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 500 | ·--·used·1. | 500 | ·--·used·1.24476s·(cpu);·0.969224s·(thread);·0s·(gc) |
| 501 | o23·=·true | 501 | o23·=·true |
| 502 | i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 502 | i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 503 | ·--·used· | 503 | ·--·used·1.08859s·(cpu);·0.847396s·(thread);·0s·(gc) |
| 504 | o24·=·true | 504 | o24·=·true |
| 505 | i25·:·StrategyCurrent#LexSmallest·=·0; | 505 | i25·:·StrategyCurrent#LexSmallest·=·0; |
| 506 | i26·:·StrategyCurrent#LexSmallestTerm·=·100; | 506 | i26·:·StrategyCurrent#LexSmallestTerm·=·100; |
| 507 | i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 507 | i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 508 | ·--·used·0. | 508 | ·--·used·0.377744s·(cpu);·0.289806s·(thread);·0s·(gc) |
| 509 | o27·=·true | 509 | o27·=·true |
| 510 | i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 510 | i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 511 | ·--·used· | 511 | ·--·used·2.07495s·(cpu);·1.52945s·(thread);·0s·(gc) |
| 512 | i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 512 | i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 513 | ·--·used·0.1 | 513 | ·--·used·0.159984s·(cpu);·0.124387s·(thread);·0s·(gc) |
| 514 | o29·=·true | 514 | o29·=·true |
| 515 | i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 515 | i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 516 | ·--·used·0.15 | 516 | ·--·used·0.215008s·(cpu);·0.17994s·(thread);·0s·(gc) |
| 517 | o30·=·true | 517 | o30·=·true |
| 518 | i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) | 518 | i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) |
| 519 | ·--·used·1. | 519 | ·--·used·1.56951s·(cpu);·1.31915s·(thread);·0s·(gc) |
| Max diff block lines reached; 208/5650 bytes (3.68%) of diff not shown. | |||
| Offset 558, 57 lines modified | Offset 558, 57 lines modified | ||
| 558 | ········</table> | 558 | ········</table> |
| 559 | ········<div> | 559 | ········<div> |
| 560 | ··········<p>Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.··For·instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that·was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.··In·other·words,·if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/J$·has·dimension·3).</p> | 560 | ··········<p>Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.··For·instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that·was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.··In·other·words,·if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/J$·has·dimension·3).</p> |
| 561 | ········</div> | 561 | ········</div> |
| 562 | ········<table·class="examples"> | 562 | ········<table·class="examples"> |
| 563 | ··········<tr> | 563 | ··········<tr> |
| 564 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) | 564 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) |
| 565 | ·--·used·0. | 565 | ·--·used·0.119366s·(cpu);·0.119073s·(thread);·0s·(gc) |
| 566 | o28·=·2</code></pre> | 566 | o28·=·2</code></pre> |
| 567 | </td>··········</tr> | 567 | </td>··········</tr> |
| 568 | ··········<tr> | 568 | ··········<tr> |
| 569 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) | 569 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) |
| 570 | ·--·used·0.2 | 570 | ·--·used·0.263386s·(cpu);·0.177442s·(thread);·0s·(gc) |
| 571 | o29·=·3</code></pre> | 571 | o29·=·3</code></pre> |
| 572 | </td>··········</tr> | 572 | </td>··········</tr> |
| 573 | ··········<tr> | 573 | ··········<tr> |
| 574 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) | 574 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) |
| 575 | ·--·used·0. | 575 | ·--·used·0.357944s·(cpu);·0.280249s·(thread);·0s·(gc) |
| 576 | o30·=·1</code></pre> | 576 | o30·=·1</code></pre> |
| 577 | </td>··········</tr> | 577 | </td>··········</tr> |
| 578 | ··········<tr> | 578 | ··········<tr> |
| 579 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) | 579 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) |
| 580 | ·--·used·0.2 | 580 | ·--·used·0.277491s·(cpu);·0.184436s·(thread);·0s·(gc) |
| 581 | o31·=·2</code></pre> | 581 | o31·=·2</code></pre> |
| 582 | </td>··········</tr> | 582 | </td>··········</tr> |
| 583 | ··········<tr> | 583 | ··········<tr> |
| 584 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) | 584 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) |
| 585 | ·--·used·0.2 | 585 | ·--·used·0.266849s·(cpu);·0.176592s·(thread);·0s·(gc) |
| 586 | o32·=·3</code></pre> | 586 | o32·=·3</code></pre> |
| 587 | </td>··········</tr> | 587 | </td>··········</tr> |
| 588 | ··········<tr> | 588 | ··········<tr> |
| 589 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm)) | 589 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm)) |
| 590 | ·--·used·0.2 | 590 | ·--·used·0.267642s·(cpu);·0.178649s·(thread);·0s·(gc) |
| 591 | o33·=·3</code></pre> | 591 | o33·=·3</code></pre> |
| 592 | </td>··········</tr> | 592 | </td>··········</tr> |
| 593 | ··········<tr> | 593 | ··········<tr> |
| 594 | <td>··············<pre><code·class="language-macaulay2">i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) | 594 | <td>··············<pre><code·class="language-macaulay2">i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) |
| 595 | ·--·used·0.2 | 595 | ·--·used·0.256235s·(cpu);·0.167778s·(thread);·0s·(gc) |
| 596 | o34·=·3</code></pre> | 596 | o34·=·3</code></pre> |
| 597 | </td>··········</tr> | 597 | </td>··········</tr> |
| 598 | ··········<tr> | 598 | ··········<tr> |
| 599 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) | 599 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) |
| 600 | ·--·used· | 600 | ·--·used·10.9639s·(cpu);·7.55967s·(thread);·0s·(gc) |
| 601 | o35·=·1</code></pre> | 601 | o35·=·1</code></pre> |
| 602 | </td>··········</tr> | 602 | </td>··········</tr> |
| 603 | ········</table> | 603 | ········</table> |
| 604 | ········<div> | 604 | ········<div> |
| 605 | ··········<p>Indeed,·in·this·example,·even·computing·determinants·of·1,000·random·submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in·codimension·1.··On·the·other·hand,·<span·class="tt">Points</span>·is·almost·always·quite·effective·at·finding·valuable·submatrices,·but·can·be·quite·slow.··In·this·particular·example,·we·can·see·that·<span·class="tt">LexSmallestTerm</span>·also·performs·very·well·(and·does·it·quickly).·Since·different·strategies·work·better·or·worse·on·different·examples,·the·default·strategy·actually·mixes·and·matches·various·strategies.··The·default·strategy,·which·we·now·elucidate,</p> | 605 | ··········<p>Indeed,·in·this·example,·even·computing·determinants·of·1,000·random·submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in·codimension·1.··On·the·other·hand,·<span·class="tt">Points</span>·is·almost·always·quite·effective·at·finding·valuable·submatrices,·but·can·be·quite·slow.··In·this·particular·example,·we·can·see·that·<span·class="tt">LexSmallestTerm</span>·also·performs·very·well·(and·does·it·quickly).·Since·different·strategies·work·better·or·worse·on·different·examples,·the·default·strategy·actually·mixes·and·matches·various·strategies.··The·default·strategy,·which·we·now·elucidate,</p> |
| 606 | ········</div> | 606 | ········</div> |
| Offset 629, 15 lines modified | Offset 629, 15 lines modified | ||
| 629 | ········</table> | 629 | ········</table> |
| 630 | ········<div> | 630 | ········<div> |
| 631 | ··········<p>says·that·we·should·use·<span·class="tt">GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest,·LexSmallestTerm,·Random,·RandomNonzero</span>·all·with·equal·probability·(note·<span·class="tt">RandomNonzero</span>,·which·we·have·not·yet·discussed·chooses·random·submatrices·where·no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).··For·instance,·if·we·run:</p> | 631 | ··········<p>says·that·we·should·use·<span·class="tt">GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest,·LexSmallestTerm,·Random,·RandomNonzero</span>·all·with·equal·probability·(note·<span·class="tt">RandomNonzero</span>,·which·we·have·not·yet·discussed·chooses·random·submatrices·where·no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).··For·instance,·if·we·run:</p> |
| 632 | ········</div> | 632 | ········</div> |
| 633 | ········<table·class="examples"> | 633 | ········<table·class="examples"> |
| 634 | ··········<tr> | 634 | ··········<tr> |
| 635 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true); | 635 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true); |
| 636 | ·--·used·0. | 636 | ·--·used·0.457038s·(cpu);·0.329306s·(thread);·0s·(gc) |
| 637 | internalChooseMinor:·Choosing·Random | 637 | internalChooseMinor:·Choosing·Random |
| 638 | internalChooseMinor:·Choosing·LexSmallest | 638 | internalChooseMinor:·Choosing·LexSmallest |
| 639 | internalChooseMinor:·Choosing·Random | 639 | internalChooseMinor:·Choosing·Random |
| 640 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 640 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 641 | internalChooseMinor:·Choosing·RandomNonZero | 641 | internalChooseMinor:·Choosing·RandomNonZero |
| 642 | internalChooseMinor:·Choosing·RandomNonZero | 642 | internalChooseMinor:·Choosing·RandomNonZero |
| 643 | internalChooseMinor:·Choosing·LexSmallest | 643 | internalChooseMinor:·Choosing·LexSmallest |
| Offset 728, 15 lines modified | Offset 728, 15 lines modified | ||
| 728 | ··········<tr> | 728 | ··········<tr> |
| 729 | <td>··············<pre><code·class="language-macaulay2">i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value | 729 | <td>··············<pre><code·class="language-macaulay2">i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value |
| 730 | o42·=·true</code></pre> | 730 | o42·=·true</code></pre> |
| 731 | </td>··········</tr> | 731 | </td>··········</tr> |
| 732 | ··········<tr> | 732 | ··········<tr> |
| 733 | <td>··············<pre><code·class="language-macaulay2">i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric)) | 733 | <td>··············<pre><code·class="language-macaulay2">i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric)) |
| 734 | ·--·used·0. | 734 | ·--·used·0.723809s·(cpu);·0.47833s·(thread);·0s·(gc) |
| 735 | o43·=·2</code></pre> | 735 | o43·=·2</code></pre> |
| 736 | </td>··········</tr> | 736 | </td>··········</tr> |
| 737 | ··········<tr> | 737 | ··········<tr> |
| 738 | <td>··············<pre><code·class="language-macaulay2">i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value | 738 | <td>··············<pre><code·class="language-macaulay2">i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value |
| 739 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} | 739 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} |
| Offset 754, 67 lines modified | Offset 754, 67 lines modified | ||
| 754 | ··········<tr> | 754 | ··········<tr> |
| 755 | <td>··············<pre><code·class="language-macaulay2">i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value | 755 | <td>··············<pre><code·class="language-macaulay2">i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value |
| 756 | o45·=·false</code></pre> | 756 | o45·=·false</code></pre> |
| 757 | </td>··········</tr> | 757 | </td>··········</tr> |
| 758 | ··········<tr> | 758 | ··········<tr> |
| 759 | <td>··············<pre><code·class="language-macaulay2">i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational)) | 759 | <td>··············<pre><code·class="language-macaulay2">i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational)) |
| 760 | ·--·used·0. | 760 | ·--·used·0.631258s·(cpu);·0.433472s·(thread);·0s·(gc) |
| 761 | o46·=·2</code></pre> | 761 | o46·=·2</code></pre> |
| 762 | </td>··········</tr> | 762 | </td>··········</tr> |
| 763 | ········</table> | 763 | ········</table> |
| 764 | ········<div> | 764 | ········<div> |
| 765 | ··········<p>Other·options·may·also·be·passed·to·the·<a·title="Obtain·random·points·in·a·variety"·href="../../RandomPoints/html/index.html">RandomPoints</a>·package·via·the·<a·title="options·to·pass·to·functions·in·the·package·RandomPoints"·href="___Point__Options.html">PointOptions</a>·option.</p> | 765 | ··········<p>Other·options·may·also·be·passed·to·the·<a·title="Obtain·random·points·in·a·variety"·href="../../RandomPoints/html/index.html">RandomPoints</a>·package·via·the·<a·title="options·to·pass·to·functions·in·the·package·RandomPoints"·href="___Point__Options.html">PointOptions</a>·option.</p> |
| 766 | ········</div> | 766 | ········</div> |
| 767 | ········<div> | 767 | ········<div> |
| 768 | ··········<p><b>regularInCodimension:</b>··It·is·reasonable·to·think·that·you·should·find·a·few·minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have·computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.··This·is·exactly·what·<span·class="tt">regularInCodimension</span>·does.··One·can·control·at·a·fine·level·how·frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we·have·computed·so·far·is·checked,·by·the·option·<span·class="tt">codimCheckFunction</span>.··For·more·on·that,·see·<a·title="A·tutorial·for·how·to·use·the·advanced·options·of·the·regularInCodimension·function"·href="___Regular__In__Codimension__Tutorial.html">RegularInCodimensionTutorial</a>·and·<a·title="attempts·to·show·that·the·ring·is·regular·in·codimension·n"·href="_regular__In__Codimension.html">regularInCodimension</a>.··Let·us·finish·running·<span·class="tt">regularInCodimension</span>·on·our·example·with·several·different·strategies.</p> | 768 | ··········<p><b>regularInCodimension:</b>··It·is·reasonable·to·think·that·you·should·find·a·few·minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have·computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.··This·is·exactly·what·<span·class="tt">regularInCodimension</span>·does.··One·can·control·at·a·fine·level·how·frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we·have·computed·so·far·is·checked,·by·the·option·<span·class="tt">codimCheckFunction</span>.··For·more·on·that,·see·<a·title="A·tutorial·for·how·to·use·the·advanced·options·of·the·regularInCodimension·function"·href="___Regular__In__Codimension__Tutorial.html">RegularInCodimensionTutorial</a>·and·<a·title="attempts·to·show·that·the·ring·is·regular·in·codimension·n"·href="_regular__In__Codimension.html">regularInCodimension</a>.··Let·us·finish·running·<span·class="tt">regularInCodimension</span>·on·our·example·with·several·different·strategies.</p> |
| 769 | ········</div> | 769 | ········</div> |
| 770 | ········<table·class="examples"> | 770 | ········<table·class="examples"> |
| 771 | ··········<tr> | 771 | ··········<tr> |
| 772 | <td>··············<pre><code·class="language-macaulay2">i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault) | 772 | <td>··············<pre><code·class="language-macaulay2">i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault) |
| 773 | ·--·used·3. | 773 | ·--·used·3.91007s·(cpu);·3.14554s·(thread);·0s·(gc)</code></pre> |
| 774 | </td>··········</tr> | 774 | </td>··········</tr> |
| 775 | ··········<tr> | 775 | ··········<tr> |
| 776 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom) | 776 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom) |
| 777 | ·--·used·0. | 777 | ·--·used·0.884992s·(cpu);·0.645128s·(thread);·0s·(gc) |
| 778 | o48·=·true</code></pre> | 778 | o48·=·true</code></pre> |
| 779 | </td>··········</tr> | 779 | </td>··········</tr> |
| 780 | ··········<tr> | 780 | ··········<tr> |
| 781 | <td>··············<pre><code·class="language-macaulay2">i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) | 781 | <td>··············<pre><code·class="language-macaulay2">i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) |
| 782 | ·--·used· | 782 | ·--·used·3.05851s·(cpu);·2.67863s·(thread);·0s·(gc)</code></pre> |
| 783 | </td>··········</tr> | 783 | </td>··········</tr> |
| 784 | ··········<tr> | 784 | ··········<tr> |
| 785 | <td>··············<pre><code·class="language-macaulay2">i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest) | 785 | <td>··············<pre><code·class="language-macaulay2">i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest) |
| 786 | ·--·used· | 786 | ·--·used·3.03217s·(cpu);·2.06215s·(thread);·0s·(gc)</code></pre> |
| 787 | </td>··········</tr> | 787 | </td>··········</tr> |
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| Offset 486, 44 lines modified | Offset 486, 44 lines modified | ||
| 486 | o27·:·Ideal·of·S | 486 | o27·:·Ideal·of·S |
| 487 | Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.·For | 487 | Here·the·$1$·passed·to·the·function·says·how·many·minors·to·compute.·For |
| 488 | instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that | 488 | instance,·let's·compute·8·minors·for·each·of·these·strategies·and·see·if·that |
| 489 | was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.·In·other·words, | 489 | was·enough·to·verify·that·the·ring·is·regular·in·codimension·1.·In·other·words, |
| 490 | if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/ | 490 | if·the·dimension·of·$J$·plus·the·ideal·of·partial·minors·is·$\leq·1$·(since·$S/ |
| 491 | J$·has·dimension·3). | 491 | J$·has·dimension·3). |
| 492 | i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) | 492 | i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) |
| 493 | ·--·used·0. | 493 | ·--·used·0.119366s·(cpu);·0.119073s·(thread);·0s·(gc) |
| 494 | o28·=·2 | 494 | o28·=·2 |
| 495 | i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) | 495 | i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) |
| 496 | ·--·used·0.2 | 496 | ·--·used·0.263386s·(cpu);·0.177442s·(thread);·0s·(gc) |
| 497 | o29·=·3 | 497 | o29·=·3 |
| 498 | i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) | 498 | i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) |
| 499 | ·--·used·0. | 499 | ·--·used·0.357944s·(cpu);·0.280249s·(thread);·0s·(gc) |
| 500 | o30·=·1 | 500 | o30·=·1 |
| 501 | i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) | 501 | i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) |
| 502 | ·--·used·0.2 | 502 | ·--·used·0.277491s·(cpu);·0.184436s·(thread);·0s·(gc) |
| 503 | o31·=·2 | 503 | o31·=·2 |
| 504 | i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) | 504 | i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) |
| 505 | ·--·used·0.2 | 505 | ·--·used·0.266849s·(cpu);·0.176592s·(thread);·0s·(gc) |
| 506 | o32·=·3 | 506 | o32·=·3 |
| 507 | i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J, | 507 | i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J, |
| 508 | Strategy=>GRevLexSmallestTerm)) | 508 | Strategy=>GRevLexSmallestTerm)) |
| 509 | ·--·used·0.2 | 509 | ·--·used·0.267642s·(cpu);·0.178649s·(thread);·0s·(gc) |
| 510 | o33·=·3 | 510 | o33·=·3 |
| 511 | i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) | 511 | i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) |
| 512 | ·--·used·0.2 | 512 | ·--·used·0.256235s·(cpu);·0.167778s·(thread);·0s·(gc) |
| 513 | o34·=·3 | 513 | o34·=·3 |
| 514 | i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) | 514 | i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) |
| 515 | ·--·used· | 515 | ·--·used·10.9639s·(cpu);·7.55967s·(thread);·0s·(gc) |
| 516 | o35·=·1 | 516 | o35·=·1 |
| 517 | Indeed,·in·this·example,·even·computing·determinants·of·1,000·random | 517 | Indeed,·in·this·example,·even·computing·determinants·of·1,000·random |
| 518 | submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in | 518 | submatrices·is·not·typically·enough·to·verify·that·$V(J)$·is·regular·in |
| 519 | codimension·1.·On·the·other·hand,·Points·is·almost·always·quite·effective·at | 519 | codimension·1.·On·the·other·hand,·Points·is·almost·always·quite·effective·at |
| 520 | finding·valuable·submatrices,·but·can·be·quite·slow.·In·this·particular | 520 | finding·valuable·submatrices,·but·can·be·quite·slow.·In·this·particular |
| 521 | example,·we·can·see·that·LexSmallestTerm·also·performs·very·well·(and·does·it | 521 | example,·we·can·see·that·LexSmallestTerm·also·performs·very·well·(and·does·it |
| Offset 544, 15 lines modified | Offset 544, 15 lines modified | ||
| 544 | says·that·we·should·use·GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest, | 544 | says·that·we·should·use·GRevLexSmallest,·GRevLexSmallestTerm,·LexSmallest, |
| 545 | LexSmallestTerm,·Random,·RandomNonzero·all·with·equal·probability·(note | 545 | LexSmallestTerm,·Random,·RandomNonzero·all·with·equal·probability·(note |
| 546 | RandomNonzero,·which·we·have·not·yet·discussed·chooses·random·submatrices·where | 546 | RandomNonzero,·which·we·have·not·yet·discussed·chooses·random·submatrices·where |
| 547 | no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).·For | 547 | no·row·or·column·is·zero,·which·is·good·for·working·in·sparse·matrices).·For |
| 548 | instance,·if·we·run: | 548 | instance,·if·we·run: |
| 549 | i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault, | 549 | i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault, |
| 550 | Verbose=>true); | 550 | Verbose=>true); |
| 551 | ·--·used·0. | 551 | ·--·used·0.457038s·(cpu);·0.329306s·(thread);·0s·(gc) |
| 552 | internalChooseMinor:·Choosing·Random | 552 | internalChooseMinor:·Choosing·Random |
| 553 | internalChooseMinor:·Choosing·LexSmallest | 553 | internalChooseMinor:·Choosing·LexSmallest |
| 554 | internalChooseMinor:·Choosing·Random | 554 | internalChooseMinor:·Choosing·Random |
| 555 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 555 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 556 | internalChooseMinor:·Choosing·RandomNonZero | 556 | internalChooseMinor:·Choosing·RandomNonZero |
| 557 | internalChooseMinor:·Choosing·RandomNonZero | 557 | internalChooseMinor:·Choosing·RandomNonZero |
| 558 | internalChooseMinor:·Choosing·LexSmallest | 558 | internalChooseMinor:·Choosing·LexSmallest |
| Offset 633, 15 lines modified | Offset 633, 15 lines modified | ||
| 633 | i41·:·ptsStratGeometric·=·new·OptionTable·from·(options | 633 | i41·:·ptsStratGeometric·=·new·OptionTable·from·(options |
| 634 | chooseGoodMinors)#PointOptions; | 634 | chooseGoodMinors)#PointOptions; |
| 635 | i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value | 635 | i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value |
| 636 | o42·=·true | 636 | o42·=·true |
| 637 | i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points, | 637 | i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points, |
| 638 | PointOptions=>ptsStratGeometric)) | 638 | PointOptions=>ptsStratGeometric)) |
| 639 | ·--·used·0. | 639 | ·--·used·0.723809s·(cpu);·0.47833s·(thread);·0s·(gc) |
| 640 | o43·=·2 | 640 | o43·=·2 |
| 641 | i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that | 641 | i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that |
| 642 | value | 642 | value |
| 643 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} | 643 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} |
| 644 | ··················DimensionFunction·=>·dim | 644 | ··················DimensionFunction·=>·dim |
| Offset 655, 58 lines modified | Offset 655, 58 lines modified | ||
| 655 | o44·:·OptionTable | 655 | o44·:·OptionTable |
| 656 | i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value | 656 | i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value |
| 657 | o45·=·false | 657 | o45·=·false |
| 658 | i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points, | 658 | i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points, |
| 659 | PointOptions=>ptsStratRational)) | 659 | PointOptions=>ptsStratRational)) |
| 660 | ·--·used·0. | 660 | ·--·used·0.631258s·(cpu);·0.433472s·(thread);·0s·(gc) |
| 661 | o46·=·2 | 661 | o46·=·2 |
| 662 | Other·options·may·also·be·passed·to·the·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s·package·via·the | 662 | Other·options·may·also·be·passed·to·the·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s·package·via·the |
| 663 | _\x8P_\x8o_\x8i_\x8n_\x8t_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s·option. | 663 | _\x8P_\x8o_\x8i_\x8n_\x8t_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s·option. |
| 664 | r\x8re\x8eg\x8gu\x8ul\x8la\x8ar\x8rI\x8In\x8nC\x8Co\x8od\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n:\x8:·It·is·reasonable·to·think·that·you·should·find·a·few | 664 | r\x8re\x8eg\x8gu\x8ul\x8la\x8ar\x8rI\x8In\x8nC\x8Co\x8od\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n:\x8:·It·is·reasonable·to·think·that·you·should·find·a·few |
| 665 | minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have | 665 | minors·(with·one·strategy·or·another),·and·see·if·perhaps·the·minors·you·have |
| 666 | computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.·This | 666 | computed·so·far·are·enough·to·verify·our·ring·is·regular·in·codimension·1.·This |
| 667 | is·exactly·what·regularInCodimension·does.·One·can·control·at·a·fine·level·how | 667 | is·exactly·what·regularInCodimension·does.·One·can·control·at·a·fine·level·how |
| 668 | frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we | 668 | frequently·new·minors·are·computed,·and·how·frequently·the·dimension·of·what·we |
| 669 | have·computed·so·far·is·checked,·by·the·option·codimCheckFunction.·For·more·on | 669 | have·computed·so·far·is·checked,·by·the·option·codimCheckFunction.·For·more·on |
| 670 | that,·see·_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8T_\x8u_\x8t_\x8o_\x8r_\x8i_\x8a_\x8l·and·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n.·Let·us·finish | 670 | that,·see·_\x8R_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8T_\x8u_\x8t_\x8o_\x8r_\x8i_\x8a_\x8l·and·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n.·Let·us·finish |
| 671 | running·regularInCodimension·on·our·example·with·several·different·strategies. | 671 | running·regularInCodimension·on·our·example·with·several·different·strategies. |
| 672 | i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 672 | i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 673 | Strategy=>StrategyDefault) | 673 | Strategy=>StrategyDefault) |
| 674 | ·--·used·3. | 674 | ·--·used·3.91007s·(cpu);·3.14554s·(thread);·0s·(gc) |
| 675 | i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 675 | i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 676 | Strategy=>StrategyDefaultNonRandom) | 676 | Strategy=>StrategyDefaultNonRandom) |
| 677 | ·--·used·0. | 677 | ·--·used·0.884992s·(cpu);·0.645128s·(thread);·0s·(gc) |
| 678 | o48·=·true | 678 | o48·=·true |
| 679 | i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) | 679 | i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) |
| 680 | ·--·used· | 680 | ·--·used·3.05851s·(cpu);·2.67863s·(thread);·0s·(gc) |
| 681 | i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 681 | i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 682 | Strategy=>LexSmallest) | 682 | Strategy=>LexSmallest) |
| 683 | ·--·used· | 683 | ·--·used·3.03217s·(cpu);·2.06215s·(thread);·0s·(gc) |
| 684 | i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 684 | i51·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 685 | Strategy=>LexSmallestTerm) | 685 | Strategy=>LexSmallestTerm) |
| 686 | ·--·used·0. | 686 | ·--·used·0.948219s·(cpu);·0.73611s·(thread);·0s·(gc) |
| 687 | o51·=·true | 687 | o51·=·true |
| 688 | i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 688 | i52·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 689 | Strategy=>GRevLexSmallest) | 689 | Strategy=>GRevLexSmallest) |
| 690 | ·--·used· | 690 | ·--·used·3.18284s·(cpu);·2.14484s·(thread);·0s·(gc) |
| 691 | i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 691 | i53·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 692 | Strategy=>GRevLexSmallestTerm) | 692 | Strategy=>GRevLexSmallestTerm) |
| 693 | ·--·used·3.1 | 693 | ·--·used·3.61743s·(cpu);·2.52589s·(thread);·0s·(gc) |
| 694 | i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points) | 694 | i54·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Points) |
| 695 | ·--·used· | 695 | ·--·used·12.297s·(cpu);·8.1522s·(thread);·0s·(gc) |
| 696 | o54·=·true | 696 | o54·=·true |
| 697 | i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, | 697 | i55·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100, |
| 698 | Strategy=>StrategyDefaultWithPoints) | 698 | Strategy=>StrategyDefaultWithPoints) |
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| Offset 67, 21 lines modified | Offset 67, 21 lines modified | ||
| 67 | ········</table> | 67 | ········</table> |
| 68 | ········<div> | 68 | ········<div> |
| 69 | ··········<p>It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.··We·have·embedded·it·with·a·Segre·embedding·inside·$P^8$.··In·particular,·this·example·is·even·regular·in·codimension·3.</p> | 69 | ··········<p>It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.··We·have·embedded·it·with·a·Segre·embedding·inside·$P^8$.··In·particular,·this·example·is·even·regular·in·codimension·3.</p> |
| 70 | ········</div> | 70 | ········</div> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·regularInCodimension(1,·S/J) | 73 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·regularInCodimension(1,·S/J) |
| 74 | ·--·used·0. | 74 | ·--·used·0.780357s·(cpu);·0.555781s·(thread);·0s·(gc) |
| 75 | o4·=·true</code></pre> | 75 | o4·=·true</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·regularInCodimension(2,·S/J) | 78 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·regularInCodimension(2,·S/J) |
| 79 | ·--·used· | 79 | ·--·used·8.80657s·(cpu);·6.74172s·(thread);·0s·(gc)</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ········</table> | 81 | ········</table> |
| 82 | ········<div> | 82 | ········<div> |
| 83 | ··········<p>We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the·ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this·example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the·singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they·generate,·we·instead·compute·a·few·of·them.··<span·class="tt">regularInCodimension</span>·returns·<span·class="tt">true</span>·if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·<span·class="tt">null</span>·if·not.··Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the·execution·time·can·actually·vary·quite·a·bit.···Let's·take·a·look·at·what·is·occurring·by·using·the·<span·class="tt">Verbose</span>·option.··We·go·through·the·output·and·explain·what·each·line·is·telling·us.</p> | 83 | ··········<p>We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the·ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this·example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the·singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they·generate,·we·instead·compute·a·few·of·them.··<span·class="tt">regularInCodimension</span>·returns·<span·class="tt">true</span>·if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·<span·class="tt">null</span>·if·not.··Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the·execution·time·can·actually·vary·quite·a·bit.···Let's·take·a·look·at·what·is·occurring·by·using·the·<span·class="tt">Verbose</span>·option.··We·go·through·the·output·and·explain·what·each·line·is·telling·us.</p> |
| 84 | ········</div> | 84 | ········</div> |
| 85 | ········<table·class="examples"> | 85 | ········<table·class="examples"> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| Offset 154, 27 lines modified | Offset 154, 27 lines modified | ||
| 154 | internalChooseMinor:·Choosing·LexSmallest | 154 | internalChooseMinor:·Choosing·LexSmallest |
| 155 | internalChooseMinor:·Choosing·LexSmallestTerm | 155 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 156 | internalChooseMinor:·Choosing·LexSmallest | 156 | internalChooseMinor:·Choosing·LexSmallest |
| 157 | internalChooseMinor:·Choosing·Random | 157 | internalChooseMinor:·Choosing·Random |
| 158 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39 | 158 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39 |
| 159 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast | 159 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast |
| 160 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 | 160 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 |
| 161 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used· | 161 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.10381s·(cpu);·0.81332s·(thread);·0s·(gc) |
| 162 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 | 162 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 |
| 163 | o6·=·true</code></pre> | 163 | o6·=·true</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ········</table> | 165 | ········</table> |
| 166 | ········<div> | 166 | ········<div> |
| 167 | ··········<p><b>MaxMinors.</b>··The·first·output·says·that·we·will·compute·up·to·452.9·minors·before·giving·up.··We·can·control·that·by·setting·the·option·<span·class="tt">MaxMinors</span>.</p> | 167 | ··········<p><b>MaxMinors.</b>··The·first·output·says·that·we·will·compute·up·to·452.9·minors·before·giving·up.··We·can·control·that·by·setting·the·option·<span·class="tt">MaxMinors</span>.</p> |
| 168 | ········</div> | 168 | ········</div> |
| 169 | ········<table·class="examples"> | 169 | ········<table·class="examples"> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) | 171 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) |
| 172 | ·--·used·0.13 | 172 | ·--·used·0.135019s·(cpu);·0.103851s·(thread);·0s·(gc) |
| 173 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 173 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 174 | regularInCodimension:·About·to·enter·loop | 174 | regularInCodimension:·About·to·enter·loop |
| 175 | internalChooseMinor:·Choosing·Random | 175 | internalChooseMinor:·Choosing·Random |
| 176 | internalChooseMinor:·Choosing·RandomNonZero | 176 | internalChooseMinor:·Choosing·RandomNonZero |
| 177 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 177 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 178 | internalChooseMinor:·Choosing·Random | 178 | internalChooseMinor:·Choosing·Random |
| 179 | internalChooseMinor:·Choosing·Random | 179 | internalChooseMinor:·Choosing·Random |
| Offset 197, 15 lines modified | Offset 197, 15 lines modified | ||
| 197 | ········</div> | 197 | ········</div> |
| 198 | ········<div> | 198 | ········<div> |
| 199 | ··········<p><b>Selecting·submatrices·of·the·Jacobian.</b>··We·also·see·output·like:·``Choosing·LexSmallest''·or·``Choosing·Random''.··This·is·saying·how·we·are·selecting·a·given·submatrix.··For·instance,·we·can·run:</p> | 199 | ··········<p><b>Selecting·submatrices·of·the·Jacobian.</b>··We·also·see·output·like:·``Choosing·LexSmallest''·or·``Choosing·Random''.··This·is·saying·how·we·are·selecting·a·given·submatrix.··For·instance,·we·can·run:</p> |
| 200 | ········</div> | 200 | ········</div> |
| 201 | ········<table·class="examples"> | 201 | ········<table·class="examples"> |
| 202 | ··········<tr> | 202 | ··········<tr> |
| 203 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true) | 203 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true) |
| 204 | ·--·used·0.11 | 204 | ·--·used·0.116705s·(cpu);·0.0869311s·(thread);·0s·(gc) |
| 205 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 205 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 206 | regularInCodimension:·About·to·enter·loop | 206 | regularInCodimension:·About·to·enter·loop |
| 207 | internalChooseMinor:·Choosing·Random | 207 | internalChooseMinor:·Choosing·Random |
| 208 | internalChooseMinor:·Choosing·Random | 208 | internalChooseMinor:·Choosing·Random |
| 209 | internalChooseMinor:·Choosing·Random | 209 | internalChooseMinor:·Choosing·Random |
| 210 | internalChooseMinor:·Choosing·Random | 210 | internalChooseMinor:·Choosing·Random |
| 211 | internalChooseMinor:·Choosing·Random | 211 | internalChooseMinor:·Choosing·Random |
| Offset 228, 15 lines modified | Offset 228, 15 lines modified | ||
| 228 | ········</div> | 228 | ········</div> |
| 229 | ········<div> | 229 | ········<div> |
| 230 | ··········<p><b>Computing·minors·vs·considering·the·dimension·of·what·has·been·computed.</b>··Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have·computed·so·far.··There·are·two·options·to·control·this.··First,·we·can·tell·the·function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of·minors.</p> | 230 | ··········<p><b>Computing·minors·vs·considering·the·dimension·of·what·has·been·computed.</b>··Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have·computed·so·far.··There·are·two·options·to·control·this.··First,·we·can·tell·the·function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of·minors.</p> |
| 231 | ········</div> | 231 | ········</div> |
| 232 | ········<table·class="examples"> | 232 | ········<table·class="examples"> |
| 233 | ··········<tr> | 233 | ··········<tr> |
| 234 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true) | 234 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true) |
| 235 | ·--·used·0. | 235 | ·--·used·0.509394s·(cpu);·0.401631s·(thread);·0s·(gc) |
| 236 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 236 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 237 | regularInCodimension:·About·to·enter·loop | 237 | regularInCodimension:·About·to·enter·loop |
| 238 | internalChooseMinor:·Choosing·RandomNonZero | 238 | internalChooseMinor:·Choosing·RandomNonZero |
| 239 | internalChooseMinor:·Choosing·Random | 239 | internalChooseMinor:·Choosing·Random |
| 240 | internalChooseMinor:·Choosing·LexSmallest | 240 | internalChooseMinor:·Choosing·LexSmallest |
| 241 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3 | 241 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3 |
| 242 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 242 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| Offset 265, 15 lines modified | Offset 265, 15 lines modified | ||
| 265 | ········</div> | 265 | ········</div> |
| 266 | ········<div> | 266 | ········<div> |
| 267 | ··········<p><b>CodimCheckFunction.</b>·The·option·<span·class="tt">CodimCheckFunction</span>·controls·how·frequently·the·dimension·of·the·partial·ideal·of·minors·is·computed.··For·instance,·setting·<span·class="tt">CodimCheckFunction·=>·t·->·t/5</span>·will·say·it·should·compute·dimension·after·every·5·minors·are·examined.··In·general,·after·the·output·of·the·CodimCheckFunction·increases·by·an·integer·we·compute·the·codimension·again.··The·default·function·has·the·space·between·computations·grow·exponentially.</p> | 267 | ··········<p><b>CodimCheckFunction.</b>·The·option·<span·class="tt">CodimCheckFunction</span>·controls·how·frequently·the·dimension·of·the·partial·ideal·of·minors·is·computed.··For·instance,·setting·<span·class="tt">CodimCheckFunction·=>·t·->·t/5</span>·will·say·it·should·compute·dimension·after·every·5·minors·are·examined.··In·general,·after·the·output·of·the·CodimCheckFunction·increases·by·an·integer·we·compute·the·codimension·again.··The·default·function·has·the·space·between·computations·grow·exponentially.</p> |
| 268 | ········</div> | 268 | ········</div> |
| 269 | ········<table·class="examples"> | 269 | ········<table·class="examples"> |
| 270 | ··········<tr> | 270 | ··········<tr> |
| 271 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) | 271 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) |
| 272 | ·--·used·0. | 272 | ·--·used·0.607128s·(cpu);·0.447729s·(thread);·0s·(gc) |
| 273 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. | 273 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. |
| 274 | regularInCodimension:·About·to·enter·loop | 274 | regularInCodimension:·About·to·enter·loop |
| 275 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 275 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 276 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 276 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 277 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2 | 277 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2 |
| 278 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 278 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 279 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·4 | 279 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·4 |
| Offset 320, 15 lines modified | Offset 320, 15 lines modified | ||
| 320 | ········</table> | 320 | ········</table> |
| 321 | ········<div> | 321 | ········<div> |
| 322 | ··········<p><b>isCodimAtLeast·and·dim</b>.··We·see·the·lines·about·the·``isCodimAtLeast·failed''.··This·means·that·<span·class="tt">isCodimAtLeast</span>·was·not·enough·on·its·own·to·verify·that·our·ring·is·regular·in·codimension·1.··After·this,·``partial·singular·locus·dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the·partial·ideal·defining·the·singular·locus.··How·<span·class="tt">isCodimAtLeast</span>·is·called·can·be·controlled·via·the·options·<span·class="tt">SPairsFunction</span>·and·<span·class="tt">PairLimit</span>,·which·are·simply·passed·to·<a·title="returns·true·if·we·can·quickly·see·whether·the·codim·is·at·least·a·given·number"·href="_is__Codim__At__Least.html">isCodimAtLeast</a>.··You·can·force·the·function·to·only·use·<span·class="tt">isCodimAtLeast</span>·and·not·call·dimension·by·setting·<span·class="tt">UseOnlyFastCodim·=>·true</span>.</p> | 322 | ··········<p><b>isCodimAtLeast·and·dim</b>.··We·see·the·lines·about·the·``isCodimAtLeast·failed''.··This·means·that·<span·class="tt">isCodimAtLeast</span>·was·not·enough·on·its·own·to·verify·that·our·ring·is·regular·in·codimension·1.··After·this,·``partial·singular·locus·dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the·partial·ideal·defining·the·singular·locus.··How·<span·class="tt">isCodimAtLeast</span>·is·called·can·be·controlled·via·the·options·<span·class="tt">SPairsFunction</span>·and·<span·class="tt">PairLimit</span>,·which·are·simply·passed·to·<a·title="returns·true·if·we·can·quickly·see·whether·the·codim·is·at·least·a·given·number"·href="_is__Codim__At__Least.html">isCodimAtLeast</a>.··You·can·force·the·function·to·only·use·<span·class="tt">isCodimAtLeast</span>·and·not·call·dimension·by·setting·<span·class="tt">UseOnlyFastCodim·=>·true</span>.</p> |
| 323 | ········</div> | 323 | ········</div> |
| 324 | ········<table·class="examples"> | 324 | ········<table·class="examples"> |
| 325 | ··········<tr> | 325 | ··········<tr> |
| 326 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true) | 326 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true) |
| 327 | ·--·used·0. | 327 | ·--·used·0.40985s·(cpu);·0.278299s·(thread);·0s·(gc) |
| 328 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. | 328 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. |
| 329 | regularInCodimension:·About·to·enter·loop | 329 | regularInCodimension:·About·to·enter·loop |
| 330 | internalChooseMinor:·Choosing·GRevLexSmallest | 330 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 331 | internalChooseMinor:·Choosing·LexSmallest | 331 | internalChooseMinor:·Choosing·LexSmallest |
| 332 | internalChooseMinor:·Choosing·RandomNonZero | 332 | internalChooseMinor:·Choosing·RandomNonZero |
| 333 | internalChooseMinor:·Choosing·RandomNonZero | 333 | internalChooseMinor:·Choosing·RandomNonZero |
| 334 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 334 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 24, 19 lines modified | Offset 24, 19 lines modified | ||
| 24 | i3·:·dim·(S/J) | 24 | i3·:·dim·(S/J) |
| 25 | o3·=·4 | 25 | o3·=·4 |
| 26 | It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.·We·have | 26 | It·is·the·cone·over·$P^2·\times·E$·where·$E$·is·an·elliptic·curve.·We·have |
| 27 | embedded·it·with·a·Segre·embedding·inside·$P^8$.·In·particular,·this·example·is | 27 | embedded·it·with·a·Segre·embedding·inside·$P^8$.·In·particular,·this·example·is |
| 28 | even·regular·in·codimension·3. | 28 | even·regular·in·codimension·3. |
| 29 | i4·:·time·regularInCodimension(1,·S/J) | 29 | i4·:·time·regularInCodimension(1,·S/J) |
| 30 | ·--·used·0. | 30 | ·--·used·0.780357s·(cpu);·0.555781s·(thread);·0s·(gc) |
| 31 | o4·=·true | 31 | o4·=·true |
| 32 | i5·:·time·regularInCodimension(2,·S/J) | 32 | i5·:·time·regularInCodimension(2,·S/J) |
| 33 | ·--·used· | 33 | ·--·used·8.80657s·(cpu);·6.74172s·(thread);·0s·(gc) |
| 34 | We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the | 34 | We·try·to·verify·that·$S/J$·is·regular·in·codimension·1·or·2·by·computing·the |
| 35 | ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this | 35 | ideal·made·up·of·a·small·number·of·minors·of·the·Jacobian·matrix.·In·this |
| 36 | example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the | 36 | example,·instead·of·computing·all·relevant·1465128·minors·to·compute·the |
| 37 | singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they | 37 | singular·locus,·and·then·trying·to·compute·the·dimension·of·the·ideal·they |
| 38 | generate,·we·instead·compute·a·few·of·them.·regularInCodimension·returns·true | 38 | generate,·we·instead·compute·a·few·of·them.·regularInCodimension·returns·true |
| 39 | if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·null | 39 | if·it·verified·that·the·ring·is·regular·in·codim·1·or·2·(respectively)·and·null |
| 40 | if·not.·Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the | 40 | if·not.·Because·of·the·randomness·that·exists·in·terms·of·selecting·minors,·the |
| Offset 121, 22 lines modified | Offset 121, 22 lines modified | ||
| 121 | internalChooseMinor:·Choosing·LexSmallest | 121 | internalChooseMinor:·Choosing·LexSmallest |
| 122 | internalChooseMinor:·Choosing·Random | 122 | internalChooseMinor:·Choosing·Random |
| 123 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices | 123 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices |
| 124 | considered:·49,·and·computed·=·39 | 124 | considered:·49,·and·computed·=·39 |
| 125 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast | 125 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast |
| 126 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 | 126 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 |
| 127 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute | 127 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute |
| 128 | --·used· | 128 | --·used·1.10381s·(cpu);·0.81332s·(thread);·0s·(gc) |
| 129 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 | 129 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 |
| 130 | o6·=·true | 130 | o6·=·true |
| 131 | M\x8Ma\x8ax\x8xM\x8Mi\x8in\x8no\x8or\x8rs\x8s.\x8.·The·first·output·says·that·we·will·compute·up·to·452.9·minors·before | 131 | M\x8Ma\x8ax\x8xM\x8Mi\x8in\x8no\x8or\x8rs\x8s.\x8.·The·first·output·says·that·we·will·compute·up·to·452.9·minors·before |
| 132 | giving·up.·We·can·control·that·by·setting·the·option·MaxMinors. | 132 | giving·up.·We·can·control·that·by·setting·the·option·MaxMinors. |
| 133 | i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) | 133 | i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) |
| 134 | ·--·used·0.13 | 134 | ·--·used·0.135019s·(cpu);·0.103851s·(thread);·0s·(gc) |
| 135 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 | 135 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 |
| 136 | minors,·we·will·compute·up·to·10·of·them. | 136 | minors,·we·will·compute·up·to·10·of·them. |
| 137 | regularInCodimension:·About·to·enter·loop | 137 | regularInCodimension:·About·to·enter·loop |
| 138 | internalChooseMinor:·Choosing·Random | 138 | internalChooseMinor:·Choosing·Random |
| 139 | internalChooseMinor:·Choosing·RandomNonZero | 139 | internalChooseMinor:·Choosing·RandomNonZero |
| 140 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 140 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 141 | internalChooseMinor:·Choosing·Random | 141 | internalChooseMinor:·Choosing·Random |
| Offset 159, 15 lines modified | Offset 159, 15 lines modified | ||
| 159 | There·are·other·finer·ways·to·control·the·MaxMinors·option,·but·they·will·not | 159 | There·are·other·finer·ways·to·control·the·MaxMinors·option,·but·they·will·not |
| 160 | be·discussed·in·this·tutorial.·See·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n. | 160 | be·discussed·in·this·tutorial.·See·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8I_\x8n_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n. |
| 161 | S\x8Se\x8el\x8le\x8ec\x8ct\x8ti\x8in\x8ng\x8g·s\x8su\x8ub\x8bm\x8ma\x8at\x8tr\x8ri\x8ic\x8ce\x8es\x8s·o\x8of\x8f·t\x8th\x8he\x8e·J\x8Ja\x8ac\x8co\x8ob\x8bi\x8ia\x8an\x8n.\x8.·We·also·see·output·like:·``Choosing | 161 | S\x8Se\x8el\x8le\x8ec\x8ct\x8ti\x8in\x8ng\x8g·s\x8su\x8ub\x8bm\x8ma\x8at\x8tr\x8ri\x8ic\x8ce\x8es\x8s·o\x8of\x8f·t\x8th\x8he\x8e·J\x8Ja\x8ac\x8co\x8ob\x8bi\x8ia\x8an\x8n.\x8.·We·also·see·output·like:·``Choosing |
| 162 | LexSmallest''·or·``Choosing·Random''.·This·is·saying·how·we·are·selecting·a | 162 | LexSmallest''·or·``Choosing·Random''.·This·is·saying·how·we·are·selecting·a |
| 163 | given·submatrix.·For·instance,·we·can·run: | 163 | given·submatrix.·For·instance,·we·can·run: |
| 164 | i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom, | 164 | i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom, |
| 165 | Verbose=>true) | 165 | Verbose=>true) |
| 166 | ·--·used·0.11 | 166 | ·--·used·0.116705s·(cpu);·0.0869311s·(thread);·0s·(gc) |
| 167 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 | 167 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 |
| 168 | minors,·we·will·compute·up·to·10·of·them. | 168 | minors,·we·will·compute·up·to·10·of·them. |
| 169 | regularInCodimension:·About·to·enter·loop | 169 | regularInCodimension:·About·to·enter·loop |
| 170 | internalChooseMinor:·Choosing·Random | 170 | internalChooseMinor:·Choosing·Random |
| 171 | internalChooseMinor:·Choosing·Random | 171 | internalChooseMinor:·Choosing·Random |
| 172 | internalChooseMinor:·Choosing·Random | 172 | internalChooseMinor:·Choosing·Random |
| 173 | internalChooseMinor:·Choosing·Random | 173 | internalChooseMinor:·Choosing·Random |
| Offset 197, 15 lines modified | Offset 197, 15 lines modified | ||
| 197 | C\x8Co\x8om\x8mp\x8pu\x8ut\x8ti\x8in\x8ng\x8g·m\x8mi\x8in\x8no\x8or\x8rs\x8s·v\x8vs\x8s·c\x8co\x8on\x8ns\x8si\x8id\x8de\x8er\x8ri\x8in\x8ng\x8g·t\x8th\x8he\x8e·d\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n·o\x8of\x8f·w\x8wh\x8ha\x8at\x8t·h\x8ha\x8as\x8s·b\x8be\x8ee\x8en\x8n·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8ed\x8d.\x8. | 197 | C\x8Co\x8om\x8mp\x8pu\x8ut\x8ti\x8in\x8ng\x8g·m\x8mi\x8in\x8no\x8or\x8rs\x8s·v\x8vs\x8s·c\x8co\x8on\x8ns\x8si\x8id\x8de\x8er\x8ri\x8in\x8ng\x8g·t\x8th\x8he\x8e·d\x8di\x8im\x8me\x8en\x8ns\x8si\x8io\x8on\x8n·o\x8of\x8f·w\x8wh\x8ha\x8at\x8t·h\x8ha\x8as\x8s·b\x8be\x8ee\x8en\x8n·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8ed\x8d.\x8. |
| 198 | Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have | 198 | Periodically·we·compute·the·codimension·of·the·partial·ideal·of·minors·we·have |
| 199 | computed·so·far.·There·are·two·options·to·control·this.·First,·we·can·tell·the | 199 | computed·so·far.·There·are·two·options·to·control·this.·First,·we·can·tell·the |
| 200 | function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of | 200 | function·when·to·first·compute·the·dimension·of·the·working·partial·ideal·of |
| 201 | minors. | 201 | minors. |
| 202 | i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t- | 202 | i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t- |
| 203 | >3,·Verbose=>true) | 203 | >3,·Verbose=>true) |
| 204 | ·--·used·0. | 204 | ·--·used·0.509394s·(cpu);·0.401631s·(thread);·0s·(gc) |
| 205 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 | 205 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 |
| 206 | minors,·we·will·compute·up·to·10·of·them. | 206 | minors,·we·will·compute·up·to·10·of·them. |
| 207 | regularInCodimension:·About·to·enter·loop | 207 | regularInCodimension:·About·to·enter·loop |
| 208 | internalChooseMinor:·Choosing·RandomNonZero | 208 | internalChooseMinor:·Choosing·RandomNonZero |
| 209 | internalChooseMinor:·Choosing·Random | 209 | internalChooseMinor:·Choosing·Random |
| 210 | internalChooseMinor:·Choosing·LexSmallest | 210 | internalChooseMinor:·Choosing·LexSmallest |
| 211 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices | 211 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices |
| Offset 243, 15 lines modified | Offset 243, 15 lines modified | ||
| 243 | dimension·of·the·partial·ideal·of·minors·is·computed.·For·instance,·setting | 243 | dimension·of·the·partial·ideal·of·minors·is·computed.·For·instance,·setting |
| 244 | CodimCheckFunction·=>·t·->·t/5·will·say·it·should·compute·dimension·after·every | 244 | CodimCheckFunction·=>·t·->·t/5·will·say·it·should·compute·dimension·after·every |
| 245 | 5·minors·are·examined.·In·general,·after·the·output·of·the·CodimCheckFunction | 245 | 5·minors·are·examined.·In·general,·after·the·output·of·the·CodimCheckFunction |
| 246 | increases·by·an·integer·we·compute·the·codimension·again.·The·default·function | 246 | increases·by·an·integer·we·compute·the·codimension·again.·The·default·function |
| 247 | has·the·space·between·computations·grow·exponentially. | 247 | has·the·space·between·computations·grow·exponentially. |
| 248 | i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t- | 248 | i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t- |
| 249 | >t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) | 249 | >t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) |
| 250 | ·--·used·0. | 250 | ·--·used·0.607128s·(cpu);·0.447729s·(thread);·0s·(gc) |
| 251 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 | 251 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 |
| 252 | minors,·we·will·compute·up·to·25·of·them. | 252 | minors,·we·will·compute·up·to·25·of·them. |
| 253 | regularInCodimension:·About·to·enter·loop | 253 | regularInCodimension:·About·to·enter·loop |
| 254 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 254 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 255 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 255 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 256 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices | 256 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices |
| 257 | considered:·2,·and·computed·=·2 | 257 | considered:·2,·and·computed·=·2 |
| Offset 308, 15 lines modified | Offset 308, 15 lines modified | ||
| 308 | dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the | 308 | dimension·computed''·indicates·we·did·a·complete·dimension·computation·of·the |
| 309 | partial·ideal·defining·the·singular·locus.·How·isCodimAtLeast·is·called·can·be | 309 | partial·ideal·defining·the·singular·locus.·How·isCodimAtLeast·is·called·can·be |
| 310 | controlled·via·the·options·SPairsFunction·and·PairLimit,·which·are·simply | 310 | controlled·via·the·options·SPairsFunction·and·PairLimit,·which·are·simply |
| 311 | passed·to·_\x8i_\x8s_\x8C_\x8o_\x8d_\x8i_\x8m_\x8A_\x8t_\x8L_\x8e_\x8a_\x8s_\x8t.·You·can·force·the·function·to·only·use·isCodimAtLeast | 311 | passed·to·_\x8i_\x8s_\x8C_\x8o_\x8d_\x8i_\x8m_\x8A_\x8t_\x8L_\x8e_\x8a_\x8s_\x8t.·You·can·force·the·function·to·only·use·isCodimAtLeast |
| 312 | and·not·call·dimension·by·setting·UseOnlyFastCodim·=>·true. | 312 | and·not·call·dimension·by·setting·UseOnlyFastCodim·=>·true. |
| 313 | i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=> | 313 | i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=> |
| 314 | true,·Verbose=>true) | 314 | true,·Verbose=>true) |
| 315 | ·--·used·0. | 315 | ·--·used·0.40985s·(cpu);·0.278299s·(thread);·0s·(gc) |
| 316 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 | 316 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5 |
| 317 | minors,·we·will·compute·up·to·25·of·them. | 317 | minors,·we·will·compute·up·to·25·of·them. |
| 318 | regularInCodimension:·About·to·enter·loop | 318 | regularInCodimension:·About·to·enter·loop |
| 319 | internalChooseMinor:·Choosing·GRevLexSmallest | 319 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 320 | internalChooseMinor:·Choosing·LexSmallest | 320 | internalChooseMinor:·Choosing·LexSmallest |
| 321 | internalChooseMinor:·Choosing·RandomNonZero | 321 | internalChooseMinor:·Choosing·RandomNonZero |
| 322 | internalChooseMinor:·Choosing·RandomNonZero | 322 | internalChooseMinor:·Choosing·RandomNonZero |
| Offset 66, 15 lines modified | Offset 66, 15 lines modified | ||
| 66 | ········</ul> | 66 | ········</ul> |
| 67 | Below·the·details·of·how·these·strategies·are·constructed·will·be·detailed·below.··But·first,·we·provide·an·example·showing·that·these·strategies·can·perform·quite·differently.··The·following·is·the·cone·over·the·product·of·two·elliptic·curves.··We·verify·that·this·ring·is·regular·in·codimension·1·using·different·strategies.··Essentially,·minors·are·computed·until·it·is·verified·that·the·ring·is·regular·in·codimension·1.········<table·class="examples"> | 67 | Below·the·details·of·how·these·strategies·are·constructed·will·be·detailed·below.··But·first,·we·provide·an·example·showing·that·these·strategies·can·perform·quite·differently.··The·following·is·the·cone·over·the·product·of·two·elliptic·curves.··We·verify·that·this·ring·is·regular·in·codimension·1·using·different·strategies.··Essentially,·minors·are·computed·until·it·is·verified·that·the·ring·is·regular·in·codimension·1.········<table·class="examples"> |
| 68 | ··········<tr> | 68 | ··········<tr> |
| 69 | <td>··············<pre><code·class="language-macaulay2">i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);</code></pre> | 69 | <td>··············<pre><code·class="language-macaulay2">i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e-b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g-e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f-a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2-g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3-h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2);</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) | 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) |
| 73 | ·--·1. | 73 | ·--·1.61954s·elapsed |
| 74 | o2·=·true</code></pre> | 74 | o2·=·true</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ········</table> | 76 | ········</table> |
| 77 | In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion·of·each·of·the·above·strategies·after·100·runs.········<ul> | 77 | In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion·of·each·of·the·above·strategies·after·100·runs.········<ul> |
| 78 | ··········<li> | 78 | ··········<li> |
| 79 | <span·class="tt">StrategyDefault</span>:·1.65·seconds··········</li> | 79 | <span·class="tt">StrategyDefault</span>:·1.65·seconds··········</li> |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | <span·class="tt">StrategyPoints</span>:·choose·all·submatrices·via·Points.··········</li> | 137 | <span·class="tt">StrategyPoints</span>:·choose·all·submatrices·via·Points.··········</li> |
| 138 | ··········<li> | 138 | ··········<li> |
| 139 | <span·class="tt">StrategyDefaultWithPoints</span>:·like·<span·class="tt">StrategyDefault</span>·but·replaces·the·<span·class="tt">Random</span>·and·RandomNonZero·submatrices·as·with·matrices·chosen·as·in·Points.··········</li> | 139 | <span·class="tt">StrategyDefaultWithPoints</span>:·like·<span·class="tt">StrategyDefault</span>·but·replaces·the·<span·class="tt">Random</span>·and·RandomNonZero·submatrices·as·with·matrices·chosen·as·in·Points.··········</li> |
| 140 | ········</ul> | 140 | ········</ul> |
| 141 | Additionally,·a·<span·class="tt">MutableHashTable</span>·named·<span·class="tt">StrategyCurrent</span>·is·also·exported.··It·begins·as·the·default·strategy,·but·the·user·can·modify·it.<br><br><b>Using·a·single·heuristic··</b>Alternatively,·if·the·user·only·wants·to·use·say·<span·class="tt">LexSmallestTerm</span>·they·can·set,·<span·class="tt">Strategy</span>·to·point·to·that·symbol,·instead·of·a·creating·a·custom·strategy·HashTable.··For·example:·········<table·class="examples"> | 141 | Additionally,·a·<span·class="tt">MutableHashTable</span>·named·<span·class="tt">StrategyCurrent</span>·is·also·exported.··It·begins·as·the·default·strategy,·but·the·user·can·modify·it.<br><br><b>Using·a·single·heuristic··</b>Alternatively,·if·the·user·only·wants·to·use·say·<span·class="tt">LexSmallestTerm</span>·they·can·set,·<span·class="tt">Strategy</span>·to·point·to·that·symbol,·instead·of·a·creating·a·custom·strategy·HashTable.··For·example:·········<table·class="examples"> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) | 143 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) |
| 144 | ·--·1. | 144 | ·--·1.01929s·elapsed |
| 145 | o4·=·true</code></pre> | 145 | o4·=·true</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ········</table> | 147 | ········</table> |
| 148 | ······</div> | 148 | ······</div> |
| 149 | ······<div·class="waystouse"> | 149 | ······<div·class="waystouse"> |
| 150 | ········<h2>For·the·programmer</h2> | 150 | ········<h2>For·the·programmer</h2> |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e- | 41 | i1·:·T=ZZ/7[a..i]/ideal(f*h-e*i,c*h-b*i,f*g-d*i,e*g-d*h,c*g-a*i,b*g-a*h,c*e- |
| 42 | b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g- | 42 | b*f,c*d-a*f,b*d-a*e,g^3-h^2*i-g*i^2,d*g^2-e*h*i-d*i^2,a*g^2-b*h*i-a*i^2,d^2*g- |
| 43 | e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f- | 43 | e^2*i-d*f*i,a*d*g-b*e*i-a*f*i,a^2*g-b^2*i-a*c*i,d^3-e^2*f-d*f^2,a*d^2-b*e*f- |
| 44 | a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2- | 44 | a*f^2,a^2*d-b^2*f-a*c*f,c^3+f^3-i^3,b*c^2+e*f^2-h*i^2,a*c^2+d*f^2- |
| 45 | g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3- | 45 | g*i^2,b^2*c+e^2*f-h^2*i,a*b*c+d*e*f-g*h*i,a^2*c+d^2*f-g^2*i,b^3+e^3- |
| 46 | h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2); | 46 | h^3,a*b^2+d*e^2-g*h^2,a^2*b+d^2*e-g^2*h,a^3+e^2*f+d*f^2-h^2*i-g*i^2); |
| 47 | i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) | 47 | i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) |
| 48 | ·--·1. | 48 | ·--·1.61954s·elapsed |
| 49 | o2·=·true | 49 | o2·=·true |
| 50 | In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion | 50 | In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion |
| 51 | of·each·of·the·above·strategies·after·100·runs. | 51 | of·each·of·the·above·strategies·after·100·runs. |
| 52 | ····*·StrategyDefault:·1.65·seconds | 52 | ····*·StrategyDefault:·1.65·seconds |
| 53 | ····*·StrategyRandom:·8.32·seconds | 53 | ····*·StrategyRandom:·8.32·seconds |
| 54 | ····*·StrategyDefaultNonRandom:·0.99·seconds | 54 | ····*·StrategyDefaultNonRandom:·0.99·seconds |
| Offset 135, 12 lines modified | Offset 135, 12 lines modified | ||
| 135 | Additionally,·a·MutableHashTable·named·StrategyCurrent·is·also·exported.·It | 135 | Additionally,·a·MutableHashTable·named·StrategyCurrent·is·also·exported.·It |
| 136 | begins·as·the·default·strategy,·but·the·user·can·modify·it. | 136 | begins·as·the·default·strategy,·but·the·user·can·modify·it. |
| 137 | U\x8Us\x8si\x8in\x8ng\x8g·a\x8a·s\x8si\x8in\x8ng\x8gl\x8le\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8c·Alternatively,·if·the·user·only·wants·to·use·say | 137 | U\x8Us\x8si\x8in\x8ng\x8g·a\x8a·s\x8si\x8in\x8ng\x8gl\x8le\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8c·Alternatively,·if·the·user·only·wants·to·use·say |
| 138 | LexSmallestTerm·they·can·set,·Strategy·to·point·to·that·symbol,·instead·of·a | 138 | LexSmallestTerm·they·can·set,·Strategy·to·point·to·that·symbol,·instead·of·a |
| 139 | creating·a·custom·strategy·HashTable.·For·example: | 139 | creating·a·custom·strategy·HashTable.·For·example: |
| 140 | i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) | 140 | i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) |
| 141 | ·--·1. | 141 | ·--·1.01929s·elapsed |
| 142 | o4·=·true | 142 | o4·=·true |
| 143 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 143 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 144 | The·object·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8D_\x8e_\x8f_\x8a_\x8u_\x8l_\x8t·is·an·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8·_\x8t_\x8a_\x8b_\x8l_\x8e. | 144 | The·object·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8D_\x8e_\x8f_\x8a_\x8u_\x8l_\x8t·is·an·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8·_\x8t_\x8a_\x8b_\x8l_\x8e. |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); | 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); |
| 108 | o6·:·Ideal·of·R</code></pre> | 108 | o6·:·Ideal·of·R</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isCodimAtLeast(3,·J) | 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isCodimAtLeast(3,·J) |
| 112 | ·--·used· | 112 | ·--·used·7.2586e-05s·(cpu);·0.00234213s·(thread);·0s·(gc) |
| 113 | o7·=·true</code></pre> | 113 | o7·=·true</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ········</table> | 115 | ········</table> |
| 116 | ········<div> | 116 | ········<div> |
| 117 | ··········<p>The·function·works·by·computing·<span·class="tt">gb(I,·PairLimit=>f(i))</span>·for·successive·values·of·<span·class="tt">i</span>.··Here·<span·class="tt">f(i)</span>·is·a·function·that·takes·<span·class="tt">t</span>,·some·approximation·of·the·base·degree·value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial·ring,·this·is·probably·expected·to·be·<span·class="tt">\{1\}</span>).··And·<span·class="tt">i</span>·is·a·counting·variable.·You·can·provide·your·own·function·by·calling·<span·class="tt">isCodimAtLeast(n,·I,·SPairsFunction=>(·(i)·->·f(i)·)</span>,·the·default·function·is·<span·class="tt">SPairsFunction=>i->ceiling(1.5^i)</span>···Perhaps·more·commonly·however,·the·user·may·want·to·instead·tell·the·function·to·compute·for·larger·values·of·<span·class="tt">i</span>.··This·is·done·via·the·option·<span·class="tt">PairLimit</span>.··This·is·the·max·value·of·<span·class="tt">i</span>·to·be·plugged·into·<span·class="tt">SPairsFunction</span>·before·the·function·gives·up.··In·other·words,·<span·class="tt">PairLimit=>5</span>·will·tell·the·function·to·check·codimension·5·times.</p> | 117 | ··········<p>The·function·works·by·computing·<span·class="tt">gb(I,·PairLimit=>f(i))</span>·for·successive·values·of·<span·class="tt">i</span>.··Here·<span·class="tt">f(i)</span>·is·a·function·that·takes·<span·class="tt">t</span>,·some·approximation·of·the·base·degree·value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial·ring,·this·is·probably·expected·to·be·<span·class="tt">\{1\}</span>).··And·<span·class="tt">i</span>·is·a·counting·variable.·You·can·provide·your·own·function·by·calling·<span·class="tt">isCodimAtLeast(n,·I,·SPairsFunction=>(·(i)·->·f(i)·)</span>,·the·default·function·is·<span·class="tt">SPairsFunction=>i->ceiling(1.5^i)</span>···Perhaps·more·commonly·however,·the·user·may·want·to·instead·tell·the·function·to·compute·for·larger·values·of·<span·class="tt">i</span>.··This·is·done·via·the·option·<span·class="tt">PairLimit</span>.··This·is·the·max·value·of·<span·class="tt">i</span>·to·be·plugged·into·<span·class="tt">SPairsFunction</span>·before·the·function·gives·up.··In·other·words,·<span·class="tt">PairLimit=>5</span>·will·tell·the·function·to·check·codimension·5·times.</p> |
| 118 | ········</div> | 118 | ········</div> |
| Offset 124, 22 lines modified | Offset 124, 22 lines modified | ||
| 124 | ···············ZZ | 124 | ···············ZZ |
| 125 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] | 125 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] |
| 126 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7</code></pre> | 126 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) | 129 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) |
| 130 | ·--·used·0.001 | 130 | ·--·used·0.00172631s·(cpu);·0.00220457s·(thread);·0s·(gc) |
| 131 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. | 131 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. |
| 132 | o9·=·true</code></pre> | 132 | o9·=·true</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) | 135 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) |
| 136 | ·--·used·0.00 | 136 | ·--·used·0.00109681s·(cpu);·0.00213519s·(thread);·0s·(gc) |
| 137 | o10·=·true</code></pre> | 137 | o10·=·true</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ········</table> | 139 | ········</table> |
| 140 | ········<div> | 140 | ········<div> |
| 141 | ··········<p>Notice·in·the·first·case·the·function·returned·<span·class="tt">null</span>,·because·the·depth·of·search·was·not·high·enough.··It·only·computed·<span·class="tt">codim</span>·5·times.··The·second·returned·true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the·<span·class="tt">PairLimit</span>·limit).</p> | 141 | ··········<p>Notice·in·the·first·case·the·function·returned·<span·class="tt">null</span>,·because·the·depth·of·search·was·not·high·enough.··It·only·computed·<span·class="tt">codim</span>·5·times.··The·second·returned·true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the·<span·class="tt">PairLimit</span>·limit).</p> |
| 142 | ········</div> | 142 | ········</div> |
| Offset 39, 15 lines modified | Offset 39, 15 lines modified | ||
| 39 | ·············30······12 | 39 | ·············30······12 |
| 40 | o4·:·Matrix·R···<--·R | 40 | o4·:·Matrix·R···<--·R |
| 41 | i5·:·r·=·rank·myDiff; | 41 | i5·:·r·=·rank·myDiff; |
| 42 | i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); | 42 | i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); |
| 43 | o6·:·Ideal·of·R | 43 | o6·:·Ideal·of·R |
| 44 | i7·:·time·isCodimAtLeast(3,·J) | 44 | i7·:·time·isCodimAtLeast(3,·J) |
| 45 | ·--·used· | 45 | ·--·used·7.2586e-05s·(cpu);·0.00234213s·(thread);·0s·(gc) |
| 46 | o7·=·true | 46 | o7·=·true |
| 47 | The·function·works·by·computing·gb(I,·PairLimit=>f(i))·for·successive·values·of | 47 | The·function·works·by·computing·gb(I,·PairLimit=>f(i))·for·successive·values·of |
| 48 | i.·Here·f(i)·is·a·function·that·takes·t,·some·approximation·of·the·base·degree | 48 | i.·Here·f(i)·is·a·function·that·takes·t,·some·approximation·of·the·base·degree |
| 49 | value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial | 49 | value·of·the·polynomial·ring·(for·example,·in·a·standard·graded·polynomial |
| 50 | ring,·this·is·probably·expected·to·be·\{1\}).·And·i·is·a·counting·variable.·You | 50 | ring,·this·is·probably·expected·to·be·\{1\}).·And·i·is·a·counting·variable.·You |
| 51 | can·provide·your·own·function·by·calling·isCodimAtLeast(n,·I,·SPairsFunction=> | 51 | can·provide·your·own·function·by·calling·isCodimAtLeast(n,·I,·SPairsFunction=> |
| Offset 73, 20 lines modified | Offset 73, 20 lines modified | ||
| 73 | x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3- | 73 | x_7^3*x_8^5*x_11^3,x_2^5*x_3^3*x_11^3- |
| 74 | 3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3); | 74 | 3*x_2^6*x_3^2*x_11^2*x_12+3*x_2^7*x_3*x_11*x_12^2-x_2^8*x_12^3); |
| 75 | ···············ZZ | 75 | ···············ZZ |
| 76 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] | 76 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] |
| 77 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7 | 77 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7 |
| 78 | i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) | 78 | i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) |
| 79 | ·--·used·0.001 | 79 | ·--·used·0.00172631s·(cpu);·0.00220457s·(thread);·0s·(gc) |
| 80 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. | 80 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. |
| 81 | o9·=·true | 81 | o9·=·true |
| 82 | i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) | 82 | i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) |
| 83 | ·--·used·0.00 | 83 | ·--·used·0.00109681s·(cpu);·0.00213519s·(thread);·0s·(gc) |
| 84 | o10·=·true | 84 | o10·=·true |
| 85 | Notice·in·the·first·case·the·function·returned·null,·because·the·depth·of | 85 | Notice·in·the·first·case·the·function·returned·null,·because·the·depth·of |
| 86 | search·was·not·high·enough.·It·only·computed·codim·5·times.·The·second·returned | 86 | search·was·not·high·enough.·It·only·computed·codim·5·times.·The·second·returned |
| 87 | true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the | 87 | true,·but·it·did·so·as·soon·as·the·answer·was·found·(and·before·we·hit·the |
| 88 | PairLimit·limit). | 88 | PairLimit·limit). |
| 89 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8od\x8di\x8im\x8mA\x8At\x8tL\x8Le\x8ea\x8as\x8st\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 89 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8od\x8di\x8im\x8mA\x8At\x8tL\x8Le\x8ea\x8as\x8st\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 100, 21 lines modified | Offset 100, 21 lines modified | ||
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·pdim(module·I) | 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·pdim(module·I) |
| 102 | o3·=·2</code></pre> | 102 | o3·=·2</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) |
| 106 | ·--·used·0. | 106 | ·--·used·0.248911s·(cpu);·0.17183s·(thread);·0s·(gc) |
| 107 | o4·=·1</code></pre> | 107 | o4·=·1</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) |
| 111 | ·--·used·0.01 | 111 | ·--·used·0.0156454s·(cpu);·0.0163892s·(thread);·0s·(gc) |
| 112 | o5·=·1</code></pre> | 112 | o5·=·1</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ········</table> | 114 | ········</table> |
| 115 | ········<div> | 115 | ········<div> |
| 116 | ··········<p>The·option·<span·class="tt">MaxMinors</span>·can·be·used·to·control·how·many·minors·are·computed·at·each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically·it·is·<span·class="tt">10·*·d·+·2·*·log_1.3(c)</span>.·Otherwise·the·user·can·set·the·option·<span·class="tt">MaxMinors·=>·ZZ</span>·to·specify·that·a·fixed·integer·is·used·for·each·step.··Alternatively,·the·user·can·control·the·number·of·minors·computed·at·each·step·by·setting·the·option·<span·class="tt">MaxMinors·=>·List</span>.··In·this·case,·the·list·specifies·how·many·minors·to·be·computed·at·each·step,·(working·backwards).·Finally,·you·can·also·set·<span·class="tt">MaxMinors</span>·to·be·a·custom·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·maximum·number·of·minors.</p> | 116 | ··········<p>The·option·<span·class="tt">MaxMinors</span>·can·be·used·to·control·how·many·minors·are·computed·at·each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically·it·is·<span·class="tt">10·*·d·+·2·*·log_1.3(c)</span>.·Otherwise·the·user·can·set·the·option·<span·class="tt">MaxMinors·=>·ZZ</span>·to·specify·that·a·fixed·integer·is·used·for·each·step.··Alternatively,·the·user·can·control·the·number·of·minors·computed·at·each·step·by·setting·the·option·<span·class="tt">MaxMinors·=>·List</span>.··In·this·case,·the·list·specifies·how·many·minors·to·be·computed·at·each·step,·(working·backwards).·Finally,·you·can·also·set·<span·class="tt">MaxMinors</span>·to·be·a·custom·function·of·the·dimension·$d$·of·the·polynomial·ring·and·the·maximum·number·of·minors.</p> |
| 117 | ········</div> | 117 | ········</div> |
| Offset 45, 19 lines modified | Offset 45, 19 lines modified | ||
| 45 | i2·:·I·=·ideal((x^3+y)^2,·(x^2+y^2)^2,·(x+y^3)^2,·(x*y)^2); | 45 | i2·:·I·=·ideal((x^3+y)^2,·(x^2+y^2)^2,·(x+y^3)^2,·(x*y)^2); |
| 46 | o2·:·Ideal·of·R | 46 | o2·:·Ideal·of·R |
| 47 | i3·:·pdim(module·I) | 47 | i3·:·pdim(module·I) |
| 48 | o3·=·2 | 48 | o3·=·2 |
| 49 | i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) | 49 | i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) |
| 50 | ·--·used·0. | 50 | ·--·used·0.248911s·(cpu);·0.17183s·(thread);·0s·(gc) |
| 51 | o4·=·1 | 51 | o4·=·1 |
| 52 | i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) | 52 | i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) |
| 53 | ·--·used·0.01 | 53 | ·--·used·0.0156454s·(cpu);·0.0163892s·(thread);·0s·(gc) |
| 54 | o5·=·1 | 54 | o5·=·1 |
| 55 | The·option·MaxMinors·can·be·used·to·control·how·many·minors·are·computed·at | 55 | The·option·MaxMinors·can·be·used·to·control·how·many·minors·are·computed·at |
| 56 | each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the | 56 | each·step.·If·this·is·not·specified,·the·number·of·minors·is·a·function·of·the |
| 57 | dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically | 57 | dimension·$d$·of·the·polynomial·ring·and·the·possible·minors·$c$.·Specifically |
| 58 | it·is·10·*·d·+·2·*·log_1.3(c).·Otherwise·the·user·can·set·the·option·MaxMinors | 58 | it·is·10·*·d·+·2·*·log_1.3(c).·Otherwise·the·user·can·set·the·option·MaxMinors |
| 59 | =>·ZZ·to·specify·that·a·fixed·integer·is·used·for·each·step.·Alternatively,·the | 59 | =>·ZZ·to·specify·that·a·fixed·integer·is·used·for·each·step.·Alternatively,·the |
| Offset 94, 21 lines modified | Offset 94, 21 lines modified | ||
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); |
| 95 | ·············6······7 | 95 | ·············6······7 |
| 96 | o2·:·Matrix·R··<--·R</code></pre> | 96 | o2·:·Matrix·R··<--·R</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); |
| 100 | ·--·used·0. | 100 | ·--·used·0.416259s·(cpu);·0.417722s·(thread);·0s·(gc) |
| 101 | o3·:·Ideal·of·R</code></pre> | 101 | o3·:·Ideal·of·R</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); | 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); |
| 105 | ·--·used·1. | 105 | ·--·used·1.18853s·(cpu);·1.07841s·(thread);·0s·(gc) |
| 106 | o4·:·Ideal·of·R</code></pre> | 106 | o4·:·Ideal·of·R</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·I1·==·I2 | 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·I1·==·I2 |
| 110 | o5·=·true</code></pre> | 110 | o5·=·true</code></pre> |
| Offset 28, 19 lines modified | Offset 28, 19 lines modified | ||
| 28 | strategy·for·minors | 28 | strategy·for·minors |
| 29 | i1·:·R·=·QQ[x,y]; | 29 | i1·:·R·=·QQ[x,y]; |
| 30 | i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); | 30 | i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); |
| 31 | ·············6······7 | 31 | ·············6······7 |
| 32 | o2·:·Matrix·R··<--·R | 32 | o2·:·Matrix·R··<--·R |
| 33 | i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); | 33 | i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); |
| 34 | ·--·used·0. | 34 | ·--·used·0.416259s·(cpu);·0.417722s·(thread);·0s·(gc) |
| 35 | o3·:·Ideal·of·R | 35 | o3·:·Ideal·of·R |
| 36 | i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); | 36 | i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); |
| 37 | ·--·used·1. | 37 | ·--·used·1.18853s·(cpu);·1.07841s·(thread);·0s·(gc) |
| 38 | o4·:·Ideal·of·R | 38 | o4·:·Ideal·of·R |
| 39 | i5·:·I1·==·I2 | 39 | i5·:·I1·==·I2 |
| 40 | o5·=·true | 40 | o5·=·true |
| 41 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 41 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 42 | ····*·_\x8m_\x8i_\x8n_\x8o_\x8r_\x8s·--·ideal·generated·by·minors | 42 | ····*·_\x8m_\x8i_\x8n_\x8o_\x8r_\x8s·--·ideal·generated·by·minors |
| Offset 129, 21 lines modified | Offset 129, 21 lines modified | ||
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i7·:·dim·S | 130 | <td>··············<pre><code·class="language-macaulay2">i7·:·dim·S |
| 131 | o7·=·3</code></pre> | 131 | o7·=·3</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S) | 134 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S) |
| 135 | ·--·used·1. | 135 | ·--·used·1.53488s·(cpu);·1.24176s·(thread);·0s·(gc) |
| 136 | o8·=·true</code></pre> | 136 | o8·=·true</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(2,·S) | 139 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(2,·S) |
| 140 | ·--·used· | 140 | ·--·used·6.05837s·(cpu);·4.79633s·(thread);·0s·(gc)</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ········</table> | 142 | ········</table> |
| 143 | ········<div> | 143 | ········<div> |
| 144 | ··········<p>There·are·numerous·examples·where·<span·class="tt">regularInCodimension</span>·is·several·orders·of·magnitude·faster·that·calls·of·<span·class="tt">dim·singularLocus</span>.</p> | 144 | ··········<p>There·are·numerous·examples·where·<span·class="tt">regularInCodimension</span>·is·several·orders·of·magnitude·faster·that·calls·of·<span·class="tt">dim·singularLocus</span>.</p> |
| 145 | ········</div> | 145 | ········</div> |
| 146 | ········<div> | 146 | ········<div> |
| 147 | ··········<p>The·following·is·a·(pruned)·affine·chart·on·an·Abelian·surface·obtained·as·a·product·of·two·elliptic·curves.··It·is·nonsingular,·as·our·function·verifies.·If·one·does·not·prune·it,·then·the·<span·class="tt">dim·singularLocus</span>·call·takes·an·enormous·amount·of·time,·otherwise·the·running·times·of·<span·class="tt">dim·singularLocus</span>·and·our·function·are·frequently·about·the·same.</p> | 147 | ··········<p>The·following·is·a·(pruned)·affine·chart·on·an·Abelian·surface·obtained·as·a·product·of·two·elliptic·curves.··It·is·nonsingular,·as·our·function·verifies.·If·one·does·not·prune·it,·then·the·<span·class="tt">dim·singularLocus</span>·call·takes·an·enormous·amount·of·time,·otherwise·the·running·times·of·<span·class="tt">dim·singularLocus</span>·and·our·function·are·frequently·about·the·same.</p> |
| Offset 155, 33 lines modified | Offset 155, 33 lines modified | ||
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim(R) | 156 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim(R) |
| 157 | o11·=·2</code></pre> | 157 | o11·=·2</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(dim·singularLocus·(R)) | 160 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(dim·singularLocus·(R)) |
| 161 | ·--·used·0.01 | 161 | ·--·used·0.0147108s·(cpu);·0.0160957s·(thread);·0s·(gc) |
| 162 | o12·=·-1</code></pre> | 162 | o12·=·-1</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·regularInCodimension(2,·R) | 165 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·regularInCodimension(2,·R) |
| 166 | ·--·used·0. | 166 | ·--·used·0.409309s·(cpu);·0.295977s·(thread);·0s·(gc) |
| 167 | o13·=·true</code></pre> | 167 | o13·=·true</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·regularInCodimension(2,·R) | 170 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·regularInCodimension(2,·R) |
| 171 | ·--·used·0. | 171 | ·--·used·0.741773s·(cpu);·0.531034s·(thread);·0s·(gc) |
| 172 | o14·=·true</code></pre> | 172 | o14·=·true</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·regularInCodimension(2,·R) | 175 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·regularInCodimension(2,·R) |
| 176 | ·--·used·0.2 | 176 | ·--·used·0.26943s·(cpu);·0.189476s·(thread);·0s·(gc) |
| 177 | o15·=·true</code></pre> | 177 | o15·=·true</code></pre> |
| 178 | </td>··········</tr> | 178 | </td>··········</tr> |
| 179 | ········</table> | 179 | ········</table> |
| 180 | ········<div> | 180 | ········<div> |
| 181 | ··········<p>The·function·works·by·choosing·interesting·looking·submatrices,·computing·their·determinants,·and·periodically·(based·on·a·logarithmic·growth·setting),·computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·<span·class="tt">Verbose</span>·can·be·used·to·see·this·in·action.</p> | 181 | ··········<p>The·function·works·by·choosing·interesting·looking·submatrices,·computing·their·determinants,·and·periodically·(based·on·a·logarithmic·growth·setting),·computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·<span·class="tt">Verbose</span>·can·be·used·to·see·this·in·action.</p> |
| 182 | ········</div> | 182 | ········</div> |
| Offset 519, 15 lines modified | Offset 519, 15 lines modified | ||
| 519 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 519 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 520 | internalChooseMinor:·Choosing·RandomNonZero | 520 | internalChooseMinor:·Choosing·RandomNonZero |
| 521 | internalChooseMinor:·Choosing·LexSmallest | 521 | internalChooseMinor:·Choosing·LexSmallest |
| 522 | internalChooseMinor:·Choosing·Random | 522 | internalChooseMinor:·Choosing·Random |
| 523 | internalChooseMinor:·Choosing·Random | 523 | internalChooseMinor:·Choosing·Random |
| 524 | internalChooseMinor:·Choosing·LexSmallestTerm | 524 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 525 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 525 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 526 | internalChooseMinor:·Choosing·--·used· | 526 | internalChooseMinor:·Choosing·--·used·5.57679s·(cpu);·4.40399s·(thread);·0s·(gc) |
| 527 | ·LexSmallestTerm | 527 | ·LexSmallestTerm |
| 528 | internalChooseMinor:·Choosing·Random | 528 | internalChooseMinor:·Choosing·Random |
| 529 | internalChooseMinor:·Choosing·Random | 529 | internalChooseMinor:·Choosing·Random |
| 530 | internalChooseMinor:·Choosing·GRevLexSmallest | 530 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 531 | internalChooseMinor:·Choosing·RandomNonZero | 531 | internalChooseMinor:·Choosing·RandomNonZero |
| 532 | internalChooseMinor:·Choosing·GRevLexSmallest | 532 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 533 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 533 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 569, 15 lines modified | Offset 569, 15 lines modified | ||
| 569 | ········</table> | 569 | ········</table> |
| 570 | ········<div> | 570 | ········<div> |
| 571 | ··········<p>The·maximum·number·of·minors·considered·can·be·controlled·by·the·option·<span·class="tt">MaxMinors</span>.··Alternatively,·it·can·be·controlled·in·a·more·precise·way·by·passing·a·function·to·the·option·<span·class="tt">MaxMinors</span>.··This·function·should·have·two·inputs;·the·first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is·regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors·available·in·the·Jacobian.·The·function·<span·class="tt">regularInCodimension</span>·does·not·recompute·determinants,·so·<span·class="tt">MaxMinors</span>·or·is·only·an·upper·bound·on·the·number·of·minors·computed.</p> | 571 | ··········<p>The·maximum·number·of·minors·considered·can·be·controlled·by·the·option·<span·class="tt">MaxMinors</span>.··Alternatively,·it·can·be·controlled·in·a·more·precise·way·by·passing·a·function·to·the·option·<span·class="tt">MaxMinors</span>.··This·function·should·have·two·inputs;·the·first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is·regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors·available·in·the·Jacobian.·The·function·<span·class="tt">regularInCodimension</span>·does·not·recompute·determinants,·so·<span·class="tt">MaxMinors</span>·or·is·only·an·upper·bound·on·the·number·of·minors·computed.</p> |
| 572 | ········</div> | 572 | ········</div> |
| 573 | ········<table·class="examples"> | 573 | ········<table·class="examples"> |
| 574 | ··········<tr> | 574 | ··········<tr> |
| 575 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) | 575 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) |
| 576 | ·--·used· | 576 | ·--·used·1.2407s·(cpu);·1.04568s·(thread);·0s·(gc) |
| 577 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them. | 577 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them. |
| 578 | regularInCodimension:·About·to·enter·loop | 578 | regularInCodimension:·About·to·enter·loop |
| 579 | internalChooseMinor:·Choosing·Random | 579 | internalChooseMinor:·Choosing·Random |
| 580 | internalChooseMinor:·Choosing·Random | 580 | internalChooseMinor:·Choosing·Random |
| 581 | internalChooseMinor:·Choosing·RandomNonZero | 581 | internalChooseMinor:·Choosing·RandomNonZero |
| 582 | internalChooseMinor:·Choosing·LexSmallestTerm | 582 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 583 | internalChooseMinor:·Choosing·RandomNonZero | 583 | internalChooseMinor:·Choosing·RandomNonZero |
| Offset 638, 73 lines modified | Offset 638, 73 lines modified | ||
| 638 | <td>··············<pre><code·class="language-macaulay2">i19·:·StrategyCurrent#LexSmallest·=·100;</code></pre> | 638 | <td>··············<pre><code·class="language-macaulay2">i19·:·StrategyCurrent#LexSmallest·=·100;</code></pre> |
| 639 | </td>··········</tr> | 639 | </td>··········</tr> |
| 640 | ··········<tr> | 640 | ··········<tr> |
| 641 | <td>··············<pre><code·class="language-macaulay2">i20·:·StrategyCurrent#LexSmallestTerm·=·0;</code></pre> | 641 | <td>··············<pre><code·class="language-macaulay2">i20·:·StrategyCurrent#LexSmallestTerm·=·0;</code></pre> |
| 642 | </td>··········</tr> | 642 | </td>··········</tr> |
| 643 | ··········<tr> | 643 | ··········<tr> |
| 644 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 644 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 645 | ·--·used·0. | 645 | ·--·used·0.12559s·(cpu);·0.0833173s·(thread);·0s·(gc) |
| 646 | o21·=·true</code></pre> | 646 | o21·=·true</code></pre> |
| 647 | </td>··········</tr> | 647 | </td>··········</tr> |
| 648 | ··········<tr> | 648 | ··········<tr> |
| 649 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 649 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 650 | ·--·used·0.1 | 650 | ·--·used·0.183571s·(cpu);·0.138521s·(thread);·0s·(gc) |
| 651 | o22·=·true</code></pre> | 651 | o22·=·true</code></pre> |
| 652 | </td>··········</tr> | 652 | </td>··········</tr> |
| 653 | ··········<tr> | 653 | ··········<tr> |
| 654 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 654 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 655 | ·--·used·1. | 655 | ·--·used·1.24476s·(cpu);·0.969224s·(thread);·0s·(gc) |
| 656 | o23·=·true</code></pre> | 656 | o23·=·true</code></pre> |
| 657 | </td>··········</tr> | 657 | </td>··········</tr> |
| 658 | ··········<tr> | 658 | ··········<tr> |
| 659 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 659 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 660 | ·--·used· | 660 | ·--·used·1.08859s·(cpu);·0.847396s·(thread);·0s·(gc) |
| 661 | o24·=·true</code></pre> | 661 | o24·=·true</code></pre> |
| 662 | </td>··········</tr> | 662 | </td>··········</tr> |
| 663 | ··········<tr> | 663 | ··········<tr> |
| 664 | <td>··············<pre><code·class="language-macaulay2">i25·:·StrategyCurrent#LexSmallest·=·0;</code></pre> | 664 | <td>··············<pre><code·class="language-macaulay2">i25·:·StrategyCurrent#LexSmallest·=·0;</code></pre> |
| 665 | </td>··········</tr> | 665 | </td>··········</tr> |
| 666 | ··········<tr> | 666 | ··········<tr> |
| 667 | <td>··············<pre><code·class="language-macaulay2">i26·:·StrategyCurrent#LexSmallestTerm·=·100;</code></pre> | 667 | <td>··············<pre><code·class="language-macaulay2">i26·:·StrategyCurrent#LexSmallestTerm·=·100;</code></pre> |
| 668 | </td>··········</tr> | 668 | </td>··········</tr> |
| 669 | ··········<tr> | 669 | ··········<tr> |
| 670 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 670 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 671 | ·--·used·0. | 671 | ·--·used·0.377744s·(cpu);·0.289806s·(thread);·0s·(gc) |
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| Offset 73, 19 lines modified | Offset 73, 19 lines modified | ||
| 73 | o5·:·Ideal·of·T | 73 | o5·:·Ideal·of·T |
| 74 | i6·:·S·=·T/I; | 74 | i6·:·S·=·T/I; |
| 75 | i7·:·dim·S | 75 | i7·:·dim·S |
| 76 | o7·=·3 | 76 | o7·=·3 |
| 77 | i8·:·time·regularInCodimension(1,·S) | 77 | i8·:·time·regularInCodimension(1,·S) |
| 78 | ·--·used·1. | 78 | ·--·used·1.53488s·(cpu);·1.24176s·(thread);·0s·(gc) |
| 79 | o8·=·true | 79 | o8·=·true |
| 80 | i9·:·time·regularInCodimension(2,·S) | 80 | i9·:·time·regularInCodimension(2,·S) |
| 81 | ·--·used· | 81 | ·--·used·6.05837s·(cpu);·4.79633s·(thread);·0s·(gc) |
| 82 | There·are·numerous·examples·where·regularInCodimension·is·several·orders·of | 82 | There·are·numerous·examples·where·regularInCodimension·is·several·orders·of |
| 83 | magnitude·faster·that·calls·of·dim·singularLocus. | 83 | magnitude·faster·that·calls·of·dim·singularLocus. |
| 84 | The·following·is·a·(pruned)·affine·chart·on·an·Abelian·surface·obtained·as·a | 84 | The·following·is·a·(pruned)·affine·chart·on·an·Abelian·surface·obtained·as·a |
| 85 | product·of·two·elliptic·curves.·It·is·nonsingular,·as·our·function·verifies.·If | 85 | product·of·two·elliptic·curves.·It·is·nonsingular,·as·our·function·verifies.·If |
| 86 | one·does·not·prune·it,·then·the·dim·singularLocus·call·takes·an·enormous·amount | 86 | one·does·not·prune·it,·then·the·dim·singularLocus·call·takes·an·enormous·amount |
| 87 | of·time,·otherwise·the·running·times·of·dim·singularLocus·and·our·function·are | 87 | of·time,·otherwise·the·running·times·of·dim·singularLocus·and·our·function·are |
| 88 | frequently·about·the·same. | 88 | frequently·about·the·same. |
| Offset 93, 27 lines modified | Offset 93, 27 lines modified | ||
| 93 | (g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3- | 93 | (g^3+h^3+1,f*g^3+f*h^3+f,c*g^3+c*h^3+c,f^2*g^3+f^2*h^3+f^2,c*f*g^3+c*f*h^3+c*f,c^2*g^3+c^2*h^3+c^2,f^3*g^3+f^3*h^3+f^3,c*f^2*g^3+c*f^2*h^3+c*f^2,c^2*f*g^3+c^2*f*h^3+c^2*f,c^3- |
| 94 | f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h- | 94 | f^2-c,c^3*h-f^2*h-c*h,c^3*g-f^2*g-c*g,c^3*h^2-f^2*h^2-c*h^2,c^3*g*h-f^2*g*h-c*g*h,c^3*g^2-f^2*g^2-c*g^2,c^3*h^3-f^2*h^3-c*h^3,c^3*g*h^2-f^2*g*h^2-c*g*h^2,c^3*g^2*h-f^2*g^2*h- |
| 95 | c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c); | 95 | c*g^2*h,c^3*g^3+f^2*h^3+c*h^3+f^2+c); |
| 96 | i11·:·dim(R) | 96 | i11·:·dim(R) |
| 97 | o11·=·2 | 97 | o11·=·2 |
| 98 | i12·:·time·(dim·singularLocus·(R)) | 98 | i12·:·time·(dim·singularLocus·(R)) |
| 99 | ·--·used·0.01 | 99 | ·--·used·0.0147108s·(cpu);·0.0160957s·(thread);·0s·(gc) |
| 100 | o12·=·-1 | 100 | o12·=·-1 |
| 101 | i13·:·time·regularInCodimension(2,·R) | 101 | i13·:·time·regularInCodimension(2,·R) |
| 102 | ·--·used·0. | 102 | ·--·used·0.409309s·(cpu);·0.295977s·(thread);·0s·(gc) |
| 103 | o13·=·true | 103 | o13·=·true |
| 104 | i14·:·time·regularInCodimension(2,·R) | 104 | i14·:·time·regularInCodimension(2,·R) |
| 105 | ·--·used·0. | 105 | ·--·used·0.741773s·(cpu);·0.531034s·(thread);·0s·(gc) |
| 106 | o14·=·true | 106 | o14·=·true |
| 107 | i15·:·time·regularInCodimension(2,·R) | 107 | i15·:·time·regularInCodimension(2,·R) |
| 108 | ·--·used·0.2 | 108 | ·--·used·0.26943s·(cpu);·0.189476s·(thread);·0s·(gc) |
| 109 | o15·=·true | 109 | o15·=·true |
| 110 | The·function·works·by·choosing·interesting·looking·submatrices,·computing·their | 110 | The·function·works·by·choosing·interesting·looking·submatrices,·computing·their |
| 111 | determinants,·and·periodically·(based·on·a·logarithmic·growth·setting), | 111 | determinants,·and·periodically·(based·on·a·logarithmic·growth·setting), |
| 112 | computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·Verbose·can | 112 | computing·the·dimension·of·a·subideal·of·the·Jacobian.·The·option·Verbose·can |
| 113 | be·used·to·see·this·in·action. | 113 | be·used·to·see·this·in·action. |
| 114 | i16·:·time·regularInCodimension(2,·S,·Verbose=>true) | 114 | i16·:·time·regularInCodimension(2,·S,·Verbose=>true) |
| Offset 462, 15 lines modified | Offset 462, 15 lines modified | ||
| 462 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 462 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 463 | internalChooseMinor:·Choosing·RandomNonZero | 463 | internalChooseMinor:·Choosing·RandomNonZero |
| 464 | internalChooseMinor:·Choosing·LexSmallest | 464 | internalChooseMinor:·Choosing·LexSmallest |
| 465 | internalChooseMinor:·Choosing·Random | 465 | internalChooseMinor:·Choosing·Random |
| 466 | internalChooseMinor:·Choosing·Random | 466 | internalChooseMinor:·Choosing·Random |
| 467 | internalChooseMinor:·Choosing·LexSmallestTerm | 467 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 468 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 468 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 469 | internalChooseMinor:·Choosing·--·used· | 469 | internalChooseMinor:·Choosing·--·used·5.57679s·(cpu);·4.40399s·(thread);·0s |
| 470 | (gc) | 470 | (gc) |
| 471 | ·LexSmallestTerm | 471 | ·LexSmallestTerm |
| 472 | internalChooseMinor:·Choosing·Random | 472 | internalChooseMinor:·Choosing·Random |
| 473 | internalChooseMinor:·Choosing·Random | 473 | internalChooseMinor:·Choosing·Random |
| 474 | internalChooseMinor:·Choosing·GRevLexSmallest | 474 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 475 | internalChooseMinor:·Choosing·RandomNonZero | 475 | internalChooseMinor:·Choosing·RandomNonZero |
| 476 | internalChooseMinor:·Choosing·GRevLexSmallest | 476 | internalChooseMinor:·Choosing·GRevLexSmallest |
| Offset 517, 15 lines modified | Offset 517, 15 lines modified | ||
| 517 | a·function·to·the·option·MaxMinors.·This·function·should·have·two·inputs;·the | 517 | a·function·to·the·option·MaxMinors.·This·function·should·have·two·inputs;·the |
| 518 | first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is | 518 | first·is·minimum·number·of·minors·needed·to·determine·whether·the·ring·is |
| 519 | regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors | 519 | regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors |
| 520 | available·in·the·Jacobian.·The·function·regularInCodimension·does·not·recompute | 520 | available·in·the·Jacobian.·The·function·regularInCodimension·does·not·recompute |
| 521 | determinants,·so·MaxMinors·or·is·only·an·upper·bound·on·the·number·of·minors | 521 | determinants,·so·MaxMinors·or·is·only·an·upper·bound·on·the·number·of·minors |
| 522 | computed. | 522 | computed. |
| 523 | i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) | 523 | i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) |
| 524 | ·--·used· | 524 | ·--·used·1.2407s·(cpu);·1.04568s·(thread);·0s·(gc) |
| 525 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4 | 525 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4 |
| 526 | minors,·we·will·compute·up·to·30·of·them. | 526 | minors,·we·will·compute·up·to·30·of·them. |
| 527 | regularInCodimension:·About·to·enter·loop | 527 | regularInCodimension:·About·to·enter·loop |
| 528 | internalChooseMinor:·Choosing·Random | 528 | internalChooseMinor:·Choosing·Random |
| 529 | internalChooseMinor:·Choosing·Random | 529 | internalChooseMinor:·Choosing·Random |
| 530 | internalChooseMinor:·Choosing·RandomNonZero | 530 | internalChooseMinor:·Choosing·RandomNonZero |
| 531 | internalChooseMinor:·Choosing·LexSmallestTerm | 531 | internalChooseMinor:·Choosing·LexSmallestTerm |
| Offset 592, 51 lines modified | Offset 592, 51 lines modified | ||
| 592 | because·there·are·a·small·number·of·entries·with·nonzero·constant·terms,·which | 592 | because·there·are·a·small·number·of·entries·with·nonzero·constant·terms,·which |
| 593 | are·selected·repeatedly).·However,·in·our·first·example,·the·LexSmallestTerm·is | 593 | are·selected·repeatedly).·However,·in·our·first·example,·the·LexSmallestTerm·is |
| 594 | much·faster,·and·Random·does·not·perform·well·at·all. | 594 | much·faster,·and·Random·does·not·perform·well·at·all. |
| 595 | i18·:·StrategyCurrent#Random·=·0; | 595 | i18·:·StrategyCurrent#Random·=·0; |
| 596 | i19·:·StrategyCurrent#LexSmallest·=·100; | 596 | i19·:·StrategyCurrent#LexSmallest·=·100; |
| 597 | i20·:·StrategyCurrent#LexSmallestTerm·=·0; | 597 | i20·:·StrategyCurrent#LexSmallestTerm·=·0; |
| 598 | i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 598 | i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 599 | ·--·used·0. | 599 | ·--·used·0.12559s·(cpu);·0.0833173s·(thread);·0s·(gc) |
| 600 | o21·=·true | 600 | o21·=·true |
| 601 | i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 601 | i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 602 | ·--·used·0.1 | 602 | ·--·used·0.183571s·(cpu);·0.138521s·(thread);·0s·(gc) |
| 603 | o22·=·true | 603 | o22·=·true |
| 604 | i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 604 | i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 605 | ·--·used·1. | 605 | ·--·used·1.24476s·(cpu);·0.969224s·(thread);·0s·(gc) |
| 606 | o23·=·true | 606 | o23·=·true |
| 607 | i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 607 | i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 608 | ·--·used· | 608 | ·--·used·1.08859s·(cpu);·0.847396s·(thread);·0s·(gc) |
| 609 | o24·=·true | 609 | o24·=·true |
| 610 | i25·:·StrategyCurrent#LexSmallest·=·0; | 610 | i25·:·StrategyCurrent#LexSmallest·=·0; |
| 611 | i26·:·StrategyCurrent#LexSmallestTerm·=·100; | 611 | i26·:·StrategyCurrent#LexSmallestTerm·=·100; |
| 612 | i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 612 | i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 613 | ·--·used·0. | 613 | ·--·used·0.377744s·(cpu);·0.289806s·(thread);·0s·(gc) |
| 614 | o27·=·true | 614 | o27·=·true |
| 615 | i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 615 | i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 616 | ·--·used· | 616 | ·--·used·2.07495s·(cpu);·1.52945s·(thread);·0s·(gc) |
| 617 | i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 617 | i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 618 | ·--·used·0.1 | 618 | ·--·used·0.159984s·(cpu);·0.124387s·(thread);·0s·(gc) |
| 619 | o29·=·true | 619 | o29·=·true |
| 620 | i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 620 | i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 621 | ·--·used·0.15 | 621 | ·--·used·0.215008s·(cpu);·0.17994s·(thread);·0s·(gc) |
| 622 | o30·=·true | 622 | o30·=·true |
| 623 | i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) | 623 | i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) |
| 624 | ·--·used·1. | 624 | ·--·used·1.56951s·(cpu);·1.31915s·(thread);·0s·(gc) |
| 625 | o31·=·true | 625 | o31·=·true |
| 626 | i32·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) | 626 | i32·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) |
| 627 | ·--·used·1. | 627 | ·--·used·1.3329s·(cpu);·1.11745s·(thread);·0s·(gc) |
| 628 | o32·=·true | 628 | o32·=·true |
| 629 | The·minimum·number·of·minors·computed·before·checking·the·codimension·can·also | 629 | The·minimum·number·of·minors·computed·before·checking·the·codimension·can·also |
| Max diff block lines reached; 223/6607 bytes (3.38%) of diff not shown. | |||
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=26 | 7 | #:len=26 |
| 8 | bmV4dERlZ3JlZShNYXRyaXgsWlosUmluZyk= | 8 | bmV4dERlZ3JlZShNYXRyaXgsWlosUmluZyk= |
| 9 | #:len=288 | 9 | #:len=288 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzU1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzU1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhuZXh0RGVncmVlLE1hdHJpeCxaWixSaW5nKSwibmV4 | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhuZXh0RGVncmVlLE1hdHJpeCxaWixSaW5nKSwibmV4 |
| Offset 81, 23 lines modified | Offset 81, 23 lines modified | ||
| 81 | i14·:·K3=nextDegree(gens·ker·Q2,2,S); | 81 | i14·:·K3=nextDegree(gens·ker·Q2,2,S); |
| 82 | ··············8······8 | 82 | ··············8······8 |
| 83 | o14·:·Matrix·R··<--·R | 83 | o14·:·Matrix·R··<--·R |
| 84 | i15·:·time·I=co1Fitting(K3) | 84 | i15·:·time·I=co1Fitting(K3) |
| 85 | ·--·used·0.00 | 85 | ·--·used·0.000859732s·(cpu);·0.00205433s·(thread);·0s·(gc) |
| 86 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) | 86 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) |
| 87 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 | 87 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 |
| 88 | o15·:·Ideal·of·R | 88 | o15·:·Ideal·of·R |
| 89 | i16·:·time·J=fittingIdeal(2-1,coker·K3); | 89 | i16·:·time·J=fittingIdeal(2-1,coker·K3); |
| 90 | ·--·used·0.00 | 90 | ·--·used·0.00508633s·(cpu);·0.00496045s·(thread);·0s·(gc) |
| 91 | o16·:·Ideal·of·R | 91 | o16·:·Ideal·of·R |
| 92 | i17·:·I==J | 92 | i17·:·I==J |
| 93 | o17·=·true | 93 | o17·=·true |
| Offset 166, 24 lines modified | Offset 166, 24 lines modified | ||
| 166 | <td>··············<pre><code·class="language-macaulay2">i14·:·K3=nextDegree(gens·ker·Q2,2,S); | 166 | <td>··············<pre><code·class="language-macaulay2">i14·:·K3=nextDegree(gens·ker·Q2,2,S); |
| 167 | ··············8······8 | 167 | ··············8······8 |
| 168 | o14·:·Matrix·R··<--·R</code></pre> | 168 | o14·:·Matrix·R··<--·R</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·I=co1Fitting(K3) | 171 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·I=co1Fitting(K3) |
| 172 | ·--·used·0.00 | 172 | ·--·used·0.000859732s·(cpu);·0.00205433s·(thread);·0s·(gc) |
| 173 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) | 173 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) |
| 174 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 | 174 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 |
| 175 | o15·:·Ideal·of·R</code></pre> | 175 | o15·:·Ideal·of·R</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ··········<tr> | 177 | ··········<tr> |
| 178 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·J=fittingIdeal(2-1,coker·K3); | 178 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·J=fittingIdeal(2-1,coker·K3); |
| 179 | ·--·used·0.00 | 179 | ·--·used·0.00508633s·(cpu);·0.00496045s·(thread);·0s·(gc) |
| 180 | o16·:·Ideal·of·R</code></pre> | 180 | o16·:·Ideal·of·R</code></pre> |
| 181 | </td>··········</tr> | 181 | </td>··········</tr> |
| 182 | ··········<tr> | 182 | ··········<tr> |
| 183 | <td>··············<pre><code·class="language-macaulay2">i17·:·I==J | 183 | <td>··············<pre><code·class="language-macaulay2">i17·:·I==J |
| 184 | o17·=·true</code></pre> | 184 | o17·=·true</code></pre> |
| Offset 95, 22 lines modified | Offset 95, 22 lines modified | ||
| 95 | ··············2······6 | 95 | ··············2······6 |
| 96 | o13·:·Matrix·R··<--·R | 96 | o13·:·Matrix·R··<--·R |
| 97 | i14·:·K3=nextDegree(gens·ker·Q2,2,S); | 97 | i14·:·K3=nextDegree(gens·ker·Q2,2,S); |
| 98 | ··············8······8 | 98 | ··············8······8 |
| 99 | o14·:·Matrix·R··<--·R | 99 | o14·:·Matrix·R··<--·R |
| 100 | i15·:·time·I=co1Fitting(K3) | 100 | i15·:·time·I=co1Fitting(K3) |
| 101 | ·--·used·0.00 | 101 | ·--·used·0.000859732s·(cpu);·0.00205433s·(thread);·0s·(gc) |
| 102 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) | 102 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) |
| 103 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 | 103 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 |
| 104 | o15·:·Ideal·of·R | 104 | o15·:·Ideal·of·R |
| 105 | i16·:·time·J=fittingIdeal(2-1,coker·K3); | 105 | i16·:·time·J=fittingIdeal(2-1,coker·K3); |
| 106 | ·--·used·0.00 | 106 | ·--·used·0.00508633s·(cpu);·0.00496045s·(thread);·0s·(gc) |
| 107 | o16·:·Ideal·of·R | 107 | o16·:·Ideal·of·R |
| 108 | i17·:·I==J | 108 | i17·:·I==J |
| 109 | o17·=·true | 109 | o17·=·true |
| 110 | Note·that·our·method·is·a·bit·faster·for·this·small·example,·and·for·rank·2 | 110 | Note·that·our·method·is·a·bit·faster·for·this·small·example,·and·for·rank·2 |
| 111 | quotients·of·S^3=\mathbb{Z}[x,y]^3·the·time·difference·is·massive. | 111 | quotients·of·S^3=\mathbb{Z}[x,y]^3·the·time·difference·is·massive. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | Rmlyc3RQYWNrYWdl | 8 | Rmlyc3RQYWNrYWdl |
| 9 | #:len=509 | 9 | #:len=509 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZXhhbXBsZSBNYWNhdWxheTIgcGFj | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZXhhbXBsZSBNYWNhdWxheTIgcGFj |
| 11 | a2FnZSIsICJsaW5lbnVtIiA9PiA1MywgImZpbGVuYW1lIiA9PiAiRmlyc3RQYWNrYWdlLm0yIiwg | 11 | a2FnZSIsICJsaW5lbnVtIiA9PiA1MywgImZpbGVuYW1lIiA9PiAiRmlyc3RQYWNrYWdlLm0yIiwg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=13 | 7 | #:len=13 |
| 8 | dmFsdWUodWludDE2KQ== | 8 | dmFsdWUodWludDE2KQ== |
| 9 | #:len=273 | 9 | #:len=273 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTY5Miwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTY5Miwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodmFsdWUsdWludDE2KSwidmFsdWUodWludDE2KSIs | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodmFsdWUsdWludDE2KSwidmFsdWUodWludDE2KSIs |
| Offset 4, 19 lines modified | Offset 4, 19 lines modified | ||
| 4 | o1·=·5 | 4 | o1·=·5 |
| 5 | o1·:·ForeignObject·of·type·int32 | 5 | o1·:·ForeignObject·of·type·int32 |
| 6 | i2·:·peek·x | 6 | i2·:·peek·x |
| 7 | o2·=·int32{Address·=>·0x7f | 7 | o2·=·int32{Address·=>·0x7f9d605b9190} |
| 8 | i3·:·address·x | 8 | i3·:·address·x |
| 9 | o3·=·0x7f | 9 | o3·=·0x7f9d605b9190 |
| 10 | o3·:·Pointer | 10 | o3·:·Pointer |
| 11 | i4·:·class·x | 11 | i4·:·class·x |
| 12 | o4·=·int32 | 12 | o4·=·int32 |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} | 11 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} |
| 12 | o2·:·ForeignObject·of·type·char** | 12 | o2·:·ForeignObject·of·type·char** |
| 13 | i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 13 | i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 14 | o3·=·{0x7f | 14 | o3·=·{0x7f1835518d10,·0x7f1835518d00,·0x7f1835518cf0} |
| 15 | o3·:·ForeignObject·of·type·void** | 15 | o3·:·ForeignObject·of·type·void** |
| 16 | i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"} | 16 | i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"} |
| 17 | o4·=·{foo,·bar,·baz} | 17 | o4·=·{foo,·bar,·baz} |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·{foo,·bar} | 4 | o1·=·{foo,·bar} |
| 5 | o1·:·ForeignObject·of·type·char** | 5 | o1·:·ForeignObject·of·type·char** |
| 6 | i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 6 | i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 7 | o2·=·{0x7f | 7 | o2·=·{0x7f4f4f0f22e0,·0x7f4f4f0f22d0,·0x7f4f4f0f22c0} |
| 8 | o2·:·ForeignObject·of·type·void** | 8 | o2·:·ForeignObject·of·type·void** |
| 9 | i3·:·int2star·=·foreignPointerArrayType(2·*·int) | 9 | i3·:·int2star·=·foreignPointerArrayType(2·*·int) |
| 10 | o3·=·int32[2]* | 10 | o3·=·int32[2]* |
| Offset 1, 15 lines modified | Offset 1, 15 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1730835169888399450 | 1 | --·-*-·M2-comint·-*-·hash:·1730835169888399450 |
| 2 | i1·:·ptr·=·address·int·0 | 2 | i1·:·ptr·=·address·int·0 |
| 3 | o1·=·0x7f | 3 | o1·=·0x7f3deead3190 |
| 4 | o1·:·Pointer | 4 | o1·:·Pointer |
| 5 | i2·:·voidstar·ptr | 5 | i2·:·voidstar·ptr |
| 6 | o2·=·0x7f | 6 | o2·=·0x7f3deead3190 |
| 7 | o2·:·ForeignObject·of·type·void* | 7 | o2·:·ForeignObject·of·type·void* |
| 8 | i3·:· | 8 | i3·:· |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·5 | 4 | o1·=·5 |
| 5 | o1·:·ForeignObject·of·type·int32 | 5 | o1·:·ForeignObject·of·type·int32 |
| 6 | i2·:·ptr·=·address·x | 6 | i2·:·ptr·=·address·x |
| 7 | o2·=·0x7f | 7 | o2·=·0x7fbf879b9280 |
| 8 | o2·:·Pointer | 8 | o2·:·Pointer |
| 9 | i3·:·int·ptr | 9 | i3·:·int·ptr |
| 10 | o3·=·5 | 10 | o3·=·5 |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731230829183683930 | 1 | --·-*-·M2-comint·-*-·hash:·1731230829183683930 |
| 2 | i1·:·ptr·=·voidstar·address·int·5 | 2 | i1·:·ptr·=·voidstar·address·int·5 |
| 3 | o1·=·0x7f | 3 | o1·=·0x7f1a28194250 |
| 4 | o1·:·ForeignObject·of·type·void* | 4 | o1·:·ForeignObject·of·type·void* |
| 5 | i2·:·int·*·ptr | 5 | i2·:·int·*·ptr |
| 6 | o2·=·5 | 6 | o2·=·5 |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·myunion | 4 | o1·=·myunion |
| 5 | o1·:·ForeignUnionType | 5 | o1·:·ForeignUnionType |
| 6 | i2·:·myunion·27 | 6 | i2·:·myunion·27 |
| 7 | o2·=·HashTable{"bar"·=>·6.9 | 7 | o2·=·HashTable{"bar"·=>·6.90073e-310} |
| 8 | ···············"foo"·=>·27 | 8 | ···············"foo"·=>·27 |
| 9 | o2·:·ForeignObject·of·type·myunion | 9 | o2·:·ForeignObject·of·type·myunion |
| 10 | i3·:·myunion·pi | 10 | i3·:·myunion·pi |
| 11 | o3·=·HashTable{"bar"·=>·3.14159···} | 11 | o3·=·HashTable{"bar"·=>·3.14159···} |
| Offset 4, 28 lines modified | Offset 4, 28 lines modified | ||
| 4 | o1·=·20 | 4 | o1·=·20 |
| 5 | o1·:·ForeignObject·of·type·int32 | 5 | o1·:·ForeignObject·of·type·int32 |
| 6 | i2·:·peek·x | 6 | i2·:·peek·x |
| 7 | o2·=·int32{Address·=>·0x7f | 7 | o2·=·int32{Address·=>·0x7f462a8f2640} |
| 8 | i3·:·ptr·=·address·x | 8 | i3·:·ptr·=·address·x |
| 9 | o3·=·0x7f | 9 | o3·=·0x7f462a8f2640 |
| 10 | o3·:·Pointer | 10 | o3·:·Pointer |
| 11 | i4·:·ptr·+·5 | 11 | i4·:·ptr·+·5 |
| 12 | o4·=·0x7f | 12 | o4·=·0x7f462a8f2645 |
| 13 | o4·:·Pointer | 13 | o4·:·Pointer |
| 14 | i5·:·ptr·-·3 | 14 | i5·:·ptr·-·3 |
| 15 | o5·=·0x7f | 15 | o5·=·0x7f462a8f263d |
| 16 | o5·:·Pointer | 16 | o5·:·Pointer |
| 17 | i6·:· | 17 | i6·:· |
| Offset 4, 10 lines modified | Offset 4, 10 lines modified | ||
| 4 | o1·=·mpfr | 4 | o1·=·mpfr |
| 5 | o1·:·SharedLibrary | 5 | o1·:·SharedLibrary |
| 6 | i2·:·peek·mpfr | 6 | i2·:·peek·mpfr |
| 7 | o2·=·SharedLibrary{0x7f | 7 | o2·=·SharedLibrary{0x7feffd2b5550,·mpfr} |
| 8 | i3·:· | 8 | i3·:· |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·5 | 4 | o1·=·5 |
| 5 | o1·:·ForeignObject·of·type·int32 | 5 | o1·:·ForeignObject·of·type·int32 |
| 6 | i2·:·ptr·=·address·x | 6 | i2·:·ptr·=·address·x |
| 7 | o2·=·0x7f | 7 | o2·=·0x7fe2b2cf2640 |
| 8 | o2·:·Pointer | 8 | o2·:·Pointer |
| 9 | i3·:·*ptr·=·int·6 | 9 | i3·:·*ptr·=·int·6 |
| 10 | o3·=·6 | 10 | o3·=·6 |
| Offset 1, 15 lines modified | Offset 1, 15 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1730181884377373595 | 1 | --·-*-·M2-comint·-*-·hash:·1730181884377373595 |
| 2 | i1·:·address·int | 2 | i1·:·address·int |
| 3 | o1·=·0x5 | 3 | o1·=·0x557ecefa6c20 |
| 4 | o1·:·Pointer | 4 | o1·:·Pointer |
| 5 | i2·:·address·int·5 | 5 | i2·:·address·int·5 |
| 6 | o2·=·0x7f | 6 | o2·=·0x7f5bed8f24d0 |
| 7 | o2·:·Pointer | 7 | o2·:·Pointer |
| 8 | i3·:· | 8 | i3·:· |
| Offset 78, 14 lines modified | Offset 78, 14 lines modified | ||
| 78 | o16·=·free | 78 | o16·=·free |
| 79 | o16·:·ForeignFunction | 79 | o16·:·ForeignFunction |
| 80 | i17·:·x·=·malloc·8 | 80 | i17·:·x·=·malloc·8 |
| 81 | o17·=·0x7f | 81 | o17·=·0x7f10240639d0 |
| 82 | o17·:·ForeignObject·of·type·void* | 82 | o17·:·ForeignObject·of·type·void* |
| 83 | i18·:·registerFinalizer(x,·free) | 83 | i18·:·registerFinalizer(x,·free) |
| 84 | i19·:· | 84 | i19·:· |
| Offset 1, 21 lines modified | Offset 1, 21 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·10647988412767280310 | 1 | --·-*-·M2-comint·-*-·hash:·10647988412767280310 |
| 2 | i1·:·ptr·=·getMemory·8 | 2 | i1·:·ptr·=·getMemory·8 |
| 3 | o1·=·0x7f | 3 | o1·=·0x7f5529bac9a0 |
| 4 | o1·:·ForeignObject·of·type·void* | 4 | o1·:·ForeignObject·of·type·void* |
| 5 | i2·:·ptr·=·getMemory(8,·Atomic·=>·true) | 5 | i2·:·ptr·=·getMemory(8,·Atomic·=>·true) |
| 6 | o2·=·0x7f | 6 | o2·=·0x7f55350f2450 |
| 7 | o2·:·ForeignObject·of·type·void* | 7 | o2·:·ForeignObject·of·type·void* |
| 8 | i3·:·ptr·=·getMemory·int | 8 | i3·:·ptr·=·getMemory·int |
| 9 | o3·=·0x7f | 9 | o3·=·0x7f55350f2360 |
| 10 | o3·:·ForeignObject·of·type·void* | 10 | o3·:·ForeignObject·of·type·void* |
| 11 | i4·:· | 11 | i4·:· |
| Offset 17, 18 lines modified | Offset 17, 18 lines modified | ||
| 17 | o3·=·finalizer | 17 | o3·=·finalizer |
| 18 | o3·:·FunctionClosure | 18 | o3·:·FunctionClosure |
| 19 | i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer)) | 19 | i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer)) |
| 20 | i5·:·collectGarbage() | 20 | i5·:·collectGarbage() |
| 21 | freeing·memory·at·0x7f44e0063bf0 | ||
| 22 | freeing·memory·at·0x7f44e0069180 | ||
| 23 | freeing·memory·at·0x7f44e0066c50 | ||
| 24 | freeing·memory·at·0x7f44e0063bc0 | ||
| 25 | freeing·memory·at·0x7f44e005f3f0 | ||
| 26 | freeing·memory·at·0x7f44e00639f0 | ||
| 27 | freeing·memory·at·0x7f44e006a210 | ||
| 28 | freeing·memory·at·0x7f44e006a230 | ||
| 29 | freeing·memory·at·0x7f | 21 | freeing·memory·at·0x7fdd600639d0 |
| 22 | freeing·memory·at·0x7fdd60069180 | ||
| 23 | freeing·memory·at·0x7fdd60066c50 | ||
| 24 | freeing·memory·at·0x7fdd6006a230 | ||
| 25 | freeing·memory·at·0x7fdd6005f3f0 | ||
| 26 | freeing·memory·at·0x7fdd600639f0 | ||
| 27 | freeing·memory·at·0x7fdd6006a210 | ||
| 28 | freeing·memory·at·0x7fdd60063bc0 | ||
| 29 | freeing·memory·at·0x7fdd60063bf0 | ||
| 30 | i6·:· | 30 | i6·:· |
| Offset 20, 21 lines modified | Offset 20, 21 lines modified | ||
| 20 | o4·=·5 | 20 | o4·=·5 |
| 21 | o4·:·RR·(of·precision·53) | 21 | o4·:·RR·(of·precision·53) |
| 22 | i5·:·x·=·voidstar·address·int·5 | 22 | i5·:·x·=·voidstar·address·int·5 |
| 23 | o5·=·0x7f4 | 23 | o5·=·0x7f4c109d7ca0 |
| 24 | o5·:·ForeignObject·of·type·void* | 24 | o5·:·ForeignObject·of·type·void* |
| 25 | i6·:·value·x | 25 | i6·:·value·x |
| 26 | o6·=·0x7f4 | 26 | o6·=·0x7f4c109d7ca0 |
| 27 | o6·:·Pointer | 27 | o6·:·Pointer |
| 28 | i7·:·x·=·charstar·"Hello,·world!" | 28 | i7·:·x·=·charstar·"Hello,·world!" |
| 29 | o7·=·Hello,·world! | 29 | o7·=·Hello,·world! |
| Offset 54, 25 lines modified | Offset 54, 25 lines modified | ||
| 54 | o1·=·5 | 54 | o1·=·5 |
| 55 | o1·:·ForeignObject·of·type·int32</code></pre> | 55 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 56 | </td>··········</tr> | 56 | </td>··········</tr> |
| 57 | ··········<tr> | 57 | ··········<tr> |
| 58 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x | 58 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x |
| 59 | o2·=·int32{Address·=>·0x7f | 59 | o2·=·int32{Address·=>·0x7f9d605b9190}</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ········</table> | 61 | ········</table> |
| 62 | ········<div> | 62 | ········<div> |
| 63 | ··········<p>To·get·this,·use·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> | 63 | ··········<p>To·get·this,·use·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> |
| 64 | ········</div> | 64 | ········</div> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·address·x | 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·address·x |
| 68 | o3·=·0x7f | 68 | o3·=·0x7f9d605b9190 |
| 69 | o3·:·Pointer</code></pre> | 69 | o3·:·Pointer</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ········</table> | 71 | ········</table> |
| 72 | ········<div> | 72 | ········<div> |
| 73 | ··········<p>Use·<a·title="class·of·an·object"·href="../../Macaulay2Doc/html/_class.html">class</a>·to·determine·the·type·of·the·object.</p> | 73 | ··········<p>Use·<a·title="class·of·an·object"·href="../../Macaulay2Doc/html/_class.html">class</a>·to·determine·the·type·of·the·object.</p> |
| 74 | ········</div> | 74 | ········</div> |
| Offset 10, 19 lines modified | Offset 10, 19 lines modified | ||
| 10 | i1·:·x·=·int·5 | 10 | i1·:·x·=·int·5 |
| 11 | o1·=·5 | 11 | o1·=·5 |
| 12 | o1·:·ForeignObject·of·type·int32 | 12 | o1·:·ForeignObject·of·type·int32 |
| 13 | i2·:·peek·x | 13 | i2·:·peek·x |
| 14 | o2·=·int32{Address·=>·0x7f | 14 | o2·=·int32{Address·=>·0x7f9d605b9190} |
| 15 | To·get·this,·use·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s. | 15 | To·get·this,·use·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s. |
| 16 | i3·:·address·x | 16 | i3·:·address·x |
| 17 | o3·=·0x7f | 17 | o3·=·0x7f9d605b9190 |
| 18 | o3·:·Pointer | 18 | o3·:·Pointer |
| 19 | Use·_\x8c_\x8l_\x8a_\x8s_\x8s·to·determine·the·type·of·the·object. | 19 | Use·_\x8c_\x8l_\x8a_\x8s_\x8s·to·determine·the·type·of·the·object. |
| 20 | i4·:·class·x | 20 | i4·:·class·x |
| 21 | o4·=·int32 | 21 | o4·=·int32 |
| Offset 62, 15 lines modified | Offset 62, 15 lines modified | ||
| 62 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} | 62 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} |
| 63 | o2·:·ForeignObject·of·type·char**</code></pre> | 63 | o2·:·ForeignObject·of·type·char**</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 67 | o3·=·{0x7f | 67 | o3·=·{0x7f1835518d10,·0x7f1835518d00,·0x7f1835518cf0} |
| 68 | o3·:·ForeignObject·of·type·void**</code></pre> | 68 | o3·:·ForeignObject·of·type·void**</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ········</table> | 70 | ········</table> |
| 71 | ········<div> | 71 | ········<div> |
| 72 | ··········<p>Foreign·pointer·arrays·may·be·subscripted·using·<a·title="a·binary·operator,·used·for·subscripting·and·access·to·elements"·href="../../Macaulay2Doc/html/__us.html">_</a>.</p> | 72 | ··········<p>Foreign·pointer·arrays·may·be·subscripted·using·<a·title="a·binary·operator,·used·for·subscripting·and·access·to·elements"·href="../../Macaulay2Doc/html/__us.html">_</a>.</p> |
| 73 | ········</div> | 73 | ········</div> |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | ·········"lazy",·"dog"} | 20 | ·········"lazy",·"dog"} |
| 21 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} | 21 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} |
| 22 | o2·:·ForeignObject·of·type·char** | 22 | o2·:·ForeignObject·of·type·char** |
| 23 | i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 23 | i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 24 | o3·=·{0x7f | 24 | o3·=·{0x7f1835518d10,·0x7f1835518d00,·0x7f1835518cf0} |
| 25 | o3·:·ForeignObject·of·type·void** | 25 | o3·:·ForeignObject·of·type·void** |
| 26 | Foreign·pointer·arrays·may·be·subscripted·using·_\x8_. | 26 | Foreign·pointer·arrays·may·be·subscripted·using·_\x8_. |
| 27 | i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"} | 27 | i4·:·x·=·charstarstar·{"foo",·"bar",·"baz"} |
| 28 | o4·=·{foo,·bar,·baz} | 28 | o4·=·{foo,·bar,·baz} |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | o1·=·{foo,·bar} | 81 | o1·=·{foo,·bar} |
| 82 | o1·:·ForeignObject·of·type·char**</code></pre> | 82 | o1·:·ForeignObject·of·type·char**</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 86 | o2·=·{0x7f | 86 | o2·=·{0x7f4f4f0f22e0,·0x7f4f4f0f22d0,·0x7f4f4f0f22c0} |
| 87 | o2·:·ForeignObject·of·type·void**</code></pre> | 87 | o2·:·ForeignObject·of·type·void**</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·int2star·=·foreignPointerArrayType(2·*·int) | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·int2star·=·foreignPointerArrayType(2·*·int) |
| 91 | o3·=·int32[2]* | 91 | o3·=·int32[2]* |
| Offset 21, 15 lines modified | Offset 21, 15 lines modified | ||
| 21 | i1·:·charstarstar·{"foo",·"bar"} | 21 | i1·:·charstarstar·{"foo",·"bar"} |
| 22 | o1·=·{foo,·bar} | 22 | o1·=·{foo,·bar} |
| 23 | o1·:·ForeignObject·of·type·char** | 23 | o1·:·ForeignObject·of·type·char** |
| 24 | i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 24 | i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 25 | o2·=·{0x7f | 25 | o2·=·{0x7f4f4f0f22e0,·0x7f4f4f0f22d0,·0x7f4f4f0f22c0} |
| 26 | o2·:·ForeignObject·of·type·void** | 26 | o2·:·ForeignObject·of·type·void** |
| 27 | i3·:·int2star·=·foreignPointerArrayType(2·*·int) | 27 | i3·:·int2star·=·foreignPointerArrayType(2·*·int) |
| 28 | o3·=·int32[2]* | 28 | o3·=·int32[2]* |
| 29 | o3·:·ForeignPointerArrayType | 29 | o3·:·ForeignPointerArrayType |
| Offset 74, 22 lines modified | Offset 74, 22 lines modified | ||
| 74 | ········<div> | 74 | ········<div> |
| 75 | ··········<p>To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the·type·followed·by·the·pointer.</p> | 75 | ··········<p>To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the·type·followed·by·the·pointer.</p> |
| 76 | ········</div> | 76 | ········</div> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·address·int·0 | 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·address·int·0 |
| 80 | o1·=·0x7f | 80 | o1·=·0x7f3deead3190 |
| 81 | o1·:·Pointer</code></pre> | 81 | o1·:·Pointer</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstar·ptr | 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstar·ptr |
| 85 | o2·=·0x7f | 85 | o2·=·0x7f3deead3190 |
| 86 | o2·:·ForeignObject·of·type·void*</code></pre> | 86 | o2·:·ForeignObject·of·type·void*</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ········</table> | 88 | ········</table> |
| 89 | ······</div> | 89 | ······</div> |
| 90 | ······<div·class="waystouse"> | 90 | ······<div·class="waystouse"> |
| 91 | ········<h2>Ways·to·use·this·method:</h2> | 91 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 16, 18 lines modified | Offset 16, 18 lines modified | ||
| 16 | ····*·Outputs: | 16 | ····*·Outputs: |
| 17 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t, | 17 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t, |
| 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 19 | To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the | 19 | To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the |
| 20 | type·followed·by·the·pointer. | 20 | type·followed·by·the·pointer. |
| 21 | i1·:·ptr·=·address·int·0 | 21 | i1·:·ptr·=·address·int·0 |
| 22 | o1·=·0x7f | 22 | o1·=·0x7f3deead3190 |
| 23 | o1·:·Pointer | 23 | o1·:·Pointer |
| 24 | i2·:·voidstar·ptr | 24 | i2·:·voidstar·ptr |
| 25 | o2·=·0x7f | 25 | o2·=·0x7f3deead3190 |
| 26 | o2·:·ForeignObject·of·type·void* | 26 | o2·:·ForeignObject·of·type·void* |
| 27 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 28 | ····*·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·cast·a·Macaulay2·pointer·to·a·foreign | 28 | ····*·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·--·cast·a·Macaulay2·pointer·to·a·foreign |
| 29 | ······pointer | 29 | ······pointer |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | o1·=·5 | 81 | o1·=·5 |
| 82 | o1·:·ForeignObject·of·type·int32</code></pre> | 82 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x |
| 86 | o2·=·0x7f | 86 | o2·=·0x7fbf879b9280 |
| 87 | o2·:·Pointer</code></pre> | 87 | o2·:·Pointer</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·int·ptr | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·int·ptr |
| 91 | o3·=·5 | 91 | o3·=·5 |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | i1·:·x·=·int·5 | 19 | i1·:·x·=·int·5 |
| 20 | o1·=·5 | 20 | o1·=·5 |
| 21 | o1·:·ForeignObject·of·type·int32 | 21 | o1·:·ForeignObject·of·type·int32 |
| 22 | i2·:·ptr·=·address·x | 22 | i2·:·ptr·=·address·x |
| 23 | o2·=·0x7f | 23 | o2·=·0x7fbf879b9280 |
| 24 | o2·:·Pointer | 24 | o2·:·Pointer |
| 25 | i3·:·int·ptr | 25 | i3·:·int·ptr |
| 26 | o3·=·5 | 26 | o3·=·5 |
| 27 | o3·:·ForeignObject·of·type·int32 | 27 | o3·:·ForeignObject·of·type·int32 |
| Offset 74, 15 lines modified | Offset 74, 15 lines modified | ||
| 74 | ········<div> | 74 | ········<div> |
| 75 | ··········<p>This·is·syntactic·sugar·for·<code·class="language-macaulay2">T·value·ptr</code>·(see·<a·title="dereference·a·pointer"·href="___Foreign__Type_sp__Pointer.html">ForeignType·Pointer</a>)·for·dereferencing·pointers.</p> | 75 | ··········<p>This·is·syntactic·sugar·for·<code·class="language-macaulay2">T·value·ptr</code>·(see·<a·title="dereference·a·pointer"·href="___Foreign__Type_sp__Pointer.html">ForeignType·Pointer</a>)·for·dereferencing·pointers.</p> |
| 76 | ········</div> | 76 | ········</div> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·voidstar·address·int·5 | 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·voidstar·address·int·5 |
| 80 | o1·=·0x7f | 80 | o1·=·0x7f1a28194250 |
| 81 | o1·:·ForeignObject·of·type·void*</code></pre> | 81 | o1·:·ForeignObject·of·type·void*</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·int·*·ptr | 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·int·*·ptr |
| 85 | o2·=·5 | 85 | o2·=·5 |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | ····*·Outputs: | 15 | ····*·Outputs: |
| 16 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,·of·type·T; | 16 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,·of·type·T; |
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | This·is·syntactic·sugar·for·T·value·ptr·(see·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r)·for | 18 | This·is·syntactic·sugar·for·T·value·ptr·(see·_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8T_\x8y_\x8p_\x8e_\x8·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r)·for |
| 19 | dereferencing·pointers. | 19 | dereferencing·pointers. |
| 20 | i1·:·ptr·=·voidstar·address·int·5 | 20 | i1·:·ptr·=·voidstar·address·int·5 |
| 21 | o1·=·0x7f | 21 | o1·=·0x7f1a28194250 |
| 22 | o1·:·ForeignObject·of·type·void* | 22 | o1·:·ForeignObject·of·type·void* |
| 23 | i2·:·int·*·ptr | 23 | i2·:·int·*·ptr |
| 24 | o2·=·5 | 24 | o2·=·5 |
| 25 | o2·:·ForeignObject·of·type·int32 | 25 | o2·:·ForeignObject·of·type·int32 |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | o1·=·myunion | 81 | o1·=·myunion |
| 82 | o1·:·ForeignUnionType</code></pre> | 82 | o1·:·ForeignUnionType</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·myunion·27 | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·myunion·27 |
| 86 | o2·=·HashTable{"bar"·=>·6.9 | 86 | o2·=·HashTable{"bar"·=>·6.90073e-310} |
| 87 | ···············"foo"·=>·27 | 87 | ···············"foo"·=>·27 |
| 88 | o2·:·ForeignObject·of·type·myunion</code></pre> | 88 | o2·:·ForeignObject·of·type·myunion</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·myunion·pi | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·myunion·pi |
| Offset 21, 15 lines modified | Offset 21, 15 lines modified | ||
| 21 | i1·:·myunion·=·foreignUnionType("myunion",·{"foo"·=>·int,·"bar"·=>·double}) | 21 | i1·:·myunion·=·foreignUnionType("myunion",·{"foo"·=>·int,·"bar"·=>·double}) |
| 22 | o1·=·myunion | 22 | o1·=·myunion |
| 23 | o1·:·ForeignUnionType | 23 | o1·:·ForeignUnionType |
| 24 | i2·:·myunion·27 | 24 | i2·:·myunion·27 |
| 25 | o2·=·HashTable{"bar"·=>·6.9 | 25 | o2·=·HashTable{"bar"·=>·6.90073e-310} |
| 26 | ···············"foo"·=>·27 | 26 | ···············"foo"·=>·27 |
| 27 | o2·:·ForeignObject·of·type·myunion | 27 | o2·:·ForeignObject·of·type·myunion |
| 28 | i3·:·myunion·pi | 28 | i3·:·myunion·pi |
| 29 | o3·=·HashTable{"bar"·=>·3.14159···} | 29 | o3·=·HashTable{"bar"·=>·3.14159···} |
| 30 | ···············"foo"·=>·1413754136 | 30 | ···············"foo"·=>·1413754136 |
| Offset 54, 44 lines modified | Offset 54, 44 lines modified | ||
| 54 | o1·=·20 | 54 | o1·=·20 |
| 55 | o1·:·ForeignObject·of·type·int32</code></pre> | 55 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 56 | </td>··········</tr> | 56 | </td>··········</tr> |
| 57 | ··········<tr> | 57 | ··········<tr> |
| 58 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x | 58 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x |
| 59 | o2·=·int32{Address·=>·0x7f | 59 | o2·=·int32{Address·=>·0x7f462a8f2640}</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ········</table> | 61 | ········</table> |
| 62 | ········<div> | 62 | ········<div> |
| 63 | ··········<p>These·pointers·can·be·accessed·using·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> | 63 | ··········<p>These·pointers·can·be·accessed·using·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> |
| 64 | ········</div> | 64 | ········</div> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·address·x | 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·address·x |
| 68 | o3·=·0x7f | 68 | o3·=·0x7f462a8f2640 |
| 69 | o3·:·Pointer</code></pre> | 69 | o3·:·Pointer</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ········</table> | 71 | ········</table> |
| 72 | ········<div> | 72 | ········<div> |
| 73 | ··········<p>Simple·arithmetic·can·be·performed·on·pointers.</p> | 73 | ··········<p>Simple·arithmetic·can·be·performed·on·pointers.</p> |
| 74 | ········</div> | 74 | ········</div> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·ptr·+·5 | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·ptr·+·5 |
| 78 | o4·=·0x7f | 78 | o4·=·0x7f462a8f2645 |
| 79 | o4·:·Pointer</code></pre> | 79 | o4·:·Pointer</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·ptr·-·3 | 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·ptr·-·3 |
| 83 | o5·=·0x7f | 83 | o5·=·0x7f462a8f263d |
| 84 | o5·:·Pointer</code></pre> | 84 | o5·:·Pointer</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ········</table> | 86 | ········</table> |
| 87 | ······</div> | 87 | ······</div> |
| 88 | ······<div·class="waystouse"> | 88 | ······<div·class="waystouse"> |
| 89 | ········<h2>Functions·and·methods·returning·a·pointer:</h2> | 89 | ········<h2>Functions·and·methods·returning·a·pointer:</h2> |
| Offset 10, 30 lines modified | Offset 10, 30 lines modified | ||
| 10 | i1·:·x·=·int·20 | 10 | i1·:·x·=·int·20 |
| 11 | o1·=·20 | 11 | o1·=·20 |
| 12 | o1·:·ForeignObject·of·type·int32 | 12 | o1·:·ForeignObject·of·type·int32 |
| 13 | i2·:·peek·x | 13 | i2·:·peek·x |
| 14 | o2·=·int32{Address·=>·0x7f | 14 | o2·=·int32{Address·=>·0x7f462a8f2640} |
| 15 | These·pointers·can·be·accessed·using·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s. | 15 | These·pointers·can·be·accessed·using·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s. |
| 16 | i3·:·ptr·=·address·x | 16 | i3·:·ptr·=·address·x |
| 17 | o3·=·0x7f | 17 | o3·=·0x7f462a8f2640 |
| 18 | o3·:·Pointer | 18 | o3·:·Pointer |
| 19 | Simple·arithmetic·can·be·performed·on·pointers. | 19 | Simple·arithmetic·can·be·performed·on·pointers. |
| 20 | i4·:·ptr·+·5 | 20 | i4·:·ptr·+·5 |
| 21 | o4·=·0x7f | 21 | o4·=·0x7f462a8f2645 |
| 22 | o4·:·Pointer | 22 | o4·:·Pointer |
| 23 | i5·:·ptr·-·3 | 23 | i5·:·ptr·-·3 |
| 24 | o5·=·0x7f | 24 | o5·=·0x7f462a8f263d |
| 25 | o5·:·Pointer | 25 | o5·:·Pointer |
| 26 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·p\x8po\x8oi\x8in\x8nt\x8te\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 26 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·p\x8po\x8oi\x8in\x8nt\x8te\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 27 | ····*·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s·--·pointer·to·type·or·object | 27 | ····*·_\x8a_\x8d_\x8d_\x8r_\x8e_\x8s_\x8s·--·pointer·to·type·or·object |
| 28 | *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·p\x8po\x8oi\x8in\x8nt\x8te\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 28 | *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·p\x8po\x8oi\x8in\x8nt\x8te\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 29 | ····*·*·Pointer·=·Thing·--·see·_\x8*_\x8·_\x8v_\x8o_\x8i_\x8d_\x8s_\x8t_\x8a_\x8r_\x8·_\x8=_\x8·_\x8T_\x8h_\x8i_\x8n_\x8g·--·assign·value·to·object·at | 29 | ····*·*·Pointer·=·Thing·--·see·_\x8*_\x8·_\x8v_\x8o_\x8i_\x8d_\x8s_\x8t_\x8a_\x8r_\x8·_\x8=_\x8·_\x8T_\x8h_\x8i_\x8n_\x8g·--·assign·value·to·object·at |
| 30 | ······address | 30 | ······address |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | o1·=·mpfr | 54 | o1·=·mpfr |
| 55 | o1·:·SharedLibrary</code></pre> | 55 | o1·:·SharedLibrary</code></pre> |
| 56 | </td>··········</tr> | 56 | </td>··········</tr> |
| 57 | ··········<tr> | 57 | ··········<tr> |
| 58 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·mpfr | 58 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·mpfr |
| 59 | o2·=·SharedLibrary{0x7f | 59 | o2·=·SharedLibrary{0x7feffd2b5550,·mpfr}</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ········</table> | 61 | ········</table> |
| 62 | ······</div> | 62 | ······</div> |
| 63 | ······<div·class="waystouse"> | 63 | ······<div·class="waystouse"> |
| 64 | ········<h2>Functions·and·methods·returning·a·shared·library:</h2> | 64 | ········<h2>Functions·and·methods·returning·a·shared·library:</h2> |
| 65 | ········<ul> | 65 | ········<ul> |
| 66 | ··········<li> | 66 | ··········<li> |
| Offset 12, 15 lines modified | Offset 12, 15 lines modified | ||
| 12 | i1·:·mpfr·=·openSharedLibrary·"mpfr" | 12 | i1·:·mpfr·=·openSharedLibrary·"mpfr" |
| 13 | o1·=·mpfr | 13 | o1·=·mpfr |
| 14 | o1·:·SharedLibrary | 14 | o1·:·SharedLibrary |
| 15 | i2·:·peek·mpfr | 15 | i2·:·peek·mpfr |
| 16 | o2·=·SharedLibrary{0x7f | 16 | o2·=·SharedLibrary{0x7feffd2b5550,·mpfr} |
| 17 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·a\x8an\x8nd\x8d·m\x8me\x8et\x8th\x8ho\x8od\x8ds\x8s·r\x8re\x8et\x8tu\x8ur\x8rn\x8ni\x8in\x8ng\x8g·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 18 | ····*·_\x8o_\x8p_\x8e_\x8n_\x8S_\x8h_\x8a_\x8r_\x8e_\x8d_\x8L_\x8i_\x8b_\x8r_\x8a_\x8r_\x8y·--·open·a·shared·library | 18 | ····*·_\x8o_\x8p_\x8e_\x8n_\x8S_\x8h_\x8a_\x8r_\x8e_\x8d_\x8L_\x8i_\x8b_\x8r_\x8a_\x8r_\x8y·--·open·a·shared·library |
| 19 | *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* | 19 | *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·s\x8sh\x8ha\x8ar\x8re\x8ed\x8d·l\x8li\x8ib\x8br\x8ra\x8ar\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 20 | ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType)·--·see | 20 | ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType)·--·see |
| 21 | ······_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n·--·construct·a·foreign·function | 21 | ······_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n·--·construct·a·foreign·function |
| 22 | ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList)·--·see | 22 | ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList)·--·see |
| 23 | ······_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n·--·construct·a·foreign·function | 23 | ······_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n·--·construct·a·foreign·function |
| Offset 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | o1·=·5 | 75 | o1·=·5 |
| 76 | o1·:·ForeignObject·of·type·int32</code></pre> | 76 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x |
| 80 | o2·=·0x7f | 80 | o2·=·0x7fe2b2cf2640 |
| 81 | o2·:·Pointer</code></pre> | 81 | o2·:·Pointer</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·*ptr·=·int·6 | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·*ptr·=·int·6 |
| 85 | o3·=·6 | 85 | o3·=·6 |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i1·:·x·=·int·5 | 17 | i1·:·x·=·int·5 |
| 18 | o1·=·5 | 18 | o1·=·5 |
| 19 | o1·:·ForeignObject·of·type·int32 | 19 | o1·:·ForeignObject·of·type·int32 |
| 20 | i2·:·ptr·=·address·x | 20 | i2·:·ptr·=·address·x |
| 21 | o2·=·0x7f | 21 | o2·=·0x7fe2b2cf2640 |
| 22 | o2·:·Pointer | 22 | o2·:·Pointer |
| 23 | i3·:·*ptr·=·int·6 | 23 | i3·:·*ptr·=·int·6 |
| 24 | o3·=·6 | 24 | o3·=·6 |
| 25 | o3·:·ForeignObject·of·type·int32 | 25 | o3·:·ForeignObject·of·type·int32 |
| Offset 70, 27 lines modified | Offset 70, 27 lines modified | ||
| 70 | ········<div> | 70 | ········<div> |
| 71 | ··········<p>If·<span·class="tt">x</span>·is·a·foreign·type,·then·this·returns·the·address·to·the·<span·class="tt">ffi_type</span>·struct·used·by·<span·class="tt">libffi</span>·to·identify·the·type.</p> | 71 | ··········<p>If·<span·class="tt">x</span>·is·a·foreign·type,·then·this·returns·the·address·to·the·<span·class="tt">ffi_type</span>·struct·used·by·<span·class="tt">libffi</span>·to·identify·the·type.</p> |
| 72 | ········</div> | 72 | ········</div> |
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·address·int | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·address·int |
| 76 | o1·=·0x5 | 76 | o1·=·0x557ecefa6c20 |
| 77 | o1·:·Pointer</code></pre> | 77 | o1·:·Pointer</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ········</table> | 79 | ········</table> |
| 80 | ········<div> | 80 | ········<div> |
| 81 | ··········<p>If·<span·class="tt">x</span>·is·a·foreign·object,·then·this·returns·the·address·to·the·object.··It·behaves·like·the·<span·class="tt">&</span>·"address-of"·operator·in·C.</p> | 81 | ··········<p>If·<span·class="tt">x</span>·is·a·foreign·object,·then·this·returns·the·address·to·the·object.··It·behaves·like·the·<span·class="tt">&</span>·"address-of"·operator·in·C.</p> |
| 82 | ········</div> | 82 | ········</div> |
| 83 | ········<table·class="examples"> | 83 | ········<table·class="examples"> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·address·int·5 | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·address·int·5 |
| 86 | o2·=·0x7f | 86 | o2·=·0x7f5bed8f24d0 |
| 87 | o2·:·Pointer</code></pre> | 87 | o2·:·Pointer</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| 90 | ······</div> | 90 | ······</div> |
| 91 | ······<div·class="waystouse"> | 91 | ······<div·class="waystouse"> |
| 92 | ········<h2>Ways·to·use·<span·class="tt">address</span>:</h2> | 92 | ········<h2>Ways·to·use·<span·class="tt">address</span>:</h2> |
| Offset 12, 22 lines modified | Offset 12, 22 lines modified | ||
| 12 | ····*·Outputs: | 12 | ····*·Outputs: |
| 13 | ··········o·a·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r, | 13 | ··········o·a·_\x8p_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r, |
| 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 15 | If·x·is·a·foreign·type,·then·this·returns·the·address·to·the·ffi_type·struct | 15 | If·x·is·a·foreign·type,·then·this·returns·the·address·to·the·ffi_type·struct |
| 16 | used·by·libffi·to·identify·the·type. | 16 | used·by·libffi·to·identify·the·type. |
| 17 | i1·:·address·int | 17 | i1·:·address·int |
| 18 | o1·=·0x5 | 18 | o1·=·0x557ecefa6c20 |
| 19 | o1·:·Pointer | 19 | o1·:·Pointer |
| 20 | If·x·is·a·foreign·object,·then·this·returns·the·address·to·the·object.·It | 20 | If·x·is·a·foreign·object,·then·this·returns·the·address·to·the·object.·It |
| 21 | behaves·like·the·&·"address-of"·operator·in·C. | 21 | behaves·like·the·&·"address-of"·operator·in·C. |
| 22 | i2·:·address·int·5 | 22 | i2·:·address·int·5 |
| 23 | o2·=·0x7f | 23 | o2·=·0x7f5bed8f24d0 |
| 24 | o2·:·Pointer | 24 | o2·:·Pointer |
| 25 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ad\x8dd\x8dr\x8re\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ad\x8dd\x8dr\x8re\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·address(ForeignObject) | 26 | ····*·address(ForeignObject) |
| 27 | ····*·address(ForeignType) | 27 | ····*·address(ForeignType) |
| 28 | ····*·address(Nothing)·(missing·documentation) | 28 | ····*·address(Nothing)·(missing·documentation) |
| 29 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 204, 15 lines modified | Offset 204, 15 lines modified | ||
| 204 | o16·=·free | 204 | o16·=·free |
| 205 | o16·:·ForeignFunction</code></pre> | 205 | o16·:·ForeignFunction</code></pre> |
| 206 | </td>··········</tr> | 206 | </td>··········</tr> |
| 207 | ··········<tr> | 207 | ··········<tr> |
| 208 | <td>··············<pre><code·class="language-macaulay2">i17·:·x·=·malloc·8 | 208 | <td>··············<pre><code·class="language-macaulay2">i17·:·x·=·malloc·8 |
| 209 | o17·=·0x7f | 209 | o17·=·0x7f10240639d0 |
| 210 | o17·:·ForeignObject·of·type·void*</code></pre> | 210 | o17·:·ForeignObject·of·type·void*</code></pre> |
| 211 | </td>··········</tr> | 211 | </td>··········</tr> |
| 212 | ··········<tr> | 212 | ··········<tr> |
| 213 | <td>··············<pre><code·class="language-macaulay2">i18·:·registerFinalizer(x,·free)</code></pre> | 213 | <td>··············<pre><code·class="language-macaulay2">i18·:·registerFinalizer(x,·free)</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ········</table> | 215 | ········</table> |
| Offset 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | i16·:·free·=·foreignFunction("free",·void,·voidstar) | 96 | i16·:·free·=·foreignFunction("free",·void,·voidstar) |
| 97 | o16·=·free | 97 | o16·=·free |
| 98 | o16·:·ForeignFunction | 98 | o16·:·ForeignFunction |
| 99 | i17·:·x·=·malloc·8 | 99 | i17·:·x·=·malloc·8 |
| 100 | o17·=·0x7f | 100 | o17·=·0x7f10240639d0 |
| 101 | o17·:·ForeignObject·of·type·void* | 101 | o17·:·ForeignObject·of·type·void* |
| 102 | i18·:·registerFinalizer(x,·free) | 102 | i18·:·registerFinalizer(x,·free) |
| 103 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fo\x8or\x8re\x8ei\x8ig\x8gn\x8nF\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8n:\x8:·*\x8**\x8**\x8**\x8**\x8* | 103 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fo\x8or\x8re\x8ei\x8ig\x8gn\x8nF\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8n:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 104 | ····*·foreignFunction(Pointer,String,ForeignType,VisibleList) | 104 | ····*·foreignFunction(Pointer,String,ForeignType,VisibleList) |
| 105 | ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType) | 105 | ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType) |
| 106 | ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList) | 106 | ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList) |
| Offset 79, 39 lines modified | Offset 79, 39 lines modified | ||
| 79 | ········<div> | 79 | ········<div> |
| 80 | ··········<p>Allocate·<span·class="tt">n</span>·bytes·of·memory·using·the·<a·href="../../Macaulay2Doc/html/___G__C_spgarbage_spcollector.html">GC·garbage·collector</a>.</p> | 80 | ··········<p>Allocate·<span·class="tt">n</span>·bytes·of·memory·using·the·<a·href="../../Macaulay2Doc/html/___G__C_spgarbage_spcollector.html">GC·garbage·collector</a>.</p> |
| 81 | ········</div> | 81 | ········</div> |
| 82 | ········<table·class="examples"> | 82 | ········<table·class="examples"> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·getMemory·8 | 84 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·getMemory·8 |
| 85 | o1·=·0x7f | 85 | o1·=·0x7f5529bac9a0 |
| 86 | o1·:·ForeignObject·of·type·void*</code></pre> | 86 | o1·:·ForeignObject·of·type·void*</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ········</table> | 88 | ········</table> |
| 89 | ········<div> | 89 | ········<div> |
| 90 | ··········<p>If·the·memory·will·not·contain·any·pointers,·then·set·the·<span·class="tt">Atomic</span>·option·to·<a·href="../../Macaulay2Doc/html/_true.html">true</a>.</p> | 90 | ··········<p>If·the·memory·will·not·contain·any·pointers,·then·set·the·<span·class="tt">Atomic</span>·option·to·<a·href="../../Macaulay2Doc/html/_true.html">true</a>.</p> |
| 91 | ········</div> | 91 | ········</div> |
| 92 | ········<table·class="examples"> | 92 | ········<table·class="examples"> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·getMemory(8,·Atomic·=>·true) | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·getMemory(8,·Atomic·=>·true) |
| 95 | o2·=·0x7f | 95 | o2·=·0x7f55350f2450 |
| 96 | o2·:·ForeignObject·of·type·void*</code></pre> | 96 | o2·:·ForeignObject·of·type·void*</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ········</table> | 98 | ········</table> |
| 99 | ········<div> | 99 | ········<div> |
| 100 | ··········<p>Alternatively,·a·foreign·object·type·<span·class="tt">T</span>·may·be·specified.··In·this·case,·the·number·of·bytes·and·whether·the·<span·class="tt">Atomic</span>·option·should·be·set·will·be·determined·automatically.</p> | 100 | ··········<p>Alternatively,·a·foreign·object·type·<span·class="tt">T</span>·may·be·specified.··In·this·case,·the·number·of·bytes·and·whether·the·<span·class="tt">Atomic</span>·option·should·be·set·will·be·determined·automatically.</p> |
| 101 | ········</div> | 101 | ········</div> |
| 102 | ········<table·class="examples"> | 102 | ········<table·class="examples"> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·getMemory·int | 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·getMemory·int |
| 105 | o3·=·0x7f | 105 | o3·=·0x7f55350f2360 |
| 106 | o3·:·ForeignObject·of·type·void*</code></pre> | 106 | o3·:·ForeignObject·of·type·void*</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ······</div> | 109 | ······</div> |
| 110 | ······<div> | 110 | ······<div> |
| 111 | ········<h2>See·also</h2> | 111 | ········<h2>See·also</h2> |
| Offset 15, 30 lines modified | Offset 15, 30 lines modified | ||
| 15 | ··········o·Atomic·=>·...,·default·value·false | 15 | ··········o·Atomic·=>·...,·default·value·false |
| 16 | ····*·Outputs: | 16 | ····*·Outputs: |
| 17 | ··········o·an·instance·of·the·type·_\x8v_\x8o_\x8i_\x8d_\x8s_\x8t_\x8a_\x8r, | 17 | ··········o·an·instance·of·the·type·_\x8v_\x8o_\x8i_\x8d_\x8s_\x8t_\x8a_\x8r, |
| 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 19 | Allocate·n·bytes·of·memory·using·the·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r. | 19 | Allocate·n·bytes·of·memory·using·the·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r. |
| 20 | i1·:·ptr·=·getMemory·8 | 20 | i1·:·ptr·=·getMemory·8 |
| 21 | o1·=·0x7f | 21 | o1·=·0x7f5529bac9a0 |
| 22 | o1·:·ForeignObject·of·type·void* | 22 | o1·:·ForeignObject·of·type·void* |
| 23 | If·the·memory·will·not·contain·any·pointers,·then·set·the·Atomic·option·to | 23 | If·the·memory·will·not·contain·any·pointers,·then·set·the·Atomic·option·to |
| 24 | _\x8t_\x8r_\x8u_\x8e. | 24 | _\x8t_\x8r_\x8u_\x8e. |
| 25 | i2·:·ptr·=·getMemory(8,·Atomic·=>·true) | 25 | i2·:·ptr·=·getMemory(8,·Atomic·=>·true) |
| 26 | o2·=·0x7f | 26 | o2·=·0x7f55350f2450 |
| 27 | o2·:·ForeignObject·of·type·void* | 27 | o2·:·ForeignObject·of·type·void* |
| 28 | Alternatively,·a·foreign·object·type·T·may·be·specified.·In·this·case,·the | 28 | Alternatively,·a·foreign·object·type·T·may·be·specified.·In·this·case,·the |
| 29 | number·of·bytes·and·whether·the·Atomic·option·should·be·set·will·be·determined | 29 | number·of·bytes·and·whether·the·Atomic·option·should·be·set·will·be·determined |
| 30 | automatically. | 30 | automatically. |
| 31 | i3·:·ptr·=·getMemory·int | 31 | i3·:·ptr·=·getMemory·int |
| 32 | o3·=·0x7f | 32 | o3·=·0x7f55350f2360 |
| 33 | o3·:·ForeignObject·of·type·void* | 33 | o3·:·ForeignObject·of·type·void* |
| 34 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 34 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 35 | ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a | 35 | ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a |
| 36 | ······foreign·object | 36 | ······foreign·object |
| 37 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8tM\x8Me\x8em\x8mo\x8or\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* | 37 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8tM\x8Me\x8em\x8mo\x8or\x8ry\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 38 | ····*·getMemory(ForeignType) | 38 | ····*·getMemory(ForeignType) |
| Offset 91, 23 lines modified | Offset 91, 23 lines modified | ||
| 91 | o3·:·FunctionClosure</code></pre> | 91 | o3·:·FunctionClosure</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))</code></pre> | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·collectGarbage() | 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·collectGarbage() |
| 98 | freeing·memory·at·0x7f | 98 | freeing·memory·at·0x7fdd600639d0 |
| 99 | freeing·memory·at·0x7f | 99 | freeing·memory·at·0x7fdd60069180 |
| 100 | freeing·memory·at·0x7f | 100 | freeing·memory·at·0x7fdd60066c50 |
| 101 | freeing·memory·at·0x7f44e0063bc0 | ||
| 102 | freeing·memory·at·0x7f44e005f3f0 | ||
| 103 | freeing·memory·at·0x7f44e00639f0 | ||
| 104 | freeing·memory·at·0x7f44e006a210 | ||
| 105 | freeing·memory·at·0x7f | 101 | freeing·memory·at·0x7fdd6006a230 |
| 102 | freeing·memory·at·0x7fdd6005f3f0 | ||
| 103 | freeing·memory·at·0x7fdd600639f0 | ||
| 104 | freeing·memory·at·0x7fdd6006a210 | ||
| 105 | freeing·memory·at·0x7fdd60063bc0 | ||
| 106 | freeing·memory·at·0x7f | 106 | freeing·memory·at·0x7fdd60063bf0</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ······</div> | 109 | ······</div> |
| 110 | ······<div> | 110 | ······<div> |
| 111 | ········<h2>See·also</h2> | 111 | ········<h2>See·also</h2> |
| 112 | ········<ul> | 112 | ········<ul> |
| 113 | ··········<li> | 113 | ··········<li> |
| Offset 32, 21 lines modified | Offset 32, 21 lines modified | ||
| 32 | i3·:·finalizer·=·x·->·(print("freeing·memory·at·"·|·net·x);·free·x) | 32 | i3·:·finalizer·=·x·->·(print("freeing·memory·at·"·|·net·x);·free·x) |
| 33 | o3·=·finalizer | 33 | o3·=·finalizer |
| 34 | o3·:·FunctionClosure | 34 | o3·:·FunctionClosure |
| 35 | i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer)) | 35 | i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer)) |
| 36 | i5·:·collectGarbage() | 36 | i5·:·collectGarbage() |
| 37 | freeing·memory·at·0x7f44e0063bf0 | ||
| 38 | freeing·memory·at·0x7f44e0069180 | ||
| 39 | freeing·memory·at·0x7f44e0066c50 | ||
| 40 | freeing·memory·at·0x7f44e0063bc0 | ||
| 41 | freeing·memory·at·0x7f44e005f3f0 | ||
| 42 | freeing·memory·at·0x7f44e00639f0 | ||
| 43 | freeing·memory·at·0x7f44e006a210 | ||
| 44 | freeing·memory·at·0x7f44e006a230 | ||
| 45 | freeing·memory·at·0x7f | 37 | freeing·memory·at·0x7fdd600639d0 |
| 38 | freeing·memory·at·0x7fdd60069180 | ||
| 39 | freeing·memory·at·0x7fdd60066c50 | ||
| 40 | freeing·memory·at·0x7fdd6006a230 | ||
| 41 | freeing·memory·at·0x7fdd6005f3f0 | ||
| 42 | freeing·memory·at·0x7fdd600639f0 | ||
| 43 | freeing·memory·at·0x7fdd6006a210 | ||
| 44 | freeing·memory·at·0x7fdd60063bc0 | ||
| 45 | freeing·memory·at·0x7fdd60063bf0 | ||
| 46 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 46 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 47 | ····*·_\x8g_\x8e_\x8t_\x8M_\x8e_\x8m_\x8o_\x8r_\x8y·--·allocate·memory·using·the·garbage·collector | 47 | ····*·_\x8g_\x8e_\x8t_\x8M_\x8e_\x8m_\x8o_\x8r_\x8y·--·allocate·memory·using·the·garbage·collector |
| 48 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 48 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 49 | ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a | 49 | ····*·_\x8r_\x8e_\x8g_\x8i_\x8s_\x8t_\x8e_\x8r_\x8F_\x8i_\x8n_\x8a_\x8l_\x8i_\x8z_\x8e_\x8r_\x8(_\x8F_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8,_\x8F_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8)·--·register·a·finalizer·for·a |
| 50 | ······foreign·object | 50 | ······foreign·object |
| Offset 108, 22 lines modified | Offset 108, 22 lines modified | ||
| 108 | ········<div> | 108 | ········<div> |
| 109 | ··········<p>Foreign·pointer·objects·are·converted·to·<a·title="pointer·to·memory·address"·href="___Pointer.html">Pointer</a>·objects.</p> | 109 | ··········<p>Foreign·pointer·objects·are·converted·to·<a·title="pointer·to·memory·address"·href="___Pointer.html">Pointer</a>·objects.</p> |
| 110 | ········</div> | 110 | ········</div> |
| 111 | ········<table·class="examples"> | 111 | ········<table·class="examples"> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·x·=·voidstar·address·int·5 | 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·x·=·voidstar·address·int·5 |
| 114 | o5·=·0x7f4 | 114 | o5·=·0x7f4c109d7ca0 |
| 115 | o5·:·ForeignObject·of·type·void*</code></pre> | 115 | o5·:·ForeignObject·of·type·void*</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·value·x | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·value·x |
| 119 | o6·=·0x7f4 | 119 | o6·=·0x7f4c109d7ca0 |
| 120 | o6·:·Pointer</code></pre> | 120 | o6·:·Pointer</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ········</table> | 122 | ········</table> |
| 123 | ········<div> | 123 | ········<div> |
| 124 | ··········<p>Foreign·string·objects·are·converted·to·strings.</p> | 124 | ··········<p>Foreign·string·objects·are·converted·to·strings.</p> |
| 125 | ········</div> | 125 | ········</div> |
| Offset 35, 20 lines modified | Offset 35, 20 lines modified | ||
| 35 | o4·=·5 | 35 | o4·=·5 |
| 36 | o4·:·RR·(of·precision·53) | 36 | o4·:·RR·(of·precision·53) |
| 37 | Foreign·pointer·objects·are·converted·to·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·objects. | 37 | Foreign·pointer·objects·are·converted·to·_\x8P_\x8o_\x8i_\x8n_\x8t_\x8e_\x8r·objects. |
| 38 | i5·:·x·=·voidstar·address·int·5 | 38 | i5·:·x·=·voidstar·address·int·5 |
| 39 | o5·=·0x7f4 | 39 | o5·=·0x7f4c109d7ca0 |
| 40 | o5·:·ForeignObject·of·type·void* | 40 | o5·:·ForeignObject·of·type·void* |
| 41 | i6·:·value·x | 41 | i6·:·value·x |
| 42 | o6·=·0x7f4 | 42 | o6·=·0x7f4c109d7ca0 |
| 43 | o6·:·Pointer | 43 | o6·:·Pointer |
| 44 | Foreign·string·objects·are·converted·to·strings. | 44 | Foreign·string·objects·are·converted·to·strings. |
| 45 | i7·:·x·=·charstar·"Hello,·world!" | 45 | i7·:·x·=·charstar·"Hello,·world!" |
| 46 | o7·=·Hello,·world! | 46 | o7·=·Hello,·world! |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | c2VyaWVzKFJpbmdFbGVtZW50LFpaKQ== | 8 | c2VyaWVzKFJpbmdFbGVtZW50LFpaKQ== |
| 9 | #:len=1234 | 9 | #:len=1234 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29uc3RydWN0aW5nIGEgZm9ybWFsIHNl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29uc3RydWN0aW5nIGEgZm9ybWFsIHNl |
| 11 | cmllcyIsICJsaW5lbnVtIiA9PiAzNzIsIElucHV0cyA9PiB7U1BBTntUVHsicyJ9LCIsICIsU1BB | 11 | cmllcyIsICJsaW5lbnVtIiA9PiAzNzIsIElucHV0cyA9PiB7U1BBTntUVHsicyJ9LCIsICIsU1BB |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=13 | 7 | #:len=13 |
| 8 | dG9yaWNHcm9lYm5lcg== | 8 | dG9yaWNHcm9lYm5lcg== |
| 9 | #:len=2522 | 9 | #:len=2522 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2FsY3VsYXRlcyBhIEdyb2VibmVyIGJh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2FsY3VsYXRlcyBhIEdyb2VibmVyIGJh |
| 11 | c2lzIG9mIHRoZSB0b3JpYyBpZGVhbCBJX0EsIGdpdmVuIEE7IGludm9rZXMgXCJncm9lYm5lclwi | 11 | c2lzIG9mIHRoZSB0b3JpYyBpZGVhbCBJX0EsIGdpdmVuIEE7IGludm9rZXMgXCJncm9lYm5lclwi |
| Offset 6, 27 lines modified | Offset 6, 27 lines modified | ||
| 6 | ·····|·1·2·3·4·| | 6 | ·····|·1·2·3·4·| |
| 7 | ··············2·······4 | 7 | ··············2·······4 |
| 8 | o1·:·Matrix·ZZ··<--·ZZ | 8 | o1·:·Matrix·ZZ··<--·ZZ |
| 9 | i2·:·s·=·temporaryFileName() | 9 | i2·:·s·=·temporaryFileName() |
| 10 | o2·=·/tmp/M2- | 10 | o2·=·/tmp/M2-3579676-0/0 |
| 11 | i3·:·F·=·openOut(s) | 11 | i3·:·F·=·openOut(s) |
| 12 | o3·=·/tmp/M2- | 12 | o3·=·/tmp/M2-3579676-0/0 |
| 13 | o3·:·File | 13 | o3·:·File |
| 14 | i4·:·putMatrix(F,A) | 14 | i4·:·putMatrix(F,A) |
| 15 | i5·:·close(F) | 15 | i5·:·close(F) |
| 16 | o5·=·/tmp/M2- | 16 | o5·=·/tmp/M2-3579676-0/0 |
| 17 | o5·:·File | 17 | o5·:·File |
| 18 | i6·:·getMatrix(s) | 18 | i6·:·getMatrix(s) |
| 19 | o6·=·|·1·1·1·1·| | 19 | o6·=·|·1·1·1·1·| |
| 20 | ·····|·1·2·3·4·| | 20 | ·····|·1·2·3·4·| |
| Offset 75, 30 lines modified | Offset 75, 30 lines modified | ||
| 75 | ··············2·······4 | 75 | ··············2·······4 |
| 76 | o1·:·Matrix·ZZ··<--·ZZ</code></pre> | 76 | o1·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·s·=·temporaryFileName() | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·s·=·temporaryFileName() |
| 80 | o2·=·/tmp/M2- | 80 | o2·=·/tmp/M2-3579676-0/0</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·F·=·openOut(s) | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·F·=·openOut(s) |
| 84 | o3·=·/tmp/M2- | 84 | o3·=·/tmp/M2-3579676-0/0 |
| 85 | o3·:·File</code></pre> | 85 | o3·:·File</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·putMatrix(F,A)</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·putMatrix(F,A)</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·close(F) | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·close(F) |
| 92 | o5·=·/tmp/M2- | 92 | o5·=·/tmp/M2-3579676-0/0 |
| 93 | o5·:·File</code></pre> | 93 | o5·:·File</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·getMatrix(s) | 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·getMatrix(s) |
| 97 | o6·=·|·1·1·1·1·| | 97 | o6·=·|·1·1·1·1·| |
| Offset 17, 24 lines modified | Offset 17, 24 lines modified | ||
| 17 | o1·=·|·1·1·1·1·| | 17 | o1·=·|·1·1·1·1·| |
| 18 | ·····|·1·2·3·4·| | 18 | ·····|·1·2·3·4·| |
| 19 | ··············2·······4 | 19 | ··············2·······4 |
| 20 | o1·:·Matrix·ZZ··<--·ZZ | 20 | o1·:·Matrix·ZZ··<--·ZZ |
| 21 | i2·:·s·=·temporaryFileName() | 21 | i2·:·s·=·temporaryFileName() |
| 22 | o2·=·/tmp/M2- | 22 | o2·=·/tmp/M2-3579676-0/0 |
| 23 | i3·:·F·=·openOut(s) | 23 | i3·:·F·=·openOut(s) |
| 24 | o3·=·/tmp/M2- | 24 | o3·=·/tmp/M2-3579676-0/0 |
| 25 | o3·:·File | 25 | o3·:·File |
| 26 | i4·:·putMatrix(F,A) | 26 | i4·:·putMatrix(F,A) |
| 27 | i5·:·close(F) | 27 | i5·:·close(F) |
| 28 | o5·=·/tmp/M2- | 28 | o5·=·/tmp/M2-3579676-0/0 |
| 29 | o5·:·File | 29 | o5·:·File |
| 30 | i6·:·getMatrix(s) | 30 | i6·:·getMatrix(s) |
| 31 | o6·=·|·1·1·1·1·| | 31 | o6·=·|·1·1·1·1·| |
| 32 | ·····|·1·2·3·4·| | 32 | ·····|·1·2·3·4·| |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | Zm91cmllck1vdHpraW4= | 8 | Zm91cmllck1vdHpraW4= |
| 9 | #:len=3383 | 9 | #:len=3383 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiaW50ZXJjaGFuZ2UgaW5lcXVhbGl0eS9n | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiaW50ZXJjaGFuZ2UgaW5lcXVhbGl0eS9n |
| 11 | ZW5lcmF0b3IgcmVwcmVzZW50YXRpb24gb2YgYSBwb2x5aGVkcmFsIGNvbmUiLCAibGluZW51bSIg | 11 | ZW5lcmF0b3IgcmVwcmVzZW50YXRpb24gb2YgYSBwb2x5aGVkcmFsIGNvbmUiLCAibGluZW51bSIg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=32 | 7 | #:len=32 |
| 8 | aXNGUFQoLi4uLFFHb3JlbnN0ZWluSW5kZXg9Pi4uLik= | 8 | aXNGUFQoLi4uLFFHb3JlbnN0ZWluSW5kZXg9Pi4uLik= |
| 9 | #:len=298 | 9 | #:len=298 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTI0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTI0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tpc0ZQVCxRR29yZW5zdGVpbkluZGV4XSwiaXNGUFQo | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tpc0ZQVCxRR29yZW5zdGVpbkluZGV4XSwiaXNGUFQo |
| Offset 155, 31 lines modified | Offset 155, 31 lines modified | ||
| 155 | i26·:·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)·--·FinalAttempt·improves·the·estimate·slightly | 155 | i26·:·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true)·--·FinalAttempt·improves·the·estimate·slightly |
| 156 | o26·=·{.142067,·.144} | 156 | o26·=·{.142067,·.144} |
| 157 | o26·:·List | 157 | o26·:·List |
| 158 | i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) | 158 | i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) |
| 159 | ·--·used·1. | 159 | ·--·used·1.77562s·(cpu);·1.11476s·(thread);·0s·(gc) |
| 160 | o27·=·{.142067,·.144} | 160 | o27·=·{.142067,·.144} |
| 161 | o27·:·List | 161 | o27·:·List |
| 162 | i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) | 162 | i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) |
| 163 | ·--·used· | 163 | ·--·used·1.09549s·(cpu);·0.706766s·(thread);·0s·(gc) |
| 164 | ······1 | 164 | ······1 |
| 165 | o28·=·- | 165 | o28·=·- |
| 166 | ······7 | 166 | ······7 |
| 167 | o28·:·QQ | 167 | o28·:·QQ |
| 168 | i29·:·time·fpt(f,·DepthOfSearch·=>·4) | 168 | i29·:·time·fpt(f,·DepthOfSearch·=>·4) |
| 169 | ·--·used·0.7 | 169 | ·--·used·0.798633s·(cpu);·0.520108s·(thread);·0s·(gc) |
| 170 | ······1 | 170 | ······1 |
| 171 | o29·=·- | 171 | o29·=·- |
| 172 | ······7 | 172 | ······7 |
| 173 | o29·:·QQ | 173 | o29·:·QQ |
| Offset 43, 34 lines modified | Offset 43, 34 lines modified | ||
| 43 | o12·=·220 | 43 | o12·=·220 |
| 44 | i13·:·R·=·ZZ/17[x,y,z]; | 44 | i13·:·R·=·ZZ/17[x,y,z]; |
| 45 | i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial | 45 | i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial |
| 46 | i15·:·time·frobeniusNu(3,·f) | 46 | i15·:·time·frobeniusNu(3,·f) |
| 47 | ·--·used·0.00 | 47 | ·--·used·0.00400092s·(cpu);·0.00364846s·(thread);·0s·(gc) |
| 48 | o15·=·3756 | 48 | o15·=·3756 |
| 49 | i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) | 49 | i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) |
| 50 | ·--·used·0.2 | 50 | ·--·used·0.288617s·(cpu);·0.214377s·(thread);·0s·(gc) |
| 51 | o16·=·3756 | 51 | o16·=·3756 |
| 52 | i17·:·R·=·ZZ/5[x,y,z]; | 52 | i17·:·R·=·ZZ/5[x,y,z]; |
| 53 | i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z; | 53 | i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z; |
| 54 | i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default | 54 | i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default |
| 55 | ·--·used·0.2 | 55 | ·--·used·0.297063s·(cpu);·0.183561s·(thread);·0s·(gc) |
| 56 | o19·=·499 | 56 | o19·=·499 |
| 57 | i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) | 57 | i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) |
| 58 | ·--·used· | 58 | ·--·used·1.14825s·(cpu);·0.971725s·(thread);·0s·(gc) |
| 59 | o20·=·499 | 59 | o20·=·499 |
| 60 | i21·:·R·=·ZZ/3[x,y]; | 60 | i21·:·R·=·ZZ/3[x,y]; |
| 61 | i22·:·M·=·ideal(x,·y); | 61 | i22·:·M·=·ideal(x,·y); |
| Offset 85, 34 lines modified | Offset 85, 34 lines modified | ||
| 85 | o24·=·8 | 85 | o24·=·8 |
| 86 | i25·:·R·=·ZZ/5[x,y,z]; | 86 | i25·:·R·=·ZZ/5[x,y,z]; |
| 87 | i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8; | 87 | i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8; |
| 88 | i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) | 88 | i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) |
| 89 | ·--·used·0. | 89 | ·--·used·0.814193s·(cpu);·0.541579s·(thread);·0s·(gc) |
| 90 | o27·=·1124 | 90 | o27·=·1124 |
| 91 | i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) | 91 | i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) |
| 92 | ·--·used· | 92 | ·--·used·1.102s·(cpu);·0.7974s·(thread);·0s·(gc) |
| 93 | o28·=·1124 | 93 | o28·=·1124 |
| 94 | i29·:·M·=·ideal(x,·y,·z); | 94 | i29·:·M·=·ideal(x,·y,·z); |
| 95 | o29·:·Ideal·of·R | 95 | o29·:·Ideal·of·R |
| 96 | i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) | 96 | i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) |
| 97 | ·--·used·1. | 97 | ·--·used·1.3517s·(cpu);·1.19908s·(thread);·0s·(gc) |
| 98 | o30·=·97 | 98 | o30·=·97 |
| 99 | i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier | 99 | i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier |
| 100 | ·--·used·0. | 100 | ·--·used·0.529203s·(cpu);·0.440303s·(thread);·0s·(gc) |
| 101 | o31·=·97 | 101 | o31·=·97 |
| 102 | i32·:·R·=·ZZ/7[x,y]; | 102 | i32·:·R·=·ZZ/7[x,y]; |
| 103 | i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2; | 103 | i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2; |
| Offset 324, 33 lines modified | Offset 324, 33 lines modified | ||
| 324 | ········</table> | 324 | ········</table> |
| 325 | ········<div> | 325 | ········<div> |
| 326 | ··········<p>The·computations·performed·when·<span·class="tt">FinalAttempt</span>·is·set·to·<span·class="tt">true</span>·are·often·slow,·and·often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be·used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·<span·class="tt">Attempts</span>·or·<span·class="tt">DepthOfSearch</span>,·instead.</p> | 326 | ··········<p>The·computations·performed·when·<span·class="tt">FinalAttempt</span>·is·set·to·<span·class="tt">true</span>·are·often·slow,·and·often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be·used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·<span·class="tt">Attempts</span>·or·<span·class="tt">DepthOfSearch</span>,·instead.</p> |
| 327 | ········</div> | 327 | ········</div> |
| 328 | ········<table·class="examples"> | 328 | ········<table·class="examples"> |
| 329 | ··········<tr> | 329 | ··········<tr> |
| 330 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) | 330 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) |
| 331 | ·--·used·1. | 331 | ·--·used·1.77562s·(cpu);·1.11476s·(thread);·0s·(gc) |
| 332 | o27·=·{.142067,·.144} | 332 | o27·=·{.142067,·.144} |
| 333 | o27·:·List</code></pre> | 333 | o27·:·List</code></pre> |
| 334 | </td>··········</tr> | 334 | </td>··········</tr> |
| 335 | ··········<tr> | 335 | ··········<tr> |
| 336 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) | 336 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) |
| 337 | ·--·used· | 337 | ·--·used·1.09549s·(cpu);·0.706766s·(thread);·0s·(gc) |
| 338 | ······1 | 338 | ······1 |
| 339 | o28·=·- | 339 | o28·=·- |
| 340 | ······7 | 340 | ······7 |
| 341 | o28·:·QQ</code></pre> | 341 | o28·:·QQ</code></pre> |
| 342 | </td>··········</tr> | 342 | </td>··········</tr> |
| 343 | ··········<tr> | 343 | ··········<tr> |
| 344 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·fpt(f,·DepthOfSearch·=>·4) | 344 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·fpt(f,·DepthOfSearch·=>·4) |
| 345 | ·--·used·0.7 | 345 | ·--·used·0.798633s·(cpu);·0.520108s·(thread);·0s·(gc) |
| 346 | ······1 | 346 | ······1 |
| 347 | o29·=·- | 347 | o29·=·- |
| 348 | ······7 | 348 | ······7 |
| 349 | o29·:·QQ</code></pre> | 349 | o29·:·QQ</code></pre> |
| 350 | </td>··········</tr> | 350 | </td>··········</tr> |
| Offset 229, 29 lines modified | Offset 229, 29 lines modified | ||
| 229 | o26·:·List | 229 | o26·:·List |
| 230 | The·computations·performed·when·FinalAttempt·is·set·to·true·are·often·slow,·and | 230 | The·computations·performed·when·FinalAttempt·is·set·to·true·are·often·slow,·and |
| 231 | often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be | 231 | often·fail·to·improve·the·estimate,·and·for·this·reason,·this·option·should·be |
| 232 | used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·Attempts | 232 | used·sparingly.·It·is·often·more·effective·to·increase·the·values·of·Attempts |
| 233 | or·DepthOfSearch,·instead. | 233 | or·DepthOfSearch,·instead. |
| 234 | i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) | 234 | i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) |
| 235 | ·--·used·1. | 235 | ·--·used·1.77562s·(cpu);·1.11476s·(thread);·0s·(gc) |
| 236 | o27·=·{.142067,·.144} | 236 | o27·=·{.142067,·.144} |
| 237 | o27·:·List | 237 | o27·:·List |
| 238 | i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) | 238 | i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) |
| 239 | ·--·used· | 239 | ·--·used·1.09549s·(cpu);·0.706766s·(thread);·0s·(gc) |
| 240 | ······1 | 240 | ······1 |
| 241 | o28·=·- | 241 | o28·=·- |
| 242 | ······7 | 242 | ······7 |
| 243 | o28·:·QQ | 243 | o28·:·QQ |
| 244 | i29·:·time·fpt(f,·DepthOfSearch·=>·4) | 244 | i29·:·time·fpt(f,·DepthOfSearch·=>·4) |
| 245 | ·--·used·0.7 | 245 | ·--·used·0.798633s·(cpu);·0.520108s·(thread);·0s·(gc) |
| 246 | ······1 | 246 | ······1 |
| 247 | o29·=·- | 247 | o29·=·- |
| 248 | ······7 | 248 | ······7 |
| 249 | o29·:·QQ | 249 | o29·:·QQ |
| 250 | As·seen·in·several·examples·above,·when·the·exact·answer·is·not·found,·a·list | 250 | As·seen·in·several·examples·above,·when·the·exact·answer·is·not·found,·a·list |
| Offset 175, 21 lines modified | Offset 175, 21 lines modified | ||
| 175 | <td>··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/17[x,y,z];</code></pre> | 175 | <td>··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/17[x,y,z];</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ··········<tr> | 177 | ··········<tr> |
| 178 | <td>··············<pre><code·class="language-macaulay2">i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial</code></pre> | 178 | <td>··············<pre><code·class="language-macaulay2">i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial</code></pre> |
| 179 | </td>··········</tr> | 179 | </td>··········</tr> |
| 180 | ··········<tr> | 180 | ··········<tr> |
| 181 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·frobeniusNu(3,·f) | 181 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·frobeniusNu(3,·f) |
| 182 | ·--·used·0.00 | 182 | ·--·used·0.00400092s·(cpu);·0.00364846s·(thread);·0s·(gc) |
| 183 | o15·=·3756</code></pre> | 183 | o15·=·3756</code></pre> |
| 184 | </td>··········</tr> | 184 | </td>··········</tr> |
| 185 | ··········<tr> | 185 | ··········<tr> |
| 186 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) | 186 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) |
| 187 | ·--·used·0.2 | 187 | ·--·used·0.288617s·(cpu);·0.214377s·(thread);·0s·(gc) |
| 188 | o16·=·3756</code></pre> | 188 | o16·=·3756</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ········</table> | 190 | ········</table> |
| 191 | ········<div> | 191 | ········<div> |
| 192 | ··········<p>The·valid·values·for·the·option·<span·class="tt">ContainmentTest</span>·are·<span·class="tt">FrobeniusPower</span>,·<span·class="tt">FrobeniusRoot</span>,·and·<span·class="tt">StandardPower</span>.·The·default·value·of·this·option·depends·on·what·is·passed·to·<span·class="tt">frobeniusNu</span>.·Indeed,·by·default,·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusRoot</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·a·ring·element·$f$,·and·is·set·to·<span·class="tt">StandardPower</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·an·ideal·$I$.·We·describe·the·consequences·of·setting·<span·class="tt">ContainmentTest</span>·to·each·of·these·values·below.</p> | 192 | ··········<p>The·valid·values·for·the·option·<span·class="tt">ContainmentTest</span>·are·<span·class="tt">FrobeniusPower</span>,·<span·class="tt">FrobeniusRoot</span>,·and·<span·class="tt">StandardPower</span>.·The·default·value·of·this·option·depends·on·what·is·passed·to·<span·class="tt">frobeniusNu</span>.·Indeed,·by·default,·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusRoot</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·a·ring·element·$f$,·and·is·set·to·<span·class="tt">StandardPower</span>·if·<span·class="tt">frobeniusNu</span>·is·passed·an·ideal·$I$.·We·describe·the·consequences·of·setting·<span·class="tt">ContainmentTest</span>·to·each·of·these·values·below.</p> |
| 193 | ··········<p>First,·if·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">StandardPower</span>,·then·the·ideal·containments·checked·when·computing·<span·class="tt">frobeniusNu(e,I,J)</span>·are·verified·directly.·That·is,·the·standard·power·$I^n$·is·first·computed,·and·a·check·is·then·run·to·see·if·it·is·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.</p> | 193 | ··········<p>First,·if·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">StandardPower</span>,·then·the·ideal·containments·checked·when·computing·<span·class="tt">frobeniusNu(e,I,J)</span>·are·verified·directly.·That·is,·the·standard·power·$I^n$·is·first·computed,·and·a·check·is·then·run·to·see·if·it·is·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.</p> |
| Offset 200, 21 lines modified | Offset 200, 21 lines modified | ||
| 200 | <td>··············<pre><code·class="language-macaulay2">i17·:·R·=·ZZ/5[x,y,z];</code></pre> | 200 | <td>··············<pre><code·class="language-macaulay2">i17·:·R·=·ZZ/5[x,y,z];</code></pre> |
| 201 | </td>··········</tr> | 201 | </td>··········</tr> |
| 202 | ··········<tr> | 202 | ··········<tr> |
| 203 | <td>··············<pre><code·class="language-macaulay2">i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;</code></pre> | 203 | <td>··············<pre><code·class="language-macaulay2">i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;</code></pre> |
| 204 | </td>··········</tr> | 204 | </td>··········</tr> |
| 205 | ··········<tr> | 205 | ··········<tr> |
| 206 | <td>··············<pre><code·class="language-macaulay2">i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default | 206 | <td>··············<pre><code·class="language-macaulay2">i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default |
| 207 | ·--·used·0.2 | 207 | ·--·used·0.297063s·(cpu);·0.183561s·(thread);·0s·(gc) |
| 208 | o19·=·499</code></pre> | 208 | o19·=·499</code></pre> |
| 209 | </td>··········</tr> | 209 | </td>··········</tr> |
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) | 211 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) |
| 212 | ·--·used· | 212 | ·--·used·1.14825s·(cpu);·0.971725s·(thread);·0s·(gc) |
| 213 | o20·=·499</code></pre> | 213 | o20·=·499</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ········</table> | 215 | ········</table> |
| 216 | ········<div> | 216 | ········<div> |
| 217 | ··········<p>Finally,·when·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusPower</span>,·then·instead·of·producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·<span·class="tt">frobeniusNu</span>·instead·outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius·power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the·$n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as·defined·in·the·paper·<i>Frobenius·Powers</i>·by·Hernández,·Teixeira,·and·Witt,·which·can·be·computed·with·the·function·<a·title="compute·a·(generalized)·Frobenius·power·of·an·ideal"·href="../../TestIdeals/html/_frobenius__Power.html">frobeniusPower</a>,·from·the·<a·title="a·package·for·calculations·of·singularities·in·positive·characteristic·"·href="../../TestIdeals/html/index.html">TestIdeals</a>·package.·In·particular,·<span·class="tt">frobeniusNu(e,I,J)</span>·and·<span·class="tt">frobeniusNu(e,I,J,ContainmentTest=>FrobeniusPower)</span>·need·not·agree.·However,·they·will·agree·when·$I$·is·a·principal·ideal.</p> | 217 | ··········<p>Finally,·when·<span·class="tt">ContainmentTest</span>·is·set·to·<span·class="tt">FrobeniusPower</span>,·then·instead·of·producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·<span·class="tt">frobeniusNu</span>·instead·outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius·power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the·$n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as·defined·in·the·paper·<i>Frobenius·Powers</i>·by·Hernández,·Teixeira,·and·Witt,·which·can·be·computed·with·the·function·<a·title="compute·a·(generalized)·Frobenius·power·of·an·ideal"·href="../../TestIdeals/html/_frobenius__Power.html">frobeniusPower</a>,·from·the·<a·title="a·package·for·calculations·of·singularities·in·positive·characteristic·"·href="../../TestIdeals/html/index.html">TestIdeals</a>·package.·In·particular,·<span·class="tt">frobeniusNu(e,I,J)</span>·and·<span·class="tt">frobeniusNu(e,I,J,ContainmentTest=>FrobeniusPower)</span>·need·not·agree.·However,·they·will·agree·when·$I$·is·a·principal·ideal.</p> |
| 218 | ········</div> | 218 | ········</div> |
| Offset 246, 38 lines modified | Offset 246, 38 lines modified | ||
| 246 | <td>··············<pre><code·class="language-macaulay2">i25·:·R·=·ZZ/5[x,y,z];</code></pre> | 246 | <td>··············<pre><code·class="language-macaulay2">i25·:·R·=·ZZ/5[x,y,z];</code></pre> |
| 247 | </td>··········</tr> | 247 | </td>··········</tr> |
| 248 | ··········<tr> | 248 | ··········<tr> |
| 249 | <td>··············<pre><code·class="language-macaulay2">i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;</code></pre> | 249 | <td>··············<pre><code·class="language-macaulay2">i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;</code></pre> |
| 250 | </td>··········</tr> | 250 | </td>··········</tr> |
| 251 | ··········<tr> | 251 | ··········<tr> |
| 252 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) | 252 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) |
| 253 | ·--·used·0. | 253 | ·--·used·0.814193s·(cpu);·0.541579s·(thread);·0s·(gc) |
| 254 | o27·=·1124</code></pre> | 254 | o27·=·1124</code></pre> |
| 255 | </td>··········</tr> | 255 | </td>··········</tr> |
| 256 | ··········<tr> | 256 | ··········<tr> |
| 257 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) | 257 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) |
| 258 | ·--·used· | 258 | ·--·used·1.102s·(cpu);·0.7974s·(thread);·0s·(gc) |
| 259 | o28·=·1124</code></pre> | 259 | o28·=·1124</code></pre> |
| 260 | </td>··········</tr> | 260 | </td>··········</tr> |
| 261 | ··········<tr> | 261 | ··········<tr> |
| 262 | <td>··············<pre><code·class="language-macaulay2">i29·:·M·=·ideal(x,·y,·z); | 262 | <td>··············<pre><code·class="language-macaulay2">i29·:·M·=·ideal(x,·y,·z); |
| 263 | o29·:·Ideal·of·R</code></pre> | 263 | o29·:·Ideal·of·R</code></pre> |
| 264 | </td>··········</tr> | 264 | </td>··········</tr> |
| 265 | ··········<tr> | 265 | ··········<tr> |
| 266 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) | 266 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) |
| 267 | ·--·used·1. | 267 | ·--·used·1.3517s·(cpu);·1.19908s·(thread);·0s·(gc) |
| 268 | o30·=·97</code></pre> | 268 | o30·=·97</code></pre> |
| 269 | </td>··········</tr> | 269 | </td>··········</tr> |
| 270 | ··········<tr> | 270 | ··········<tr> |
| 271 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier | 271 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier |
| 272 | ·--·used·0. | 272 | ·--·used·0.529203s·(cpu);·0.440303s·(thread);·0s·(gc) |
| 273 | o31·=·97</code></pre> | 273 | o31·=·97</code></pre> |
| 274 | </td>··········</tr> | 274 | </td>··········</tr> |
| 275 | ········</table> | 275 | ········</table> |
| 276 | ········<div> | 276 | ········<div> |
| 277 | ··········<p>The·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">true</span>)·can·be·turned·off·to·tell·<span·class="tt">frobeniusNu</span>·to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take·the·minimum.</p> | 277 | ··········<p>The·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">true</span>)·can·be·turned·off·to·tell·<span·class="tt">frobeniusNu</span>·to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take·the·minimum.</p> |
| 278 | ········</div> | 278 | ········</div> |
| Offset 107, 19 lines modified | Offset 107, 19 lines modified | ||
| 107 | algorithms,·namely·diagonal·polynomials,·binomials,·forms·in·two·variables,·and | 107 | algorithms,·namely·diagonal·polynomials,·binomials,·forms·in·two·variables,·and |
| 108 | polynomials·whose·factors·are·in·simple·normal·crossing.·This·feature·can·be | 108 | polynomials·whose·factors·are·in·simple·normal·crossing.·This·feature·can·be |
| 109 | disabled·by·setting·the·option·UseSpecialAlgorithms·(default·value·true)·to | 109 | disabled·by·setting·the·option·UseSpecialAlgorithms·(default·value·true)·to |
| 110 | false. | 110 | false. |
| 111 | i13·:·R·=·ZZ/17[x,y,z]; | 111 | i13·:·R·=·ZZ/17[x,y,z]; |
| 112 | i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial | 112 | i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial |
| 113 | i15·:·time·frobeniusNu(3,·f) | 113 | i15·:·time·frobeniusNu(3,·f) |
| 114 | ·--·used·0.00 | 114 | ·--·used·0.00400092s·(cpu);·0.00364846s·(thread);·0s·(gc) |
| 115 | o15·=·3756 | 115 | o15·=·3756 |
| 116 | i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) | 116 | i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) |
| 117 | ·--·used·0.2 | 117 | ·--·used·0.288617s·(cpu);·0.214377s·(thread);·0s·(gc) |
| 118 | o16·=·3756 | 118 | o16·=·3756 |
| 119 | The·valid·values·for·the·option·ContainmentTest·are·FrobeniusPower, | 119 | The·valid·values·for·the·option·ContainmentTest·are·FrobeniusPower, |
| 120 | FrobeniusRoot,·and·StandardPower.·The·default·value·of·this·option·depends·on | 120 | FrobeniusRoot,·and·StandardPower.·The·default·value·of·this·option·depends·on |
| 121 | what·is·passed·to·frobeniusNu.·Indeed,·by·default,·ContainmentTest·is·set·to | 121 | what·is·passed·to·frobeniusNu.·Indeed,·by·default,·ContainmentTest·is·set·to |
| 122 | FrobeniusRoot·if·frobeniusNu·is·passed·a·ring·element·$f$,·and·is·set·to | 122 | FrobeniusRoot·if·frobeniusNu·is·passed·a·ring·element·$f$,·and·is·set·to |
| 123 | StandardPower·if·frobeniusNu·is·passed·an·ideal·$I$.·We·describe·the | 123 | StandardPower·if·frobeniusNu·is·passed·an·ideal·$I$.·We·describe·the |
| Offset 134, 19 lines modified | Offset 134, 19 lines modified | ||
| 134 | is·contained·in·$J$.·The·output·is·unaffected,·but·this·option·often·speeds·up | 134 | is·contained·in·$J$.·The·output·is·unaffected,·but·this·option·often·speeds·up |
| 135 | computations,·specially·when·a·polynomial·or·principal·ideal·is·passed·as·the | 135 | computations,·specially·when·a·polynomial·or·principal·ideal·is·passed·as·the |
| 136 | second·argument. | 136 | second·argument. |
| 137 | i17·:·R·=·ZZ/5[x,y,z]; | 137 | i17·:·R·=·ZZ/5[x,y,z]; |
| 138 | i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z; | 138 | i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z; |
| 139 | i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by | 139 | i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by |
| 140 | default | 140 | default |
| 141 | ·--·used·0.2 | 141 | ·--·used·0.297063s·(cpu);·0.183561s·(thread);·0s·(gc) |
| 142 | o19·=·499 | 142 | o19·=·499 |
| 143 | i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) | 143 | i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) |
| 144 | ·--·used· | 144 | ·--·used·1.14825s·(cpu);·0.971725s·(thread);·0s·(gc) |
| 145 | o20·=·499 | 145 | o20·=·499 |
| 146 | Finally,·when·ContainmentTest·is·set·to·FrobeniusPower,·then·instead·of | 146 | Finally,·when·ContainmentTest·is·set·to·FrobeniusPower,·then·instead·of |
| 147 | producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·frobeniusNu·instead | 147 | producing·the·invariant·$\nu_I^J(p^e)$·as·defined·above,·frobeniusNu·instead |
| 148 | outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius | 148 | outputs·the·maximal·integer·$n$·such·that·the·$n$^{th}·(generalized)·Frobenius |
| 149 | power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the | 149 | power·of·$I$·is·not·contained·in·the·$p^e$-th·Frobenius·power·of·$J$.·Here,·the |
| 150 | $n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as | 150 | $n$^{th}·Frobenius·power·of·$I$,·when·$n$·is·a·nonnegative·integer,·is·as |
| Offset 168, 31 lines modified | Offset 168, 31 lines modified | ||
| 168 | The·function·frobeniusNu·works·by·searching·through·the·list·of·potential | 168 | The·function·frobeniusNu·works·by·searching·through·the·list·of·potential |
| 169 | integers·$n$·and·checking·containments·of·$I^n$·in·the·specified·Frobenius | 169 | integers·$n$·and·checking·containments·of·$I^n$·in·the·specified·Frobenius |
| 170 | power·of·$J$.·The·way·this·search·is·approached·is·specified·by·the·option | 170 | power·of·$J$.·The·way·this·search·is·approached·is·specified·by·the·option |
| 171 | Search,·which·can·be·set·to·Binary·(the·default·value)·or·Linear. | 171 | Search,·which·can·be·set·to·Binary·(the·default·value)·or·Linear. |
| 172 | i25·:·R·=·ZZ/5[x,y,z]; | 172 | i25·:·R·=·ZZ/5[x,y,z]; |
| 173 | i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8; | 173 | i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8; |
| 174 | i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) | 174 | i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) |
| 175 | ·--·used·0. | 175 | ·--·used·0.814193s·(cpu);·0.541579s·(thread);·0s·(gc) |
| 176 | o27·=·1124 | 176 | o27·=·1124 |
| 177 | i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) | 177 | i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) |
| 178 | ·--·used· | 178 | ·--·used·1.102s·(cpu);·0.7974s·(thread);·0s·(gc) |
| 179 | o28·=·1124 | 179 | o28·=·1124 |
| 180 | i29·:·M·=·ideal(x,·y,·z); | 180 | i29·:·M·=·ideal(x,·y,·z); |
| 181 | o29·:·Ideal·of·R | 181 | o29·:·Ideal·of·R |
| 182 | i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) | 182 | i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) |
| 183 | ·--·used·1. | 183 | ·--·used·1.3517s·(cpu);·1.19908s·(thread);·0s·(gc) |
| 184 | o30·=·97 | 184 | o30·=·97 |
| 185 | i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets | 185 | i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets |
| 186 | luckier | 186 | luckier |
| 187 | ·--·used·0. | 187 | ·--·used·0.529203s·(cpu);·0.440303s·(thread);·0s·(gc) |
| 188 | o31·=·97 | 188 | o31·=·97 |
| 189 | The·option·AtOrigin·(default·value·true)·can·be·turned·off·to·tell·frobeniusNu | 189 | The·option·AtOrigin·(default·value·true)·can·be·turned·off·to·tell·frobeniusNu |
| 190 | to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take | 190 | to·effectively·do·the·computation·over·all·possible·maximal·ideals·$J$·and·take |
| 191 | the·minimum. | 191 | the·minimum. |
| 192 | i32·:·R·=·ZZ/7[x,y]; | 192 | i32·:·R·=·ZZ/7[x,y]; |
| 193 | i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2; | 193 | i33·:·f·=·(x·-·1)^3·-·(y·-·2)^2; |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 7 | #:len=4 | 7 | #:len=4 |
| 8 | YXJjcw== | 8 | YXJjcw== |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| Offset 208, 21 lines modified | Offset 208, 21 lines modified | ||
| 208 | ······|·7/9··7/10·3/7·2/3·| | 208 | ······|·7/9··7/10·3/7·2/3·| |
| 209 | ······|·7/10·7/3··5/2·1···| | 209 | ······|·7/10·7/3··5/2·1···| |
| 210 | ···············3·······4 | 210 | ···············3·······4 |
| 211 | o26·:·Matrix·QQ··<--·QQ | 211 | o26·:·Matrix·QQ··<--·QQ |
| 212 | i27·:·time·C·=·orbitClosure(X,Mat) | 212 | i27·:·time·C·=·orbitClosure(X,Mat) |
| 213 | ·--·used·2 | 213 | ·--·used·26.4249s·(cpu);·3.25724s·(thread);·0s·(gc) |
| 214 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety· | 214 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety· |
| 215 | o27·:·KClass | 215 | o27·:·KClass |
| 216 | i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) | 216 | i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) |
| 217 | ·--·used· | 217 | ·--·used·26.9537s·(cpu);·3.85994s·(thread);·0s·(gc) |
| 218 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety· | 218 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety· |
| 219 | o28·:·KClass | 219 | o28·:·KClass |
| 220 | i29·:· | 220 | i29·:· |
| Offset 336, 23 lines modified | Offset 336, 23 lines modified | ||
| 336 | ······|·7/10·7/3··5/2·1···| | 336 | ······|·7/10·7/3··5/2·1···| |
| 337 | ···············3·······4 | 337 | ···············3·······4 |
| 338 | o26·:·Matrix·QQ··<--·QQ</code></pre> | 338 | o26·:·Matrix·QQ··<--·QQ</code></pre> |
| 339 | </td>··········</tr> | 339 | </td>··········</tr> |
| 340 | ··········<tr> | 340 | ··········<tr> |
| 341 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·C·=·orbitClosure(X,Mat) | 341 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·C·=·orbitClosure(X,Mat) |
| 342 | ·--·used·2 | 342 | ·--·used·26.4249s·(cpu);·3.25724s·(thread);·0s·(gc) |
| 343 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety· | 343 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety· |
| 344 | o27·:·KClass</code></pre> | 344 | o27·:·KClass</code></pre> |
| 345 | </td>··········</tr> | 345 | </td>··········</tr> |
| 346 | ··········<tr> | 346 | ··········<tr> |
| 347 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) | 347 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) |
| 348 | ·--·used· | 348 | ·--·used·26.9537s·(cpu);·3.85994s·(thread);·0s·(gc) |
| 349 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety· | 349 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety· |
| 350 | o28·:·KClass</code></pre> | 350 | o28·:·KClass</code></pre> |
| 351 | </td>··········</tr> | 351 | </td>··········</tr> |
| 352 | ········</table> | 352 | ········</table> |
| 353 | ······</div> | 353 | ······</div> |
| Offset 242, 21 lines modified | Offset 242, 21 lines modified | ||
| 242 | o26·=·|·7/4··1/2··7···6/7·| | 242 | o26·=·|·7/4··1/2··7···6/7·| |
| 243 | ······|·7/9··7/10·3/7·2/3·| | 243 | ······|·7/9··7/10·3/7·2/3·| |
| 244 | ······|·7/10·7/3··5/2·1···| | 244 | ······|·7/10·7/3··5/2·1···| |
| 245 | ···············3·······4 | 245 | ···············3·······4 |
| 246 | o26·:·Matrix·QQ··<--·QQ | 246 | o26·:·Matrix·QQ··<--·QQ |
| 247 | i27·:·time·C·=·orbitClosure(X,Mat) | 247 | i27·:·time·C·=·orbitClosure(X,Mat) |
| 248 | ·--·used·2 | 248 | ·--·used·26.4249s·(cpu);·3.25724s·(thread);·0s·(gc) |
| 249 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety | 249 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety |
| 250 | o27·:·KClass | 250 | o27·:·KClass |
| 251 | i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) | 251 | i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) |
| 252 | ·--·used· | 252 | ·--·used·26.9537s·(cpu);·3.85994s·(thread);·0s·(gc) |
| 253 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety | 253 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety |
| 254 | o28·:·KClass | 254 | o28·:·KClass |
| 255 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 255 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 256 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8l_\x8i_\x8z_\x8e_\x8d_\x8F_\x8l_\x8a_\x8g_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·makes·a·generalized·flag·variety·as·a·GKM | 256 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8l_\x8i_\x8z_\x8e_\x8d_\x8F_\x8l_\x8a_\x8g_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·makes·a·generalized·flag·variety·as·a·GKM |
| 257 | ······variety | 257 | ······variety |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| Offset 32, 12 lines modified | Offset 32, 12 lines modified | ||
| 32 | ·········································5·=>·{6} | 32 | ·········································5·=>·{6} |
| 33 | ·········································6·=>·{} | 33 | ·········································6·=>·{} |
| 34 | o2·:·SortedDigraph | 34 | o2·:·SortedDigraph |
| 35 | i3·:·keys·H | 35 | i3·:·keys·H |
| 36 | o3·=·{newDigraph | 36 | o3·=·{map,·newDigraph,·digraph} |
| 37 | o3·:·List | 37 | o3·:·List |
| 38 | i4·:· | 38 | i4·:· |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | ·········································6·=>·{} | 83 | ·········································6·=>·{} |
| 84 | o2·:·SortedDigraph</code></pre> | 84 | o2·:·SortedDigraph</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·H | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·H |
| 88 | o3·=·{newDigraph | 88 | o3·=·{map,·newDigraph,·digraph} |
| 89 | o3·:·List</code></pre> | 89 | o3·:·List</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ········</table> | 91 | ········</table> |
| 92 | ······</div> | 92 | ······</div> |
| 93 | ······<div> | 93 | ······<div> |
| 94 | ········<h2>See·also</h2> | 94 | ········<h2>See·also</h2> |
| Offset 36, 15 lines modified | Offset 36, 15 lines modified | ||
| 36 | ·········································4·=>·{} | 36 | ·········································4·=>·{} |
| 37 | ·········································5·=>·{6} | 37 | ·········································5·=>·{6} |
| 38 | ·········································6·=>·{} | 38 | ·········································6·=>·{} |
| 39 | o2·:·SortedDigraph | 39 | o2·:·SortedDigraph |
| 40 | i3·:·keys·H | 40 | i3·:·keys·H |
| 41 | o3·=·{newDigraph | 41 | o3·=·{map,·newDigraph,·digraph} |
| 42 | o3·:·List | 42 | o3·:·List |
| 43 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 43 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 44 | ····*·_\x8t_\x8o_\x8p_\x8S_\x8o_\x8r_\x8t·--·topologically·sort·the·vertices·of·a·digraph | 44 | ····*·_\x8t_\x8o_\x8p_\x8S_\x8o_\x8r_\x8t·--·topologically·sort·the·vertices·of·a·digraph |
| 45 | ····*·_\x8S_\x8o_\x8r_\x8t_\x8e_\x8d_\x8D_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h·--·hashtable·used·in·topSort | 45 | ····*·_\x8S_\x8o_\x8r_\x8t_\x8e_\x8d_\x8D_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h·--·hashtable·used·in·topSort |
| 46 | ····*·_\x8t_\x8o_\x8p_\x8o_\x8l_\x8o_\x8g_\x8i_\x8c_\x8a_\x8l_\x8S_\x8o_\x8r_\x8t·--·outputs·a·list·of·vertices·in·a·topologically·sorted | 46 | ····*·_\x8t_\x8o_\x8p_\x8o_\x8l_\x8o_\x8g_\x8i_\x8c_\x8a_\x8l_\x8S_\x8o_\x8r_\x8t·--·outputs·a·list·of·vertices·in·a·topologically·sorted |
| 47 | ······order·of·a·DAG. | 47 | ······order·of·a·DAG. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | ZmluZFdlaWdodENvbnN0cmFpbnRz | 8 | ZmluZFdlaWdodENvbnN0cmFpbnRz |
| 9 | #:len=2630 | 9 | #:len=2630 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyBhIG1hdHJpeCBvZiB3ZWln | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyBhIG1hdHJpeCBvZiB3ZWln |
| 11 | aHQgY29uc3RyYWludHMiLCAibGluZW51bSIgPT4gNjcyLCBJbnB1dHMgPT4ge1NQQU57VFR7Ik0i | 11 | aHQgY29uc3RyYWludHMiLCAibGluZW51bSIgPT4gNjcyLCBJbnB1dHMgPT4ge1NQQU57VFR7Ik0i |
| Offset 103, 17 lines modified | Offset 103, 17 lines modified | ||
| 103 | i13·:·#compsJ | 103 | i13·:·#compsJ |
| 104 | o13·=·2 | 104 | o13·=·2 |
| 105 | i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 105 | i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 106 | o14·=·|·- | 106 | o14·=·|·-6·48·44·-23·-2·-11·-35·-26·27·-43·48·27·15·-22·25·-16·34·-29·46·-20 |
| 107 | ······----------------------------------------------------------------------- | 107 | ······----------------------------------------------------------------------- |
| 108 | ······ | 108 | ······40·21·-30·-38·-19·-8·-36·39·19·-29·-16·-29·-10·19·24·-24·| |
| 109 | ···············1·······36 | 109 | ···············1·······36 |
| 110 | o14·:·Matrix·kk··<--·kk | 110 | o14·:·Matrix·kk··<--·kk |
| 111 | i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 111 | i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 112 | o15·=·|·-48·-46·16·17·-1·-43·15·-1·12·-18·-6·-28·14·-28·-9·32·-22·-39·6·-47 | 112 | o15·=·|·-48·-46·16·17·-1·-43·15·-1·12·-18·-6·-28·14·-28·-9·32·-22·-39·6·-47 |
| Offset 121, 28 lines modified | Offset 121, 28 lines modified | ||
| 121 | ······28·-37·-47·38·-16·-15·34·27·-13·-43·22·16·0·-18·19·2·| | 121 | ······28·-37·-47·38·-16·-15·34·27·-13·-43·22·16·0·-18·19·2·| |
| 122 | ···············1·······36 | 122 | ···············1·······36 |
| 123 | o15·:·Matrix·kk··<--·kk | 123 | o15·:·Matrix·kk··<--·kk |
| 124 | i16·:·F1·=·sub(F,·(vars·S)|pt1) | 124 | i16·:·F1·=·sub(F,·(vars·S)|pt1) |
| 125 | ··············2·············2·····························2··············· | 125 | ··············2··············2·····························2··············· |
| 126 | o16·=·ideal·(a·· | 126 | o16·=·ideal·(a··+·25b*c·-·43c··+·27a*d·-·11b*d·+·44c*d·-·6d·,·a*b·-·19b*c·+ |
| 127 | ······----------------------------------------------------------------------- | 127 | ······----------------------------------------------------------------------- |
| 128 | ·········2······························2·················· | 128 | ·········2······························2··················2················ |
| 129 | ······ | 129 | ······46c··+·40a*d·+·15b*d·+·27c*d·+·48d·,·a*c·-·29b*c·-·8c··+·39a*d·-·20b*d |
| 130 | ······----------------------------------------------------------------------- | 130 | ······----------------------------------------------------------------------- |
| 131 | ·················2···2··············2······························2·····2·· | 131 | ··················2···2··············2······························2·····2·· |
| 132 | ······ | 132 | ······-·22c*d·-·2d·,·b··+·24b*c·+·19c··-·10a*d·+·21b*d·-·16c*d·-·35d·,·b*c··- |
| 133 | ······----------------------------------------------------------------------- | 133 | ······----------------------------------------------------------------------- |
| 134 | ···················2·········2········2········2······3···3················2· | 134 | ···················2·········2········2········2······3···3················2· |
| 135 | ······2 | 135 | ······29b*c*d·-·30c·d·-·36a*d··+·34b*d··+·48c*d··-·23d·,·c··-·24b*c*d·-·16c·d |
| 136 | ······----------------------------------------------------------------------- | 136 | ······----------------------------------------------------------------------- |
| 137 | ············2········2········2·····3 | 137 | ·············2········2········2······3 |
| 138 | ······ | 138 | ······+·19a*d··-·38b*d··-·29c*d··-·26d·) |
| 139 | o16·:·Ideal·of·S | 139 | o16·:·Ideal·of·S |
| 140 | i17·:·betti·res·F1 | 140 | i17·:·betti·res·F1 |
| 141 | ·············0·1·2·3 | 141 | ·············0·1·2·3 |
| 142 | o17·=·total:·1·6·8·3 | 142 | o17·=·total:·1·6·8·3 |
| Offset 179, 24 lines modified | Offset 179, 20 lines modified | ||
| 179 | ··········1:·.·4·4·1 | 179 | ··········1:·.·4·4·1 |
| 180 | ··········2:·.·2·4·2 | 180 | ··········2:·.·2·4·2 |
| 181 | o19·:·BettiTally | 181 | o19·:·BettiTally |
| 182 | i20·:·netList·decompose·F1 | 182 | i20·:·netList·decompose·F1 |
| 183 | ······+---------------------------------------------------------------------------------------------------------+ | 183 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 184 | o20·=·|ideal·(c· | 184 | o20·=·|ideal·(c·+·39d,·b·+·27d,·a·-·18d)························································································································| |
| 185 | ······+---------------------------------------------------------------------------------------------------------+ | 185 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 186 | ······| | 186 | ······|····························2··············2·····················2···3················2········2········2······3·····2················2·········2······3·| |
| 187 | ······|ideal·(a·-·29b·-·8c·-·13d,·b··+·24b*c·+·19c··+·34b*d·+·5c*d·+·37d·,·c··-·24b*c*d·-·16c·d·+·8b*d··+·22c*d··+·19d·,·b*c··-·29b*c*d·-·30c·d·-·38c*d··+·14d·)| | ||
| 187 | ······+---------------------------------------------------------------------------------------------------------+ | 188 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 188 | ······|ideal·(c·+·13d,·b·-·22d,·a·-·28d)········································································| | ||
| 189 | ······+---------------------------------------------------------------------------------------------------------+ | ||
| 190 | ······|·····························2······················2·························2···2····················2·| | ||
| 191 | ······|ideal·(a·-·24b·-·29c·+·22d,·c··+·33b*d·+·43c*d·+·41d·,·b*c·-·16b*d·+·4c*d·-·2d·,·b··-·9b*d·-·8c*d·-·19d·)| | ||
| 192 | ······+---------------------------------------------------------------------------------------------------------+ | ||
| 193 | i21·:·netList·decompose·F2 | 189 | i21·:·netList·decompose·F2 |
| 194 | ······+-------------------------------------------------------+ | 190 | ······+-------------------------------------------------------+ |
| 195 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| | 191 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| |
| 196 | ······+-------------------------------------------------------+ | 192 | ······+-------------------------------------------------------+ |
| 197 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| | 193 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| |
| Offset 12, 15 lines modified | Offset 12, 15 lines modified | ||
| 12 | ·············································2 | 12 | ·············································2 |
| 13 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 13 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 14 | o3·:·Ideal·of·S | 14 | o3·:·Ideal·of·S |
| 15 | i4·:·pt·=·randomPointOnRationalVariety·I | 15 | i4·:·pt·=·randomPointOnRationalVariety·I |
| 16 | o4·=·|· | 16 | o4·=·|·-25·20·-30·-16·24·-36·| |
| 17 | ··············1·······6 | 17 | ··············1·······6 |
| 18 | o4·:·Matrix·kk··<--·kk | 18 | o4·:·Matrix·kk··<--·kk |
| 19 | i5·:·sub(I,·pt)·==·0 | 19 | i5·:·sub(I,·pt)·==·0 |
| 20 | o5·=·true | 20 | o5·=·true |
| Offset 200, 67 lines modified | Offset 200, 67 lines modified | ||
| 200 | o12·=·{11,·8} | 200 | o12·=·{11,·8} |
| 201 | o12·:·List | 201 | o12·:·List |
| 202 | i13·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 202 | i13·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 203 | o13·=·|· | 203 | o13·=·|·2·-18·6·4·20·-11·44·-13·0·19·11·-47·-29·-8·-19·-22·19·-20·-29·-38·-24 |
| 204 | ······----------------------------------------------------------------------- | 204 | ······----------------------------------------------------------------------- |
| 205 | ······- | 205 | ······-16·-10·-29·| |
| 206 | ···············1·······24 | 206 | ···············1·······24 |
| 207 | o13·:·Matrix·kk··<--·kk | 207 | o13·:·Matrix·kk··<--·kk |
| 208 | i14·:·F1·=·sub(F,·(vars·S)|pt1) | 208 | i14·:·F1·=·sub(F,·(vars·S)|pt1) |
| 209 | ··············2····· | 209 | ··············2·····2·····························2···················2·· |
| 210 | o14·=·ideal·(a··+· | 210 | o14·=·ideal·(a··+·4c··+·19a*d·+·20b*d·-·18c*d·+·2d·,·a*b·-·19b*c·+·11c··- |
| 211 | ······----------------------------------------------------------------------- | 211 | ······----------------------------------------------------------------------- |
| 212 | ········ | 212 | ································2···················2························ |
| 213 | ······2 | 213 | ······22a*d·-·47b*d·-·11c*d·+·6d·,·a*c·-·24b*c·+·19c··-·16a*d·-·20b*d·-·29c*d |
| 214 | ······----------------------------------------------------------------------- | 214 | ······----------------------------------------------------------------------- |
| 215 | ··········· | 215 | ···········2···2··············2·····························2 |
| 216 | ······ | 216 | ······+·44d·,·b··-·10b*c·-·29c··-·29a*d·-·38b*d·-·8c*d·-·13d·) |
| 217 | o14·:·Ideal·of·S | 217 | o14·:·Ideal·of·S |
| 218 | i15·:·decompose·F1 | 218 | i15·:·decompose·F1 |
| 219 | ····································2··············2······················2 | 219 | ····································2··············2······················2 |
| 220 | o15·=·{ideal·(a·-· | 220 | o15·=·{ideal·(a·-·24b·+·19c·-·28d,·b··-·10b*c·-·29c··-·27b*d·+·38c*d·-·17d·), |
| 221 | ······----------------------------------------------------------------------- | 221 | ······----------------------------------------------------------------------- |
| 222 | ······ideal·(c·-· | 222 | ······ideal·(c·-·16d,·b·-·33d,·a·-·32d)} |
| 223 | o15·:·List | 223 | o15·:·List |
| 224 | i16·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 224 | i16·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 225 | o16·=·|·- | 225 | o16·=·|·-8·28·25·30·-12·-42·-20·-35·-7·-37·-5·45·19·20·-24·34·39·21·-47·-39 |
| 226 | ······----------------------------------------------------------------------- | 226 | ······----------------------------------------------------------------------- |
| 227 | ······- | 227 | ······-13·-18·34·0·| |
| 228 | ···············1·······24 | 228 | ···············1·······24 |
| 229 | o16·:·Matrix·kk··<--·kk | 229 | o16·:·Matrix·kk··<--·kk |
| 230 | i17·:·F2·=·sub(F,·(vars·S)|pt2) | 230 | i17·:·F2·=·sub(F,·(vars·S)|pt2) |
| 231 | ··············2·············2····························· | 231 | ··············2·············2·····························2··············· |
| 232 | o17·=·ideal·(a··-· | 232 | o17·=·ideal·(a··-·7b*c·+·30c··-·37a*d·-·12b*d·+·28c*d·-·8d·,·a*b·-·24b*c·- |
| 233 | ······----------------------------------------------------------------------- | 233 | ······----------------------------------------------------------------------- |
| 234 | ········ | 234 | ········2······························2···················2················ |
| 235 | ······ | 235 | ······5c··+·34a*d·+·45b*d·-·42c*d·+·25d·,·a*c·-·13b*c·+·39c··-·18a*d·+·21b*d |
| 236 | ······----------------------------------------------------------------------- | 236 | ······----------------------------------------------------------------------- |
| 237 | ···················2···2··············2······················2 | 237 | ···················2···2··············2······················2 |
| 238 | ······ | 238 | ······+·19c*d·-·20d·,·b··+·34b*c·-·47c··-·39b*d·+·20c*d·-·35d·) |
| 239 | o17·:·Ideal·of·S | 239 | o17·:·Ideal·of·S |
| 240 | i18·:·decompose·F2 | 240 | i18·:·decompose·F2 |
| 241 | o18·=·{ideal·(b· | 241 | o18·=·{ideal·(b·-·12c·+·48d,·a·-·16c·+·d),·ideal·(b·+·46c·+·14d,·a·+·31c·- |
| 242 | ······----------------------------------------------------------------------- | 242 | ······----------------------------------------------------------------------- |
| 243 | ······ | 243 | ······5d)} |
| 244 | o18·:·List | 244 | o18·:·List |
| 245 | i19·:· | 245 | i19·:· |
| Offset 12, 17 lines modified | Offset 12, 17 lines modified | ||
| 12 | ·············································2 | 12 | ·············································2 |
| 13 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 13 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 14 | o3·:·Ideal·of·S | 14 | o3·:·Ideal·of·S |
| 15 | i4·:·pts·=·randomPointsOnRationalVariety(I,·4) | 15 | i4·:·pts·=·randomPointsOnRationalVariety(I,·4) |
| 16 | o4·=·{|· | 16 | o4·=·{|·-25·20·-30·-16·24·-36·|,·|·19·-29·19·23·-29·19·|,·|·-44·46·-8·7·-10 |
| 17 | ·····------------------------------------------------------------------------ | 17 | ·····------------------------------------------------------------------------ |
| 18 | ·····- | 18 | ·····-29·|,·|·8·41·-24·46·-22·-29·|} |
| 19 | o4·:·List | 19 | o4·:·List |
| 20 | i5·:·for·p·in·pts·list·sub(I,·p)·==·0 | 20 | i5·:·for·p·in·pts·list·sub(I,·p)·==·0 |
| 21 | o5·=·{true,·true,·true,·true} | 21 | o5·=·{true,·true,·true,·true} |
| Offset 68, 54 lines modified | Offset 68, 54 lines modified | ||
| 68 | o12·=·{11,·8} | 68 | o12·=·{11,·8} |
| 69 | o12·:·List | 69 | o12·:·List |
| 70 | i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) | 70 | i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) |
| 71 | ······+----------------------------------------------------------------------------------------+ | ||
| 72 | o13·=·||·-15·9·-4·9·-47·-7·19·31·-22·-13·-23·-30·-38·-16·-19·39·-18·16·21·34·-47·19·-43·-39·|··| | ||
| 73 | ······+----------------------------------------------------------------------------------------+ | ||
| 74 | ······||·47·2·-38·-35·-49·-35·-20·48·-42·-48·-28·21·-15·-28·-10·-47·-34·49·38·2·22·16·-47·45·|·| | ||
| 75 | ······+----------------------------------------------------------------------------------------+ | ||
| 76 | ······||·15·-40·-13·-45·-32·9·34·10·-2·-11·30·18·47·19·30·-16·-17·12·7·15·39·-23·48·43·|·······| | ||
| 77 | ······+----------------------------------------------------------------------------------------+ | ||
| 78 | ······||·-22·-35·14·-29·-36·-14·-18·-44·-50·1·14·16·36·35·5·11·-28·36·-38·33·11·40·-3·46·|·····| | ||
| 79 | ······+----------------------------------------------------------------------------------------+ | ||
| 80 | ······||·13·-35·-39·35·16·-18·41·35·-15·-13·-26·-46·22·-47·-2·-23·-37·-50·-7·2·-47·29·-10·15·|·| | ||
| 81 | ······+----------------------------------------------------------------------------------------+ | ||
| 82 | ······||·19·-11·-23·-31·-35·-36·28·40·38·24·41·-47·30·-18·13·39·-20·15·27·-22·-9·32·-30·-32·|··| | ||
| 83 | ······+----------------------------------------------------------------------------------------+ | ||
| 84 | ······||·41·29·49·14·-11·20·16·28·-48·-20·0·-5·-48·-15·-46·39·17·1·0·33·-33·-49·44·-19·|·······| | ||
| 85 | ······+----------------------------------------------------------------------------------------+ | ||
| 86 | ······||·39·-35·49·20·-8·41·-3·19·23·-11·-4·-12·-39·36·46·9·-49·-35·-39·4·-26·13·-8·22·|·······| | ||
| 87 | ······+----------------------------------------------------------------------------------------+ | ||
| 88 | ······||·27·-7·-28·31·30·41·-27·41·26·-6·22·-5·43·-8·-49·36·-28·-18·-3·-22·41·-30·35·16·|······| | ||
| 89 | ······+----------------------------------------------------------------------------------------+ | ||
| 90 | ······||·36·-33·-45·-12·-50·-48·-13·-28·-15·-49·10·-31·-9·-35·-19·6·-41·33·40·3·25·-31·-13·-2·|| | ||
| 91 | ······+----------------------------------------------------------------------------------------+ | ||
| 92 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | ||
| 71 | ······+--------------------------------------------------------------------------------------+ | 93 | ······+--------------------------------------------------------------------------------------+ |
| 72 | o1 | 94 | o14·=·||·-35·39·-4·-3·-26·4·20·45·43·-3·-44·23·-40·-50·-6·-24·37·-35·27·30·-47·4·-31·0·|·····| |
| 73 | ······+--------------------------------------------------------------------------------------+ | 95 | ······+--------------------------------------------------------------------------------------+ |
| 74 | ······||· | 96 | ······||·-9·18·13·-46·44·-19·-4·10·-33·13·22·-48·-48·-33·-37·-8·30·-37·-29·-31·-48·-39·47·0·|| |
| 75 | ······+--------------------------------------------------------------------------------------+ | 97 | ······+--------------------------------------------------------------------------------------+ |
| 76 | ······||· | 98 | ······||·24·-43·-8·-28·-37·48·45·16·34·47·20·-25·1·1·18·-44·40·-22·46·28·-18·-49·10·0·|······| |
| 77 | ······+--------------------------------------------------------------------------------------+ | 99 | ······+--------------------------------------------------------------------------------------+ |
| 78 | ······||·-41 | 100 | ······||·2·-44·10·47·22·42·-37·22·-39·-29·19·-42·-13·-39·0·-13·3·-41·-17·30·13·7·8·0·|·······| |
| 79 | ······+--------------------------------------------------------------------------------------+ | 101 | ······+--------------------------------------------------------------------------------------+ |
| 80 | ······||·-1 | 102 | ······||·-18·31·14·-11·-10·-1·7·-12·-36·3·-34·-2·49·-4·-1·45·-18·42·-46·-29·30·8·23·0·|······| |
| 81 | ······+--------------------------------------------------------------------------------------+ | 103 | ······+--------------------------------------------------------------------------------------+ |
| 82 | ······||· | 104 | ······||·22·22·21·25·-34·13·-42·42·34·7·-15·-2·-46·43·31·32·12·-18·-16·15·18·-28·27·0·|······| |
| 83 | ······+--------------------------------------------------------------------------------------+ | 105 | ······+--------------------------------------------------------------------------------------+ |
| 84 | ······||· | 106 | ······||·20·34·11·19·24·-34·-32·-18·-4·44·-43·-14·44·26·-43·9·-39·20·-23·23·-37·-21·19·0·|···| |
| 85 | ······+--------------------------------------------------------------------------------------+ | 107 | ······+--------------------------------------------------------------------------------------+ |
| 86 | ······||· | 108 | ······||·9·44·22·48·-27·-22·-41·22·17·48·3·27·-28·18·-9·27·6·-9·47·-47·-28·0·-33·0·|·········| |
| 87 | ······+--------------------------------------------------------------------------------------+ | 109 | ······+--------------------------------------------------------------------------------------+ |
| 88 | ······||·4 | 110 | ······||·-45·5·15·-32·-3·-14·-30·44·10·44·-29·-48·-37·23·-14·-47·-33·-28·5·-29·26·28·42·0·|··| |
| 89 | ······+--------------------------------------------------------------------------------------+ | 111 | ······+--------------------------------------------------------------------------------------+ |
| 90 | ······||· | 112 | ······||·-2·-29·-50·-48·-22·17·-41·-21·-1·-4·13·17·5·-33·-5·47·-20·-13·22·30·4·44·-29·0·|····| |
| 91 | ······+--------------------------------------------------------------------------------------+ | 113 | ······+--------------------------------------------------------------------------------------+ |
| 92 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | ||
| 93 | ······+-------------------------------------------------------------------------------------+ | ||
| 94 | o14·=·||·38·-31·49·39·4·46·-29·-5·-39·-40·14·-11·-31·46·43·-26·4·30·-35·27·-40·37·-47·0·|···| | ||
| 95 | ······+-------------------------------------------------------------------------------------+ | ||
| 96 | ······||·-1·-5·-10·-10·-11·42·6·46·-4·47·42·-40·47·-27·-20·49·-39·-31·-37·-29·-48·30·-48·0·|| | ||
| 97 | ······+-------------------------------------------------------------------------------------+ | ||
| 98 | ······||·29·18·20·1·18·26·-31·-45·-21·10·22·-30·10·32·-31·-21·-49·28·-22·46·1·40·-18·0·|····| | ||
| 99 | ······+-------------------------------------------------------------------------------------+ | ||
| 100 | ······||·-17·3·17·-9·-36·-45·49·30·-45·24·-28·41·8·-4·-26·-28·7·30·-41·-17·-13·3·13·0·|·····| | ||
| 101 | ······+-------------------------------------------------------------------------------------+ | ||
| 102 | ······||·37·33·-47·-20·-49·45·29·19·41·13·-38·44·23·40·-48·45·8·-29·42·-46·49·-18·30·0·|····| | ||
| 103 | ······+-------------------------------------------------------------------------------------+ | ||
| 104 | ······||·-9·-3·-26·13·35·49·-8·49·-40·13·-20·9·27·5·-8·-15·-28·15·-18·-16·-46·12·18·0·|·····| | ||
| 105 | ······+-------------------------------------------------------------------------------------+ | ||
| 106 | ······||·28·32·0·0·-17·-44·25·42·7·-35·29·-17·19·8·-9·-26·-21·23·20·-23·44·-39·-37·0·|······| | ||
| 107 | ······+-------------------------------------------------------------------------------------+ | ||
| 108 | ······||·-30·-29·27·14·17·39·33·15·-35·50·-50·45·-33·13·24·-44·0·-47·-9·47·-28·6·-28·0·|····| | ||
| 109 | ······+-------------------------------------------------------------------------------------+ | ||
| 110 | ······||·7·-12·42·-29·30·1·3·-28·-7·36·-26·-40·42·38·-20·-23·28·-29·-28·5·-37·-33·26·0·|····| | ||
| 111 | ······+-------------------------------------------------------------------------------------+ | ||
| 112 | ······||·28·-10·13·-39·-20·11·13·-13·-37·8·-36·-29·-29·17·24·-50·44·30·-13·22·5·-20·4·0·|···| | ||
| 113 | ······+-------------------------------------------------------------------------------------+ | ||
| 114 | i15·:· | 114 | i15·:· |
| Offset 206, 17 lines modified | Offset 206, 17 lines modified | ||
| 206 | <td>··············<pre><code·class="language-macaulay2">i13·:·#compsJ | 206 | <td>··············<pre><code·class="language-macaulay2">i13·:·#compsJ |
| 207 | o13·=·2</code></pre> | 207 | o13·=·2</code></pre> |
| 208 | </td>··········</tr> | 208 | </td>··········</tr> |
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 210 | <td>··············<pre><code·class="language-macaulay2">i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 211 | o14·=·|·- | 211 | o14·=·|·-6·48·44·-23·-2·-11·-35·-26·27·-43·48·27·15·-22·25·-16·34·-29·46·-20 |
| 212 | ······----------------------------------------------------------------------- | 212 | ······----------------------------------------------------------------------- |
| 213 | ······ | 213 | ······40·21·-30·-38·-19·-8·-36·39·19·-29·-16·-29·-10·19·24·-24·| |
| 214 | ···············1·······36 | 214 | ···············1·······36 |
| 215 | o14·:·Matrix·kk··<--·kk</code></pre> | 215 | o14·:·Matrix·kk··<--·kk</code></pre> |
| 216 | </td>··········</tr> | 216 | </td>··········</tr> |
| 217 | ··········<tr> | 217 | ··········<tr> |
| 218 | <td>··············<pre><code·class="language-macaulay2">i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 218 | <td>··············<pre><code·class="language-macaulay2">i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| Offset 226, 28 lines modified | Offset 226, 28 lines modified | ||
| 226 | ···············1·······36 | 226 | ···············1·······36 |
| 227 | o15·:·Matrix·kk··<--·kk</code></pre> | 227 | o15·:·Matrix·kk··<--·kk</code></pre> |
| 228 | </td>··········</tr> | 228 | </td>··········</tr> |
| 229 | ··········<tr> | 229 | ··········<tr> |
| 230 | <td>··············<pre><code·class="language-macaulay2">i16·:·F1·=·sub(F,·(vars·S)|pt1) | 230 | <td>··············<pre><code·class="language-macaulay2">i16·:·F1·=·sub(F,·(vars·S)|pt1) |
| 231 | ··············2·············2·····························2··············· | 231 | ··············2··············2·····························2··············· |
| 232 | o16·=·ideal·(a·· | 232 | o16·=·ideal·(a··+·25b*c·-·43c··+·27a*d·-·11b*d·+·44c*d·-·6d·,·a*b·-·19b*c·+ |
| 233 | ······----------------------------------------------------------------------- | 233 | ······----------------------------------------------------------------------- |
| 234 | ·········2······························2·················· | 234 | ·········2······························2··················2················ |
| 235 | ······ | 235 | ······46c··+·40a*d·+·15b*d·+·27c*d·+·48d·,·a*c·-·29b*c·-·8c··+·39a*d·-·20b*d |
| 236 | ······----------------------------------------------------------------------- | 236 | ······----------------------------------------------------------------------- |
| 237 | ·················2···2··············2······························2·····2·· | 237 | ··················2···2··············2······························2·····2·· |
| 238 | ······ | 238 | ······-·22c*d·-·2d·,·b··+·24b*c·+·19c··-·10a*d·+·21b*d·-·16c*d·-·35d·,·b*c··- |
| 239 | ······----------------------------------------------------------------------- | 239 | ······----------------------------------------------------------------------- |
| 240 | ···················2·········2········2········2······3···3················2· | 240 | ···················2·········2········2········2······3···3················2· |
| 241 | ······2 | 241 | ······29b*c*d·-·30c·d·-·36a*d··+·34b*d··+·48c*d··-·23d·,·c··-·24b*c*d·-·16c·d |
| 242 | ······----------------------------------------------------------------------- | 242 | ······----------------------------------------------------------------------- |
| 243 | ············2········2········2·····3 | 243 | ·············2········2········2······3 |
| 244 | ······ | 244 | ······+·19a*d··-·38b*d··-·29c*d··-·26d·) |
| 245 | o16·:·Ideal·of·S</code></pre> | 245 | o16·:·Ideal·of·S</code></pre> |
| 246 | </td>··········</tr> | 246 | </td>··········</tr> |
| 247 | ··········<tr> | 247 | ··········<tr> |
| 248 | <td>··············<pre><code·class="language-macaulay2">i17·:·betti·res·F1 | 248 | <td>··············<pre><code·class="language-macaulay2">i17·:·betti·res·F1 |
| 249 | ·············0·1·2·3 | 249 | ·············0·1·2·3 |
| Offset 293, 24 lines modified | Offset 293, 20 lines modified | ||
| 293 | ········<div> | 293 | ········<div> |
| 294 | ··········<p>What·are·the·ideals·F1·and·F2?</p> | 294 | ··········<p>What·are·the·ideals·F1·and·F2?</p> |
| 295 | ········</div> | 295 | ········</div> |
| 296 | ········<table·class="examples"> | 296 | ········<table·class="examples"> |
| 297 | ··········<tr> | 297 | ··········<tr> |
| 298 | <td>··············<pre><code·class="language-macaulay2">i20·:·netList·decompose·F1 | 298 | <td>··············<pre><code·class="language-macaulay2">i20·:·netList·decompose·F1 |
| 299 | ······+---------------------------------------------------------------------------------------------------------+ | 299 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 300 | o20·=·|ideal·(c· | 300 | o20·=·|ideal·(c·+·39d,·b·+·27d,·a·-·18d)························································································································| |
| 301 | ······+---------------------------------------------------------------------------------------------------------+ | 301 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 302 | ······|····························2··············2·····················2···3················2········2········2······3·····2················2·········2······3·| | ||
| 303 | ······|ideal·(a·-·29b·-·8c·-·13d,·b··+·24b*c·+·19c··+·34b*d·+·5c*d·+·37d·,·c··-·24b*c*d·-·16c·d·+·8b*d··+·22c*d··+·19d·,·b*c··-·29b*c*d·-·30c·d·-·38c*d··+·14d·)| | ||
| 302 | ······|ideal·(c·+·21d,·b·+·36d,·a·-·12d)········································································| | ||
| 303 | ······+---------------------------------------------------------------------------------------------------------+ | ||
| 304 | ······|ideal·(c·+·13d,·b·-·22d,·a·-·28d)········································································| | ||
| 305 | ······+---------------------------------------------------------------------------------------------------------+ | ||
| 306 | ······|·····························2······················2·························2···2····················2·| | ||
| 307 | ······|ideal·(a·-·24b·-·29c·+·22d,·c··+·33b*d·+·43c*d·+·41d·,·b*c·-·16b*d·+·4c*d·-·2d·,·b··-·9b*d·-·8c*d·-·19d·)| | ||
| 308 | ······+---------------------------------------------------------------------------------------------------------+</code></pre> | 304 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+</code></pre> |
| 309 | </td>··········</tr> | 305 | </td>··········</tr> |
| 310 | ··········<tr> | 306 | ··········<tr> |
| 311 | <td>··············<pre><code·class="language-macaulay2">i21·:·netList·decompose·F2 | 307 | <td>··············<pre><code·class="language-macaulay2">i21·:·netList·decompose·F2 |
| 312 | ······+-------------------------------------------------------+ | 308 | ······+-------------------------------------------------------+ |
| 313 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| | 309 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| |
| 314 | ······+-------------------------------------------------------+ | 310 | ······+-------------------------------------------------------+ |
| Offset 171, 44 lines modified | Offset 171, 44 lines modified | ||
| 171 | 32···13···21···33···19···31 | 171 | 32···13···21···33···19···31 |
| 172 | i12·:·compsJ·=·decompose·J; | 172 | i12·:·compsJ·=·decompose·J; |
| 173 | i13·:·#compsJ | 173 | i13·:·#compsJ |
| 174 | o13·=·2 | 174 | o13·=·2 |
| 175 | i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 175 | i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 176 | o14·=·|·- | 176 | o14·=·|·-6·48·44·-23·-2·-11·-35·-26·27·-43·48·27·15·-22·25·-16·34·-29·46·-20 |
| 177 | ······----------------------------------------------------------------------- | 177 | ······----------------------------------------------------------------------- |
| 178 | ······ | 178 | ······40·21·-30·-38·-19·-8·-36·39·19·-29·-16·-29·-10·19·24·-24·| |
| 179 | ···············1·······36 | 179 | ···············1·······36 |
| 180 | o14·:·Matrix·kk··<--·kk | 180 | o14·:·Matrix·kk··<--·kk |
| 181 | i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 181 | i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 182 | o15·=·|·-48·-46·16·17·-1·-43·15·-1·12·-18·-6·-28·14·-28·-9·32·-22·-39·6·-47 | 182 | o15·=·|·-48·-46·16·17·-1·-43·15·-1·12·-18·-6·-28·14·-28·-9·32·-22·-39·6·-47 |
| 183 | ······----------------------------------------------------------------------- | 183 | ······----------------------------------------------------------------------- |
| 184 | ······28·-37·-47·38·-16·-15·34·27·-13·-43·22·16·0·-18·19·2·| | 184 | ······28·-37·-47·38·-16·-15·34·27·-13·-43·22·16·0·-18·19·2·| |
| 185 | ···············1·······36 | 185 | ···············1·······36 |
| 186 | o15·:·Matrix·kk··<--·kk | 186 | o15·:·Matrix·kk··<--·kk |
| 187 | i16·:·F1·=·sub(F,·(vars·S)|pt1) | 187 | i16·:·F1·=·sub(F,·(vars·S)|pt1) |
| 188 | ··············2·············2·····························2 | 188 | ··············2··············2·····························2 |
| 189 | o16·=·ideal·(a·· | 189 | o16·=·ideal·(a··+·25b*c·-·43c··+·27a*d·-·11b*d·+·44c*d·-·6d·,·a*b·-·19b*c·+ |
| 190 | ······----------------------------------------------------------------------- | 190 | ······----------------------------------------------------------------------- |
| 191 | ·········2······························2·················· | 191 | ·········2······························2··················2 |
| 192 | ······ | 192 | ······46c··+·40a*d·+·15b*d·+·27c*d·+·48d·,·a*c·-·29b*c·-·8c··+·39a*d·-·20b*d |
| 193 | ······----------------------------------------------------------------------- | 193 | ······----------------------------------------------------------------------- |
| 194 | ·················2···2··············2······························2·····2 | 194 | ··················2···2··············2······························2·····2 |
| 195 | ······ | 195 | ······-·22c*d·-·2d·,·b··+·24b*c·+·19c··-·10a*d·+·21b*d·-·16c*d·-·35d·,·b*c··- |
| 196 | ······----------------------------------------------------------------------- | 196 | ······----------------------------------------------------------------------- |
| 197 | ···················2·········2········2········2······3···3················2 | 197 | ···················2·········2········2········2······3···3················2 |
| 198 | ······2 | 198 | ······29b*c*d·-·30c·d·-·36a*d··+·34b*d··+·48c*d··-·23d·,·c··-·24b*c*d·-·16c·d |
| 199 | ······----------------------------------------------------------------------- | 199 | ······----------------------------------------------------------------------- |
| 200 | ············2········2········2·····3 | 200 | ·············2········2········2······3 |
| 201 | ······ | 201 | ······+·19a*d··-·38b*d··-·29c*d··-·26d·) |
| 202 | o16·:·Ideal·of·S | 202 | o16·:·Ideal·of·S |
| 203 | i17·:·betti·res·F1 | 203 | i17·:·betti·res·F1 |
| 204 | ·············0·1·2·3 | 204 | ·············0·1·2·3 |
| 205 | o17·=·total:·1·6·8·3 | 205 | o17·=·total:·1·6·8·3 |
| 206 | ··········0:·1·.·.·. | 206 | ··········0:·1·.·.·. |
| Offset 243, 33 lines modified | Offset 243, 29 lines modified | ||
| 243 | ··········2:·.·2·4·2 | 243 | ··········2:·.·2·4·2 |
| 244 | o19·:·BettiTally | 244 | o19·:·BettiTally |
| 245 | What·are·the·ideals·F1·and·F2? | 245 | What·are·the·ideals·F1·and·F2? |
| 246 | i20·:·netList·decompose·F1 | 246 | i20·:·netList·decompose·F1 |
| 247 | ······+------------------------------------------------------------------------ | 247 | ······+------------------------------------------------------------------------ |
| 248 | --------------------------------- | 248 | ------------------------------------------------------------------------------- |
| 249 | --+ | ||
| 249 | o20·=·|ideal·(c· | 250 | o20·=·|ideal·(c·+·39d,·b·+·27d,·a·-·18d) |
| 250 | | | 251 | | |
| 251 | ······+------------------------------------------------------------------------ | 252 | ······+------------------------------------------------------------------------ |
| 252 | ---------------------------------+ | ||
| 253 | ······|ideal·(c·+·21d,·b·+·36d,·a·-·12d) | ||
| 254 | | | ||
| 255 | 253 | ------------------------------------------------------------------------------- | |
| 254 | --+ | ||
| 256 | ---------------------------------+ | ||
| 257 | ······|ideal·(c·+·13d,·b·-·22d,·a·-·28d) | ||
| 258 | | | ||
| 259 | ······+------------------------------------------------------------------------ | ||
| 260 | ---------------------------------+ | ||
| 261 | ······|·····························2······················ | 255 | ······|····························2··············2·····················2···3 |
| 262 | 2···2····················2·| | ||
| 263 | ······|ideal·(a·-·24b·-·29c·+·22d,·c··+·33b*d·+·43c*d·+·41d·,·b*c·-·16b*d·+ | ||
| 264 | 256 | 2········2········2······3·····2················2·········2······3·| | |
| 257 | ······|ideal·(a·-·29b·-·8c·-·13d,·b··+·24b*c·+·19c··+·34b*d·+·5c*d·+·37d·,·c··- | ||
| 258 | 24b*c*d·-·16c·d·+·8b*d··+·22c*d··+·19d·,·b*c··-·29b*c*d·-·30c·d·-·38c*d··+·14d | ||
| 259 | )| | ||
| 265 | ······+------------------------------------------------------------------------ | 260 | ······+------------------------------------------------------------------------ |
| 266 | --------------------------------- | 261 | ------------------------------------------------------------------------------- |
| 262 | --+ | ||
| 267 | i21·:·netList·decompose·F2 | 263 | i21·:·netList·decompose·F2 |
| 268 | ······+-------------------------------------------------------+ | 264 | ······+-------------------------------------------------------+ |
| 269 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| | 265 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| |
| 270 | ······+-------------------------------------------------------+ | 266 | ······+-------------------------------------------------------+ |
| 271 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| | 267 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| |
| 272 | ······+-------------------------------------------------------+ | 268 | ······+-------------------------------------------------------+ |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 90 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 91 | o3·:·Ideal·of·S</code></pre> | 91 | o3·:·Ideal·of·S</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·pt·=·randomPointOnRationalVariety·I | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·pt·=·randomPointOnRationalVariety·I |
| 95 | o4·=·|· | 95 | o4·=·|·-25·20·-30·-16·24·-36·| |
| 96 | ··············1·······6 | 96 | ··············1·······6 |
| 97 | o4·:·Matrix·kk··<--·kk</code></pre> | 97 | o4·:·Matrix·kk··<--·kk</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·sub(I,·pt)·==·0 | 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·sub(I,·pt)·==·0 |
| Offset 294, 80 lines modified | Offset 294, 80 lines modified | ||
| 294 | ········<div> | 294 | ········<div> |
| 295 | ··········<p>There·are·2·components.··We·attempt·to·find·a·point·on·the·first·component</p> | 295 | ··········<p>There·are·2·components.··We·attempt·to·find·a·point·on·the·first·component</p> |
| 296 | ········</div> | 296 | ········</div> |
| 297 | ········<table·class="examples"> | 297 | ········<table·class="examples"> |
| 298 | ··········<tr> | 298 | ··········<tr> |
| 299 | <td>··············<pre><code·class="language-macaulay2">i13·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 299 | <td>··············<pre><code·class="language-macaulay2">i13·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 300 | o13·=·|· | 300 | o13·=·|·2·-18·6·4·20·-11·44·-13·0·19·11·-47·-29·-8·-19·-22·19·-20·-29·-38·-24 |
| 301 | ······----------------------------------------------------------------------- | 301 | ······----------------------------------------------------------------------- |
| 302 | ······- | 302 | ······-16·-10·-29·| |
| 303 | ···············1·······24 | 303 | ···············1·······24 |
| 304 | o13·:·Matrix·kk··<--·kk</code></pre> | 304 | o13·:·Matrix·kk··<--·kk</code></pre> |
| 305 | </td>··········</tr> | 305 | </td>··········</tr> |
| 306 | ··········<tr> | 306 | ··········<tr> |
| 307 | <td>··············<pre><code·class="language-macaulay2">i14·:·F1·=·sub(F,·(vars·S)|pt1) | 307 | <td>··············<pre><code·class="language-macaulay2">i14·:·F1·=·sub(F,·(vars·S)|pt1) |
| 308 | ··············2····· | 308 | ··············2·····2·····························2···················2·· |
| 309 | o14·=·ideal·(a··+· | 309 | o14·=·ideal·(a··+·4c··+·19a*d·+·20b*d·-·18c*d·+·2d·,·a*b·-·19b*c·+·11c··- |
| 310 | ······----------------------------------------------------------------------- | 310 | ······----------------------------------------------------------------------- |
| 311 | ········ | 311 | ································2···················2························ |
| 312 | ······2 | 312 | ······22a*d·-·47b*d·-·11c*d·+·6d·,·a*c·-·24b*c·+·19c··-·16a*d·-·20b*d·-·29c*d |
| 313 | ······----------------------------------------------------------------------- | 313 | ······----------------------------------------------------------------------- |
| 314 | ··········· | 314 | ···········2···2··············2·····························2 |
| 315 | ······ | 315 | ······+·44d·,·b··-·10b*c·-·29c··-·29a*d·-·38b*d·-·8c*d·-·13d·) |
| 316 | o14·:·Ideal·of·S</code></pre> | 316 | o14·:·Ideal·of·S</code></pre> |
| 317 | </td>··········</tr> | 317 | </td>··········</tr> |
| 318 | ··········<tr> | 318 | ··········<tr> |
| 319 | <td>··············<pre><code·class="language-macaulay2">i15·:·decompose·F1 | 319 | <td>··············<pre><code·class="language-macaulay2">i15·:·decompose·F1 |
| 320 | ····································2··············2······················2 | 320 | ····································2··············2······················2 |
| 321 | o15·=·{ideal·(a·-· | 321 | o15·=·{ideal·(a·-·24b·+·19c·-·28d,·b··-·10b*c·-·29c··-·27b*d·+·38c*d·-·17d·), |
| 322 | ······----------------------------------------------------------------------- | 322 | ······----------------------------------------------------------------------- |
| 323 | ······ideal·(c·-· | 323 | ······ideal·(c·-·16d,·b·-·33d,·a·-·32d)} |
| 324 | o15·:·List</code></pre> | 324 | o15·:·List</code></pre> |
| 325 | </td>··········</tr> | 325 | </td>··········</tr> |
| 326 | ········</table> | 326 | ········</table> |
| 327 | ········<div> | 327 | ········<div> |
| 328 | ··········<p>We·attempt·to·find·a·point·on·the·second·component·in·parameter·space,·and·its·corresponding·ideal.</p> | 328 | ··········<p>We·attempt·to·find·a·point·on·the·second·component·in·parameter·space,·and·its·corresponding·ideal.</p> |
| 329 | ········</div> | 329 | ········</div> |
| 330 | ········<table·class="examples"> | 330 | ········<table·class="examples"> |
| 331 | ··········<tr> | 331 | ··········<tr> |
| 332 | <td>··············<pre><code·class="language-macaulay2">i16·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 332 | <td>··············<pre><code·class="language-macaulay2">i16·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 333 | o16·=·|·- | 333 | o16·=·|·-8·28·25·30·-12·-42·-20·-35·-7·-37·-5·45·19·20·-24·34·39·21·-47·-39 |
| 334 | ······----------------------------------------------------------------------- | 334 | ······----------------------------------------------------------------------- |
| 335 | ······- | 335 | ······-13·-18·34·0·| |
| 336 | ···············1·······24 | 336 | ···············1·······24 |
| 337 | o16·:·Matrix·kk··<--·kk</code></pre> | 337 | o16·:·Matrix·kk··<--·kk</code></pre> |
| 338 | </td>··········</tr> | 338 | </td>··········</tr> |
| 339 | ··········<tr> | 339 | ··········<tr> |
| 340 | <td>··············<pre><code·class="language-macaulay2">i17·:·F2·=·sub(F,·(vars·S)|pt2) | 340 | <td>··············<pre><code·class="language-macaulay2">i17·:·F2·=·sub(F,·(vars·S)|pt2) |
| 341 | ··············2·············2····························· | 341 | ··············2·············2·····························2··············· |
| 342 | o17·=·ideal·(a··-· | 342 | o17·=·ideal·(a··-·7b*c·+·30c··-·37a*d·-·12b*d·+·28c*d·-·8d·,·a*b·-·24b*c·- |
| 343 | ······----------------------------------------------------------------------- | 343 | ······----------------------------------------------------------------------- |
| 344 | ········ | 344 | ········2······························2···················2················ |
| 345 | ······ | 345 | ······5c··+·34a*d·+·45b*d·-·42c*d·+·25d·,·a*c·-·13b*c·+·39c··-·18a*d·+·21b*d |
| 346 | ······----------------------------------------------------------------------- | 346 | ······----------------------------------------------------------------------- |
| 347 | ···················2···2··············2······················2 | 347 | ···················2···2··············2······················2 |
| 348 | ······ | 348 | ······+·19c*d·-·20d·,·b··+·34b*c·-·47c··-·39b*d·+·20c*d·-·35d·) |
| 349 | o17·:·Ideal·of·S</code></pre> | 349 | o17·:·Ideal·of·S</code></pre> |
| 350 | </td>··········</tr> | 350 | </td>··········</tr> |
| 351 | ··········<tr> | 351 | ··········<tr> |
| 352 | <td>··············<pre><code·class="language-macaulay2">i18·:·decompose·F2 | 352 | <td>··············<pre><code·class="language-macaulay2">i18·:·decompose·F2 |
| 353 | o18·=·{ideal·(b· | 353 | o18·=·{ideal·(b·-·12c·+·48d,·a·-·16c·+·d),·ideal·(b·+·46c·+·14d,·a·+·31c·- |
| 354 | ······----------------------------------------------------------------------- | 354 | ······----------------------------------------------------------------------- |
| 355 | ······ | 355 | ······5d)} |
| 356 | o18·:·List</code></pre> | 356 | o18·:·List</code></pre> |
| 357 | </td>··········</tr> | 357 | </td>··········</tr> |
| 358 | ········</table> | 358 | ········</table> |
| 359 | ········<div> | 359 | ········<div> |
| 360 | ··········<p>It·turns·out·that·this·is·the·ideal·of·2·skew·lines,·just·not·defined·over·this·field.</p> | 360 | ··········<p>It·turns·out·that·this·is·the·ideal·of·2·skew·lines,·just·not·defined·over·this·field.</p> |
| 361 | ········</div> | 361 | ········</div> |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ·············································2 | 30 | ·············································2 |
| 31 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 31 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 32 | o3·:·Ideal·of·S | 32 | o3·:·Ideal·of·S |
| 33 | i4·:·pt·=·randomPointOnRationalVariety·I | 33 | i4·:·pt·=·randomPointOnRationalVariety·I |
| 34 | o4·=·|· | 34 | o4·=·|·-25·20·-30·-16·24·-36·| |
| 35 | ··············1·······6 | 35 | ··············1·······6 |
| 36 | o4·:·Matrix·kk··<--·kk | 36 | o4·:·Matrix·kk··<--·kk |
| 37 | i5·:·sub(I,·pt)·==·0 | 37 | i5·:·sub(I,·pt)·==·0 |
| 38 | o5·=·true | 38 | o5·=·true |
| 39 | i6·:·S·=·kk[a..d]; | 39 | i6·:·S·=·kk[a..d]; |
| Offset 213, 67 lines modified | Offset 213, 67 lines modified | ||
| 213 | o12·=·{11,·8} | 213 | o12·=·{11,·8} |
| 214 | o12·:·List | 214 | o12·:·List |
| 215 | There·are·2·components.·We·attempt·to·find·a·point·on·the·first·component | 215 | There·are·2·components.·We·attempt·to·find·a·point·on·the·first·component |
| 216 | i13·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 216 | i13·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 217 | o13·=·|· | 217 | o13·=·|·2·-18·6·4·20·-11·44·-13·0·19·11·-47·-29·-8·-19·-22·19·-20·-29·-38·-24 |
| 218 | ······----------------------------------------------------------------------- | 218 | ······----------------------------------------------------------------------- |
| 219 | ······- | 219 | ······-16·-10·-29·| |
| 220 | ···············1·······24 | 220 | ···············1·······24 |
| 221 | o13·:·Matrix·kk··<--·kk | 221 | o13·:·Matrix·kk··<--·kk |
| 222 | i14·:·F1·=·sub(F,·(vars·S)|pt1) | 222 | i14·:·F1·=·sub(F,·(vars·S)|pt1) |
| 223 | ··············2·············· | 223 | ··············2·····2·····························2···················2 |
| 224 | o14·=·ideal·(a··+· | 224 | o14·=·ideal·(a··+·4c··+·19a*d·+·20b*d·-·18c*d·+·2d·,·a*b·-·19b*c·+·11c··- |
| 225 | ······----------------------------------------------------------------------- | 225 | ······----------------------------------------------------------------------- |
| 226 | ········ | 226 | ································2···················2 |
| 227 | ······2 | 227 | ······22a*d·-·47b*d·-·11c*d·+·6d·,·a*c·-·24b*c·+·19c··-·16a*d·-·20b*d·-·29c*d |
| 228 | ······----------------------------------------------------------------------- | 228 | ······----------------------------------------------------------------------- |
| 229 | ··········· | 229 | ···········2···2··············2·····························2 |
| 230 | ······ | 230 | ······+·44d·,·b··-·10b*c·-·29c··-·29a*d·-·38b*d·-·8c*d·-·13d·) |
| 231 | o14·:·Ideal·of·S | 231 | o14·:·Ideal·of·S |
| 232 | i15·:·decompose·F1 | 232 | i15·:·decompose·F1 |
| 233 | ····································2··············2······················2 | 233 | ····································2··············2······················2 |
| 234 | o15·=·{ideal·(a·-· | 234 | o15·=·{ideal·(a·-·24b·+·19c·-·28d,·b··-·10b*c·-·29c··-·27b*d·+·38c*d·-·17d·), |
| 235 | ······----------------------------------------------------------------------- | 235 | ······----------------------------------------------------------------------- |
| 236 | ······ideal·(c·-· | 236 | ······ideal·(c·-·16d,·b·-·33d,·a·-·32d)} |
| 237 | o15·:·List | 237 | o15·:·List |
| 238 | We·attempt·to·find·a·point·on·the·second·component·in·parameter·space,·and·its | 238 | We·attempt·to·find·a·point·on·the·second·component·in·parameter·space,·and·its |
| 239 | corresponding·ideal. | 239 | corresponding·ideal. |
| 240 | i16·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 240 | i16·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 241 | o16·=·|·- | 241 | o16·=·|·-8·28·25·30·-12·-42·-20·-35·-7·-37·-5·45·19·20·-24·34·39·21·-47·-39 |
| 242 | ······----------------------------------------------------------------------- | 242 | ······----------------------------------------------------------------------- |
| 243 | ······- | 243 | ······-13·-18·34·0·| |
| 244 | ···············1·······24 | 244 | ···············1·······24 |
| 245 | o16·:·Matrix·kk··<--·kk | 245 | o16·:·Matrix·kk··<--·kk |
| 246 | i17·:·F2·=·sub(F,·(vars·S)|pt2) | 246 | i17·:·F2·=·sub(F,·(vars·S)|pt2) |
| 247 | ··············2·············2····························· | 247 | ··············2·············2·····························2 |
| 248 | o17·=·ideal·(a··-· | 248 | o17·=·ideal·(a··-·7b*c·+·30c··-·37a*d·-·12b*d·+·28c*d·-·8d·,·a*b·-·24b*c·- |
| 249 | ······----------------------------------------------------------------------- | 249 | ······----------------------------------------------------------------------- |
| 250 | ········ | 250 | ········2······························2···················2 |
| 251 | ······ | 251 | ······5c··+·34a*d·+·45b*d·-·42c*d·+·25d·,·a*c·-·13b*c·+·39c··-·18a*d·+·21b*d |
| 252 | ······----------------------------------------------------------------------- | 252 | ······----------------------------------------------------------------------- |
| 253 | ···················2···2··············2······················2 | 253 | ···················2···2··············2······················2 |
| 254 | ······ | 254 | ······+·19c*d·-·20d·,·b··+·34b*c·-·47c··-·39b*d·+·20c*d·-·35d·) |
| 255 | o17·:·Ideal·of·S | 255 | o17·:·Ideal·of·S |
| 256 | i18·:·decompose·F2 | 256 | i18·:·decompose·F2 |
| 257 | o18·=·{ideal·(b· | 257 | o18·=·{ideal·(b·-·12c·+·48d,·a·-·16c·+·d),·ideal·(b·+·46c·+·14d,·a·+·31c·- |
| 258 | ······----------------------------------------------------------------------- | 258 | ······----------------------------------------------------------------------- |
| 259 | ······ | 259 | ······5d)} |
| 260 | o18·:·List | 260 | o18·:·List |
| 261 | It·turns·out·that·this·is·the·ideal·of·2·skew·lines,·just·not·defined·over·this | 261 | It·turns·out·that·this·is·the·ideal·of·2·skew·lines,·just·not·defined·over·this |
| 262 | field. | 262 | field. |
| 263 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 263 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 264 | This·routine·expects·the·input·to·represent·an·irreducible·variety | 264 | This·routine·expects·the·input·to·represent·an·irreducible·variety |
| 265 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 265 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 92, 17 lines modified | Offset 92, 17 lines modified | ||
| 92 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 92 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 93 | o3·:·Ideal·of·S</code></pre> | 93 | o3·:·Ideal·of·S</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·pts·=·randomPointsOnRationalVariety(I,·4) | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·pts·=·randomPointsOnRationalVariety(I,·4) |
| 97 | o4·=·{|· | 97 | o4·=·{|·-25·20·-30·-16·24·-36·|,·|·19·-29·19·23·-29·19·|,·|·-44·46·-8·7·-10 |
| 98 | ·····------------------------------------------------------------------------ | 98 | ·····------------------------------------------------------------------------ |
| 99 | ·····- | 99 | ·····-29·|,·|·8·41·-24·46·-22·-29·|} |
| 100 | o4·:·List</code></pre> | 100 | o4·:·List</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·for·p·in·pts·list·sub(I,·p)·==·0 | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·for·p·in·pts·list·sub(I,·p)·==·0 |
| 104 | o5·=·{true,·true,·true,·true} | 104 | o5·=·{true,·true,·true,·true} |
| Offset 164, 61 lines modified | Offset 164, 61 lines modified | ||
| 164 | ········<div> | 164 | ········<div> |
| 165 | ··········<p>There·are·2·components.··We·attempt·to·find·points·on·each·of·these·two·components.·We·are·successful.··This·indicates·that·the·corresponding·varieties·are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we·want.</p> | 165 | ··········<p>There·are·2·components.··We·attempt·to·find·points·on·each·of·these·two·components.·We·are·successful.··This·indicates·that·the·corresponding·varieties·are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we·want.</p> |
| 166 | ········</div> | 166 | ········</div> |
| 167 | ········<table·class="examples"> | 167 | ········<table·class="examples"> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) | 169 | <td>··············<pre><code·class="language-macaulay2">i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) |
| 170 | ······+----------------------------------------------------------------------------------------+ | ||
| 171 | o13·=·||·-15·9·-4·9·-47·-7·19·31·-22·-13·-23·-30·-38·-16·-19·39·-18·16·21·34·-47·19·-43·-39·|··| | ||
| 172 | ······+----------------------------------------------------------------------------------------+ | ||
| 173 | ······||·47·2·-38·-35·-49·-35·-20·48·-42·-48·-28·21·-15·-28·-10·-47·-34·49·38·2·22·16·-47·45·|·| | ||
| 174 | ······+----------------------------------------------------------------------------------------+ | ||
| 175 | ······||·15·-40·-13·-45·-32·9·34·10·-2·-11·30·18·47·19·30·-16·-17·12·7·15·39·-23·48·43·|·······| | ||
| 176 | ······+----------------------------------------------------------------------------------------+ | ||
| 177 | ······||·-22·-35·14·-29·-36·-14·-18·-44·-50·1·14·16·36·35·5·11·-28·36·-38·33·11·40·-3·46·|·····| | ||
| 178 | ······+----------------------------------------------------------------------------------------+ | ||
| 179 | ······||·13·-35·-39·35·16·-18·41·35·-15·-13·-26·-46·22·-47·-2·-23·-37·-50·-7·2·-47·29·-10·15·|·| | ||
| 180 | ······+----------------------------------------------------------------------------------------+ | ||
| 181 | ······||·19·-11·-23·-31·-35·-36·28·40·38·24·41·-47·30·-18·13·39·-20·15·27·-22·-9·32·-30·-32·|··| | ||
| 182 | ······+----------------------------------------------------------------------------------------+ | ||
| 183 | ······||·41·29·49·14·-11·20·16·28·-48·-20·0·-5·-48·-15·-46·39·17·1·0·33·-33·-49·44·-19·|·······| | ||
| 184 | ······+----------------------------------------------------------------------------------------+ | ||
| 185 | ······||·39·-35·49·20·-8·41·-3·19·23·-11·-4·-12·-39·36·46·9·-49·-35·-39·4·-26·13·-8·22·|·······| | ||
| 186 | ······+----------------------------------------------------------------------------------------+ | ||
| 187 | ······||·27·-7·-28·31·30·41·-27·41·26·-6·22·-5·43·-8·-49·36·-28·-18·-3·-22·41·-30·35·16·|······| | ||
| 188 | ······+----------------------------------------------------------------------------------------+ | ||
| 189 | ······||·36·-33·-45·-12·-50·-48·-13·-28·-15·-49·10·-31·-9·-35·-19·6·-41·33·40·3·25·-31·-13·-2·|| | ||
| 190 | ······+----------------------------------------------------------------------------------------+</code></pre> | ||
| 191 | </td>··········</tr> | ||
| 192 | ··········<tr> | ||
| 193 | <td>··············<pre><code·class="language-macaulay2">i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | ||
| 170 | ······+--------------------------------------------------------------------------------------+ | 194 | ······+--------------------------------------------------------------------------------------+ |
| 171 | o1 | 195 | o14·=·||·-35·39·-4·-3·-26·4·20·45·43·-3·-44·23·-40·-50·-6·-24·37·-35·27·30·-47·4·-31·0·|·····| |
| 172 | ······+--------------------------------------------------------------------------------------+ | 196 | ······+--------------------------------------------------------------------------------------+ |
| 173 | ······||· | 197 | ······||·-9·18·13·-46·44·-19·-4·10·-33·13·22·-48·-48·-33·-37·-8·30·-37·-29·-31·-48·-39·47·0·|| |
| 174 | ······+--------------------------------------------------------------------------------------+ | 198 | ······+--------------------------------------------------------------------------------------+ |
| 175 | ······||· | 199 | ······||·24·-43·-8·-28·-37·48·45·16·34·47·20·-25·1·1·18·-44·40·-22·46·28·-18·-49·10·0·|······| |
| 176 | ······+--------------------------------------------------------------------------------------+ | 200 | ······+--------------------------------------------------------------------------------------+ |
| 177 | ······||·-41 | 201 | ······||·2·-44·10·47·22·42·-37·22·-39·-29·19·-42·-13·-39·0·-13·3·-41·-17·30·13·7·8·0·|·······| |
| 178 | ······+--------------------------------------------------------------------------------------+ | 202 | ······+--------------------------------------------------------------------------------------+ |
| 179 | ······||·-1 | 203 | ······||·-18·31·14·-11·-10·-1·7·-12·-36·3·-34·-2·49·-4·-1·45·-18·42·-46·-29·30·8·23·0·|······| |
| 180 | ······+--------------------------------------------------------------------------------------+ | 204 | ······+--------------------------------------------------------------------------------------+ |
| 181 | ······||· | 205 | ······||·22·22·21·25·-34·13·-42·42·34·7·-15·-2·-46·43·31·32·12·-18·-16·15·18·-28·27·0·|······| |
| 182 | ······+--------------------------------------------------------------------------------------+ | 206 | ······+--------------------------------------------------------------------------------------+ |
| 183 | ······||· | 207 | ······||·20·34·11·19·24·-34·-32·-18·-4·44·-43·-14·44·26·-43·9·-39·20·-23·23·-37·-21·19·0·|···| |
| 184 | ······+--------------------------------------------------------------------------------------+ | 208 | ······+--------------------------------------------------------------------------------------+ |
| 185 | ······||· | 209 | ······||·9·44·22·48·-27·-22·-41·22·17·48·3·27·-28·18·-9·27·6·-9·47·-47·-28·0·-33·0·|·········| |
| 186 | ······+--------------------------------------------------------------------------------------+ | 210 | ······+--------------------------------------------------------------------------------------+ |
| 187 | ······||·4 | 211 | ······||·-45·5·15·-32·-3·-14·-30·44·10·44·-29·-48·-37·23·-14·-47·-33·-28·5·-29·26·28·42·0·|··| |
| 188 | ······+--------------------------------------------------------------------------------------+ | 212 | ······+--------------------------------------------------------------------------------------+ |
| 189 | ······||· | 213 | ······||·-2·-29·-50·-48·-22·17·-41·-21·-1·-4·13·17·5·-33·-5·47·-20·-13·22·30·4·44·-29·0·|····| |
| 190 | ······+--------------------------------------------------------------------------------------+</code></pre> | 214 | ······+--------------------------------------------------------------------------------------+</code></pre> |
| 191 | </td>··········</tr> | 215 | </td>··········</tr> |
| 192 | ··········<tr> | ||
| 193 | <td>··············<pre><code·class="language-macaulay2">i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | ||
| 194 | ······+-------------------------------------------------------------------------------------+ | ||
| 195 | o14·=·||·38·-31·49·39·4·46·-29·-5·-39·-40·14·-11·-31·46·43·-26·4·30·-35·27·-40·37·-47·0·|···| | ||
| 196 | ······+-------------------------------------------------------------------------------------+ | ||
| 197 | ······||·-1·-5·-10·-10·-11·42·6·46·-4·47·42·-40·47·-27·-20·49·-39·-31·-37·-29·-48·30·-48·0·|| | ||
| 198 | ······+-------------------------------------------------------------------------------------+ | ||
| 199 | ······||·29·18·20·1·18·26·-31·-45·-21·10·22·-30·10·32·-31·-21·-49·28·-22·46·1·40·-18·0·|····| | ||
| 200 | ······+-------------------------------------------------------------------------------------+ | ||
| 201 | ······||·-17·3·17·-9·-36·-45·49·30·-45·24·-28·41·8·-4·-26·-28·7·30·-41·-17·-13·3·13·0·|·····| | ||
| 202 | ······+-------------------------------------------------------------------------------------+ | ||
| 203 | ······||·37·33·-47·-20·-49·45·29·19·41·13·-38·44·23·40·-48·45·8·-29·42·-46·49·-18·30·0·|····| | ||
| 204 | ······+-------------------------------------------------------------------------------------+ | ||
| 205 | ······||·-9·-3·-26·13·35·49·-8·49·-40·13·-20·9·27·5·-8·-15·-28·15·-18·-16·-46·12·18·0·|·····| | ||
| 206 | ······+-------------------------------------------------------------------------------------+ | ||
| 207 | ······||·28·32·0·0·-17·-44·25·42·7·-35·29·-17·19·8·-9·-26·-21·23·20·-23·44·-39·-37·0·|······| | ||
| 208 | ······+-------------------------------------------------------------------------------------+ | ||
| 209 | ······||·-30·-29·27·14·17·39·33·15·-35·50·-50·45·-33·13·24·-44·0·-47·-9·47·-28·6·-28·0·|····| | ||
| 210 | ······+-------------------------------------------------------------------------------------+ | ||
| 211 | ······||·7·-12·42·-29·30·1·3·-28·-7·36·-26·-40·42·38·-20·-23·28·-29·-28·5·-37·-33·26·0·|····| | ||
| 212 | ······+-------------------------------------------------------------------------------------+ | ||
| 213 | ······||·28·-10·13·-39·-20·11·13·-13·-37·8·-36·-29·-29·17·24·-50·44·30·-13·22·5·-20·4·0·|···| | ||
| 214 | ······+-------------------------------------------------------------------------------------+</code></pre> | ||
| 215 | </td>··········</tr> | ||
| 216 | ········</table> | 216 | ········</table> |
| 217 | ······</div> | 217 | ······</div> |
| 218 | ······<div> | 218 | ······<div> |
| 219 | ········<h2>Caveat</h2> | 219 | ········<h2>Caveat</h2> |
| 220 | ········<div> | 220 | ········<div> |
| 221 | ··········<p>This·routine·expects·the·input·to·represent·an·irreducible·variety</p> | 221 | ··········<p>This·routine·expects·the·input·to·represent·an·irreducible·variety</p> |
| 222 | ········</div> | 222 | ········</div> |
| Offset 29, 17 lines modified | Offset 29, 17 lines modified | ||
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ·············································2 | 30 | ·············································2 |
| 31 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 31 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 32 | o3·:·Ideal·of·S | 32 | o3·:·Ideal·of·S |
| 33 | i4·:·pts·=·randomPointsOnRationalVariety(I,·4) | 33 | i4·:·pts·=·randomPointsOnRationalVariety(I,·4) |
| 34 | o4·=·{|· | 34 | o4·=·{|·-25·20·-30·-16·24·-36·|,·|·19·-29·19·23·-29·19·|,·|·-44·46·-8·7·-10 |
| 35 | ·····------------------------------------------------------------------------ | 35 | ·····------------------------------------------------------------------------ |
| 36 | ·····- | 36 | ·····-29·|,·|·8·41·-24·46·-22·-29·|} |
| 37 | o4·:·List | 37 | o4·:·List |
| 38 | i5·:·for·p·in·pts·list·sub(I,·p)·==·0 | 38 | i5·:·for·p·in·pts·list·sub(I,·p)·==·0 |
| 39 | o5·=·{true,·true,·true,·true} | 39 | o5·=·{true,·true,·true,·true} |
| 40 | o5·:·List | 40 | o5·:·List |
| Offset 85, 99 lines modified | Offset 85, 99 lines modified | ||
| 85 | There·are·2·components.·We·attempt·to·find·points·on·each·of·these·two | 85 | There·are·2·components.·We·attempt·to·find·points·on·each·of·these·two |
| 86 | components.·We·are·successful.·This·indicates·that·the·corresponding·varieties | 86 | components.·We·are·successful.·This·indicates·that·the·corresponding·varieties |
| 87 | are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we | 87 | are·both·rational.·Also,·if·we·can·find·one·point,·we·can·find·as·many·as·we |
| 88 | want. | 88 | want. |
| 89 | i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) | 89 | i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) |
| 90 | ······+------------------------------------------------------------------------ | 90 | ······+------------------------------------------------------------------------ |
| 91 | --------------+ | 91 | ----------------+ |
| 92 | o13·=·||·29·-40·15·-49·3·-13·-6·-39·2·39·47·15·19·-47·-46·-39·-16·32·-43·34·-13 | ||
| 93 | -18· | 92 | o13·=·||·-15·9·-4·9·-47·-7·19·31·-22·-13·-23·-30·-38·-16·-19·39·-18·16·21·34·- |
| 93 | 47·19·-43·-39·|··| | ||
| 94 | ······+------------------------------------------------------------------------ | ||
| 95 | ----------------+ | ||
| 96 | ······||·47·2·-38·-35·-49·-35·-20·48·-42·-48·-28·21·-15·-28·-10·-47·-34·49·38·2 | ||
| 97 | 22·16·-47·45·|·| | ||
| 98 | ······+------------------------------------------------------------------------ | ||
| 99 | ----------------+ | ||
| 100 | ······||·15·-40·-13·-45·-32·9·34·10·-2·-11·30·18·47·19·30·-16·-17·12·7·15·39·- | ||
| 101 | 23·48·43·|·······| | ||
| 102 | ······+------------------------------------------------------------------------ | ||
| 103 | ----------------+ | ||
| 104 | ······||·-22·-35·14·-29·-36·-14·-18·-44·-50·1·14·16·36·35·5·11·-28·36·-38·33·11 | ||
| 105 | 40·-3·46·|·····| | ||
| 106 | ······+------------------------------------------------------------------------ | ||
| 107 | ----------------+ | ||
| 108 | ······||·13·-35·-39·35·16·-18·41·35·-15·-13·-26·-46·22·-47·-2·-23·-37·-50·-7·2 | ||
| 109 | -47·29·-10·15·|·| | ||
| 110 | ······+------------------------------------------------------------------------ | ||
| 111 | ----------------+ | ||
| 112 | ······||·19·-11·-23·-31·-35·-36·28·40·38·24·41·-47·30·-18·13·39·-20·15·27·-22·- | ||
| 113 | 9·32·-30·-32·|··| | ||
| 114 | ······+------------------------------------------------------------------------ | ||
| 115 | ----------------+ | ||
| 116 | ······||·41·29·49·14·-11·20·16·28·-48·-20·0·-5·-48·-15·-46·39·17·1·0·33·-33·-49 | ||
| 117 | 44·-19·|·······| | ||
| 118 | ······+------------------------------------------------------------------------ | ||
| 119 | ----------------+ | ||
| 120 | ······||·39·-35·49·20·-8·41·-3·19·23·-11·-4·-12·-39·36·46·9·-49·-35·-39·4·-26 | ||
| 121 | 13·-8·22·|·······| | ||
| 122 | ······+------------------------------------------------------------------------ | ||
| 123 | ----------------+ | ||
| 124 | ······||·27·-7·-28·31·30·41·-27·41·26·-6·22·-5·43·-8·-49·36·-28·-18·-3·-22·41·- | ||
| 125 | 30·35·16·|······| | ||
| 126 | ······+------------------------------------------------------------------------ | ||
| 127 | ----------------+ | ||
| 128 | ······||·36·-33·-45·-12·-50·-48·-13·-28·-15·-49·10·-31·-9·-35·-19·6·-41·33·40·3 | ||
| 129 | 25·-31·-13·-2·|| | ||
| 94 | ······+------------------------------------------------------------------------ | 130 | ······+------------------------------------------------------------------------ |
| 95 | --------------+ | 131 | ----------------+ |
| 96 | ······||·37·-7·-24·8·-26·38·9·-31·24·-47·-34·12·16·22·-22·45·-28·16·-47·2·-48·- | ||
| 97 | 132 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | |
| 98 | ······+------------------------------------------------------------------------ | 133 | ······+------------------------------------------------------------------------ |
| 99 | --------------+ | 134 | --------------+ |
| 100 | ······||·6·1·-31·-7·44·8·-50·24·-48·-16·23·23·-23·39·-5·43·19·-15·48·15·-11·-17 | ||
| 101 | 135 | o14·=·||·-35·39·-4·-3·-26·4·20·45·43·-3·-44·23·-40·-50·-6·-24·37·-35·27·30·-47 | |
| 136 | 4·-31·0·|·····| | ||
| 102 | ······+------------------------------------------------------------------------ | 137 | ······+------------------------------------------------------------------------ |
| 103 | --------------+ | 138 | --------------+ |
| 104 | ······||·-41·-49·6·-16·-12·31·23·6·-7·11·3·-42·40·11·-28·46·35·-28·-3·33·1·-28 | ||
| 105 | - | 139 | ······||·-9·18·13·-46·44·-19·-4·10·-33·13·22·-48·-48·-33·-37·-8·30·-37·-29·-31 |
| 140 | -48·-39·47·0·|| | ||
| 106 | ······+------------------------------------------------------------------------ | 141 | ······+------------------------------------------------------------------------ |
| 107 | --------------+ | 142 | --------------+ |
| 108 | ······||·-11·-27·-4·40·-34·6·44·-2·19·-23·-29·21·29·-47·-37·15·-47·-24·-10·2·- | ||
| 109 | 143 | ······||·24·-43·-8·-28·-37·48·45·16·34·47·20·-25·1·1·18·-44·40·-22·46·28·-18·- | |
| 144 | 49·10·0·|······| | ||
| 110 | ······+------------------------------------------------------------------------ | 145 | ······+------------------------------------------------------------------------ |
| 111 | --------------+ | 146 | --------------+ |
| 112 | ······||·-50·42·20·-30·-46·-48·-5·40·-47·39·13·47·32·-9·41·-32·-18·25·-30·-22 | ||
| 113 | 24·-2 | 147 | ······||·2·-44·10·47·22·42·-37·22·-39·-29·19·-42·-13·-39·0·-13·3·-41·-17·30·13 |
| 148 | 7·8·0·|·······| | ||
| 114 | ······+------------------------------------------------------------------------ | 149 | ······+------------------------------------------------------------------------ |
| 115 | --------------+ | 150 | --------------+ |
| 116 | ······||·50·22·-30·3·-43·-29·-33·-18·6·39·-29·24·-49·-33·-15·-19·-15·-37·44·33 | ||
| 117 | - | 151 | ······||·-18·31·14·-11·-10·-1·7·-12·-36·3·-34·-2·49·-4·-1·45·-18·42·-46·-29·30 |
| 152 | 8·23·0·|······| | ||
| 118 | ······+------------------------------------------------------------------------ | 153 | ······+------------------------------------------------------------------------ |
| 119 | --------------+ | 154 | --------------+ |
| 120 | ······||·-9·31·-37·-42·-7·-8·-11·-21·12·9·13·-9·13·-26·11·22·36·34·-8·4·-11·-49 | ||
| 121 | -3 | 155 | ······||·22·22·21·25·-34·13·-42·42·34·7·-15·-2·-46·43·31·32·12·-18·-16·15·18·- |
| 156 | 28·27·0·|······| | ||
| 122 | ······+------------------------------------------------------------------------ | 157 | ······+------------------------------------------------------------------------ |
| 123 | --------------+ | 158 | --------------+ |
| 124 | ······||·47·14·-11·-16·-20·-40·42·5·-2·36·8·-45·-30·41·-26·16·-8·-34·35·-22·- | ||
| 125 | 159 | ······||·20·34·11·19·24·-34·-32·-18·-4·44·-43·-14·44·26·-43·9·-39·20·-23·23·-37 | |
| 160 | -21·19·0·|···| | ||
| 126 | ······+------------------------------------------------------------------------ | 161 | ······+------------------------------------------------------------------------ |
| 127 | --------------+ | 162 | --------------+ |
| 128 | ······||·23·-8·-3·-17·38·0·11·-33·-7·6·-31·-4·-31·25·6·-2·-35·-11·-13·3·-49·-41 | ||
| 129 | 4 | 163 | ······||·9·44·22·48·-27·-22·-41·22·17·48·3·27·-28·18·-9·27·6·-9·47·-47·-28·0·- |
| 164 | 33·0·|·········| | ||
| 130 | ······+------------------------------------------------------------------------ | 165 | ······+------------------------------------------------------------------------ |
| 131 | --------------+ | 166 | --------------+ |
| 132 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | ||
| 167 | ······||·-45·5·15·-32·-3·-14·-30·44·10·44·-29·-48·-37·23·-14·-47·-33·-28·5·-29 | ||
| 168 | 26·28·42·0·|··| | ||
| 133 | ······+------------------------------------------------------------------------ | 169 | ······+------------------------------------------------------------------------ |
| 134 | -------------+ | 170 | --------------+ |
| 171 | ······||·-2·-29·-50·-48·-22·17·-41·-21·-1·-4·13·17·5·-33·-5·47·-20·-13·22·30·4 | ||
| 135 | o14·=·||·38·-31·49·39·4·46·-29·-5·-39·-40·14·-11·-31·46·43·-26·4·30·-35·27·-40 | ||
| 136 | 37·-47·0·|···| | ||
| 137 | ······+------------------------------------------------------------------------ | ||
| 138 | -------------+ | ||
| 139 | ······||·-1·-5·-10·-10·-11·42·6·46·-4·47·42·-40·47·-27·-20·49·-39·-31·-37·-29·- | ||
| 140 | 48·30·-48·0·|| | ||
| 141 | ······+------------------------------------------------------------------------ | ||
| 142 | -------------+ | ||
| 143 | ······||·29·18·20·1·18·26·-31·-45·-21·10·22·-30·10·32·-31·-21·-49·28·-22·46·1 | ||
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | c2V0V2Fsa1RyYWNlKFpaKQ== | 8 | c2V0V2Fsa1RyYWNlKFpaKQ== |
| 9 | #:len=251 | 9 | #:len=251 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTYxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTYxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzZXRXYWxrVHJhY2UsWlopLCJzZXRXYWxrVHJhY2Uo | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzZXRXYWxrVHJhY2UsWlopLCJzZXRXYWxrVHJhY2Uo |
| Offset 11, 21 lines modified | Offset 11, 21 lines modified | ||
| 11 | i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}]; | 11 | i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}]; |
| 12 | i4·:·I2·=·sub(I1,·R2); | 12 | i4·:·I2·=·sub(I1,·R2); |
| 13 | o4·:·Ideal·of·R2 | 13 | o4·:·Ideal·of·R2 |
| 14 | i5·:·elapsedTime·gb·I2 | 14 | i5·:·elapsedTime·gb·I2 |
| 15 | ·--·2. | 15 | ·--·2.97278s·elapsed |
| 16 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] | 16 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] |
| 17 | o5·:·GroebnerBasis | 17 | o5·:·GroebnerBasis |
| 18 | i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) | 18 | i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) |
| 19 | ·--· | 19 | ·--·2.27111s·elapsed |
| 20 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] | 20 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] |
| 21 | o6·:·GroebnerBasis | 21 | o6·:·GroebnerBasis |
| 22 | i7·:· | 22 | i7·:· |
| Offset 76, 28 lines modified | Offset 76, 28 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·I2·=·sub(I1,·R2); | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·I2·=·sub(I1,·R2); |
| 78 | o4·:·Ideal·of·R2</code></pre> | 78 | o4·:·Ideal·of·R2</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·gb·I2 | 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·gb·I2 |
| 82 | ·--·2. | 82 | ·--·2.97278s·elapsed |
| 83 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] | 83 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] |
| 84 | o5·:·GroebnerBasis</code></pre> | 84 | o5·:·GroebnerBasis</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ········</table> | 86 | ········</table> |
| 87 | ········<div> | 87 | ········<div> |
| 88 | ··········<p>but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the·Groebner·walk.</p> | 88 | ··········<p>but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the·Groebner·walk.</p> |
| 89 | ········</div> | 89 | ········</div> |
| 90 | ········<table·class="examples"> | 90 | ········<table·class="examples"> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) | 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) |
| 93 | ·--· | 93 | ·--·2.27111s·elapsed |
| 94 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] | 94 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] |
| 95 | o6·:·GroebnerBasis</code></pre> | 95 | o6·:·GroebnerBasis</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ········</table> | 97 | ········</table> |
| 98 | ······</div> | 98 | ······</div> |
| Offset 38, 23 lines modified | Offset 38, 23 lines modified | ||
| 38 | using·a·different·weight·vector·and·then·graded·reverse·lexicographic·we·could | 38 | using·a·different·weight·vector·and·then·graded·reverse·lexicographic·we·could |
| 39 | substitute·and·compute·directly, | 39 | substitute·and·compute·directly, |
| 40 | i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}]; | 40 | i3·:·R2·=·QQ[x,y,z,u,v,·MonomialOrder=>Weights=>{0,0,0,1,1}]; |
| 41 | i4·:·I2·=·sub(I1,·R2); | 41 | i4·:·I2·=·sub(I1,·R2); |
| 42 | o4·:·Ideal·of·R2 | 42 | o4·:·Ideal·of·R2 |
| 43 | i5·:·elapsedTime·gb·I2 | 43 | i5·:·elapsedTime·gb·I2 |
| 44 | ·--·2. | 44 | ·--·2.97278s·elapsed |
| 45 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] | 45 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] |
| 46 | o5·:·GroebnerBasis | 46 | o5·:·GroebnerBasis |
| 47 | but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the | 47 | but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the |
| 48 | Groebner·walk. | 48 | Groebner·walk. |
| 49 | i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) | 49 | i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) |
| 50 | ·--· | 50 | ·--·2.27111s·elapsed |
| 51 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] | 51 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] |
| 52 | o6·:·GroebnerBasis | 52 | o6·:·GroebnerBasis |
| 53 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 53 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 54 | The·target·ring·must·be·the·same·ring·as·the·ring·of·the·starting·ideal,·except | 54 | The·target·ring·must·be·the·same·ring·as·the·ring·of·the·starting·ideal,·except |
| 55 | with·different·monomial·order.·The·ring·must·be·a·polynomial·ring·over·a·field. | 55 | with·different·monomial·order.·The·ring·must·be·a·polynomial·ring·over·a·field. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=23 | 7 | #:len=23 |
| 8 | aWRlYWxPZlByb2plY3RpdmVQb2ludHM= | 8 | aWRlYWxPZlByb2plY3RpdmVQb2ludHM= |
| 9 | #:len=1240 | 9 | #:len=1240 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgdGhlIGlkZWFsIG9mIHNl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgdGhlIGlkZWFsIG9mIHNl |
| 11 | dCBvZiBwb2ludHMiLCAibGluZW51bSIgPT4gNDI0LCBJbnB1dHMgPT4ge1NQQU57VFR7IkwifSwi | 11 | dCBvZiBwb2ludHMiLCAibGluZW51bSIgPT4gNDI0LCBJbnB1dHMgPT4ge1NQQU57VFR7IkwifSwi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | Y2lPcGVyYXRvclJlc29sdXRpb24= | 8 | Y2lPcGVyYXRvclJlc29sdXRpb24= |
| 9 | #:len=2668 | 9 | #:len=2668 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiXCJsaWZ0IHJlc29sdXRpb24gZnJvbSBj | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiXCJsaWZ0IHJlc29sdXRpb24gZnJvbSBj |
| 11 | b21wbGV0ZSBpbnRlcnNlY3Rpb24gdXNpbmcgaGlnaGVyIGNpLW9wZXJhdG9yc1wiIiwgImxpbmVu | 11 | b21wbGV0ZSBpbnRlcnNlY3Rpb24gdXNpbmcgaGlnaGVyIGNpLW9wZXJhdG9yc1wiIiwgImxpbmVu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=11 | 7 | #:len=11 |
| 8 | R3JvdXBBY3Rpbmc= | 8 | R3JvdXBBY3Rpbmc= |
| 9 | #:len=621 | 9 | #:len=621 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAic3RvcmVzIHRoZSBEeW5raW4gdHlwZSBv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAic3RvcmVzIHRoZSBEeW5raW4gdHlwZSBv |
| 11 | ZiB0aGUgZ3JvdXAgYWN0aW5nIG9uIGEgcmluZyIsICJsaW5lbnVtIiA9PiA4MywgU2VlQWxzbyA9 | 11 | ZiB0aGUgZ3JvdXAgYWN0aW5nIG9uIGEgcmluZyIsICJsaW5lbnVtIiA9PiA4MywgU2VlQWxzbyA9 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=5 | 7 | #:len=5 |
| 8 | a2FwcGE= | 8 | a2FwcGE= |
| 9 | #:len=1396 | 9 | #:len=1396 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTWlsbGVyLU1vcml0YS1NdW1mb3JkIGNs | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTWlsbGVyLU1vcml0YS1NdW1mb3JkIGNs |
| 11 | YXNzZXMiLCAibGluZW51bSIgPT4gNzM4LCBJbnB1dHMgPT4ge1NQQU57VFR7ImEifSwiLCAiLFNQ | 11 | YXNzZXMiLCAibGluZW51bSIgPT4gNzM4LCBJbnB1dHMgPT4ge1NQQU57VFR7ImEifSwiLCAiLFNQ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | ZXVsZXJPcGVyYXRvcnM= | 8 | ZXVsZXJPcGVyYXRvcnM= |
| 9 | #:len=1959 | 9 | #:len=1959 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRXVsZXIgT3BlcmF0b3JzIiwgImxpbmVu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRXVsZXIgT3BlcmF0b3JzIiwgImxpbmVu |
| 11 | dW0iID0+IDE0MCwgSW5wdXRzID0+IHtTUEFOe1RUeyJBIn0sIiwgIixTUEFOeyJhICIsVE8ye25l | 11 | dW0iID0+IDE0MCwgSW5wdXRzID0+IHtTUEFOe1RUeyJBIn0sIiwgIixTUEFOeyJhICIsVE8ye25l |
| Offset 42, 19 lines modified | Offset 42, 19 lines modified | ||
| 42 | i5·:·w·=·{9,1,99999,·9999999,·3,·999} | 42 | i5·:·w·=·{9,1,99999,·9999999,·3,·999} |
| 43 | o5·=·{9,·1,·99999,·9999999,·3,·999} | 43 | o5·=·{9,·1,·99999,·9999999,·3,·999} |
| 44 | o5·:·List | 44 | o5·:·List |
| 45 | i6·:·netList·cssLeadTerm(Hbeta,·w) | 45 | i6·:·netList·cssLeadTerm(Hbeta,·w) |
| 46 | ·--·.000004799s·elapsed | ||
| 46 | ·--·.00000 | 47 | ·--·.00000543s·elapsed |
| 48 | ·--·.000005501s·elapsed | ||
| 47 | ·--·.00000 | 49 | ·--·.00000541s·elapsed |
| 48 | ·--·.000003275s·elapsed | ||
| 49 | ·--·.00000 | 50 | ·--·.000004068s·elapsed |
| 50 | ·--·.000002444s·elapsed | ||
| 51 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 51 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 52 | Converting·to·Naive·algorithm. | 52 | Converting·to·Naive·algorithm. |
| 53 | ·····+----------------------------------------------------+ | 53 | ·····+----------------------------------------------------+ |
| 54 | ·····|···1·5···5·5········································| | 54 | ·····|···1·5···5·5········································| |
| 55 | ·····|·-·-·-·-·-·-········································| | 55 | ·····|·-·-·-·-·-·-········································| |
| 56 | ·····|···2·2···2·2········································| | 56 | ·····|···2·2···2·2········································| |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·R·=·QQ[t_1..t_5]; | 3 | i1·:·R·=·QQ[t_1..t_5]; |
| 4 | i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,·t_2*t_4); | 4 | i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,·t_2*t_4); |
| 5 | o2·:·Ideal·of·R | 5 | o2·:·Ideal·of·R |
| 6 | i3·:·solveFrobeniusIdeal·I | 6 | i3·:·solveFrobeniusIdeal·I |
| 7 | ·--·.00000 | 7 | ·--·.000005109s·elapsed |
| 8 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 8 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 9 | Converting·to·Naive·algorithm. | 9 | Converting·to·Naive·algorithm. |
| 10 | ············································································· | 10 | ············································································· |
| 11 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 11 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 12 | ················0········1········2·······3········0·······1·······2·······4· | 12 | ················0········1········2·······3········0·······1·······2·······4· |
| 13 | ·····------------------------------------------------------------------------ | 13 | ·····------------------------------------------------------------------------ |
| Offset 24, 15 lines modified | Offset 24, 15 lines modified | ||
| 24 | ·······2····4····0···4····4····1···2····4····2···4····4····3·······4 | 24 | ·······2····4····0···4····4····1···2····4····2···4····4····3·······4 |
| 25 | o3·:·List | 25 | o3·:·List |
| 26 | i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]); | 26 | i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]); |
| 27 | i5·:·solveFrobeniusIdeal(I,·W) | 27 | i5·:·solveFrobeniusIdeal(I,·W) |
| 28 | ·--·.00000 | 28 | ·--·.000005741s·elapsed |
| 29 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 29 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 30 | Converting·to·Naive·algorithm. | 30 | Converting·to·Naive·algorithm. |
| 31 | ············································································· | 31 | ············································································· |
| 32 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 32 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 33 | ················0········1········2·······3········0·······1·······2·······4· | 33 | ················0········1········2·······3········0·······1·······2·······4· |
| 34 | ·····------------------------------------------------------------------------ | 34 | ·····------------------------------------------------------------------------ |
| Offset 122, 19 lines modified | Offset 122, 19 lines modified | ||
| 122 | o5·=·{9,·1,·99999,·9999999,·3,·999} | 122 | o5·=·{9,·1,·99999,·9999999,·3,·999} |
| 123 | o5·:·List</code></pre> | 123 | o5·:·List</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i6·:·netList·cssLeadTerm(Hbeta,·w) | 126 | <td>··············<pre><code·class="language-macaulay2">i6·:·netList·cssLeadTerm(Hbeta,·w) |
| 127 | ·--·.000004799s·elapsed | ||
| 127 | ·--·.00000 | 128 | ·--·.00000543s·elapsed |
| 129 | ·--·.000005501s·elapsed | ||
| 128 | ·--·.00000 | 130 | ·--·.00000541s·elapsed |
| 129 | ·--·.000003275s·elapsed | ||
| 130 | ·--·.00000 | 131 | ·--·.000004068s·elapsed |
| 131 | ·--·.000002444s·elapsed | ||
| 132 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 132 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 133 | Converting·to·Naive·algorithm. | 133 | Converting·to·Naive·algorithm. |
| 134 | ·····+----------------------------------------------------+ | 134 | ·····+----------------------------------------------------+ |
| 135 | ·····|···1·5···5·5········································| | 135 | ·····|···1·5···5·5········································| |
| 136 | ·····|·-·-·-·-·-·-········································| | 136 | ·····|·-·-·-·-·-·-········································| |
| 137 | ·····|···2·2···2·2········································| | 137 | ·····|···2·2···2·2········································| |
| Offset 55, 19 lines modified | Offset 55, 19 lines modified | ||
| 55 | ··················1···6···1···6 | 55 | ··················1···6···1···6 |
| 56 | i5·:·w·=·{9,1,99999,·9999999,·3,·999} | 56 | i5·:·w·=·{9,1,99999,·9999999,·3,·999} |
| 57 | o5·=·{9,·1,·99999,·9999999,·3,·999} | 57 | o5·=·{9,·1,·99999,·9999999,·3,·999} |
| 58 | o5·:·List | 58 | o5·:·List |
| 59 | i6·:·netList·cssLeadTerm(Hbeta,·w) | 59 | i6·:·netList·cssLeadTerm(Hbeta,·w) |
| 60 | ·--·.000004799s·elapsed | ||
| 60 | ·--·.00000 | 61 | ·--·.00000543s·elapsed |
| 62 | ·--·.000005501s·elapsed | ||
| 61 | ·--·.00000 | 63 | ·--·.00000541s·elapsed |
| 62 | ·--·.000003275s·elapsed | ||
| 63 | ·--·.00000 | 64 | ·--·.000004068s·elapsed |
| 64 | ·--·.000002444s·elapsed | ||
| 65 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or | 65 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or |
| 66 | inhomogeneous·ideal. | 66 | inhomogeneous·ideal. |
| 67 | Converting·to·Naive·algorithm. | 67 | Converting·to·Naive·algorithm. |
| 68 | ·····+----------------------------------------------------+ | 68 | ·····+----------------------------------------------------+ |
| 69 | ·····|···1·5···5·5········································| | 69 | ·····|···1·5···5·5········································| |
| 70 | ·····|·-·-·-·-·-·-········································| | 70 | ·····|·-·-·-·-·-·-········································| |
| Offset 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,·t_2*t_4); | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3,·t_2*t_4); |
| 81 | o2·:·Ideal·of·R</code></pre> | 81 | o2·:·Ideal·of·R</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·solveFrobeniusIdeal·I | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·solveFrobeniusIdeal·I |
| 85 | ·--·.00000 | 85 | ·--·.000005109s·elapsed |
| 86 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 86 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 87 | Converting·to·Naive·algorithm. | 87 | Converting·to·Naive·algorithm. |
| 88 | ············································································· | 88 | ············································································· |
| 89 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 89 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 90 | ················0········1········2·······3········0·······1·······2·······4· | 90 | ················0········1········2·······3········0·······1·······2·······4· |
| 91 | ·····------------------------------------------------------------------------ | 91 | ·····------------------------------------------------------------------------ |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | ········</table> | 104 | ········</table> |
| 105 | ········<table·class="examples"> | 105 | ········<table·class="examples"> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·solveFrobeniusIdeal(I,·W) | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·solveFrobeniusIdeal(I,·W) |
| 111 | ·--·.00000 | 111 | ·--·.000005741s·elapsed |
| 112 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 112 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 113 | Converting·to·Naive·algorithm. | 113 | Converting·to·Naive·algorithm. |
| 114 | ············································································· | 114 | ············································································· |
| 115 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 115 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 116 | ················0········1········2·······3········0·······1·······2·······4· | 116 | ················0········1········2·······3········0·······1·······2·······4· |
| 117 | ·····------------------------------------------------------------------------ | 117 | ·····------------------------------------------------------------------------ |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | Here·is·[_\x8S_\x8S_\x8T,·Example·2.3.16]: | 17 | Here·is·[_\x8S_\x8S_\x8T,·Example·2.3.16]: |
| 18 | i1·:·R·=·QQ[t_1..t_5]; | 18 | i1·:·R·=·QQ[t_1..t_5]; |
| 19 | i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3, | 19 | i2·:·I·=·ideal(t_1+t_2+t_3+t_4+t_5,·t_1+t_2-t_4,·t_2+t_3-t_4,·t_1*t_3, |
| 20 | t_2*t_4); | 20 | t_2*t_4); |
| 21 | o2·:·Ideal·of·R | 21 | o2·:·Ideal·of·R |
| 22 | i3·:·solveFrobeniusIdeal·I | 22 | i3·:·solveFrobeniusIdeal·I |
| 23 | ·--·.00000 | 23 | ·--·.000005109s·elapsed |
| 24 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or | 24 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or |
| 25 | inhomogeneous·ideal. | 25 | inhomogeneous·ideal. |
| 26 | Converting·to·Naive·algorithm. | 26 | Converting·to·Naive·algorithm. |
| 27 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 27 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 28 | ················0········1········2·······3········0·······1·······2·······4 | 28 | ················0········1········2·······3········0·······1·······2·······4 |
| Offset 37, 15 lines modified | Offset 37, 15 lines modified | ||
| 37 | ·······1·············1·············1·············3·················2 | 37 | ·······1·············1·············1·············3·················2 |
| 38 | ·····-·-logX·logX··-·-logX·logX··-·-logX·logX··-·-logX·logX··+·logX·} | 38 | ·····-·-logX·logX··-·-logX·logX··-·-logX·logX··-·-logX·logX··+·logX·} |
| 39 | ·······2····4····0···4····4····1···2····4····2···4····4····3·······4 | 39 | ·······2····4····0···4····4····1···2····4····2···4····4····3·······4 |
| 40 | o3·:·List | 40 | o3·:·List |
| 41 | i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]); | 41 | i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]); |
| 42 | i5·:·solveFrobeniusIdeal(I,·W) | 42 | i5·:·solveFrobeniusIdeal(I,·W) |
| 43 | ·--·.00000 | 43 | ·--·.000005741s·elapsed |
| 44 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or | 44 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or |
| 45 | inhomogeneous·ideal. | 45 | inhomogeneous·ideal. |
| 46 | Converting·to·Naive·algorithm. | 46 | Converting·to·Naive·algorithm. |
| 47 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 47 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 48 | ················0········1········2·······3········0·······1·······2·······4 | 48 | ················0········1········2·······3········0·······1·······2·······4 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | YWxsZ2VucyhER0FsZ2VicmEsWlop | 8 | YWxsZ2VucyhER0FsZ2VicmEsWlop |
| 9 | #:len=269 | 9 | #:len=269 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbGxnZW5zLERHQWxnZWJyYSxaWiksImFsbGdlbnMo | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhbGxnZW5zLERHQWxnZWJyYSxaWiksImFsbGdlbnMo |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=29 | 7 | #:len=29 |
| 8 | cmVzdHJpY3Rpb24oQXJyYW5nZW1lbnQsTGlzdCk= | 8 | cmVzdHJpY3Rpb24oQXJyYW5nZW1lbnQsTGlzdCk= |
| 9 | #:len=343 | 9 | #:len=343 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc3Nywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc3Nywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmVzdHJpY3Rpb24sQXJyYW5nZW1lbnQsTGlzdCks | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmVzdHJpY3Rpb24sQXJyYW5nZW1lbnQsTGlzdCks |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | aW50ZWdyYWxDbG9zdXJlKC4uLixMaW1pdD0+Li4uKQ== | 8 | aW50ZWdyYWxDbG9zdXJlKC4uLixMaW1pdD0+Li4uKQ== |
| 9 | #:len=1120 | 9 | #:len=1120 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZG8gYSBwYXJ0aWFsIGludGVncmFsIGNs | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZG8gYSBwYXJ0aWFsIGludGVncmFsIGNs |
| 11 | b3N1cmUiLCAibGluZW51bSIgPT4gMTQyOCwgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT | 11 | b3N1cmUiLCAibGluZW51bSIgPT4gMTQyOCwgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | i3·:·R·=·S/f | 16 | i3·:·R·=·S/f |
| 17 | o3·=·R | 17 | o3·=·R |
| 18 | o3·:·QuotientRing | 18 | o3·:·QuotientRing |
| 19 | i4·:·time·R'·=·integralClosure·R | 19 | i4·:·time·R'·=·integralClosure·R |
| 20 | ·--·used·0. | 20 | ·--·used·0.560416s·(cpu);·0.327425s·(thread);·0s·(gc) |
| 21 | o4·=·R' | 21 | o4·=·R' |
| 22 | o4·:·QuotientRing | 22 | o4·:·QuotientRing |
| 23 | i5·:·netList·(ideal·R')_* | 23 | i5·:·netList·(ideal·R')_* |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | i9·:·R·=·S/f | 83 | i9·:·R·=·S/f |
| 84 | o9·=·R | 84 | o9·=·R |
| 85 | o9·:·QuotientRing | 85 | o9·:·QuotientRing |
| 86 | i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 86 | i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 87 | ·--·used·0. | 87 | ·--·used·0.620489s·(cpu);·0.331237s·(thread);·0s·(gc) |
| 88 | o10·=·R' | 88 | o10·=·R' |
| 89 | o10·:·QuotientRing | 89 | o10·:·QuotientRing |
| 90 | i11·:·netList·(ideal·R')_* | 90 | i11·:·netList·(ideal·R')_* |
| Offset 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | i15·:·R·=·S/f | 150 | i15·:·R·=·S/f |
| 151 | o15·=·R | 151 | o15·=·R |
| 152 | o15·:·QuotientRing | 152 | o15·:·QuotientRing |
| 153 | i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) | 153 | i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) |
| 154 | ·--·used·0. | 154 | ·--·used·0.606748s·(cpu);·0.362465s·(thread);·0s·(gc) |
| 155 | o16·=·R' | 155 | o16·=·R' |
| 156 | o16·:·QuotientRing | 156 | o16·:·QuotientRing |
| 157 | i17·:·netList·(ideal·R')_* | 157 | i17·:·netList·(ideal·R')_* |
| Offset 208, 15 lines modified | Offset 208, 15 lines modified | ||
| 208 | i20·:·R·=·S/f | 208 | i20·:·R·=·S/f |
| 209 | o20·=·R | 209 | o20·=·R |
| 210 | o20·:·QuotientRing | 210 | o20·:·QuotientRing |
| 211 | i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) | 211 | i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) |
| 212 | ·--·used·0. | 212 | ·--·used·0.724314s·(cpu);·0.389522s·(thread);·0s·(gc) |
| 213 | o21·=·R' | 213 | o21·=·R' |
| 214 | o21·:·QuotientRing | 214 | o21·:·QuotientRing |
| 215 | i22·:·netList·(ideal·R')_* | 215 | i22·:·netList·(ideal·R')_* |
| Offset 266, 15 lines modified | Offset 266, 15 lines modified | ||
| 266 | i25·:·R·=·S/f | 266 | i25·:·R·=·S/f |
| 267 | o25·=·R | 267 | o25·=·R |
| 268 | o25·:·QuotientRing | 268 | o25·:·QuotientRing |
| 269 | i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) | 269 | i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) |
| 270 | ·--·used·1. | 270 | ·--·used·1.28379s·(cpu);·0.668703s·(thread);·0s·(gc) |
| 271 | o26·=·R' | 271 | o26·=·R' |
| 272 | o26·:·QuotientRing | 272 | o26·:·QuotientRing |
| 273 | i27·:·netList·(ideal·R')_* | 273 | i27·:·netList·(ideal·R')_* |
| Offset 324, 15 lines modified | Offset 324, 15 lines modified | ||
| 324 | i30·:·R·=·S/f | 324 | i30·:·R·=·S/f |
| 325 | o30·=·R | 325 | o30·=·R |
| 326 | o30·:·QuotientRing | 326 | o30·:·QuotientRing |
| 327 | i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) | 327 | i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) |
| 328 | ·--·used·0. | 328 | ·--·used·0.70235s·(cpu);·0.346305s·(thread);·0s·(gc) |
| 329 | o31·=·R' | 329 | o31·=·R' |
| 330 | o31·:·QuotientRing | 330 | o31·:·QuotientRing |
| 331 | i32·:·netList·(ideal·R')_* | 331 | i32·:·netList·(ideal·R')_* |
| Offset 382, 15 lines modified | Offset 382, 15 lines modified | ||
| 382 | i35·:·R·=·S/f | 382 | i35·:·R·=·S/f |
| 383 | o35·=·R | 383 | o35·=·R |
| 384 | o35·:·QuotientRing | 384 | o35·:·QuotientRing |
| 385 | i36·:·time·R'·=·integralClosure·R | 385 | i36·:·time·R'·=·integralClosure·R |
| 386 | ·--·used·0. | 386 | ·--·used·0.120637s·(cpu);·0.0813641s·(thread);·0s·(gc) |
| 387 | o36·=·R' | 387 | o36·=·R' |
| 388 | o36·:·QuotientRing | 388 | o36·:·QuotientRing |
| 389 | i37·:·netList·(ideal·R')_* | 389 | i37·:·netList·(ideal·R')_* |
| Offset 432, 15 lines modified | Offset 432, 15 lines modified | ||
| 432 | i40·:·R·=·S/I | 432 | i40·:·R·=·S/I |
| 433 | o40·=·R | 433 | o40·=·R |
| 434 | o40·:·QuotientRing | 434 | o40·:·QuotientRing |
| 435 | i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 435 | i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 436 | ·--·used·0.09 | 436 | ·--·used·0.0930629s·(cpu);·0.0515045s·(thread);·0s·(gc) |
| 437 | o41·=·R' | 437 | o41·=·R' |
| 438 | o41·:·QuotientRing | 438 | o41·:·QuotientRing |
| 439 | i42·:·icFractions·R | 439 | i42·:·icFractions·R |
| Max diff block lines reached; 3532/5962 bytes (59.24%) of diff not shown. | |||
| Offset 3, 48 lines modified | Offset 3, 48 lines modified | ||
| 3 | i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); | 3 | i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
| 4 | i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) | 4 | i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) |
| 5 | ·[jacobian·time·0·sec·#minors·3] | 5 | ·[jacobian·time·0·sec·#minors·3] |
| 6 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 | 6 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 |
| 7 | ·[step·0:· | 7 | ·[step·0:· |
| 8 | ······radical·(use·minprimes)·0·seconds | 8 | ······radical·(use·minprimes)·.00442039·seconds |
| 9 | ······idlizer1:··.00 | 9 | ······idlizer1:··.0079955·seconds |
| 10 | ······idlizer2:··.0079 | 10 | ······idlizer2:··.00798629·seconds |
| 11 | ······minpres:···.00 | 11 | ······minpres:···.00802342·seconds |
| 12 | ··time·.0 | 12 | ··time·.0936761·sec··#fractions·4] |
| 13 | ·[step·1:· | 13 | ·[step·1:· |
| 14 | ······radical·(use·minprimes)·0·seconds | 14 | ······radical·(use·minprimes)·0·seconds |
| 15 | ······idlizer1:··.01 | 15 | ······idlizer1:··.0120032·seconds |
| 16 | ······idlizer2:··.05 | 16 | ······idlizer2:··.0656393·seconds |
| 17 | ······minpres:···.0 | 17 | ······minpres:···.0118829·seconds |
| 18 | ··time·.0 | 18 | ··time·.0975076·sec··#fractions·4] |
| 19 | ·[step·2:· | 19 | ·[step·2:· |
| 20 | ······radical·(use·minprimes)·.0040 | 20 | ······radical·(use·minprimes)·.00401973·seconds |
| 21 | ······idlizer1:··.0114618·seconds | ||
| 21 | ······idlizer | 22 | ······idlizer2:··.0118492·seconds |
| 22 | ······idlizer2:··.00791753·seconds | ||
| 23 | ······minpres:···.0 | 23 | ······minpres:···.0113339·seconds |
| 24 | ··time·. | 24 | ··time·.10085·sec··#fractions·5] |
| 25 | ·[step·3:· | 25 | ·[step·3:· |
| 26 | ······radical·(use·minprimes)·0·seconds | 26 | ······radical·(use·minprimes)·.00413541·seconds |
| 27 | ······idlizer1:··.01 | 27 | ······idlizer1:··.0119402·seconds |
| 28 | ······idlizer2:··.01 | 28 | ······idlizer2:··.0142618·seconds |
| 29 | ······minpres:···.0 | 29 | ······minpres:···.0754548·seconds |
| 30 | ··time·.1 | 30 | ··time·.117546·sec··#fractions·5] |
| 31 | ·[step·4:· | 31 | ·[step·4:· |
| 32 | ······radical·(use·minprimes)·.0021 | 32 | ······radical·(use·minprimes)·.00281709·seconds |
| 33 | ······idlizer1:··.00 | 33 | ······idlizer1:··.00698267·seconds |
| 34 | ······idlizer2:··.01 | 34 | ······idlizer2:··.0120152·seconds |
| 35 | ······minpres:···.0 | 35 | ······minpres:···.00840574·seconds |
| 36 | ··time·.04 | 36 | ··time·.0489774·sec··#fractions·5] |
| 37 | ·[step·5:· | 37 | ·[step·5:· |
| 38 | ······radical·(use·minprimes)·.00 | 38 | ······radical·(use·minprimes)·.00222753·seconds |
| 39 | ······idlizer1:···--·used·0. | 39 | ······idlizer1:···--·used·0.544859s·(cpu);·0.32879s·(thread);·0s·(gc) |
| 40 | .0 | 40 | .00808308·seconds |
| 41 | ··time·.0 | 41 | ··time·.0822958·sec··#fractions·5] |
| 42 | o2·=·R' | 42 | o2·=·R' |
| 43 | o2·:·QuotientRing | 43 | o2·:·QuotientRing |
| 44 | i3·:·trim·ideal·R' | 44 | i3·:·trim·ideal·R' |
| Offset 13, 26 lines modified | Offset 13, 26 lines modified | ||
| 13 | ················2······2····2········2···2·2·····2 | 13 | ················2······2····2········2···2·2·····2 |
| 14 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) | 14 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) |
| 15 | o3·:·Ideal·of·S | 15 | o3·:·Ideal·of·S |
| 16 | i4·:·time·integralClosure·J | 16 | i4·:·time·integralClosure·J |
| 17 | ·--·used· | 17 | ·--·used·6.04271s·(cpu);·1.35001s·(thread);·0s·(gc) |
| 18 | ·············2·2··············2·2················2··········2···2····· | 18 | ·············2·2··············2·2················2··········2···2····· |
| 19 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 19 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ···········2···3···············2·2·····2···5 | 21 | ···········2···3···············2·2·····2···5 |
| 22 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 22 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| 23 | o4·:·Ideal·of·S | 23 | o4·:·Ideal·of·S |
| 24 | i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) | 24 | i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) |
| 25 | ·--·used· | 25 | ·--·used·7.59434s·(cpu);·1.35015s·(thread);·0s·(gc) |
| 26 | ·············2·2··············2·2················2··········2···2····· | 26 | ·············2·2··············2·2················2··········2···2····· |
| 27 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 27 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 28 | ·····------------------------------------------------------------------------ | 28 | ·····------------------------------------------------------------------------ |
| 29 | ···········2···3···············2·2·····2···5 | 29 | ···········2···3···············2·2·····2···5 |
| 30 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 30 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | o3·=·R | 90 | o3·=·R |
| 91 | o3·:·QuotientRing</code></pre> | 91 | o3·:·QuotientRing</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·R'·=·integralClosure·R | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·R'·=·integralClosure·R |
| 95 | ·--·used·0. | 95 | ·--·used·0.560416s·(cpu);·0.327425s·(thread);·0s·(gc) |
| 96 | o4·=·R' | 96 | o4·=·R' |
| 97 | o4·:·QuotientRing</code></pre> | 97 | o4·:·QuotientRing</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·netList·(ideal·R')_* | 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·netList·(ideal·R')_* |
| Offset 165, 15 lines modified | Offset 165, 15 lines modified | ||
| 165 | o9·=·R | 165 | o9·=·R |
| 166 | o9·:·QuotientRing</code></pre> | 166 | o9·:·QuotientRing</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 169 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 170 | ·--·used·0. | 170 | ·--·used·0.620489s·(cpu);·0.331237s·(thread);·0s·(gc) |
| 171 | o10·=·R' | 171 | o10·=·R' |
| 172 | o10·:·QuotientRing</code></pre> | 172 | o10·:·QuotientRing</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·netList·(ideal·R')_* | 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·netList·(ideal·R')_* |
| Offset 240, 15 lines modified | Offset 240, 15 lines modified | ||
| 240 | o15·=·R | 240 | o15·=·R |
| 241 | o15·:·QuotientRing</code></pre> | 241 | o15·:·QuotientRing</code></pre> |
| 242 | </td>··········</tr> | 242 | </td>··········</tr> |
| 243 | ··········<tr> | 243 | ··········<tr> |
| 244 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) | 244 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) |
| 245 | ·--·used·0. | 245 | ·--·used·0.606748s·(cpu);·0.362465s·(thread);·0s·(gc) |
| 246 | o16·=·R' | 246 | o16·=·R' |
| 247 | o16·:·QuotientRing</code></pre> | 247 | o16·:·QuotientRing</code></pre> |
| 248 | </td>··········</tr> | 248 | </td>··········</tr> |
| 249 | ··········<tr> | 249 | ··········<tr> |
| 250 | <td>··············<pre><code·class="language-macaulay2">i17·:·netList·(ideal·R')_* | 250 | <td>··············<pre><code·class="language-macaulay2">i17·:·netList·(ideal·R')_* |
| Offset 305, 15 lines modified | Offset 305, 15 lines modified | ||
| 305 | o20·=·R | 305 | o20·=·R |
| 306 | o20·:·QuotientRing</code></pre> | 306 | o20·:·QuotientRing</code></pre> |
| 307 | </td>··········</tr> | 307 | </td>··········</tr> |
| 308 | ··········<tr> | 308 | ··········<tr> |
| 309 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) | 309 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) |
| 310 | ·--·used·0. | 310 | ·--·used·0.724314s·(cpu);·0.389522s·(thread);·0s·(gc) |
| 311 | o21·=·R' | 311 | o21·=·R' |
| 312 | o21·:·QuotientRing</code></pre> | 312 | o21·:·QuotientRing</code></pre> |
| 313 | </td>··········</tr> | 313 | </td>··········</tr> |
| 314 | ··········<tr> | 314 | ··········<tr> |
| 315 | <td>··············<pre><code·class="language-macaulay2">i22·:·netList·(ideal·R')_* | 315 | <td>··············<pre><code·class="language-macaulay2">i22·:·netList·(ideal·R')_* |
| Offset 370, 15 lines modified | Offset 370, 15 lines modified | ||
| 370 | o25·=·R | 370 | o25·=·R |
| 371 | o25·:·QuotientRing</code></pre> | 371 | o25·:·QuotientRing</code></pre> |
| 372 | </td>··········</tr> | 372 | </td>··········</tr> |
| 373 | ··········<tr> | 373 | ··········<tr> |
| 374 | <td>··············<pre><code·class="language-macaulay2">i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) | 374 | <td>··············<pre><code·class="language-macaulay2">i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) |
| 375 | ·--·used·1. | 375 | ·--·used·1.28379s·(cpu);·0.668703s·(thread);·0s·(gc) |
| 376 | o26·=·R' | 376 | o26·=·R' |
| 377 | o26·:·QuotientRing</code></pre> | 377 | o26·:·QuotientRing</code></pre> |
| 378 | </td>··········</tr> | 378 | </td>··········</tr> |
| 379 | ··········<tr> | 379 | ··········<tr> |
| 380 | <td>··············<pre><code·class="language-macaulay2">i27·:·netList·(ideal·R')_* | 380 | <td>··············<pre><code·class="language-macaulay2">i27·:·netList·(ideal·R')_* |
| Offset 435, 15 lines modified | Offset 435, 15 lines modified | ||
| 435 | o30·=·R | 435 | o30·=·R |
| 436 | o30·:·QuotientRing</code></pre> | 436 | o30·:·QuotientRing</code></pre> |
| 437 | </td>··········</tr> | 437 | </td>··········</tr> |
| 438 | ··········<tr> | 438 | ··········<tr> |
| 439 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) | 439 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) |
| 440 | ·--·used·0. | 440 | ·--·used·0.70235s·(cpu);·0.346305s·(thread);·0s·(gc) |
| 441 | o31·=·R' | 441 | o31·=·R' |
| 442 | o31·:·QuotientRing</code></pre> | 442 | o31·:·QuotientRing</code></pre> |
| 443 | </td>··········</tr> | 443 | </td>··········</tr> |
| 444 | ··········<tr> | 444 | ··········<tr> |
| 445 | <td>··············<pre><code·class="language-macaulay2">i32·:·netList·(ideal·R')_* | 445 | <td>··············<pre><code·class="language-macaulay2">i32·:·netList·(ideal·R')_* |
| Offset 500, 15 lines modified | Offset 500, 15 lines modified | ||
| 500 | o35·=·R | 500 | o35·=·R |
| 501 | o35·:·QuotientRing</code></pre> | 501 | o35·:·QuotientRing</code></pre> |
| 502 | </td>··········</tr> | 502 | </td>··········</tr> |
| 503 | ··········<tr> | 503 | ··········<tr> |
| 504 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·R'·=·integralClosure·R | 504 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·R'·=·integralClosure·R |
| 505 | ·--·used·0. | 505 | ·--·used·0.120637s·(cpu);·0.0813641s·(thread);·0s·(gc) |
| 506 | o36·=·R' | 506 | o36·=·R' |
| 507 | o36·:·QuotientRing</code></pre> | 507 | o36·:·QuotientRing</code></pre> |
| 508 | </td>··········</tr> | 508 | </td>··········</tr> |
| 509 | ··········<tr> | 509 | ··········<tr> |
| 510 | <td>··············<pre><code·class="language-macaulay2">i37·:·netList·(ideal·R')_* | 510 | <td>··············<pre><code·class="language-macaulay2">i37·:·netList·(ideal·R')_* |
| Offset 560, 15 lines modified | Offset 560, 15 lines modified | ||
| 560 | o40·=·R | 560 | o40·=·R |
| 561 | o40·:·QuotientRing</code></pre> | 561 | o40·:·QuotientRing</code></pre> |
| 562 | </td>··········</tr> | 562 | </td>··········</tr> |
| 563 | ··········<tr> | 563 | ··········<tr> |
| 564 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 564 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 565 | ·--·used·0.09 | 565 | ·--·used·0.0930629s·(cpu);·0.0515045s·(thread);·0s·(gc) |
| 566 | o41·=·R' | 566 | o41·=·R' |
| 567 | o41·:·QuotientRing</code></pre> | 567 | o41·:·QuotientRing</code></pre> |
| 568 | </td>··········</tr> | 568 | </td>··········</tr> |
| 569 | ··········<tr> | 569 | ··········<tr> |
| 570 | <td>··············<pre><code·class="language-macaulay2">i42·:·icFractions·R | 570 | <td>··············<pre><code·class="language-macaulay2">i42·:·icFractions·R |
| Max diff block lines reached; 5305/9283 bytes (57.15%) of diff not shown. | |||
| Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
| 49 | o2·:·Ideal·of·S | 49 | o2·:·Ideal·of·S |
| 50 | i3·:·R·=·S/f | 50 | i3·:·R·=·S/f |
| 51 | o3·=·R | 51 | o3·=·R |
| 52 | o3·:·QuotientRing | 52 | o3·:·QuotientRing |
| 53 | i4·:·time·R'·=·integralClosure·R | 53 | i4·:·time·R'·=·integralClosure·R |
| 54 | ·--·used·0. | 54 | ·--·used·0.560416s·(cpu);·0.327425s·(thread);·0s·(gc) |
| 55 | o4·=·R' | 55 | o4·=·R' |
| 56 | o4·:·QuotientRing | 56 | o4·:·QuotientRing |
| 57 | i5·:·netList·(ideal·R')_* | 57 | i5·:·netList·(ideal·R')_* |
| 58 | ·····+------------------------------------------------------------------------+ | 58 | ·····+------------------------------------------------------------------------+ |
| Offset 110, 15 lines modified | Offset 110, 15 lines modified | ||
| 110 | o8·:·Ideal·of·S | 110 | o8·:·Ideal·of·S |
| 111 | i9·:·R·=·S/f | 111 | i9·:·R·=·S/f |
| 112 | o9·=·R | 112 | o9·=·R |
| 113 | o9·:·QuotientRing | 113 | o9·:·QuotientRing |
| 114 | i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 114 | i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 115 | ·--·used·0. | 115 | ·--·used·0.620489s·(cpu);·0.331237s·(thread);·0s·(gc) |
| 116 | o10·=·R' | 116 | o10·=·R' |
| 117 | o10·:·QuotientRing | 117 | o10·:·QuotientRing |
| 118 | i11·:·netList·(ideal·R')_* | 118 | i11·:·netList·(ideal·R')_* |
| 119 | ······+------------------------------------------------------------------------ | 119 | ······+------------------------------------------------------------------------ |
| Offset 200, 15 lines modified | Offset 200, 15 lines modified | ||
| 200 | o14·:·Ideal·of·S | 200 | o14·:·Ideal·of·S |
| 201 | i15·:·R·=·S/f | 201 | i15·:·R·=·S/f |
| 202 | o15·=·R | 202 | o15·=·R |
| 203 | o15·:·QuotientRing | 203 | o15·:·QuotientRing |
| 204 | i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) | 204 | i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) |
| 205 | ·--·used·0. | 205 | ·--·used·0.606748s·(cpu);·0.362465s·(thread);·0s·(gc) |
| 206 | o16·=·R' | 206 | o16·=·R' |
| 207 | o16·:·QuotientRing | 207 | o16·:·QuotientRing |
| 208 | i17·:·netList·(ideal·R')_* | 208 | i17·:·netList·(ideal·R')_* |
| 209 | ······+------------------------------------------------------------------------ | 209 | ······+------------------------------------------------------------------------ |
| Offset 282, 15 lines modified | Offset 282, 15 lines modified | ||
| 282 | o19·:·Ideal·of·S | 282 | o19·:·Ideal·of·S |
| 283 | i20·:·R·=·S/f | 283 | i20·:·R·=·S/f |
| 284 | o20·=·R | 284 | o20·=·R |
| 285 | o20·:·QuotientRing | 285 | o20·:·QuotientRing |
| 286 | i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) | 286 | i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) |
| 287 | ·--·used·0. | 287 | ·--·used·0.724314s·(cpu);·0.389522s·(thread);·0s·(gc) |
| 288 | o21·=·R' | 288 | o21·=·R' |
| 289 | o21·:·QuotientRing | 289 | o21·:·QuotientRing |
| 290 | i22·:·netList·(ideal·R')_* | 290 | i22·:·netList·(ideal·R')_* |
| 291 | ······+------------------------------------------------------------------------ | 291 | ······+------------------------------------------------------------------------ |
| Offset 364, 15 lines modified | Offset 364, 15 lines modified | ||
| 364 | o24·:·Ideal·of·S | 364 | o24·:·Ideal·of·S |
| 365 | i25·:·R·=·S/f | 365 | i25·:·R·=·S/f |
| 366 | o25·=·R | 366 | o25·=·R |
| 367 | o25·:·QuotientRing | 367 | o25·:·QuotientRing |
| 368 | i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) | 368 | i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) |
| 369 | ·--·used·1. | 369 | ·--·used·1.28379s·(cpu);·0.668703s·(thread);·0s·(gc) |
| 370 | o26·=·R' | 370 | o26·=·R' |
| 371 | o26·:·QuotientRing | 371 | o26·:·QuotientRing |
| 372 | i27·:·netList·(ideal·R')_* | 372 | i27·:·netList·(ideal·R')_* |
| 373 | ······+------------------------------------------------------------------------ | 373 | ······+------------------------------------------------------------------------ |
| Offset 446, 15 lines modified | Offset 446, 15 lines modified | ||
| 446 | o29·:·Ideal·of·S | 446 | o29·:·Ideal·of·S |
| 447 | i30·:·R·=·S/f | 447 | i30·:·R·=·S/f |
| 448 | o30·=·R | 448 | o30·=·R |
| 449 | o30·:·QuotientRing | 449 | o30·:·QuotientRing |
| 450 | i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) | 450 | i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) |
| 451 | ·--·used·0. | 451 | ·--·used·0.70235s·(cpu);·0.346305s·(thread);·0s·(gc) |
| 452 | o31·=·R' | 452 | o31·=·R' |
| 453 | o31·:·QuotientRing | 453 | o31·:·QuotientRing |
| 454 | i32·:·netList·(ideal·R')_* | 454 | i32·:·netList·(ideal·R')_* |
| 455 | ······+------------------------------------------------------------------------ | 455 | ······+------------------------------------------------------------------------ |
| Offset 528, 15 lines modified | Offset 528, 15 lines modified | ||
| 528 | o34·:·Ideal·of·S | 528 | o34·:·Ideal·of·S |
| 529 | i35·:·R·=·S/f | 529 | i35·:·R·=·S/f |
| 530 | o35·=·R | 530 | o35·=·R |
| 531 | o35·:·QuotientRing | 531 | o35·:·QuotientRing |
| 532 | i36·:·time·R'·=·integralClosure·R | 532 | i36·:·time·R'·=·integralClosure·R |
| 533 | ·--·used·0. | 533 | ·--·used·0.120637s·(cpu);·0.0813641s·(thread);·0s·(gc) |
| 534 | o36·=·R' | 534 | o36·=·R' |
| 535 | o36·:·QuotientRing | 535 | o36·:·QuotientRing |
| 536 | i37·:·netList·(ideal·R')_* | 536 | i37·:·netList·(ideal·R')_* |
| 537 | ······+-----------+ | 537 | ······+-----------+ |
| Offset 574, 15 lines modified | Offset 574, 15 lines modified | ||
| 574 | o39·:·Ideal·of·S | 574 | o39·:·Ideal·of·S |
| 575 | i40·:·R·=·S/I | 575 | i40·:·R·=·S/I |
| 576 | o40·=·R | 576 | o40·=·R |
| 577 | o40·:·QuotientRing | 577 | o40·:·QuotientRing |
| 578 | i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 578 | i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 579 | ·--·used·0.09 | 579 | ·--·used·0.0930629s·(cpu);·0.0515045s·(thread);·0s·(gc) |
| 580 | o41·=·R' | 580 | o41·=·R' |
| 581 | o41·:·QuotientRing | 581 | o41·:·QuotientRing |
| 582 | i42·:·icFractions·R | 582 | i42·:·icFractions·R |
| 583 | ········2 | 583 | ········2 |
| Max diff block lines reached; 3855/6915 bytes (55.75%) of diff not shown. | |||
| Offset 70, 48 lines modified | Offset 70, 48 lines modified | ||
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) | 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) |
| 73 | ·[jacobian·time·0·sec·#minors·3] | 73 | ·[jacobian·time·0·sec·#minors·3] |
| 74 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 | 74 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 |
| 75 | ·[step·0:· | 75 | ·[step·0:· |
| 76 | ······radical·(use·minprimes)·0·seconds | 76 | ······radical·(use·minprimes)·.00442039·seconds |
| 77 | ······idlizer1:··.00 | 77 | ······idlizer1:··.0079955·seconds |
| 78 | ······idlizer2:··.0079 | 78 | ······idlizer2:··.00798629·seconds |
| 79 | ······minpres:···.00 | 79 | ······minpres:···.00802342·seconds |
| 80 | ··time·.0 | 80 | ··time·.0936761·sec··#fractions·4] |
| 81 | ·[step·1:· | 81 | ·[step·1:· |
| 82 | ······radical·(use·minprimes)·0·seconds | 82 | ······radical·(use·minprimes)·0·seconds |
| 83 | ······idlizer1:··.01 | 83 | ······idlizer1:··.0120032·seconds |
| 84 | ······idlizer2:··.05 | 84 | ······idlizer2:··.0656393·seconds |
| 85 | ······minpres:···.0 | 85 | ······minpres:···.0118829·seconds |
| 86 | ··time·.0 | 86 | ··time·.0975076·sec··#fractions·4] |
| 87 | ·[step·2:· | 87 | ·[step·2:· |
| 88 | ······radical·(use·minprimes)·.0040 | 88 | ······radical·(use·minprimes)·.00401973·seconds |
| 89 | ······idlizer1:··.0114618·seconds | ||
| 89 | ······idlizer | 90 | ······idlizer2:··.0118492·seconds |
| 90 | ······idlizer2:··.00791753·seconds | ||
| 91 | ······minpres:···.0 | 91 | ······minpres:···.0113339·seconds |
| 92 | ··time·. | 92 | ··time·.10085·sec··#fractions·5] |
| 93 | ·[step·3:· | 93 | ·[step·3:· |
| 94 | ······radical·(use·minprimes)·0·seconds | 94 | ······radical·(use·minprimes)·.00413541·seconds |
| 95 | ······idlizer1:··.01 | 95 | ······idlizer1:··.0119402·seconds |
| 96 | ······idlizer2:··.01 | 96 | ······idlizer2:··.0142618·seconds |
| 97 | ······minpres:···.0 | 97 | ······minpres:···.0754548·seconds |
| 98 | ··time·.1 | 98 | ··time·.117546·sec··#fractions·5] |
| 99 | ·[step·4:· | 99 | ·[step·4:· |
| 100 | ······radical·(use·minprimes)·.0021 | 100 | ······radical·(use·minprimes)·.00281709·seconds |
| 101 | ······idlizer1:··.00 | 101 | ······idlizer1:··.00698267·seconds |
| 102 | ······idlizer2:··.01 | 102 | ······idlizer2:··.0120152·seconds |
| 103 | ······minpres:···.0 | 103 | ······minpres:···.00840574·seconds |
| 104 | ··time·.04 | 104 | ··time·.0489774·sec··#fractions·5] |
| 105 | ·[step·5:· | 105 | ·[step·5:· |
| 106 | ······radical·(use·minprimes)·.00 | 106 | ······radical·(use·minprimes)·.00222753·seconds |
| 107 | ······idlizer1:···--·used·0. | 107 | ······idlizer1:···--·used·0.544859s·(cpu);·0.32879s·(thread);·0s·(gc) |
| 108 | .0 | 108 | .00808308·seconds |
| 109 | ··time·.0 | 109 | ··time·.0822958·sec··#fractions·5] |
| 110 | o2·=·R' | 110 | o2·=·R' |
| 111 | o2·:·QuotientRing</code></pre> | 111 | o2·:·QuotientRing</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i3·:·trim·ideal·R' | 114 | <td>··············<pre><code·class="language-macaulay2">i3·:·trim·ideal·R' |
| Offset 17, 48 lines modified | Offset 17, 48 lines modified | ||
| 17 | the·computation. | 17 | the·computation. |
| 18 | i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); | 18 | i1·:·R·=·QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
| 19 | i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) | 19 | i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) |
| 20 | ·[jacobian·time·0·sec·#minors·3] | 20 | ·[jacobian·time·0·sec·#minors·3] |
| 21 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 | 21 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 |
| 22 | ·[step·0: | 22 | ·[step·0: |
| 23 | ······radical·(use·minprimes)·0·seconds | 23 | ······radical·(use·minprimes)·.00442039·seconds |
| 24 | ······idlizer1:··.00 | 24 | ······idlizer1:··.0079955·seconds |
| 25 | ······idlizer2:··.0079 | 25 | ······idlizer2:··.00798629·seconds |
| 26 | ······minpres:···.00 | 26 | ······minpres:···.00802342·seconds |
| 27 | ··time·.0 | 27 | ··time·.0936761·sec··#fractions·4] |
| 28 | ·[step·1: | 28 | ·[step·1: |
| 29 | ······radical·(use·minprimes)·0·seconds | 29 | ······radical·(use·minprimes)·0·seconds |
| 30 | ······idlizer1:··.01 | 30 | ······idlizer1:··.0120032·seconds |
| 31 | ······idlizer2:··.05 | 31 | ······idlizer2:··.0656393·seconds |
| 32 | ······minpres:···.0 | 32 | ······minpres:···.0118829·seconds |
| 33 | ··time·.0 | 33 | ··time·.0975076·sec··#fractions·4] |
| 34 | ·[step·2: | 34 | ·[step·2: |
| 35 | ······radical·(use·minprimes)·.0040 | 35 | ······radical·(use·minprimes)·.00401973·seconds |
| 36 | ······idlizer1:··.0114618·seconds | ||
| 36 | ······idlizer | 37 | ······idlizer2:··.0118492·seconds |
| 37 | ······idlizer2:··.00791753·seconds | ||
| 38 | ······minpres:···.0 | 38 | ······minpres:···.0113339·seconds |
| 39 | ··time·. | 39 | ··time·.10085·sec··#fractions·5] |
| 40 | ·[step·3: | 40 | ·[step·3: |
| 41 | ······radical·(use·minprimes)·0·seconds | 41 | ······radical·(use·minprimes)·.00413541·seconds |
| 42 | ······idlizer1:··.01 | 42 | ······idlizer1:··.0119402·seconds |
| 43 | ······idlizer2:··.01 | 43 | ······idlizer2:··.0142618·seconds |
| 44 | ······minpres:···.0 | 44 | ······minpres:···.0754548·seconds |
| 45 | ··time·.1 | 45 | ··time·.117546·sec··#fractions·5] |
| 46 | ·[step·4: | 46 | ·[step·4: |
| 47 | ······radical·(use·minprimes)·.0021 | 47 | ······radical·(use·minprimes)·.00281709·seconds |
| 48 | ······idlizer1:··.00 | 48 | ······idlizer1:··.00698267·seconds |
| 49 | ······idlizer2:··.01 | 49 | ······idlizer2:··.0120152·seconds |
| 50 | ······minpres:···.0 | 50 | ······minpres:···.00840574·seconds |
| 51 | ··time·.04 | 51 | ··time·.0489774·sec··#fractions·5] |
| 52 | ·[step·5: | 52 | ·[step·5: |
| 53 | ······radical·(use·minprimes)·.00 | 53 | ······radical·(use·minprimes)·.00222753·seconds |
| 54 | ······idlizer1:···--·used·0. | 54 | ······idlizer1:···--·used·0.544859s·(cpu);·0.32879s·(thread);·0s·(gc) |
| 55 | .0 | 55 | .00808308·seconds |
| 56 | ··time·.0 | 56 | ··time·.0822958·sec··#fractions·5] |
| 57 | o2·=·R' | 57 | o2·=·R' |
| 58 | o2·:·QuotientRing | 58 | o2·:·QuotientRing |
| 59 | i3·:·trim·ideal·R' | 59 | i3·:·trim·ideal·R' |
| 60 | ·····················3···2·····················2·2····4···········4 | 60 | ·····················3···2·····················2·2····4···········4 |
| Offset 111, 27 lines modified | Offset 111, 27 lines modified | ||
| 111 | ················2······2····2········2···2·2·····2 | 111 | ················2······2····2········2···2·2·····2 |
| 112 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) | 112 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) |
| 113 | o3·:·Ideal·of·S</code></pre> | 113 | o3·:·Ideal·of·S</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·integralClosure·J | 116 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·integralClosure·J |
| 117 | ·--·used· | 117 | ·--·used·6.04271s·(cpu);·1.35001s·(thread);·0s·(gc) |
| 118 | ·············2·2··············2·2················2··········2···2····· | 118 | ·············2·2··············2·2················2··········2···2····· |
| 119 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 119 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 120 | ·····------------------------------------------------------------------------ | 120 | ·····------------------------------------------------------------------------ |
| 121 | ···········2···3···············2·2·····2···5 | 121 | ···········2···3···············2·2·····2···5 |
| 122 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 122 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| 123 | o4·:·Ideal·of·S</code></pre> | 123 | o4·:·Ideal·of·S</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) | 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) |
| 127 | ·--·used· | 127 | ·--·used·7.59434s·(cpu);·1.35015s·(thread);·0s·(gc) |
| 128 | ·············2·2··············2·2················2··········2···2····· | 128 | ·············2·2··············2·2················2··········2···2····· |
| 129 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 129 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 130 | ·····------------------------------------------------------------------------ | 130 | ·····------------------------------------------------------------------------ |
| 131 | ···········2···3···············2·2·····2···5 | 131 | ···········2···3···············2·2·····2···5 |
| 132 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 132 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| Offset 47, 25 lines modified | Offset 47, 25 lines modified | ||
| 47 | i3·:·J·=·ideal·jacobian·ideal·F | 47 | i3·:·J·=·ideal·jacobian·ideal·F |
| 48 | ················2······2····2········2···2·2·····2 | 48 | ················2······2····2········2···2·2·····2 |
| 49 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) | 49 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) |
| 50 | o3·:·Ideal·of·S | 50 | o3·:·Ideal·of·S |
| 51 | i4·:·time·integralClosure·J | 51 | i4·:·time·integralClosure·J |
| 52 | ·--·used· | 52 | ·--·used·6.04271s·(cpu);·1.35001s·(thread);·0s·(gc) |
| 53 | ·············2·2··············2·2················2··········2···2 | 53 | ·············2·2··············2·2················2··········2···2 |
| 54 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 54 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 55 | ·····------------------------------------------------------------------------ | 55 | ·····------------------------------------------------------------------------ |
| 56 | ···········2···3···············2·2·····2···5 | 56 | ···········2···3···············2·2·····2···5 |
| 57 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 57 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| 58 | o4·:·Ideal·of·S | 58 | o4·:·Ideal·of·S |
| 59 | i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) | 59 | i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) |
| 60 | ·--·used· | 60 | ·--·used·7.59434s·(cpu);·1.35015s·(thread);·0s·(gc) |
| 61 | ·············2·2··············2·2················2··········2···2 | 61 | ·············2·2··············2·2················2··········2···2 |
| 62 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 62 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 63 | ·····------------------------------------------------------------------------ | 63 | ·····------------------------------------------------------------------------ |
| 64 | ···········2···3···············2·2·····2···5 | 64 | ···········2···3···············2·2·····2···5 |
| 65 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 65 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=13 | 7 | #:len=13 |
| 8 | c2NocmVpZXJHcmFwaA== | 8 | c2NocmVpZXJHcmFwaA== |
| 9 | #:len=1712 | 9 | #:len=1712 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU2NocmVpZXIgZ3JhcGggb2YgYSBmaW5p | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU2NocmVpZXIgZ3JhcGggb2YgYSBmaW5p |
| 11 | dGUgZ3JvdXAiLCAibGluZW51bSIgPT4gMjYxLCBJbnB1dHMgPT4ge1NQQU57VFR7IkcifSwiLCAi | 11 | dGUgZ3JvdXAiLCAibGluZW51bSIgPT4gMjYxLCBJbnB1dHMgPT4ge1NQQU57VFR7IkcifSwiLCAi |
| Offset 25, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | o3·:·DiagonalAction | 25 | o3·:·DiagonalAction |
| 26 | i4·:·T.cache.?equivariantHilbert | 26 | i4·:·T.cache.?equivariantHilbert |
| 27 | o4·=·false | 27 | o4·=·false |
| 28 | i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) | 28 | i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) |
| 29 | ·--·.00 | 29 | ·--·.00279439s·elapsed |
| 30 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2·· | 30 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2·· |
| 31 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ | 31 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ |
| 32 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······ | 32 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······ |
| 33 | ·····------------------------------------------------------------------------ | 33 | ·····------------------------------------------------------------------------ |
| 34 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 | 34 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 |
| 35 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T· | 35 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T· |
| Offset 51, 10 lines modified | Offset 51, 10 lines modified | ||
| 51 | ·········0···1 | 51 | ·········0···1 |
| 52 | i6·:·T.cache.?equivariantHilbert | 52 | i6·:·T.cache.?equivariantHilbert |
| 53 | o6·=·true | 53 | o6·=·true |
| 54 | i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); | 54 | i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); |
| 55 | ·--·.000 | 55 | ·--·.000582172s·elapsed |
| 56 | i8·:· | 56 | i8·:· |
| Offset 5, 13 lines modified | Offset 5, 13 lines modified | ||
| 5 | o1·=·QQ[x..y]·<-·{|·0·-1·|} | 5 | o1·=·QQ[x..y]·<-·{|·0·-1·|} |
| 6 | ··················|·1·0··| | 6 | ··················|·1·0··| |
| 7 | o1·:·FiniteGroupAction | 7 | o1·:·FiniteGroupAction |
| 8 | i2·:·hironakaDecomposition·C4 | 8 | i2·:·hironakaDecomposition·C4 |
| 9 | ········2····2··· | 9 | ········2····2·····3·······3········4····4 |
| 10 | o2·=·({x··+·y·,·x·y·},·{1,·x· | 10 | o2·=·({x··+·y·,·-·x·y·+·x*y·},·{1,·x··+·y·}) |
| 11 | o2·:·Sequence | 11 | o2·:·Sequence |
| 12 | i3·:· | 12 | i3·:· |
| Offset 23, 23 lines modified | Offset 23, 23 lines modified | ||
| 23 | o3·=·QQ[x..z]·<-·{|·0·-1·0··|,·|·0·-1·0·|} | 23 | o3·=·QQ[x..z]·<-·{|·0·-1·0··|,·|·0·-1·0·|} |
| 24 | ··················|·1·0··0··|··|·1·0··0·| | 24 | ··················|·1·0··0··|··|·1·0··0·| |
| 25 | ··················|·0·0··-1·|··|·0·0··1·| | 25 | ··················|·0·0··-1·|··|·0·0··1·| |
| 26 | o3·:·FiniteGroupAction | 26 | o3·:·FiniteGroupAction |
| 27 | i4·:·time·P1=primaryInvariants·C4xC2 | 27 | i4·:·time·P1=primaryInvariants·C4xC2 |
| 28 | ·--·used·0. | 28 | ·--·used·0.617199s·(cpu);·0.468691s·(thread);·0s·(gc) |
| 29 | ·······2····2···2···4····4 | 29 | ·······2····2···2···4····4 |
| 30 | o4·=·{x··+·y·,·z·,·x··+·y·} | 30 | o4·=·{x··+·y·,·z·,·x··+·y·} |
| 31 | o4·:·List | 31 | o4·:·List |
| 32 | i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) | 32 | i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) |
| 33 | ·--·used·0. | 33 | ·--·used·0.552342s·(cpu);·0.360284s·(thread);·0s·(gc) |
| 34 | ···········8·········7··········6·2·········5·3·········4·4·········3·5·· | 34 | ···········8·········7··········6·2·········5·3·········4·4·········3·5·· |
| 35 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ | 35 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ |
| 36 | ·····------------------------------------------------------------------------ | 36 | ·····------------------------------------------------------------------------ |
| 37 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2·· | 37 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2·· |
| 38 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- | 38 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| Offset 81, 23 lines modified | Offset 81, 23 lines modified | ||
| 81 | ·····------------------------------------------------------------------------ | 81 | ·····------------------------------------------------------------------------ |
| 82 | ···············2·6·············2·6············8 | 82 | ···············2·6·············2·6············8 |
| 83 | ·····348625296x·z··-·348625296y·z··+·43046721z·} | 83 | ·····348625296x·z··-·348625296y·z··+·43046721z·} |
| 84 | o5·:·List | 84 | o5·:·List |
| 85 | i6·:·time·secondaryInvariants(P1,C4xC2) | 85 | i6·:·time·secondaryInvariants(P1,C4xC2) |
| 86 | ·--·used·0.0 | 86 | ·--·used·0.0994819s·(cpu);·0.0550436s·(thread);·0s·(gc) |
| 87 | ··········3·······3 | 87 | ··········3·······3 |
| 88 | o6·=·{1,·x·y·-·x*y·} | 88 | o6·=·{1,·x·y·-·x*y·} |
| 89 | o6·:·List | 89 | o6·:·List |
| 90 | i7·:·time·secondaryInvariants(P2,C4xC2) | 90 | i7·:·time·secondaryInvariants(P2,C4xC2) |
| 91 | ·--·used·1. | 91 | ·--·used·1.59852s·(cpu);·1.15865s·(thread);·0s·(gc) |
| 92 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4·· | 92 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4·· |
| 93 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ | 93 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ |
| 94 | ·····------------------------------------------------------------------------ | 94 | ·····------------------------------------------------------------------------ |
| 95 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 | 95 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 |
| 96 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x· | 96 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x· |
| 97 | ·····------------------------------------------------------------------------ | 97 | ·····------------------------------------------------------------------------ |
| Offset 14, 28 lines modified | Offset 14, 28 lines modified | ||
| 14 | ···········|·1·0·0·0·|··|·1·0·0·0·| | 14 | ···········|·1·0·0·0·|··|·1·0·0·0·| |
| 15 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 15 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 16 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 16 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 17 | o3·:·FiniteGroupAction | 17 | o3·:·FiniteGroupAction |
| 18 | i4·:·elapsedTime·invariants·S4 | 18 | i4·:·elapsedTime·invariants·S4 |
| 19 | ·--·. | 19 | ·--·.661509s·elapsed |
| 20 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 20 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| 21 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 21 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 22 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· | 22 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· |
| 23 | ·····------------------------------------------------------------------------ | 23 | ·····------------------------------------------------------------------------ |
| 24 | ······4 | 24 | ······4 |
| 25 | ·····x·} | 25 | ·····x·} |
| 26 | ······4 | 26 | ······4 |
| 27 | o4·:·List | 27 | o4·:·List |
| 28 | i5·:·elapsedTime·invariants(S4,DegreeBound=>4) | 28 | i5·:·elapsedTime·invariants(S4,DegreeBound=>4) |
| 29 | ·--·. | 29 | ·--·.486951s·elapsed |
| 30 | Warning:·stopping·condition·not·met! | 30 | Warning:·stopping·condition·not·met! |
| 31 | Output·may·not·generate·the·entire·ring·of·invariants. | 31 | Output·may·not·generate·the·entire·ring·of·invariants. |
| 32 | Increase·value·of·DegreeBound. | 32 | Increase·value·of·DegreeBound. |
| 33 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 33 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| Offset 14, 28 lines modified | Offset 14, 28 lines modified | ||
| 14 | ···········|·1·0·0·0·|··|·1·0·0·0·| | 14 | ···········|·1·0·0·0·|··|·1·0·0·0·| |
| 15 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 15 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 16 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 16 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 17 | o3·:·FiniteGroupAction | 17 | o3·:·FiniteGroupAction |
| 18 | i4·:·elapsedTime·invariants·S4 | 18 | i4·:·elapsedTime·invariants·S4 |
| 19 | ·--·. | 19 | ·--·1.06624s·elapsed |
| 20 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 20 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| 21 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 21 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 22 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· | 22 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· |
| 23 | ·····------------------------------------------------------------------------ | 23 | ·····------------------------------------------------------------------------ |
| 24 | ······4 | 24 | ······4 |
| 25 | ·····x·} | 25 | ·····x·} |
| 26 | ······4 | 26 | ······4 |
| 27 | o4·:·List | 27 | o4·:·List |
| 28 | i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) | 28 | i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) |
| 29 | ·--·.04 | 29 | ·--·.0409314s·elapsed |
| 30 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ | 30 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ |
| 31 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3·· | 31 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3·· |
| 32 | ·····------------------------------------------------------------------------ | 32 | ·····------------------------------------------------------------------------ |
| 33 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} | 33 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} |
| 34 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 | 34 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 |
| Offset 16, 16 lines modified | Offset 16, 16 lines modified | ||
| 16 | ··················|·0·0·1·|··|·1·0·0·| | 16 | ··················|·0·0·1·|··|·1·0·0·| |
| 17 | ··················|·1·0·0·|··|·0·0·1·| | 17 | ··················|·1·0·0·|··|·0·0·1·| |
| 18 | o3·:·FiniteGroupAction | 18 | o3·:·FiniteGroupAction |
| 19 | i4·:·primaryInvariants·S3 | 19 | i4·:·primaryInvariants·S3 |
| 20 | ··················2····2····2···2·······2····2·····2·······2······2 | ||
| 21 | 20 | ···································3····3····3 | |
| 21 | o4·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·} | ||
| 22 | o4·:·List | 22 | o4·:·List |
| 23 | i5·:·K=GF(101) | 23 | i5·:·K=GF(101) |
| 24 | o5·=·K | 24 | o5·=·K |
| Offset 80, 16 lines modified | Offset 80, 16 lines modified | ||
| 80 | ············6 | 80 | ············6 |
| 81 | ·····104976z·} | 81 | ·····104976z·} |
| 82 | o4·:·List | 82 | o4·:·List |
| 83 | i5·:·primaryInvariants(S3) | 83 | i5·:·primaryInvariants(S3) |
| 84 | ··················2····2····2···2·······2····2·····2·······2······2 | ||
| 85 | 84 | ···································3····3····3 | |
| 85 | o5·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·} | ||
| 86 | o5·:·List | 86 | o5·:·List |
| 87 | i6·:·K=GF(101) | 87 | i6·:·K=GF(101) |
| 88 | o6·=·K | 88 | o6·=·K |
| Offset 16, 13 lines modified | Offset 16, 13 lines modified | ||
| 16 | ··················|·0·0·1·|··|·1·0·0·| | 16 | ··················|·0·0·1·|··|·1·0·0·| |
| 17 | ··················|·1·0·0·|··|·0·0·1·| | 17 | ··················|·1·0·0·|··|·0·0·1·| |
| 18 | o3·:·FiniteGroupAction | 18 | o3·:·FiniteGroupAction |
| 19 | i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) | 19 | i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) |
| 20 | ······· | 20 | ·······2·······2····2·····2·······2······2··········4····4····4 |
| 21 | o4·=·{x··+· | 21 | o4·=·{x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x*y*z,·x··+·y··+·z·} |
| 22 | o4·:·List | 22 | o4·:·List |
| 23 | i5·:· | 23 | i5·:· |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·T.cache.?equivariantHilbert | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·T.cache.?equivariantHilbert |
| 78 | o4·=·false</code></pre> | 78 | o4·=·false</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) | 81 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) |
| 82 | ·--·.00 | 82 | ·--·.00279439s·elapsed |
| 83 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2·· | 83 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2·· |
| 84 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ | 84 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ |
| 85 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······ | 85 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······ |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| 87 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 | 87 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 |
| 88 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T· | 88 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T· |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·T.cache.?equivariantHilbert | 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·T.cache.?equivariantHilbert |
| 106 | o6·=·true</code></pre> | 106 | o6·=·true</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); | 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); |
| 110 | ·--·.000 | 110 | ·--·.000582172s·elapsed</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ······</div> | 113 | ······</div> |
| 114 | ······<div·class="waystouse"> | 114 | ······<div·class="waystouse"> |
| 115 | ········<h2>For·the·programmer</h2> | 115 | ········<h2>For·the·programmer</h2> |
| 116 | ········<p>The·object·<a·title="stores·equivariant·Hilbert·series·expansions"·href="_equivariant__Hilbert.html">equivariantHilbert</a>·is·<span>a·<a·title="the·class·of·all·symbols"·href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p> | 116 | ········<p>The·object·<a·title="stores·equivariant·Hilbert·series·expansions"·href="_equivariant__Hilbert.html">equivariantHilbert</a>·is·<span>a·<a·title="the·class·of·all·symbols"·href="../../Macaulay2Doc/html/___Symbol.html">symbol</a></span>.</p> |
| 117 | ······</div> | 117 | ······</div> |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | ·····|·0··-1·1·| | 30 | ·····|·0··-1·1·| |
| 31 | o3·:·DiagonalAction | 31 | o3·:·DiagonalAction |
| 32 | i4·:·T.cache.?equivariantHilbert | 32 | i4·:·T.cache.?equivariantHilbert |
| 33 | o4·=·false | 33 | o4·=·false |
| 34 | i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) | 34 | i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) |
| 35 | ·--·.00 | 35 | ·--·.00279439s·elapsed |
| 36 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2 | 36 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2 |
| 37 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ | 37 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ |
| 38 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0 | 38 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0 |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 | 40 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 |
| 41 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T | 41 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T |
| Offset 54, 10 lines modified | Offset 54, 10 lines modified | ||
| 54 | o5·:·ZZ[z·..z·][T] | 54 | o5·:·ZZ[z·..z·][T] |
| 55 | ·········0···1 | 55 | ·········0···1 |
| 56 | i6·:·T.cache.?equivariantHilbert | 56 | i6·:·T.cache.?equivariantHilbert |
| 57 | o6·=·true | 57 | o6·=·true |
| 58 | i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); | 58 | i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); |
| 59 | ·--·.000 | 59 | ·--·.000582172s·elapsed |
| 60 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 60 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 61 | The·object·_\x8e_\x8q_\x8u_\x8i_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8H_\x8i_\x8l_\x8b_\x8e_\x8r_\x8t·is·a·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l. | 61 | The·object·_\x8e_\x8q_\x8u_\x8i_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8H_\x8i_\x8l_\x8b_\x8e_\x8r_\x8t·is·a·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l. |
| Offset 87, 16 lines modified | Offset 87, 16 lines modified | ||
| 87 | ··················|·1·0··| | 87 | ··················|·1·0··| |
| 88 | o1·:·FiniteGroupAction</code></pre> | 88 | o1·:·FiniteGroupAction</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·hironakaDecomposition·C4 | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·hironakaDecomposition·C4 |
| 92 | ········2····2··· | 92 | ········2····2·····3·······3········4····4 |
| 93 | o2·=·({x··+·y·,·x·y·},·{1,·x· | 93 | o2·=·({x··+·y·,·-·x·y·+·x*y·},·{1,·x··+·y·}) |
| 94 | o2·:·Sequence</code></pre> | 94 | o2·:·Sequence</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ········</table> | 96 | ········</table> |
| 97 | ········<p>From·the·output·one·sees·that·<span·class="tt">QQ[x,y]</span><sup><span·class="tt">C4</span></sup><span·class="tt">=QQ[f</span><sub><span·class="tt">1</span></sub><span·class="tt">f</span><sub><span·class="tt">2</span></sub><span·class="tt">]</span>\oplus<span·class="tt">QQ[f</span><sub><span·class="tt">1</span></sub><span·class="tt">f</span><sub><span·class="tt">2</span></sub><span·class="tt">](x</span><sup><span·class="tt">4</span></sup><span·class="tt">+y</span><sup><span·class="tt">4</span></sup><span·class="tt">)</span>,·where·<span·class="tt">f</span><sub><span·class="tt">1</span></sub><span·class="tt">=x</span><sup><span·class="tt">2</span></sup><span·class="tt">+y</span><sup><span·class="tt">2</span></sup>·and·<span·class="tt">f</span><sub><span·class="tt">2</span></sub><span·class="tt">=xy</span><sup><span·class="tt">3</span></sup><span·class="tt">-x</span><sup><span·class="tt">3</span></sup><span·class="tt">y</span>.</p> | 97 | ········<p>From·the·output·one·sees·that·<span·class="tt">QQ[x,y]</span><sup><span·class="tt">C4</span></sup><span·class="tt">=QQ[f</span><sub><span·class="tt">1</span></sub><span·class="tt">f</span><sub><span·class="tt">2</span></sub><span·class="tt">]</span>\oplus<span·class="tt">QQ[f</span><sub><span·class="tt">1</span></sub><span·class="tt">f</span><sub><span·class="tt">2</span></sub><span·class="tt">](x</span><sup><span·class="tt">4</span></sup><span·class="tt">+y</span><sup><span·class="tt">4</span></sup><span·class="tt">)</span>,·where·<span·class="tt">f</span><sub><span·class="tt">1</span></sub><span·class="tt">=x</span><sup><span·class="tt">2</span></sup><span·class="tt">+y</span><sup><span·class="tt">2</span></sup>·and·<span·class="tt">f</span><sub><span·class="tt">2</span></sub><span·class="tt">=xy</span><sup><span·class="tt">3</span></sup><span·class="tt">-x</span><sup><span·class="tt">3</span></sup><span·class="tt">y</span>.</p> |
| 98 | ······</div> | 98 | ······</div> |
| 99 | ······<div> | 99 | ······<div> |
| Offset 40, 16 lines modified | Offset 40, 16 lines modified | ||
| 40 | o1·=·QQ[x..y]·<-·{|·0·-1·|} | 40 | o1·=·QQ[x..y]·<-·{|·0·-1·|} |
| 41 | ··················|·1·0··| | 41 | ··················|·1·0··| |
| 42 | o1·:·FiniteGroupAction | 42 | o1·:·FiniteGroupAction |
| 43 | i2·:·hironakaDecomposition·C4 | 43 | i2·:·hironakaDecomposition·C4 |
| 44 | ········2····2··· | 44 | ········2····2·····3·······3········4····4 |
| 45 | o2·=·({x··+·y·,·x·y·},·{1,·x· | 45 | o2·=·({x··+·y·,·-·x·y·+·x*y·},·{1,·x··+·y·}) |
| 46 | o2·:·Sequence | 46 | o2·:·Sequence |
| 47 | From·the·output·one·sees·that·QQ[x,y]C4=QQ[f1f2]\oplusQQ[f1f2](x4+y4),·where | 47 | From·the·output·one·sees·that·QQ[x,y]C4=QQ[f1f2]\oplusQQ[f1f2](x4+y4),·where |
| 48 | f1=x2+y2·and·f2=xy3-x3y. | 48 | f1=x2+y2·and·f2=xy3-x3y. |
| 49 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 49 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 50 | Currently·hironakaDecomposition·works·only·with·polynomial·rings·and·matrices | 50 | Currently·hironakaDecomposition·works·only·with·polynomial·rings·and·matrices |
| 51 | over·fields·of·characteristic·0. | 51 | over·fields·of·characteristic·0. |
| Offset 78, 24 lines modified | Offset 78, 24 lines modified | ||
| 78 | o3·:·FiniteGroupAction</code></pre> | 78 | o3·:·FiniteGroupAction</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ········</table> | 80 | ········</table> |
| 81 | ········<p>The·two·algorithms·used·in·<a·title="computes·a·list·of·primary·invariants·for·the·invariant·ring·of·a·finite·group"·href="_primary__Invariants.html">primaryInvariants</a>·are·timed.·One·sees·that·the·Dade·algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8·and·have·ugly·coefficients.</p> | 81 | ········<p>The·two·algorithms·used·in·<a·title="computes·a·list·of·primary·invariants·for·the·invariant·ring·of·a·finite·group"·href="_primary__Invariants.html">primaryInvariants</a>·are·timed.·One·sees·that·the·Dade·algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8·and·have·ugly·coefficients.</p> |
| 82 | ········<table·class="examples"> | 82 | ········<table·class="examples"> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·P1=primaryInvariants·C4xC2 | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·P1=primaryInvariants·C4xC2 |
| 85 | ·--·used·0. | 85 | ·--·used·0.617199s·(cpu);·0.468691s·(thread);·0s·(gc) |
| 86 | ·······2····2···2···4····4 | 86 | ·······2····2···2···4····4 |
| 87 | o4·=·{x··+·y·,·z·,·x··+·y·} | 87 | o4·=·{x··+·y·,·z·,·x··+·y·} |
| 88 | o4·:·List</code></pre> | 88 | o4·:·List</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) |
| 92 | ·--·used·0. | 92 | ·--·used·0.552342s·(cpu);·0.360284s·(thread);·0s·(gc) |
| 93 | ···········8·········7··········6·2·········5·3·········4·4·········3·5·· | 93 | ···········8·········7··········6·2·········5·3·········4·4·········3·5·· |
| 94 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ | 94 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ |
| 95 | ·····------------------------------------------------------------------------ | 95 | ·····------------------------------------------------------------------------ |
| 96 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2·· | 96 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2·· |
| 97 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- | 97 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- |
| 98 | ·····------------------------------------------------------------------------ | 98 | ·····------------------------------------------------------------------------ |
| Offset 141, 24 lines modified | Offset 141, 24 lines modified | ||
| 141 | o5·:·List</code></pre> | 141 | o5·:·List</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ········</table> | 143 | ········</table> |
| 144 | ········<p>The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is·rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding·secondary·invariants.··In·fact,·it·has·proved·quicker·overall·to·calculate·the·invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm.</p> | 144 | ········<p>The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is·rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding·secondary·invariants.··In·fact,·it·has·proved·quicker·overall·to·calculate·the·invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm.</p> |
| 145 | ········<table·class="examples"> | 145 | ········<table·class="examples"> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·secondaryInvariants(P1,C4xC2) | 147 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·secondaryInvariants(P1,C4xC2) |
| 148 | ·--·used·0.0 | 148 | ·--·used·0.0994819s·(cpu);·0.0550436s·(thread);·0s·(gc) |
| 149 | ··········3·······3 | 149 | ··········3·······3 |
| 150 | o6·=·{1,·x·y·-·x*y·} | 150 | o6·=·{1,·x·y·-·x*y·} |
| 151 | o6·:·List</code></pre> | 151 | o6·:·List</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·secondaryInvariants(P2,C4xC2) | 154 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·secondaryInvariants(P2,C4xC2) |
| 155 | ·--·used·1. | 155 | ·--·used·1.59852s·(cpu);·1.15865s·(thread);·0s·(gc) |
| 156 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4·· | 156 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4·· |
| 157 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ | 157 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ |
| 158 | ·····------------------------------------------------------------------------ | 158 | ·····------------------------------------------------------------------------ |
| 159 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 | 159 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 |
| 160 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x· | 160 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x· |
| 161 | ·····------------------------------------------------------------------------ | 161 | ·····------------------------------------------------------------------------ |
| Offset 69, 22 lines modified | Offset 69, 22 lines modified | ||
| 69 | ··················|·0·0··-1·|··|·0·0··1·| | 69 | ··················|·0·0··-1·|··|·0·0··1·| |
| 70 | o3·:·FiniteGroupAction | 70 | o3·:·FiniteGroupAction |
| 71 | The·two·algorithms·used·in·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·are·timed.·One·sees·that·the·Dade | 71 | The·two·algorithms·used·in·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·are·timed.·One·sees·that·the·Dade |
| 72 | algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8 | 72 | algorithm·is·faster,·however·the·primary·invariants·output·are·all·of·degree·8 |
| 73 | and·have·ugly·coefficients. | 73 | and·have·ugly·coefficients. |
| 74 | i4·:·time·P1=primaryInvariants·C4xC2 | 74 | i4·:·time·P1=primaryInvariants·C4xC2 |
| 75 | ·--·used·0. | 75 | ·--·used·0.617199s·(cpu);·0.468691s·(thread);·0s·(gc) |
| 76 | ·······2····2···2···4····4 | 76 | ·······2····2···2···4····4 |
| 77 | o4·=·{x··+·y·,·z·,·x··+·y·} | 77 | o4·=·{x··+·y·,·z·,·x··+·y·} |
| 78 | o4·:·List | 78 | o4·:·List |
| 79 | i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) | 79 | i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) |
| 80 | ·--·used·0. | 80 | ·--·used·0.552342s·(cpu);·0.360284s·(thread);·0s·(gc) |
| 81 | ···········8·········7··········6·2·········5·3·········4·4·········3·5 | 81 | ···········8·········7··········6·2·········5·3·········4·4·········3·5 |
| 82 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ | 82 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ |
| 83 | ·····------------------------------------------------------------------------ | 83 | ·····------------------------------------------------------------------------ |
| 84 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2 | 84 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2 |
| 85 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- | 85 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| Offset 129, 22 lines modified | Offset 129, 22 lines modified | ||
| 129 | o5·:·List | 129 | o5·:·List |
| 130 | The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is | 130 | The·extra·work·done·by·the·default·algorithm·to·ensure·an·optimal·hsop·is |
| 131 | rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding | 131 | rewarded·by·needing·to·calculate·a·smaller·collection·of·corresponding |
| 132 | secondary·invariants.·In·fact,·it·has·proved·quicker·overall·to·calculate·the | 132 | secondary·invariants.·In·fact,·it·has·proved·quicker·overall·to·calculate·the |
| 133 | invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm. | 133 | invariant·ring·based·on·the·optimal·algorithm·rather·than·the·Dade·algorithm. |
| 134 | i6·:·time·secondaryInvariants(P1,C4xC2) | 134 | i6·:·time·secondaryInvariants(P1,C4xC2) |
| 135 | ·--·used·0.0 | 135 | ·--·used·0.0994819s·(cpu);·0.0550436s·(thread);·0s·(gc) |
| 136 | ··········3·······3 | 136 | ··········3·······3 |
| 137 | o6·=·{1,·x·y·-·x*y·} | 137 | o6·=·{1,·x·y·-·x*y·} |
| 138 | o6·:·List | 138 | o6·:·List |
| 139 | i7·:·time·secondaryInvariants(P2,C4xC2) | 139 | i7·:·time·secondaryInvariants(P2,C4xC2) |
| 140 | ·--·used·1. | 140 | ·--·used·1.59852s·(cpu);·1.15865s·(thread);·0s·(gc) |
| 141 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4 | 141 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4 |
| 142 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ | 142 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ |
| 143 | ·····------------------------------------------------------------------------ | 143 | ·····------------------------------------------------------------------------ |
| 144 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 | 144 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 |
| 145 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x | 145 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x |
| 146 | ·····------------------------------------------------------------------------ | 146 | ·····------------------------------------------------------------------------ |
| Offset 89, 29 lines modified | Offset 89, 29 lines modified | ||
| 89 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 89 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 90 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 90 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 91 | o3·:·FiniteGroupAction</code></pre> | 91 | o3·:·FiniteGroupAction</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 |
| 95 | ·--·. | 95 | ·--·.661509s·elapsed |
| 96 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 96 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| 97 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 97 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 98 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· | 98 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ······4 | 100 | ······4 |
| 101 | ·····x·} | 101 | ·····x·} |
| 102 | ······4 | 102 | ······4 |
| 103 | o4·:·List</code></pre> | 103 | o4·:·List</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,DegreeBound=>4) | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,DegreeBound=>4) |
| 107 | ·--·. | 107 | ·--·.486951s·elapsed |
| 108 | Warning:·stopping·condition·not·met! | 108 | Warning:·stopping·condition·not·met! |
| 109 | Output·may·not·generate·the·entire·ring·of·invariants. | 109 | Output·may·not·generate·the·entire·ring·of·invariants. |
| 110 | Increase·value·of·DegreeBound. | 110 | Increase·value·of·DegreeBound. |
| 111 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 111 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| Offset 34, 27 lines modified | Offset 34, 27 lines modified | ||
| 34 | o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|} | 34 | o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|} |
| 35 | ···········|·1·0·0·0·|··|·1·0·0·0·| | 35 | ···········|·1·0·0·0·|··|·1·0·0·0·| |
| 36 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 36 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 37 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 37 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 38 | o3·:·FiniteGroupAction | 38 | o3·:·FiniteGroupAction |
| 39 | i4·:·elapsedTime·invariants·S4 | 39 | i4·:·elapsedTime·invariants·S4 |
| 40 | ·--·. | 40 | ·--·.661509s·elapsed |
| 41 | ··························2····2····2····2···3····3····3····3···4····4····4 | 41 | ··························2····2····2····2···3····3····3····3···4····4····4 |
| 42 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 42 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 43 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3 | 43 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3 |
| 44 | ·····------------------------------------------------------------------------ | 44 | ·····------------------------------------------------------------------------ |
| 45 | ······4 | 45 | ······4 |
| 46 | ·····x·} | 46 | ·····x·} |
| 47 | ······4 | 47 | ······4 |
| 48 | o4·:·List | 48 | o4·:·List |
| 49 | i5·:·elapsedTime·invariants(S4,DegreeBound=>4) | 49 | i5·:·elapsedTime·invariants(S4,DegreeBound=>4) |
| 50 | ·--·. | 50 | ·--·.486951s·elapsed |
| 51 | Warning:·stopping·condition·not·met! | 51 | Warning:·stopping·condition·not·met! |
| 52 | Output·may·not·generate·the·entire·ring·of·invariants. | 52 | Output·may·not·generate·the·entire·ring·of·invariants. |
| 53 | Increase·value·of·DegreeBound. | 53 | Increase·value·of·DegreeBound. |
| 54 | ··························2····2····2····2···3····3····3····3···4····4····4 | 54 | ··························2····2····2····2···3····3····3····3···4····4····4 |
| Offset 89, 29 lines modified | Offset 89, 29 lines modified | ||
| 89 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 89 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 90 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 90 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 91 | o3·:·FiniteGroupAction</code></pre> | 91 | o3·:·FiniteGroupAction</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 |
| 95 | ·--·. | 95 | ·--·1.06624s·elapsed |
| 96 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 96 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| 97 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 97 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 98 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· | 98 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ······4 | 100 | ······4 |
| 101 | ·····x·} | 101 | ·····x·} |
| 102 | ······4 | 102 | ······4 |
| 103 | o4·:·List</code></pre> | 103 | o4·:·List</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) |
| 107 | ·--·.04 | 107 | ·--·.0409314s·elapsed |
| 108 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ | 108 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ |
| 109 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3·· | 109 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3·· |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} | 111 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} |
| 112 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 | 112 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 |
| Offset 36, 27 lines modified | Offset 36, 27 lines modified | ||
| 36 | o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|} | 36 | o3·=·R·<-·{|·0·1·0·0·|,·|·0·0·0·1·|} |
| 37 | ···········|·1·0·0·0·|··|·1·0·0·0·| | 37 | ···········|·1·0·0·0·|··|·1·0·0·0·| |
| 38 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 38 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 39 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 39 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 40 | o3·:·FiniteGroupAction | 40 | o3·:·FiniteGroupAction |
| 41 | i4·:·elapsedTime·invariants·S4 | 41 | i4·:·elapsedTime·invariants·S4 |
| 42 | ·--·. | 42 | ·--·1.06624s·elapsed |
| 43 | ··························2····2····2····2···3····3····3····3···4····4····4 | 43 | ··························2····2····2····2···3····3····3····3···4····4····4 |
| 44 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 44 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 45 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3 | 45 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3 |
| 46 | ·····------------------------------------------------------------------------ | 46 | ·····------------------------------------------------------------------------ |
| 47 | ······4 | 47 | ······4 |
| 48 | ·····x·} | 48 | ·····x·} |
| 49 | ······4 | 49 | ······4 |
| 50 | o4·:·List | 50 | o4·:·List |
| 51 | i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) | 51 | i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) |
| 52 | ·--·.04 | 52 | ·--·.0409314s·elapsed |
| 53 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ | 53 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ |
| 54 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3 | 54 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3 |
| 55 | ·····------------------------------------------------------------------------ | 55 | ·····------------------------------------------------------------------------ |
| 56 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} | 56 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} |
| 57 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 | 57 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 |
| Offset 97, 16 lines modified | Offset 97, 16 lines modified | ||
| 97 | ··················|·1·0·0·|··|·0·0·1·| | 97 | ··················|·1·0·0·|··|·0·0·1·| |
| 98 | o3·:·FiniteGroupAction</code></pre> | 98 | o3·:·FiniteGroupAction</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants·S3 | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants·S3 |
| 102 | ··················2····2····2···2·······2····2·····2·······2······2 | ||
| 103 | 102 | ···································3····3····3 | |
| 103 | o4·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·} | ||
| 104 | o4·:·List</code></pre> | 104 | o4·:·List</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | ········<p>Below,·the·invariant·ring·<span·class="tt">QQ[x,y,z]</span><sup><span·class="tt">S3</span></sup>·is·calculated·with·<span·class="tt">K</span>·being·the·field·with·101·elements.</p> | 107 | ········<p>Below,·the·invariant·ring·<span·class="tt">QQ[x,y,z]</span><sup><span·class="tt">S3</span></sup>·is·calculated·with·<span·class="tt">K</span>·being·the·field·with·101·elements.</p> |
| 108 | ········<table·class="examples"> | 108 | ········<table·class="examples"> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| Offset 39, 16 lines modified | Offset 39, 16 lines modified | ||
| 39 | o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|} | 39 | o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|} |
| 40 | ··················|·0·0·1·|··|·1·0·0·| | 40 | ··················|·0·0·1·|··|·1·0·0·| |
| 41 | ··················|·1·0·0·|··|·0·0·1·| | 41 | ··················|·1·0·0·|··|·0·0·1·| |
| 42 | o3·:·FiniteGroupAction | 42 | o3·:·FiniteGroupAction |
| 43 | i4·:·primaryInvariants·S3 | 43 | i4·:·primaryInvariants·S3 |
| 44 | ··················2····2····2···2·······2····2·····2·······2······2 | ||
| 45 | 44 | ···································3····3····3 | |
| 45 | o4·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·} | ||
| 46 | o4·:·List | 46 | o4·:·List |
| 47 | Below,·the·invariant·ring·QQ[x,y,z]S3·is·calculated·with·K·being·the·field·with | 47 | Below,·the·invariant·ring·QQ[x,y,z]S3·is·calculated·with·K·being·the·field·with |
| 48 | 101·elements. | 48 | 101·elements. |
| 49 | i5·:·K=GF(101) | 49 | i5·:·K=GF(101) |
| 50 | o5·=·K | 50 | o5·=·K |
| Offset 158, 16 lines modified | Offset 158, 16 lines modified | ||
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ········</table> | 159 | ········</table> |
| 160 | ········<p>Compare·this·result·to·the·hsop·output·when·Dade·is·left·to·its·default·value·<a·href="../../Macaulay2Doc/html/_false.html">false</a>.</p> | 160 | ········<p>Compare·this·result·to·the·hsop·output·when·Dade·is·left·to·its·default·value·<a·href="../../Macaulay2Doc/html/_false.html">false</a>.</p> |
| 161 | ········<table·class="examples"> | 161 | ········<table·class="examples"> |
| 162 | ··········<tr> | 162 | ··········<tr> |
| 163 | <td>··············<pre><code·class="language-macaulay2">i5·:·primaryInvariants(S3) | 163 | <td>··············<pre><code·class="language-macaulay2">i5·:·primaryInvariants(S3) |
| 164 | ··················2····2····2···2·······2····2·····2·······2······2 | ||
| 165 | 164 | ···································3····3····3 | |
| 165 | o5·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·} | ||
| 166 | o5·:·List</code></pre> | 166 | o5·:·List</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ········</table> | 168 | ········</table> |
| 169 | ········<p>Below,·the·invariant·ring·<span·class="tt">QQ[x,y,z]</span><sup><span·class="tt">S3</span></sup>·is·calculated·with·<span·class="tt">K</span>·being·the·field·with·101·elements.</p> | 169 | ········<p>Below,·the·invariant·ring·<span·class="tt">QQ[x,y,z]</span><sup><span·class="tt">S3</span></sup>·is·calculated·with·<span·class="tt">K</span>·being·the·field·with·101·elements.</p> |
| 170 | ········<table·class="examples"> | 170 | ········<table·class="examples"> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| Offset 98, 16 lines modified | Offset 98, 16 lines modified | ||
| 98 | ·····104976z·} | 98 | ·····104976z·} |
| 99 | o4·:·List | 99 | o4·:·List |
| 100 | Compare·this·result·to·the·hsop·output·when·Dade·is·left·to·its·default·value | 100 | Compare·this·result·to·the·hsop·output·when·Dade·is·left·to·its·default·value |
| 101 | _\x8f_\x8a_\x8l_\x8s_\x8e. | 101 | _\x8f_\x8a_\x8l_\x8s_\x8e. |
| 102 | i5·:·primaryInvariants(S3) | 102 | i5·:·primaryInvariants(S3) |
| 103 | ··················2····2····2···2·······2····2·····2·······2······2 | ||
| 104 | 103 | ···································3····3····3 | |
| 104 | o5·=·{x·+·y·+·z,·x*y·+·x*z·+·y*z,·x··+·y··+·z·} | ||
| 105 | o5·:·List | 105 | o5·:·List |
| 106 | Below,·the·invariant·ring·QQ[x,y,z]S3·is·calculated·with·K·being·the·field·with | 106 | Below,·the·invariant·ring·QQ[x,y,z]S3·is·calculated·with·K·being·the·field·with |
| 107 | 101·elements. | 107 | 101·elements. |
| 108 | i6·:·K=GF(101) | 108 | i6·:·K=GF(101) |
| 109 | o6·=·K | 109 | o6·=·K |
| Offset 90, 16 lines modified | Offset 90, 16 lines modified | ||
| 90 | ··················|·1·0·0·|··|·0·0·1·| | 90 | ··················|·1·0·0·|··|·0·0·1·| |
| 91 | o3·:·FiniteGroupAction</code></pre> | 91 | o3·:·FiniteGroupAction</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) |
| 95 | ······· | 95 | ·······2·······2····2·····2·······2······2··········4····4····4 |
| 96 | o4·=·{x··+· | 96 | o4·=·{x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x*y*z,·x··+·y··+·z·} |
| 97 | o4·:·List</code></pre> | 97 | o4·:·List</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ········</table> | 99 | ········</table> |
| 100 | ······</div> | 100 | ······</div> |
| 101 | ······<div> | 101 | ······<div> |
| 102 | ········<h2>Further·information</h2> | 102 | ········<h2>Further·information</h2> |
| Offset 35, 16 lines modified | Offset 35, 16 lines modified | ||
| 35 | o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|} | 35 | o3·=·QQ[x..z]·<-·{|·0·1·0·|,·|·0·1·0·|} |
| 36 | ··················|·0·0·1·|··|·1·0·0·| | 36 | ··················|·0·0·1·|··|·1·0·0·| |
| 37 | ··················|·1·0·0·|··|·0·0·1·| | 37 | ··················|·1·0·0·|··|·0·0·1·| |
| 38 | o3·:·FiniteGroupAction | 38 | o3·:·FiniteGroupAction |
| 39 | i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) | 39 | i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) |
| 40 | ······· | 40 | ·······2·······2····2·····2·······2······2··········4····4····4 |
| 41 | o4·=·{x··+· | 41 | o4·=·{x·y·+·x*y··+·x·z·+·y·z·+·x*z··+·y*z·,·x*y*z,·x··+·y··+·z·} |
| 42 | o4·:·List | 42 | o4·:·List |
| 43 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 43 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 44 | ····*·Default·value:·0 | 44 | ····*·Default·value:·0 |
| 45 | ····*·Function:·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·--·computes·a·list·of·primary·invariants·for | 45 | ····*·Function:·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8I_\x8n_\x8v_\x8a_\x8r_\x8i_\x8a_\x8n_\x8t_\x8s·--·computes·a·list·of·primary·invariants·for |
| 46 | ······the·invariant·ring·of·a·finite·group | 46 | ······the·invariant·ring·of·a·finite·group |
| 47 | ····*·Option·key:·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r·--·an·optional·argument·for·primaryInvariants | 47 | ····*·Option·key:·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r·--·an·optional·argument·for·primaryInvariants |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | ZnJvbUR1YWwoTWF0cml4KQ== | 8 | ZnJvbUR1YWwoTWF0cml4KQ== |
| 9 | #:len=249 | 9 | #:len=249 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzI5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzI5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmcm9tRHVhbCxNYXRyaXgpLCJmcm9tRHVhbChNYXRy | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmcm9tRHVhbCxNYXRyaXgpLCJmcm9tRHVhbChNYXRy |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=38 | 7 | #:len=38 |
| 8 | aW52UmVkdWNlKFJpbmdFbGVtZW50LEludm9sdXRpdmVCYXNpcyk= | 8 | aW52UmVkdWNlKFJpbmdFbGVtZW50LEludm9sdXRpdmVCYXNpcyk= |
| 9 | #:len=299 | 9 | #:len=299 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzMywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzMywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaW52UmVkdWNlLFJpbmdFbGVtZW50LEludm9sdXRp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaW52UmVkdWNlLFJpbmdFbGVtZW50LEludm9sdXRp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=27 | 7 | #:len=27 |
| 8 | aXNJc29tb3JwaGljKE1hdHJpeCxNYXRyaXgp | 8 | aXNJc29tb3JwaGljKE1hdHJpeCxNYXRyaXgp |
| 9 | #:len=270 | 9 | #:len=270 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpc0lzb21vcnBoaWMsTWF0cml4LE1hdHJpeCksImlz | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpc0lzb21vcnBoaWMsTWF0cml4LE1hdHJpeCksImlz |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=13 | 7 | #:len=13 |
| 8 | TmFtZVNlcGFyYXRvcg== | 8 | TmFtZVNlcGFyYXRvcg== |
| 9 | #:len=210 | 9 | #:len=210 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJOYW1lU2VwYXJhdG9yIiwiTmFtZVNlcGFyYXRvciIs | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJOYW1lU2VwYXJhdG9yIiwiTmFtZVNlcGFyYXRvciIs |
| Offset 39, 19 lines modified | Offset 39, 19 lines modified | ||
| 39 | o8·=·{1,·2,·3} | 39 | o8·=·{1,·2,·3} |
| 40 | o8·:·List | 40 | o8·:·List |
| 41 | i9·:·jsonFile·=·temporaryFileName()·|·".json" | 41 | i9·:·jsonFile·=·temporaryFileName()·|·".json" |
| 42 | o9·=·/tmp/M2- | 42 | o9·=·/tmp/M2-3800301-0/0.json |
| 43 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close | 43 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close |
| 44 | o10·=·/tmp/M2- | 44 | o10·=·/tmp/M2-3800301-0/0.json |
| 45 | o10·:·File | 45 | o10·:·File |
| 46 | i11·:·fromJSON·openIn·jsonFile | 46 | i11·:·fromJSON·openIn·jsonFile |
| 47 | o11·=·{1,·2,·3} | 47 | o11·=·{1,·2,·3} |
| Offset 150, 20 lines modified | Offset 150, 20 lines modified | ||
| 150 | ········<div> | 150 | ········<div> |
| 151 | ··········<p>The·input·may·also·be·a·file·containing·JSON·data.</p> | 151 | ··········<p>The·input·may·also·be·a·file·containing·JSON·data.</p> |
| 152 | ········</div> | 152 | ········</div> |
| 153 | ········<table·class="examples"> | 153 | ········<table·class="examples"> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i9·:·jsonFile·=·temporaryFileName()·|·".json" | 155 | <td>··············<pre><code·class="language-macaulay2">i9·:·jsonFile·=·temporaryFileName()·|·".json" |
| 156 | o9·=·/tmp/M2- | 156 | o9·=·/tmp/M2-3800301-0/0.json</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close | 159 | <td>··············<pre><code·class="language-macaulay2">i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close |
| 160 | o10·=·/tmp/M2- | 160 | o10·=·/tmp/M2-3800301-0/0.json |
| 161 | o10·:·File</code></pre> | 161 | o10·:·File</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i11·:·fromJSON·openIn·jsonFile | 164 | <td>··············<pre><code·class="language-macaulay2">i11·:·fromJSON·openIn·jsonFile |
| 165 | o11·=·{1,·2,·3} | 165 | o11·=·{1,·2,·3} |
| Offset 54, 18 lines modified | Offset 54, 18 lines modified | ||
| 54 | o8·=·{1,·2,·3} | 54 | o8·=·{1,·2,·3} |
| 55 | o8·:·List | 55 | o8·:·List |
| 56 | The·input·may·also·be·a·file·containing·JSON·data. | 56 | The·input·may·also·be·a·file·containing·JSON·data. |
| 57 | i9·:·jsonFile·=·temporaryFileName()·|·".json" | 57 | i9·:·jsonFile·=·temporaryFileName()·|·".json" |
| 58 | o9·=·/tmp/M2- | 58 | o9·=·/tmp/M2-3800301-0/0.json |
| 59 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close | 59 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close |
| 60 | o10·=·/tmp/M2- | 60 | o10·=·/tmp/M2-3800301-0/0.json |
| 61 | o10·:·File | 61 | o10·:·File |
| 62 | i11·:·fromJSON·openIn·jsonFile | 62 | i11·:·fromJSON·openIn·jsonFile |
| 63 | o11·=·{1,·2,·3} | 63 | o11·=·{1,·2,·3} |
| 64 | o11·:·List | 64 | o11·:·List |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | amV0cyhaWixBZmZpbmVWYXJpZXR5KQ== | 8 | amV0cyhaWixBZmZpbmVWYXJpZXR5KQ== |
| 9 | #:len=2469 | 9 | #:len=2469 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGpldHMgb2YgYW4gYWZmaW5lIHZh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGpldHMgb2YgYW4gYWZmaW5lIHZh |
| 11 | cmlldHkiLCAibGluZW51bSIgPT4gMTY2NywgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT | 11 | cmlldHkiLCAibGluZW51bSIgPT4gMTY2NywgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT |
| Offset 17, 24 lines modified | Offset 17, 24 lines modified | ||
| 17 | o3·=·ideal·(y0*z0*x2·+·x0*z0*y2·+·x0*y0*z2·+·z0*x1*y1·+·y0*x1*z1·+·x0*y1*z1, | 17 | o3·=·ideal·(y0*z0*x2·+·x0*z0*y2·+·x0*y0*z2·+·z0*x1*y1·+·y0*x1*z1·+·x0*y1*z1, |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ·····y0*z0*x1·+·x0*z0*y1·+·x0*y0*z1,·x0*y0*z0) | 19 | ·····y0*z0*x1·+·x0*z0*y1·+·x0*y0*z1,·x0*y0*z0) |
| 20 | o3·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] | 20 | o3·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] |
| 21 | i4·:·elapsedTime·jetsRadical(2,I) | 21 | i4·:·elapsedTime·jetsRadical(2,I) |
| 22 | ·--·.0 | 22 | ·--·.0107969s·elapsed |
| 23 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, | 23 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, |
| 24 | ·····------------------------------------------------------------------------ | 24 | ·····------------------------------------------------------------------------ |
| 25 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) | 25 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) |
| 26 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] | 26 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] |
| 27 | i5·:·elapsedTime·radical·J2I | 27 | i5·:·elapsedTime·radical·J2I |
| 28 | ·--·. | 28 | ·--·.529232s·elapsed |
| 29 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, | 29 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) | 31 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) |
| 32 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] | 32 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | o6·:·Ideal·of·R | 33 | o6·:·Ideal·of·R |
| 34 | i7·:·I.cache.?jet | 34 | i7·:·I.cache.?jet |
| 35 | o7·=·false | 35 | o7·=·false |
| 36 | i8·:·elapsedTime·jets(3,I) | 36 | i8·:·elapsedTime·jets(3,I) |
| 37 | ·--·.00 | 37 | ·--·.00941599s·elapsed |
| 38 | ··················································2·················2 | 38 | ··················································2·················2 |
| 39 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 39 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 40 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 40 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| 41 | i9·:·I.cache.?jet | 41 | i9·:·I.cache.?jet |
| Offset 53, 23 lines modified | Offset 53, 23 lines modified | ||
| 53 | o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|} | 53 | o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|} |
| 54 | ·······························|·2x0x2-y2+x1^2··| | 54 | ·······························|·2x0x2-y2+x1^2··| |
| 55 | ·······························|·2x0x1-y1·······| | 55 | ·······························|·2x0x1-y1·······| |
| 56 | ·······························|·x0^2-y0········| | 56 | ·······························|·x0^2-y0········| |
| 57 | ·················jetsMaxOrder·=>·3 | 57 | ·················jetsMaxOrder·=>·3 |
| 58 | i11·:·elapsedTime·jets(3,I) | 58 | i11·:·elapsedTime·jets(3,I) |
| 59 | ·--·.00 | 59 | ·--·.00238269s·elapsed |
| 60 | ···················································2·················2 | 60 | ···················································2·················2 |
| 61 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 61 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 62 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 62 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| 63 | i12·:·elapsedTime·jets(2,I) | 63 | i12·:·elapsedTime·jets(2,I) |
| 64 | ·--·.00 | 64 | ·--·.0020777s·elapsed |
| 65 | ·····························2·················2 | 65 | ·····························2·················2 |
| 66 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 66 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 67 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2] | 67 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2] |
| 68 | i13·:·Q·=·R/I | 68 | i13·:·Q·=·R/I |
| Offset 148, 15 lines modified | Offset 148, 15 lines modified | ||
| 148 | o22·=·true | 148 | o22·=·true |
| 149 | i23·:·f.cache.?jet | 149 | i23·:·f.cache.?jet |
| 150 | o23·=·false | 150 | o23·=·false |
| 151 | i24·:·elapsedTime·jets(3,f) | 151 | i24·:·elapsedTime·jets(3,f) |
| 152 | ·--·.0 | 152 | ·--·.0117174s·elapsed |
| 153 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2 | 153 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2 |
| 154 | o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 154 | o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 155 | ······································································2·················2 | 155 | ······································································2·················2 |
| 156 | ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 156 | ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 157 | ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 157 | ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| Offset 173, 15 lines modified | Offset 173, 15 lines modified | ||
| 173 | o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|} | 173 | o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|} |
| 174 | ·······························|·t2·2t0t2+t1^2··| | 174 | ·······························|·t2·2t0t2+t1^2··| |
| 175 | ·······························|·t1·2t0t1·······| | 175 | ·······························|·t1·2t0t1·······| |
| 176 | ·······························|·t0·t0^2········| | 176 | ·······························|·t0·t0^2········| |
| 177 | ·················jetsMaxOrder·=>·3 | 177 | ·················jetsMaxOrder·=>·3 |
| 178 | i27·:·elapsedTime·jets(2,f) | 178 | i27·:·elapsedTime·jets(2,f) |
| 179 | ·--·.000 | 179 | ·--·.000683141s·elapsed |
| 180 | ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2 | 180 | ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2 |
| 181 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 181 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 182 | ············································2·················2 | 182 | ············································2·················2 |
| 183 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 183 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 184 | ·········································QQ[x0,·y0][x1,·y1][x2,·y2] | 184 | ·········································QQ[x0,·y0][x1,·y1][x2,·y2] |
| Offset 73, 25 lines modified | Offset 73, 25 lines modified | ||
| 73 | ········</table> | 73 | ········</table> |
| 74 | ········<div> | 74 | ········<div> |
| 75 | ··········<p>However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial·ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is·generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This·observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of·monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in·Macaulay2.</p> | 75 | ··········<p>However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial·ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is·generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This·observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of·monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in·Macaulay2.</p> |
| 76 | ········</div> | 76 | ········</div> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jetsRadical(2,I) | 79 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jetsRadical(2,I) |
| 80 | ·--·.0 | 80 | ·--·.0107969s·elapsed |
| 81 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, | 81 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, |
| 82 | ·····------------------------------------------------------------------------ | 82 | ·····------------------------------------------------------------------------ |
| 83 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) | 83 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) |
| 84 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> | 84 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·radical·J2I | 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·radical·J2I |
| 88 | ·--·. | 88 | ·--·.529232s·elapsed |
| 89 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, | 89 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, |
| 90 | ·····------------------------------------------------------------------------ | 90 | ·····------------------------------------------------------------------------ |
| 91 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) | 91 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) |
| 92 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> | 92 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| Offset 27, 23 lines modified | Offset 27, 23 lines modified | ||
| 27 | However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial | 27 | However,·by·[GS06,·Theorem·3.1],·the·radical·is·always·a·(squarefree)·monomial |
| 28 | ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is | 28 | ideal.·In·fact,·the·proof·of·[GS06,·Theorem·3.2]·shows·that·the·radical·is |
| 29 | generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This | 29 | generated·by·the·individual·terms·in·the·generators·of·the·ideal·of·jets.·This |
| 30 | observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of | 30 | observation·provides·an·alternative·algorithm·for·computing·radicals·of·jets·of |
| 31 | monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in | 31 | monomial·ideals,·which·can·be·faster·than·the·default·radical·computation·in |
| 32 | Macaulay2. | 32 | Macaulay2. |
| 33 | i4·:·elapsedTime·jetsRadical(2,I) | 33 | i4·:·elapsedTime·jetsRadical(2,I) |
| 34 | ·--·.0 | 34 | ·--·.0107969s·elapsed |
| 35 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, | 35 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, |
| 36 | ·····------------------------------------------------------------------------ | 36 | ·····------------------------------------------------------------------------ |
| 37 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) | 37 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) |
| 38 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] | 38 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] |
| 39 | i5·:·elapsedTime·radical·J2I | 39 | i5·:·elapsedTime·radical·J2I |
| 40 | ·--·. | 40 | ·--·.529232s·elapsed |
| 41 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, | 41 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) | 43 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) |
| 44 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] | 44 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2] |
| 45 | For·a·monomial·hypersurface,·[GS06,·Theorem·3.2]·describes·the·minimal·primes | 45 | For·a·monomial·hypersurface,·[GS06,·Theorem·3.2]·describes·the·minimal·primes |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·I.cache.?jet | 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·I.cache.?jet |
| 97 | o7·=·false</code></pre> | 97 | o7·=·false</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·jets(3,I) | 100 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·jets(3,I) |
| 101 | ·--·.00 | 101 | ·--·.00941599s·elapsed |
| 102 | ··················································2·················2 | 102 | ··················································2·················2 |
| 103 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 103 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 104 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> | 104 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| Offset 118, 24 lines modified | Offset 118, 24 lines modified | ||
| 118 | ·······························|·2x0x2-y2+x1^2··| | 118 | ·······························|·2x0x2-y2+x1^2··| |
| 119 | ·······························|·2x0x1-y1·······| | 119 | ·······························|·2x0x1-y1·······| |
| 120 | ·······························|·x0^2-y0········| | 120 | ·······························|·x0^2-y0········| |
| 121 | ·················jetsMaxOrder·=>·3</code></pre> | 121 | ·················jetsMaxOrder·=>·3</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·jets(3,I) | 124 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·jets(3,I) |
| 125 | ·--·.00 | 125 | ·--·.00238269s·elapsed |
| 126 | ···················································2·················2 | 126 | ···················································2·················2 |
| 127 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 127 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 128 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> | 128 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·jets(2,I) | 131 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·jets(2,I) |
| 132 | ·--·.00 | 132 | ·--·.0020777s·elapsed |
| 133 | ·····························2·················2 | 133 | ·····························2·················2 |
| 134 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 134 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 135 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]</code></pre> | 135 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ········</table> | 137 | ········</table> |
| Offset 236, 15 lines modified | Offset 236, 15 lines modified | ||
| 236 | ··········<tr> | 236 | ··········<tr> |
| 237 | <td>··············<pre><code·class="language-macaulay2">i23·:·f.cache.?jet | 237 | <td>··············<pre><code·class="language-macaulay2">i23·:·f.cache.?jet |
| 238 | o23·=·false</code></pre> | 238 | o23·=·false</code></pre> |
| 239 | </td>··········</tr> | 239 | </td>··········</tr> |
| 240 | ··········<tr> | 240 | ··········<tr> |
| 241 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·jets(3,f) | 241 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·jets(3,f) |
| 242 | ·--·.0 | 242 | ·--·.0117174s·elapsed |
| 243 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2 | 243 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2 |
| 244 | o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 244 | o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 245 | ······································································2·················2 | 245 | ······································································2·················2 |
| 246 | ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 246 | ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 247 | ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 247 | ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| Offset 264, 15 lines modified | Offset 264, 15 lines modified | ||
| 264 | ·······························|·t2·2t0t2+t1^2··| | 264 | ·······························|·t2·2t0t2+t1^2··| |
| 265 | ·······························|·t1·2t0t1·······| | 265 | ·······························|·t1·2t0t1·······| |
| 266 | ·······························|·t0·t0^2········| | 266 | ·······························|·t0·t0^2········| |
| 267 | ·················jetsMaxOrder·=>·3</code></pre> | 267 | ·················jetsMaxOrder·=>·3</code></pre> |
| 268 | </td>··········</tr> | 268 | </td>··········</tr> |
| 269 | ··········<tr> | 269 | ··········<tr> |
| 270 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·jets(2,f) | 270 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·jets(2,f) |
| 271 | ·--·.000 | 271 | ·--·.000683141s·elapsed |
| 272 | ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2 | 272 | ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2 |
| 273 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 273 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 274 | ············································2·················2 | 274 | ············································2·················2 |
| 275 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 275 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 276 | ·········································QQ[x0,·y0][x1,·y1][x2,·y2] | 276 | ·········································QQ[x0,·y0][x1,·y1][x2,·y2] |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | o6·=·ideal(x··-·y) | 41 | o6·=·ideal(x··-·y) |
| 42 | o6·:·Ideal·of·R | 42 | o6·:·Ideal·of·R |
| 43 | i7·:·I.cache.?jet | 43 | i7·:·I.cache.?jet |
| 44 | o7·=·false | 44 | o7·=·false |
| 45 | i8·:·elapsedTime·jets(3,I) | 45 | i8·:·elapsedTime·jets(3,I) |
| 46 | ·--·.00 | 46 | ·--·.00941599s·elapsed |
| 47 | ··················································2·················2 | 47 | ··················································2·················2 |
| 48 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 48 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 49 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 49 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| 50 | i9·:·I.cache.?jet | 50 | i9·:·I.cache.?jet |
| Offset 58, 22 lines modified | Offset 58, 22 lines modified | ||
| 58 | o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|} | 58 | o10·=·CacheTable{jetsMatrix·=>·|·2x0x3-y3+2x1x2·|} |
| 59 | ·······························|·2x0x2-y2+x1^2··| | 59 | ·······························|·2x0x2-y2+x1^2··| |
| 60 | ·······························|·2x0x1-y1·······| | 60 | ·······························|·2x0x1-y1·······| |
| 61 | ·······························|·x0^2-y0········| | 61 | ·······························|·x0^2-y0········| |
| 62 | ·················jetsMaxOrder·=>·3 | 62 | ·················jetsMaxOrder·=>·3 |
| 63 | i11·:·elapsedTime·jets(3,I) | 63 | i11·:·elapsedTime·jets(3,I) |
| 64 | ·--·.00 | 64 | ·--·.00238269s·elapsed |
| 65 | ···················································2·················2 | 65 | ···················································2·················2 |
| 66 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 66 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 67 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 67 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| 68 | i12·:·elapsedTime·jets(2,I) | 68 | i12·:·elapsedTime·jets(2,I) |
| 69 | ·--·.00 | 69 | ·--·.0020777s·elapsed |
| 70 | ·····························2·················2 | 70 | ·····························2·················2 |
| 71 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 71 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 72 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2] | 72 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2] |
| 73 | For·quotient·rings,·data·is·stored·under·*.jet.·Each·jets·order·gives·rise·to·a | 73 | For·quotient·rings,·data·is·stored·under·*.jet.·Each·jets·order·gives·rise·to·a |
| 74 | different·quotient·that·is·stored·separately·under·*.jet.jetsRing·(order·zero | 74 | different·quotient·that·is·stored·separately·under·*.jet.jetsRing·(order·zero |
| Offset 153, 15 lines modified | Offset 153, 15 lines modified | ||
| 153 | i22·:·isWellDefined·f | 153 | i22·:·isWellDefined·f |
| 154 | o22·=·true | 154 | o22·=·true |
| 155 | i23·:·f.cache.?jet | 155 | i23·:·f.cache.?jet |
| 156 | o23·=·false | 156 | o23·=·false |
| 157 | i24·:·elapsedTime·jets(3,f) | 157 | i24·:·elapsedTime·jets(3,f) |
| 158 | ·--·.0 | 158 | ·--·.0117174s·elapsed |
| 159 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3, | 159 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3, |
| 160 | y3]······················································2····················2 | 160 | y3]······················································2····················2 |
| 161 | o24·=·map·(QQ[t0][t1][t2][t3],·------------------------------------------------ | 161 | o24·=·map·(QQ[t0][t1][t2][t3],·------------------------------------------------ |
| 162 | ----------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 162 | ----------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 163 | ······································································2 | 163 | ······································································2 |
| 164 | 2 | 164 | 2 |
| Offset 183, 15 lines modified | Offset 183, 15 lines modified | ||
| 183 | o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|} | 183 | o26·=·CacheTable{jetsMatrix·=>·|·t3·2t0t3+2t1t2·|} |
| 184 | ·······························|·t2·2t0t2+t1^2··| | 184 | ·······························|·t2·2t0t2+t1^2··| |
| 185 | ·······························|·t1·2t0t1·······| | 185 | ·······························|·t1·2t0t1·······| |
| 186 | ·······························|·t0·t0^2········| | 186 | ·······························|·t0·t0^2········| |
| 187 | ·················jetsMaxOrder·=>·3 | 187 | ·················jetsMaxOrder·=>·3 |
| 188 | i27·:·elapsedTime·jets(2,f) | 188 | i27·:·elapsedTime·jets(2,f) |
| 189 | ·--·.000 | 189 | ·--·.000683141s·elapsed |
| 190 | ···································QQ[x0,·y0][x1,·y1][x2,·y2] | 190 | ···································QQ[x0,·y0][x1,·y1][x2,·y2] |
| 191 | 2····················2 | 191 | 2····················2 |
| 192 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2, | 192 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2, |
| 193 | 2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 193 | 2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 194 | ············································2·················2 | 194 | ············································2·················2 |
| 195 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 195 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=41 | 7 | #:len=41 |
| 8 | Y2Fub25pY2FsSG9tb3RvcGllcyguLi4sRmluZUdyYWRpbmc9Pi4uLik= | 8 | Y2Fub25pY2FsSG9tb3RvcGllcyguLi4sRmluZUdyYWRpbmc9Pi4uLik= |
| 9 | #:len=298 | 9 | #:len=298 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTU4NSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTU4NSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbY2Fub25pY2FsSG9tb3RvcGllcyxGaW5lR3JhZGlu | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbY2Fub25pY2FsSG9tb3RvcGllcyxGaW5lR3JhZGlu |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | ······32003··0···5···0···5·········32003··0···5···0···5··········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5··········32003··0···5···0···5········· | 19 | ······32003··0···5···0···5·········32003··0···5···0···5··········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5···········32003··0···5···0···5··········32003··0···5···0···5········· |
| 20 | ·····················································································································································································································································································································10 | 20 | ·····················································································································································································································································································································10 |
| 21 | ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9 | 21 | ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9 |
| 22 | o3·:·ChainComplex | 22 | o3·:·ChainComplex |
| 23 | i4·:·L·=·analyzeStrand(F,a);·#L | 23 | i4·:·L·=·analyzeStrand(F,a);·#L |
| 24 | ·--·.0 | 24 | ·--·.0317391s·elapsed |
| 25 | o5·=·350 | 25 | o5·=·350 |
| 26 | i6·:·betti·F_a,·betti·F | 26 | i6·:·betti·F_a,·betti·F |
| 27 | ···············0·········0··1···2···3···4···5···6···7··8·9 | 27 | ···············0·········0··1···2···3···4···5···6···7··8·9 |
| 28 | o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7) | 28 | o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7) |
| Offset 46, 19 lines modified | Offset 46, 19 lines modified | ||
| 46 | o7·:·Expression·of·class·Product | 46 | o7·:·Expression·of·class·Product |
| 47 | i8·:·L3·=·select(L,c->c%3==0);·#L3 | 47 | i8·:·L3·=·select(L,c->c%3==0);·#L3 |
| 48 | o9·=·14 | 48 | o9·=·14 |
| 49 | i10·:·carpetBettiTable(a,b,3) | 49 | i10·:·carpetBettiTable(a,b,3) |
| 50 | ·--·.00175459s·elapsed | ||
| 51 | ·--·.00 | 50 | ·--·.00204641s·elapsed |
| 52 | ·--·.0 | 51 | ·--·.00692888s·elapsed |
| 53 | ·--·.00862634s·elapsed | ||
| 54 | ·--·.0 | 52 | ·--·.0263095s·elapsed |
| 53 | ·--·.0108969s·elapsed | ||
| 54 | ·--·.00367411s·elapsed | ||
| 55 | ·············0··1···2···3···4···5···6···7··8·9 | 55 | ·············0··1···2···3···4···5···6···7··8·9 |
| 56 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 | 56 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 57 | ··········0:·1··.···.···.···.···.···.···.··.·. | 57 | ··········0:·1··.···.···.···.···.···.···.··.·. |
| 58 | ··········1:·.·36·160·315·288··14···.···.··.·. | 58 | ··········1:·.·36·160·315·288··14···.···.··.·. |
| 59 | ··········2:·.··.···.···.··14·288·315·160·36·. | 59 | ··········2:·.··.···.···.··14·288·315·160·36·. |
| 60 | ··········3:·.··.···.···.···.···.···.···.··.·1 | 60 | ··········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 3, 20 lines modified | Offset 3, 20 lines modified | ||
| 3 | i1·:·a=5,b=5 | 3 | i1·:·a=5,b=5 |
| 4 | o1·=·(5,·5) | 4 | o1·=·(5,·5) |
| 5 | o1·:·Sequence | 5 | o1·:·Sequence |
| 6 | i2·:·elapsedTime·T=carpetBettiTable(a,b,3) | 6 | i2·:·elapsedTime·T=carpetBettiTable(a,b,3) |
| 7 | ·--·.001 | 7 | ·--·.00190592s·elapsed |
| 8 | ·--·.00488555s·elapsed | ||
| 9 | ·--·.0 | 8 | ·--·.00527802s·elapsed |
| 10 | ·--·.0 | 9 | ·--·.0409511s·elapsed |
| 10 | ·--·.012454s·elapsed | ||
| 11 | ·--·.00 | 11 | ·--·.00333897s·elapsed |
| 12 | ·--·. | 12 | ·--·.33973s·elapsed |
| 13 | ············0··1···2···3···4···5···6···7··8·9 | 13 | ············0··1···2···3···4···5···6···7··8·9 |
| 14 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 | 14 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 15 | ·········0:·1··.···.···.···.···.···.···.··.·. | 15 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 16 | ·········1:·.·36·160·315·288··14···.···.··.·. | 16 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 17 | ·········2:·.··.···.···.··14·288·315·160·36·. | 17 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 18 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 18 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 26, 15 lines modified | Offset 26, 15 lines modified | ||
| 26 | i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); | 26 | i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); |
| 27 | ··············ZZ | 27 | ··············ZZ |
| 28 | o3·:·Ideal·of·--[x·..x·,·y·..y·] | 28 | o3·:·Ideal·of·--[x·..x·,·y·..y·] |
| 29 | ···············3··0···5···0···5 | 29 | ···············3··0···5···0···5 |
| 30 | i4·:·elapsedTime·T'=minimalBetti·J | 30 | i4·:·elapsedTime·T'=minimalBetti·J |
| 31 | ·--·. | 31 | ·--·.28955s·elapsed |
| 32 | ············0··1···2···3···4···5···6···7··8·9 | 32 | ············0··1···2···3···4···5···6···7··8·9 |
| 33 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 | 33 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 34 | ·········0:·1··.···.···.···.···.···.···.··.·. | 34 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 35 | ·········1:·.·36·160·315·288··14···.···.··.·. | 35 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 36 | ·········2:·.··.···.···.··14·288·315·160·36·. | 36 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 37 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 37 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 48, 22 lines modified | Offset 48, 22 lines modified | ||
| 48 | ·········1:·.·.·.·.·.·.·.·.·.·. | 48 | ·········1:·.·.·.·.·.·.·.·.·.·. |
| 49 | ·········2:·.·.·.·.·.·.·.·.·.·. | 49 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 50 | ·········3:·.·.·.·.·.·.·.·.·.·. | 50 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 51 | o5·:·BettiTally | 51 | o5·:·BettiTally |
| 52 | i6·:·elapsedTime·h=carpetBettiTables(6,6); | 52 | i6·:·elapsedTime·h=carpetBettiTables(6,6); |
| 53 | ·--·.003 | 53 | ·--·.00389664s·elapsed |
| 54 | ·--·.0144133s·elapsed | ||
| 55 | ·--·.0985938s·elapsed | ||
| 56 | ·--·1.09889s·elapsed | ||
| 57 | ·--·.305891s·elapsed | ||
| 54 | ·--·.0 | 58 | ·--·.0421898s·elapsed |
| 55 | ·--·.0937147s·elapsed | ||
| 56 | ·--·.929948s·elapsed | ||
| 57 | ·--·.233203s·elapsed | ||
| 58 | ·--·.0500267s·elapsed | ||
| 59 | ·--·.00 | 59 | ·--·.00703313s·elapsed |
| 60 | ·--· | 60 | ·--·4.69855s·elapsed |
| 61 | i7·:·carpetBettiTable(h,7) | 61 | i7·:·carpetBettiTable(h,7) |
| 62 | ············0··1···2···3····4····5····6····7···8···9·10·11 | 62 | ············0··1···2···3····4····5····6····7···8···9·10·11 |
| 63 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 | 63 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 |
| 64 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. | 64 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. |
| 65 | ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··. | 65 | ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··. |
| Offset 3, 19 lines modified | Offset 3, 19 lines modified | ||
| 3 | i1·:·a=5,b=5 | 3 | i1·:·a=5,b=5 |
| 4 | o1·=·(5,·5) | 4 | o1·=·(5,·5) |
| 5 | o1·:·Sequence | 5 | o1·:·Sequence |
| 6 | i2·:·h=carpetBettiTables(a,b) | 6 | i2·:·h=carpetBettiTables(a,b) |
| 7 | ·--·.001 | 7 | ·--·.0019681s·elapsed |
| 8 | ·--·.00520524s·elapsed | ||
| 8 | ·--·.0 | 9 | ·--·.0230106s·elapsed |
| 9 | ·--·.01 | 10 | ·--·.0106439s·elapsed |
| 10 | ·--·.008 | 11 | ·--·.00809513s·elapsed |
| 11 | ·--·.00303588s·elapsed | ||
| 12 | ···························0··1···2···3···4···5···6···7··8·9 | 12 | ···························0··1···2···3···4···5···6···7··8·9 |
| 13 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 13 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 14 | ························0:·1··.···.···.···.···.···.···.··.·. | 14 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 15 | ························1:·.·36·160·315·288···.···.···.··.·. | 15 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 16 | ························2:·.··.···.···.···.·288·315·160·36·. | 16 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 17 | ························3:·.··.···.···.···.···.···.···.··.·1 | 17 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 48, 15 lines modified | Offset 48, 15 lines modified | ||
| 48 | i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); | 48 | i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); |
| 49 | ··············ZZ | 49 | ··············ZZ |
| 50 | o4·:·Ideal·of·--[x·..x·,·y·..y·] | 50 | o4·:·Ideal·of·--[x·..x·,·y·..y·] |
| 51 | ···············3··0···5···0···5 | 51 | ···············3··0···5···0···5 |
| 52 | i5·:·elapsedTime·T'=minimalBetti·J | 52 | i5·:·elapsedTime·T'=minimalBetti·J |
| 53 | ·--·. | 53 | ·--·.367505s·elapsed |
| 54 | ············0··1···2···3···4···5···6···7··8·9 | 54 | ············0··1···2···3···4···5···6···7··8·9 |
| 55 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 | 55 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 56 | ·········0:·1··.···.···.···.···.···.···.··.·. | 56 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 57 | ·········1:·.·36·160·315·288··14···.···.··.·. | 57 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 58 | ·········2:·.··.···.···.··14·288·315·160·36·. | 58 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 59 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 59 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 70, 22 lines modified | Offset 70, 22 lines modified | ||
| 70 | ·········1:·.·.·.·.·.·.·.·.·.·. | 70 | ·········1:·.·.·.·.·.·.·.·.·.·. |
| 71 | ·········2:·.·.·.·.·.·.·.·.·.·. | 71 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 72 | ·········3:·.·.·.·.·.·.·.·.·.·. | 72 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 73 | o6·:·BettiTally | 73 | o6·:·BettiTally |
| 74 | i7·:·elapsedTime·h=carpetBettiTables(6,6); | 74 | i7·:·elapsedTime·h=carpetBettiTables(6,6); |
| 75 | ·--·.00 | 75 | ·--·.00418403s·elapsed |
| 76 | ·--·.0149094s·elapsed | ||
| 77 | ·--·.0975395s·elapsed | ||
| 78 | ·--·1.15878s·elapsed | ||
| 79 | ·--·.323041s·elapsed | ||
| 76 | ·--·.0 | 80 | ·--·.0414671s·elapsed |
| 77 | ·--·.0856513s·elapsed | ||
| 78 | ·--·1.03922s·elapsed | ||
| 79 | ·--·.337457s·elapsed | ||
| 80 | ·--·.037078s·elapsed | ||
| 81 | ·--·.005 | 81 | ·--·.00586998s·elapsed |
| 82 | ·--· | 82 | ·--·5.74986s·elapsed |
| 83 | i8·:·keys·h | 83 | i8·:·keys·h |
| 84 | o8·=·{0,·2,·3,·5} | 84 | o8·=·{0,·2,·3,·5} |
| 85 | o8·:·List | 85 | o8·:·List |
| Offset 3, 42 lines modified | Offset 3, 42 lines modified | ||
| 3 | i1·:·a=4,b=4 | 3 | i1·:·a=4,b=4 |
| 4 | o1·=·(4,·4) | 4 | o1·=·(4,·4) |
| 5 | o1·:·Sequence | 5 | o1·:·Sequence |
| 6 | i2·:·d=carpetDet(a,b) | 6 | i2·:·d=carpetDet(a,b) |
| 7 | ·--·.00519111s·elapsed | ||
| 8 | ·--·.0111231s·elapsed | ||
| 9 | ·--·.0 | 7 | ·--·.0100376s·elapsed |
| 10 | ·--·.0 | 8 | ·--·.0196823s·elapsed |
| 9 | ·--·.000237154s·elapsed | ||
| 10 | ·--·.0001549s·elapsed | ||
| 11 | ·--·.0001088 | 11 | ·--·.000140885s·elapsed |
| 12 | ·--·.0001 | 12 | ·--·.00014934s·elapsed |
| 13 | ·--·.00027706s·elapsed | ||
| 14 | ·--·.000147637s·elapsed | ||
| 15 | ·--·.000252383s·elapsed | ||
| 13 | ·--·.0001 | 16 | ·--·.000172063s·elapsed |
| 17 | ·--·.000360175s·elapsed | ||
| 18 | ·--·.000126728s·elapsed | ||
| 14 | ·--·.0001 | 19 | ·--·.000113192s·elapsed |
| 20 | ·--·.000119975s·elapsed | ||
| 21 | ·--·.000110657s·elapsed | ||
| 22 | ·--·.000108884s·elapsed | ||
| 23 | ·--·.000115797s·elapsed | ||
| 24 | ·--·.000109796s·elapsed | ||
| 25 | ·--·.000160401s·elapsed | ||
| 26 | ·--·.000125956s·elapsed | ||
| 15 | ·--·.0001 | 27 | ·--·.000137568s·elapsed |
| 28 | ·--·.0001334s·elapsed | ||
| 16 | ·--·.00012 | 29 | ·--·.00012811s·elapsed |
| 17 | ·--·.000232581s·elapsed | ||
| 18 | ·--·.000118698s·elapsed | ||
| 19 | ·--·.000102826s·elapsed | ||
| 20 | ·--·.000096897s·elapsed | ||
| 21 | ·--·.000091619s·elapsed | ||
| 22 | ·--·.000089584s·elapsed | ||
| 23 | ·--·.000092769s·elapsed | ||
| 24 | ·--·.000093812s·elapsed | ||
| 25 | ·--·.000102846s·elapsed | ||
| 26 | ·--·.0001 | 30 | ·--·.000122089s·elapsed |
| 27 | ·--·.000120221s·elapsed | ||
| 28 | ·--·.000220613s·elapsed | ||
| 29 | ·--·.00011 | 31 | ·--·.000119464s·elapsed |
| 30 | ·--·.000099771s·elapsed | ||
| 31 | ·--·.000099651s·elapsed | ||
| 32 | ·--·.0001 | 32 | ·--·.000125545s·elapsed |
| 33 | ·--·.0001 | 33 | ·--·.000121839s·elapsed |
| 34 | ·--·.000 | 34 | ·--·.000125735s·elapsed |
| 35 | (number·Of·blocks,·26) | 35 | (number·Of·blocks,·26) |
| 36 | 1 | 36 | 1 |
| 37 | 1 | 37 | 1 |
| 38 | 1 | 38 | 1 |
| 39 | 1 | 39 | 1 |
| 40 | 2 | 40 | 2 |
| 41 | ·2 | 41 | ·2 |
| Offset 3, 17 lines modified | Offset 3, 17 lines modified | ||
| 3 | i1·:·(a,b)=computeBound(6,4,3) | 3 | i1·:·(a,b)=computeBound(6,4,3) |
| 4 | o1·=·(9,·7) | 4 | o1·=·(9,·7) |
| 5 | o1·:·Sequence | 5 | o1·:·Sequence |
| 6 | i2·:·computeBound·3 | 6 | i2·:·computeBound·3 |
| 7 | ·--·.807772s·elapsed | ||
| 8 | ·--·.6 | 7 | ·--·.761674s·elapsed |
| 8 | ·--·.685197s·elapsed | ||
| 9 | ·--·.425204s·elapsed | ||
| 10 | ·--·.88314s·elapsed | ||
| 9 | ·--·. | 11 | ·--·.505886s·elapsed |
| 10 | ·--·1. | 12 | ·--·1.21429s·elapsed |
| 11 | ·--·.496217s·elapsed | ||
| 12 | ·--·.971603s·elapsed | ||
| 13 | o2·=·6 | 13 | o2·=·6 |
| 14 | i3·:· | 14 | i3·:· |
| Offset 9, 19 lines modified | Offset 9, 19 lines modified | ||
| 9 | i2·:·e=(-1,5) | 9 | i2·:·e=(-1,5) |
| 10 | o2·=·(-1,·5) | 10 | o2·=·(-1,·5) |
| 11 | o2·:·Sequence | 11 | o2·:·Sequence |
| 12 | i3·:·h=degenerateK3BettiTables(a,b,e) | 12 | i3·:·h=degenerateK3BettiTables(a,b,e) |
| 13 | ·--·.0149255s·elapsed | ||
| 14 | ·--·.0156362s·elapsed | ||
| 15 | ·--·.046755s·elapsed | ||
| 13 | ·--·.00 | 16 | ·--·.00770785s·elapsed |
| 14 | ·--·.00491676s·elapsed | ||
| 15 | ·--·.0196774s·elapsed | ||
| 16 | ·--·.00729439s·elapsed | ||
| 17 | ·--·.00 | 17 | ·--·.0031691s·elapsed |
| 18 | ···························0··1···2···3···4···5···6···7··8·9 | 18 | ···························0··1···2···3···4···5···6···7··8·9 |
| 19 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 19 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 20 | ························0:·1··.···.···.···.···.···.···.··.·. | 20 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 21 | ························1:·.·36·160·315·288···.···.···.··.·. | 21 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 22 | ························2:·.··.···.···.···.·288·315·160·36·. | 22 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 23 | ························3:·.··.···.···.···.···.···.···.··.·1 | 23 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
| 49 | i4·:·keys·h | 49 | i4·:·keys·h |
| 50 | o4·=·{0,·2,·3,·5} | 50 | o4·=·{0,·2,·3,·5} |
| 51 | o4·:·List | 51 | o4·:·List |
| 52 | i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) | 52 | i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) |
| 53 | ·--·. | 53 | ·--·.464921s·elapsed |
| 54 | ············0··1···2···3···4···5···6···7··8·9 | 54 | ············0··1···2···3···4···5···6···7··8·9 |
| 55 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 | 55 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 |
| 56 | ·········0:·1··.···.···.···.···.···.···.··.·. | 56 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 57 | ·········1:·.·36·160·322·336·140··48···7··.·. | 57 | ·········1:·.·36·160·322·336·140··48···7··.·. |
| 58 | ·········2:·.··.···7··48·140·336·322·160·36·. | 58 | ·········2:·.··.···7··48·140·336·322·160·36·. |
| 59 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 59 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 77, 19 lines modified | Offset 77, 19 lines modified | ||
| 77 | i7·:·e=(-1,5^2) | 77 | i7·:·e=(-1,5^2) |
| 78 | o7·=·(-1,·25) | 78 | o7·=·(-1,·25) |
| 79 | o7·:·Sequence | 79 | o7·:·Sequence |
| 80 | i8·:·h=degenerateK3BettiTables(a,b,e) | 80 | i8·:·h=degenerateK3BettiTables(a,b,e) |
| 81 | ·--·.0022681s·elapsed | ||
| 81 | ·--·.00 | 82 | ·--·.00597535s·elapsed |
| 83 | ·--·.0387189s·elapsed | ||
| 84 | ·--·.0135303s·elapsed | ||
| 82 | ·--·.0051 | 85 | ·--·.00510383s·elapsed |
| 83 | ·--·.0192936s·elapsed | ||
| 84 | ·--·.0121788s·elapsed | ||
| 85 | ·--·.00701235s·elapsed | ||
| 86 | ···························0··1···2···3···4···5···6···7··8·9 | 86 | ···························0··1···2···3···4···5···6···7··8·9 |
| 87 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} | 87 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} |
| 88 | ························0:·1··.···.···.···.···.···.···.··.·. | 88 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 89 | ························1:·.·36·160·315·288···.···.···.··.·. | 89 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 90 | ························2:·.··.···.···.···.·288·315·160·36·. | 90 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 91 | ························3:·.··.···.···.···.···.···.···.··.·1 | 91 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 1, 33 lines modified | Offset 1, 33 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1729182891690704738 | 1 | --·-*-·M2-comint·-*-·hash:·1729182891690704738 |
| 2 | i1·:·a=4 | 2 | i1·:·a=4 |
| 3 | o1·=·4 | 3 | o1·=·4 |
| 4 | i2·:·(d1,d2)=resonanceDet(a) | 4 | i2·:·(d1,d2)=resonanceDet(a) |
| 5 | ·--·.0131232s·elapsed | ||
| 5 | ·--·.0 | 6 | ·--·.000049603s·elapsed |
| 7 | ·--·.000071534s·elapsed | ||
| 6 | ·--·.0000 | 8 | ·--·.000055865s·elapsed |
| 7 | ·--·.000064188s·elapsed | ||
| 8 | ·--·.000051828s·elapsed | ||
| 9 | ·--·.00005899s·elapsed | ||
| 10 | ·--·.00007 | 9 | ·--·.000070753s·elapsed |
| 11 | ·--·.00006 | 10 | ·--·.000069961s·elapsed |
| 12 | ·--·.0000 | 11 | ·--·.000068197s·elapsed |
| 13 | ·--·.0 | 12 | ·--·.000018855s·elapsed |
| 13 | ·--·.0500783s·elapsed | ||
| 14 | ·--·.00019 | 14 | ·--·.00019729s·elapsed |
| 15 | ·--·.000115997s·elapsed | ||
| 16 | ·--·.000098404s·elapsed | ||
| 17 | ·--·.000088245s·elapsed | ||
| 15 | ·--·.00008005s·elapsed | 18 | ·--·.000083005s·elapsed |
| 19 | ·--·.0001282s·elapsed | ||
| 16 | ·--·.0000615 | 20 | ·--·.000061556s·elapsed |
| 17 | ·--·.0000 | 21 | ·--·.000021s·elapsed |
| 18 | ·--·.000061394s·elapsed | ||
| 19 | ·--·.000048934s·elapsed | ||
| 20 | ·--·.0000 | 22 | ·--·.000057959s·elapsed |
| 21 | ·--·.0000 | 23 | ·--·.000021441s·elapsed |
| 22 | ·--·.000058138s·elapsed | ||
| 23 | ·--·.000016675s·elapsed | ||
| 24 | (number·of·blocks=·,·18) | 24 | (number·of·blocks=·,·18) |
| 25 | (size·of·the·matrices,·Tally{1·=>·4}) | 25 | (size·of·the·matrices,·Tally{1·=>·4}) |
| 26 | ·····························2·=>·6 | 26 | ·····························2·=>·6 |
| 27 | ·····························3·=>·2 | 27 | ·····························3·=>·2 |
| 28 | ·····························4·=>·6 | 28 | ·····························4·=>·6 |
| 29 | ·······0·1 | 29 | ·······0·1 |
| 30 | total:·1·1 | 30 | total:·1·1 |
| Offset 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | ·····················································································································································································································································································································10 | 96 | ·····················································································································································································································································································································10 |
| 97 | ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9 | 97 | ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9 |
| 98 | o3·:·ChainComplex</code></pre> | 98 | o3·:·ChainComplex</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·L·=·analyzeStrand(F,a);·#L | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·L·=·analyzeStrand(F,a);·#L |
| 102 | ·--·.0 | 102 | ·--·.0317391s·elapsed |
| 103 | o5·=·350</code></pre> | 103 | o5·=·350</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·betti·F_a,·betti·F | 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·betti·F_a,·betti·F |
| 107 | ···············0·········0··1···2···3···4···5···6···7··8·9 | 107 | ···············0·········0··1···2···3···4···5···6···7··8·9 |
| Offset 127, 19 lines modified | Offset 127, 19 lines modified | ||
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i8·:·L3·=·select(L,c->c%3==0);·#L3 | 128 | <td>··············<pre><code·class="language-macaulay2">i8·:·L3·=·select(L,c->c%3==0);·#L3 |
| 129 | o9·=·14</code></pre> | 129 | o9·=·14</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i10·:·carpetBettiTable(a,b,3) | 132 | <td>··············<pre><code·class="language-macaulay2">i10·:·carpetBettiTable(a,b,3) |
| 133 | ·--·.00175459s·elapsed | ||
| 134 | ·--·.00 | 133 | ·--·.00204641s·elapsed |
| 135 | ·--·.0 | 134 | ·--·.00692888s·elapsed |
| 136 | ·--·.00862634s·elapsed | ||
| 137 | ·--·.0 | 135 | ·--·.0263095s·elapsed |
| 136 | ·--·.0108969s·elapsed | ||
| 137 | ·--·.00367411s·elapsed | ||
| 138 | ·············0··1···2···3···4···5···6···7··8·9 | 138 | ·············0··1···2···3···4···5···6···7··8·9 |
| 139 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 | 139 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 140 | ··········0:·1··.···.···.···.···.···.···.··.·. | 140 | ··········0:·1··.···.···.···.···.···.···.··.·. |
| 141 | ··········1:·.·36·160·315·288··14···.···.··.·. | 141 | ··········1:·.·36·160·315·288··14···.···.··.·. |
| 142 | ··········2:·.··.···.···.··14·288·315·160·36·. | 142 | ··········2:·.··.···.···.··14·288·315·160·36·. |
| 143 | ··········3:·.··.···.···.···.···.···.···.··.·1 | 143 | ··········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
| 50 | ·····0····························1·····························2 | 50 | ·····0····························1·····························2 |
| 51 | 3······························4······························5 | 51 | 3······························4······························5 |
| 52 | 6······························7······························8 | 52 | 6······························7······························8 |
| 53 | 9 | 53 | 9 |
| 54 | o3·:·ChainComplex | 54 | o3·:·ChainComplex |
| 55 | i4·:·L·=·analyzeStrand(F,a);·#L | 55 | i4·:·L·=·analyzeStrand(F,a);·#L |
| 56 | ·--·.0 | 56 | ·--·.0317391s·elapsed |
| 57 | o5·=·350 | 57 | o5·=·350 |
| 58 | i6·:·betti·F_a,·betti·F | 58 | i6·:·betti·F_a,·betti·F |
| 59 | ···············0·········0··1···2···3···4···5···6···7··8·9 | 59 | ···············0·········0··1···2···3···4···5···6···7··8·9 |
| 60 | o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7) | 60 | o6·=·(total:·833,·total:·1·36·187·491·793·833·573·250·63·7) |
| 61 | ··········6:·350······0:·1··.···.···.···.···.···.···.··.·. | 61 | ··········6:·350······0:·1··.···.···.···.···.···.···.··.·. |
| Offset 73, 19 lines modified | Offset 73, 19 lines modified | ||
| 73 | o7·=·2···3 | 73 | o7·=·2···3 |
| 74 | o7·:·Expression·of·class·Product | 74 | o7·:·Expression·of·class·Product |
| 75 | i8·:·L3·=·select(L,c->c%3==0);·#L3 | 75 | i8·:·L3·=·select(L,c->c%3==0);·#L3 |
| 76 | o9·=·14 | 76 | o9·=·14 |
| 77 | i10·:·carpetBettiTable(a,b,3) | 77 | i10·:·carpetBettiTable(a,b,3) |
| 78 | ·--·.00175459s·elapsed | ||
| 79 | ·--·.00 | 78 | ·--·.00204641s·elapsed |
| 80 | ·--·.0 | 79 | ·--·.00692888s·elapsed |
| 81 | ·--·.00862634s·elapsed | ||
| 82 | ·--·.0 | 80 | ·--·.0263095s·elapsed |
| 81 | ·--·.0108969s·elapsed | ||
| 82 | ·--·.00367411s·elapsed | ||
| 83 | ·············0··1···2···3···4···5···6···7··8·9 | 83 | ·············0··1···2···3···4···5···6···7··8·9 |
| 84 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 | 84 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 85 | ··········0:·1··.···.···.···.···.···.···.··.·. | 85 | ··········0:·1··.···.···.···.···.···.···.··.·. |
| 86 | ··········1:·.·36·160·315·288··14···.···.··.·. | 86 | ··········1:·.·36·160·315·288··14···.···.··.·. |
| 87 | ··········2:·.··.···.···.··14·288·315·160·36·. | 87 | ··········2:·.··.···.···.··14·288·315·160·36·. |
| 88 | ··········3:·.··.···.···.···.···.···.···.··.·1 | 88 | ··········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 83, 20 lines modified | Offset 83, 20 lines modified | ||
| 83 | o1·=·(5,·5) | 83 | o1·=·(5,·5) |
| 84 | o1·:·Sequence</code></pre> | 84 | o1·:·Sequence</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·T=carpetBettiTable(a,b,3) | 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·T=carpetBettiTable(a,b,3) |
| 88 | ·--·.001 | 88 | ·--·.00190592s·elapsed |
| 89 | ·--·.00488555s·elapsed | ||
| 90 | ·--·.0 | 89 | ·--·.00527802s·elapsed |
| 91 | ·--·.0 | 90 | ·--·.0409511s·elapsed |
| 91 | ·--·.012454s·elapsed | ||
| 92 | ·--·.00 | 92 | ·--·.00333897s·elapsed |
| 93 | ·--·. | 93 | ·--·.33973s·elapsed |
| 94 | ············0··1···2···3···4···5···6···7··8·9 | 94 | ············0··1···2···3···4···5···6···7··8·9 |
| 95 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 | 95 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 96 | ·········0:·1··.···.···.···.···.···.···.··.·. | 96 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 97 | ·········1:·.·36·160·315·288··14···.···.··.·. | 97 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 98 | ·········2:·.··.···.···.··14·288·315·160·36·. | 98 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 99 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 99 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 108, 15 lines modified | Offset 108, 15 lines modified | ||
| 108 | ··············ZZ | 108 | ··············ZZ |
| 109 | o3·:·Ideal·of·--[x·..x·,·y·..y·] | 109 | o3·:·Ideal·of·--[x·..x·,·y·..y·] |
| 110 | ···············3··0···5···0···5</code></pre> | 110 | ···············3··0···5···0···5</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·T'=minimalBetti·J | 113 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·T'=minimalBetti·J |
| 114 | ·--·. | 114 | ·--·.28955s·elapsed |
| 115 | ············0··1···2···3···4···5···6···7··8·9 | 115 | ············0··1···2···3···4···5···6···7··8·9 |
| 116 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 | 116 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 117 | ·········0:·1··.···.···.···.···.···.···.··.·. | 117 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 118 | ·········1:·.·36·160·315·288··14···.···.··.·. | 118 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 119 | ·········2:·.··.···.···.··14·288·315·160·36·. | 119 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 120 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 120 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 132, 22 lines modified | Offset 132, 22 lines modified | ||
| 132 | ·········2:·.·.·.·.·.·.·.·.·.·. | 132 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 133 | ·········3:·.·.·.·.·.·.·.·.·.·. | 133 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 134 | o5·:·BettiTally</code></pre> | 134 | o5·:·BettiTally</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·h=carpetBettiTables(6,6); | 137 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·h=carpetBettiTables(6,6); |
| 138 | ·--·.003 | 138 | ·--·.00389664s·elapsed |
| 139 | ·--·.0144133s·elapsed | ||
| 140 | ·--·.0985938s·elapsed | ||
| 141 | ·--·1.09889s·elapsed | ||
| 142 | ·--·.305891s·elapsed | ||
| 139 | ·--·.0 | 143 | ·--·.0421898s·elapsed |
| 140 | ·--·.0937147s·elapsed | ||
| 141 | ·--·.929948s·elapsed | ||
| 142 | ·--·.233203s·elapsed | ||
| 143 | ·--·.0500267s·elapsed | ||
| 144 | ·--·.00 | 144 | ·--·.00703313s·elapsed |
| 145 | ·--· | 145 | ·--·4.69855s·elapsed</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i7·:·carpetBettiTable(h,7) | 148 | <td>··············<pre><code·class="language-macaulay2">i7·:·carpetBettiTable(h,7) |
| 149 | ············0··1···2···3····4····5····6····7···8···9·10·11 | 149 | ············0··1···2···3····4····5····6····7···8···9·10·11 |
| 150 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 | 150 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 |
| 151 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. | 151 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. |
| Offset 26, 20 lines modified | Offset 26, 20 lines modified | ||
| 26 | resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes. | 26 | resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes. |
| 27 | i1·:·a=5,b=5 | 27 | i1·:·a=5,b=5 |
| 28 | o1·=·(5,·5) | 28 | o1·=·(5,·5) |
| 29 | o1·:·Sequence | 29 | o1·:·Sequence |
| 30 | i2·:·elapsedTime·T=carpetBettiTable(a,b,3) | 30 | i2·:·elapsedTime·T=carpetBettiTable(a,b,3) |
| 31 | ·--·.001 | 31 | ·--·.00190592s·elapsed |
| 32 | ·--·.00488555s·elapsed | ||
| 33 | ·--·.0 | 32 | ·--·.00527802s·elapsed |
| 34 | ·--·.0 | 33 | ·--·.0409511s·elapsed |
| 34 | ·--·.012454s·elapsed | ||
| 35 | ·--·.00 | 35 | ·--·.00333897s·elapsed |
| 36 | ·--·. | 36 | ·--·.33973s·elapsed |
| 37 | ············0··1···2···3···4···5···6···7··8·9 | 37 | ············0··1···2···3···4···5···6···7··8·9 |
| 38 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 | 38 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 39 | ·········0:·1··.···.···.···.···.···.···.··.·. | 39 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 40 | ·········1:·.·36·160·315·288··14···.···.··.·. | 40 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 41 | ·········2:·.··.···.···.··14·288·315·160·36·. | 41 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 42 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 42 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 47, 15 lines modified | Offset 47, 15 lines modified | ||
| 47 | o2·:·BettiTally | 47 | o2·:·BettiTally |
| 48 | i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); | 48 | i3·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); |
| 49 | ··············ZZ | 49 | ··············ZZ |
| 50 | o3·:·Ideal·of·--[x·..x·,·y·..y·] | 50 | o3·:·Ideal·of·--[x·..x·,·y·..y·] |
| 51 | ···············3··0···5···0···5 | 51 | ···············3··0···5···0···5 |
| 52 | i4·:·elapsedTime·T'=minimalBetti·J | 52 | i4·:·elapsedTime·T'=minimalBetti·J |
| 53 | ·--·. | 53 | ·--·.28955s·elapsed |
| 54 | ············0··1···2···3···4···5···6···7··8·9 | 54 | ············0··1···2···3···4···5···6···7··8·9 |
| 55 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 | 55 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 56 | ·········0:·1··.···.···.···.···.···.···.··.·. | 56 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 57 | ·········1:·.·36·160·315·288··14···.···.··.·. | 57 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 58 | ·········2:·.··.···.···.··14·288·315·160·36·. | 58 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 59 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 59 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 67, 22 lines modified | Offset 67, 22 lines modified | ||
| 67 | o5·=·total:·.·.·.·.·.·.·.·.·.·. | 67 | o5·=·total:·.·.·.·.·.·.·.·.·.·. |
| 68 | ·········1:·.·.·.·.·.·.·.·.·.·. | 68 | ·········1:·.·.·.·.·.·.·.·.·.·. |
| 69 | ·········2:·.·.·.·.·.·.·.·.·.·. | 69 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 70 | ·········3:·.·.·.·.·.·.·.·.·.·. | 70 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 71 | o5·:·BettiTally | 71 | o5·:·BettiTally |
| 72 | i6·:·elapsedTime·h=carpetBettiTables(6,6); | 72 | i6·:·elapsedTime·h=carpetBettiTables(6,6); |
| 73 | ·--·.003 | 73 | ·--·.00389664s·elapsed |
| 74 | ·--·.0144133s·elapsed | ||
| 75 | ·--·.0985938s·elapsed | ||
| 76 | ·--·1.09889s·elapsed | ||
| 77 | ·--·.305891s·elapsed | ||
| 74 | ·--·.0 | 78 | ·--·.0421898s·elapsed |
| 75 | ·--·.0937147s·elapsed | ||
| 76 | ·--·.929948s·elapsed | ||
| 77 | ·--·.233203s·elapsed | ||
| 78 | ·--·.0500267s·elapsed | ||
| 79 | ·--·.00 | 79 | ·--·.00703313s·elapsed |
| 80 | ·--· | 80 | ·--·4.69855s·elapsed |
| 81 | i7·:·carpetBettiTable(h,7) | 81 | i7·:·carpetBettiTable(h,7) |
| 82 | ············0··1···2···3····4····5····6····7···8···9·10·11 | 82 | ············0··1···2···3····4····5····6····7···8···9·10·11 |
| 83 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 | 83 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 |
| 84 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. | 84 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. |
| 85 | ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··. | 85 | ·········1:·.·55·320·891·1408·1155····.····.···.···.··.··. |
| 86 | ·········2:·.··.···.···.····.····.·1155·1408·891·320·55··. | 86 | ·········2:·.··.···.···.····.····.·1155·1408·891·320·55··. |
| Offset 78, 19 lines modified | Offset 78, 19 lines modified | ||
| 78 | o1·=·(5,·5) | 78 | o1·=·(5,·5) |
| 79 | o1·:·Sequence</code></pre> | 79 | o1·:·Sequence</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·h=carpetBettiTables(a,b) | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·h=carpetBettiTables(a,b) |
| 83 | ·--·.001 | 83 | ·--·.0019681s·elapsed |
| 84 | ·--·.00520524s·elapsed | ||
| 84 | ·--·.0 | 85 | ·--·.0230106s·elapsed |
| 85 | ·--·.01 | 86 | ·--·.0106439s·elapsed |
| 86 | ·--·.008 | 87 | ·--·.00809513s·elapsed |
| 87 | ·--·.00303588s·elapsed | ||
| 88 | ···························0··1···2···3···4···5···6···7··8·9 | 88 | ···························0··1···2···3···4···5···6···7··8·9 |
| 89 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 89 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 90 | ························0:·1··.···.···.···.···.···.···.··.·. | 90 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 91 | ························1:·.·36·160·315·288···.···.···.··.·. | 91 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 92 | ························2:·.··.···.···.···.·288·315·160·36·. | 92 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 93 | ························3:·.··.···.···.···.···.···.···.··.·1 | 93 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 126, 15 lines modified | Offset 126, 15 lines modified | ||
| 126 | ··············ZZ | 126 | ··············ZZ |
| 127 | o4·:·Ideal·of·--[x·..x·,·y·..y·] | 127 | o4·:·Ideal·of·--[x·..x·,·y·..y·] |
| 128 | ···············3··0···5···0···5</code></pre> | 128 | ···············3··0···5···0···5</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T'=minimalBetti·J | 131 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T'=minimalBetti·J |
| 132 | ·--·. | 132 | ·--·.367505s·elapsed |
| 133 | ············0··1···2···3···4···5···6···7··8·9 | 133 | ············0··1···2···3···4···5···6···7··8·9 |
| 134 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 | 134 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 135 | ·········0:·1··.···.···.···.···.···.···.··.·. | 135 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 136 | ·········1:·.·36·160·315·288··14···.···.··.·. | 136 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 137 | ·········2:·.··.···.···.··14·288·315·160·36·. | 137 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 138 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 138 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 150, 22 lines modified | Offset 150, 22 lines modified | ||
| 150 | ·········2:·.·.·.·.·.·.·.·.·.·. | 150 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 151 | ·········3:·.·.·.·.·.·.·.·.·.·. | 151 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 152 | o6·:·BettiTally</code></pre> | 152 | o6·:·BettiTally</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·h=carpetBettiTables(6,6); | 155 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·h=carpetBettiTables(6,6); |
| 156 | ·--·.00 | 156 | ·--·.00418403s·elapsed |
| 157 | ·--·.0149094s·elapsed | ||
| 158 | ·--·.0975395s·elapsed | ||
| 159 | ·--·1.15878s·elapsed | ||
| 160 | ·--·.323041s·elapsed | ||
| 157 | ·--·.0 | 161 | ·--·.0414671s·elapsed |
| 158 | ·--·.0856513s·elapsed | ||
| 159 | ·--·1.03922s·elapsed | ||
| 160 | ·--·.337457s·elapsed | ||
| 161 | ·--·.037078s·elapsed | ||
| 162 | ·--·.005 | 162 | ·--·.00586998s·elapsed |
| 163 | ·--· | 163 | ·--·5.74986s·elapsed</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i8·:·keys·h | 166 | <td>··············<pre><code·class="language-macaulay2">i8·:·keys·h |
| 167 | o8·=·{0,·2,·3,·5} | 167 | o8·=·{0,·2,·3,·5} |
| 168 | o8·:·List</code></pre> | 168 | o8·:·List</code></pre> |
| Offset 22, 19 lines modified | Offset 22, 19 lines modified | ||
| 22 | resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes. | 22 | resulting·data·allow·us·to·compute·the·Betti·tables·for·arbitrary·primes. |
| 23 | i1·:·a=5,b=5 | 23 | i1·:·a=5,b=5 |
| 24 | o1·=·(5,·5) | 24 | o1·=·(5,·5) |
| 25 | o1·:·Sequence | 25 | o1·:·Sequence |
| 26 | i2·:·h=carpetBettiTables(a,b) | 26 | i2·:·h=carpetBettiTables(a,b) |
| 27 | ·--·.001 | 27 | ·--·.0019681s·elapsed |
| 28 | ·--·.00520524s·elapsed | ||
| 28 | ·--·.0 | 29 | ·--·.0230106s·elapsed |
| 29 | ·--·.01 | 30 | ·--·.0106439s·elapsed |
| 30 | ·--·.008 | 31 | ·--·.00809513s·elapsed |
| 31 | ·--·.00303588s·elapsed | ||
| 32 | ···························0··1···2···3···4···5···6···7··8·9 | 32 | ···························0··1···2···3···4···5···6···7··8·9 |
| 33 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 33 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 34 | ························0:·1··.···.···.···.···.···.···.··.·. | 34 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 35 | ························1:·.·36·160·315·288···.···.···.··.·. | 35 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 36 | ························2:·.··.···.···.···.·288·315·160·36·. | 36 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 37 | ························3:·.··.···.···.···.···.···.···.··.·1 | 37 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 64, 15 lines modified | Offset 64, 15 lines modified | ||
| 64 | o3·:·BettiTally | 64 | o3·:·BettiTally |
| 65 | i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); | 65 | i4·:·J=canonicalCarpet(a+b+1,b,Characteristic=>3); |
| 66 | ··············ZZ | 66 | ··············ZZ |
| 67 | o4·:·Ideal·of·--[x·..x·,·y·..y·] | 67 | o4·:·Ideal·of·--[x·..x·,·y·..y·] |
| 68 | ···············3··0···5···0···5 | 68 | ···············3··0···5···0···5 |
| 69 | i5·:·elapsedTime·T'=minimalBetti·J | 69 | i5·:·elapsedTime·T'=minimalBetti·J |
| 70 | ·--·. | 70 | ·--·.367505s·elapsed |
| 71 | ············0··1···2···3···4···5···6···7··8·9 | 71 | ············0··1···2···3···4···5···6···7··8·9 |
| 72 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 | 72 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 73 | ·········0:·1··.···.···.···.···.···.···.··.·. | 73 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 74 | ·········1:·.·36·160·315·288··14···.···.··.·. | 74 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 75 | ·········2:·.··.···.···.··14·288·315·160·36·. | 75 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 76 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 76 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 84, 22 lines modified | Offset 84, 22 lines modified | ||
| 84 | o6·=·total:·.·.·.·.·.·.·.·.·.·. | 84 | o6·=·total:·.·.·.·.·.·.·.·.·.·. |
| 85 | ·········1:·.·.·.·.·.·.·.·.·.·. | 85 | ·········1:·.·.·.·.·.·.·.·.·.·. |
| 86 | ·········2:·.·.·.·.·.·.·.·.·.·. | 86 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 87 | ·········3:·.·.·.·.·.·.·.·.·.·. | 87 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 88 | o6·:·BettiTally | 88 | o6·:·BettiTally |
| 89 | i7·:·elapsedTime·h=carpetBettiTables(6,6); | 89 | i7·:·elapsedTime·h=carpetBettiTables(6,6); |
| 90 | ·--·.00 | 90 | ·--·.00418403s·elapsed |
| 91 | ·--·.0149094s·elapsed | ||
| 92 | ·--·.0975395s·elapsed | ||
| 93 | ·--·1.15878s·elapsed | ||
| 94 | ·--·.323041s·elapsed | ||
| 91 | ·--·.0 | 95 | ·--·.0414671s·elapsed |
| 92 | ·--·.0856513s·elapsed | ||
| 93 | ·--·1.03922s·elapsed | ||
| 94 | ·--·.337457s·elapsed | ||
| 95 | ·--·.037078s·elapsed | ||
| 96 | ·--·.005 | 96 | ·--·.00586998s·elapsed |
| 97 | ·--· | 97 | ·--·5.74986s·elapsed |
| 98 | i8·:·keys·h | 98 | i8·:·keys·h |
| 99 | o8·=·{0,·2,·3,·5} | 99 | o8·=·{0,·2,·3,·5} |
| 100 | o8·:·List | 100 | o8·:·List |
| 101 | i9·:·carpetBettiTable(h,7) | 101 | i9·:·carpetBettiTable(h,7) |
| Offset 78, 42 lines modified | Offset 78, 42 lines modified | ||
| 78 | o1·=·(4,·4) | 78 | o1·=·(4,·4) |
| 79 | o1·:·Sequence</code></pre> | 79 | o1·:·Sequence</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·d=carpetDet(a,b) | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·d=carpetDet(a,b) |
| 83 | ·--·.00519111s·elapsed | ||
| 84 | ·--·.0111231s·elapsed | ||
| 85 | ·--·.0 | 83 | ·--·.0100376s·elapsed |
| 86 | ·--·.0 | 84 | ·--·.0196823s·elapsed |
| 85 | ·--·.000237154s·elapsed | ||
| 86 | ·--·.0001549s·elapsed | ||
| 87 | ·--·.0001088 | 87 | ·--·.000140885s·elapsed |
| 88 | ·--·.0001 | 88 | ·--·.00014934s·elapsed |
| 89 | ·--·.00027706s·elapsed | ||
| 90 | ·--·.000147637s·elapsed | ||
| 91 | ·--·.000252383s·elapsed | ||
| 89 | ·--·.0001 | 92 | ·--·.000172063s·elapsed |
| 93 | ·--·.000360175s·elapsed | ||
| 94 | ·--·.000126728s·elapsed | ||
| 90 | ·--·.0001 | 95 | ·--·.000113192s·elapsed |
| 96 | ·--·.000119975s·elapsed | ||
| 97 | ·--·.000110657s·elapsed | ||
| 98 | ·--·.000108884s·elapsed | ||
| 99 | ·--·.000115797s·elapsed | ||
| 100 | ·--·.000109796s·elapsed | ||
| 101 | ·--·.000160401s·elapsed | ||
| 102 | ·--·.000125956s·elapsed | ||
| 91 | ·--·.0001 | 103 | ·--·.000137568s·elapsed |
| 104 | ·--·.0001334s·elapsed | ||
| 92 | ·--·.00012 | 105 | ·--·.00012811s·elapsed |
| 93 | ·--·.000232581s·elapsed | ||
| 94 | ·--·.000118698s·elapsed | ||
| 95 | ·--·.000102826s·elapsed | ||
| 96 | ·--·.000096897s·elapsed | ||
| 97 | ·--·.000091619s·elapsed | ||
| 98 | ·--·.000089584s·elapsed | ||
| 99 | ·--·.000092769s·elapsed | ||
| 100 | ·--·.000093812s·elapsed | ||
| 101 | ·--·.000102846s·elapsed | ||
| 102 | ·--·.0001 | 106 | ·--·.000122089s·elapsed |
| 103 | ·--·.000120221s·elapsed | ||
| 104 | ·--·.000220613s·elapsed | ||
| 105 | ·--·.00011 | 107 | ·--·.000119464s·elapsed |
| 106 | ·--·.000099771s·elapsed | ||
| 107 | ·--·.000099651s·elapsed | ||
| 108 | ·--·.0001 | 108 | ·--·.000125545s·elapsed |
| 109 | ·--·.0001 | 109 | ·--·.000121839s·elapsed |
| 110 | ·--·.000 | 110 | ·--·.000125735s·elapsed |
| 111 | (number·Of·blocks,·26) | 111 | (number·Of·blocks,·26) |
| 112 | 1 | 112 | 1 |
| 113 | 1 | 113 | 1 |
| 114 | 1 | 114 | 1 |
| 115 | 1 | 115 | 1 |
| 116 | 2 | 116 | 2 |
| 117 | ·2 | 117 | ·2 |
| Offset 20, 42 lines modified | Offset 20, 42 lines modified | ||
| 20 | determinants·and·return·their·product. | 20 | determinants·and·return·their·product. |
| 21 | i1·:·a=4,b=4 | 21 | i1·:·a=4,b=4 |
| 22 | o1·=·(4,·4) | 22 | o1·=·(4,·4) |
| 23 | o1·:·Sequence | 23 | o1·:·Sequence |
| 24 | i2·:·d=carpetDet(a,b) | 24 | i2·:·d=carpetDet(a,b) |
| 25 | ·--·.00519111s·elapsed | ||
| 26 | ·--·.0111231s·elapsed | ||
| 27 | ·--·.0 | 25 | ·--·.0100376s·elapsed |
| 28 | ·--·.0 | 26 | ·--·.0196823s·elapsed |
| 27 | ·--·.000237154s·elapsed | ||
| 28 | ·--·.0001549s·elapsed | ||
| 29 | ·--·.0001088 | 29 | ·--·.000140885s·elapsed |
| 30 | ·--·.0001 | 30 | ·--·.00014934s·elapsed |
| 31 | ·--·.00027706s·elapsed | ||
| 32 | ·--·.000147637s·elapsed | ||
| 33 | ·--·.000252383s·elapsed | ||
| 31 | ·--·.0001 | 34 | ·--·.000172063s·elapsed |
| 35 | ·--·.000360175s·elapsed | ||
| 36 | ·--·.000126728s·elapsed | ||
| 32 | ·--·.0001 | 37 | ·--·.000113192s·elapsed |
| 38 | ·--·.000119975s·elapsed | ||
| 39 | ·--·.000110657s·elapsed | ||
| 40 | ·--·.000108884s·elapsed | ||
| 41 | ·--·.000115797s·elapsed | ||
| 42 | ·--·.000109796s·elapsed | ||
| 43 | ·--·.000160401s·elapsed | ||
| 44 | ·--·.000125956s·elapsed | ||
| 33 | ·--·.0001 | 45 | ·--·.000137568s·elapsed |
| 46 | ·--·.0001334s·elapsed | ||
| 34 | ·--·.00012 | 47 | ·--·.00012811s·elapsed |
| 35 | ·--·.000232581s·elapsed | ||
| 36 | ·--·.000118698s·elapsed | ||
| 37 | ·--·.000102826s·elapsed | ||
| 38 | ·--·.000096897s·elapsed | ||
| 39 | ·--·.000091619s·elapsed | ||
| 40 | ·--·.000089584s·elapsed | ||
| 41 | ·--·.000092769s·elapsed | ||
| 42 | ·--·.000093812s·elapsed | ||
| 43 | ·--·.000102846s·elapsed | ||
| 44 | ·--·.0001 | 48 | ·--·.000122089s·elapsed |
| 45 | ·--·.000120221s·elapsed | ||
| 46 | ·--·.000220613s·elapsed | ||
| 47 | ·--·.00011 | 49 | ·--·.000119464s·elapsed |
| 48 | ·--·.000099771s·elapsed | ||
| 49 | ·--·.000099651s·elapsed | ||
| 50 | ·--·.0001 | 50 | ·--·.000125545s·elapsed |
| 51 | ·--·.0001 | 51 | ·--·.000121839s·elapsed |
| 52 | ·--·.000 | 52 | ·--·.000125735s·elapsed |
| 53 | (number·Of·blocks,·26) | 53 | (number·Of·blocks,·26) |
| 54 | 1 | 54 | 1 |
| 55 | 1 | 55 | 1 |
| 56 | 1 | 56 | 1 |
| 57 | 1 | 57 | 1 |
| 58 | 2 | 58 | 2 |
| 59 | ·2 | 59 | ·2 |
| Offset 86, 20 lines modified | Offset 86, 20 lines modified | ||
| 86 | o1·=·(9,·7) | 86 | o1·=·(9,·7) |
| 87 | o1·:·Sequence</code></pre> | 87 | o1·:·Sequence</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·computeBound·3 | 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·computeBound·3 |
| 91 | ·--·.807772s·elapsed | ||
| 92 | ·--·.6 | 91 | ·--·.761674s·elapsed |
| 92 | ·--·.685197s·elapsed | ||
| 93 | ·--·.425204s·elapsed | ||
| 94 | ·--·.88314s·elapsed | ||
| 93 | ·--·. | 95 | ·--·.505886s·elapsed |
| 94 | ·--·1. | 96 | ·--·1.21429s·elapsed |
| 95 | ·--·.496217s·elapsed | ||
| 96 | ·--·.971603s·elapsed | ||
| 97 | o2·=·6</code></pre> | 97 | o2·=·6</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ········</table> | 99 | ········</table> |
| 100 | ······</div> | 100 | ······</div> |
| 101 | ······<div> | 101 | ······<div> |
| 102 | ········<h2>See·also</h2> | 102 | ········<h2>See·also</h2> |
| Offset 26, 20 lines modified | Offset 26, 20 lines modified | ||
| 26 | classes·mod·k.·We·conjecture·that·c=k^2-k. | 26 | classes·mod·k.·We·conjecture·that·c=k^2-k. |
| 27 | i1·:·(a,b)=computeBound(6,4,3) | 27 | i1·:·(a,b)=computeBound(6,4,3) |
| 28 | o1·=·(9,·7) | 28 | o1·=·(9,·7) |
| 29 | o1·:·Sequence | 29 | o1·:·Sequence |
| 30 | i2·:·computeBound·3 | 30 | i2·:·computeBound·3 |
| 31 | ·--·.807772s·elapsed | ||
| 32 | ·--·.6 | 31 | ·--·.761674s·elapsed |
| 32 | ·--·.685197s·elapsed | ||
| 33 | ·--·.425204s·elapsed | ||
| 34 | ·--·.88314s·elapsed | ||
| 33 | ·--·. | 35 | ·--·.505886s·elapsed |
| 34 | ·--·1. | 36 | ·--·1.21429s·elapsed |
| 35 | ·--·.496217s·elapsed | ||
| 36 | ·--·.971603s·elapsed | ||
| 37 | o2·=·6 | 37 | o2·=·6 |
| 38 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 38 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 39 | ····*·_\x8r_\x8e_\x8l_\x8a_\x8t_\x8i_\x8v_\x8e_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·compute·the·relative·quadrics | 39 | ····*·_\x8r_\x8e_\x8l_\x8a_\x8t_\x8i_\x8v_\x8e_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·compute·the·relative·quadrics |
| 40 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8eB\x8Bo\x8ou\x8un\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 40 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8co\x8om\x8mp\x8pu\x8ut\x8te\x8eB\x8Bo\x8ou\x8un\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 41 | ····*·computeBound(ZZ) | 41 | ····*·computeBound(ZZ) |
| 42 | ····*·computeBound(ZZ,ZZ,ZZ) | 42 | ····*·computeBound(ZZ,ZZ,ZZ) |
| Offset 87, 19 lines modified | Offset 87, 19 lines modified | ||
| 87 | o2·=·(-1,·5) | 87 | o2·=·(-1,·5) |
| 88 | o2·:·Sequence</code></pre> | 88 | o2·:·Sequence</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·h=degenerateK3BettiTables(a,b,e) | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·h=degenerateK3BettiTables(a,b,e) |
| 92 | ·--·.0149255s·elapsed | ||
| 93 | ·--·.0156362s·elapsed | ||
| 94 | ·--·.046755s·elapsed | ||
| 92 | ·--·.00 | 95 | ·--·.00770785s·elapsed |
| 93 | ·--·.00491676s·elapsed | ||
| 94 | ·--·.0196774s·elapsed | ||
| 95 | ·--·.00729439s·elapsed | ||
| 96 | ·--·.00 | 96 | ·--·.0031691s·elapsed |
| 97 | ···························0··1···2···3···4···5···6···7··8·9 | 97 | ···························0··1···2···3···4···5···6···7··8·9 |
| 98 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 98 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 99 | ························0:·1··.···.···.···.···.···.···.··.·. | 99 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 100 | ························1:·.·36·160·315·288···.···.···.··.·. | 100 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 101 | ························2:·.··.···.···.···.·288·315·160·36·. | 101 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 102 | ························3:·.··.···.···.···.···.···.···.··.·1 | 102 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 129 | o4·=·{0,·2,·3,·5} | 129 | o4·=·{0,·2,·3,·5} |
| 130 | o4·:·List</code></pre> | 130 | o4·:·List</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) | 133 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) |
| 134 | ·--·. | 134 | ·--·.464921s·elapsed |
| 135 | ············0··1···2···3···4···5···6···7··8·9 | 135 | ············0··1···2···3···4···5···6···7··8·9 |
| 136 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 | 136 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 |
| 137 | ·········0:·1··.···.···.···.···.···.···.··.·. | 137 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 138 | ·········1:·.·36·160·322·336·140··48···7··.·. | 138 | ·········1:·.·36·160·322·336·140··48···7··.·. |
| 139 | ·········2:·.··.···7··48·140·336·322·160·36·. | 139 | ·········2:·.··.···7··48·140·336·322·160·36·. |
| 140 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 140 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 165, 19 lines modified | Offset 165, 19 lines modified | ||
| 165 | o7·=·(-1,·25) | 165 | o7·=·(-1,·25) |
| 166 | o7·:·Sequence</code></pre> | 166 | o7·:·Sequence</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i8·:·h=degenerateK3BettiTables(a,b,e) | 169 | <td>··············<pre><code·class="language-macaulay2">i8·:·h=degenerateK3BettiTables(a,b,e) |
| 170 | ·--·.0022681s·elapsed | ||
| 170 | ·--·.00 | 171 | ·--·.00597535s·elapsed |
| 172 | ·--·.0387189s·elapsed | ||
| 173 | ·--·.0135303s·elapsed | ||
| 171 | ·--·.0051 | 174 | ·--·.00510383s·elapsed |
| 172 | ·--·.0192936s·elapsed | ||
| 173 | ·--·.0121788s·elapsed | ||
| 174 | ·--·.00701235s·elapsed | ||
| 175 | ···························0··1···2···3···4···5···6···7··8·9 | 175 | ···························0··1···2···3···4···5···6···7··8·9 |
| 176 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} | 176 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} |
| 177 | ························0:·1··.···.···.···.···.···.···.··.·. | 177 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 178 | ························1:·.·36·160·315·288···.···.···.··.·. | 178 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 179 | ························2:·.··.···.···.···.·288·315·160·36·. | 179 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 180 | ························3:·.··.···.···.···.···.···.···.··.·1 | 180 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 28, 19 lines modified | Offset 28, 19 lines modified | ||
| 28 | o1·:·Sequence | 28 | o1·:·Sequence |
| 29 | i2·:·e=(-1,5) | 29 | i2·:·e=(-1,5) |
| 30 | o2·=·(-1,·5) | 30 | o2·=·(-1,·5) |
| 31 | o2·:·Sequence | 31 | o2·:·Sequence |
| 32 | i3·:·h=degenerateK3BettiTables(a,b,e) | 32 | i3·:·h=degenerateK3BettiTables(a,b,e) |
| 33 | ·--·.0149255s·elapsed | ||
| 34 | ·--·.0156362s·elapsed | ||
| 35 | ·--·.046755s·elapsed | ||
| 33 | ·--·.00 | 36 | ·--·.00770785s·elapsed |
| 34 | ·--·.00491676s·elapsed | ||
| 35 | ·--·.0196774s·elapsed | ||
| 36 | ·--·.00729439s·elapsed | ||
| 37 | ·--·.00 | 37 | ·--·.0031691s·elapsed |
| 38 | ···························0··1···2···3···4···5···6···7··8·9 | 38 | ···························0··1···2···3···4···5···6···7··8·9 |
| 39 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 39 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 40 | ························0:·1··.···.···.···.···.···.···.··.·. | 40 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 41 | ························1:·.·36·160·315·288···.···.···.··.·. | 41 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 42 | ························2:·.··.···.···.···.·288·315·160·36·. | 42 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 43 | ························3:·.··.···.···.···.···.···.···.··.·1 | 43 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 66, 15 lines modified | Offset 66, 15 lines modified | ||
| 66 | o3·:·HashTable | 66 | o3·:·HashTable |
| 67 | i4·:·keys·h | 67 | i4·:·keys·h |
| 68 | o4·=·{0,·2,·3,·5} | 68 | o4·=·{0,·2,·3,·5} |
| 69 | o4·:·List | 69 | o4·:·List |
| 70 | i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) | 70 | i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) |
| 71 | ·--·. | 71 | ·--·.464921s·elapsed |
| 72 | ············0··1···2···3···4···5···6···7··8·9 | 72 | ············0··1···2···3···4···5···6···7··8·9 |
| 73 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 | 73 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 |
| 74 | ·········0:·1··.···.···.···.···.···.···.··.·. | 74 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 75 | ·········1:·.·36·160·322·336·140··48···7··.·. | 75 | ·········1:·.·36·160·322·336·140··48···7··.·. |
| 76 | ·········2:·.··.···7··48·140·336·322·160·36·. | 76 | ·········2:·.··.···7··48·140·336·322·160·36·. |
| 77 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 77 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 95, 19 lines modified | Offset 95, 19 lines modified | ||
| 95 | these·mistakes. | 95 | these·mistakes. |
| 96 | i7·:·e=(-1,5^2) | 96 | i7·:·e=(-1,5^2) |
| 97 | o7·=·(-1,·25) | 97 | o7·=·(-1,·25) |
| 98 | o7·:·Sequence | 98 | o7·:·Sequence |
| 99 | i8·:·h=degenerateK3BettiTables(a,b,e) | 99 | i8·:·h=degenerateK3BettiTables(a,b,e) |
| 100 | ·--·.0022681s·elapsed | ||
| 100 | ·--·.00 | 101 | ·--·.00597535s·elapsed |
| 102 | ·--·.0387189s·elapsed | ||
| 103 | ·--·.0135303s·elapsed | ||
| 101 | ·--·.0051 | 104 | ·--·.00510383s·elapsed |
| 102 | ·--·.0192936s·elapsed | ||
| 103 | ·--·.0121788s·elapsed | ||
| 104 | ·--·.00701235s·elapsed | ||
| 105 | ···························0··1···2···3···4···5···6···7··8·9 | 105 | ···························0··1···2···3···4···5···6···7··8·9 |
| 106 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} | 106 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} |
| 107 | ························0:·1··.···.···.···.···.···.···.··.·. | 107 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 108 | ························1:·.·36·160·315·288···.···.···.··.·. | 108 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 109 | ························2:·.··.···.···.···.·288·315·160·36·. | 109 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 110 | ························3:·.··.···.···.···.···.···.···.··.·1 | 110 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 76, 33 lines modified | Offset 76, 33 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·a=4 | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·a=4 |
| 78 | o1·=·4</code></pre> | 78 | o1·=·4</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·(d1,d2)=resonanceDet(a) | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·(d1,d2)=resonanceDet(a) |
| 82 | ·--·.0131232s·elapsed | ||
| 82 | ·--·.0 | 83 | ·--·.000049603s·elapsed |
| 84 | ·--·.000071534s·elapsed | ||
| 83 | ·--·.0000 | 85 | ·--·.000055865s·elapsed |
| 84 | ·--·.000064188s·elapsed | ||
| 85 | ·--·.000051828s·elapsed | ||
| 86 | ·--·.00005899s·elapsed | ||
| 87 | ·--·.00007 | 86 | ·--·.000070753s·elapsed |
| 88 | ·--·.00006 | 87 | ·--·.000069961s·elapsed |
| 89 | ·--·.0000 | 88 | ·--·.000068197s·elapsed |
| 90 | ·--·.0 | 89 | ·--·.000018855s·elapsed |
| 90 | ·--·.0500783s·elapsed | ||
| 91 | ·--·.00019 | 91 | ·--·.00019729s·elapsed |
| 92 | ·--·.000115997s·elapsed | ||
| 93 | ·--·.000098404s·elapsed | ||
| 94 | ·--·.000088245s·elapsed | ||
| 92 | ·--·.00008005s·elapsed | 95 | ·--·.000083005s·elapsed |
| 96 | ·--·.0001282s·elapsed | ||
| 93 | ·--·.0000615 | 97 | ·--·.000061556s·elapsed |
| 94 | ·--·.0000 | 98 | ·--·.000021s·elapsed |
| 95 | ·--·.000061394s·elapsed | ||
| 96 | ·--·.000048934s·elapsed | ||
| 97 | ·--·.0000 | 99 | ·--·.000057959s·elapsed |
| 98 | ·--·.0000 | 100 | ·--·.000021441s·elapsed |
| 99 | ·--·.000058138s·elapsed | ||
| 100 | ·--·.000016675s·elapsed | ||
| 101 | (number·of·blocks=·,·18) | 101 | (number·of·blocks=·,·18) |
| 102 | (size·of·the·matrices,·Tally{1·=>·4}) | 102 | (size·of·the·matrices,·Tally{1·=>·4}) |
| 103 | ·····························2·=>·6 | 103 | ·····························2·=>·6 |
| 104 | ·····························3·=>·2 | 104 | ·····························3·=>·2 |
| 105 | ·····························4·=>·6 | 105 | ·····························4·=>·6 |
| 106 | ·······0·1 | 106 | ·······0·1 |
| 107 | total:·1·1 | 107 | total:·1·1 |
| Offset 20, 33 lines modified | Offset 20, 33 lines modified | ||
| 20 | grading.·Viewed·as·a·resolution·over·QQ(e_1,e_2),·this·resolution·is·non- | 20 | grading.·Viewed·as·a·resolution·over·QQ(e_1,e_2),·this·resolution·is·non- |
| 21 | minimal·and·carries·further·gradings.·We·decompose·the·crucial·map·of·the·a-th | 21 | minimal·and·carries·further·gradings.·We·decompose·the·crucial·map·of·the·a-th |
| 22 | strand·into·blocks,·compute·their·determinants,·and·factor·the·product. | 22 | strand·into·blocks,·compute·their·determinants,·and·factor·the·product. |
| 23 | i1·:·a=4 | 23 | i1·:·a=4 |
| 24 | o1·=·4 | 24 | o1·=·4 |
| 25 | i2·:·(d1,d2)=resonanceDet(a) | 25 | i2·:·(d1,d2)=resonanceDet(a) |
| 26 | ·--·.0131232s·elapsed | ||
| 26 | ·--·.0 | 27 | ·--·.000049603s·elapsed |
| 28 | ·--·.000071534s·elapsed | ||
| 27 | ·--·.0000 | 29 | ·--·.000055865s·elapsed |
| 28 | ·--·.000064188s·elapsed | ||
| 29 | ·--·.000051828s·elapsed | ||
| 30 | ·--·.00005899s·elapsed | ||
| 31 | ·--·.00007 | 30 | ·--·.000070753s·elapsed |
| 32 | ·--·.00006 | 31 | ·--·.000069961s·elapsed |
| 33 | ·--·.0000 | 32 | ·--·.000068197s·elapsed |
| 34 | ·--·.0 | 33 | ·--·.000018855s·elapsed |
| 34 | ·--·.0500783s·elapsed | ||
| 35 | ·--·.00019 | 35 | ·--·.00019729s·elapsed |
| 36 | ·--·.000115997s·elapsed | ||
| 37 | ·--·.000098404s·elapsed | ||
| 38 | ·--·.000088245s·elapsed | ||
| 36 | ·--·.00008005s·elapsed | 39 | ·--·.000083005s·elapsed |
| 40 | ·--·.0001282s·elapsed | ||
| 37 | ·--·.0000615 | 41 | ·--·.000061556s·elapsed |
| 38 | ·--·.0000 | 42 | ·--·.000021s·elapsed |
| 39 | ·--·.000061394s·elapsed | ||
| 40 | ·--·.000048934s·elapsed | ||
| 41 | ·--·.0000 | 43 | ·--·.000057959s·elapsed |
| 42 | ·--·.0000 | 44 | ·--·.000021441s·elapsed |
| 43 | ·--·.000058138s·elapsed | ||
| 44 | ·--·.000016675s·elapsed | ||
| 45 | (number·of·blocks=·,·18) | 45 | (number·of·blocks=·,·18) |
| 46 | (size·of·the·matrices,·Tally{1·=>·4}) | 46 | (size·of·the·matrices,·Tally{1·=>·4}) |
| 47 | ·····························2·=>·6 | 47 | ·····························2·=>·6 |
| 48 | ·····························3·=>·2 | 48 | ·····························3·=>·2 |
| 49 | ·····························4·=>·6 | 49 | ·····························4·=>·6 |
| 50 | ·······0·1 | 50 | ·······0·1 |
| 51 | total:·1·1 | 51 | total:·1·1 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=38 | 7 | #:len=38 |
| 8 | cHJvamVjdChWaXNpYmxlTGlzdCxFbWJlZGRlZEszc3VyZmFjZSk= | 8 | cHJvamVjdChWaXNpYmxlTGlzdCxFbWJlZGRlZEszc3VyZmFjZSk= |
| 9 | #:len=279 | 9 | #:len=279 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTU5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTU5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=27 | 7 | #:len=27 |
| 8 | a3JvbmVja2VyTm9ybWFsRm9ybShNYXRyaXgp | 8 | a3JvbmVja2VyTm9ybWFsRm9ybShNYXRyaXgp |
| 9 | #:len=279 | 9 | #:len=279 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTA5Nywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTA5Nywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoa3JvbmVja2VyTm9ybWFsRm9ybSxNYXRyaXgpLCJr | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoa3JvbmVja2VyTm9ybWFsRm9ybSxNYXRyaXgpLCJr |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=37 | 7 | #:len=37 |
| 8 | a3VzdGluTWlsbGVyQ29tcGxleCguLi4sVmVyYm9zZT0+Li4uKQ== | 8 | a3VzdGluTWlsbGVyQ29tcGxleCguLi4sVmVyYm9zZT0+Li4uKQ== |
| 9 | #:len=577 | 9 | #:len=577 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3B0aW9uIHRvIHByaW50IGludGVybWVk | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3B0aW9uIHRvIHByaW50IGludGVybWVk |
| 11 | aWF0ZSBkYXRhIiwgRGVzY3JpcHRpb24gPT4gMTooRElWe1BBUkF7VE97bmV3IERvY3VtZW50VGFn | 11 | aWF0ZSBkYXRhIiwgRGVzY3JpcHRpb24gPT4gMTooRElWe1BBUkF7VE97bmV3IERvY3VtZW50VGFn |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=6 | 7 | #:len=6 |
| 8 | UmVhbFhE | 8 | UmVhbFhE |
| 9 | #:len=499 | 9 | #:len=499 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidXNlIGV4dGVuZGVkIGV4cG9uZW50IHJl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidXNlIGV4dGVuZGVkIGV4cG9uZW50IHJl |
| 11 | YWwgbnVtYmVycyIsIERlc2NyaXB0aW9uID0+IChUVHsiUmVhbFhEIn0sIiAtLSBhIHN0cmF0ZWd5 | 11 | YWwgbnVtYmVycyIsIERlc2NyaXB0aW9uID0+IChUVHsiUmVhbFhEIn0sIiAtLSBhIHN0cmF0ZWd5 |
| Offset 7, 55 lines modified | Offset 7, 55 lines modified | ||
| 7 | i2·:·m·=·syz·m1; | 7 | i2·:·m·=·syz·m1; |
| 8 | ··············50·······47 | 8 | ··············50·······47 |
| 9 | o2·:·Matrix·ZZ···<--·ZZ | 9 | o2·:·Matrix·ZZ···<--·ZZ |
| 10 | i3·:·time·LLL·m; | 10 | i3·:·time·LLL·m; |
| 11 | ·--·used·0.006 | 11 | ·--·used·0.00685322s·(cpu);·0.00723181s·(thread);·0s·(gc) |
| 12 | ··············50·······47 | 12 | ··············50·······47 |
| 13 | o3·:·Matrix·ZZ···<--·ZZ | 13 | o3·:·Matrix·ZZ···<--·ZZ |
| 14 | i4·:·time·LLL(m,·Strategy=>CohenEngine); | 14 | i4·:·time·LLL(m,·Strategy=>CohenEngine); |
| 15 | ·--·used·0.02 | 15 | ·--·used·0.0229539s·(cpu);·0.0240208s·(thread);·0s·(gc) |
| 16 | ··············50·······47 | 16 | ··············50·······47 |
| 17 | o4·:·Matrix·ZZ···<--·ZZ | 17 | o4·:·Matrix·ZZ···<--·ZZ |
| 18 | i5·:·time·LLL(m,·Strategy=>CohenTopLevel); | 18 | i5·:·time·LLL(m,·Strategy=>CohenTopLevel); |
| 19 | ·--·used·0.0 | 19 | ·--·used·0.103655s·(cpu);·0.103552s·(thread);·0s·(gc) |
| 20 | ··············50·······47 | 20 | ··············50·······47 |
| 21 | o5·:·Matrix·ZZ···<--·ZZ | 21 | o5·:·Matrix·ZZ···<--·ZZ |
| 22 | i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); | 22 | i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); |
| 23 | ·--·used·0.0 | 23 | ·--·used·0.0101428s·(cpu);·0.0110462s·(thread);·0s·(gc) |
| 24 | ··············50·······47 | 24 | ··············50·······47 |
| 25 | o6·:·Matrix·ZZ···<--·ZZ | 25 | o6·:·Matrix·ZZ···<--·ZZ |
| 26 | i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); | 26 | i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); |
| 27 | ·--·used·0.0 | 27 | ·--·used·0.050579s·(cpu);·0.0511744s·(thread);·0s·(gc) |
| 28 | ··············50·······47 | 28 | ··············50·······47 |
| 29 | o7·:·Matrix·ZZ···<--·ZZ | 29 | o7·:·Matrix·ZZ···<--·ZZ |
| 30 | i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); | 30 | i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); |
| 31 | ·--·used·0.05 | 31 | ·--·used·0.0545178s·(cpu);·0.0559211s·(thread);·0s·(gc) |
| 32 | ··············50·······47 | 32 | ··············50·······47 |
| 33 | o8·:·Matrix·ZZ···<--·ZZ | 33 | o8·:·Matrix·ZZ···<--·ZZ |
| 34 | i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); | 34 | i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); |
| 35 | ·--·used·0.2 | 35 | ·--·used·0.289721s·(cpu);·0.290878s·(thread);·0s·(gc) |
| 36 | ··············50·······47 | 36 | ··············50·······47 |
| 37 | o9·:·Matrix·ZZ···<--·ZZ | 37 | o9·:·Matrix·ZZ···<--·ZZ |
| 38 | i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); | 38 | i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); |
| 39 | ·--·used·0.12 | 39 | ·--·used·0.129151s·(cpu);·0.130841s·(thread);·0s·(gc) |
| 40 | ···············50·······47 | 40 | ···············50·······47 |
| 41 | o10·:·Matrix·ZZ···<--·ZZ | 41 | o10·:·Matrix·ZZ···<--·ZZ |
| 42 | i11·:· | 42 | i11·:· |
| Offset 162, 64 lines modified | Offset 162, 64 lines modified | ||
| 162 | <td>··············<pre><code·class="language-macaulay2">i2·:·m·=·syz·m1; | 162 | <td>··············<pre><code·class="language-macaulay2">i2·:·m·=·syz·m1; |
| 163 | ··············50·······47 | 163 | ··············50·······47 |
| 164 | o2·:·Matrix·ZZ···<--·ZZ</code></pre> | 164 | o2·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·LLL·m; | 167 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·LLL·m; |
| 168 | ·--·used·0.006 | 168 | ·--·used·0.00685322s·(cpu);·0.00723181s·(thread);·0s·(gc) |
| 169 | ··············50·······47 | 169 | ··············50·······47 |
| 170 | o3·:·Matrix·ZZ···<--·ZZ</code></pre> | 170 | o3·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 171 | </td>··········</tr> | 171 | </td>··········</tr> |
| 172 | ··········<tr> | 172 | ··········<tr> |
| 173 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·LLL(m,·Strategy=>CohenEngine); | 173 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·LLL(m,·Strategy=>CohenEngine); |
| 174 | ·--·used·0.02 | 174 | ·--·used·0.0229539s·(cpu);·0.0240208s·(thread);·0s·(gc) |
| 175 | ··············50·······47 | 175 | ··············50·······47 |
| 176 | o4·:·Matrix·ZZ···<--·ZZ</code></pre> | 176 | o4·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ··········<tr> | 178 | ··········<tr> |
| 179 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·LLL(m,·Strategy=>CohenTopLevel); | 179 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·LLL(m,·Strategy=>CohenTopLevel); |
| 180 | ·--·used·0.0 | 180 | ·--·used·0.103655s·(cpu);·0.103552s·(thread);·0s·(gc) |
| 181 | ··············50·······47 | 181 | ··············50·······47 |
| 182 | o5·:·Matrix·ZZ···<--·ZZ</code></pre> | 182 | o5·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 183 | </td>··········</tr> | 183 | </td>··········</tr> |
| 184 | ··········<tr> | 184 | ··········<tr> |
| 185 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); | 185 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); |
| 186 | ·--·used·0.0 | 186 | ·--·used·0.0101428s·(cpu);·0.0110462s·(thread);·0s·(gc) |
| 187 | ··············50·······47 | 187 | ··············50·······47 |
| 188 | o6·:·Matrix·ZZ···<--·ZZ</code></pre> | 188 | o6·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); | 191 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); |
| 192 | ·--·used·0.0 | 192 | ·--·used·0.050579s·(cpu);·0.0511744s·(thread);·0s·(gc) |
| 193 | ··············50·······47 | 193 | ··············50·······47 |
| 194 | o7·:·Matrix·ZZ···<--·ZZ</code></pre> | 194 | o7·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); | 197 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); |
| 198 | ·--·used·0.05 | 198 | ·--·used·0.0545178s·(cpu);·0.0559211s·(thread);·0s·(gc) |
| 199 | ··············50·······47 | 199 | ··············50·······47 |
| 200 | o8·:·Matrix·ZZ···<--·ZZ</code></pre> | 200 | o8·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 201 | </td>··········</tr> | 201 | </td>··········</tr> |
| 202 | ··········<tr> | 202 | ··········<tr> |
| 203 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); | 203 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); |
| 204 | ·--·used·0.2 | 204 | ·--·used·0.289721s·(cpu);·0.290878s·(thread);·0s·(gc) |
| 205 | ··············50·······47 | 205 | ··············50·······47 |
| 206 | o9·:·Matrix·ZZ···<--·ZZ</code></pre> | 206 | o9·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 207 | </td>··········</tr> | 207 | </td>··········</tr> |
| 208 | ··········<tr> | 208 | ··········<tr> |
| 209 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); | 209 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); |
| 210 | ·--·used·0.12 | 210 | ·--·used·0.129151s·(cpu);·0.130841s·(thread);·0s·(gc) |
| 211 | ···············50·······47 | 211 | ···············50·······47 |
| 212 | o10·:·Matrix·ZZ···<--·ZZ</code></pre> | 212 | o10·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ········</table> | 214 | ········</table> |
| 215 | ······</div> | 215 | ······</div> |
| 216 | ······<div> | 216 | ······<div> |
| Offset 116, 50 lines modified | Offset 116, 50 lines modified | ||
| 116 | ··············50·······50 | 116 | ··············50·······50 |
| 117 | o1·:·Matrix·ZZ···<--·ZZ | 117 | o1·:·Matrix·ZZ···<--·ZZ |
| 118 | i2·:·m·=·syz·m1; | 118 | i2·:·m·=·syz·m1; |
| 119 | ··············50·······47 | 119 | ··············50·······47 |
| 120 | o2·:·Matrix·ZZ···<--·ZZ | 120 | o2·:·Matrix·ZZ···<--·ZZ |
| 121 | i3·:·time·LLL·m; | 121 | i3·:·time·LLL·m; |
| 122 | ·--·used·0.006 | 122 | ·--·used·0.00685322s·(cpu);·0.00723181s·(thread);·0s·(gc) |
| 123 | ··············50·······47 | 123 | ··············50·······47 |
| 124 | o3·:·Matrix·ZZ···<--·ZZ | 124 | o3·:·Matrix·ZZ···<--·ZZ |
| 125 | i4·:·time·LLL(m,·Strategy=>CohenEngine); | 125 | i4·:·time·LLL(m,·Strategy=>CohenEngine); |
| 126 | ·--·used·0.02 | 126 | ·--·used·0.0229539s·(cpu);·0.0240208s·(thread);·0s·(gc) |
| 127 | ··············50·······47 | 127 | ··············50·······47 |
| 128 | o4·:·Matrix·ZZ···<--·ZZ | 128 | o4·:·Matrix·ZZ···<--·ZZ |
| 129 | i5·:·time·LLL(m,·Strategy=>CohenTopLevel); | 129 | i5·:·time·LLL(m,·Strategy=>CohenTopLevel); |
| 130 | ·--·used·0.0 | 130 | ·--·used·0.103655s·(cpu);·0.103552s·(thread);·0s·(gc) |
| 131 | ··············50·······47 | 131 | ··············50·······47 |
| 132 | o5·:·Matrix·ZZ···<--·ZZ | 132 | o5·:·Matrix·ZZ···<--·ZZ |
| 133 | i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); | 133 | i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); |
| 134 | ·--·used·0.0 | 134 | ·--·used·0.0101428s·(cpu);·0.0110462s·(thread);·0s·(gc) |
| 135 | ··············50·······47 | 135 | ··············50·······47 |
| 136 | o6·:·Matrix·ZZ···<--·ZZ | 136 | o6·:·Matrix·ZZ···<--·ZZ |
| 137 | i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); | 137 | i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); |
| 138 | ·--·used·0.0 | 138 | ·--·used·0.050579s·(cpu);·0.0511744s·(thread);·0s·(gc) |
| 139 | ··············50·······47 | 139 | ··············50·······47 |
| 140 | o7·:·Matrix·ZZ···<--·ZZ | 140 | o7·:·Matrix·ZZ···<--·ZZ |
| 141 | i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); | 141 | i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); |
| 142 | ·--·used·0.05 | 142 | ·--·used·0.0545178s·(cpu);·0.0559211s·(thread);·0s·(gc) |
| 143 | ··············50·······47 | 143 | ··············50·······47 |
| 144 | o8·:·Matrix·ZZ···<--·ZZ | 144 | o8·:·Matrix·ZZ···<--·ZZ |
| 145 | i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); | 145 | i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); |
| 146 | ·--·used·0.2 | 146 | ·--·used·0.289721s·(cpu);·0.290878s·(thread);·0s·(gc) |
| 147 | ··············50·······47 | 147 | ··············50·······47 |
| 148 | o9·:·Matrix·ZZ···<--·ZZ | 148 | o9·:·Matrix·ZZ···<--·ZZ |
| 149 | i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); | 149 | i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); |
| 150 | ·--·used·0.12 | 150 | ·--·used·0.129151s·(cpu);·0.130841s·(thread);·0s·(gc) |
| 151 | ···············50·······47 | 151 | ···············50·······47 |
| 152 | o10·:·Matrix·ZZ···<--·ZZ | 152 | o10·:·Matrix·ZZ···<--·ZZ |
| 153 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 153 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 154 | ····*·Default·value:·_\x8N_\x8T_\x8L | 154 | ····*·Default·value:·_\x8N_\x8T_\x8L |
| 155 | ····*·Function:·_\x8L_\x8L_\x8L·--·compute·an·LLL·basis | 155 | ····*·Function:·_\x8L_\x8L_\x8L·--·compute·an·LLL·basis |
| 156 | ····*·Option·key:·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument | 156 | ····*·Option·key:·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=28 | 7 | #:len=28 |
| 8 | YXJlSXNvbW9ycGhpYyhNYXRyaXgsTWF0cml4KQ== | 8 | YXJlSXNvbW9ycGhpYyhNYXRyaXgsTWF0cml4KQ== |
| 9 | #:len=289 | 9 | #:len=289 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODg4LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODg4LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhcmVJc29tb3JwaGljLE1hdHJpeCxNYXRyaXgpLCJh | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhcmVJc29tb3JwaGljLE1hdHJpeCxNYXRyaXgpLCJh |
| Offset 16, 14 lines modified | Offset 16, 14 lines modified | ||
| 16 | ··············3·······8 | 16 | ··············3·······8 |
| 17 | o4·:·Matrix·ZZ··<--·ZZ | 17 | o4·:·Matrix·ZZ··<--·ZZ |
| 18 | i5·:·P·=·convexHull(M); | 18 | i5·:·P·=·convexHull(M); |
| 19 | i6·:·time·areIsomorphic(P,P); | 19 | i6·:·time·areIsomorphic(P,P); |
| 20 | ·--·used· | 20 | ·--·used·4.98851s·(cpu);·0.968255s·(thread);·0s·(gc) |
| 21 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); | 21 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); |
| 22 | ·--·used·2. | 22 | ·--·used·2.63173s·(cpu);·0.561967s·(thread);·0s·(gc) |
| 23 | i8·:· | 23 | i8·:· |
| 24 | ····· | 24 | ····· |
| Offset 114, 19 lines modified | Offset 114, 19 lines modified | ||
| 114 | o4·:·Matrix·ZZ··<--·ZZ</code></pre> | 114 | o4·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i5·:·P·=·convexHull(M);</code></pre> | 117 | <td>··············<pre><code·class="language-macaulay2">i5·:·P·=·convexHull(M);</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·areIsomorphic(P,P); | 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·areIsomorphic(P,P); |
| 121 | ·--·used· | 121 | ·--·used·4.98851s·(cpu);·0.968255s·(thread);·0s·(gc)</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·areIsomorphic(P,P,smoothTest=>false); | 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·areIsomorphic(P,P,smoothTest=>false); |
| 125 | ·--·used·2. | 125 | ·--·used·2.63173s·(cpu);·0.561967s·(thread);·0s·(gc)</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ········</table> | 127 | ········</table> |
| 128 | ······</div> | 128 | ······</div> |
| 129 | ······<div·class="waystouse"> | 129 | ······<div·class="waystouse"> |
| 130 | ········<h2>Ways·to·use·<span·class="tt">areIsomorphic</span>:</h2> | 130 | ········<h2>Ways·to·use·<span·class="tt">areIsomorphic</span>:</h2> |
| 131 | ········<ul> | 131 | ········<ul> |
| 132 | ··········<li> | 132 | ··········<li> |
| Offset 36, 15 lines modified | Offset 36, 15 lines modified | ||
| 36 | ·····|·0·0·1·0·1·0·1·1·| | 36 | ·····|·0·0·1·0·1·0·1·1·| |
| 37 | ·····|·0·0·0·1·0·1·1·1·| | 37 | ·····|·0·0·0·1·0·1·1·1·| |
| 38 | ··············3·······8 | 38 | ··············3·······8 |
| 39 | o4·:·Matrix·ZZ··<--·ZZ | 39 | o4·:·Matrix·ZZ··<--·ZZ |
| 40 | i5·:·P·=·convexHull(M); | 40 | i5·:·P·=·convexHull(M); |
| 41 | i6·:·time·areIsomorphic(P,P); | 41 | i6·:·time·areIsomorphic(P,P); |
| 42 | ·--·used· | 42 | ·--·used·4.98851s·(cpu);·0.968255s·(thread);·0s·(gc) |
| 43 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); | 43 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); |
| 44 | ·--·used·2. | 44 | ·--·used·2.63173s·(cpu);·0.561967s·(thread);·0s·(gc) |
| 45 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ar\x8re\x8eI\x8Is\x8so\x8om\x8mo\x8or\x8rp\x8ph\x8hi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8* | 45 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·a\x8ar\x8re\x8eI\x8Is\x8so\x8om\x8mo\x8or\x8rp\x8ph\x8hi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 46 | ····*·areIsomorphic(Matrix,Matrix) | 46 | ····*·areIsomorphic(Matrix,Matrix) |
| 47 | ····*·areIsomorphic(Polyhedron,Polyhedron) | 47 | ····*·areIsomorphic(Polyhedron,Polyhedron) |
| 48 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 48 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 49 | The·object·_\x8a_\x8r_\x8e_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 49 | The·object·_\x8a_\x8r_\x8e_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=9 | 7 | #:len=9 |
| 8 | TGV4SWRlYWxz | 8 | TGV4SWRlYWxz |
| 9 | #:len=470 | 9 | #:len=470 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZvciB3b3JraW5nIHdp | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZvciB3b3JraW5nIHdp |
| 11 | dGggbGV4IGlkZWFscyIsIERlc2NyaXB0aW9uID0+IDE6KERJVntQQVJBe1RFWHsiIixFTXsiTGV4 | 11 | dGggbGV4IGlkZWFscyIsIERlc2NyaXB0aW9uID0+IDE6KERJVntQQVJBe1RFWHsiIixFTXsiTGV4 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | TGljZW5zZXM= | 8 | TGljZW5zZXM= |
| 9 | #:len=349 | 9 | #:len=349 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtEZXNjcmlwdGlvbiA9PiAxOihESVZ7UEFSQXtURVh7IlRoaXMg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtEZXNjcmlwdGlvbiA9PiAxOihESVZ7UEFSQXtURVh7IlRoaXMg |
| 11 | cGFja2FnZSBleGFtaW5lcyB0aGUgdmVyc2lvbiBudW1iZXIgb2YgdGhlIHZhcmlvdXMgcGFja2Fn | 11 | cGFja2FnZSBleGFtaW5lcyB0aGUgdmVyc2lvbiBudW1iZXIgb2YgdGhlIHZhcmlvdXMgcGFja2Fn |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | TGllQWxnZWJyYU1vZHVsZSA9PSBaWg== | 8 | TGllQWxnZWJyYU1vZHVsZSA9PSBaWg== |
| 9 | #:len=205 | 9 | #:len=205 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU2MywgInVuZG9jdW1lbnRlZCIgPT4g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU2MywgInVuZG9jdW1lbnRlZCIgPT4g |
| 11 | dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ltYm9s | 11 | dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ltYm9s |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | bGluZWFyVHJ1bmNhdGlvbnNCb3VuZA== | 8 | bGluZWFyVHJ1bmNhdGlvbnNCb3VuZA== |
| 9 | #:len=2355 | 9 | #:len=2355 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYm91bmRzIHRoZSByZWdpb24gd2hlcmUg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYm91bmRzIHRoZSByZWdpb24gd2hlcmUg |
| 11 | dHJ1bmNhdGlvbnMgb2YgYSBtb2R1bGUgaGF2ZSBsaW5lYXIgcmVzb2x1dGlvbnMiLCAibGluZW51 | 11 | dHJ1bmNhdGlvbnMgb2YgYSBtb2R1bGUgaGF2ZSBsaW5lYXIgcmVzb2x1dGlvbnMiLCAibGluZW51 |
| Offset 29, 21 lines modified | Offset 29, 21 lines modified | ||
| 29 | i5·:·findRegion({{0,0},{4,4}},M,f) | 29 | i5·:·findRegion({{0,0},{4,4}},M,f) |
| 30 | o5·=·{{1,·2},·{3,·1}} | 30 | o5·=·{{1,·2},·{3,·1}} |
| 31 | o5·:·List | 31 | o5·:·List |
| 32 | i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) | 32 | i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) |
| 33 | ·--·. | 33 | ·--·.0811193s·elapsed |
| 34 | o6·=·{{1,·2},·{3,·1}} | 34 | o6·=·{{1,·2},·{3,·1}} |
| 35 | o6·:·List | 35 | o6·:·List |
| 36 | i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}}) | 36 | i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}}) |
| 37 | ·--·.01 | 37 | ·--·.0117973s·elapsed |
| 38 | o7·=·{{1,·2},·{3,·1}} | 38 | o7·=·{{1,·2},·{3,·1}} |
| 39 | o7·:·List | 39 | o7·:·List |
| 40 | i8·:· | 40 | i8·:· |
| Offset 30, 21 lines modified | Offset 30, 21 lines modified | ||
| 30 | i5·:·apply(L,·d·->·isLinearComplex·res·prune·truncate(d,M)) | 30 | i5·:·apply(L,·d·->·isLinearComplex·res·prune·truncate(d,M)) |
| 31 | o5·=·{true,·true} | 31 | o5·=·{true,·true} |
| 32 | o5·:·List | 32 | o5·:·List |
| 33 | i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) | 33 | i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) |
| 34 | ·--· | 34 | ·--·49.4911s·elapsed |
| 35 | o6·=·{{4,·3,·3},·{4,·4,·2}} | 35 | o6·=·{{4,·3,·3},·{4,·4,·2}} |
| 36 | o6·:·List | 36 | o6·:·List |
| 37 | i7·:·elapsedTime·linearTruncationsBound·M | 37 | i7·:·elapsedTime·linearTruncationsBound·M |
| 38 | ·--·.0 | 38 | ·--·.0244531s·elapsed |
| 39 | o7·=·{{4,·3,·3},·{4,·4,·2}} | 39 | o7·=·{{4,·3,·3},·{4,·4,·2}} |
| 40 | o7·:·List | 40 | o7·:·List |
| 41 | i8·:· | 41 | i8·:· |
| Offset 117, 23 lines modified | Offset 117, 23 lines modified | ||
| 117 | ········</table> | 117 | ········</table> |
| 118 | ········<div> | 118 | ········<div> |
| 119 | ··········<p>If·some·degrees·<span·class="tt">d</span>·are·known·to·satisfy·<span·class="tt">f(d,M)</span>,·then·they·can·be·specified·using·the·option·<span·class="tt">Inner</span>·in·order·to·expedite·the·computation.··Similarly,·degrees·not·above·those·given·in·<span·class="tt">Outer</span>·will·be·assumed·not·to·satisfy·<span·class="tt">f(d,M)</span>.·If·<span·class="tt">f</span>·takes·options·these·can·also·be·given·to·<span·class="tt">findRegion</span>.</p> | 119 | ··········<p>If·some·degrees·<span·class="tt">d</span>·are·known·to·satisfy·<span·class="tt">f(d,M)</span>,·then·they·can·be·specified·using·the·option·<span·class="tt">Inner</span>·in·order·to·expedite·the·computation.··Similarly,·degrees·not·above·those·given·in·<span·class="tt">Outer</span>·will·be·assumed·not·to·satisfy·<span·class="tt">f(d,M)</span>.·If·<span·class="tt">f</span>·takes·options·these·can·also·be·given·to·<span·class="tt">findRegion</span>.</p> |
| 120 | ········</div> | 120 | ········</div> |
| 121 | ········<table·class="examples"> | 121 | ········<table·class="examples"> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) | 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) |
| 124 | ·--·. | 124 | ·--·.0811193s·elapsed |
| 125 | o6·=·{{1,·2},·{3,·1}} | 125 | o6·=·{{1,·2},·{3,·1}} |
| 126 | o6·:·List</code></pre> | 126 | o6·:·List</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}}) | 129 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}}) |
| 130 | ·--·.01 | 130 | ·--·.0117973s·elapsed |
| 131 | o7·=·{{1,·2},·{3,·1}} | 131 | o7·=·{{1,·2},·{3,·1}} |
| 132 | o7·:·List</code></pre> | 132 | o7·:·List</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ········</table> | 134 | ········</table> |
| 135 | ······</div> | 135 | ······</div> |
| Offset 49, 22 lines modified | Offset 49, 22 lines modified | ||
| 49 | o5·:·List | 49 | o5·:·List |
| 50 | If·some·degrees·d·are·known·to·satisfy·f(d,M),·then·they·can·be·specified·using | 50 | If·some·degrees·d·are·known·to·satisfy·f(d,M),·then·they·can·be·specified·using |
| 51 | the·option·Inner·in·order·to·expedite·the·computation.·Similarly,·degrees·not | 51 | the·option·Inner·in·order·to·expedite·the·computation.·Similarly,·degrees·not |
| 52 | above·those·given·in·Outer·will·be·assumed·not·to·satisfy·f(d,M).·If·f·takes | 52 | above·those·given·in·Outer·will·be·assumed·not·to·satisfy·f(d,M).·If·f·takes |
| 53 | options·these·can·also·be·given·to·findRegion. | 53 | options·these·can·also·be·given·to·findRegion. |
| 54 | i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) | 54 | i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) |
| 55 | ·--·. | 55 | ·--·.0811193s·elapsed |
| 56 | o6·=·{{1,·2},·{3,·1}} | 56 | o6·=·{{1,·2},·{3,·1}} |
| 57 | o6·:·List | 57 | o6·:·List |
| 58 | i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{ | 58 | i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{ |
| 59 | {1,1}}) | 59 | {1,1}}) |
| 60 | ·--·.01 | 60 | ·--·.0117973s·elapsed |
| 61 | o7·=·{{1,·2},·{3,·1}} | 61 | o7·=·{{1,·2},·{3,·1}} |
| 62 | o7·:·List | 62 | o7·:·List |
| 63 | *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nt\x8tr\x8ri\x8ib\x8bu\x8ut\x8to\x8or\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8* | 63 | *\x8**\x8**\x8**\x8**\x8*·C\x8Co\x8on\x8nt\x8tr\x8ri\x8ib\x8bu\x8ut\x8to\x8or\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 64 | Mahrud·Sayrafi·contributed·to·the·code·for·this·function. | 64 | Mahrud·Sayrafi·contributed·to·the·code·for·this·function. |
| 65 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 65 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| Offset 112, 23 lines modified | Offset 112, 23 lines modified | ||
| 112 | ········</table> | 112 | ········</table> |
| 113 | ········<div> | 113 | ········<div> |
| 114 | ··········<p>The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the·positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in·the·<span·class="tt">i</span>-th·step·of·the·resolution·of·$M$.</p> | 114 | ··········<p>The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the·positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in·the·<span·class="tt">i</span>-th·step·of·the·resolution·of·$M$.</p> |
| 115 | ········</div> | 115 | ········</div> |
| 116 | ········<table·class="examples"> | 116 | ········<table·class="examples"> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) |
| 119 | ·--· | 119 | ·--·49.4911s·elapsed |
| 120 | o6·=·{{4,·3,·3},·{4,·4,·2}} | 120 | o6·=·{{4,·3,·3},·{4,·4,·2}} |
| 121 | o6·:·List</code></pre> | 121 | o6·:·List</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·linearTruncationsBound·M | 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·linearTruncationsBound·M |
| 125 | ·--·.0 | 125 | ·--·.0244531s·elapsed |
| 126 | o7·=·{{4,·3,·3},·{4,·4,·2}} | 126 | o7·=·{{4,·3,·3},·{4,·4,·2}} |
| 127 | o7·:·List</code></pre> | 127 | o7·:·List</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ········</table> | 129 | ········</table> |
| 130 | ······</div> | 130 | ······</div> |
| Offset 49, 21 lines modified | Offset 49, 21 lines modified | ||
| 49 | o5·=·{true,·true} | 49 | o5·=·{true,·true} |
| 50 | o5·:·List | 50 | o5·:·List |
| 51 | The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the | 51 | The·output·is·a·list·of·the·minimal·multidegrees·$d$·such·that·the·sum·of·the |
| 52 | positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in | 52 | positive·coordinates·of·$b-d$·is·at·most·$i$·for·all·degrees·$b$·appearing·in |
| 53 | the·i-th·step·of·the·resolution·of·$M$. | 53 | the·i-th·step·of·the·resolution·of·$M$. |
| 54 | i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) | 54 | i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) |
| 55 | ·--· | 55 | ·--·49.4911s·elapsed |
| 56 | o6·=·{{4,·3,·3},·{4,·4,·2}} | 56 | o6·=·{{4,·3,·3},·{4,·4,·2}} |
| 57 | o6·:·List | 57 | o6·:·List |
| 58 | i7·:·elapsedTime·linearTruncationsBound·M | 58 | i7·:·elapsedTime·linearTruncationsBound·M |
| 59 | ·--·.0 | 59 | ·--·.0244531s·elapsed |
| 60 | o7·=·{{4,·3,·3},·{4,·4,·2}} | 60 | o7·=·{{4,·3,·3},·{4,·4,·2}} |
| 61 | o7·:·List | 61 | o7·:·List |
| 62 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 62 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 63 | In·general·linearTruncationsBound·will·not·find·the·minimal·degrees·where·$M$ | 63 | In·general·linearTruncationsBound·will·not·find·the·minimal·degrees·where·$M$ |
| 64 | has·a·linear·resolution·but·will·be·faster·than·repeatedly·truncating·$M$. | 64 | has·a·linear·resolution·but·will·be·faster·than·repeatedly·truncating·$M$. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=10 | 7 | #:len=10 |
| 8 | TG9jYWxSaW5ncw== | 8 | TG9jYWxSaW5ncw== |
| 9 | #:len=5276 | 9 | #:len=5276 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTG9jYWxpemF0aW9ucyBvZiBwb2x5bm9t | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTG9jYWxpemF0aW9ucyBvZiBwb2x5bm9t |
| 11 | aWFsIHJpbmdzIGF0IHByaW1lIGlkZWFscyIsICJsaW5lbnVtIiA9PiA2NCwgImZpbGVuYW1lIiA9 | 11 | aWFsIHJpbmdzIGF0IHByaW1lIGlkZWFscyIsICJsaW5lbnVtIiA9PiA2NCwgImZpbGVuYW1lIiA9 |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| | 15 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| |
| 16 | ······························1 | 16 | ······························1 |
| 17 | o4·:·RP-module,·quotient·of·RP | 17 | o4·:·RP-module,·quotient·of·RP |
| 18 | i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) | 18 | i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) |
| 19 | ·--·. | 19 | ·--·.387876s·elapsed |
| 20 | o5·=·{1,·3,·6,·7,·6,·3,·1} | 20 | o5·=·{1,·3,·6,·7,·6,·3,·1} |
| 21 | o5·:·List | 21 | o5·:·List |
| 22 | i6·:·oo//sum | 22 | i6·:·oo//sum |
| Offset 44, 21 lines modified | Offset 44, 21 lines modified | ||
| 44 | ··············2···3 | 44 | ··············2···3 |
| 45 | o10·=·ideal·(x·,·y·) | 45 | o10·=·ideal·(x·,·y·) |
| 46 | o10·:·Ideal·of·RP | 46 | o10·:·Ideal·of·RP |
| 47 | i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds | 47 | i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds |
| 48 | ·--·.0 | 48 | ·--·.0134371s·elapsed |
| 49 | o11·=·{1,·2,·3,·4,·5,·6} | 49 | o11·=·{1,·2,·3,·4,·5,·6} |
| 50 | o11·:·List | 50 | o11·:·List |
| 51 | i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds | 51 | i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds |
| 52 | ·--·. | 52 | ·--·.614769s·elapsed |
| 53 | o12·=·{6,·12,·18,·24,·30,·36} | 53 | o12·=·{6,·12,·18,·24,·30,·36} |
| 54 | o12·:·List | 54 | o12·:·List |
| 55 | i13·:· | 55 | i13·:· |
| Offset 107, 15 lines modified | Offset 107, 15 lines modified | ||
| 107 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| | 107 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| |
| 108 | ······························1 | 108 | ······························1 |
| 109 | o4·:·RP-module,·quotient·of·RP</code></pre> | 109 | o4·:·RP-module,·quotient·of·RP</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) | 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) |
| 113 | ·--·. | 113 | ·--·.387876s·elapsed |
| 114 | o5·=·{1,·3,·6,·7,·6,·3,·1} | 114 | o5·=·{1,·3,·6,·7,·6,·3,·1} |
| 115 | o5·:·List</code></pre> | 115 | o5·:·List</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·oo//sum | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·oo//sum |
| Offset 147, 23 lines modified | Offset 147, 23 lines modified | ||
| 147 | ··············2···3 | 147 | ··············2···3 |
| 148 | o10·=·ideal·(x·,·y·) | 148 | o10·=·ideal·(x·,·y·) |
| 149 | o10·:·Ideal·of·RP</code></pre> | 149 | o10·:·Ideal·of·RP</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds | 152 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds |
| 153 | ·--·.0 | 153 | ·--·.0134371s·elapsed |
| 154 | o11·=·{1,·2,·3,·4,·5,·6} | 154 | o11·=·{1,·2,·3,·4,·5,·6} |
| 155 | o11·:·List</code></pre> | 155 | o11·:·List</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds | 158 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds |
| 159 | ·--·. | 159 | ·--·.614769s·elapsed |
| 160 | o12·=·{6,·12,·18,·24,·30,·36} | 160 | o12·=·{6,·12,·18,·24,·30,·36} |
| 161 | o12·:·List</code></pre> | 161 | o12·:·List</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ········</table> | 163 | ········</table> |
| 164 | ······</div> | 164 | ······</div> |
| Offset 42, 15 lines modified | Offset 42, 15 lines modified | ||
| 42 | i4·:·M·=·RP^1/I | 42 | i4·:·M·=·RP^1/I |
| 43 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| | 43 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| |
| 44 | ······························1 | 44 | ······························1 |
| 45 | o4·:·RP-module,·quotient·of·RP | 45 | o4·:·RP-module,·quotient·of·RP |
| 46 | i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) | 46 | i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) |
| 47 | ·--·. | 47 | ·--·.387876s·elapsed |
| 48 | o5·=·{1,·3,·6,·7,·6,·3,·1} | 48 | o5·=·{1,·3,·6,·7,·6,·3,·1} |
| 49 | o5·:·List | 49 | o5·:·List |
| 50 | i6·:·oo//sum | 50 | i6·:·oo//sum |
| 51 | o6·=·27 | 51 | o6·=·27 |
| Offset 66, 21 lines modified | Offset 66, 21 lines modified | ||
| 66 | i10·:·q·=·ideal"x2,y3" | 66 | i10·:·q·=·ideal"x2,y3" |
| 67 | ··············2···3 | 67 | ··············2···3 |
| 68 | o10·=·ideal·(x·,·y·) | 68 | o10·=·ideal·(x·,·y·) |
| 69 | o10·:·Ideal·of·RP | 69 | o10·:·Ideal·of·RP |
| 70 | i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds | 70 | i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds |
| 71 | ·--·.0 | 71 | ·--·.0134371s·elapsed |
| 72 | o11·=·{1,·2,·3,·4,·5,·6} | 72 | o11·=·{1,·2,·3,·4,·5,·6} |
| 73 | o11·:·List | 73 | o11·:·List |
| 74 | i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds | 74 | i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds |
| 75 | ·--·. | 75 | ·--·.614769s·elapsed |
| 76 | o12·=·{6,·12,·18,·24,·30,·36} | 76 | o12·=·{6,·12,·18,·24,·30,·36} |
| 77 | o12·:·List | 77 | o12·:·List |
| 78 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 78 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 79 | Hilbert-Samuel·function·with·respect·to·a·parameter·ideal·other·than·the | 79 | Hilbert-Samuel·function·with·respect·to·a·parameter·ideal·other·than·the |
| 80 | maximal·ideal·can·be·slower. | 80 | maximal·ideal·can·be·slower. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=35 | 7 | #:len=35 |
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| 9 | #:len=923 | 9 | #:len=923 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
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| 9 | #:len=293 | 9 | #:len=293 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=24 | 7 | #:len=24 |
| 8 | dW5pbnN0YWxsUGFja2FnZShTdHJpbmcp | 8 | dW5pbnN0YWxsUGFja2FnZShTdHJpbmcp |
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| Offset 12973, 40 lines modified | Offset 12973, 40 lines modified | ||
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| Offset 5, 12 lines modified | Offset 5, 12 lines modified | ||
| 5 | i2·:·f | 5 | i2·:·f |
| 6 | o2·=·1073741824 | 6 | o2·=·1073741824 |
| 7 | i3·:·(c·=·Command·"date";) | 7 | i3·:·(c·=·Command·"date";) |
| 8 | i4·:·c | 8 | i4·:·c |
| 9 | 9 | Wed·Dec·17·09:59:07·+14·2025 | |
| 10 | o4·=·0 | 10 | o4·=·0 |
| 11 | i5·:· | 11 | i5·:· |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·9579076464446459296 | 1 | --·-*-·M2-comint·-*-·hash:·9579076464446459296 |
| 2 | i1·:·filename·=·temporaryFileName·()·|·".dbm" | 2 | i1·:·filename·=·temporaryFileName·()·|·".dbm" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3506553-0/0.dbm |
| 4 | i2·:·x·=·openDatabaseOut·filename | 4 | i2·:·x·=·openDatabaseOut·filename |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3506553-0/0.dbm |
| 6 | o2·:·Database | 6 | o2·:·Database |
| 7 | i3·:·x#"first"·=·"hi·there" | 7 | i3·:·x#"first"·=·"hi·there" |
| 8 | o3·=·hi·there | 8 | o3·=·hi·there |
| Offset 9, 25 lines modified | Offset 9, 25 lines modified | ||
| 9 | i2·:·S·=·ring·I | 9 | i2·:·S·=·ring·I |
| 10 | o2·=·S | 10 | o2·=·S |
| 11 | o2·:·PolynomialRing | 11 | o2·:·PolynomialRing |
| 12 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 12 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 13 | ·--· | 13 | ·--·2.30122s·elapsed |
| 14 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 | 14 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 15 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 | 15 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 |
| 16 | ········································································································· | 16 | ········································································································· |
| 17 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 | 17 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 |
| 18 | o3·:·ChainComplex | 18 | o3·:·ChainComplex |
| 19 | i4·:·elapsedTime·C1·=·res·ideal(I_*) | 19 | i4·:·elapsedTime·C1·=·res·ideal(I_*) |
| 20 | ·--·. | 20 | ·--·1.16245s·elapsed |
| 21 | ······1······35······140······385······819······1080······819······385······140······35······1 | 21 | ······1······35······140······385······819······1080······819······385······140······35······1 |
| 22 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0 | 22 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0 |
| 23 | ···································································································· | 23 | ···································································································· |
| 24 | ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11 | 24 | ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11 |
| 25 | o4·:·ChainComplex | 25 | o4·:·ChainComplex |
| Offset 12, 19 lines modified | Offset 12, 19 lines modified | ||
| 12 | o2·=·stdio | 12 | o2·=·stdio |
| 13 | o2·:·File | 13 | o2·:·File |
| 14 | i3·:·fn·=·temporaryFileName() | 14 | i3·:·fn·=·temporaryFileName() |
| 15 | o3·=·/tmp/M2- | 15 | o3·=·/tmp/M2-3507066-0/0 |
| 16 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close | 16 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close |
| 17 | o4·=·/tmp/M2- | 17 | o4·=·/tmp/M2-3507066-0/0 |
| 18 | o4·:·File | 18 | o4·:·File |
| 19 | i5·:·get·fn | 19 | i5·:·get·fn |
| 20 | o5·=·hi·there | 20 | o5·=·hi·there |
| Offset 49, 27 lines modified | Offset 49, 27 lines modified | ||
| 49 | x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·1 | 49 | x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·1 |
| 50 | o8·=·stdio | 50 | o8·=·stdio |
| 51 | o8·:·File | 51 | o8·:·File |
| 52 | i9·:·fn·<<·f·<<·close | 52 | i9·:·fn·<<·f·<<·close |
| 53 | o9·=·/tmp/M2- | 53 | o9·=·/tmp/M2-3507066-0/0 |
| 54 | o9·:·File | 54 | o9·:·File |
| 55 | i10·:·get·fn | 55 | i10·:·get·fn |
| 56 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 | 56 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 |
| 57 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x | 57 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x |
| 58 | ······+·1 | 58 | ······+·1 |
| 59 | i11·:·fn·<<·toExternalString·f·<<·close | 59 | i11·:·fn·<<·toExternalString·f·<<·close |
| 60 | o11·=·/tmp/M2- | 60 | o11·=·/tmp/M2-3507066-0/0 |
| 61 | o11·:·File | 61 | o11·:·File |
| 62 | i12·:·get·fn | 62 | i12·:·get·fn |
| 63 | o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+ | 63 | o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+ |
| 64 | ······1 | 64 | ······1 |
| Offset 1, 19 lines modified | Offset 1, 19 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731899428494721487 | 1 | --·-*-·M2-comint·-*-·hash:·1731899428494721487 |
| 2 | i1·:·s·=·GCstats() | 2 | i1·:·s·=·GCstats() |
| 3 | o1·=·HashTable{"bytesAlloc"·=>·15 | 3 | o1·=·HashTable{"bytesAlloc"·=>·15386744698········} |
| 4 | ···············"GC_free_space_divisor"·=>·3 | 4 | ···············"GC_free_space_divisor"·=>·3 |
| 5 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 | 5 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 |
| 6 | ···············"gcCpuTimeSecs"·=>·0 | 6 | ···············"gcCpuTimeSecs"·=>·0 |
| 7 | ···············"heapSize"·=>·218 | 7 | ···············"heapSize"·=>·218669056 |
| 8 | ···············"numGCs"·=>·82 | 8 | ···············"numGCs"·=>·826 |
| 9 | ···············"numGCThreads"·=>·12 | 9 | ···············"numGCThreads"·=>·12 |
| 10 | o1·:·HashTable | 10 | o1·:·HashTable |
| 11 | i2·:·s#"heapSize" | 11 | i2·:·s#"heapSize" |
| 12 | o2·=·218 | 12 | o2·=·218669056 |
| 13 | i3·:· | 13 | i3·:· |
| Offset 40, 26 lines modified | Offset 40, 26 lines modified | ||
| 40 | o6·:·PolynomialRing | 40 | o6·:·PolynomialRing |
| 41 | i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); | 41 | i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); |
| 42 | o7·:·Ideal·of·R | 42 | o7·:·Ideal·of·R |
| 43 | i8·:·time·gens·gb·I; | 43 | i8·:·time·gens·gb·I; |
| 44 | ·--·used·0.0 | 44 | ·--·used·0.0366555s·(cpu);·0.0366568s·(thread);·0s·(gc) |
| 45 | ·············1······428 | 45 | ·············1······428 |
| 46 | o8·:·Matrix·R··<--·R | 46 | o8·:·Matrix·R··<--·R |
| 47 | i9·:·time·J1·=·saturate(I); | 47 | i9·:·time·J1·=·saturate(I); |
| 48 | ·--·used·0. | 48 | ·--·used·0.438808s·(cpu);·0.219843s·(thread);·0s·(gc) |
| 49 | o9·:·Ideal·of·R | 49 | o9·:·Ideal·of·R |
| 50 | i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); | 50 | i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); |
| 51 | ·--·used· | 51 | ·--·used·0.000136806s·(cpu);·0.000136536s·(thread);·0s·(gc) |
| 52 | o10·:·Ideal·of·R | 52 | o10·:·Ideal·of·R |
| 53 | i11·:·numgens·J | 53 | i11·:·numgens·J |
| 54 | o11·=·7 | 54 | o11·=·7 |
| Offset 3, 13 lines modified | Offset 3, 13 lines modified | ||
| 3 | i1·:·M·=·random(RR^200,·RR^200); | 3 | i1·:·M·=·random(RR^200,·RR^200); |
| 4 | ················200·········200 | 4 | ················200·········200 |
| 5 | o1·:·Matrix·RR······<--·RR | 5 | o1·:·Matrix·RR······<--·RR |
| 6 | ··············53··········53 | 6 | ··············53··········53 |
| 7 | i2·:·time·SVD(M); | 7 | i2·:·time·SVD(M); |
| 8 | ·--·used·0.0 | 8 | ·--·used·0.0362439s·(cpu);·0.0362423s·(thread);·0s·(gc) |
| 9 | i3·:·time·SVD(M,·DivideConquer=>true); | 9 | i3·:·time·SVD(M,·DivideConquer=>true); |
| 10 | ·--·used·0.0 | 10 | ·--·used·0.035935s·(cpu);·0.0359422s·(thread);·0s·(gc) |
| 11 | i4·:· | 11 | i4·:· |
| Offset 351, 15 lines modified | Offset 351, 15 lines modified | ||
| 351 | ···············|·b·e·h·k·n·q·| | 351 | ···············|·b·e·h·k·n·q·| |
| 352 | ···············|·c·f·i·l·o·r·| | 352 | ···············|·c·f·i·l·o·r·| |
| 353 | ·····························3 | 353 | ·····························3 |
| 354 | o58·:·R-module,·quotient·of·R | 354 | o58·:·R-module,·quotient·of·R |
| 355 | i59·:·time·C·=·resolution·M | 355 | i59·:·time·C·=·resolution·M |
| 356 | ·--·used·0.001 | 356 | ·--·used·0.00190209s·(cpu);·0.00189298s·(thread);·0s·(gc) |
| 357 | ·······3······6······15······18······6 | 357 | ·······3······6······15······18······6 |
| 358 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 | 358 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 |
| 359 | ············································ | 359 | ············································ |
| 360 | ······0······1······2·······3·······4······5 | 360 | ······0······1······2·······3·······4······5 |
| 361 | o59·:·ChainComplex | 361 | o59·:·ChainComplex |
| Offset 14, 10 lines modified | Offset 14, 10 lines modified | ||
| 14 | i4·:·peek·read·f | 14 | i4·:·peek·read·f |
| 15 | o4·=·"hi·there" | 15 | o4·=·"hi·there" |
| 16 | i5·:·atEndOfFile·f | 16 | i5·:·atEndOfFile·f |
| 17 | o5·=· | 17 | o5·=·true |
| 18 | i6·:· | 18 | i6·:· |
| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1330379359420 | 1 | --·-*-·M2-comint·-*-·hash:·1330379359420 |
| 2 | i1·:·benchmark·"sqrt·2p100000" | 2 | i1·:·benchmark·"sqrt·2p100000" |
| 3 | o1·=·.000 | 3 | o1·=·.0004037596391364607 |
| 4 | o1·:·RR·(of·precision·53) | 4 | o1·:·RR·(of·precision·53) |
| 5 | i2·:· | 5 | i2·:· |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i2·:·S·=·ring·I | 9 | i2·:·S·=·ring·I |
| 10 | o2·=·S | 10 | o2·=·S |
| 11 | o2·:·PolynomialRing | 11 | o2·:·PolynomialRing |
| 12 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 12 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 13 | ·--· | 13 | ·--·2.5971s·elapsed |
| 14 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 | 14 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 15 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 | 15 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 |
| 16 | ········································································································· | 16 | ········································································································· |
| 17 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 | 17 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 |
| 18 | o3·:·ChainComplex | 18 | o3·:·ChainComplex |
| Offset 18, 29 lines modified | Offset 18, 29 lines modified | ||
| 18 | o4·=·<<task,·running>> | 18 | o4·=·<<task,·running>> |
| 19 | o4·:·Task | 19 | o4·:·Task |
| 20 | i5·:·n | 20 | i5·:·n |
| 21 | o5·=·9 | 21 | o5·=·946905 |
| 22 | i6·:·sleep·1 | 22 | i6·:·sleep·1 |
| 23 | o6·=·0 | 23 | o6·=·0 |
| 24 | i7·:·t | 24 | i7·:·t |
| 25 | o7·=·<<task,·running>> | 25 | o7·=·<<task,·running>> |
| 26 | o7·:·Task | 26 | o7·:·Task |
| 27 | i8·:·n | 27 | i8·:·n |
| 28 | o8·=·191 | 28 | o8·=·1911803 |
| 29 | i9·:·isReady·t | 29 | i9·:·isReady·t |
| 30 | o9·=·false | 30 | o9·=·false |
| 31 | i10·:·cancelTask·t | 31 | i10·:·cancelTask·t |
| Offset 53, 22 lines modified | Offset 53, 22 lines modified | ||
| 53 | o12·=·<<task,·canceled>> | 53 | o12·=·<<task,·canceled>> |
| 54 | o12·:·Task | 54 | o12·:·Task |
| 55 | i13·:·n | 55 | i13·:·n |
| 56 | o13·=·1912 | 56 | o13·=·1912007 |
| 57 | i14·:·sleep·1 | 57 | i14·:·sleep·1 |
| 58 | o14·=·0 | 58 | o14·=·0 |
| 59 | i15·:·n | 59 | i15·:·n |
| 60 | o15·=·1912 | 60 | o15·=·1912007 |
| 61 | i16·:·isReady·t | 61 | i16·:·isReady·t |
| 62 | o16·=·false | 62 | o16·=·false |
| 63 | i17·:· | 63 | i17·:· |
| Offset 1, 19 lines modified | Offset 1, 19 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·8535510246140175278 | 1 | --·-*-·M2-comint·-*-·hash:·8535510246140175278 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3493357-0/0 |
| 4 | i2·:·makeDirectory·dir | 4 | i2·:·makeDirectory·dir |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3493357-0/0 |
| 6 | i3·:·changeDirectory·dir | 6 | i3·:·changeDirectory·dir |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3493357-0/0/ |
| 8 | i4·:·currentDirectory() | 8 | i4·:·currentDirectory() |
| 9 | o4·=·/tmp/M2- | 9 | o4·=·/tmp/M2-3493357-0/0/ |
| 10 | i5·:· | 10 | i5·:· |
| Offset 1, 27 lines modified | Offset 1, 27 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·10986518019608335719 | 1 | --·-*-·M2-comint·-*-·hash:·10986518019608335719 |
| 2 | i1·:·run·"uname·-a" | 2 | i1·:·run·"uname·-a" |
| 3 | Linux·i | 3 | Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 4 | o1·=·0 | 4 | o1·=·0 |
| 5 | i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close | 5 | i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close |
| 6 | ·ba· | 6 | ·ba· |
| 7 | ·ad· | 7 | ·ad· |
| 8 | o2·=·!grep·a | 8 | o2·=·!grep·a |
| 9 | o2·:·File | 9 | o2·:·File |
| 10 | i3·:·peek·get·"!uname·-a" | 10 | i3·:·peek·get·"!uname·-a" |
| 11 | o3·=·"Linux·i | 11 | o3·=·"Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC |
| 12 | ·····" | 12 | ·····" |
| 13 | ·····6.1.11 | 13 | ·····Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 14 | i4·:·f·=·openInOut·"!egrep·'^in'" | 14 | i4·:·f·=·openInOut·"!egrep·'^in'" |
| 15 | o4·=·!egrep·'^in' | 15 | o4·=·!egrep·'^in' |
| 16 | o4·:·File | 16 | o4·:·File |
| Offset 126, 15 lines modified | Offset 126, 15 lines modified | ||
| 126 | ················ZZ | 126 | ················ZZ |
| 127 | o23·:·Ideal·of·----[x..z,·w] | 127 | o23·:·Ideal·of·----[x..z,·w] |
| 128 | ···············1277 | 128 | ···············1277 |
| 129 | i24·:·gb·I | 129 | i24·:·gb·I |
| 130 | ···--·registering·gb·5·at·0x7f9 | 130 | ···--·registering·gb·5·at·0x7f99ef4b4700 |
| 131 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 | 131 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 |
| 132 | ···--·number·of·monomials················=·8 | 132 | ···--·number·of·monomials················=·8 |
| 133 | ···--·#reduction·steps·=·2 | 133 | ···--·#reduction·steps·=·2 |
| 134 | ···--·#spairs·done·=·6 | 134 | ···--·#spairs·done·=·6 |
| 135 | ···--·ncalls·=·0 | 135 | ···--·ncalls·=·0 |
| 136 | ···--·nloop·=·0 | 136 | ···--·nloop·=·0 |
| Offset 177, 15 lines modified | Offset 177, 15 lines modified | ||
| 177 | i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); | 177 | i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); |
| 178 | ··············1······4 | 178 | ··············1······4 |
| 179 | o32·:·Matrix·R··<--·R | 179 | o32·:·Matrix·R··<--·R |
| 180 | i33·:·time·betti·gb·f | 180 | i33·:·time·betti·gb·f |
| 181 | ·--·used·0. | 181 | ·--·used·0.280001s·(cpu);·0.278478s·(thread);·0s·(gc) |
| 182 | ·············0··1 | 182 | ·············0··1 |
| 183 | o33·=·total:·1·53 | 183 | o33·=·total:·1·53 |
| 184 | ··········0:·1··. | 184 | ··········0:·1··. |
| 185 | ··········1:·.··. | 185 | ··········1:·.··. |
| 186 | ··········2:·.··2 | 186 | ··········2:·.··2 |
| 187 | ··········3:·.··1 | 187 | ··········3:·.··1 |
| Offset 208, 15 lines modified | Offset 208, 15 lines modified | ||
| 208 | ············3····5·····8·····9····12·····14····17 | 208 | ············3····5·····8·····9····12·····14····17 |
| 209 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T | 209 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T |
| 210 | o35·:·ZZ[T] | 210 | o35·:·ZZ[T] |
| 211 | i36·:·time·betti·gb·f | 211 | i36·:·time·betti·gb·f |
| 212 | ·--·used·0.00 | 212 | ·--·used·0.00400271s·(cpu);·0.00581119s·(thread);·0s·(gc) |
| 213 | ·············0··1 | 213 | ·············0··1 |
| 214 | o36·=·total:·1·53 | 214 | o36·=·total:·1·53 |
| 215 | ··········0:·1··. | 215 | ··········0:·1··. |
| 216 | ··········1:·.··. | 216 | ··········1:·.··. |
| 217 | ··········2:·.··2 | 217 | ··········2:·.··2 |
| 218 | ··········3:·.··1 | 218 | ··········3:·.··1 |
| Offset 36, 16 lines modified | Offset 36, 16 lines modified | ||
| 36 | ··········<<·res·M·<<·endl·<<·endl; | 36 | ··········<<·res·M·<<·endl·<<·endl; |
| 37 | ··········break; | 37 | ··········break; |
| 38 | ··········)·else·( | 38 | ··········)·else·( |
| 39 | ··········<<·"--·computation·interrupted"·<<·endl; | 39 | ··········<<·"--·computation·interrupted"·<<·endl; |
| 40 | ··········status·M.cache.resolution; | 40 | ··········status·M.cache.resolution; |
| 41 | ··········<<·"--·continuing·the·computation"·<<·endl; | 41 | ··········<<·"--·continuing·the·computation"·<<·endl; |
| 42 | ··········)) | 42 | ··········)) |
| 43 | ·--·used·1. | 43 | ·--·used·1.17098s·(cpu);·0.994858s·(thread);·0s·(gc) |
| 44 | ·--·used·0. | 44 | ·--·used·0.677089s·(cpu);·0.586337s·(thread);·0s·(gc) |
| 45 | --·computation·started:· | 45 | --·computation·started:· |
| 46 | --·computation·interrupted | 46 | --·computation·interrupted |
| 47 | --·continuing·the·computation | 47 | --·continuing·the·computation |
| 48 | --·computation·complete | 48 | --·computation·complete |
| 49 | ·4······11······89······122······40 | 49 | ·4······11······89······122······40 |
| 50 | R··<--·R···<--·R···<--·R····<--·R···<--·0 | 50 | R··<--·R···<--·R···<--·R····<--·R···<--·0 |
| 51 | ········································· | 51 | ········································· |
| Offset 1, 76 lines modified | Offset 1, 76 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·11422793294564310273 | 1 | --·-*-·M2-comint·-*-·hash:·11422793294564310273 |
| 2 | i1·:·src·=·temporaryFileName()·|·"/" | 2 | i1·:·src·=·temporaryFileName()·|·"/" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3502475-0/0/ |
| 4 | i2·:·dst·=·temporaryFileName()·|·"/" | 4 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3502475-0/1/ |
| 6 | i3·:·makeDirectory·(src|"a/") | 6 | i3·:·makeDirectory·(src|"a/") |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3502475-0/0/a/ |
| 8 | i4·:·makeDirectory·(src|"b/") | 8 | i4·:·makeDirectory·(src|"b/") |
| 9 | o4·=·/tmp/M2- | 9 | o4·=·/tmp/M2-3502475-0/0/b/ |
| 10 | i5·:·makeDirectory·(src|"b/c/") | 10 | i5·:·makeDirectory·(src|"b/c/") |
| 11 | o5·=·/tmp/M2- | 11 | o5·=·/tmp/M2-3502475-0/0/b/c/ |
| 12 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 12 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 13 | o6·=·/tmp/M2- | 13 | o6·=·/tmp/M2-3502475-0/0/a/f |
| 14 | o6·:·File | 14 | o6·:·File |
| 15 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 15 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 16 | o7·=·/tmp/M2- | 16 | o7·=·/tmp/M2-3502475-0/0/a/g |
| 17 | o7·:·File | 17 | o7·:·File |
| 18 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 18 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 19 | o8·=·/tmp/M2- | 19 | o8·=·/tmp/M2-3502475-0/0/b/c/g |
| 20 | o8·:·File | 20 | o8·:·File |
| 21 | i9·:·stack·findFiles·src | 21 | i9·:·stack·findFiles·src |
| 22 | o9·=·/tmp/M2- | 22 | o9·=·/tmp/M2-3502475-0/0/ |
| 23 | ·····/tmp/M2- | 23 | ·····/tmp/M2-3502475-0/0/b/ |
| 24 | ·····/tmp/M2- | 24 | ·····/tmp/M2-3502475-0/0/b/c/ |
| 25 | ·····/tmp/M2- | 25 | ·····/tmp/M2-3502475-0/0/b/c/g |
| 26 | ·····/tmp/M2- | 26 | ·····/tmp/M2-3502475-0/0/a/ |
| 27 | ·····/tmp/M2-1763734-0/0/a/f | ||
| 28 | ·····/tmp/M2- | 27 | ·····/tmp/M2-3502475-0/0/a/g |
| 28 | ·····/tmp/M2-3502475-0/0/a/f | ||
| 29 | i10·:·copyDirectory(src,dst,Verbose=>true) | 29 | i10·:·copyDirectory(src,dst,Verbose=>true) |
| 30 | ·--·copying:·/tmp/M2- | 30 | ·--·copying:·/tmp/M2-3502475-0/0/b/c/g·->·/tmp/M2-3502475-0/1/b/c/g |
| 31 | ·--·copying:·/tmp/M2-1763734-0/0/a/f·->·/tmp/M2-1763734-0/1/a/f | ||
| 32 | ·--·copying:·/tmp/M2- | 31 | ·--·copying:·/tmp/M2-3502475-0/0/a/g·->·/tmp/M2-3502475-0/1/a/g |
| 32 | ·--·copying:·/tmp/M2-3502475-0/0/a/f·->·/tmp/M2-3502475-0/1/a/f | ||
| 33 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) | 33 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 34 | ·--·skipping:·/tmp/M2- | 34 | ·--·skipping:·/tmp/M2-3502475-0/0/b/c/g·not·newer·than·/tmp/M2-3502475-0/1/b/c/g |
| 35 | ·--·skipping:·/tmp/M2-1763734-0/0/a/f·not·newer·than·/tmp/M2-1763734-0/1/a/f | ||
| 36 | ·--·skipping:·/tmp/M2- | 35 | ·--·skipping:·/tmp/M2-3502475-0/0/a/g·not·newer·than·/tmp/M2-3502475-0/1/a/g |
| 36 | ·--·skipping:·/tmp/M2-3502475-0/0/a/f·not·newer·than·/tmp/M2-3502475-0/1/a/f | ||
| 37 | i12·:·stack·findFiles·dst | 37 | i12·:·stack·findFiles·dst |
| 38 | o12·=·/tmp/M2- | 38 | o12·=·/tmp/M2-3502475-0/1/ |
| 39 | ······/tmp/M2- | 39 | ······/tmp/M2-3502475-0/1/b/ |
| 40 | ······/tmp/M2- | 40 | ······/tmp/M2-3502475-0/1/b/c/ |
| 41 | ······/tmp/M2- | 41 | ······/tmp/M2-3502475-0/1/b/c/g |
| 42 | ······/tmp/M2- | 42 | ······/tmp/M2-3502475-0/1/a/ |
| 43 | ······/tmp/M2-1763734-0/1/a/f | ||
| 44 | ······/tmp/M2- | 43 | ······/tmp/M2-3502475-0/1/a/g |
| 44 | ······/tmp/M2-3502475-0/1/a/f | ||
| 45 | i13·:·get·(dst|"b/c/g") | 45 | i13·:·get·(dst|"b/c/g") |
| 46 | o13·=·ho·there | 46 | o13·=·ho·there |
| 47 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 47 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| Offset 1, 41 lines modified | Offset 1, 41 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·11539475420155775110 | 1 | --·-*-·M2-comint·-*-·hash:·11539475420155775110 |
| 2 | i1·:·src·=·temporaryFileName() | 2 | i1·:·src·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3500588-0/0 |
| 4 | i2·:·dst·=·temporaryFileName() | 4 | i2·:·dst·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3500588-0/1 |
| 6 | i3·:·src·<<·"hi·there"·<<·close | 6 | i3·:·src·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3500588-0/0 |
| 8 | o3·:·File | 8 | o3·:·File |
| 9 | i4·:·copyFile(src,dst,Verbose=>true) | 9 | i4·:·copyFile(src,dst,Verbose=>true) |
| 10 | ·--·copying:·/tmp/M2- | 10 | ·--·copying:·/tmp/M2-3500588-0/0·->·/tmp/M2-3500588-0/1 |
| 11 | i5·:·get·dst | 11 | i5·:·get·dst |
| 12 | o5·=·hi·there | 12 | o5·=·hi·there |
| 13 | i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 13 | i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 14 | ·--·skipping:·/tmp/M2- | 14 | ·--·skipping:·/tmp/M2-3500588-0/0·not·newer·than·/tmp/M2-3500588-0/1 |
| 15 | i7·:·src·<<·"ho·there"·<<·close | 15 | i7·:·src·<<·"ho·there"·<<·close |
| 16 | o7·=·/tmp/M2- | 16 | o7·=·/tmp/M2-3500588-0/0 |
| 17 | o7·:·File | 17 | o7·:·File |
| 18 | i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 18 | i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 19 | ·--·skipping:·/tmp/M2- | 19 | ·--·skipping:·/tmp/M2-3500588-0/0·not·newer·than·/tmp/M2-3500588-0/1 |
| 20 | i9·:·get·dst | 20 | i9·:·get·dst |
| 21 | o9·=·hi·there | 21 | o9·=·hi·there |
| 22 | i10·:·removeFile·src | 22 | i10·:·removeFile·src |
| Offset 1, 23 lines modified | Offset 1, 23 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·15508153783232232453 | 1 | --·-*-·M2-comint·-*-·hash:·15508153783232232453 |
| 2 | i1·:·t1·=·cpuTime() | 2 | i1·:·t1·=·cpuTime() |
| 3 | o1·=· | 3 | o1·=·236.202283615 |
| 4 | o1·:·RR·(of·precision·53) | 4 | o1·:·RR·(of·precision·53) |
| 5 | i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324; | 5 | i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324; |
| 6 | i3·:·t2·=·cpuTime() | 6 | i3·:·t2·=·cpuTime() |
| 7 | o3·=· | 7 | o3·=·237.254696625 |
| 8 | o3·:·RR·(of·precision·53) | 8 | o3·:·RR·(of·precision·53) |
| 9 | i4·:·t2-t1 | 9 | i4·:·t2-t1 |
| 10 | o4·=·. | 10 | o4·=·1.052413009999981 |
| 11 | o4·:·RR·(of·precision·53) | 11 | o4·:·RR·(of·precision·53) |
| 12 | i5·:· | 12 | i5·:· |
| Offset 1, 24 lines modified | Offset 1, 24 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·3660839476107967259 | 1 | --·-*-·M2-comint·-*-·hash:·3660839476107967259 |
| 2 | i1·:·currentTime() | 2 | i1·:·currentTime() |
| 3 | o1·=·17 | 3 | o1·=·1765915218 |
| 4 | i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) | 4 | i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) |
| 5 | o2·=·5 | 5 | o2·=·55.95962556840091 |
| 6 | o2·:·RR·(of·precision·53) | 6 | o2·:·RR·(of·precision·53) |
| 7 | i3·:·12·*·(oo·-·floor·oo) | 7 | i3·:·12·*·(oo·-·floor·oo) |
| 8 | o3·=·1 | 8 | o3·=·11.51550682081091 |
| 9 | o3·:·RR·(of·precision·53) | 9 | o3·:·RR·(of·precision·53) |
| 10 | i4·:·run·"date" | 10 | i4·:·run·"date" |
| 11 | 11 | Wed·Dec·17·10:00:18·+14·2025 | |
| 12 | o4·=·0 | 12 | o4·=·0 |
| 13 | i5·:· | 13 | i5·:· |
| Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1330565958025 | 1 | --·-*-·M2-comint·-*-·hash:·1330565958025 |
| 2 | i1·:·elapsedTime·sleep·1 | 2 | i1·:·elapsedTime·sleep·1 |
| 3 | ·--·1.0001s·elapsed | 3 | ·--·1.00014s·elapsed |
| 4 | o1·=·0 | 4 | o1·=·0 |
| 5 | i2·:· | 5 | i2·:· |
| Offset 6, 15 lines modified | Offset 6, 15 lines modified | ||
| 6 | ···············3···················3·····2···············3 | 6 | ···············3···················3·····2···············3 |
| 7 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) | 7 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) |
| 8 | o2·:·Ideal·of·R | 8 | o2·:·Ideal·of·R |
| 9 | i3·:·time·leadTerm·gens·gb·I | 9 | i3·:·time·leadTerm·gens·gb·I |
| 10 | ·--·used·0. | 10 | ·--·used·0.167644s·(cpu);·0.167644s·(thread);·0s·(gc) |
| 11 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 | 11 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 |
| 12 | ·····------------------------------------------------------------------------ | 12 | ·····------------------------------------------------------------------------ |
| 13 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 | 13 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 |
| 14 | ·····------------------------------------------------------------------------ | 14 | ·····------------------------------------------------------------------------ |
| 15 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 | 15 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| Offset 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ···············3···················3·····2···············3 | 85 | ···············3···················3·····2···············3 |
| 86 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) | 86 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) |
| 87 | o7·:·Ideal·of·R | 87 | o7·:·Ideal·of·R |
| 88 | i8·:·time·G·=·eliminate(I,{s,t}) | 88 | i8·:·time·G·=·eliminate(I,{s,t}) |
| 89 | ·--·used·0. | 89 | ·--·used·0.191404s·(cpu);·0.191405s·(thread);·0s·(gc) |
| 90 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· | 90 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· |
| 91 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 91 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 92 | ·····------------------------------------------------------------------------ | 92 | ·····------------------------------------------------------------------------ |
| 93 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· | 93 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· |
| 94 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 94 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 95 | ·····------------------------------------------------------------------------ | 95 | ·····------------------------------------------------------------------------ |
| Offset 154, 15 lines modified | Offset 154, 15 lines modified | ||
| 154 | i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}]; | 154 | i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}]; |
| 155 | i11·:·I1·=·substitute(I,R1); | 155 | i11·:·I1·=·substitute(I,R1); |
| 156 | o11·:·Ideal·of·R1 | 156 | o11·:·Ideal·of·R1 |
| 157 | i12·:·time·G·=·eliminate(I1,{s,t}) | 157 | i12·:·time·G·=·eliminate(I1,{s,t}) |
| 158 | ·--·used·0.0 | 158 | ·--·used·0.0585885s·(cpu);·0.0585922s·(thread);·0s·(gc) |
| 159 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7·· | 159 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7·· |
| 160 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- | 160 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- |
| 161 | ······----------------------------------------------------------------------- | 161 | ······----------------------------------------------------------------------- |
| 162 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2·· | 162 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2·· |
| 163 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- | 163 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- |
| 164 | ······----------------------------------------------------------------------- | 164 | ······----------------------------------------------------------------------- |
| Offset 228, 15 lines modified | Offset 228, 15 lines modified | ||
| 228 | ···················3·············3·····2·········3 | 228 | ···················3·············3·····2·········3 |
| 229 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) | 229 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) |
| 230 | o16·:·RingMap·A·<--·B | 230 | o16·:·RingMap·A·<--·B |
| 231 | i17·:·time·G·=·kernel·F | 231 | i17·:·time·G·=·kernel·F |
| 232 | ·--·used·0. | 232 | ·--·used·0.164034s·(cpu);·0.163851s·(thread);·0s·(gc) |
| 233 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· | 233 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· |
| 234 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 234 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 235 | ······----------------------------------------------------------------------- | 235 | ······----------------------------------------------------------------------- |
| 236 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· | 236 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· |
| 237 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 237 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 238 | ······----------------------------------------------------------------------- | 238 | ······----------------------------------------------------------------------- |
| Offset 297, 23 lines modified | Offset 297, 23 lines modified | ||
| 297 | i19·:·use·ring·I | 297 | i19·:·use·ring·I |
| 298 | o19·=·R | 298 | o19·=·R |
| 299 | o19·:·PolynomialRing | 299 | o19·:·PolynomialRing |
| 300 | i20·:·time·f1·=·resultant(I_0,I_2,s) | 300 | i20·:·time·f1·=·resultant(I_0,I_2,s) |
| 301 | ·--·used·0.00 | 301 | ·--·used·0.00239778s·(cpu);·0.00239694s·(thread);·0s·(gc) |
| 302 | ·········9····9······7····3 | 302 | ·········9····9······7····3 |
| 303 | o20·=·x*t··-·t··-·z*t··-·z | 303 | o20·=·x*t··-·t··-·z*t··-·z |
| 304 | o20·:·R | 304 | o20·:·R |
| 305 | i21·:·time·f2·=·resultant(I_1,f1,t) | 305 | i21·:·time·f2·=·resultant(I_1,f1,t) |
| 306 | ·--·used·0.0 | 306 | ·--·used·0.0441614s·(cpu);·0.0441708s·(thread);·0s·(gc) |
| 307 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2·· | 307 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2·· |
| 308 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ | 308 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ |
| 309 | ······----------------------------------------------------------------------- | 309 | ······----------------------------------------------------------------------- |
| 310 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8··· | 310 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8··· |
| 311 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ | 311 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ |
| 312 | ······----------------------------------------------------------------------- | 312 | ······----------------------------------------------------------------------- |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 59 | ····································Version·=>·0.0 | 59 | ····································Version·=>·0.0 |
| 60 | ·············package·prefix·=>·/usr/ | 60 | ·············package·prefix·=>·/usr/ |
| 61 | ·············PackageIsLoaded·=>·true | 61 | ·············PackageIsLoaded·=>·true |
| 62 | ·············pkgname·=>·Foo | 62 | ·············pkgname·=>·Foo |
| 63 | ·············private·dictionary·=>·Foo#"private·dictionary" | 63 | ·············private·dictionary·=>·Foo#"private·dictionary" |
| 64 | ·············processed·documentation·=>·MutableHashTable{} | 64 | ·············processed·documentation·=>·MutableHashTable{} |
| 65 | ·············raw·documentation·=>·MutableHashTable{} | 65 | ·············raw·documentation·=>·MutableHashTable{} |
| 66 | ·············source·directory·=>·/tmp/M2- | 66 | ·············source·directory·=>·/tmp/M2-3485508-0/88-rundir/ |
| 67 | ·············source·file·=>·stdio | 67 | ·············source·file·=>·stdio |
| 68 | ·············test·inputs·=>·MutableList{} | 68 | ·············test·inputs·=>·MutableList{} |
| 69 | i7·:·dictionaryPath | 69 | i7·:·dictionaryPath |
| 70 | o7·=·{Foo.Dictionary,·PackageCitations.Dictionary,·Varieties.Dictionary, | 70 | o7·=·{Foo.Dictionary,·PackageCitations.Dictionary,·Varieties.Dictionary, |
| 71 | ·····------------------------------------------------------------------------ | 71 | ·····------------------------------------------------------------------------ |
| Offset 1, 20 lines modified | Offset 1, 20 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·7475038936570224899 | 1 | --·-*-·M2-comint·-*-·hash:·7475038936570224899 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3498018-0/0 |
| 4 | i2·:·fileExists·fn | 4 | i2·:·fileExists·fn |
| 5 | o2·=·false | 5 | o2·=·false |
| 6 | i3·:·fn·<<·"hi·there"·<<·close | 6 | i3·:·fn·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3498018-0/0 |
| 8 | o3·:·File | 8 | o3·:·File |
| 9 | i4·:·fileExists·fn | 9 | i4·:·fileExists·fn |
| 10 | o4·=·true | 10 | o4·=·true |
| Offset 1, 28 lines modified | Offset 1, 28 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1216695447195237994 | 1 | --·-*-·M2-comint·-*-·hash:·1216695447195237994 |
| 2 | i1·:·f·=·temporaryFileName()·<<·"hi·there" | 2 | i1·:·f·=·temporaryFileName()·<<·"hi·there" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3518510-0/0 |
| 4 | o1·:·File | 4 | o1·:·File |
| 5 | i2·:·fileLength·f | 5 | i2·:·fileLength·f |
| 6 | o2·=·8 | 6 | o2·=·8 |
| 7 | i3·:·close·f | 7 | i3·:·close·f |
| 8 | o3·=·/tmp/M2- | 8 | o3·=·/tmp/M2-3518510-0/0 |
| 9 | o3·:·File | 9 | o3·:·File |
| 10 | i4·:·filename·=·toString·f | 10 | i4·:·filename·=·toString·f |
| 11 | o4·=·/tmp/M2- | 11 | o4·=·/tmp/M2-3518510-0/0 |
| 12 | i5·:·fileLength·filename | 12 | i5·:·fileLength·filename |
| 13 | o5·=·8 | 13 | o5·=·8 |
| 14 | i6·:·get·filename | 14 | i6·:·get·filename |
| Offset 1, 25 lines modified | Offset 1, 25 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·11202140621123993633 | 1 | --·-*-·M2-comint·-*-·hash:·11202140621123993633 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3505439-0/0 |
| 4 | i2·:·f·=·fn·<<·"hi·there" | 4 | i2·:·f·=·fn·<<·"hi·there" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3505439-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·fileMode·f | 7 | i3·:·fileMode·f |
| 8 | o3·=·420 | 8 | o3·=·420 |
| 9 | i4·:·close·f | 9 | i4·:·close·f |
| 10 | o4·=·/tmp/M2- | 10 | o4·=·/tmp/M2-3505439-0/0 |
| 11 | o4·:·File | 11 | o4·:·File |
| 12 | i5·:·removeFile·fn | 12 | i5·:·removeFile·fn |
| 13 | i6·:· | 13 | i6·:· |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·4782570202197464532 | 1 | --·-*-·M2-comint·-*-·hash:·4782570202197464532 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3500648-0/0 |
| 4 | i2·:·fn·<<·"hi·there"·<<·close | 4 | i2·:·fn·<<·"hi·there"·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3500648-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·fileMode·fn | 7 | i3·:·fileMode·fn |
| 8 | o3·=·420 | 8 | o3·=·420 |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·17473878267845575442 | 1 | --·-*-·M2-comint·-*-·hash:·17473878267845575442 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3500015-0/0 |
| 4 | i2·:·f·=·fn·<<·"hi·there" | 4 | i2·:·f·=·fn·<<·"hi·there" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3500015-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·m·=·7·+·7*8·+·7*64 | 7 | i3·:·m·=·7·+·7*8·+·7*64 |
| 8 | o3·=·511 | 8 | o3·=·511 |
| Offset 18, 15 lines modified | Offset 18, 15 lines modified | ||
| 18 | i5·:·fileMode·f | 18 | i5·:·fileMode·f |
| 19 | o5·=·511 | 19 | o5·=·511 |
| 20 | i6·:·close·f | 20 | i6·:·close·f |
| 21 | o6·=·/tmp/M2- | 21 | o6·=·/tmp/M2-3500015-0/0 |
| 22 | o6·:·File | 22 | o6·:·File |
| 23 | i7·:·fileMode·fn | 23 | i7·:·fileMode·fn |
| 24 | o7·=·511 | 24 | o7·=·511 |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·16772784390799334723 | 1 | --·-*-·M2-comint·-*-·hash:·16772784390799334723 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3509447-0/0 |
| 4 | i2·:·fn·<<·"hi·there"·<<·close | 4 | i2·:·fn·<<·"hi·there"·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3509447-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·m·=·fileMode·fn | 7 | i3·:·m·=·fileMode·fn |
| 8 | o3·=·420 | 8 | o3·=·420 |
| Offset 1, 7 lines modified | Offset 1, 7 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1331310711075 | 1 | --·-*-·M2-comint·-*-·hash:·1331310711075 |
| 2 | i1·:·currentTime()·-·fileTime·"." | 2 | i1·:·currentTime()·-·fileTime·"." |
| 3 | o1·=· | 3 | o1·=·40 |
| 4 | i2·:· | 4 | i2·:· |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | ·····{4}·|·0·····x2-3··y3-1··| | 29 | ·····{4}·|·0·····x2-3··y3-1··| |
| 30 | ·············3······3 | 30 | ·············3······3 |
| 31 | o6·:·Matrix·R··<--·R | 31 | o6·:·Matrix·R··<--·R |
| 32 | i7·:·syz·f | 32 | i7·:·syz·f |
| 33 | ···--·registering·gb·0·at·0x7f | 33 | ···--·registering·gb·0·at·0x7f6e96451000 |
| 34 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3 | 34 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3 |
| 35 | ···--·number·of·monomials················=·9 | 35 | ···--·number·of·monomials················=·9 |
| 36 | ···--·#reduction·steps·=·6 | 36 | ···--·#reduction·steps·=·6 |
| 37 | ···--·#spairs·done·=·6 | 37 | ···--·#spairs·done·=·6 |
| 38 | ···--·ncalls·=·0 | 38 | ···--·ncalls·=·0 |
| 39 | ···--·nloop·=·0 | 39 | ···--·nloop·=·0 |
| Offset 10, 11 lines modified | Offset 10, 11 lines modified | ||
| 10 | o2·=·hi·there | 10 | o2·=·hi·there |
| 11 | i3·:·removeFile·"test-file" | 11 | i3·:·removeFile·"test-file" |
| 12 | i4·:·get·"!date" | 12 | i4·:·get·"!date" |
| 13 | o4·=· | 13 | o4·=·Wed·Dec·17·09:59:35·+14·2025 |
| 14 | i5·:· | 14 | i5·:· |
| Offset 1, 7 lines modified | Offset 1, 7 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1330975614323 | 1 | --·-*-·M2-comint·-*-·hash:·1330975614323 |
| 2 | i1·:·groupID() | 2 | i1·:·groupID() |
| 3 | o1·=· | 3 | o1·=·3420128 |
| 4 | i2·:· | 4 | i2·:· |
| Offset 2, 19 lines modified | Offset 2, 19 lines modified | ||
| 2 | i1·:·isDirectory·"." | 2 | i1·:·isDirectory·"." |
| 3 | o1·=·true | 3 | o1·=·true |
| 4 | i2·:·fn·=·temporaryFileName() | 4 | i2·:·fn·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3486683-0/0 |
| 6 | i3·:·fn·<<·"hi·there"·<<·close | 6 | i3·:·fn·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3486683-0/0 |
| 8 | o3·:·File | 8 | o3·:·File |
| 9 | i4·:·isDirectory·fn | 9 | i4·:·isDirectory·fn |
| 10 | o4·=·false | 10 | o4·=·false |
| Offset 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | o17·=·false | 75 | o17·=·false |
| 76 | i18·:·isPrime(m*m*m1*m1*m2^6) | 76 | i18·:·isPrime(m*m*m1*m1*m2^6) |
| 77 | o18·=·false | 77 | o18·=·false |
| 78 | i19·:·elapsedTime·facs·=·factor(m*m1) | 78 | i19·:·elapsedTime·facs·=·factor(m*m1) |
| 79 | ·--· | 79 | ·--·9.32182s·elapsed |
| 80 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 | 80 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 |
| 81 | o19·:·Expression·of·class·Product | 81 | o19·:·Expression·of·class·Product |
| 82 | i20·:·facs·=·facs//toList/toList | 82 | i20·:·facs·=·facs//toList/toList |
| Offset 97, 17 lines modified | Offset 97, 17 lines modified | ||
| 97 | i22·:·m3·=·nextPrime·(m^3) | 97 | i22·:·m3·=·nextPrime·(m^3) |
| 98 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 | 98 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 |
| 99 | ······00000000000000185613 | 99 | ······00000000000000185613 |
| 100 | i23·:·elapsedTime·isPrime·m3 | 100 | i23·:·elapsedTime·isPrime·m3 |
| 101 | ·--·.0 | 101 | ·--·.0618019s·elapsed |
| 102 | o23·=·true | 102 | o23·=·true |
| 103 | i24·:·elapsedTime·isPseudoprime·m3 | 103 | i24·:·elapsedTime·isPseudoprime·m3 |
| 104 | ·--·.000 | 104 | ·--·.000220213s·elapsed |
| 105 | o24·=·true | 105 | o24·=·true |
| 106 | i25·:· | 106 | i25·:· |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·4782205245758053629 | 1 | --·-*-·M2-comint·-*-·hash:·4782205245758053629 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3519111-0/0 |
| 4 | i2·:·fn·<<·"hi·there"·<<·close | 4 | i2·:·fn·<<·"hi·there"·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3519111-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·isRegularFile·fn | 7 | i3·:·isRegularFile·fn |
| 8 | o3·=·true | 8 | o3·=·true |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·5113372159204571746 | 1 | --·-*-·M2-comint·-*-·hash:·5113372159204571746 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3499660-0/0 |
| 4 | i2·:·makeDirectory·(dir|"/a/b/c") | 4 | i2·:·makeDirectory·(dir|"/a/b/c") |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3499660-0/0/a/b/c |
| 6 | i3·:·removeDirectory·(dir|"/a/b/c") | 6 | i3·:·removeDirectory·(dir|"/a/b/c") |
| 7 | i4·:·removeDirectory·(dir|"/a/b") | 7 | i4·:·removeDirectory·(dir|"/a/b") |
| 8 | i5·:·removeDirectory·(dir|"/a") | 8 | i5·:·removeDirectory·(dir|"/a") |
| Offset 3, 31 lines modified | Offset 3, 31 lines modified | ||
| 3 | i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2) | 3 | i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2) |
| 4 | o1·=·fib | 4 | o1·=·fib |
| 5 | o1·:·FunctionClosure | 5 | o1·:·FunctionClosure |
| 6 | i2·:·time·fib·28 | 6 | i2·:·time·fib·28 |
| 7 | ·--·used·0. | 7 | ·--·used·0.922778s·(cpu);·0.743792s·(thread);·0s·(gc) |
| 8 | o2·=·514229 | 8 | o2·=·514229 |
| 9 | i3·:·fib·=·memoize·fib | 9 | i3·:·fib·=·memoize·fib |
| 10 | o3·=·fib | 10 | o3·=·fib |
| 11 | o3·:·FunctionClosure | 11 | o3·:·FunctionClosure |
| 12 | i4·:·time·fib·28 | 12 | i4·:·time·fib·28 |
| 13 | ·--·used· | 13 | ·--·used·9.9246e-05s·(cpu);·9.8545e-05s·(thread);·0s·(gc) |
| 14 | o4·=·514229 | 14 | o4·=·514229 |
| 15 | i5·:·time·fib·28 | 15 | i5·:·time·fib·28 |
| 16 | ·--·used· | 16 | ·--·used·4.158e-06s·(cpu);·3.417e-06s·(thread);·0s·(gc) |
| 17 | o5·=·514229 | 17 | o5·=·514229 |
| 18 | i6·:·fib·=·memoize(·n·->·fib(n-1)·+·fib(n-2)·) | 18 | i6·:·fib·=·memoize(·n·->·fib(n-1)·+·fib(n-2)·) |
| 19 | o6·=·fib | 19 | o6·=·fib |
| Offset 4, 34 lines modified | Offset 4, 34 lines modified | ||
| 4 | o1·=·{0·=>·(==,·BettiTally,·BettiTally)···························} | 4 | o1·=·{0·=>·(==,·BettiTally,·BettiTally)···························} |
| 5 | ·····{1·=>·(++,·BettiTally,·BettiTally)···························} | 5 | ·····{1·=>·(++,·BettiTally,·BettiTally)···························} |
| 6 | ·····{2·=>·(**,·BettiTally,·BettiTally)···························} | 6 | ·····{2·=>·(**,·BettiTally,·BettiTally)···························} |
| 7 | ·····{3·=>·(SPACE,·BettiTally,·Array)·····························} | 7 | ·····{3·=>·(SPACE,·BettiTally,·Array)·····························} |
| 8 | ·····{4·=>·(SPACE,·BettiTally,·ZZ)································} | 8 | ·····{4·=>·(SPACE,·BettiTally,·ZZ)································} |
| 9 | ·····{5·=>·(lift,·BettiTally,·ZZ)·································} | 9 | ·····{5·=>·(lift,·BettiTally,·ZZ)·································} |
| 10 | ·····{6·=>·(*,·QQ,·BettiTally)····································} | ||
| 11 | ·····{ | 10 | ·····{6·=>·(*,·ZZ,·BettiTally)····································} |
| 11 | ·····{7·=>·(*,·QQ,·BettiTally)····································} | ||
| 12 | ·····{8·=>·(multigraded,·BettiTally)······························} | 12 | ·····{8·=>·(multigraded,·BettiTally)······························} |
| 13 | ·····{9·=>·(net,·BettiTally)······································} | 13 | ·····{9·=>·(net,·BettiTally)······································} |
| 14 | ·····{10·=>·(texMath,·BettiTally)·································} | 14 | ·····{10·=>·(texMath,·BettiTally)·································} |
| 15 | ·····{11·=>·(betti,·BettiTally)···································} | 15 | ·····{11·=>·(betti,·BettiTally)···································} |
| 16 | ·····{12·=>·(pdim,·BettiTally)····································} | 16 | ·····{12·=>·(pdim,·BettiTally)····································} |
| 17 | ·····{13·=>·(poincare,·BettiTally)································} | 17 | ·····{13·=>·(poincare,·BettiTally)································} |
| 18 | ·····{14·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················} | 18 | ·····{14·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················} |
| 19 | ·····{15·=>·(degree,·BettiTally)··································} | 19 | ·····{15·=>·(degree,·BettiTally)··································} |
| 20 | ·····{16·=>·(hilbertSeries,·ZZ,·BettiTally)·······················} | 20 | ·····{16·=>·(hilbertSeries,·ZZ,·BettiTally)·······················} |
| 21 | ·····{17·=>·(^,·Ring,·BettiTally)·································} | 21 | ·····{17·=>·(^,·Ring,·BettiTally)·································} |
| 22 | ·····{18·=>·(regularity,·BettiTally)······························} | 22 | ·····{18·=>·(regularity,·BettiTally)······························} |
| 23 | ·····{19·=>·(mathML,·BettiTally)··································} | 23 | ·····{19·=>·(mathML,·BettiTally)··································} |
| 24 | ·····{20·=>·(dual,·BettiTally)····································} | ||
| 25 | ·····{2 | 24 | ·····{20·=>·(codim,·BettiTally)···································} |
| 25 | ·····{21·=>·(truncate,·BettiTally,·ZZ,·ZZ)························} | ||
| 26 | ·····{22·=>·(truncate,·BettiTally,·InfiniteNumber | 26 | ·····{22·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············} |
| 27 | ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············} | 27 | ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············} |
| 28 | ·····{24·=>·(truncate,·BettiTally,· | 28 | ·····{24·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)} |
| 29 | ·····{25·=>·( | 29 | ·····{25·=>·(dual,·BettiTally)····································} |
| 30 | o1·:·NumberedVerticalList | 30 | o1·:·NumberedVerticalList |
| 31 | i2·:·methods·resolution | 31 | i2·:·methods·resolution |
| 32 | o2·=·{0·=>·(resolution,·Ideal)·} | 32 | o2·=·{0·=>·(resolution,·Ideal)·} |
| 33 | ·····{1·=>·(resolution,·Module)} | 33 | ·····{1·=>·(resolution,·Module)} |
| Offset 60, 20 lines modified | Offset 60, 20 lines modified | ||
| 60 | ·····{1·=>·(++,·Module,·GradedModule)} | 60 | ·····{1·=>·(++,·Module,·GradedModule)} |
| 61 | ·····{2·=>·(++,·Module,·Module)······} | 61 | ·····{2·=>·(++,·Module,·Module)······} |
| 62 | o4·:·NumberedVerticalList | 62 | o4·:·NumberedVerticalList |
| 63 | i5·:·methods(·Matrix,·Matrix·) | 63 | i5·:·methods(·Matrix,·Matrix·) |
| 64 | o5·=·{0·=>·(contract,·Matrix,·Matrix)····························} | ||
| 65 | ·····{1·=>·(-,·Matrix,·Matrix)···································} | ||
| 66 | 64 | o5·=·{0·=>·(diff,·Matrix,·Matrix)································} | |
| 67 | ·····{ | 65 | ·····{1·=>·(diff',·Matrix,·Matrix)·······························} |
| 68 | ·····{ | 66 | ·····{2·=>·(+,·Matrix,·Matrix)···································} |
| 67 | ·····{3·=>·(-,·Matrix,·Matrix)···································} | ||
| 69 | ·····{ | 68 | ·····{4·=>·(contract',·Matrix,·Matrix)···························} |
| 69 | ·····{5·=>·(contract,·Matrix,·Matrix)····························} | ||
| 70 | ·····{6·=>·(markedGB,·Matrix,·Matrix)····························} | 70 | ·····{6·=>·(markedGB,·Matrix,·Matrix)····························} |
| 71 | ·····{7·=>·(Hom,·Matrix,·Matrix)·································} | 71 | ·····{7·=>·(Hom,·Matrix,·Matrix)·································} |
| 72 | ·····{8·=>·(==,·Matrix,·Matrix)··································} | 72 | ·····{8·=>·(==,·Matrix,·Matrix)··································} |
| 73 | ·····{9·=>·(*,·Matrix,·Matrix)···································} | 73 | ·····{9·=>·(*,·Matrix,·Matrix)···································} |
| 74 | ·····{10·=>·(|,·Matrix,·Matrix)··································} | 74 | ·····{10·=>·(|,·Matrix,·Matrix)··································} |
| 75 | ·····{11·=>·(||,·Matrix,·Matrix)·································} | 75 | ·····{11·=>·(||,·Matrix,·Matrix)·································} |
| 76 | ·····{12·=>·(subquotient,·Matrix,·Matrix)························} | 76 | ·····{12·=>·(subquotient,·Matrix,·Matrix)························} |
| Offset 88, 18 lines modified | Offset 88, 18 lines modified | ||
| 88 | ·····{21·=>·(quotient',·Matrix,·Matrix)··························} | 88 | ·····{21·=>·(quotient',·Matrix,·Matrix)··························} |
| 89 | ·····{22·=>·(quotient,·Matrix,·Matrix)···························} | 89 | ·····{22·=>·(quotient,·Matrix,·Matrix)···························} |
| 90 | ·····{23·=>·(remainder',·Matrix,·Matrix)·························} | 90 | ·····{23·=>·(remainder',·Matrix,·Matrix)·························} |
| 91 | ·····{24·=>·(remainder,·Matrix,·Matrix)··························} | 91 | ·····{24·=>·(remainder,·Matrix,·Matrix)··························} |
| 92 | ·····{25·=>·(%,·Matrix,·Matrix)··································} | 92 | ·····{25·=>·(%,·Matrix,·Matrix)··································} |
| 93 | ·····{26·=>·(pushout,·Matrix,·Matrix)····························} | 93 | ·····{26·=>·(pushout,·Matrix,·Matrix)····························} |
| 94 | ·····{27·=>·(solve,·Matrix,·Matrix)······························} | 94 | ·····{27·=>·(solve,·Matrix,·Matrix)······························} |
| 95 | ·····{28·=>·(intersection,·Matrix,·Matrix)·······················} | ||
| 96 | ·····{29·=>·(tensor,·Matrix,·Matrix)·····························} | ||
| 97 | ·····{30·=>·(intersection,·Matrix,·Matrix,·Matrix,·Matrix)·······} | ||
| 98 | ·····{ | 95 | ·····{28·=>·(pullback,·Matrix,·Matrix)···························} |
| 96 | ·····{29·=>·(intersection,·Matrix,·Matrix,·Matrix,·Matrix)·······} | ||
| 97 | ·····{30·=>·(tensor,·Matrix,·Matrix)·····························} | ||
| 98 | ·····{31·=>·(intersection,·Matrix,·Matrix)·······················} | ||
| 99 | ·····{32·=>·(substitute,·Matrix,·Matrix)·························} | 99 | ·····{32·=>·(substitute,·Matrix,·Matrix)·························} |
| 100 | ·····{33·=>·(checkDegrees,·Matrix,·Matrix)·······················} | 100 | ·····{33·=>·(checkDegrees,·Matrix,·Matrix)·······················} |
| 101 | ·····{34·=>·(isIsomorphic,·Matrix,·Matrix)·······················} | 101 | ·····{34·=>·(isIsomorphic,·Matrix,·Matrix)·······················} |
| 102 | ·····{35·=>·(coneFromVData,·Matrix,·Matrix)······················} | 102 | ·····{35·=>·(coneFromVData,·Matrix,·Matrix)······················} |
| 103 | ·····{36·=>·(coneFromHData,·Matrix,·Matrix)······················} | 103 | ·····{36·=>·(coneFromHData,·Matrix,·Matrix)······················} |
| 104 | ·····{37·=>·(fan,·Matrix,·Matrix,·List)··························} | 104 | ·····{37·=>·(fan,·Matrix,·Matrix,·List)··························} |
| 105 | ·····{38·=>·(fan,·Matrix,·Matrix,·Sequence)······················} | 105 | ·····{38·=>·(fan,·Matrix,·Matrix,·Sequence)······················} |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i2·:·S·=·ring·I | 9 | i2·:·S·=·ring·I |
| 10 | o2·=·S | 10 | o2·=·S |
| 11 | o2·:·PolynomialRing | 11 | o2·:·PolynomialRing |
| 12 | i3·:·elapsedTime·C·=·minimalBetti·I | 12 | i3·:·elapsedTime·C·=·minimalBetti·I |
| 13 | ·--· | 13 | ·--·2.19295s·elapsed |
| 14 | ············0··1···2···3···4····5···6···7···8··9·10 | 14 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 15 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 15 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 16 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 16 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 17 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 17 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 18 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 18 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 19 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 19 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 26, 44 lines modified | Offset 26, 44 lines modified | ||
| 26 | o3·:·BettiTally | 26 | o3·:·BettiTally |
| 27 | i4·:·I·=·ideal·I_*; | 27 | i4·:·I·=·ideal·I_*; |
| 28 | o4·:·Ideal·of·S | 28 | o4·:·Ideal·of·S |
| 29 | i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) | 29 | i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) |
| 30 | ·--·. | 30 | ·--·.801544s·elapsed |
| 31 | ············0··1···2···3···4····5···6···7 | 31 | ············0··1···2···3···4····5···6···7 |
| 32 | o5·=·total:·1·35·140·385·819·1080·735·196 | 32 | o5·=·total:·1·35·140·385·819·1080·735·196 |
| 33 | ·········0:·1··.···.···.···.····.···.···. | 33 | ·········0:·1··.···.···.···.····.···.···. |
| 34 | ·········1:·.·35·140·189··84····.···.···. | 34 | ·········1:·.·35·140·189··84····.···.···. |
| 35 | ·········2:·.··.···.·196·735·1080·735·196 | 35 | ·········2:·.··.···.·196·735·1080·735·196 |
| 36 | o5·:·BettiTally | 36 | o5·:·BettiTally |
| 37 | i6·:·I·=·ideal·I_*; | 37 | i6·:·I·=·ideal·I_*; |
| 38 | o6·:·Ideal·of·S | 38 | o6·:·Ideal·of·S |
| 39 | i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) | 39 | i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) |
| 40 | ·--·.0 | 40 | ·--·.0304048s·elapsed |
| 41 | ············0··1···2···3··4 | 41 | ············0··1···2···3··4 |
| 42 | o7·=·total:·1·35·140·189·84 | 42 | o7·=·total:·1·35·140·189·84 |
| 43 | ·········0:·1··.···.···.··. | 43 | ·········0:·1··.···.···.··. |
| 44 | ·········1:·.·35·140·189·84 | 44 | ·········1:·.·35·140·189·84 |
| 45 | o7·:·BettiTally | 45 | o7·:·BettiTally |
| 46 | i8·:·I·=·ideal·I_*; | 46 | i8·:·I·=·ideal·I_*; |
| 47 | o8·:·Ideal·of·S | 47 | o8·:·Ideal·of·S |
| 48 | i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) | 48 | i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) |
| 49 | ·--·1. | 49 | ·--·1.69004s·elapsed |
| 50 | ············0··1···2···3···4····5 | 50 | ············0··1···2···3···4····5 |
| 51 | o9·=·total:·1·35·140·385·819·1080 | 51 | o9·=·total:·1·35·140·385·819·1080 |
| 52 | ·········0:·1··.···.···.···.····. | 52 | ·········0:·1··.···.···.···.····. |
| 53 | ·········1:·.·35·140·189··84····. | 53 | ·········1:·.·35·140·189··84····. |
| 54 | ·········2:·.··.···.·196·735·1080 | 54 | ·········2:·.··.···.·196·735·1080 |
| Offset 1, 22 lines modified | Offset 1, 22 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·15555226809509933135 | 1 | --·-*-·M2-comint·-*-·hash:·15555226809509933135 |
| 2 | i1·:·p·=·temporaryFileName()·|·"/" | 2 | i1·:·p·=·temporaryFileName()·|·"/" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3499710-0/0/ |
| 4 | i2·:·mkdir·p | 4 | i2·:·mkdir·p |
| 5 | i3·:·isDirectory·p | 5 | i3·:·isDirectory·p |
| 6 | o3·=·true | 6 | o3·=·true |
| 7 | i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close | 7 | i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close |
| 8 | o4·=·/tmp/M2- | 8 | o4·=·/tmp/M2-3499710-0/0/foo |
| 9 | o4·:·File | 9 | o4·:·File |
| 10 | i5·:·get·fn | 10 | i5·:·get·fn |
| 11 | o5·=·hi·there | 11 | o5·=·hi·there |
| Offset 1, 31 lines modified | Offset 1, 31 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·4857944042471093218 | 1 | --·-*-·M2-comint·-*-·hash:·4857944042471093218 |
| 2 | i1·:·src·=·temporaryFileName() | 2 | i1·:·src·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3498163-0/0 |
| 4 | i2·:·dst·=·temporaryFileName() | 4 | i2·:·dst·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3498163-0/1 |
| 6 | i3·:·src·<<·"hi·there"·<<·close | 6 | i3·:·src·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3498163-0/0 |
| 8 | o3·:·File | 8 | o3·:·File |
| 9 | i4·:·moveFile(src,dst,Verbose=>true) | 9 | i4·:·moveFile(src,dst,Verbose=>true) |
| 10 | --moving:·/tmp/M2- | 10 | --moving:·/tmp/M2-3498163-0/0·->·/tmp/M2-3498163-0/1 |
| 11 | i5·:·get·dst | 11 | i5·:·get·dst |
| 12 | o5·=·hi·there | 12 | o5·=·hi·there |
| 13 | i6·:·bak·=·moveFile(dst,Verbose=>true) | 13 | i6·:·bak·=·moveFile(dst,Verbose=>true) |
| 14 | --backup·file·created:·/tmp/M2- | 14 | --backup·file·created:·/tmp/M2-3498163-0/1.bak |
| 15 | o6·=·/tmp/M2- | 15 | o6·=·/tmp/M2-3498163-0/1.bak |
| 16 | i7·:·removeFile·bak | 16 | i7·:·removeFile·bak |
| 17 | i8·:· | 17 | i8·:· |
| Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1331114612441 | 1 | --·-*-·M2-comint·-*-·hash:·1331114612441 |
| 2 | i1·:·elapsedTime·nanosleep·500000000 | 2 | i1·:·elapsedTime·nanosleep·500000000 |
| 3 | ·--·.5000 | 3 | ·--·.500108s·elapsed |
| 4 | o1·=·0 | 4 | o1·=·0 |
| 5 | i2·:· | 5 | i2·:· |
| Offset 5, 18 lines modified | Offset 5, 18 lines modified | ||
| 5 | o1·=·{1,·2,·6,·24,·120,·720,·5040,·40320,·362880,·3628800} | 5 | o1·=·{1,·2,·6,·24,·120,·720,·5040,·40320,·362880,·3628800} |
| 6 | o1·:·List | 6 | o1·:·List |
| 7 | i2·:·L·=·random·toList·(1..10000); | 7 | i2·:·L·=·random·toList·(1..10000); |
| 8 | i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); | 8 | i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); |
| 9 | ·--·. | 9 | ·--·.900132s·elapsed |
| 10 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); | 10 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); |
| 11 | ·--·. | 11 | ·--·.239973s·elapsed |
| 12 | i5·:·allowableThreads | 12 | i5·:·allowableThreads |
| 13 | o5·=·5 | 13 | o5·=·5 |
| 14 | i6·:·allowableThreads·=·maxAllowableThreads | 14 | i6·:·allowableThreads·=·maxAllowableThreads |
| Offset 47, 15 lines modified | Offset 47, 15 lines modified | ||
| 47 | o11·=·<<task,·created>> | 47 | o11·=·<<task,·created>> |
| 48 | o11·:·Task | 48 | o11·:·Task |
| 49 | i12·:·t | 49 | i12·:·t |
| 50 | o12·=·<<task,· | 50 | o12·=·<<task,·running>> |
| 51 | o12·:·Task | 51 | o12·:·Task |
| 52 | i13·:·isReady·t | 52 | i13·:·isReady·t |
| 53 | o13·=·false | 53 | o13·=·false |
| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | i3·:·S·=·ring·I | 67 | i3·:·S·=·ring·I |
| 68 | o3·=·S | 68 | o3·=·S |
| 69 | o3·:·PolynomialRing | 69 | o3·:·PolynomialRing |
| 70 | i4·:·elapsedTime·minimalBetti·I | 70 | i4·:·elapsedTime·minimalBetti·I |
| 71 | ·--· | 71 | ·--·2.57235s·elapsed |
| 72 | ············0··1···2···3···4····5···6···7···8··9·10 | 72 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 73 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 73 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 74 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 74 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 75 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 75 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 76 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 76 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 77 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 77 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | o4·:·BettiTally | 84 | o4·:·BettiTally |
| 85 | i5·:·I·=·ideal·I_*; | 85 | i5·:·I·=·ideal·I_*; |
| 86 | o5·:·Ideal·of·S | 86 | o5·:·Ideal·of·S |
| 87 | i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) | 87 | i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) |
| 88 | ·--· | 88 | ·--·2.70669s·elapsed |
| 89 | ············0··1···2···3···4····5···6···7···8··9·10 | 89 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 90 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 90 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 91 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 91 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 92 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 92 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 93 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 93 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 94 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 94 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | o7·:·Ideal·of·S | 105 | o7·:·Ideal·of·S |
| 106 | i8·:·numTBBThreads·=·1 | 106 | i8·:·numTBBThreads·=·1 |
| 107 | o8·=·1 | 107 | o8·=·1 |
| 108 | i9·:·elapsedTime·minimalBetti(I) | 108 | i9·:·elapsedTime·minimalBetti(I) |
| 109 | ·--· | 109 | ·--·2.6306s·elapsed |
| 110 | ············0··1···2···3···4····5···6···7···8··9·10 | 110 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 111 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 111 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 112 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 112 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 113 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 113 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 114 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 114 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 115 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 115 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 132, 15 lines modified | Offset 132, 15 lines modified | ||
| 132 | o11·=·0 | 132 | o11·=·0 |
| 133 | i12·:·I·=·ideal·I_*; | 133 | i12·:·I·=·ideal·I_*; |
| 134 | o12·:·Ideal·of·S | 134 | o12·:·Ideal·of·S |
| 135 | i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 135 | i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 136 | ·--· | 136 | ·--·2.44039s·elapsed |
| 137 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 | 137 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 138 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S | 138 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S |
| 139 | ·································································································· | 139 | ·································································································· |
| 140 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 | 140 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 |
| 141 | o13·:·Complex | 141 | o13·:·Complex |
| Offset 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | o14·=·1 | 150 | o14·=·1 |
| 151 | i15·:·I·=·ideal·I_*; | 151 | i15·:·I·=·ideal·I_*; |
| 152 | o15·:·Ideal·of·S | 152 | o15·:·Ideal·of·S |
| 153 | i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 153 | i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 154 | ·--· | 154 | ·--·2.62356s·elapsed |
| 155 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 | 155 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 156 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S | 156 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S |
| 157 | ·································································································· | 157 | ·································································································· |
| 158 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 | 158 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 |
| 159 | o16·:·Complex | 159 | o16·:·Complex |
| Offset 174, 43 lines modified | Offset 174, 43 lines modified | ||
| 174 | o18·:·PolynomialRing | 174 | o18·:·PolynomialRing |
| 175 | i19·:·I·=·ideal·random(S^1,·S^{4:-5}); | 175 | i19·:·I·=·ideal·random(S^1,·S^{4:-5}); |
| 176 | o19·:·Ideal·of·S | 176 | o19·:·Ideal·of·S |
| 177 | i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 177 | i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 178 | ·--· | 178 | ·--·4.30019s·elapsed |
| 179 | ··············1······108 | 179 | ··············1······108 |
| 180 | o20·:·Matrix·S··<--·S | 180 | o20·:·Matrix·S··<--·S |
| 181 | i21·:·numTBBThreads·=·1 | 181 | i21·:·numTBBThreads·=·1 |
| 182 | o21·=·1 | 182 | o21·=·1 |
| 183 | i22·:·I·=·ideal·I_*; | 183 | i22·:·I·=·ideal·I_*; |
| 184 | o22·:·Ideal·of·S | 184 | o22·:·Ideal·of·S |
| 185 | i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 185 | i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 186 | ·--· | 186 | ·--·10.041s·elapsed |
| 187 | ··············1······108 | 187 | ··············1······108 |
| 188 | o23·:·Matrix·S··<--·S | 188 | o23·:·Matrix·S··<--·S |
| 189 | i24·:·numTBBThreads·=·10 | 189 | i24·:·numTBBThreads·=·10 |
| 190 | o24·=·10 | 190 | o24·=·10 |
| 191 | i25·:·I·=·ideal·I_*; | 191 | i25·:·I·=·ideal·I_*; |
| 192 | o25·:·Ideal·of·S | 192 | o25·:·Ideal·of·S |
| 193 | i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 193 | i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 194 | ·--· | 194 | ·--·4.87683s·elapsed |
| 195 | ··············1······108 | 195 | ··············1······108 |
| 196 | o26·:·Matrix·S··<--·S | 196 | o26·:·Matrix·S··<--·S |
| 197 | i27·:·needsPackage·"AssociativeAlgebras" | 197 | i27·:·needsPackage·"AssociativeAlgebras" |
| 198 | o27·=·AssociativeAlgebras | 198 | o27·=·AssociativeAlgebras |
| Offset 233, 15 lines modified | Offset 233, 15 lines modified | ||
| 233 | o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·) | 233 | o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·) |
| 234 | ················ZZ | 234 | ················ZZ |
| Max diff block lines reached; 595/4200 bytes (14.17%) of diff not shown. | |||
| Offset 146, 65 lines modified | Offset 146, 65 lines modified | ||
| 146 | o26·:·ZZ[T] | 146 | o26·:·ZZ[T] |
| 147 | i27·:·gbTrace·=·3 | 147 | i27·:·gbTrace·=·3 |
| 148 | o27·=·3 | 148 | o27·=·3 |
| 149 | i28·:·time·poincare·I | 149 | i28·:·time·poincare·I |
| 150 | ·--·used·0.00 | 150 | ·--·used·0.00361402s·(cpu);·1.2253e-05s·(thread);·0s·(gc) |
| 151 | ············3·····6····9 | 151 | ············3·····6····9 |
| 152 | o28·=·1·-·3T··+·3T··-·T | 152 | o28·=·1·-·3T··+·3T··-·T |
| 153 | o28·:·ZZ[T] | 153 | o28·:·ZZ[T] |
| 154 | i29·:·time·gens·gb·I; | 154 | i29·:·time·gens·gb·I; |
| 155 | ···--·registering·gb·19·at·0x7f | 155 | ···--·registering·gb·19·at·0x7f1ed7243e00 |
| 156 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11 | 156 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11 |
| 157 | ···--·number·of·monomials················=·4186 | 157 | ···--·number·of·monomials················=·4186 |
| 158 | ···--·#reduction·steps·=·38 | 158 | ···--·#reduction·steps·=·38 |
| 159 | ···--·#spairs·done·=·11 | 159 | ···--·#spairs·done·=·11 |
| 160 | ···--·ncalls·=·10 | 160 | ···--·ncalls·=·10 |
| 161 | ···--·nloop·=·29 | 161 | ···--·nloop·=·29 |
| 162 | ···--·nsaved·=·0 | 162 | ···--·nsaved·=·0 |
| 163 | ···--··--·used·0.0 | 163 | ···--··--·used·0.0123727s·(cpu);·0.0157315s·(thread);·0s·(gc) |
| 164 | ··············1······11 | 164 | ··············1······11 |
| 165 | o29·:·Matrix·R··<--·R | 165 | o29·:·Matrix·R··<--·R |
| 166 | i30·:·R·=·QQ[a..d]; | 166 | i30·:·R·=·QQ[a..d]; |
| 167 | i31·:·I·=·ideal·random(R^1,·R^{3:-3}); | 167 | i31·:·I·=·ideal·random(R^1,·R^{3:-3}); |
| 168 | ···--·registering·gb·20·at·0x7f | 168 | ···--·registering·gb·20·at·0x7f1ed7243c40 |
| 169 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 | 169 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 |
| 170 | ···--·number·of·monomials················=·0 | 170 | ···--·number·of·monomials················=·0 |
| 171 | ···--·#reduction·steps·=·0 | 171 | ···--·#reduction·steps·=·0 |
| 172 | ···--·#spairs·done·=·0 | 172 | ···--·#spairs·done·=·0 |
| 173 | ···--·ncalls·=·0 | 173 | ···--·ncalls·=·0 |
| 174 | ···--·nloop·=·0 | 174 | ···--·nloop·=·0 |
| 175 | ···--·nsaved·=·0 | 175 | ···--·nsaved·=·0 |
| 176 | ···--· | 176 | ···--· |
| 177 | o31·:·Ideal·of·R | 177 | o31·:·Ideal·of·R |
| 178 | i32·:·time·p·=·poincare·I | 178 | i32·:·time·p·=·poincare·I |
| 179 | ···--·registering·gb·21·at·0x7f | 179 | ···--·registering·gb·21·at·0x7f1ed72438c0 |
| 180 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11 | 180 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11 |
| 181 | ···--·number·of·monomials················=·267 | 181 | ···--·number·of·monomials················=·267 |
| 182 | ···--·#reduction·steps·=·236 | 182 | ···--·#reduction·steps·=·236 |
| 183 | ···--·#spairs·done·=·30 | 183 | ···--·#spairs·done·=·30 |
| 184 | ···--·ncalls·=·10 | 184 | ···--·ncalls·=·10 |
| 185 | ···--·nloop·=·20 | 185 | ···--·nloop·=·20 |
| 186 | ···--·nsaved·=·0 | 186 | ···--·nsaved·=·0 |
| 187 | ···--··--·used·0.00 | 187 | ···--··--·used·0.0079994s·(cpu);·0.00685187s·(thread);·0s·(gc) |
| 188 | ············3·····6····9 | 188 | ············3·····6····9 |
| 189 | o32·=·1·-·3T··+·3T··-·T | 189 | o32·=·1·-·3T··+·3T··-·T |
| 190 | o32·:·ZZ[T] | 190 | o32·:·ZZ[T] |
| 191 | i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2] | 191 | i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2] |
| Offset 254, 27 lines modified | Offset 254, 27 lines modified | ||
| 254 | i36·:·gbTrace·=·3 | 254 | i36·:·gbTrace·=·3 |
| 255 | o36·=·3 | 255 | o36·=·3 |
| 256 | i37·:·time·gens·gb·J; | 256 | i37·:·time·gens·gb·J; |
| 257 | ···--·registering·gb·22·at·0x7f | 257 | ···--·registering·gb·22·at·0x7f1ed7243700 |
| 258 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m | 258 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m |
| 259 | ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m | 259 | ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m |
| 260 | ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m | 260 | ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m |
| 261 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39 | 261 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39 |
| 262 | ···--·number·of·monomials················=·1051 | 262 | ···--·number·of·monomials················=·1051 |
| 263 | ···--·#reduction·steps·=·284 | 263 | ···--·#reduction·steps·=·284 |
| 264 | ···--·#spairs·done·=·53 | 264 | ···--·#spairs·done·=·53 |
| 265 | ···--·ncalls·=·46 | 265 | ···--·ncalls·=·46 |
| 266 | ···--·nloop·=·54 | 266 | ···--·nloop·=·54 |
| 267 | ···--·nsaved·=·0 | 267 | ···--·nsaved·=·0 |
| 268 | ···--··--·used·0.0 | 268 | ···--··--·used·0.0639807s·(cpu);·0.066879s·(thread);·0s·(gc) |
| 269 | ··············1······39 | 269 | ··············1······39 |
| 270 | o37·:·Matrix·S··<--·S | 270 | o37·:·Matrix·S··<--·S |
| 271 | i38·:·selectInSubring(1,·gens·gb·J) | 271 | i38·:·selectInSubring(1,·gens·gb·J) |
| 272 | o38·=·|·243873059890414515367459726418219472801881021280016638460434780718278 | 272 | o38·=·|·243873059890414515367459726418219472801881021280016638460434780718278 |
| Offset 1, 7 lines modified | Offset 1, 7 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1330513630563 | 1 | --·-*-·M2-comint·-*-·hash:·1330513630563 |
| 2 | i1·:·processID() | 2 | i1·:·processID() |
| 3 | o1·=· | 3 | o1·=·3485508 |
| 4 | i2·:· | 4 | i2·:· |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | ······123····110····13 | 10 | ······123····110····13 |
| 11 | o2·=·x····+·x····+·x···+·1 | 11 | o2·=·x····+·x····+·x···+·1 |
| 12 | o2·:·R | 12 | o2·:·R |
| 13 | i3·:·time·factor·f | 13 | i3·:·time·factor·f |
| 14 | ·--·used·0.00 | 14 | ·--·used·0.00402279s·(cpu);·0.00401581s·(thread);·0s·(gc) |
| 15 | ··············2········2·······2·······2·······2·······4·····3······2············4·····3·····2············4·····3·····2············10·····8·····6·····4······2·······10·····8······6·····4······2·······10······8····6····4·····2·······10······8·····6·····4······2·······10······8·····6·····4·····2·······10······8·····6······4·····2·······10······8·····6·····4······2·······10······8·····6······4·····2·······10·····8····6····4······2·······10·····8······6·····4······2 | 15 | ··············2········2·······2·······2·······2·······4·····3······2············4·····3·····2············4·····3·····2············10·····8·····6·····4······2·······10·····8······6·····4······2·······10······8····6····4·····2·······10······8·····6·····4······2·······10······8·····6·····4·····2·······10······8·····6······4·····2·······10······8·····6·····4······2·······10······8·····6······4·····2·······10·····8····6····4······2·······10·····8······6·····4······2 |
| 16 | o3·=·(x·+·1)(x··-·15)(x··+·8)(x··+·4)(x··+·2)(x··+·1)(x··-·4x··+·11x··-·4x·+·1)(x··-·6x··-·2x··-·6x·+·1)(x··+·9x··-·4x··+·9x·+·1)(x···-·5x··-·8x··-·4x··-·13x··+·1)(x···-·9x··+·15x··-·2x··+·10x··+·1)(x···-·10x··-·x··-·x··+·9x··+·1)(x···-·11x··-·8x··-·4x··+·11x··+·1)(x···-·13x··-·4x··-·8x··-·5x··+·1)(x···+·13x··-·2x··+·15x··+·5x··+·1)(x···+·11x··-·4x··-·8x··-·11x··+·1)(x···+·10x··-·2x··+·15x··-·9x··+·1)(x···+·9x··-·x··-·x··-·10x··+·1)(x···+·5x··+·15x··-·2x··+·13x··+·1) | 16 | o3·=·(x·+·1)(x··-·15)(x··+·8)(x··+·4)(x··+·2)(x··+·1)(x··-·4x··+·11x··-·4x·+·1)(x··-·6x··-·2x··-·6x·+·1)(x··+·9x··-·4x··+·9x·+·1)(x···-·5x··-·8x··-·4x··-·13x··+·1)(x···-·9x··+·15x··-·2x··+·10x··+·1)(x···-·10x··-·x··-·x··+·9x··+·1)(x···-·11x··-·8x··-·4x··+·11x··+·1)(x···-·13x··-·4x··-·8x··-·5x··+·1)(x···+·13x··-·2x··+·15x··+·5x··+·1)(x···+·11x··-·4x··-·8x··-·11x··+·1)(x···+·10x··-·2x··+·15x··-·9x··+·1)(x···+·9x··-·x··-·x··-·10x··+·1)(x···+·5x··+·15x··-·2x··+·13x··+·1) |
| 17 | o3·:·Expression·of·class·Product | 17 | o3·:·Expression·of·class·Product |
| 18 | i4·:·g·=·()·->·factor·f | 18 | i4·:·g·=·()·->·factor·f |
| Offset 38, 11 lines modified | Offset 38, 11 lines modified | ||
| 38 | o6·=·h | 38 | o6·=·h |
| 39 | o6·:·FunctionClosure | 39 | o6·:·FunctionClosure |
| 40 | i7·:·for·i·to·10·do·(g();h();h()) | 40 | i7·:·for·i·to·10·do·(g();h();h()) |
| 41 | i8·:·profileSummary | 41 | i8·:·profileSummary |
| 42 | g:·11·times,·used·.0 | 42 | g:·11·times,·used·.0393458·seconds |
| 43 | h:·22·times,·used·.0 | 43 | h:·22·times,·used·.0787814·seconds |
| 44 | i9·:· | 44 | i9·:· |
| Offset 13, 15 lines modified | Offset 13, 15 lines modified | ||
| 13 | i5·:·codim·I,·degree·I | 13 | i5·:·codim·I,·degree·I |
| 14 | o5·=·(2,·10) | 14 | o5·=·(2,·10) |
| 15 | o5·:·Sequence | 15 | o5·:·Sequence |
| 16 | i6·:·time·randomKRationalPoint(I) | 16 | i6·:·time·randomKRationalPoint(I) |
| 17 | ·--·used·0. | 17 | ·--·used·0.112493s·(cpu);·0.0977693s·(thread);·0s·(gc) |
| 18 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) | 18 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) |
| 19 | ·············2······3···1·····3···0·····3 | 19 | ·············2······3···1·····3···0·····3 |
| 20 | o6·:·Ideal·of·R | 20 | o6·:·Ideal·of·R |
| 21 | i7·:·R=kk[x_0..x_5]; | 21 | i7·:·R=kk[x_0..x_5]; |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | i9·:·codim·I,·degree·I | 33 | i9·:·codim·I,·degree·I |
| 34 | o9·=·(3,·10) | 34 | o9·=·(3,·10) |
| 35 | o9·:·Sequence | 35 | o9·:·Sequence |
| 36 | i10·:·time·randomKRationalPoint(I) | 36 | i10·:·time·randomKRationalPoint(I) |
| 37 | ·--·used·0. | 37 | ·--·used·0.348078s·(cpu);·0.305079s·(thread);·0s·(gc) |
| 38 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) | 38 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) |
| 39 | ··············4······5···3······5···2·····5···1······5···0······5 | 39 | ··············4······5···3······5···2·····5···1······5···0······5 |
| 40 | o10·:·Ideal·of·R | 40 | o10·:·Ideal·of·R |
| 41 | i11·:·p=10007,kk=ZZ/p,R=kk[x_0..x_2] | 41 | i11·:·p=10007,kk=ZZ/p,R=kk[x_0..x_2] |
| Offset 58, 12 lines modified | Offset 58, 12 lines modified | ||
| 58 | i14·:·I=ideal·random(n,R); | 58 | i14·:·I=ideal·random(n,R); |
| 59 | o14·:·Ideal·of·R | 59 | o14·:·Ideal·of·R |
| 60 | i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c); | 60 | i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c); |
| 61 | ·····················#select(degs,d->d==1))),f->f>0)) | 61 | ·····················#select(degs,d->d==1))),f->f>0)) |
| 62 | ·--·used· | 62 | ·--·used·3.34962s·(cpu);·1.918s·(thread);·0s·(gc) |
| 63 | o15·=·58 | 63 | o15·=·58 |
| 64 | i16·:· | 64 | i16·:· |
| Offset 1, 26 lines modified | Offset 1, 26 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·20910736704070514 | 1 | --·-*-·M2-comint·-*-·hash:·20910736704070514 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3506286-0/0 |
| 4 | i2·:·makeDirectory·dir | 4 | i2·:·makeDirectory·dir |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3506286-0/0 |
| 6 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close | 6 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3506286-0/0/foo |
| 8 | o3·:·File | 8 | o3·:·File |
| 9 | i4·:·readDirectory·dir | 9 | i4·:·readDirectory·dir |
| 10 | o4·=·{ | 10 | o4·=·{foo,·.,·..} |
| 11 | o4·:·List | 11 | o4·:·List |
| 12 | i5·:·removeFile·fn | 12 | i5·:·removeFile·fn |
| 13 | i6·:·removeDirectory·dir | 13 | i6·:·removeDirectory·dir |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·13513555104200944796 | 1 | --·-*-·M2-comint·-*-·hash:·13513555104200944796 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3502046-0/0 |
| 4 | i2·:·fn·<<·"z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"·<<·endl·<<·close | 4 | i2·:·fn·<<·"z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"·<<·endl·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3502046-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·get·fn | 7 | i3·:·get·fn |
| 8 | o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2 | 8 | o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2 |
| 9 | ·····+8*y^3 | 9 | ·····+8*y^3 |
| Offset 38, 15 lines modified | Offset 38, 15 lines modified | ||
| 38 | o6·:·Expression·of·class·Product | 38 | o6·:·Expression·of·class·Product |
| 39 | i7·:·fn·<<·"sample·=·2^100 | 39 | i7·:·fn·<<·"sample·=·2^100 |
| 40 | ·····print·sample | 40 | ·····print·sample |
| 41 | ·····"·<<·close | 41 | ·····"·<<·close |
| 42 | o7·=·/tmp/M2- | 42 | o7·=·/tmp/M2-3502046-0/0 |
| 43 | o7·:·File | 43 | o7·:·File |
| 44 | i8·:·get·fn | 44 | i8·:·get·fn |
| 45 | o8·=·sample·=·2^100 | 45 | o8·=·sample·=·2^100 |
| 46 | ·····print·sample | 46 | ·····print·sample |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·4408639611478781130 | 1 | --·-*-·M2-comint·-*-·hash:·4408639611478781130 |
| 2 | i1·:·p·=·temporaryFileName·() | 2 | i1·:·p·=·temporaryFileName·() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3507307-0/0 |
| 4 | i2·:·symlinkFile·("foo",·p) | 4 | i2·:·symlinkFile·("foo",·p) |
| 5 | i3·:·readlink·p | 5 | i3·:·readlink·p |
| 6 | o3·=·foo | 6 | o3·=·foo |
| Offset 1, 39 lines modified | Offset 1, 39 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·324072347213224656 | 1 | --·-*-·M2-comint·-*-·hash:·324072347213224656 |
| 2 | i1·:·realpath·"." | 2 | i1·:·realpath·"." |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3485508-0/83-rundir/ |
| 4 | i2·:·p·=·temporaryFileName() | 4 | i2·:·p·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3507339-0/0 |
| 6 | i3·:·q·=·temporaryFileName() | 6 | i3·:·q·=·temporaryFileName() |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3507339-0/1 |
| 8 | i4·:·symlinkFile(p,q) | 8 | i4·:·symlinkFile(p,q) |
| 9 | i5·:·p·<<·close | 9 | i5·:·p·<<·close |
| 10 | o5·=·/tmp/M2- | 10 | o5·=·/tmp/M2-3507339-0/0 |
| 11 | o5·:·File | 11 | o5·:·File |
| 12 | i6·:·readlink·q | 12 | i6·:·readlink·q |
| 13 | o6·=·/tmp/M2- | 13 | o6·=·/tmp/M2-3507339-0/0 |
| 14 | i7·:·realpath·q | 14 | i7·:·realpath·q |
| 15 | o7·=·/tmp/M2- | 15 | o7·=·/tmp/M2-3507339-0/0 |
| 16 | i8·:·removeFile·p | 16 | i8·:·removeFile·p |
| 17 | i9·:·removeFile·q | 17 | i9·:·removeFile·q |
| 18 | i10·:·realpath·"" | 18 | i10·:·realpath·"" |
| 19 | o10·=·/tmp/M2- | 19 | o10·=·/tmp/M2-3485508-0/83-rundir/ |
| 20 | i11·:· | 20 | i11·:· |
| Offset 1, 15 lines modified | Offset 1, 15 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1729384374372662693 | 1 | --·-*-·M2-comint·-*-·hash:·1729384374372662693 |
| 2 | i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--")) | 2 | i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--")) |
| 3 | i2·:·collectGarbage()· | 3 | i2·:·collectGarbage()· |
| 4 | --finalization:·(1)[4]:·--·finalizing·sequence·#5·-- | ||
| 5 | --finalization:·( | 4 | --finalization:·(1)[3]:·--·finalizing·sequence·#4·-- |
| 6 | --finalization:·(3)[2]:·--·finalizing·sequence·#3·-- | ||
| 7 | --finalization:·(4)[7]:·--·finalizing·sequence·#8·-- | ||
| 8 | --finalization:·(5)[0]:·--·finalizing·sequence·#1·-- | ||
| 9 | --finalization:·( | 5 | --finalization:·(2)[6]:·--·finalizing·sequence·#7·-- |
| 10 | --finalization:·(7)[5]:·--·finalizing·sequence·#6·-- | ||
| 11 | --finalization:·( | 6 | --finalization:·(3)[1]:·--·finalizing·sequence·#2·-- |
| 7 | --finalization:·(4)[5]:·--·finalizing·sequence·#6·-- | ||
| 8 | --finalization:·(5)[2]:·--·finalizing·sequence·#3·-- | ||
| 9 | --finalization:·(6)[0]:·--·finalizing·sequence·#1·-- | ||
| 10 | --finalization:·(7)[7]:·--·finalizing·sequence·#8·-- | ||
| 11 | --finalization:·(8)[4]:·--·finalizing·sequence·#5·-- | ||
| 12 | i3·:· | 12 | i3·:· |
| Offset 1, 19 lines modified | Offset 1, 19 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·8532980310097060089 | 1 | --·-*-·M2-comint·-*-·hash:·8532980310097060089 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3499826-0/0 |
| 4 | i2·:·makeDirectory·dir | 4 | i2·:·makeDirectory·dir |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3499826-0/0 |
| 6 | i3·:·readDirectory·dir | 6 | i3·:·readDirectory·dir |
| 7 | o3·=·{. | 7 | o3·=·{.,·..} |
| 8 | o3·:·List | 8 | o3·:·List |
| 9 | i4·:·removeDirectory·dir | 9 | i4·:·removeDirectory·dir |
| 10 | i5·:· | 10 | i5·:· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731420232148149387 | 1 | --·-*-·M2-comint·-*-·hash:·1731420232148149387 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3486057-0/0 |
| 4 | i2·:·rootPath·|·fn | 4 | i2·:·rootPath·|·fn |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3486057-0/0 |
| 6 | i3·:· | 6 | i3·:· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731420231525572968 | 1 | --·-*-·M2-comint·-*-·hash:·1731420231525572968 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3506000-0/0 |
| 4 | i2·:·rootURI·|·fn | 4 | i2·:·rootURI·|·fn |
| 5 | o2·=·file:///tmp/M2- | 5 | o2·=·file:///tmp/M2-3506000-0/0 |
| 6 | i3·:· | 6 | i3·:· |
| Offset 25, 19 lines modified | Offset 25, 19 lines modified | ||
| 25 | o4·=·image·|·x2·x2-y2·xyz7·| | 25 | o4·=·image·|·x2·x2-y2·xyz7·| |
| 26 | ·····························1 | 26 | ·····························1 |
| 27 | o4·:·R-module,·submodule·of·R | 27 | o4·:·R-module,·submodule·of·R |
| 28 | i5·:·f·=·temporaryFileName() | 28 | i5·:·f·=·temporaryFileName() |
| 29 | o5·=·/tmp/M2- | 29 | o5·=·/tmp/M2-3505340-0/0 |
| 30 | i6·:·f·<<·toString·(p,m,M)·<<·close | 30 | i6·:·f·<<·toString·(p,m,M)·<<·close |
| 31 | o6·=·/tmp/M2- | 31 | o6·=·/tmp/M2-3505340-0/0 |
| 32 | o6·:·File | 32 | o6·:·File |
| 33 | i7·:·get·f | 33 | i7·:·get·f |
| 34 | o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2, | 34 | o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2, |
| 35 | ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}}) | 35 | ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}}) |
| Offset 191, 18 lines modified | Offset 191, 18 lines modified | ||
| 191 | o25·=·40 | 191 | o25·=·40 |
| 192 | i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A; | 192 | i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A; |
| 193 | i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B; | 193 | i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B; |
| 194 | i30·:·time·X·=·solve(A,B); | 194 | i30·:·time·X·=·solve(A,B); |
| 195 | ·--·used·0.000 | 195 | ·--·used·0.000648597s·(cpu);·0.000642826s·(thread);·0s·(gc) |
| 196 | i31·:·time·X·=·solve(A,B,·MaximalRank=>true); | 196 | i31·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 197 | ·--·used· | 197 | ·--·used·0.00013313s·(cpu);·0.00013318s·(thread);·0s·(gc) |
| 198 | i32·:·norm(A*X-B) | 198 | i32·:·norm(A*X-B) |
| 199 | o32·=·5.111850690840453e-15 | 199 | o32·=·5.111850690840453e-15 |
| 200 | o32·:·RR·(of·precision·53) | 200 | o32·:·RR·(of·precision·53) |
| Offset 211, 18 lines modified | Offset 211, 18 lines modified | ||
| 211 | o33·=·100 | 211 | o33·=·100 |
| 212 | i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A; | 212 | i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A; |
| 213 | i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B; | 213 | i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B; |
| 214 | i38·:·time·X·=·solve(A,B); | 214 | i38·:·time·X·=·solve(A,B); |
| 215 | ·--·used·0.1 | 215 | ·--·used·0.152198s·(cpu);·0.151826s·(thread);·0s·(gc) |
| 216 | i39·:·time·X·=·solve(A,B,·MaximalRank=>true); | 216 | i39·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 217 | ·--·used·0.1 | 217 | ·--·used·0.161831s·(cpu);·0.161927s·(thread);·0s·(gc) |
| 218 | i40·:·norm(A*X-B) | 218 | i40·:·norm(A*X-B) |
| 219 | o40·=·1.491578274689709814082355885932e-28 | 219 | o40·=·1.491578274689709814082355885932e-28 |
| 220 | o40·:·RR·(of·precision·100) | 220 | o40·:·RR·(of·precision·100) |
| Offset 1, 60 lines modified | Offset 1, 60 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·2989513528213557691 | 1 | --·-*-·M2-comint·-*-·hash:·2989513528213557691 |
| 2 | i1·:·src·=·temporaryFileName()·|·"/" | 2 | i1·:·src·=·temporaryFileName()·|·"/" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3502392-0/0/ |
| 4 | i2·:·dst·=·temporaryFileName()·|·"/" | 4 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3502392-0/1/ |
| 6 | i3·:·makeDirectory·(src|"a/") | 6 | i3·:·makeDirectory·(src|"a/") |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-3502392-0/0/a/ |
| 8 | i4·:·makeDirectory·(src|"b/") | 8 | i4·:·makeDirectory·(src|"b/") |
| 9 | o4·=·/tmp/M2- | 9 | o4·=·/tmp/M2-3502392-0/0/b/ |
| 10 | i5·:·makeDirectory·(src|"b/c/") | 10 | i5·:·makeDirectory·(src|"b/c/") |
| 11 | o5·=·/tmp/M2- | 11 | o5·=·/tmp/M2-3502392-0/0/b/c/ |
| 12 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 12 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 13 | o6·=·/tmp/M2- | 13 | o6·=·/tmp/M2-3502392-0/0/a/f |
| 14 | o6·:·File | 14 | o6·:·File |
| 15 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 15 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 16 | o7·=·/tmp/M2- | 16 | o7·=·/tmp/M2-3502392-0/0/a/g |
| 17 | o7·:·File | 17 | o7·:·File |
| 18 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 18 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 19 | o8·=·/tmp/M2- | 19 | o8·=·/tmp/M2-3502392-0/0/b/c/g |
| 20 | o8·:·File | 20 | o8·:·File |
| 21 | i9·:·symlinkDirectory(src,dst,Verbose=>true) | 21 | i9·:·symlinkDirectory(src,dst,Verbose=>true) |
| 22 | --symlinking:·../../../0/b/c/g·->·/tmp/M2- | 22 | --symlinking:·../../../0/b/c/g·->·/tmp/M2-3502392-0/1/b/c/g |
| 23 | --symlinking:·../../0/a/f·->·/tmp/M2-1763448-0/1/a/f | ||
| 24 | --symlinking:·../../0/a/g·->·/tmp/M2- | 23 | --symlinking:·../../0/a/g·->·/tmp/M2-3502392-0/1/a/g |
| 24 | --symlinking:·../../0/a/f·->·/tmp/M2-3502392-0/1/a/f | ||
| 25 | i10·:·get·(dst|"b/c/g") | 25 | i10·:·get·(dst|"b/c/g") |
| 26 | o10·=·ho·there | 26 | o10·=·ho·there |
| 27 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) | 27 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) |
| 28 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2- | 28 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-3502392-0/1/b/c/g |
| 29 | --unsymlinking:·../../0/a/f·->·/tmp/M2-1763448-0/1/a/f | ||
| 30 | --unsymlinking:·../../0/a/g·->·/tmp/M2- | 29 | --unsymlinking:·../../0/a/g·->·/tmp/M2-3502392-0/1/a/g |
| 30 | --unsymlinking:·../../0/a/f·->·/tmp/M2-3502392-0/1/a/f | ||
| 31 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 31 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 32 | o12·=·rm | 32 | o12·=·rm |
| 33 | o12·:·FunctionClosure | 33 | o12·:·FunctionClosure |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·9343844672940306595 | 1 | --·-*-·M2-comint·-*-·hash:·9343844672940306595 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3502663-0/0 |
| 4 | i2·:·symlinkFile("qwert",·fn) | 4 | i2·:·symlinkFile("qwert",·fn) |
| 5 | i3·:·fileExists·fn | 5 | i3·:·fileExists·fn |
| 6 | o3·=·false | 6 | o3·=·false |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1731926531291302106 | 1 | --·-*-·M2-comint·-*-·hash:·1731926531291302106 |
| 2 | i1·:·temporaryFileName·()·|·".tex" | 2 | i1·:·temporaryFileName·()·|·".tex" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3518772-0/0.tex |
| 4 | i2·:·temporaryFileName·()·|·".html" | 4 | i2·:·temporaryFileName·()·|·".html" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-3518772-0/1.html |
| 6 | i3·:· | 6 | i3·:· |
| Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1332435500723 | 1 | --·-*-·M2-comint·-*-·hash:·1332435500723 |
| 2 | i1·:·time·3^30 | 2 | i1·:·time·3^30 |
| 3 | ·--·used· | 3 | ·--·used·2.1891e-05s·(cpu);·7.263e-06s·(thread);·0s·(gc) |
| 4 | o1·=·205891132094649 | 4 | o1·=·205891132094649 |
| 5 | i2·:· | 5 | i2·:· |
| Offset 1, 14 lines modified | Offset 1, 14 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1730988300469098603 | 1 | --·-*-·M2-comint·-*-·hash:·1730988300469098603 |
| 2 | i1·:·timing·3^30 | 2 | i1·:·timing·3^30 |
| 3 | o1·=·205891132094649 | 3 | o1·=·205891132094649 |
| 4 | ·····--·.00001 | 4 | ·····--·.000015199·seconds |
| 5 | o1·:·Time | 5 | o1·:·Time |
| 6 | i2·:·peek·oo | 6 | i2·:·peek·oo |
| 7 | o2·=·Time{.00001 | 7 | o2·=·Time{.000015199,·205891132094649} |
| 8 | i3·:· | 8 | i3·:· |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | ···············"memtailor·version"·=>·1.0 | 33 | ···············"memtailor·version"·=>·1.0 |
| 34 | ···············"mpfi·version"·=>·1.5.4 | 34 | ···············"mpfi·version"·=>·1.5.4 |
| 35 | ···············"mpfr·version"·=>·4.2.1 | 35 | ···············"mpfr·version"·=>·4.2.1 |
| 36 | ···············"mpsolve·version"·=>·3.2.1 | 36 | ···············"mpsolve·version"·=>·3.2.1 |
| 37 | ···············"mysql·version"·=>·not·present | 37 | ···············"mysql·version"·=>·not·present |
| 38 | ···············"normaliz·version"·=>·3.10.4 | 38 | ···············"normaliz·version"·=>·3.10.4 |
| 39 | ···············"ntl·version"·=>·11.5.1 | 39 | ···············"ntl·version"·=>·11.5.1 |
| 40 | ···············"operating·system·release"·=>·6.1 | 40 | ···············"operating·system·release"·=>·6.10.11+bpo-amd64 |
| 41 | ···············"operating·system"·=>·Linux | 41 | ···············"operating·system"·=>·Linux |
| 42 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic·Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition·FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth·Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements·LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings·SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone·ChainComplexExtras·Varieties·Schubert2·PushForward·LocalRings·PruneComplex·BoijSoederberg·BGG·Bruns·InvolutiveBases·ConwayPolynomials·EdgeIdeals·FourTiTwo·StatePolytope·Polyhedra·Truncations·Polymake·gfanInterface·PieriMaps·Normaliz·Posets·XML·OpenMath·SCSCP·RationalPoints·MapleInterface·ConvexInterface·SRdeformations·NumericalAlgebraicGeometry·BeginningMacaulay2·FormalGroupLaws·Graphics·WeylGroups·HodgeIntegrals·Cyclotomic·Binomials·Kronecker·Nauty·ToricVectorBundles·ModuleDeformations·PHCpack·SimplicialDecomposability·BooleanGB·AdjointIdeal·Parametrization·Serialization·NAGtypes·NormalToricVarieties·DGAlgebras·Graphs·GraphicalModels·BIBasis·KustinMiller·Units·NautyGraphs·VersalDeformations·CharacteristicClasses·RandomIdeals·RandomObjects·RandomPlaneCurves·RandomSpaceCurves·RandomGenus14Curves·RandomCanonicalCurves·RandomCurves·TensorComplexes·MonomialAlgebras·QthPower·EliminationMatrices·EllipticIntegrals·Triplets·CompleteIntersectionResolutions·EagonResolution·MCMApproximations·MultiplierIdeals·InvariantRing·QuillenSuslin·EnumerationCurves·Book3264Examples·Divisor·EllipticCurves·HighestWeights·MinimalPrimes·Bertini·TorAlgebra·Permanents·BinomialEdgeIdeals·TateOnProducts·LatticePolytopes·FiniteFittingIdeals·HigherCIOperators·LieTypes·ConformalBlocks·M0nbar·AnalyzeSheafOnP1·MultiplierIdealsDim2·RunExternalM2·NumericalSchubertCalculus·ToricTopology·Cremona·Resultants·VectorFields·SLPexpressions·Miura·ResidualIntersections·Visualize·EquivariantGB·ExampleSystems·RationalMaps·FastMinors·RandomPoints·SwitchingFields·SpectralSequences·SectionRing·OldPolyhedra·OldToricVectorBundles·K3Carpets·ChainComplexOperations·NumericalCertification·PhylogeneticTrees·MonodromySolver·ReactionNetworks·PackageCitations·NumericSolutions·GradedLieAlgebras·InverseSystems·Pullback·EngineTests·SVDComplexes·RandomComplexes·CohomCalg·Topcom·Triangulations·ReflexivePolytopesDB·AbstractToricVarieties·Licenses·TestIdeals·FrobeniusThresholds·Seminormalization·AlgebraicSplines·TriangularSets·Chordal·Tropical·SymbolicPowers·Complexes·GroebnerWalk·RandomMonomialIdeals·Matroids·NumericalImplicitization·NonminimalComplexes·CoincidentRootLoci·RelativeCanonicalResolution·RandomCurvesOverVerySmallFiniteFields·StronglyStableIdeals·SLnEquivariantMatrices·CorrespondenceScrolls·NCAlgebra·SpaceCurves·ExteriorIdeals·ToricInvariants·SegreClasses·SemidefiniteProgramming·SumsOfSquares·MultiGradedRationalMap·AssociativeAlgebras·VirtualResolutions·Quasidegrees·DiffAlg·DeterminantalRepresentations·FGLM·SpechtModule·SchurComplexes·SimplicialPosets·SlackIdeals·PositivityToricBundles·SparseResultants·DecomposableSparseSystems·MixedMultiplicity·PencilsOfQuadrics·ThreadedGB·AdjunctionForSurfaces·VectorGraphics·GKMVarieties·MonomialIntegerPrograms·NoetherianOperators·Hadamard·StatGraphs·GraphicalModelsMLE·EigenSolver·MultiplicitySequence·ResolutionsOfStanleyReisnerRings·NumericalLinearAlgebra·ResLengthThree·MonomialOrbits·MultiprojectiveVarieties·SpecialFanoFourfolds·RationalPoints2·SuperLinearAlgebra·SubalgebraBases·AInfinity·LinearTruncations·ThinSincereQuivers·Python·BettiCharacters·Jets·FunctionFieldDesingularization·HomotopyLieAlgebra·TSpreadIdeals·RealRoots·ExteriorModules·K3Surfaces·GroebnerStrata·QuaternaryQuartics·CotangentSchubert·OnlineLookup·MergeTeX·Probability·Isomorphism·CodingTheory·WhitneyStratifications·JSON·ForeignFunctions·GeometricDecomposability·PseudomonomialPrimaryDecomposition·PolyominoIdeals·MatchingFields·CellularResolutions·SagbiGbDetection·A1BrouwerDegrees·QuadraticIdealExamplesByRoos·TerraciniLoci·MatrixSchubert·RInterface·OIGroebnerBases·PlaneCurveLinearSeries·Valuations·SchurVeronese·VNumber·TropicalToric·MultigradedBGG·AbstractSimplicialComplexes·MultigradedImplicitization·Msolve·Permutations·SCMAlgebras·NumericalSemigroups | 42 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic·Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition·FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth·Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements·LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings·SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone·ChainComplexExtras·Varieties·Schubert2·PushForward·LocalRings·PruneComplex·BoijSoederberg·BGG·Bruns·InvolutiveBases·ConwayPolynomials·EdgeIdeals·FourTiTwo·StatePolytope·Polyhedra·Truncations·Polymake·gfanInterface·PieriMaps·Normaliz·Posets·XML·OpenMath·SCSCP·RationalPoints·MapleInterface·ConvexInterface·SRdeformations·NumericalAlgebraicGeometry·BeginningMacaulay2·FormalGroupLaws·Graphics·WeylGroups·HodgeIntegrals·Cyclotomic·Binomials·Kronecker·Nauty·ToricVectorBundles·ModuleDeformations·PHCpack·SimplicialDecomposability·BooleanGB·AdjointIdeal·Parametrization·Serialization·NAGtypes·NormalToricVarieties·DGAlgebras·Graphs·GraphicalModels·BIBasis·KustinMiller·Units·NautyGraphs·VersalDeformations·CharacteristicClasses·RandomIdeals·RandomObjects·RandomPlaneCurves·RandomSpaceCurves·RandomGenus14Curves·RandomCanonicalCurves·RandomCurves·TensorComplexes·MonomialAlgebras·QthPower·EliminationMatrices·EllipticIntegrals·Triplets·CompleteIntersectionResolutions·EagonResolution·MCMApproximations·MultiplierIdeals·InvariantRing·QuillenSuslin·EnumerationCurves·Book3264Examples·Divisor·EllipticCurves·HighestWeights·MinimalPrimes·Bertini·TorAlgebra·Permanents·BinomialEdgeIdeals·TateOnProducts·LatticePolytopes·FiniteFittingIdeals·HigherCIOperators·LieTypes·ConformalBlocks·M0nbar·AnalyzeSheafOnP1·MultiplierIdealsDim2·RunExternalM2·NumericalSchubertCalculus·ToricTopology·Cremona·Resultants·VectorFields·SLPexpressions·Miura·ResidualIntersections·Visualize·EquivariantGB·ExampleSystems·RationalMaps·FastMinors·RandomPoints·SwitchingFields·SpectralSequences·SectionRing·OldPolyhedra·OldToricVectorBundles·K3Carpets·ChainComplexOperations·NumericalCertification·PhylogeneticTrees·MonodromySolver·ReactionNetworks·PackageCitations·NumericSolutions·GradedLieAlgebras·InverseSystems·Pullback·EngineTests·SVDComplexes·RandomComplexes·CohomCalg·Topcom·Triangulations·ReflexivePolytopesDB·AbstractToricVarieties·Licenses·TestIdeals·FrobeniusThresholds·Seminormalization·AlgebraicSplines·TriangularSets·Chordal·Tropical·SymbolicPowers·Complexes·GroebnerWalk·RandomMonomialIdeals·Matroids·NumericalImplicitization·NonminimalComplexes·CoincidentRootLoci·RelativeCanonicalResolution·RandomCurvesOverVerySmallFiniteFields·StronglyStableIdeals·SLnEquivariantMatrices·CorrespondenceScrolls·NCAlgebra·SpaceCurves·ExteriorIdeals·ToricInvariants·SegreClasses·SemidefiniteProgramming·SumsOfSquares·MultiGradedRationalMap·AssociativeAlgebras·VirtualResolutions·Quasidegrees·DiffAlg·DeterminantalRepresentations·FGLM·SpechtModule·SchurComplexes·SimplicialPosets·SlackIdeals·PositivityToricBundles·SparseResultants·DecomposableSparseSystems·MixedMultiplicity·PencilsOfQuadrics·ThreadedGB·AdjunctionForSurfaces·VectorGraphics·GKMVarieties·MonomialIntegerPrograms·NoetherianOperators·Hadamard·StatGraphs·GraphicalModelsMLE·EigenSolver·MultiplicitySequence·ResolutionsOfStanleyReisnerRings·NumericalLinearAlgebra·ResLengthThree·MonomialOrbits·MultiprojectiveVarieties·SpecialFanoFourfolds·RationalPoints2·SuperLinearAlgebra·SubalgebraBases·AInfinity·LinearTruncations·ThinSincereQuivers·Python·BettiCharacters·Jets·FunctionFieldDesingularization·HomotopyLieAlgebra·TSpreadIdeals·RealRoots·ExteriorModules·K3Surfaces·GroebnerStrata·QuaternaryQuartics·CotangentSchubert·OnlineLookup·MergeTeX·Probability·Isomorphism·CodingTheory·WhitneyStratifications·JSON·ForeignFunctions·GeometricDecomposability·PseudomonomialPrimaryDecomposition·PolyominoIdeals·MatchingFields·CellularResolutions·SagbiGbDetection·A1BrouwerDegrees·QuadraticIdealExamplesByRoos·TerraciniLoci·MatrixSchubert·RInterface·OIGroebnerBases·PlaneCurveLinearSeries·Valuations·SchurVeronese·VNumber·TropicalToric·MultigradedBGG·AbstractSimplicialComplexes·MultigradedImplicitization·Msolve·Permutations·SCMAlgebras·NumericalSemigroups |
| 43 | ···············"pointer·size"·=>·8 | 43 | ···············"pointer·size"·=>·8 |
| 44 | ···············"python·version"·=>·3.12.7 | 44 | ···············"python·version"·=>·3.12.7 |
| 45 | ···············"readline·version"·=>·8.2 | 45 | ···············"readline·version"·=>·8.2 |
| 46 | ···············"scscp·version"·=>·not·present | 46 | ···············"scscp·version"·=>·not·present |
| 47 | ···············"tbb·version"·=>·2021.12 | 47 | ···············"tbb·version"·=>·2021.12 |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Basis__Element__Limit.html">BasisElementLimit</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Basis__Element__Limit.html">BasisElementLimit</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Degree__Limit.html">next</a>·|·<a·href="___Strategy.html">previous</a>·|·<a·href="___Degree__Limit.html">forward</a>·|·<a·href="___Strategy.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>BasisElementLimit·--·an·optional·argument</h1> | 44 | ······<h1>BasisElementLimit·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Codimension__Limit.html">CodimensionLimit</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Codimension__Limit.html">CodimensionLimit</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Verify.html">next</a>·|·<a·href="___Verbosity.html">previous</a>·|·<a·href="___Verify.html">forward</a>·|·<a·href="___Verbosity.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>CodimensionLimit·--·an·optional·argument</h1> | 44 | ······<h1>CodimensionLimit·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Coefficient__Ring.html">CoefficientRing</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Coefficient__Ring.html">CoefficientRing</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___Follow__Links.html">next</a>·|·<a·href="___ | 41 | </form><a·href="___Follow__Links.html">next</a>·|·<a·href="___Verify.html">previous</a>·|·<a·href="___Follow__Links.html">forward</a>·|·<a·href="___Verify.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>CoefficientRing·--·an·optional·argument</h1> | 44 | ······<h1>CoefficientRing·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 77 | o2·=·1073741824</code></pre> | 77 | o2·=·1073741824</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·(c·=·Command·"date";)</code></pre> | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·(c·=·Command·"date";)</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·c | 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·c |
| 84 | 84 | Wed·Dec·17·09:59:07·+14·2025 | |
| 85 | o4·=·0</code></pre> | 85 | o4·=·0</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ········</table> | 87 | ········</table> |
| 88 | ······</div> | 88 | ······</div> |
| 89 | ······<div> | 89 | ······<div> |
| 90 | ········<h2>See·also</h2> | 90 | ········<h2>See·also</h2> |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | in·a·file),·then·it·gets·executed·with·empty·argument·list. | 19 | in·a·file),·then·it·gets·executed·with·empty·argument·list. |
| 20 | i1·:·(f·=·Command·(·()·->·2^30·);) | 20 | i1·:·(f·=·Command·(·()·->·2^30·);) |
| 21 | i2·:·f | 21 | i2·:·f |
| 22 | o2·=·1073741824 | 22 | o2·=·1073741824 |
| 23 | i3·:·(c·=·Command·"date";) | 23 | i3·:·(c·=·Command·"date";) |
| 24 | i4·:·c | 24 | i4·:·c |
| 25 | 25 | Wed·Dec·17·09:59:07·+14·2025 | |
| 26 | o4·=·0 | 26 | o4·=·0 |
| 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 28 | ····*·_\x8r_\x8u_\x8n·--·run·an·external·command | 28 | ····*·_\x8r_\x8u_\x8n·--·run·an·external·command |
| 29 | ····*·_\x8A_\x8f_\x8t_\x8e_\x8r_\x8E_\x8v_\x8a_\x8l·--·top·level·method·applied·after·evaluation | 29 | ····*·_\x8A_\x8f_\x8t_\x8e_\x8r_\x8E_\x8v_\x8a_\x8l·--·top·level·method·applied·after·evaluation |
| 30 | *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·c\x8co\x8om\x8mm\x8ma\x8an\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·M\x8Me\x8et\x8th\x8ho\x8od\x8ds\x8s·t\x8th\x8ha\x8at\x8t·u\x8us\x8se\x8e·a\x8a·c\x8co\x8om\x8mm\x8ma\x8an\x8nd\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 31 | ····*·?·Command·(missing·documentation) | 31 | ····*·?·Command·(missing·documentation) |
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| 44 | ······<h1>Database·--·the·class·of·all·database·files</h1> | 44 | ······<h1>Database·--·the·class·of·all·database·files</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have·to·be·strings.··In·this·example·we·create·a·database·file,·store·a·few·entries,·remove·an·entry·with·<a·title="remove·an·entry·from·a·mutable·hash·table,·list,·or·database"·href="_remove.html">remove</a>,·close·the·file,·and·then·remove·the·file.········<table·class="examples"> | 47 | A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have·to·be·strings.··In·this·example·we·create·a·database·file,·store·a·few·entries,·remove·an·entry·with·<a·title="remove·an·entry·from·a·mutable·hash·table,·list,·or·database"·href="_remove.html">remove</a>,·close·the·file,·and·then·remove·the·file.········<table·class="examples"> |
| 48 | ··········<tr> | 48 | ··········<tr> |
| 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·filename·=·temporaryFileName·()·|·".dbm" | 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·filename·=·temporaryFileName·()·|·".dbm" |
| 50 | o1·=·/tmp/M2- | 50 | o1·=·/tmp/M2-3506553-0/0.dbm</code></pre> |
| 51 | </td>··········</tr> | 51 | </td>··········</tr> |
| 52 | ··········<tr> | 52 | ··········<tr> |
| 53 | <td>··············<pre><code·class="language-macaulay2">i2·:·x·=·openDatabaseOut·filename | 53 | <td>··············<pre><code·class="language-macaulay2">i2·:·x·=·openDatabaseOut·filename |
| 54 | o2·=·/tmp/M2- | 54 | o2·=·/tmp/M2-3506553-0/0.dbm |
| 55 | o2·:·Database</code></pre> | 55 | o2·:·Database</code></pre> |
| 56 | </td>··········</tr> | 56 | </td>··········</tr> |
| 57 | ··········<tr> | 57 | ··········<tr> |
| 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·x#"first"·=·"hi·there" | 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·x#"first"·=·"hi·there" |
| 59 | o3·=·hi·there</code></pre> | 59 | o3·=·hi·there</code></pre> |
| Offset 6, 18 lines modified | Offset 6, 18 lines modified | ||
| 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8Da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·-\x8--\x8-·t\x8th\x8he\x8e·c\x8cl\x8la\x8as\x8ss\x8s·o\x8of\x8f·a\x8al\x8ll\x8l·d\x8da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·f\x8fi\x8il\x8le\x8es\x8s·*\x8**\x8**\x8**\x8**\x8**\x8* | 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·D\x8Da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·-\x8--\x8-·t\x8th\x8he\x8e·c\x8cl\x8la\x8as\x8ss\x8s·o\x8of\x8f·a\x8al\x8ll\x8l·d\x8da\x8at\x8ta\x8ab\x8ba\x8as\x8se\x8e·f\x8fi\x8il\x8le\x8es\x8s·*\x8**\x8**\x8**\x8**\x8**\x8* |
| 7 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 7 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 8 | A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have | 8 | A·database·file·is·just·like·a·hash·table,·except·both·the·keys·and·values·have |
| 9 | to·be·strings.·In·this·example·we·create·a·database·file,·store·a·few·entries, | 9 | to·be·strings.·In·this·example·we·create·a·database·file,·store·a·few·entries, |
| 10 | remove·an·entry·with·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e,·close·the·file,·and·then·remove·the·file. | 10 | remove·an·entry·with·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e,·close·the·file,·and·then·remove·the·file. |
| 11 | i1·:·filename·=·temporaryFileName·()·|·".dbm" | 11 | i1·:·filename·=·temporaryFileName·()·|·".dbm" |
| 12 | o1·=·/tmp/M2- | 12 | o1·=·/tmp/M2-3506553-0/0.dbm |
| 13 | i2·:·x·=·openDatabaseOut·filename | 13 | i2·:·x·=·openDatabaseOut·filename |
| 14 | o2·=·/tmp/M2- | 14 | o2·=·/tmp/M2-3506553-0/0.dbm |
| 15 | o2·:·Database | 15 | o2·:·Database |
| 16 | i3·:·x#"first"·=·"hi·there" | 16 | i3·:·x#"first"·=·"hi·there" |
| 17 | o3·=·hi·there | 17 | o3·=·hi·there |
| 18 | i4·:·x#"first" | 18 | i4·:·x#"first" |
| Offset 34, 15 lines modified | Offset 34, 15 lines modified | ||
| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Degree__Group.html">DegreeGroup</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Degree__Group.html">DegreeGroup</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___Variables.html">next</a>·|·<a·href="___ | 41 | </form><a·href="___Variables.html">next</a>·|·<a·href="___Generic.html">previous</a>·|·<a·href="___Variables.html">forward</a>·|·<a·href="___Generic.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>DegreeGroup·--·an·optional·argument</h1> | 44 | ······<h1>DegreeGroup·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Degree__Limit.html">DegreeLimit</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Degree__Limit.html">DegreeLimit</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Pair__Limit.html">next</a>·|·<a·href="___Basis__Element__Limit.html">previous</a>·|·<a·href="___Pair__Limit.html">forward</a>·|·<a·href="___Basis__Element__Limit.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>DegreeLimit·--·an·optional·argument</h1> | 44 | ······<h1>DegreeLimit·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Degree__Map.html">DegreeMap</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Degree__Map.html">DegreeMap</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Verbosity.html">next</a>·|·<a·href="___Skew__Commutative.html">previous</a>·|·<a·href="___Verbosity.html">forward</a>·|·<a·href="___Skew__Commutative.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>DegreeMap·--·an·optional·argument</h1> | 44 | ······<h1>DegreeMap·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
| Offset 84, 26 lines modified | Offset 84, 26 lines modified | ||
| 84 | o2·=·S | 84 | o2·=·S |
| 85 | o2·:·PolynomialRing</code></pre> | 85 | o2·:·PolynomialRing</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 89 | ·--· | 89 | ·--·2.30122s·elapsed |
| 90 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 | 90 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 91 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 | 91 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 |
| 92 | ········································································································· | 92 | ········································································································· |
| 93 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 | 93 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 |
| 94 | o3·:·ChainComplex</code></pre> | 94 | o3·:·ChainComplex</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C1·=·res·ideal(I_*) | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C1·=·res·ideal(I_*) |
| 98 | ·--·. | 98 | ·--·1.16245s·elapsed |
| 99 | ······1······35······140······385······819······1080······819······385······140······35······1 | 99 | ······1······35······140······385······819······1080······819······385······140······35······1 |
| 100 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0 | 100 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0 |
| 101 | ···································································································· | 101 | ···································································································· |
| 102 | ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11 | 102 | ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11 |
| 103 | o4·:·ChainComplex</code></pre> | 103 | o4·:·ChainComplex</code></pre> |
| Offset 30, 28 lines modified | Offset 30, 28 lines modified | ||
| 30 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 | 30 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 |
| 31 | i2·:·S·=·ring·I | 31 | i2·:·S·=·ring·I |
| 32 | o2·=·S | 32 | o2·=·S |
| 33 | o2·:·PolynomialRing | 33 | o2·:·PolynomialRing |
| 34 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 34 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 35 | ·--· | 35 | ·--·2.30122s·elapsed |
| 36 | ······1······35······241······841······1781······2464······2294······1432 | 36 | ······1······35······241······841······1781······2464······2294······1432 |
| 37 | 576······135······14 | 37 | 576······135······14 |
| 38 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S | 38 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S |
| 39 | <--·S····<--·S···<--·0 | 39 | <--·S····<--·S···<--·0 |
| 40 | ·····0······1·······2········3········4·········5·········6·········7·········8 | 40 | ·····0······1·······2········3········4·········5·········6·········7·········8 |
| 41 | 9········10······11 | 41 | 9········10······11 |
| 42 | o3·:·ChainComplex | 42 | o3·:·ChainComplex |
| 43 | i4·:·elapsedTime·C1·=·res·ideal(I_*) | 43 | i4·:·elapsedTime·C1·=·res·ideal(I_*) |
| 44 | ·--·. | 44 | ·--·1.16245s·elapsed |
| 45 | ······1······35······140······385······819······1080······819······385······140 | 45 | ······1······35······140······385······819······1080······819······385······140 |
| 46 | 35······1 | 46 | 35······1 |
| 47 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S | 47 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S |
| 48 | <--·S···<--·S··<--·0 | 48 | <--·S···<--·S··<--·0 |
| Offset 97, 20 lines modified | Offset 97, 20 lines modified | ||
| 97 | o2·=·stdio | 97 | o2·=·stdio |
| 98 | o2·:·File</code></pre> | 98 | o2·:·File</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·=·temporaryFileName() | 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·=·temporaryFileName() |
| 102 | o3·=·/tmp/M2- | 102 | o3·=·/tmp/M2-3507066-0/0</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·fn·<<·"hi·there"·<<·endl·<<·close | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·fn·<<·"hi·there"·<<·endl·<<·close |
| 106 | o4·=·/tmp/M2- | 106 | o4·=·/tmp/M2-3507066-0/0 |
| 107 | o4·:·File</code></pre> | 107 | o4·:·File</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn |
| 111 | o5·=·hi·there</code></pre> | 111 | o5·=·hi·there</code></pre> |
| Offset 139, 29 lines modified | Offset 139, 29 lines modified | ||
| 139 | o8·=·stdio | 139 | o8·=·stdio |
| 140 | o8·:·File</code></pre> | 140 | o8·:·File</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i9·:·fn·<<·f·<<·close | 143 | <td>··············<pre><code·class="language-macaulay2">i9·:·fn·<<·f·<<·close |
| 144 | o9·=·/tmp/M2- | 144 | o9·=·/tmp/M2-3507066-0/0 |
| 145 | o9·:·File</code></pre> | 145 | o9·:·File</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·fn | 148 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·fn |
| 149 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 | 149 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 |
| 150 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x | 150 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x |
| 151 | ······+·1</code></pre> | 151 | ······+·1</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i11·:·fn·<<·toExternalString·f·<<·close | 154 | <td>··············<pre><code·class="language-macaulay2">i11·:·fn·<<·toExternalString·f·<<·close |
| 155 | o11·=·/tmp/M2- | 155 | o11·=·/tmp/M2-3507066-0/0 |
| 156 | o11·:·File</code></pre> | 156 | o11·:·File</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i12·:·get·fn | 159 | <td>··············<pre><code·class="language-macaulay2">i12·:·get·fn |
| 160 | o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+ | 160 | o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+ |
| Offset 38, 18 lines modified | Offset 38, 18 lines modified | ||
| 38 | --·ho·there·-- | 38 | --·ho·there·-- |
| 39 | o2·=·stdio | 39 | o2·=·stdio |
| 40 | o2·:·File | 40 | o2·:·File |
| 41 | i3·:·fn·=·temporaryFileName() | 41 | i3·:·fn·=·temporaryFileName() |
| 42 | o3·=·/tmp/M2- | 42 | o3·=·/tmp/M2-3507066-0/0 |
| 43 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close | 43 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close |
| 44 | o4·=·/tmp/M2- | 44 | o4·=·/tmp/M2-3507066-0/0 |
| 45 | o4·:·File | 45 | o4·:·File |
| 46 | i5·:·get·fn | 46 | i5·:·get·fn |
| 47 | o5·=·hi·there | 47 | o5·=·hi·there |
| 48 | i6·:·R·=·QQ[x] | 48 | i6·:·R·=·QQ[x] |
| Offset 68, 25 lines modified | Offset 68, 25 lines modified | ||
| 68 | ·10······9······8·······7·······6·······5·······4·······3······2 | 68 | ·10······9······8·······7·······6·······5·······4·······3······2 |
| 69 | x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·1 | 69 | x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x·+·1 |
| 70 | o8·=·stdio | 70 | o8·=·stdio |
| 71 | o8·:·File | 71 | o8·:·File |
| 72 | i9·:·fn·<<·f·<<·close | 72 | i9·:·fn·<<·f·<<·close |
| 73 | o9·=·/tmp/M2- | 73 | o9·=·/tmp/M2-3507066-0/0 |
| 74 | o9·:·File | 74 | o9·:·File |
| 75 | i10·:·get·fn | 75 | i10·:·get·fn |
| 76 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 | 76 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 |
| 77 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x | 77 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x |
| 78 | ······+·1 | 78 | ······+·1 |
| 79 | i11·:·fn·<<·toExternalString·f·<<·close | 79 | i11·:·fn·<<·toExternalString·f·<<·close |
| 80 | o11·=·/tmp/M2- | 80 | o11·=·/tmp/M2-3507066-0/0 |
| 81 | o11·:·File | 81 | o11·:·File |
| 82 | i12·:·get·fn | 82 | i12·:·get·fn |
| 83 | o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+ | 83 | o12·=·x^10+10*x^9+45*x^8+120*x^7+210*x^6+252*x^5+210*x^4+120*x^3+45*x^2+10*x+ |
| 84 | ······1 | 84 | ······1 |
| 85 | i13·:·value·get·fn | 85 | i13·:·value·get·fn |
| Offset 45, 31 lines modified | Offset 45, 31 lines modified | ||
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | ········<p>Macaulay2·uses·the·Hans·Boehm·<a·href="___G__C_spgarbage_spcollector.html">garbage·collector</a>·to·reclaim·unused·memory.··The·function·<span·class="tt">GCstats</span>·provides·information·about·its·status,·such·as·the·total·number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage·collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu·time·spent·in·garbage·collection,·etc.</p> | 47 | ········<p>Macaulay2·uses·the·Hans·Boehm·<a·href="___G__C_spgarbage_spcollector.html">garbage·collector</a>·to·reclaim·unused·memory.··The·function·<span·class="tt">GCstats</span>·provides·information·about·its·status,·such·as·the·total·number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage·collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu·time·spent·in·garbage·collection,·etc.</p> |
| 48 | ········<table·class="examples"> | 48 | ········<table·class="examples"> |
| 49 | ··········<tr> | 49 | ··········<tr> |
| 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·s·=·GCstats() | 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·s·=·GCstats() |
| 51 | o1·=·HashTable{"bytesAlloc"·=>·15 | 51 | o1·=·HashTable{"bytesAlloc"·=>·15386744698········} |
| 52 | ···············"GC_free_space_divisor"·=>·3 | 52 | ···············"GC_free_space_divisor"·=>·3 |
| 53 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 | 53 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 |
| 54 | ···············"gcCpuTimeSecs"·=>·0 | 54 | ···············"gcCpuTimeSecs"·=>·0 |
| 55 | ···············"heapSize"·=>·218 | 55 | ···············"heapSize"·=>·218669056 |
| 56 | ···············"numGCs"·=>·82 | 56 | ···············"numGCs"·=>·826 |
| 57 | ···············"numGCThreads"·=>·12 | 57 | ···············"numGCThreads"·=>·12 |
| 58 | o1·:·HashTable</code></pre> | 58 | o1·:·HashTable</code></pre> |
| 59 | </td>··········</tr> | 59 | </td>··········</tr> |
| 60 | ········</table> | 60 | ········</table> |
| 61 | ········<p>The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information·can·be·easily·extracted,·as·follows.</p> | 61 | ········<p>The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information·can·be·easily·extracted,·as·follows.</p> |
| 62 | ········<table·class="examples"> | 62 | ········<table·class="examples"> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i2·:·s#"heapSize" | 64 | <td>··············<pre><code·class="language-macaulay2">i2·:·s#"heapSize" |
| 65 | o2·=·218 | 65 | o2·=·218669056</code></pre> |
| 66 | </td>··········</tr> | 66 | </td>··········</tr> |
| 67 | ········</table> | 67 | ········</table> |
| 68 | ········<p>Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment·variables·affecting·the·operation·of·the·garbage·collector·that·have·been·specified·by·the·user.</p> | 68 | ········<p>Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment·variables·affecting·the·operation·of·the·garbage·collector·that·have·been·specified·by·the·user.</p> |
| 69 | ········<p>For·further·information·about·the·individual·items·in·the·table,·we·refer·the·user·to·the·source·code·and·documentation·of·the·garbage·collector.</p> | 69 | ········<p>For·further·information·about·the·individual·items·in·the·table,·we·refer·the·user·to·the·source·code·and·documentation·of·the·garbage·collector.</p> |
| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>See·also</h2> | 72 | ········<h2>See·also</h2> |
| Offset 8, 28 lines modified | Offset 8, 28 lines modified | ||
| 8 | Macaulay2·uses·the·Hans·Boehm·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r·to·reclaim·unused·memory.·The | 8 | Macaulay2·uses·the·Hans·Boehm·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r·to·reclaim·unused·memory.·The |
| 9 | function·GCstats·provides·information·about·its·status,·such·as·the·total | 9 | function·GCstats·provides·information·about·its·status,·such·as·the·total |
| 10 | number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage | 10 | number·of·bytes·allocated,·the·current·heap·size,·the·number·of·garbage |
| 11 | collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu | 11 | collections·done,·the·number·of·threads·used·in·each·collection,·the·total·cpu |
| 12 | time·spent·in·garbage·collection,·etc. | 12 | time·spent·in·garbage·collection,·etc. |
| 13 | i1·:·s·=·GCstats() | 13 | i1·:·s·=·GCstats() |
| 14 | o1·=·HashTable{"bytesAlloc"·=>·15 | 14 | o1·=·HashTable{"bytesAlloc"·=>·15386744698········} |
| 15 | ···············"GC_free_space_divisor"·=>·3 | 15 | ···············"GC_free_space_divisor"·=>·3 |
| 16 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 | 16 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 |
| 17 | ···············"gcCpuTimeSecs"·=>·0 | 17 | ···············"gcCpuTimeSecs"·=>·0 |
| 18 | ···············"heapSize"·=>·218 | 18 | ···············"heapSize"·=>·218669056 |
| 19 | ···············"numGCs"·=>·82 | 19 | ···············"numGCs"·=>·826 |
| 20 | ···············"numGCThreads"·=>·12 | 20 | ···············"numGCThreads"·=>·12 |
| 21 | o1·:·HashTable | 21 | o1·:·HashTable |
| 22 | The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information | 22 | The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information |
| 23 | can·be·easily·extracted,·as·follows. | 23 | can·be·easily·extracted,·as·follows. |
| 24 | i2·:·s#"heapSize" | 24 | i2·:·s#"heapSize" |
| 25 | o2·=·218 | 25 | o2·=·218669056 |
| 26 | Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment | 26 | Any·entries·whose·keys·are·all·upper·case·give·the·values·of·environment |
| 27 | variables·affecting·the·operation·of·the·garbage·collector·that·have·been | 27 | variables·affecting·the·operation·of·the·garbage·collector·that·have·been |
| 28 | specified·by·the·user. | 28 | specified·by·the·user. |
| 29 | For·further·information·about·the·individual·items·in·the·table,·we·refer·the | 29 | For·further·information·about·the·individual·items·in·the·table,·we·refer·the |
| 30 | user·to·the·source·code·and·documentation·of·the·garbage·collector. | 30 | user·to·the·source·code·and·documentation·of·the·garbage·collector. |
| 31 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 31 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 32 | ····*·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r | 32 | ····*·_\x8G_\x8C_\x8·_\x8g_\x8a_\x8r_\x8b_\x8a_\x8g_\x8e_\x8·_\x8c_\x8o_\x8l_\x8l_\x8e_\x8c_\x8t_\x8o_\x8r |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Generic.html">Generic</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Generic.html">Generic</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Degree__Group.html">next</a>·|·<a·href="___Pair__Limit.html">previous</a>·|·<a·href="___Degree__Group.html">forward</a>·|·<a·href="___Pair__Limit.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>Generic·--·an·optional·argument</h1> | 44 | ······<h1>Generic·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); | 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); |
| 108 | o7·:·Ideal·of·R</code></pre> | 108 | o7·:·Ideal·of·R</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·gens·gb·I; | 111 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·gens·gb·I; |
| 112 | ·--·used·0.0 | 112 | ·--·used·0.0366555s·(cpu);·0.0366568s·(thread);·0s·(gc) |
| 113 | ·············1······428 | 113 | ·············1······428 |
| 114 | o8·:·Matrix·R··<--·R</code></pre> | 114 | o8·:·Matrix·R··<--·R</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J1·=·saturate(I); | 117 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J1·=·saturate(I); |
| 118 | ·--·used·0. | 118 | ·--·used·0.438808s·(cpu);·0.219843s·(thread);·0s·(gc) |
| 119 | o9·:·Ideal·of·R</code></pre> | 119 | o9·:·Ideal·of·R</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); | 122 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); |
| 123 | ·--·used· | 123 | ·--·used·0.000136806s·(cpu);·0.000136536s·(thread);·0s·(gc) |
| 124 | o10·:·Ideal·of·R</code></pre> | 124 | o10·:·Ideal·of·R</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·J | 127 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·J |
| 128 | o11·=·7</code></pre> | 128 | o11·=·7</code></pre> |
| Offset 44, 24 lines modified | Offset 44, 24 lines modified | ||
| 44 | o6·=·R | 44 | o6·=·R |
| 45 | o6·:·PolynomialRing | 45 | o6·:·PolynomialRing |
| 46 | i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); | 46 | i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); |
| 47 | o7·:·Ideal·of·R | 47 | o7·:·Ideal·of·R |
| 48 | i8·:·time·gens·gb·I; | 48 | i8·:·time·gens·gb·I; |
| 49 | ·--·used·0.0 | 49 | ·--·used·0.0366555s·(cpu);·0.0366568s·(thread);·0s·(gc) |
| 50 | ·············1······428 | 50 | ·············1······428 |
| 51 | o8·:·Matrix·R··<--·R | 51 | o8·:·Matrix·R··<--·R |
| 52 | i9·:·time·J1·=·saturate(I); | 52 | i9·:·time·J1·=·saturate(I); |
| 53 | ·--·used·0. | 53 | ·--·used·0.438808s·(cpu);·0.219843s·(thread);·0s·(gc) |
| 54 | o9·:·Ideal·of·R | 54 | o9·:·Ideal·of·R |
| 55 | i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); | 55 | i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); |
| 56 | ·--·used· | 56 | ·--·used·0.000136806s·(cpu);·0.000136536s·(thread);·0s·(gc) |
| 57 | o10·:·Ideal·of·R | 57 | o10·:·Ideal·of·R |
| 58 | i11·:·numgens·J | 58 | i11·:·numgens·J |
| 59 | o11·=·7 | 59 | o11·=·7 |
| 60 | i12·:·numgens·J1 | 60 | i12·:·numgens·J1 |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Pair__Limit.html">PairLimit</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Pair__Limit.html">PairLimit</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Generic.html">next</a>·|·<a·href="___Degree__Limit.html">previous</a>·|·<a·href="___Generic.html">forward</a>·|·<a·href="___Degree__Limit.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>PairLimit·--·an·optional·argument</h1> | 44 | ······<h1>PairLimit·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 61 | ················200·········200 | 61 | ················200·········200 |
| 62 | o1·:·Matrix·RR······<--·RR | 62 | o1·:·Matrix·RR······<--·RR |
| 63 | ··············53··········53</code></pre> | 63 | ··············53··········53</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·SVD(M); | 66 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·SVD(M); |
| 67 | ·--·used·0.0 | 67 | ·--·used·0.0362439s·(cpu);·0.0362423s·(thread);·0s·(gc)</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·SVD(M,·DivideConquer=>true); | 70 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·SVD(M,·DivideConquer=>true); |
| 71 | ·--·used·0.0 | 71 | ·--·used·0.035935s·(cpu);·0.0359422s·(thread);·0s·(gc)</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ········</table> | 73 | ········</table> |
| 74 | ······</div> | 74 | ······</div> |
| 75 | ······<div> | 75 | ······<div> |
| 76 | ········<h2>Further·information</h2> | 76 | ········<h2>Further·information</h2> |
| 77 | ········<ul> | 77 | ········<ul> |
| 78 | ··········<li> | 78 | ··········<li> |
| Offset 12, 17 lines modified | Offset 12, 17 lines modified | ||
| 12 | For·large·matrices,·this·algorithm·is·often·much·faster. | 12 | For·large·matrices,·this·algorithm·is·often·much·faster. |
| 13 | i1·:·M·=·random(RR^200,·RR^200); | 13 | i1·:·M·=·random(RR^200,·RR^200); |
| 14 | ················200·········200 | 14 | ················200·········200 |
| 15 | o1·:·Matrix·RR······<--·RR | 15 | o1·:·Matrix·RR······<--·RR |
| 16 | ··············53··········53 | 16 | ··············53··········53 |
| 17 | i2·:·time·SVD(M); | 17 | i2·:·time·SVD(M); |
| 18 | ·--·used·0.0 | 18 | ·--·used·0.0362439s·(cpu);·0.0362423s·(thread);·0s·(gc) |
| 19 | i3·:·time·SVD(M,·DivideConquer=>true); | 19 | i3·:·time·SVD(M,·DivideConquer=>true); |
| 20 | ·--·used·0.0 | 20 | ·--·used·0.035935s·(cpu);·0.0359422s·(thread);·0s·(gc) |
| 21 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 21 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 22 | ····*·Default·value:·_\x8t_\x8r_\x8u_\x8e | 22 | ····*·Default·value:·_\x8t_\x8r_\x8u_\x8e |
| 23 | ····*·Function:·_\x8S_\x8V_\x8D·--·singular·value·decomposition·of·a·matrix | 23 | ····*·Function:·_\x8S_\x8V_\x8D·--·singular·value·decomposition·of·a·matrix |
| 24 | ····*·Option·key:·_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r·--·an·optional·argument | 24 | ····*·Option·key:·_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r·--·an·optional·argument |
| 25 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·D\x8Di\x8iv\x8vi\x8id\x8de\x8eC\x8Co\x8on\x8nq\x8qu\x8ue\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·D\x8Di\x8iv\x8vi\x8id\x8de\x8eC\x8Co\x8on\x8nq\x8qu\x8ue\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·_\x8S_\x8V_\x8D_\x8(_\x8._\x8._\x8._\x8,_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r_\x8=_\x8>_\x8._\x8._\x8._\x8)·--·Use·the·lapack·divide·and·conquer·SVD | 26 | ····*·_\x8S_\x8V_\x8D_\x8(_\x8._\x8._\x8._\x8,_\x8D_\x8i_\x8v_\x8i_\x8d_\x8e_\x8C_\x8o_\x8n_\x8q_\x8u_\x8e_\x8r_\x8=_\x8>_\x8._\x8._\x8._\x8)·--·Use·the·lapack·divide·and·conquer·SVD |
| 27 | ······algorithm | 27 | ······algorithm |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Strategy.html">Strategy</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Strategy.html">Strategy</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Basis__Element__Limit.html">next</a>·|·<a·href="___Threads.html">previous</a>·|·<a·href="___Basis__Element__Limit.html">forward</a>·|·<a·href="___Threads.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>Strategy·--·an·optional·argument</h1> | 44 | ······<h1>Strategy·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Threads.html">Threads</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Threads.html">Threads</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Strategy.html">next</a>·|·<a·href="___Syzygies.html">previous</a>·|·<a·href="___Strategy.html">forward</a>·|·<a·href="___Syzygies.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>Threads·--·an·optional·argument</h1> | 44 | ······<h1>Threads·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div·class="waystouse"> | 48 | ······<div·class="waystouse"> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Verbosity.html">Verbosity</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Verbosity.html">Verbosity</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___ | 41 | </form><a·href="___Codimension__Limit.html">next</a>·|·<a·href="___Degree__Map.html">previous</a>·|·<a·href="___Codimension__Limit.html">forward</a>·|·<a·href="___Degree__Map.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>Verbosity·--·an·optional·argument</h1> | 44 | ······<h1>Verbosity·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
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| 34 | ····<div·id="buttons"> | 34 | ····<div·id="buttons"> |
| 35 | ······<div> | 35 | ······<div> |
| 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Verify.html">Verify</a></span>······</div> | 36 | <a·href="https://macaulay2.com/">Macaulay2</a>·<span·id="version-select-container"></span>·»·<a·title="Macaulay2·documentation"·href="index.html">Documentation·</a>·<br><a·href="_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a>·»·<span><a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">symbols·used·as·the·name·or·value·of·an·optional·argument</a>·>·<a·title="an·optional·argument"·href="___Verify.html">Verify</a></span>······</div> |
| 37 | ······<div·class="right"> | 37 | ······<div·class="right"> |
| 38 | <form·method="get"·action="https://www.google.com/search"> | 38 | <form·method="get"·action="https://www.google.com/search"> |
| 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> | 39 | ··<input·placeholder="Search"·type="text"·name="q"·value=""> |
| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___Co | 41 | </form><a·href="___Coefficient__Ring.html">next</a>·|·<a·href="___Codimension__Limit.html">previous</a>·|·<a·href="___Coefficient__Ring.html">forward</a>·|·<a·href="___Codimension__Limit.html">backward</a>·|·<a·href="_symbols_spused_spas_spthe_spname_spor_spvalue_spof_span_spoptional_spargument.html">up</a>·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>Verify·--·an·optional·argument</h1> | 44 | ······<h1>Verify·--·an·optional·argument</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> | 47 | A·symbol·used·as·the·name·of·an·optional·argument.······</div> |
| 48 | ······<div> | 48 | ······<div> |
| Offset 554, 15 lines modified | Offset 554, 15 lines modified | ||
| 554 | ·····························3 | 554 | ·····························3 |
| 555 | o58·:·R-module,·quotient·of·R</code></pre> | 555 | o58·:·R-module,·quotient·of·R</code></pre> |
| 556 | </td>··········</tr> | 556 | </td>··········</tr> |
| 557 | ········</table> | 557 | ········</table> |
| 558 | We·may·use·<a·title="projective·resolution"·href="_resolution.html">resolution</a>·to·produce·a·projective·resolution·of·it,·and·<a·title="time·a·computation"·href="_time.html">time</a>·to·report·the·time·required.········<table·class="examples"> | 558 | We·may·use·<a·title="projective·resolution"·href="_resolution.html">resolution</a>·to·produce·a·projective·resolution·of·it,·and·<a·title="time·a·computation"·href="_time.html">time</a>·to·report·the·time·required.········<table·class="examples"> |
| 559 | ··········<tr> | 559 | ··········<tr> |
| 560 | <td>··············<pre><code·class="language-macaulay2">i59·:·time·C·=·resolution·M | 560 | <td>··············<pre><code·class="language-macaulay2">i59·:·time·C·=·resolution·M |
| 561 | ·--·used·0.001 | 561 | ·--·used·0.00190209s·(cpu);·0.00189298s·(thread);·0s·(gc) |
| 562 | ·······3······6······15······18······6 | 562 | ·······3······6······15······18······6 |
| 563 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 | 563 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 |
| 564 | ············································ | 564 | ············································ |
| 565 | ······0······1······2·······3·······4······5 | 565 | ······0······1······2·······3·······4······5 |
| 566 | o59·:·ChainComplex</code></pre> | 566 | o59·:·ChainComplex</code></pre> |
| Offset 386, 15 lines modified | Offset 386, 15 lines modified | ||
| 386 | ···············|·c·f·i·l·o·r·| | 386 | ···············|·c·f·i·l·o·r·| |
| 387 | ·····························3 | 387 | ·····························3 |
| 388 | o58·:·R-module,·quotient·of·R | 388 | o58·:·R-module,·quotient·of·R |
| 389 | We·may·use·_\x8r_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n·to·produce·a·projective·resolution·of·it,·and·_\x8t_\x8i_\x8m_\x8e·to | 389 | We·may·use·_\x8r_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n·to·produce·a·projective·resolution·of·it,·and·_\x8t_\x8i_\x8m_\x8e·to |
| 390 | report·the·time·required. | 390 | report·the·time·required. |
| 391 | i59·:·time·C·=·resolution·M | 391 | i59·:·time·C·=·resolution·M |
| 392 | ·--·used·0.001 | 392 | ·--·used·0.00190209s·(cpu);·0.00189298s·(thread);·0s·(gc) |
| 393 | ·······3······6······15······18······6 | 393 | ·······3······6······15······18······6 |
| 394 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 | 394 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 |
| 395 | ······0······1······2·······3·······4······5 | 395 | ······0······1······2·······3·······4······5 |
| 396 | o59·:·ChainComplex | 396 | o59·:·ChainComplex |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·peek·read·f | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·peek·read·f |
| 90 | o4·=·"hi·there"</code></pre> | 90 | o4·=·"hi·there"</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·atEndOfFile·f | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·atEndOfFile·f |
| 94 | o5·=· | 94 | o5·=·true</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ········</table> | 96 | ········</table> |
| 97 | ······</div> | 97 | ······</div> |
| 98 | ······<div·class="waystouse"> | 98 | ······<div·class="waystouse"> |
| 99 | ········<h2>Ways·to·use·this·method:</h2> | 99 | ········<h2>Ways·to·use·this·method:</h2> |
| 100 | ········<ul> | 100 | ········<ul> |
| 101 | ··········<li> | 101 | ··········<li> |
| Offset 23, 10 lines modified | Offset 23, 10 lines modified | ||
| 23 | o3·=·false | 23 | o3·=·false |
| 24 | i4·:·peek·read·f | 24 | i4·:·peek·read·f |
| 25 | o4·=·"hi·there" | 25 | o4·=·"hi·there" |
| 26 | i5·:·atEndOfFile·f | 26 | i5·:·atEndOfFile·f |
| 27 | o5·=· | 27 | o5·=·true |
| 28 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 28 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 29 | ····*·_\x8a_\x8t_\x8E_\x8n_\x8d_\x8O_\x8f_\x8F_\x8i_\x8l_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·test·for·end·of·file | 29 | ····*·_\x8a_\x8t_\x8E_\x8n_\x8d_\x8O_\x8f_\x8F_\x8i_\x8l_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·test·for·end·of·file |
| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | ······</div> | 67 | ······</div> |
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | Produces·an·accurate·timing·for·the·code·contained·in·the·string·<span·class="tt">s</span>.··The·value·returned·is·the·number·of·seconds.········<table·class="examples"> | 70 | Produces·an·accurate·timing·for·the·code·contained·in·the·string·<span·class="tt">s</span>.··The·value·returned·is·the·number·of·seconds.········<table·class="examples"> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·benchmark·"sqrt·2p100000" | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·benchmark·"sqrt·2p100000" |
| 73 | o1·=·.000 | 73 | o1·=·.0004037596391364607 |
| 74 | o1·:·RR·(of·precision·53)</code></pre> | 74 | o1·:·RR·(of·precision·53)</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ········</table> | 76 | ········</table> |
| 77 | The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully·on·the·clock,·and·the·garbage·collector·will·be·called·beforehand.······</div> | 77 | The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully·on·the·clock,·and·the·garbage·collector·will·be·called·beforehand.······</div> |
| 78 | ······<div·class="waystouse"> | 78 | ······<div·class="waystouse"> |
| 79 | ········<h2>For·the·programmer</h2> | 79 | ········<h2>For·the·programmer</h2> |
| Offset 13, 14 lines modified | Offset 13, 14 lines modified | ||
| 13 | ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·it·takes·to·evaluate·the·code | 13 | ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·it·takes·to·evaluate·the·code |
| 14 | ············in·s | 14 | ············in·s |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | Produces·an·accurate·timing·for·the·code·contained·in·the·string·s.·The·value | 16 | Produces·an·accurate·timing·for·the·code·contained·in·the·string·s.·The·value |
| 17 | returned·is·the·number·of·seconds. | 17 | returned·is·the·number·of·seconds. |
| 18 | i1·:·benchmark·"sqrt·2p100000" | 18 | i1·:·benchmark·"sqrt·2p100000" |
| 19 | o1·=·.000 | 19 | o1·=·.0004037596391364607 |
| 20 | o1·:·RR·(of·precision·53) | 20 | o1·:·RR·(of·precision·53) |
| 21 | The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully | 21 | The·snippet·of·code·provided·will·be·run·enough·times·to·register·meaningfully |
| 22 | on·the·clock,·and·the·garbage·collector·will·be·called·beforehand. | 22 | on·the·clock,·and·the·garbage·collector·will·be·called·beforehand. |
| 23 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 23 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 24 | The·object·_\x8b_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k·is·a·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8c_\x8l_\x8o_\x8s_\x8u_\x8r_\x8e. | 24 | The·object·_\x8b_\x8e_\x8n_\x8c_\x8h_\x8m_\x8a_\x8r_\x8k·is·a·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8c_\x8l_\x8o_\x8s_\x8u_\x8r_\x8e. |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | o2·=·S | 83 | o2·=·S |
| 84 | o2·:·PolynomialRing</code></pre> | 84 | o2·:·PolynomialRing</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 88 | ·--· | 88 | ·--·2.5971s·elapsed |
| 89 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 | 89 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 90 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 | 90 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 |
| 91 | ········································································································· | 91 | ········································································································· |
| 92 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 | 92 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 |
| 93 | o3·:·ChainComplex</code></pre> | 93 | o3·:·ChainComplex</code></pre> |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 | 27 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 |
| 28 | i2·:·S·=·ring·I | 28 | i2·:·S·=·ring·I |
| 29 | o2·=·S | 29 | o2·=·S |
| 30 | o2·:·PolynomialRing | 30 | o2·:·PolynomialRing |
| 31 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 31 | i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 32 | ·--· | 32 | ·--·2.5971s·elapsed |
| 33 | ······1······35······241······841······1781······2464······2294······1432 | 33 | ······1······35······241······841······1781······2464······2294······1432 |
| 34 | 576······135······14 | 34 | 576······135······14 |
| 35 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S | 35 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S |
| 36 | <--·S····<--·S···<--·0 | 36 | <--·S····<--·S···<--·0 |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | o4·=·<<task,·running>> | 95 | o4·=·<<task,·running>> |
| 96 | o4·:·Task</code></pre> | 96 | o4·:·Task</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·n | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·n |
| 100 | o5·=·9 | 100 | o5·=·946905</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·sleep·1 | 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·sleep·1 |
| 104 | o6·=·0</code></pre> | 104 | o6·=·0</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| Offset 112, 15 lines modified | Offset 112, 15 lines modified | ||
| 112 | o7·=·<<task,·running>> | 112 | o7·=·<<task,·running>> |
| 113 | o7·:·Task</code></pre> | 113 | o7·:·Task</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i8·:·n | 116 | <td>··············<pre><code·class="language-macaulay2">i8·:·n |
| 117 | o8·=·191 | 117 | o8·=·1911803</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i9·:·isReady·t | 120 | <td>··············<pre><code·class="language-macaulay2">i9·:·isReady·t |
| 121 | o9·=·false</code></pre> | 121 | o9·=·false</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| Offset 138, 25 lines modified | Offset 138, 25 lines modified | ||
| 138 | o12·=·<<task,·canceled>> | 138 | o12·=·<<task,·canceled>> |
| 139 | o12·:·Task</code></pre> | 139 | o12·:·Task</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i13·:·n | 142 | <td>··············<pre><code·class="language-macaulay2">i13·:·n |
| 143 | o13·=·1912 | 143 | o13·=·1912007</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i14·:·sleep·1 | 146 | <td>··············<pre><code·class="language-macaulay2">i14·:·sleep·1 |
| 147 | o14·=·0</code></pre> | 147 | o14·=·0</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i15·:·n | 150 | <td>··············<pre><code·class="language-macaulay2">i15·:·n |
| 151 | o15·=·1912 | 151 | o15·=·1912007</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i16·:·isReady·t | 154 | <td>··············<pre><code·class="language-macaulay2">i16·:·isReady·t |
| 155 | o16·=·false</code></pre> | 155 | o16·=·false</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ········</table> | 157 | ········</table> |
| Offset 29, 26 lines modified | Offset 29, 26 lines modified | ||
| 29 | i4·:·t | 29 | i4·:·t |
| 30 | o4·=·<<task,·running>> | 30 | o4·=·<<task,·running>> |
| 31 | o4·:·Task | 31 | o4·:·Task |
| 32 | i5·:·n | 32 | i5·:·n |
| 33 | o5·=·9 | 33 | o5·=·946905 |
| 34 | i6·:·sleep·1 | 34 | i6·:·sleep·1 |
| 35 | o6·=·0 | 35 | o6·=·0 |
| 36 | i7·:·t | 36 | i7·:·t |
| 37 | o7·=·<<task,·running>> | 37 | o7·=·<<task,·running>> |
| 38 | o7·:·Task | 38 | o7·:·Task |
| 39 | i8·:·n | 39 | i8·:·n |
| 40 | o8·=·191 | 40 | o8·=·1911803 |
| 41 | i9·:·isReady·t | 41 | i9·:·isReady·t |
| 42 | o9·=·false | 42 | o9·=·false |
| 43 | i10·:·cancelTask·t | 43 | i10·:·cancelTask·t |
| 44 | i11·:·sleep·2 | 44 | i11·:·sleep·2 |
| 45 | stdio:2:25:(3):[1]:·error:·interrupted | 45 | stdio:2:25:(3):[1]:·error:·interrupted |
| Offset 56, 19 lines modified | Offset 56, 19 lines modified | ||
| 56 | i12·:·t | 56 | i12·:·t |
| 57 | o12·=·<<task,·canceled>> | 57 | o12·=·<<task,·canceled>> |
| 58 | o12·:·Task | 58 | o12·:·Task |
| 59 | i13·:·n | 59 | i13·:·n |
| 60 | o13·=·1912 | 60 | o13·=·1912007 |
| 61 | i14·:·sleep·1 | 61 | i14·:·sleep·1 |
| 62 | o14·=·0 | 62 | o14·=·0 |
| 63 | i15·:·n | 63 | i15·:·n |
| 64 | o15·=·1912 | 64 | o15·=·1912007 |
| 65 | i16·:·isReady·t | 65 | i16·:·isReady·t |
| 66 | o16·=·false | 66 | o16·=·false |
| 67 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 67 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 68 | ····*·_\x8c_\x8a_\x8n_\x8c_\x8e_\x8l_\x8T_\x8a_\x8s_\x8k_\x8(_\x8T_\x8a_\x8s_\x8k_\x8)·--·stop·a·task | 68 | ····*·_\x8c_\x8a_\x8n_\x8c_\x8e_\x8l_\x8T_\x8a_\x8s_\x8k_\x8(_\x8T_\x8a_\x8s_\x8k_\x8)·--·stop·a·task |
| Offset 70, 30 lines modified | Offset 70, 30 lines modified | ||
| 70 | ········<div> | 70 | ········<div> |
| 71 | ··········<p>Change·the·current·working·directory·to·<var>dir</var>.</p> | 71 | ··········<p>Change·the·current·working·directory·to·<var>dir</var>.</p> |
| 72 | ········</div> | 72 | ········</div> |
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() |
| 76 | o1·=·/tmp/M2- | 76 | o1·=·/tmp/M2-3493357-0/0</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir |
| 80 | o2·=·/tmp/M2- | 80 | o2·=·/tmp/M2-3493357-0/0</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·changeDirectory·dir | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·changeDirectory·dir |
| 84 | o3·=·/tmp/M2- | 84 | o3·=·/tmp/M2-3493357-0/0/</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·currentDirectory() | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·currentDirectory() |
| 88 | o4·=·/tmp/M2- | 88 | o4·=·/tmp/M2-3493357-0/0/</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ········</table> | 90 | ········</table> |
| 91 | ········<div> | 91 | ········<div> |
| 92 | ··········<p>If·<var>dir</var>·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's·home·directory.</p> | 92 | ··········<p>If·<var>dir</var>·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's·home·directory.</p> |
| 93 | ········</div> | 93 | ········</div> |
| 94 | ······</div> | 94 | ······</div> |
| 95 | ······<div> | 95 | ······<div> |
| Offset 11, 23 lines modified | Offset 11, 23 lines modified | ||
| 11 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g, | 11 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g, |
| 12 | ····*·Outputs: | 12 | ····*·Outputs: |
| 13 | ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·new·working·directory; | 13 | ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·new·working·directory; |
| 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 15 | Change·the·current·working·directory·to·dir. | 15 | Change·the·current·working·directory·to·dir. |
| 16 | i1·:·dir·=·temporaryFileName() | 16 | i1·:·dir·=·temporaryFileName() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3493357-0/0 |
| 18 | i2·:·makeDirectory·dir | 18 | i2·:·makeDirectory·dir |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-3493357-0/0 |
| 20 | i3·:·changeDirectory·dir | 20 | i3·:·changeDirectory·dir |
| 21 | o3·=·/tmp/M2- | 21 | o3·=·/tmp/M2-3493357-0/0/ |
| 22 | i4·:·currentDirectory() | 22 | i4·:·currentDirectory() |
| 23 | o4·=·/tmp/M2- | 23 | o4·=·/tmp/M2-3493357-0/0/ |
| 24 | If·dir·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's | 24 | If·dir·is·omitted,·then·the·current·working·directory·is·changed·to·the·user's |
| 25 | home·directory. | 25 | home·directory. |
| 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 27 | ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·current·working·directory | 27 | ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·current·working·directory |
| 28 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 28 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 29 | The·object·_\x8c_\x8h_\x8a_\x8n_\x8g_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 29 | The·object·_\x8c_\x8h_\x8a_\x8n_\x8g_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 42, 15 lines modified | Offset 42, 15 lines modified | ||
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>communicating·with·programs</h1> | 44 | ······<h1>communicating·with·programs</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it·communicate·directly·with·the·user,·and·wait·for·it·to·finish.··This·is·done·with·the·<a·title="run·an·external·command"·href="_run.html">run</a>·command.········<table·class="examples"> | 46 | The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it·communicate·directly·with·the·user,·and·wait·for·it·to·finish.··This·is·done·with·the·<a·title="run·an·external·command"·href="_run.html">run</a>·command.········<table·class="examples"> |
| 47 | ··········<tr> | 47 | ··········<tr> |
| 48 | <td>··············<pre><code·class="language-macaulay2">i1·:·run·"uname·-a" | 48 | <td>··············<pre><code·class="language-macaulay2">i1·:·run·"uname·-a" |
| 49 | Linux·i | 49 | Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 50 | o1·=·0</code></pre> | 50 | o1·=·0</code></pre> |
| 51 | </td>··········</tr> | 51 | </td>··········</tr> |
| 52 | ········</table> | 52 | ········</table> |
| 53 | To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·<a·title="a·binary·operator·(file·output,·...)"·href="__lt_lt.html"><<</a>,·with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the·file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example.········<table·class="examples"> | 53 | To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·<a·title="a·binary·operator·(file·output,·...)"·href="__lt_lt.html"><<</a>,·with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the·file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example.········<table·class="examples"> |
| 54 | ··········<tr> | 54 | ··········<tr> |
| 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close | 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close |
| Offset 62, 17 lines modified | Offset 62, 17 lines modified | ||
| 62 | o2·:·File</code></pre> | 62 | o2·:·File</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ········</table> | 64 | ········</table> |
| 65 | More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the·output·from·the·other·program.··If·the·program·requires·no·input·data,·then·we·can·use·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·with·a·file·name·whose·first·character·is·an·exclamation·point.··In·the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a·newline·character.········<table·class="examples"> | 65 | More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the·output·from·the·other·program.··If·the·program·requires·no·input·data,·then·we·can·use·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·with·a·file·name·whose·first·character·is·an·exclamation·point.··In·the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a·newline·character.········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·peek·get·"!uname·-a" | 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·peek·get·"!uname·-a" |
| 68 | o3·=·"Linux·i | 68 | o3·=·"Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC |
| 69 | ·····" | 69 | ·····" |
| 70 | ·····6.1.11 | 70 | ·····Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ········</table> | 72 | ········</table> |
| 73 | Bidirectional·communication·with·a·program·is·also·possible.··We·use·<a·title="open·an·input·output·file"·href="_open__In__Out.html">openInOut</a>·to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.··That·file·is·called·an·input·output·file.··In·this·example·we·open·a·connection·to·the·unix·utility·<span·class="tt">egrep</span>·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that·begin·with·<span·class="tt">in</span>.········<table·class="examples"> | 73 | Bidirectional·communication·with·a·program·is·also·possible.··We·use·<a·title="open·an·input·output·file"·href="_open__In__Out.html">openInOut</a>·to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.··That·file·is·called·an·input·output·file.··In·this·example·we·open·a·connection·to·the·unix·utility·<span·class="tt">egrep</span>·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that·begin·with·<span·class="tt">in</span>.········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i4·:·f·=·openInOut·"!egrep·'^in'" | 75 | <td>··············<pre><code·class="language-macaulay2">i4·:·f·=·openInOut·"!egrep·'^in'" |
| 76 | o4·=·!egrep·'^in' | 76 | o4·=·!egrep·'^in' |
| Offset 4, 16 lines modified | Offset 4, 16 lines modified | ||
| 4 | _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c | 4 | _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c |
| 5 | =============================================================================== | 5 | =============================================================================== |
| 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·c\x8co\x8om\x8mm\x8mu\x8un\x8ni\x8ic\x8ca\x8at\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8ms\x8s·*\x8**\x8**\x8**\x8**\x8**\x8* | 6 | *\x8**\x8**\x8**\x8**\x8**\x8*·c\x8co\x8om\x8mm\x8mu\x8un\x8ni\x8ic\x8ca\x8at\x8ti\x8in\x8ng\x8g·w\x8wi\x8it\x8th\x8h·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8ms\x8s·*\x8**\x8**\x8**\x8**\x8**\x8* |
| 7 | The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it | 7 | The·most·naive·way·to·interact·with·another·program·is·simply·to·run·it,·let·it |
| 8 | communicate·directly·with·the·user,·and·wait·for·it·to·finish.·This·is·done | 8 | communicate·directly·with·the·user,·and·wait·for·it·to·finish.·This·is·done |
| 9 | with·the·_\x8r_\x8u_\x8n·command. | 9 | with·the·_\x8r_\x8u_\x8n·command. |
| 10 | i1·:·run·"uname·-a" | 10 | i1·:·run·"uname·-a" |
| 11 | Linux·infom01-amd64·6.1.0-27-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.115- | ||
| 12 | 11 | Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian | |
| 12 | 6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux | ||
| 13 | o1·=·0 | 13 | o1·=·0 |
| 14 | To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·_\x8<_\x8<, | 14 | To·run·a·program·and·provide·it·with·input,·one·way·is·use·the·operator·_\x8<_\x8<, |
| 15 | with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the | 15 | with·a·file·name·whose·first·character·is·an·exclamation·point;·the·rest·of·the |
| 16 | file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example. | 16 | file·name·will·be·taken·as·the·command·to·run,·as·in·the·following·example. |
| 17 | i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close | 17 | i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close |
| 18 | ·ba | 18 | ·ba |
| Offset 25, 17 lines modified | Offset 25, 17 lines modified | ||
| 25 | More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the | 25 | More·often,·one·wants·to·write·Macaulay2·code·to·obtain·and·manipulate·the |
| 26 | output·from·the·other·program.·If·the·program·requires·no·input·data,·then·we | 26 | output·from·the·other·program.·If·the·program·requires·no·input·data,·then·we |
| 27 | can·use·_\x8g_\x8e_\x8t·with·a·file·name·whose·first·character·is·an·exclamation·point.·In | 27 | can·use·_\x8g_\x8e_\x8t·with·a·file·name·whose·first·character·is·an·exclamation·point.·In |
| 28 | the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a | 28 | the·following·example,·we·also·peek·at·the·string·to·see·whether·it·includes·a |
| 29 | newline·character. | 29 | newline·character. |
| 30 | i3·:·peek·get·"!uname·-a" | 30 | i3·:·peek·get·"!uname·-a" |
| 31 | o3·=·"Linux·i | 31 | o3·=·"Linux·i-capture-the-hostname·6.10.11+bpo-amd64·#1·SMP·PREEMPT_DYNAMIC |
| 32 | ·····" | 32 | ·····" |
| 33 | ·····6.1.11 | 33 | ·····Debian·6.10.11-1~bpo12+1·(2024-10-03)·x86_64·GNU/Linux |
| 34 | Bidirectional·communication·with·a·program·is·also·possible.·We·use·_\x8o_\x8p_\x8e_\x8n_\x8I_\x8n_\x8O_\x8u_\x8t | 34 | Bidirectional·communication·with·a·program·is·also·possible.·We·use·_\x8o_\x8p_\x8e_\x8n_\x8I_\x8n_\x8O_\x8u_\x8t |
| 35 | to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.·That | 35 | to·create·a·file·that·serves·as·a·bidirectional·connection·to·a·program.·That |
| 36 | file·is·called·an·input·output·file.·In·this·example·we·open·a·connection·to | 36 | file·is·called·an·input·output·file.·In·this·example·we·open·a·connection·to |
| 37 | the·unix·utility·egrep·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that | 37 | the·unix·utility·egrep·and·use·it·to·locate·the·symbol·names·in·Macaulay2·that |
| 38 | begin·with·in. | 38 | begin·with·in. |
| 39 | i4·:·f·=·openInOut·"!egrep·'^in'" | 39 | i4·:·f·=·openInOut·"!egrep·'^in'" |
| Offset 215, 15 lines modified | Offset 215, 15 lines modified | ||
| 215 | ················ZZ | 215 | ················ZZ |
| 216 | o23·:·Ideal·of·----[x..z,·w] | 216 | o23·:·Ideal·of·----[x..z,·w] |
| 217 | ···············1277</code></pre> | 217 | ···············1277</code></pre> |
| 218 | </td>··········</tr> | 218 | </td>··········</tr> |
| 219 | ··········<tr> | 219 | ··········<tr> |
| 220 | <td>··············<pre><code·class="language-macaulay2">i24·:·gb·I | 220 | <td>··············<pre><code·class="language-macaulay2">i24·:·gb·I |
| 221 | ···--·registering·gb·5·at·0x7f9 | 221 | ···--·registering·gb·5·at·0x7f99ef4b4700 |
| 222 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 | 222 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 |
| 223 | ···--·number·of·monomials················=·8 | 223 | ···--·number·of·monomials················=·8 |
| 224 | ···--·#reduction·steps·=·2 | 224 | ···--·#reduction·steps·=·2 |
| 225 | ···--·#spairs·done·=·6 | 225 | ···--·#spairs·done·=·6 |
| 226 | ···--·ncalls·=·0 | 226 | ···--·ncalls·=·0 |
| 227 | ···--·nloop·=·0 | 227 | ···--·nloop·=·0 |
| Offset 301, 15 lines modified | Offset 301, 15 lines modified | ||
| 301 | <td>··············<pre><code·class="language-macaulay2">i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); | 301 | <td>··············<pre><code·class="language-macaulay2">i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); |
| 302 | ··············1······4 | 302 | ··············1······4 |
| 303 | o32·:·Matrix·R··<--·R</code></pre> | 303 | o32·:·Matrix·R··<--·R</code></pre> |
| 304 | </td>··········</tr> | 304 | </td>··········</tr> |
| 305 | ··········<tr> | 305 | ··········<tr> |
| 306 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·betti·gb·f | 306 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·betti·gb·f |
| 307 | ·--·used·0. | 307 | ·--·used·0.280001s·(cpu);·0.278478s·(thread);·0s·(gc) |
| 308 | ·············0··1 | 308 | ·············0··1 |
| 309 | o33·=·total:·1·53 | 309 | o33·=·total:·1·53 |
| 310 | ··········0:·1··. | 310 | ··········0:·1··. |
| 311 | ··········1:·.··. | 311 | ··········1:·.··. |
| 312 | ··········2:·.··2 | 312 | ··········2:·.··2 |
| 313 | ··········3:·.··1 | 313 | ··········3:·.··1 |
| Offset 339, 15 lines modified | Offset 339, 15 lines modified | ||
| 339 | ············3····5·····8·····9····12·····14····17 | 339 | ············3····5·····8·····9····12·····14····17 |
| 340 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T | 340 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T |
| 341 | o35·:·ZZ[T]</code></pre> | 341 | o35·:·ZZ[T]</code></pre> |
| 342 | </td>··········</tr> | 342 | </td>··········</tr> |
| 343 | ··········<tr> | 343 | ··········<tr> |
| 344 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·betti·gb·f | 344 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·betti·gb·f |
| 345 | ·--·used·0.00 | 345 | ·--·used·0.00400271s·(cpu);·0.00581119s·(thread);·0s·(gc) |
| 346 | ·············0··1 | 346 | ·············0··1 |
| 347 | o36·=·total:·1·53 | 347 | o36·=·total:·1·53 |
| 348 | ··········0:·1··. | 348 | ··········0:·1··. |
| 349 | ··········1:·.··. | 349 | ··········1:·.··. |
| 350 | ··········2:·.··2 | 350 | ··········2:·.··2 |
| 351 | ··········3:·.··1 | 351 | ··········3:·.··1 |
| Offset 139, 15 lines modified | Offset 139, 15 lines modified | ||
| 139 | o23·=·ideal·(x*y·-·z·,·y··-·w·) | 139 | o23·=·ideal·(x*y·-·z·,·y··-·w·) |
| 140 | ················ZZ | 140 | ················ZZ |
| 141 | o23·:·Ideal·of·----[x..z,·w] | 141 | o23·:·Ideal·of·----[x..z,·w] |
| 142 | ···············1277 | 142 | ···············1277 |
| 143 | i24·:·gb·I | 143 | i24·:·gb·I |
| 144 | ···--·registering·gb·5·at·0x7f9 | 144 | ···--·registering·gb·5·at·0x7f99ef4b4700 |
| 145 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 | 145 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 |
| 146 | ···--·number·of·monomials················=·8 | 146 | ···--·number·of·monomials················=·8 |
| 147 | ···--·#reduction·steps·=·2 | 147 | ···--·#reduction·steps·=·2 |
| 148 | ···--·#spairs·done·=·6 | 148 | ···--·#spairs·done·=·6 |
| 149 | ···--·ncalls·=·0 | 149 | ···--·ncalls·=·0 |
| 150 | ···--·nloop·=·0 | 150 | ···--·nloop·=·0 |
| Offset 212, 15 lines modified | Offset 212, 15 lines modified | ||
| 212 | o31·:·ZZ[T] | 212 | o31·:·ZZ[T] |
| 213 | i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); | 213 | i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); |
| 214 | ··············1······4 | 214 | ··············1······4 |
| 215 | o32·:·Matrix·R··<--·R | 215 | o32·:·Matrix·R··<--·R |
| 216 | i33·:·time·betti·gb·f | 216 | i33·:·time·betti·gb·f |
| 217 | ·--·used·0. | 217 | ·--·used·0.280001s·(cpu);·0.278478s·(thread);·0s·(gc) |
| 218 | ·············0··1 | 218 | ·············0··1 |
| 219 | o33·=·total:·1·53 | 219 | o33·=·total:·1·53 |
| 220 | ··········0:·1··. | 220 | ··········0:·1··. |
| 221 | ··········1:·.··. | 221 | ··········1:·.··. |
| 222 | ··········2:·.··2 | 222 | ··········2:·.··2 |
| 223 | ··········3:·.··1 | 223 | ··········3:·.··1 |
| Offset 244, 15 lines modified | Offset 244, 15 lines modified | ||
| 244 | i35·:·poincare·cokernel·f·=·(1-T^3)*(1-T^3)*(1-T^5)*(1-T^6)·--·cache·poincare | 244 | i35·:·poincare·cokernel·f·=·(1-T^3)*(1-T^3)*(1-T^5)*(1-T^6)·--·cache·poincare |
| 245 | ············3····5·····8·····9····12·····14····17 | 245 | ············3····5·····8·····9····12·····14····17 |
| 246 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T | 246 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T |
| 247 | o35·:·ZZ[T] | 247 | o35·:·ZZ[T] |
| 248 | i36·:·time·betti·gb·f | 248 | i36·:·time·betti·gb·f |
| 249 | ·--·used·0.00 | 249 | ·--·used·0.00400271s·(cpu);·0.00581119s·(thread);·0s·(gc) |
| 250 | ·············0··1 | 250 | ·············0··1 |
| 251 | o36·=·total:·1·53 | 251 | o36·=·total:·1·53 |
| 252 | ··········0:·1··. | 252 | ··········0:·1··. |
| 253 | ··········1:·.··. | 253 | ··········1:·.··. |
| 254 | ··········2:·.··2 | 254 | ··········2:·.··2 |
| 255 | ··········3:·.··1 | 255 | ··········3:·.··1 |
| Offset 92, 16 lines modified | Offset 92, 16 lines modified | ||
| 92 | ··········<<·res·M·<<·endl·<<·endl; | 92 | ··········<<·res·M·<<·endl·<<·endl; |
| 93 | ··········break; | 93 | ··········break; |
| 94 | ··········)·else·( | 94 | ··········)·else·( |
| 95 | ··········<<·"--·computation·interrupted"·<<·endl; | 95 | ··········<<·"--·computation·interrupted"·<<·endl; |
| 96 | ··········status·M.cache.resolution; | 96 | ··········status·M.cache.resolution; |
| 97 | ··········<<·"--·continuing·the·computation"·<<·endl; | 97 | ··········<<·"--·continuing·the·computation"·<<·endl; |
| 98 | ··········)) | 98 | ··········)) |
| 99 | ·--·used·1. | 99 | ·--·used·1.17098s·(cpu);·0.994858s·(thread);·0s·(gc) |
| 100 | ·--·used·0. | 100 | ·--·used·0.677089s·(cpu);·0.586337s·(thread);·0s·(gc) |
| 101 | --·computation·started:· | 101 | --·computation·started:· |
| 102 | --·computation·interrupted | 102 | --·computation·interrupted |
| 103 | --·continuing·the·computation | 103 | --·continuing·the·computation |
| 104 | --·computation·complete | 104 | --·computation·complete |
| 105 | ·4······11······89······122······40 | 105 | ·4······11······89······122······40 |
| 106 | R··<--·R···<--·R···<--·R····<--·R···<--·0 | 106 | R··<--·R···<--·R···<--·R····<--·R···<--·0 |
| 107 | ········································· | 107 | ········································· |
| Offset 50, 16 lines modified | Offset 50, 16 lines modified | ||
| 50 | ··········<<·res·M·<<·endl·<<·endl; | 50 | ··········<<·res·M·<<·endl·<<·endl; |
| 51 | ··········break; | 51 | ··········break; |
| 52 | ··········)·else·( | 52 | ··········)·else·( |
| 53 | ··········<<·"--·computation·interrupted"·<<·endl; | 53 | ··········<<·"--·computation·interrupted"·<<·endl; |
| 54 | ··········status·M.cache.resolution; | 54 | ··········status·M.cache.resolution; |
| 55 | ··········<<·"--·continuing·the·computation"·<<·endl; | 55 | ··········<<·"--·continuing·the·computation"·<<·endl; |
| 56 | ··········)) | 56 | ··········)) |
| 57 | ·--·used·1. | 57 | ·--·used·1.17098s·(cpu);·0.994858s·(thread);·0s·(gc) |
| 58 | ·--·used·0. | 58 | ·--·used·0.677089s·(cpu);·0.586337s·(thread);·0s·(gc) |
| 59 | --·computation·started: | 59 | --·computation·started: |
| 60 | --·computation·interrupted | 60 | --·computation·interrupted |
| 61 | --·continuing·the·computation | 61 | --·continuing·the·computation |
| 62 | --·computation·complete | 62 | --·computation·complete |
| 63 | ·4······11······89······122······40 | 63 | ·4······11······89······122······40 |
| 64 | R··<--·R···<--·R···<--·R····<--·R···<--·0 | 64 | R··<--·R···<--·R···<--·R····<--·R···<--·0 |
| Offset 85, 90 lines modified | Offset 85, 90 lines modified | ||
| 85 | ······</div> | 85 | ······</div> |
| 86 | ······<div> | 86 | ······<div> |
| 87 | ········<h2>Description</h2> | 87 | ········<h2>Description</h2> |
| 88 | ········<table·class="examples"> | 88 | ········<table·class="examples"> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" | 90 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" |
| 91 | o1·=·/tmp/M2- | 91 | o1·=·/tmp/M2-3502475-0/0/</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" |
| 95 | o2·=·/tmp/M2- | 95 | o2·=·/tmp/M2-3502475-0/1/</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/") | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/") |
| 99 | o3·=·/tmp/M2- | 99 | o3·=·/tmp/M2-3502475-0/0/a/</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/") | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/") |
| 103 | o4·=·/tmp/M2- | 103 | o4·=·/tmp/M2-3502475-0/0/b/</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/") | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/") |
| 107 | o5·=·/tmp/M2- | 107 | o5·=·/tmp/M2-3502475-0/0/b/c/</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close | 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 111 | o6·=·/tmp/M2- | 111 | o6·=·/tmp/M2-3502475-0/0/a/f |
| 112 | o6·:·File</code></pre> | 112 | o6·:·File</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close | 115 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 116 | o7·=·/tmp/M2- | 116 | o7·=·/tmp/M2-3502475-0/0/a/g |
| 117 | o7·:·File</code></pre> | 117 | o7·:·File</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 120 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 121 | o8·=·/tmp/M2- | 121 | o8·=·/tmp/M2-3502475-0/0/b/c/g |
| 122 | o8·:·File</code></pre> | 122 | o8·:·File</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i9·:·stack·findFiles·src | 125 | <td>··············<pre><code·class="language-macaulay2">i9·:·stack·findFiles·src |
| 126 | o9·=·/tmp/M2- | 126 | o9·=·/tmp/M2-3502475-0/0/ |
| 127 | ·····/tmp/M2- | 127 | ·····/tmp/M2-3502475-0/0/b/ |
| 128 | ·····/tmp/M2- | 128 | ·····/tmp/M2-3502475-0/0/b/c/ |
| 129 | ·····/tmp/M2- | 129 | ·····/tmp/M2-3502475-0/0/b/c/g |
| 130 | ·····/tmp/M2- | 130 | ·····/tmp/M2-3502475-0/0/a/ |
| 131 | ·····/tmp/M2- | 131 | ·····/tmp/M2-3502475-0/0/a/g |
| 132 | ·····/tmp/M2- | 132 | ·····/tmp/M2-3502475-0/0/a/f</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i10·:·copyDirectory(src,dst,Verbose=>true) | 135 | <td>··············<pre><code·class="language-macaulay2">i10·:·copyDirectory(src,dst,Verbose=>true) |
| 136 | ·--·copying:·/tmp/M2- | 136 | ·--·copying:·/tmp/M2-3502475-0/0/b/c/g·->·/tmp/M2-3502475-0/1/b/c/g |
| 137 | ·--·copying:·/tmp/M2- | 137 | ·--·copying:·/tmp/M2-3502475-0/0/a/g·->·/tmp/M2-3502475-0/1/a/g |
| 138 | ·--·copying:·/tmp/M2- | 138 | ·--·copying:·/tmp/M2-3502475-0/0/a/f·->·/tmp/M2-3502475-0/1/a/f</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) | 141 | <td>··············<pre><code·class="language-macaulay2">i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 142 | ·--·skipping:·/tmp/M2- | 142 | ·--·skipping:·/tmp/M2-3502475-0/0/b/c/g·not·newer·than·/tmp/M2-3502475-0/1/b/c/g |
| 143 | ·--·skipping:·/tmp/M2- | 143 | ·--·skipping:·/tmp/M2-3502475-0/0/a/g·not·newer·than·/tmp/M2-3502475-0/1/a/g |
| 144 | ·--·skipping:·/tmp/M2- | 144 | ·--·skipping:·/tmp/M2-3502475-0/0/a/f·not·newer·than·/tmp/M2-3502475-0/1/a/f</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i12·:·stack·findFiles·dst | 147 | <td>··············<pre><code·class="language-macaulay2">i12·:·stack·findFiles·dst |
| 148 | o12·=·/tmp/M2- | 148 | o12·=·/tmp/M2-3502475-0/1/ |
| 149 | ······/tmp/M2- | 149 | ······/tmp/M2-3502475-0/1/b/ |
| 150 | ······/tmp/M2- | 150 | ······/tmp/M2-3502475-0/1/b/c/ |
| 151 | ······/tmp/M2- | 151 | ······/tmp/M2-3502475-0/1/b/c/g |
| 152 | ······/tmp/M2- | 152 | ······/tmp/M2-3502475-0/1/a/ |
| 153 | ······/tmp/M2- | 153 | ······/tmp/M2-3502475-0/1/a/g |
| 154 | ······/tmp/M2- | 154 | ······/tmp/M2-3502475-0/1/a/f</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i13·:·get·(dst|"b/c/g") | 157 | <td>··············<pre><code·class="language-macaulay2">i13·:·get·(dst|"b/c/g") |
| 158 | o13·=·ho·there</code></pre> | 158 | o13·=·ho·there</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ········</table> | 160 | ········</table> |
| Offset 26, 69 lines modified | Offset 26, 69 lines modified | ||
| 26 | ············individual·file·operations | 26 | ············individual·file·operations |
| 27 | ····*·Consequences: | 27 | ····*·Consequences: |
| 28 | ··········o·a·copy·of·the·directory·tree·rooted·at·src·is·created,·rooted·at | 28 | ··········o·a·copy·of·the·directory·tree·rooted·at·src·is·created,·rooted·at |
| 29 | ············dst | 29 | ············dst |
| 30 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 31 | i1·:·src·=·temporaryFileName()·|·"/" | 31 | i1·:·src·=·temporaryFileName()·|·"/" |
| 32 | o1·=·/tmp/M2- | 32 | o1·=·/tmp/M2-3502475-0/0/ |
| 33 | i2·:·dst·=·temporaryFileName()·|·"/" | 33 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 34 | o2·=·/tmp/M2- | 34 | o2·=·/tmp/M2-3502475-0/1/ |
| 35 | i3·:·makeDirectory·(src|"a/") | 35 | i3·:·makeDirectory·(src|"a/") |
| 36 | o3·=·/tmp/M2- | 36 | o3·=·/tmp/M2-3502475-0/0/a/ |
| 37 | i4·:·makeDirectory·(src|"b/") | 37 | i4·:·makeDirectory·(src|"b/") |
| 38 | o4·=·/tmp/M2- | 38 | o4·=·/tmp/M2-3502475-0/0/b/ |
| 39 | i5·:·makeDirectory·(src|"b/c/") | 39 | i5·:·makeDirectory·(src|"b/c/") |
| 40 | o5·=·/tmp/M2- | 40 | o5·=·/tmp/M2-3502475-0/0/b/c/ |
| 41 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 41 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 42 | o6·=·/tmp/M2- | 42 | o6·=·/tmp/M2-3502475-0/0/a/f |
| 43 | o6·:·File | 43 | o6·:·File |
| 44 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 44 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 45 | o7·=·/tmp/M2- | 45 | o7·=·/tmp/M2-3502475-0/0/a/g |
| 46 | o7·:·File | 46 | o7·:·File |
| 47 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 47 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 48 | o8·=·/tmp/M2- | 48 | o8·=·/tmp/M2-3502475-0/0/b/c/g |
| 49 | o8·:·File | 49 | o8·:·File |
| 50 | i9·:·stack·findFiles·src | 50 | i9·:·stack·findFiles·src |
| 51 | o9·=·/tmp/M2- | 51 | o9·=·/tmp/M2-3502475-0/0/ |
| 52 | ·····/tmp/M2- | 52 | ·····/tmp/M2-3502475-0/0/b/ |
| 53 | ·····/tmp/M2- | 53 | ·····/tmp/M2-3502475-0/0/b/c/ |
| 54 | ·····/tmp/M2- | 54 | ·····/tmp/M2-3502475-0/0/b/c/g |
| 55 | ·····/tmp/M2- | 55 | ·····/tmp/M2-3502475-0/0/a/ |
| 56 | ·····/tmp/M2-1763734-0/0/a/f | ||
| 57 | ·····/tmp/M2- | 56 | ·····/tmp/M2-3502475-0/0/a/g |
| 57 | ·····/tmp/M2-3502475-0/0/a/f | ||
| 58 | i10·:·copyDirectory(src,dst,Verbose=>true) | 58 | i10·:·copyDirectory(src,dst,Verbose=>true) |
| 59 | ·--·copying:·/tmp/M2- | 59 | ·--·copying:·/tmp/M2-3502475-0/0/b/c/g·->·/tmp/M2-3502475-0/1/b/c/g |
| 60 | ·--·copying:·/tmp/M2-1763734-0/0/a/f·->·/tmp/M2-1763734-0/1/a/f | ||
| 61 | ·--·copying:·/tmp/M2- | 60 | ·--·copying:·/tmp/M2-3502475-0/0/a/g·->·/tmp/M2-3502475-0/1/a/g |
| 61 | ·--·copying:·/tmp/M2-3502475-0/0/a/f·->·/tmp/M2-3502475-0/1/a/f | ||
| 62 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) | 62 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 63 | ·--·skipping:·/tmp/M2- | 63 | ·--·skipping:·/tmp/M2-3502475-0/0/b/c/g·not·newer·than·/tmp/M2-3502475-0/1/b/c/ |
| 64 | g | 64 | g |
| 65 | ·--·skipping:·/tmp/M2-1763734-0/0/a/f·not·newer·than·/tmp/M2-1763734-0/1/a/f | ||
| 66 | ·--·skipping:·/tmp/M2- | 65 | ·--·skipping:·/tmp/M2-3502475-0/0/a/g·not·newer·than·/tmp/M2-3502475-0/1/a/g |
| 66 | ·--·skipping:·/tmp/M2-3502475-0/0/a/f·not·newer·than·/tmp/M2-3502475-0/1/a/f | ||
| 67 | i12·:·stack·findFiles·dst | 67 | i12·:·stack·findFiles·dst |
| 68 | o12·=·/tmp/M2- | 68 | o12·=·/tmp/M2-3502475-0/1/ |
| 69 | ······/tmp/M2- | 69 | ······/tmp/M2-3502475-0/1/b/ |
| 70 | ······/tmp/M2- | 70 | ······/tmp/M2-3502475-0/1/b/c/ |
| 71 | ······/tmp/M2- | 71 | ······/tmp/M2-3502475-0/1/b/c/g |
| 72 | ······/tmp/M2- | 72 | ······/tmp/M2-3502475-0/1/a/ |
| 73 | ······/tmp/M2-1763734-0/1/a/f | ||
| 74 | ······/tmp/M2- | 73 | ······/tmp/M2-3502475-0/1/a/g |
| 74 | ······/tmp/M2-3502475-0/1/a/f | ||
| 75 | i13·:·get·(dst|"b/c/g") | 75 | i13·:·get·(dst|"b/c/g") |
| 76 | o13·=·ho·there | 76 | o13·=·ho·there |
| 77 | Now·we·remove·the·files·and·directories·we·created. | 77 | Now·we·remove·the·files·and·directories·we·created. |
| 78 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 78 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 79 | o14·=·rm | 79 | o14·=·rm |
| Offset 81, 51 lines modified | Offset 81, 51 lines modified | ||
| 81 | ······</div> | 81 | ······</div> |
| 82 | ······<div> | 82 | ······<div> |
| 83 | ········<h2>Description</h2> | 83 | ········<h2>Description</h2> |
| 84 | ········<table·class="examples"> | 84 | ········<table·class="examples"> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() | 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() |
| 87 | o1·=·/tmp/M2- | 87 | o1·=·/tmp/M2-3500588-0/0</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() | 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() |
| 91 | o2·=·/tmp/M2- | 91 | o2·=·/tmp/M2-3500588-0/1</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close | 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close |
| 95 | o3·=·/tmp/M2- | 95 | o3·=·/tmp/M2-3500588-0/0 |
| 96 | o3·:·File</code></pre> | 96 | o3·:·File</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·copyFile(src,dst,Verbose=>true) | 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·copyFile(src,dst,Verbose=>true) |
| 100 | ·--·copying:·/tmp/M2- | 100 | ·--·copying:·/tmp/M2-3500588-0/0·->·/tmp/M2-3500588-0/1</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst |
| 104 | o5·=·hi·there</code></pre> | 104 | o5·=·hi·there</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 108 | ·--·skipping:·/tmp/M2- | 108 | ·--·skipping:·/tmp/M2-3500588-0/0·not·newer·than·/tmp/M2-3500588-0/1</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·src·<<·"ho·there"·<<·close | 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·src·<<·"ho·there"·<<·close |
| 112 | o7·=·/tmp/M2- | 112 | o7·=·/tmp/M2-3500588-0/0 |
| 113 | o7·:·File</code></pre> | 113 | o7·:·File</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 116 | <td>··············<pre><code·class="language-macaulay2">i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 117 | ·--·skipping:·/tmp/M2- | 117 | ·--·skipping:·/tmp/M2-3500588-0/0·not·newer·than·/tmp/M2-3500588-0/1</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i9·:·get·dst | 120 | <td>··············<pre><code·class="language-macaulay2">i9·:·get·dst |
| 121 | o9·=·hi·there</code></pre> | 121 | o9·=·hi·there</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| Offset 19, 37 lines modified | Offset 19, 37 lines modified | ||
| 19 | ··········o·Verbose·=>·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·default·value·false,·whether·to·report | 19 | ··········o·Verbose·=>·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·default·value·false,·whether·to·report |
| 20 | ············individual·file·operations | 20 | ············individual·file·operations |
| 21 | ····*·Consequences: | 21 | ····*·Consequences: |
| 22 | ··········o·the·file·may·be·copied | 22 | ··········o·the·file·may·be·copied |
| 23 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 23 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 24 | i1·:·src·=·temporaryFileName() | 24 | i1·:·src·=·temporaryFileName() |
| 25 | o1·=·/tmp/M2- | 25 | o1·=·/tmp/M2-3500588-0/0 |
| 26 | i2·:·dst·=·temporaryFileName() | 26 | i2·:·dst·=·temporaryFileName() |
| 27 | o2·=·/tmp/M2- | 27 | o2·=·/tmp/M2-3500588-0/1 |
| 28 | i3·:·src·<<·"hi·there"·<<·close | 28 | i3·:·src·<<·"hi·there"·<<·close |
| 29 | o3·=·/tmp/M2- | 29 | o3·=·/tmp/M2-3500588-0/0 |
| 30 | o3·:·File | 30 | o3·:·File |
| 31 | i4·:·copyFile(src,dst,Verbose=>true) | 31 | i4·:·copyFile(src,dst,Verbose=>true) |
| 32 | ·--·copying:·/tmp/M2- | 32 | ·--·copying:·/tmp/M2-3500588-0/0·->·/tmp/M2-3500588-0/1 |
| 33 | i5·:·get·dst | 33 | i5·:·get·dst |
| 34 | o5·=·hi·there | 34 | o5·=·hi·there |
| 35 | i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 35 | i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 36 | ·--·skipping:·/tmp/M2- | 36 | ·--·skipping:·/tmp/M2-3500588-0/0·not·newer·than·/tmp/M2-3500588-0/1 |
| 37 | i7·:·src·<<·"ho·there"·<<·close | 37 | i7·:·src·<<·"ho·there"·<<·close |
| 38 | o7·=·/tmp/M2- | 38 | o7·=·/tmp/M2-3500588-0/0 |
| 39 | o7·:·File | 39 | o7·:·File |
| 40 | i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 40 | i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 41 | ·--·skipping:·/tmp/M2- | 41 | ·--·skipping:·/tmp/M2-3500588-0/0·not·newer·than·/tmp/M2-3500588-0/1 |
| 42 | i9·:·get·dst | 42 | i9·:·get·dst |
| 43 | o9·=·hi·there | 43 | o9·=·hi·there |
| 44 | i10·:·removeFile·src | 44 | i10·:·removeFile·src |
| 45 | i11·:·removeFile·dst | 45 | i11·:·removeFile·dst |
| 46 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 46 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 47 | ····*·_\x8c_\x8o_\x8p_\x8y_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y | 47 | ····*·_\x8c_\x8o_\x8p_\x8y_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y |
| Offset 61, 32 lines modified | Offset 61, 32 lines modified | ||
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | ········<table·class="examples"> | 64 | ········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·t1·=·cpuTime() | 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·t1·=·cpuTime() |
| 67 | o1·=· | 67 | o1·=·236.202283615 |
| 68 | o1·:·RR·(of·precision·53)</code></pre> | 68 | o1·:·RR·(of·precision·53)</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;</code></pre> | 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i3·:·t2·=·cpuTime() | 74 | <td>··············<pre><code·class="language-macaulay2">i3·:·t2·=·cpuTime() |
| 75 | o3·=· | 75 | o3·=·237.254696625 |
| 76 | o3·:·RR·(of·precision·53)</code></pre> | 76 | o3·:·RR·(of·precision·53)</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i4·:·t2-t1 | 79 | <td>··············<pre><code·class="language-macaulay2">i4·:·t2-t1 |
| 80 | o4·=·. | 80 | o4·=·1.052413009999981 |
| 81 | o4·:·RR·(of·precision·53)</code></pre> | 81 | o4·:·RR·(of·precision·53)</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ········</table> | 83 | ········</table> |
| 84 | ······</div> | 84 | ······</div> |
| 85 | ······<div> | 85 | ······<div> |
| 86 | ········<h2>See·also</h2> | 86 | ········<h2>See·also</h2> |
| Offset 9, 26 lines modified | Offset 9, 26 lines modified | ||
| 9 | ············cpuTime() | 9 | ············cpuTime() |
| 10 | ····*·Outputs: | 10 | ····*·Outputs: |
| 11 | ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·of·cpu·time·used·since·the | 11 | ··········o·a·_\x8r_\x8e_\x8a_\x8l_\x8·_\x8n_\x8u_\x8m_\x8b_\x8e_\x8r,·the·number·of·seconds·of·cpu·time·used·since·the |
| 12 | ············program·was·started | 12 | ············program·was·started |
| 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 14 | i1·:·t1·=·cpuTime() | 14 | i1·:·t1·=·cpuTime() |
| 15 | o1·=· | 15 | o1·=·236.202283615 |
| 16 | o1·:·RR·(of·precision·53) | 16 | o1·:·RR·(of·precision·53) |
| 17 | i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324; | 17 | i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324; |
| 18 | i3·:·t2·=·cpuTime() | 18 | i3·:·t2·=·cpuTime() |
| 19 | o3·=· | 19 | o3·=·237.254696625 |
| 20 | o3·:·RR·(of·precision·53) | 20 | o3·:·RR·(of·precision·53) |
| 21 | i4·:·t2-t1 | 21 | i4·:·t2-t1 |
| 22 | o4·=·. | 22 | o4·=·1.052413009999981 |
| 23 | o4·:·RR·(of·precision·53) | 23 | o4·:·RR·(of·precision·53) |
| 24 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 25 | ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation | 25 | ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation |
| 26 | ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation | 26 | ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation |
| 27 | ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time | 27 | ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time |
| 28 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 28 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 61, 42 lines modified | Offset 61, 42 lines modified | ||
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | ········<table·class="examples"> | 64 | ········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime() | 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime() |
| 67 | o1·=·17 | 67 | o1·=·1765915218</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ········</table> | 69 | ········</table> |
| 70 | ········<p>We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.</p> | 70 | ········<p>We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.</p> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) | 73 | <td>··············<pre><code·class="language-macaulay2">i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) |
| 74 | o2·=·5 | 74 | o2·=·55.95962556840091 |
| 75 | o2·:·RR·(of·precision·53)</code></pre> | 75 | o2·:·RR·(of·precision·53)</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ········</table> | 77 | ········</table> |
| 78 | ········<p>We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that·number.</p> | 78 | ········<p>We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that·number.</p> |
| 79 | ········<table·class="examples"> | 79 | ········<table·class="examples"> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·12·*·(oo·-·floor·oo) | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·12·*·(oo·-·floor·oo) |
| 82 | o3·=·1 | 82 | o3·=·11.51550682081091 |
| 83 | o3·:·RR·(of·precision·53)</code></pre> | 83 | o3·:·RR·(of·precision·53)</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ········</table> | 85 | ········</table> |
| 86 | ········<p>Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.</p> | 86 | ········<p>Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.</p> |
| 87 | ········<table·class="examples"> | 87 | ········<table·class="examples"> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·run·"date" | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·run·"date" |
| 90 | 90 | Wed·Dec·17·10:00:18·+14·2025 | |
| 91 | o4·=·0</code></pre> | 91 | o4·=·0</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ········</table> | 93 | ········</table> |
| 94 | ······</div> | 94 | ······</div> |
| 95 | ······<div·class="waystouse"> | 95 | ······<div·class="waystouse"> |
| 96 | ········<h2>For·the·programmer</h2> | 96 | ········<h2>For·the·programmer</h2> |
| Offset 9, 28 lines modified | Offset 9, 28 lines modified | ||
| 9 | ············currentTime() | 9 | ············currentTime() |
| 10 | ····*·Outputs: | 10 | ····*·Outputs: |
| 11 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·current·time,·in·seconds·since·00:00:00·1970-01-01 | 11 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·current·time,·in·seconds·since·00:00:00·1970-01-01 |
| 12 | ············UTC,·the·beginning·of·the·epoch | 12 | ············UTC,·the·beginning·of·the·epoch |
| 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 14 | i1·:·currentTime() | 14 | i1·:·currentTime() |
| 15 | o1·=·17 | 15 | o1·=·1765915218 |
| 16 | We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows. | 16 | We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows. |
| 17 | i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) | 17 | i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) |
| 18 | o2·=·5 | 18 | o2·=·55.95962556840091 |
| 19 | o2·:·RR·(of·precision·53) | 19 | o2·:·RR·(of·precision·53) |
| 20 | We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that | 20 | We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that |
| 21 | number. | 21 | number. |
| 22 | i3·:·12·*·(oo·-·floor·oo) | 22 | i3·:·12·*·(oo·-·floor·oo) |
| 23 | o3·=·1 | 23 | o3·=·11.51550682081091 |
| 24 | o3·:·RR·(of·precision·53) | 24 | o3·:·RR·(of·precision·53) |
| 25 | Compare·that·to·the·current·date,·available·from·a·standard·Unix·command. | 25 | Compare·that·to·the·current·date,·available·from·a·standard·Unix·command. |
| 26 | i4·:·run·"date" | 26 | i4·:·run·"date" |
| 27 | 27 | Wed·Dec·17·10:00:18·+14·2025 | |
| 28 | o4·=·0 | 28 | o4·=·0 |
| 29 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 30 | The·object·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 30 | The·object·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
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| 54 | ········</ul> | 54 | ········</ul> |
| 55 | ······</div> | 55 | ······</div> |
| 56 | ······<div> | 56 | ······<div> |
| 57 | ········<h2>Description</h2> | 57 | ········<h2>Description</h2> |
| 58 | <span·class="tt">elapsedTime·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·time·elapsed,·and·returns·the·value·of·<span·class="tt">e</span>.········<table·class="examples"> | 58 | <span·class="tt">elapsedTime·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·time·elapsed,·and·returns·the·value·of·<span·class="tt">e</span>.········<table·class="examples"> |
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·sleep·1 | 60 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·sleep·1 |
| 61 | ·--·1.0001s·elapsed | 61 | ·--·1.00014s·elapsed |
| 62 | o1·=·0</code></pre> | 62 | o1·=·0</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ········</table> | 64 | ········</table> |
| 65 | ······</div> | 65 | ······</div> |
| 66 | ······<div> | 66 | ······<div> |
| 67 | ········<h2>See·also</h2> | 67 | ········<h2>See·also</h2> |
| Offset 8, 15 lines modified | Offset 8, 15 lines modified | ||
| 8 | *\x8**\x8**\x8**\x8**\x8*·S\x8Sy\x8yn\x8no\x8op\x8ps\x8si\x8is\x8s·*\x8**\x8**\x8**\x8**\x8* | 8 | *\x8**\x8**\x8**\x8**\x8*·S\x8Sy\x8yn\x8no\x8op\x8ps\x8si\x8is\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 9 | ····*···Usage: | 9 | ····*···Usage: |
| 10 | ············elapsedTime·e | 10 | ············elapsedTime·e |
| 11 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 11 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 12 | elapsedTime·e·evaluates·e,·prints·the·amount·of·time·elapsed,·and·returns·the | 12 | elapsedTime·e·evaluates·e,·prints·the·amount·of·time·elapsed,·and·returns·the |
| 13 | value·of·e. | 13 | value·of·e. |
| 14 | i1·:·elapsedTime·sleep·1 | 14 | i1·:·elapsedTime·sleep·1 |
| 15 | ·--·1.0001s·elapsed | 15 | ·--·1.00014s·elapsed |
| 16 | o1·=·0 | 16 | o1·=·0 |
| 17 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 18 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed | 18 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed |
| 19 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began | 19 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began |
| 20 | ····*·_\x8G_\x8C_\x8s_\x8t_\x8a_\x8t_\x8s·--·information·about·the·status·of·the·garbage·collector | 20 | ····*·_\x8G_\x8C_\x8s_\x8t_\x8a_\x8t_\x8s·--·information·about·the·status·of·the·garbage·collector |
| 21 | ····*·_\x8p_\x8a_\x8r_\x8a_\x8l_\x8l_\x8e_\x8l_\x8·_\x8p_\x8r_\x8o_\x8g_\x8r_\x8a_\x8m_\x8m_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8t_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s_\x8·_\x8a_\x8n_\x8d_\x8·_\x8t_\x8a_\x8s_\x8k_\x8s | 21 | ····*·_\x8p_\x8a_\x8r_\x8a_\x8l_\x8l_\x8e_\x8l_\x8·_\x8p_\x8r_\x8o_\x8g_\x8r_\x8a_\x8m_\x8m_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8t_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s_\x8·_\x8a_\x8n_\x8d_\x8·_\x8t_\x8a_\x8s_\x8k_\x8s |
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| 53 | ···············3···················3·····2···············3 | 53 | ···············3···················3·····2···············3 |
| 54 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) | 54 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) |
| 55 | o2·:·Ideal·of·R</code></pre> | 55 | o2·:·Ideal·of·R</code></pre> |
| 56 | </td>··········</tr> | 56 | </td>··········</tr> |
| 57 | ··········<tr> | 57 | ··········<tr> |
| 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·leadTerm·gens·gb·I | 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·leadTerm·gens·gb·I |
| 59 | ·--·used·0. | 59 | ·--·used·0.167644s·(cpu);·0.167644s·(thread);·0s·(gc) |
| 60 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 | 60 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 |
| 61 | ·····------------------------------------------------------------------------ | 61 | ·····------------------------------------------------------------------------ |
| 62 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 | 62 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 |
| 63 | ·····------------------------------------------------------------------------ | 63 | ·····------------------------------------------------------------------------ |
| 64 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 | 64 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 |
| 65 | ·····------------------------------------------------------------------------ | 65 | ·····------------------------------------------------------------------------ |
| Offset 140, 15 lines modified | Offset 140, 15 lines modified | ||
| 140 | ···············3···················3·····2···············3 | 140 | ···············3···················3·····2···············3 |
| 141 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) | 141 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) |
| 142 | o7·:·Ideal·of·R</code></pre> | 142 | o7·:·Ideal·of·R</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·G·=·eliminate(I,{s,t}) | 145 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·G·=·eliminate(I,{s,t}) |
| 146 | ·--·used·0. | 146 | ·--·used·0.191404s·(cpu);·0.191405s·(thread);·0s·(gc) |
| 147 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· | 147 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· |
| 148 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 148 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 149 | ·····------------------------------------------------------------------------ | 149 | ·····------------------------------------------------------------------------ |
| 150 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· | 150 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· |
| 151 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 151 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 152 | ·····------------------------------------------------------------------------ | 152 | ·····------------------------------------------------------------------------ |
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| 215 | ··········<tr> | 215 | ··········<tr> |
| 216 | <td>··············<pre><code·class="language-macaulay2">i11·:·I1·=·substitute(I,R1); | 216 | <td>··············<pre><code·class="language-macaulay2">i11·:·I1·=·substitute(I,R1); |
| 217 | o11·:·Ideal·of·R1</code></pre> | 217 | o11·:·Ideal·of·R1</code></pre> |
| 218 | </td>··········</tr> | 218 | </td>··········</tr> |
| 219 | ··········<tr> | 219 | ··········<tr> |
| 220 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·G·=·eliminate(I1,{s,t}) | 220 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·G·=·eliminate(I1,{s,t}) |
| 221 | ·--·used·0.0 | 221 | ·--·used·0.0585885s·(cpu);·0.0585922s·(thread);·0s·(gc) |
| 222 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7·· | 222 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7·· |
| 223 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- | 223 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- |
| 224 | ······----------------------------------------------------------------------- | 224 | ······----------------------------------------------------------------------- |
| 225 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2·· | 225 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2·· |
| 226 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- | 226 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- |
| 227 | ······----------------------------------------------------------------------- | 227 | ······----------------------------------------------------------------------- |
| Offset 297, 15 lines modified | Offset 297, 15 lines modified | ||
| 297 | ···················3·············3·····2·········3 | 297 | ···················3·············3·····2·········3 |
| 298 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) | 298 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) |
| 299 | o16·:·RingMap·A·<--·B</code></pre> | 299 | o16·:·RingMap·A·<--·B</code></pre> |
| 300 | </td>··········</tr> | 300 | </td>··········</tr> |
| 301 | ··········<tr> | 301 | ··········<tr> |
| 302 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·G·=·kernel·F | 302 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·G·=·kernel·F |
| 303 | ·--·used·0. | 303 | ·--·used·0.164034s·(cpu);·0.163851s·(thread);·0s·(gc) |
| 304 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· | 304 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· |
| 305 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 305 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 306 | ······----------------------------------------------------------------------- | 306 | ······----------------------------------------------------------------------- |
| 307 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· | 307 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· |
| 308 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 308 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 309 | ······----------------------------------------------------------------------- | 309 | ······----------------------------------------------------------------------- |
| Offset 372, 24 lines modified | Offset 372, 24 lines modified | ||
| 372 | o19·=·R | 372 | o19·=·R |
| 373 | o19·:·PolynomialRing</code></pre> | 373 | o19·:·PolynomialRing</code></pre> |
| 374 | </td>··········</tr> | 374 | </td>··········</tr> |
| 375 | ··········<tr> | 375 | ··········<tr> |
| 376 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·f1·=·resultant(I_0,I_2,s) | 376 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·f1·=·resultant(I_0,I_2,s) |
| 377 | ·--·used·0.00 | 377 | ·--·used·0.00239778s·(cpu);·0.00239694s·(thread);·0s·(gc) |
| 378 | ·········9····9······7····3 | 378 | ·········9····9······7····3 |
| 379 | o20·=·x*t··-·t··-·z*t··-·z | 379 | o20·=·x*t··-·t··-·z*t··-·z |
| 380 | o20·:·R</code></pre> | 380 | o20·:·R</code></pre> |
| 381 | </td>··········</tr> | 381 | </td>··········</tr> |
| 382 | ··········<tr> | 382 | ··········<tr> |
| 383 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f2·=·resultant(I_1,f1,t) | 383 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f2·=·resultant(I_1,f1,t) |
| 384 | ·--·used·0.0 | 384 | ·--·used·0.0441614s·(cpu);·0.0441708s·(thread);·0s·(gc) |
| 385 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2·· | 385 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2·· |
| 386 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ | 386 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ |
| 387 | ······----------------------------------------------------------------------- | 387 | ······----------------------------------------------------------------------- |
| 388 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8··· | 388 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8··· |
| 389 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ | 389 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ |
| 390 | ······----------------------------------------------------------------------- | 390 | ······----------------------------------------------------------------------- |
| Offset 13, 15 lines modified | Offset 13, 15 lines modified | ||
| 13 | i2·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3) | 13 | i2·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3) |
| 14 | ···············3···················3·····2···············3 | 14 | ···············3···················3·····2···············3 |
| 15 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) | 15 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) |
| 16 | o2·:·Ideal·of·R | 16 | o2·:·Ideal·of·R |
| 17 | i3·:·time·leadTerm·gens·gb·I | 17 | i3·:·time·leadTerm·gens·gb·I |
| 18 | ·--·used·0. | 18 | ·--·used·0.167644s·(cpu);·0.167644s·(thread);·0s·(gc) |
| 19 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 | 19 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 | 21 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 |
| 22 | ·····------------------------------------------------------------------------ | 22 | ·····------------------------------------------------------------------------ |
| 23 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 | 23 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 |
| 24 | ·····------------------------------------------------------------------------ | 24 | ·····------------------------------------------------------------------------ |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | i7·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3) | 89 | i7·:·I·=·ideal(x-s^3-s*t-1,·y-t^3-3*t^2-t,·z-s*t^3) |
| 90 | ···············3···················3·····2···············3 | 90 | ···············3···················3·····2···············3 |
| 91 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) | 91 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) |
| 92 | o7·:·Ideal·of·R | 92 | o7·:·Ideal·of·R |
| 93 | i8·:·time·G·=·eliminate(I,{s,t}) | 93 | i8·:·time·G·=·eliminate(I,{s,t}) |
| 94 | ·--·used·0. | 94 | ·--·used·0.191404s·(cpu);·0.191405s·(thread);·0s·(gc) |
| 95 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8 | 95 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8 |
| 96 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 96 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 97 | ·····------------------------------------------------------------------------ | 97 | ·····------------------------------------------------------------------------ |
| 98 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7 | 98 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7 |
| 99 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 99 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| Offset 156, 15 lines modified | Offset 156, 15 lines modified | ||
| 156 | Sometimes·giving·the·variables·different·degrees·will·speed·up·the | 156 | Sometimes·giving·the·variables·different·degrees·will·speed·up·the |
| 157 | computations.·Here,·we·set·the·degrees·of·x,·y,·and·z·to·be·the·total·degrees. | 157 | computations.·Here,·we·set·the·degrees·of·x,·y,·and·z·to·be·the·total·degrees. |
| 158 | i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}]; | 158 | i10·:·R1·=·QQ[x,y,z,s,t,·Degrees=>{3,3,4,1,1}]; |
| 159 | i11·:·I1·=·substitute(I,R1); | 159 | i11·:·I1·=·substitute(I,R1); |
| 160 | o11·:·Ideal·of·R1 | 160 | o11·:·Ideal·of·R1 |
| 161 | i12·:·time·G·=·eliminate(I1,{s,t}) | 161 | i12·:·time·G·=·eliminate(I1,{s,t}) |
| 162 | ·--·used·0.0 | 162 | ·--·used·0.0585885s·(cpu);·0.0585922s·(thread);·0s·(gc) |
| 163 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7 | 163 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7 |
| 164 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- | 164 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- |
| 165 | ······----------------------------------------------------------------------- | 165 | ······----------------------------------------------------------------------- |
| 166 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2 | 166 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2 |
| 167 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- | 167 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- |
| 168 | ······----------------------------------------------------------------------- | 168 | ······----------------------------------------------------------------------- |
| Offset 227, 15 lines modified | Offset 227, 15 lines modified | ||
| 227 | i16·:·F·=·map(A,B,{s^3+s*t+1,·t^3+3*t^2+t,·s*t^3}) | 227 | i16·:·F·=·map(A,B,{s^3+s*t+1,·t^3+3*t^2+t,·s*t^3}) |
| 228 | ···················3·············3·····2·········3 | 228 | ···················3·············3·····2·········3 |
| 229 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) | 229 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) |
| 230 | o16·:·RingMap·A·<--·B | 230 | o16·:·RingMap·A·<--·B |
| 231 | i17·:·time·G·=·kernel·F | 231 | i17·:·time·G·=·kernel·F |
| 232 | ·--·used·0. | 232 | ·--·used·0.164034s·(cpu);·0.163851s·(thread);·0s·(gc) |
| 233 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8 | 233 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8 |
| 234 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 234 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 235 | ······----------------------------------------------------------------------- | 235 | ······----------------------------------------------------------------------- |
| 236 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7 | 236 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7 |
| 237 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 237 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 238 | ······----------------------------------------------------------------------- | 238 | ······----------------------------------------------------------------------- |
| Offset 296, 22 lines modified | Offset 296, 22 lines modified | ||
| 296 | involve·the·variables·s·and·t. | 296 | involve·the·variables·s·and·t. |
| 297 | i19·:·use·ring·I | 297 | i19·:·use·ring·I |
| 298 | o19·=·R | 298 | o19·=·R |
| 299 | o19·:·PolynomialRing | 299 | o19·:·PolynomialRing |
| 300 | i20·:·time·f1·=·resultant(I_0,I_2,s) | 300 | i20·:·time·f1·=·resultant(I_0,I_2,s) |
| 301 | ·--·used·0.00 | 301 | ·--·used·0.00239778s·(cpu);·0.00239694s·(thread);·0s·(gc) |
| 302 | ·········9····9······7····3 | 302 | ·········9····9······7····3 |
| 303 | o20·=·x*t··-·t··-·z*t··-·z | 303 | o20·=·x*t··-·t··-·z*t··-·z |
| 304 | o20·:·R | 304 | o20·:·R |
| 305 | i21·:·time·f2·=·resultant(I_1,f1,t) | 305 | i21·:·time·f2·=·resultant(I_1,f1,t) |
| 306 | ·--·used·0.0 | 306 | ·--·used·0.0441614s·(cpu);·0.0441708s·(thread);·0s·(gc) |
| 307 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2 | 307 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2 |
| 308 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ | 308 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ |
| 309 | ······----------------------------------------------------------------------- | 309 | ······----------------------------------------------------------------------- |
| 310 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8 | 310 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8 |
| 311 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ | 311 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ |
| 312 | ······----------------------------------------------------------------------- | 312 | ······----------------------------------------------------------------------- |
| Offset 144, 15 lines modified | Offset 144, 15 lines modified | ||
| 144 | ····································Version·=>·0.0 | 144 | ····································Version·=>·0.0 |
| 145 | ·············package·prefix·=>·/usr/ | 145 | ·············package·prefix·=>·/usr/ |
| 146 | ·············PackageIsLoaded·=>·true | 146 | ·············PackageIsLoaded·=>·true |
| 147 | ·············pkgname·=>·Foo | 147 | ·············pkgname·=>·Foo |
| 148 | ·············private·dictionary·=>·Foo#"private·dictionary" | 148 | ·············private·dictionary·=>·Foo#"private·dictionary" |
| 149 | ·············processed·documentation·=>·MutableHashTable{} | 149 | ·············processed·documentation·=>·MutableHashTable{} |
| 150 | ·············raw·documentation·=>·MutableHashTable{} | 150 | ·············raw·documentation·=>·MutableHashTable{} |
| 151 | ·············source·directory·=>·/tmp/M2- | 151 | ·············source·directory·=>·/tmp/M2-3485508-0/88-rundir/ |
| 152 | ·············source·file·=>·stdio | 152 | ·············source·file·=>·stdio |
| 153 | ·············test·inputs·=>·MutableList{}</code></pre> | 153 | ·············test·inputs·=>·MutableList{}</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i7·:·dictionaryPath | 156 | <td>··············<pre><code·class="language-macaulay2">i7·:·dictionaryPath |
| 157 | o7·=·{Foo.Dictionary,·PackageCitations.Dictionary,·Varieties.Dictionary, | 157 | o7·=·{Foo.Dictionary,·PackageCitations.Dictionary,·Varieties.Dictionary, |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | ····································Version·=>·0.0 | 78 | ····································Version·=>·0.0 |
| 79 | ·············package·prefix·=>·/usr/ | 79 | ·············package·prefix·=>·/usr/ |
| 80 | ·············PackageIsLoaded·=>·true | 80 | ·············PackageIsLoaded·=>·true |
| 81 | ·············pkgname·=>·Foo | 81 | ·············pkgname·=>·Foo |
| 82 | ·············private·dictionary·=>·Foo#"private·dictionary" | 82 | ·············private·dictionary·=>·Foo#"private·dictionary" |
| 83 | ·············processed·documentation·=>·MutableHashTable{} | 83 | ·············processed·documentation·=>·MutableHashTable{} |
| 84 | ·············raw·documentation·=>·MutableHashTable{} | 84 | ·············raw·documentation·=>·MutableHashTable{} |
| 85 | ·············source·directory·=>·/tmp/M2- | 85 | ·············source·directory·=>·/tmp/M2-3485508-0/88-rundir/ |
| 86 | ·············source·file·=>·stdio | 86 | ·············source·file·=>·stdio |
| 87 | ·············test·inputs·=>·MutableList{} | 87 | ·············test·inputs·=>·MutableList{} |
| 88 | i7·:·dictionaryPath | 88 | i7·:·dictionaryPath |
| 89 | o7·=·{Foo.Dictionary,·PackageCitations.Dictionary,·Varieties.Dictionary, | 89 | o7·=·{Foo.Dictionary,·PackageCitations.Dictionary,·Varieties.Dictionary, |
| 90 | ·····------------------------------------------------------------------------ | 90 | ·····------------------------------------------------------------------------ |
| 91 | ·····Truncations.Dictionary,·Polyhedra.Dictionary,·Saturation.Dictionary, | 91 | ·····Truncations.Dictionary,·Polyhedra.Dictionary,·Saturation.Dictionary, |
| Offset 67, 25 lines modified | Offset 67, 25 lines modified | ||
| 67 | ······</div> | 67 | ······</div> |
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | ········<table·class="examples"> | 70 | ········<table·class="examples"> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 73 | o1·=·/tmp/M2- | 73 | o1·=·/tmp/M2-3498018-0/0</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileExists·fn | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileExists·fn |
| 77 | o2·=·false</code></pre> | 77 | o2·=·false</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close |
| 81 | o3·=·/tmp/M2- | 81 | o3·=·/tmp/M2-3498018-0/0 |
| 82 | o3·:·File</code></pre> | 82 | o3·:·File</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·fileExists·fn | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·fileExists·fn |
| 86 | o4·=·true</code></pre> | 86 | o4·=·true</code></pre> |
| Offset 11, 21 lines modified | Offset 11, 21 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g | 12 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g |
| 13 | ····*·Outputs: | 13 | ····*·Outputs: |
| 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·a·file·with·the·filename·or·path·fn·exists | 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·a·file·with·the·filename·or·path·fn·exists |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·fn·=·temporaryFileName() | 16 | i1·:·fn·=·temporaryFileName() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3498018-0/0 |
| 18 | i2·:·fileExists·fn | 18 | i2·:·fileExists·fn |
| 19 | o2·=·false | 19 | o2·=·false |
| 20 | i3·:·fn·<<·"hi·there"·<<·close | 20 | i3·:·fn·<<·"hi·there"·<<·close |
| 21 | o3·=·/tmp/M2- | 21 | o3·=·/tmp/M2-3498018-0/0 |
| 22 | o3·:·File | 22 | o3·:·File |
| 23 | i4·:·fileExists·fn | 23 | i4·:·fileExists·fn |
| 24 | o4·=·true | 24 | o4·=·true |
| 25 | i5·:·removeFile·fn | 25 | i5·:·removeFile·fn |
| 26 | If·fn·refers·to·a·symbolic·link,·then·whether·the·file·exists·is·determined·by | 26 | If·fn·refers·to·a·symbolic·link,·then·whether·the·file·exists·is·determined·by |
| Offset 68, 34 lines modified | Offset 68, 34 lines modified | ||
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | ········<p>The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the·number·of·bytes·written·so·far.</p> | 70 | ········<p>The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the·number·of·bytes·written·so·far.</p> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·temporaryFileName()·<<·"hi·there" | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·temporaryFileName()·<<·"hi·there" |
| 74 | o1·=·/tmp/M2- | 74 | o1·=·/tmp/M2-3518510-0/0 |
| 75 | o1·:·File</code></pre> | 75 | o1·:·File</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileLength·f | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileLength·f |
| 79 | o2·=·8</code></pre> | 79 | o2·=·8</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·close·f | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·close·f |
| 83 | o3·=·/tmp/M2- | 83 | o3·=·/tmp/M2-3518510-0/0 |
| 84 | o3·:·File</code></pre> | 84 | o3·:·File</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·filename·=·toString·f | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·filename·=·toString·f |
| 88 | o4·=·/tmp/M2- | 88 | o4·=·/tmp/M2-3518510-0/0</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileLength·filename | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileLength·filename |
| 92 | o5·=·8</code></pre> | 92 | o5·=·8</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| Offset 12, 28 lines modified | Offset 12, 28 lines modified | ||
| 12 | ····*·Outputs: | 12 | ····*·Outputs: |
| 13 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·length·of·the·file·f·or·the·file·whose·name·is·f | 13 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·length·of·the·file·f·or·the·file·whose·name·is·f |
| 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 15 | The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the | 15 | The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the |
| 16 | number·of·bytes·written·so·far. | 16 | number·of·bytes·written·so·far. |
| 17 | i1·:·f·=·temporaryFileName()·<<·"hi·there" | 17 | i1·:·f·=·temporaryFileName()·<<·"hi·there" |
| 18 | o1·=·/tmp/M2- | 18 | o1·=·/tmp/M2-3518510-0/0 |
| 19 | o1·:·File | 19 | o1·:·File |
| 20 | i2·:·fileLength·f | 20 | i2·:·fileLength·f |
| 21 | o2·=·8 | 21 | o2·=·8 |
| 22 | i3·:·close·f | 22 | i3·:·close·f |
| 23 | o3·=·/tmp/M2- | 23 | o3·=·/tmp/M2-3518510-0/0 |
| 24 | o3·:·File | 24 | o3·:·File |
| 25 | i4·:·filename·=·toString·f | 25 | i4·:·filename·=·toString·f |
| 26 | o4·=·/tmp/M2- | 26 | o4·=·/tmp/M2-3518510-0/0 |
| 27 | i5·:·fileLength·filename | 27 | i5·:·fileLength·filename |
| 28 | o5·=·8 | 28 | o5·=·8 |
| 29 | i6·:·get·filename | 29 | i6·:·get·filename |
| 30 | o6·=·hi·there | 30 | o6·=·hi·there |
| 31 | i7·:·length·oo | 31 | i7·:·length·oo |
| Offset 69, 32 lines modified | Offset 69, 32 lines modified | ||
| 69 | ······</div> | 69 | ······</div> |
| 70 | ······<div> | 70 | ······<div> |
| 71 | ········<h2>Description</h2> | 71 | ········<h2>Description</h2> |
| 72 | ········<table·class="examples"> | 72 | ········<table·class="examples"> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 75 | o1·=·/tmp/M2- | 75 | o1·=·/tmp/M2-3505439-0/0</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" |
| 79 | o2·=·/tmp/M2- | 79 | o2·=·/tmp/M2-3505439-0/0 |
| 80 | o2·:·File</code></pre> | 80 | o2·:·File</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·f | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·f |
| 84 | o3·=·420</code></pre> | 84 | o3·=·420</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·close·f | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·close·f |
| 88 | o4·=·/tmp/M2- | 88 | o4·=·/tmp/M2-3505439-0/0 |
| 89 | o4·:·File</code></pre> | 89 | o4·:·File</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre> | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ········</table> | 94 | ········</table> |
| Offset 11, 24 lines modified | Offset 11, 24 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·f | 12 | ··········o·f |
| 13 | ····*·Outputs: | 13 | ····*·Outputs: |
| 14 | ··········o·the·mode·of·the·open·file·f | 14 | ··········o·the·mode·of·the·open·file·f |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·fn·=·temporaryFileName() | 16 | i1·:·fn·=·temporaryFileName() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3505439-0/0 |
| 18 | i2·:·f·=·fn·<<·"hi·there" | 18 | i2·:·f·=·fn·<<·"hi·there" |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-3505439-0/0 |
| 20 | o2·:·File | 20 | o2·:·File |
| 21 | i3·:·fileMode·f | 21 | i3·:·fileMode·f |
| 22 | o3·=·420 | 22 | o3·=·420 |
| 23 | i4·:·close·f | 23 | i4·:·close·f |
| 24 | o4·=·/tmp/M2- | 24 | o4·=·/tmp/M2-3505439-0/0 |
| 25 | o4·:·File | 25 | o4·:·File |
| 26 | i5·:·removeFile·fn | 26 | i5·:·removeFile·fn |
| 27 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 28 | ····*·_\x8f_\x8i_\x8l_\x8e_\x8M_\x8o_\x8d_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·get·file·mode | 28 | ····*·_\x8f_\x8i_\x8l_\x8e_\x8M_\x8o_\x8d_\x8e_\x8(_\x8F_\x8i_\x8l_\x8e_\x8)·--·get·file·mode |
| Offset 69, 20 lines modified | Offset 69, 20 lines modified | ||
| 69 | ······</div> | 69 | ······</div> |
| 70 | ······<div> | 70 | ······<div> |
| 71 | ········<h2>Description</h2> | 71 | ········<h2>Description</h2> |
| 72 | ········<table·class="examples"> | 72 | ········<table·class="examples"> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 75 | o1·=·/tmp/M2- | 75 | o1·=·/tmp/M2-3500648-0/0</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close |
| 79 | o2·=·/tmp/M2- | 79 | o2·=·/tmp/M2-3500648-0/0 |
| 80 | o2·:·File</code></pre> | 80 | o2·:·File</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·fn | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·fn |
| 84 | o3·=·420</code></pre> | 84 | o3·=·420</code></pre> |
| Offset 11, 18 lines modified | Offset 11, 18 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·fn | 12 | ··········o·fn |
| 13 | ····*·Outputs: | 13 | ····*·Outputs: |
| 14 | ··········o·the·mode·of·the·file·located·at·the·filename·or·path·fn | 14 | ··········o·the·mode·of·the·file·located·at·the·filename·or·path·fn |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·fn·=·temporaryFileName() | 16 | i1·:·fn·=·temporaryFileName() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3500648-0/0 |
| 18 | i2·:·fn·<<·"hi·there"·<<·close | 18 | i2·:·fn·<<·"hi·there"·<<·close |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-3500648-0/0 |
| 20 | o2·:·File | 20 | o2·:·File |
| 21 | i3·:·fileMode·fn | 21 | i3·:·fileMode·fn |
| 22 | o3·=·420 | 22 | o3·=·420 |
| 23 | i4·:·removeFile·fn | 23 | i4·:·removeFile·fn |
| 24 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 73, 20 lines modified | Offset 73, 20 lines modified | ||
| 73 | ······</div> | 73 | ······</div> |
| 74 | ······<div> | 74 | ······<div> |
| 75 | ········<h2>Description</h2> | 75 | ········<h2>Description</h2> |
| 76 | ········<table·class="examples"> | 76 | ········<table·class="examples"> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 79 | o1·=·/tmp/M2- | 79 | o1·=·/tmp/M2-3500015-0/0</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" |
| 83 | o2·=·/tmp/M2- | 83 | o2·=·/tmp/M2-3500015-0/0 |
| 84 | o2·:·File</code></pre> | 84 | o2·:·File</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·7·+·7*8·+·7*64 | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·7·+·7*8·+·7*64 |
| 88 | o3·=·511</code></pre> | 88 | o3·=·511</code></pre> |
| Offset 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileMode·f | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileMode·f |
| 99 | o5·=·511</code></pre> | 99 | o5·=·511</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i6·:·close·f | 102 | <td>··············<pre><code·class="language-macaulay2">i6·:·close·f |
| 103 | o6·=·/tmp/M2- | 103 | o6·=·/tmp/M2-3500015-0/0 |
| 104 | o6·:·File</code></pre> | 104 | o6·:·File</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·fileMode·fn | 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·fileMode·fn |
| 108 | o7·=·511</code></pre> | 108 | o7·=·511</code></pre> |
| Offset 12, 30 lines modified | Offset 12, 30 lines modified | ||
| 12 | ··········o·mo | 12 | ··········o·mo |
| 13 | ··········o·f | 13 | ··········o·f |
| 14 | ····*·Consequences: | 14 | ····*·Consequences: |
| 15 | ··········o·the·mode·of·the·open·file·f·is·set·to·mo | 15 | ··········o·the·mode·of·the·open·file·f·is·set·to·mo |
| 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 17 | i1·:·fn·=·temporaryFileName() | 17 | i1·:·fn·=·temporaryFileName() |
| 18 | o1·=·/tmp/M2- | 18 | o1·=·/tmp/M2-3500015-0/0 |
| 19 | i2·:·f·=·fn·<<·"hi·there" | 19 | i2·:·f·=·fn·<<·"hi·there" |
| 20 | o2·=·/tmp/M2- | 20 | o2·=·/tmp/M2-3500015-0/0 |
| 21 | o2·:·File | 21 | o2·:·File |
| 22 | i3·:·m·=·7·+·7*8·+·7*64 | 22 | i3·:·m·=·7·+·7*8·+·7*64 |
| 23 | o3·=·511 | 23 | o3·=·511 |
| 24 | i4·:·fileMode(m,f) | 24 | i4·:·fileMode(m,f) |
| 25 | i5·:·fileMode·f | 25 | i5·:·fileMode·f |
| 26 | o5·=·511 | 26 | o5·=·511 |
| 27 | i6·:·close·f | 27 | i6·:·close·f |
| 28 | o6·=·/tmp/M2- | 28 | o6·=·/tmp/M2-3500015-0/0 |
| 29 | o6·:·File | 29 | o6·:·File |
| 30 | i7·:·fileMode·fn | 30 | i7·:·fileMode·fn |
| 31 | o7·=·511 | 31 | o7·=·511 |
| 32 | i8·:·removeFile·fn | 32 | i8·:·removeFile·fn |
| 33 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 33 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 73, 20 lines modified | Offset 73, 20 lines modified | ||
| 73 | ······</div> | 73 | ······</div> |
| 74 | ······<div> | 74 | ······<div> |
| 75 | ········<h2>Description</h2> | 75 | ········<h2>Description</h2> |
| 76 | ········<table·class="examples"> | 76 | ········<table·class="examples"> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 79 | o1·=·/tmp/M2- | 79 | o1·=·/tmp/M2-3509447-0/0</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close |
| 83 | o2·=·/tmp/M2- | 83 | o2·=·/tmp/M2-3509447-0/0 |
| 84 | o2·:·File</code></pre> | 84 | o2·:·File</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·fileMode·fn | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·fileMode·fn |
| 88 | o3·=·420</code></pre> | 88 | o3·=·420</code></pre> |
| Offset 13, 18 lines modified | Offset 13, 18 lines modified | ||
| 13 | ··········o·fn | 13 | ··········o·fn |
| 14 | ····*·Consequences: | 14 | ····*·Consequences: |
| 15 | ··········o·the·mode·of·the·file·located·at·the·filename·or·path·fn·is·set·to | 15 | ··········o·the·mode·of·the·file·located·at·the·filename·or·path·fn·is·set·to |
| 16 | ············mo | 16 | ············mo |
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | i1·:·fn·=·temporaryFileName() | 18 | i1·:·fn·=·temporaryFileName() |
| 19 | o1·=·/tmp/M2- | 19 | o1·=·/tmp/M2-3509447-0/0 |
| 20 | i2·:·fn·<<·"hi·there"·<<·close | 20 | i2·:·fn·<<·"hi·there"·<<·close |
| 21 | o2·=·/tmp/M2- | 21 | o2·=·/tmp/M2-3509447-0/0 |
| 22 | o2·:·File | 22 | o2·:·File |
| 23 | i3·:·m·=·fileMode·fn | 23 | i3·:·m·=·fileMode·fn |
| 24 | o3·=·420 | 24 | o3·=·420 |
| 25 | i4·:·fileMode(m|7,fn) | 25 | i4·:·fileMode(m|7,fn) |
| 26 | i5·:·fileMode·fn | 26 | i5·:·fileMode·fn |
| Offset 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ······</div> | 77 | ······</div> |
| 78 | ······<div> | 78 | ······<div> |
| 79 | ········<h2>Description</h2> | 79 | ········<h2>Description</h2> |
| 80 | The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning·of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may·be·found·by·using·the·following·code.········<table·class="examples"> | 80 | The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning·of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may·be·found·by·using·the·following·code.········<table·class="examples"> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime()·-·fileTime·"." | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime()·-·fileTime·"." |
| 83 | o1·=· | 83 | o1·=·40</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ········</table> | 85 | ········</table> |
| 86 | ······</div> | 86 | ······</div> |
| 87 | ······<div> | 87 | ······<div> |
| 88 | ········<h2>See·also</h2> | 88 | ········<h2>See·also</h2> |
| 89 | ········<ul> | 89 | ········<ul> |
| 90 | ··········<li> | 90 | ··········<li> |
| Offset 19, 13 lines modified | Offset 19, 13 lines modified | ||
| 19 | ············returns·null·if·no·error·occurs | 19 | ············returns·null·if·no·error·occurs |
| 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 20 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 21 | The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning | 21 | The·value·is·the·number·of·seconds·since·00:00:00·1970-01-01·UTC,·the·beginning |
| 22 | of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may | 22 | of·the·epoch,·so·the·number·of·seconds·ago·a·file·or·directory·was·modified·may |
| 23 | be·found·by·using·the·following·code. | 23 | be·found·by·using·the·following·code. |
| 24 | i1·:·currentTime()·-·fileTime·"." | 24 | i1·:·currentTime()·-·fileTime·"." |
| 25 | o1·=· | 25 | o1·=·40 |
| 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 27 | ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time | 27 | ····*·_\x8c_\x8u_\x8r_\x8r_\x8e_\x8n_\x8t_\x8T_\x8i_\x8m_\x8e·--·get·the·current·time |
| 28 | ····*·_\x8f_\x8i_\x8l_\x8e_\x8·_\x8m_\x8a_\x8n_\x8i_\x8p_\x8u_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n·--·Unix·file·manipulation·functions | 28 | ····*·_\x8f_\x8i_\x8l_\x8e_\x8·_\x8m_\x8a_\x8n_\x8i_\x8p_\x8u_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n·--·Unix·file·manipulation·functions |
| 29 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 30 | The·object·_\x8f_\x8i_\x8l_\x8e_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 30 | The·object·_\x8f_\x8i_\x8l_\x8e_\x8T_\x8i_\x8m_\x8e·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | ·············3······3 | 106 | ·············3······3 |
| 107 | o6·:·Matrix·R··<--·R</code></pre> | 107 | o6·:·Matrix·R··<--·R</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·syz·f | 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·syz·f |
| 111 | ···--·registering·gb·0·at·0x7f | 111 | ···--·registering·gb·0·at·0x7f6e96451000 |
| 112 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3 | 112 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3 |
| 113 | ···--·number·of·monomials················=·9 | 113 | ···--·number·of·monomials················=·9 |
| 114 | ···--·#reduction·steps·=·6 | 114 | ···--·#reduction·steps·=·6 |
| 115 | ···--·#spairs·done·=·6 | 115 | ···--·#spairs·done·=·6 |
| 116 | ···--·ncalls·=·0 | 116 | ···--·ncalls·=·0 |
| 117 | ···--·nloop·=·0 | 117 | ···--·nloop·=·0 |
| Offset 37, 15 lines modified | Offset 37, 15 lines modified | ||
| 37 | ·····{3}·|·x2-3··0·····-z4+2·| | 37 | ·····{3}·|·x2-3··0·····-z4+2·| |
| 38 | ·····{4}·|·0·····x2-3··y3-1··| | 38 | ·····{4}·|·0·····x2-3··y3-1··| |
| 39 | ·············3······3 | 39 | ·············3······3 |
| 40 | o6·:·Matrix·R··<--·R | 40 | o6·:·Matrix·R··<--·R |
| 41 | i7·:·syz·f | 41 | i7·:·syz·f |
| 42 | ···--·registering·gb·0·at·0x7f | 42 | ···--·registering·gb·0·at·0x7f6e96451000 |
| 43 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb | 43 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb |
| 44 | elements·=·3 | 44 | elements·=·3 |
| 45 | ···--·number·of·monomials················=·9 | 45 | ···--·number·of·monomials················=·9 |
| 46 | ···--·#reduction·steps·=·6 | 46 | ···--·#reduction·steps·=·6 |
| 47 | ···--·#spairs·done·=·6 | 47 | ···--·#spairs·done·=·6 |
| 48 | ···--·ncalls·=·0 | 48 | ···--·ncalls·=·0 |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeFile·"test-file"</code></pre> | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeFile·"test-file"</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·get·"!date" | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·get·"!date" |
| 96 | o4·=· | 96 | o4·=·Wed·Dec·17·09:59:35·+14·2025</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ········</table> | 98 | ········</table> |
| 99 | ······</div> | 99 | ······</div> |
| 100 | ······<div> | 100 | ······<div> |
| 101 | ········<h2>See·also</h2> | 101 | ········<h2>See·also</h2> |
| 102 | ········<ul> | 102 | ········<ul> |
| 103 | ··········<li> | 103 | ··········<li> |
| Offset 25, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | o1·:·File | 25 | o1·:·File |
| 26 | i2·:·get·"test-file" | 26 | i2·:·get·"test-file" |
| 27 | o2·=·hi·there | 27 | o2·=·hi·there |
| 28 | i3·:·removeFile·"test-file" | 28 | i3·:·removeFile·"test-file" |
| 29 | i4·:·get·"!date" | 29 | i4·:·get·"!date" |
| 30 | o4·=· | 30 | o4·=·Wed·Dec·17·09:59:35·+14·2025 |
| 31 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 31 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 32 | ····*·_\x8r_\x8e_\x8a_\x8d·--·read·from·a·file | 32 | ····*·_\x8r_\x8e_\x8a_\x8d·--·read·from·a·file |
| 33 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file | 33 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file |
| 34 | ····*·_\x8c_\x8l_\x8o_\x8s_\x8e·--·close·a·file | 34 | ····*·_\x8c_\x8l_\x8o_\x8s_\x8e·--·close·a·file |
| 35 | ····*·_\x8F_\x8i_\x8l_\x8e_\x8·_\x8<_\x8<_\x8·_\x8T_\x8h_\x8i_\x8n_\x8g·--·print·to·a·file | 35 | ····*·_\x8F_\x8i_\x8l_\x8e_\x8·_\x8<_\x8<_\x8·_\x8T_\x8h_\x8i_\x8n_\x8g·--·print·to·a·file |
| 36 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8ge\x8et\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·get(File) | 37 | ····*·get(File) |
| Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | ········<table·class="examples"> | 64 | ········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·groupID() | 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·groupID() |
| 67 | o1·=· | 67 | o1·=·3420128</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ········</table> | 69 | ········</table> |
| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>See·also</h2> | 72 | ········<h2>See·also</h2> |
| 73 | ········<ul> | 73 | ········<ul> |
| 74 | ··········<li> | 74 | ··········<li> |
| Offset 9, 13 lines modified | Offset 9, 13 lines modified | ||
| 9 | ············groupID() | 9 | ············groupID() |
| 10 | ····*·Outputs: | 10 | ····*·Outputs: |
| 11 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·group·identifier·of·the·current·Macaulay2 | 11 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·group·identifier·of·the·current·Macaulay2 |
| 12 | ············process | 12 | ············process |
| 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 14 | i1·:·groupID() | 14 | i1·:·groupID() |
| 15 | o1·=· | 15 | o1·=·3420128 |
| 16 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 16 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 17 | ····*·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·--·the·process·identifier | 17 | ····*·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·--·the·process·identifier |
| 18 | ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier | 18 | ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier |
| 19 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 19 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 20 | The·object·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 20 | The·object·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 72, 20 lines modified | Offset 72, 20 lines modified | ||
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·isDirectory·"." | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·isDirectory·"." |
| 73 | o1·=·true</code></pre> | 73 | o1·=·true</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·=·temporaryFileName() | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·=·temporaryFileName() |
| 77 | o2·=·/tmp/M2- | 77 | o2·=·/tmp/M2-3486683-0/0</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close |
| 81 | o3·=·/tmp/M2- | 81 | o3·=·/tmp/M2-3486683-0/0 |
| 82 | o3·:·File</code></pre> | 82 | o3·:·File</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·isDirectory·fn | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·isDirectory·fn |
| 86 | o4·=·false</code></pre> | 86 | o4·=·false</code></pre> |
| Offset 14, 18 lines modified | Offset 14, 18 lines modified | ||
| 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·directory | 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·directory |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·isDirectory·"." | 16 | i1·:·isDirectory·"." |
| 17 | o1·=·true | 17 | o1·=·true |
| 18 | i2·:·fn·=·temporaryFileName() | 18 | i2·:·fn·=·temporaryFileName() |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-3486683-0/0 |
| 20 | i3·:·fn·<<·"hi·there"·<<·close | 20 | i3·:·fn·<<·"hi·there"·<<·close |
| 21 | o3·=·/tmp/M2- | 21 | o3·=·/tmp/M2-3486683-0/0 |
| 22 | o3·:·File | 22 | o3·:·File |
| 23 | i4·:·isDirectory·fn | 23 | i4·:·isDirectory·fn |
| 24 | o4·=·false | 24 | o4·=·false |
| 25 | i5·:·removeFile·fn | 25 | i5·:·removeFile·fn |
| 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 175, 15 lines modified | Offset 175, 15 lines modified | ||
| 175 | ··········<tr> | 175 | ··········<tr> |
| 176 | <td>··············<pre><code·class="language-macaulay2">i18·:·isPrime(m*m*m1*m1*m2^6) | 176 | <td>··············<pre><code·class="language-macaulay2">i18·:·isPrime(m*m*m1*m1*m2^6) |
| 177 | o18·=·false</code></pre> | 177 | o18·=·false</code></pre> |
| 178 | </td>··········</tr> | 178 | </td>··········</tr> |
| 179 | ··········<tr> | 179 | ··········<tr> |
| 180 | <td>··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·facs·=·factor(m*m1) | 180 | <td>··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·facs·=·factor(m*m1) |
| 181 | ·--· | 181 | ·--·9.32182s·elapsed |
| 182 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 | 182 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 |
| 183 | o19·:·Expression·of·class·Product</code></pre> | 183 | o19·:·Expression·of·class·Product</code></pre> |
| 184 | </td>··········</tr> | 184 | </td>··········</tr> |
| 185 | ··········<tr> | 185 | ··········<tr> |
| 186 | <td>··············<pre><code·class="language-macaulay2">i20·:·facs·=·facs//toList/toList | 186 | <td>··············<pre><code·class="language-macaulay2">i20·:·facs·=·facs//toList/toList |
| Offset 201, 21 lines modified | Offset 201, 21 lines modified | ||
| 201 | <td>··············<pre><code·class="language-macaulay2">i22·:·m3·=·nextPrime·(m^3) | 201 | <td>··············<pre><code·class="language-macaulay2">i22·:·m3·=·nextPrime·(m^3) |
| 202 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 | 202 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 |
| 203 | ······00000000000000185613</code></pre> | 203 | ······00000000000000185613</code></pre> |
| 204 | </td>··········</tr> | 204 | </td>··········</tr> |
| 205 | ··········<tr> | 205 | ··········<tr> |
| 206 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·m3 | 206 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·m3 |
| 207 | ·--·.0 | 207 | ·--·.0618019s·elapsed |
| 208 | o23·=·true</code></pre> | 208 | o23·=·true</code></pre> |
| 209 | </td>··········</tr> | 209 | </td>··········</tr> |
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isPseudoprime·m3 | 211 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isPseudoprime·m3 |
| 212 | ·--·.000 | 212 | ·--·.000220213s·elapsed |
| 213 | o24·=·true</code></pre> | 213 | o24·=·true</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ········</table> | 215 | ········</table> |
| 216 | ······</div> | 216 | ······</div> |
| 217 | ······<div> | 217 | ······<div> |
| 218 | ········<h2>See·also</h2> | 218 | ········<h2>See·also</h2> |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | i17·:·isPrime·(m*m1) | 80 | i17·:·isPrime·(m*m1) |
| 81 | o17·=·false | 81 | o17·=·false |
| 82 | i18·:·isPrime(m*m*m1*m1*m2^6) | 82 | i18·:·isPrime(m*m*m1*m1*m2^6) |
| 83 | o18·=·false | 83 | o18·=·false |
| 84 | i19·:·elapsedTime·facs·=·factor(m*m1) | 84 | i19·:·elapsedTime·facs·=·factor(m*m1) |
| 85 | ·--· | 85 | ·--·9.32182s·elapsed |
| 86 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 | 86 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 |
| 87 | o19·:·Expression·of·class·Product | 87 | o19·:·Expression·of·class·Product |
| 88 | i20·:·facs·=·facs//toList/toList | 88 | i20·:·facs·=·facs//toList/toList |
| 89 | o20·=·{{1000000000000000000000000000057,·1}, | 89 | o20·=·{{1000000000000000000000000000057,·1}, |
| Offset 98, 19 lines modified | Offset 98, 19 lines modified | ||
| 98 | o20·:·List | 98 | o20·:·List |
| 99 | i21·:·assert(set·facs·===·set·{{m,1},·{m1,1}}) | 99 | i21·:·assert(set·facs·===·set·{{m,1},·{m1,1}}) |
| 100 | i22·:·m3·=·nextPrime·(m^3) | 100 | i22·:·m3·=·nextPrime·(m^3) |
| 101 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 | 101 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 |
| 102 | ······00000000000000185613 | 102 | ······00000000000000185613 |
| 103 | i23·:·elapsedTime·isPrime·m3 | 103 | i23·:·elapsedTime·isPrime·m3 |
| 104 | ·--·.0 | 104 | ·--·.0618019s·elapsed |
| 105 | o23·=·true | 105 | o23·=·true |
| 106 | i24·:·elapsedTime·isPseudoprime·m3 | 106 | i24·:·elapsedTime·isPseudoprime·m3 |
| 107 | ·--·.000 | 107 | ·--·.000220213s·elapsed |
| 108 | o24·=·true | 108 | o24·=·true |
| 109 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 109 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 110 | ····*·_\x8i_\x8s_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8Z_\x8Z_\x8)·--·whether·a·integer·or·polynomial·is·prime | 110 | ····*·_\x8i_\x8s_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8Z_\x8Z_\x8)·--·whether·a·integer·or·polynomial·is·prime |
| 111 | ····*·_\x8f_\x8a_\x8c_\x8t_\x8o_\x8r_\x8(_\x8Z_\x8Z_\x8)·--·factor·a·ring·element | 111 | ····*·_\x8f_\x8a_\x8c_\x8t_\x8o_\x8r_\x8(_\x8Z_\x8Z_\x8)·--·factor·a·ring·element |
| 112 | ····*·_\x8n_\x8e_\x8x_\x8t_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8N_\x8u_\x8m_\x8b_\x8e_\x8r_\x8)·--·compute·the·smallest·prime·greater·than·or·equal·to | 112 | ····*·_\x8n_\x8e_\x8x_\x8t_\x8P_\x8r_\x8i_\x8m_\x8e_\x8(_\x8N_\x8u_\x8m_\x8b_\x8e_\x8r_\x8)·--·compute·the·smallest·prime·greater·than·or·equal·to |
| 113 | ······a·given·number | 113 | ······a·given·number |
| Offset 67, 20 lines modified | Offset 67, 20 lines modified | ||
| 67 | ······</div> | 67 | ······</div> |
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.··Special·files·include·symbolic·links·and·directories.··A·regular·file·is·a·sequence·of·bytes·stored·permanently·in·a·file·system.········<table·class="examples"> | 70 | In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.··Special·files·include·symbolic·links·and·directories.··A·regular·file·is·a·sequence·of·bytes·stored·permanently·in·a·file·system.········<table·class="examples"> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 73 | o1·=·/tmp/M2- | 73 | o1·=·/tmp/M2-3519111-0/0</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close |
| 77 | o2·=·/tmp/M2- | 77 | o2·=·/tmp/M2-3519111-0/0 |
| 78 | o2·:·File</code></pre> | 78 | o2·:·File</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·isRegularFile·fn | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·isRegularFile·fn |
| 82 | o3·=·true</code></pre> | 82 | o3·=·true</code></pre> |
| Offset 14, 18 lines modified | Offset 14, 18 lines modified | ||
| 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·regular·file | 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·regular·file |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.·Special·files | 16 | In·UNIX,·a·regular·file·is·one·that·is·not·special·in·some·way.·Special·files |
| 17 | include·symbolic·links·and·directories.·A·regular·file·is·a·sequence·of·bytes | 17 | include·symbolic·links·and·directories.·A·regular·file·is·a·sequence·of·bytes |
| 18 | stored·permanently·in·a·file·system. | 18 | stored·permanently·in·a·file·system. |
| 19 | i1·:·fn·=·temporaryFileName() | 19 | i1·:·fn·=·temporaryFileName() |
| 20 | o1·=·/tmp/M2- | 20 | o1·=·/tmp/M2-3519111-0/0 |
| 21 | i2·:·fn·<<·"hi·there"·<<·close | 21 | i2·:·fn·<<·"hi·there"·<<·close |
| 22 | o2·=·/tmp/M2- | 22 | o2·=·/tmp/M2-3519111-0/0 |
| 23 | o2·:·File | 23 | o2·:·File |
| 24 | i3·:·isRegularFile·fn | 24 | i3·:·isRegularFile·fn |
| 25 | o3·=·true | 25 | o3·=·true |
| 26 | i4·:·removeFile·fn | 26 | i4·:·removeFile·fn |
| 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 77, 20 lines modified | Offset 77, 20 lines modified | ||
| 77 | ······</div> | 77 | ······</div> |
| 78 | ······<div> | 78 | ······<div> |
| 79 | ········<h2>Description</h2> | 79 | ········<h2>Description</h2> |
| 80 | ········<table·class="examples"> | 80 | ········<table·class="examples"> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() |
| 83 | o1·=·/tmp/M2- | 83 | o1·=·/tmp/M2-3499660-0/0</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·(dir|"/a/b/c") | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·(dir|"/a/b/c") |
| 87 | o2·=·/tmp/M2- | 87 | o2·=·/tmp/M2-3499660-0/0/a/b/c</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeDirectory·(dir|"/a/b/c")</code></pre> | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeDirectory·(dir|"/a/b/c")</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·removeDirectory·(dir|"/a/b")</code></pre> | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·removeDirectory·(dir|"/a/b")</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| Offset 14, 18 lines modified | Offset 14, 18 lines modified | ||
| 14 | ····*·Outputs: | 14 | ····*·Outputs: |
| 15 | ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·name·of·the·newly·made·directory | 15 | ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·the·name·of·the·newly·made·directory |
| 16 | ····*·Consequences: | 16 | ····*·Consequences: |
| 17 | ··········o·the·directory·is·made,·with·as·many·new·path·components·as·needed | 17 | ··········o·the·directory·is·made,·with·as·many·new·path·components·as·needed |
| 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 19 | i1·:·dir·=·temporaryFileName() | 19 | i1·:·dir·=·temporaryFileName() |
| 20 | o1·=·/tmp/M2- | 20 | o1·=·/tmp/M2-3499660-0/0 |
| 21 | i2·:·makeDirectory·(dir|"/a/b/c") | 21 | i2·:·makeDirectory·(dir|"/a/b/c") |
| 22 | o2·=·/tmp/M2- | 22 | o2·=·/tmp/M2-3499660-0/0/a/b/c |
| 23 | i3·:·removeDirectory·(dir|"/a/b/c") | 23 | i3·:·removeDirectory·(dir|"/a/b/c") |
| 24 | i4·:·removeDirectory·(dir|"/a/b") | 24 | i4·:·removeDirectory·(dir|"/a/b") |
| 25 | i5·:·removeDirectory·(dir|"/a") | 25 | i5·:·removeDirectory·(dir|"/a") |
| 26 | A·filename·starting·with·~/·will·have·the·tilde·replaced·by·the·home·directory. | 26 | A·filename·starting·with·~/·will·have·the·tilde·replaced·by·the·home·directory. |
| 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 28 | ····*·_\x8m_\x8k_\x8d_\x8i_\x8r | 28 | ····*·_\x8m_\x8k_\x8d_\x8i_\x8r |
| 29 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 51, 34 lines modified | Offset 51, 34 lines modified | ||
| 51 | o1·=·fib | 51 | o1·=·fib |
| 52 | o1·:·FunctionClosure</code></pre> | 52 | o1·:·FunctionClosure</code></pre> |
| 53 | </td>··········</tr> | 53 | </td>··········</tr> |
| 54 | ··········<tr> | 54 | ··········<tr> |
| 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fib·28 | 55 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fib·28 |
| 56 | ·--·used·0. | 56 | ·--·used·0.922778s·(cpu);·0.743792s·(thread);·0s·(gc) |
| 57 | o2·=·514229</code></pre> | 57 | o2·=·514229</code></pre> |
| 58 | </td>··········</tr> | 58 | </td>··········</tr> |
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·fib·=·memoize·fib | 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·fib·=·memoize·fib |
| 61 | o3·=·fib | 61 | o3·=·fib |
| 62 | o3·:·FunctionClosure</code></pre> | 62 | o3·:·FunctionClosure</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·fib·28 | 65 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·fib·28 |
| 66 | ·--·used· | 66 | ·--·used·9.9246e-05s·(cpu);·9.8545e-05s·(thread);·0s·(gc) |
| 67 | o4·=·514229</code></pre> | 67 | o4·=·514229</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·fib·28 | 70 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·fib·28 |
| 71 | ·--·used· | 71 | ·--·used·4.158e-06s·(cpu);·3.417e-06s·(thread);·0s·(gc) |
| 72 | o5·=·514229</code></pre> | 72 | o5·=·514229</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ········</table> | 74 | ········</table> |
| 75 | ········<p>An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each·of·the·form·<span·class="tt">x·=>·v</span>,·where·<span·class="tt">v</span>·is·the·value·to·be·provided·for·the·argument·<span·class="tt">x</span>.</p> | 75 | ········<p>An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each·of·the·form·<span·class="tt">x·=>·v</span>,·where·<span·class="tt">v</span>·is·the·value·to·be·provided·for·the·argument·<span·class="tt">x</span>.</p> |
| 76 | ········<p>Alternatively,·values·can·be·provided·after·defining·the·memoized·function·using·the·syntax·<span·class="tt">f·x·=·v</span>.·A·slightly·more·efficient·implementation·of·the·above·would·be</p> | 76 | ········<p>Alternatively,·values·can·be·provided·after·defining·the·memoized·function·using·the·syntax·<span·class="tt">f·x·=·v</span>.·A·slightly·more·efficient·implementation·of·the·above·would·be</p> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| Offset 10, 28 lines modified | Offset 10, 28 lines modified | ||
| 10 | arguments·are·presented. | 10 | arguments·are·presented. |
| 11 | i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2) | 11 | i1·:·fib·=·n·->·if·n·<=·1·then·1·else·fib(n-1)·+·fib(n-2) |
| 12 | o1·=·fib | 12 | o1·=·fib |
| 13 | o1·:·FunctionClosure | 13 | o1·:·FunctionClosure |
| 14 | i2·:·time·fib·28 | 14 | i2·:·time·fib·28 |
| 15 | ·--·used·0. | 15 | ·--·used·0.922778s·(cpu);·0.743792s·(thread);·0s·(gc) |
| 16 | o2·=·514229 | 16 | o2·=·514229 |
| 17 | i3·:·fib·=·memoize·fib | 17 | i3·:·fib·=·memoize·fib |
| 18 | o3·=·fib | 18 | o3·=·fib |
| 19 | o3·:·FunctionClosure | 19 | o3·:·FunctionClosure |
| 20 | i4·:·time·fib·28 | 20 | i4·:·time·fib·28 |
| 21 | ·--·used· | 21 | ·--·used·9.9246e-05s·(cpu);·9.8545e-05s·(thread);·0s·(gc) |
| 22 | o4·=·514229 | 22 | o4·=·514229 |
| 23 | i5·:·time·fib·28 | 23 | i5·:·time·fib·28 |
| 24 | ·--·used· | 24 | ·--·used·4.158e-06s·(cpu);·3.417e-06s·(thread);·0s·(gc) |
| 25 | o5·=·514229 | 25 | o5·=·514229 |
| 26 | An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each | 26 | An·optional·second·argument·to·memoize·provides·a·list·of·initial·values,·each |
| 27 | of·the·form·x·=>·v,·where·v·is·the·value·to·be·provided·for·the·argument·x. | 27 | of·the·form·x·=>·v,·where·v·is·the·value·to·be·provided·for·the·argument·x. |
| 28 | Alternatively,·values·can·be·provided·after·defining·the·memoized·function | 28 | Alternatively,·values·can·be·provided·after·defining·the·memoized·function |
| 29 | using·the·syntax·f·x·=·v.·A·slightly·more·efficient·implementation·of·the·above | 29 | using·the·syntax·f·x·=·v.·A·slightly·more·efficient·implementation·of·the·above |
| 30 | would·be | 30 | would·be |
| Offset 72, 34 lines modified | Offset 72, 34 lines modified | ||
| 72 | o1·=·{0·=>·(==,·BettiTally,·BettiTally)···························} | 72 | o1·=·{0·=>·(==,·BettiTally,·BettiTally)···························} |
| 73 | ·····{1·=>·(++,·BettiTally,·BettiTally)···························} | 73 | ·····{1·=>·(++,·BettiTally,·BettiTally)···························} |
| 74 | ·····{2·=>·(**,·BettiTally,·BettiTally)···························} | 74 | ·····{2·=>·(**,·BettiTally,·BettiTally)···························} |
| 75 | ·····{3·=>·(SPACE,·BettiTally,·Array)·····························} | 75 | ·····{3·=>·(SPACE,·BettiTally,·Array)·····························} |
| 76 | ·····{4·=>·(SPACE,·BettiTally,·ZZ)································} | 76 | ·····{4·=>·(SPACE,·BettiTally,·ZZ)································} |
| 77 | ·····{5·=>·(lift,·BettiTally,·ZZ)·································} | 77 | ·····{5·=>·(lift,·BettiTally,·ZZ)·································} |
| 78 | ·····{6·=>·(*,·QQ,·BettiTally)····································} | ||
| 79 | ·····{ | 78 | ·····{6·=>·(*,·ZZ,·BettiTally)····································} |
| 79 | ·····{7·=>·(*,·QQ,·BettiTally)····································} | ||
| 80 | ·····{8·=>·(multigraded,·BettiTally)······························} | 80 | ·····{8·=>·(multigraded,·BettiTally)······························} |
| 81 | ·····{9·=>·(net,·BettiTally)······································} | 81 | ·····{9·=>·(net,·BettiTally)······································} |
| 82 | ·····{10·=>·(texMath,·BettiTally)·································} | 82 | ·····{10·=>·(texMath,·BettiTally)·································} |
| 83 | ·····{11·=>·(betti,·BettiTally)···································} | 83 | ·····{11·=>·(betti,·BettiTally)···································} |
| 84 | ·····{12·=>·(pdim,·BettiTally)····································} | 84 | ·····{12·=>·(pdim,·BettiTally)····································} |
| 85 | ·····{13·=>·(poincare,·BettiTally)································} | 85 | ·····{13·=>·(poincare,·BettiTally)································} |
| 86 | ·····{14·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················} | 86 | ·····{14·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················} |
| 87 | ·····{15·=>·(degree,·BettiTally)··································} | 87 | ·····{15·=>·(degree,·BettiTally)··································} |
| 88 | ·····{16·=>·(hilbertSeries,·ZZ,·BettiTally)·······················} | 88 | ·····{16·=>·(hilbertSeries,·ZZ,·BettiTally)·······················} |
| 89 | ·····{17·=>·(^,·Ring,·BettiTally)·································} | 89 | ·····{17·=>·(^,·Ring,·BettiTally)·································} |
| 90 | ·····{18·=>·(regularity,·BettiTally)······························} | 90 | ·····{18·=>·(regularity,·BettiTally)······························} |
| 91 | ·····{19·=>·(mathML,·BettiTally)··································} | 91 | ·····{19·=>·(mathML,·BettiTally)··································} |
| 92 | ·····{20·=>·(dual,·BettiTally)····································} | ||
| 93 | ·····{2 | 92 | ·····{20·=>·(codim,·BettiTally)···································} |
| 93 | ·····{21·=>·(truncate,·BettiTally,·ZZ,·ZZ)························} | ||
| 94 | ·····{22·=>·(truncate,·BettiTally,·InfiniteNumber | 94 | ·····{22·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············} |
| 95 | ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············} | 95 | ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············} |
| 96 | ·····{24·=>·(truncate,·BettiTally,· | 96 | ·····{24·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)} |
| 97 | ·····{25·=>·( | 97 | ·····{25·=>·(dual,·BettiTally)····································} |
| 98 | o1·:·NumberedVerticalList</code></pre> | 98 | o1·:·NumberedVerticalList</code></pre> |
| 99 | </td>············</tr> | 99 | </td>············</tr> |
| 100 | ············<tr> | 100 | ············<tr> |
| 101 | <td>················<pre><code·class="language-macaulay2">i2·:·methods·resolution | 101 | <td>················<pre><code·class="language-macaulay2">i2·:·methods·resolution |
| 102 | o2·=·{0·=>·(resolution,·Ideal)·} | 102 | o2·=·{0·=>·(resolution,·Ideal)·} |
| Offset 186, 20 lines modified | Offset 186, 20 lines modified | ||
| 186 | ··············</ul> | 186 | ··············</ul> |
| 187 | ············</li> | 187 | ············</li> |
| 188 | ··········</ul> | 188 | ··········</ul> |
| 189 | ··········<table·class="examples"> | 189 | ··········<table·class="examples"> |
| 190 | ············<tr> | 190 | ············<tr> |
| 191 | <td>················<pre><code·class="language-macaulay2">i5·:·methods(·Matrix,·Matrix·) | 191 | <td>················<pre><code·class="language-macaulay2">i5·:·methods(·Matrix,·Matrix·) |
| 192 | o5·=·{0·=>·(contract,·Matrix,·Matrix)····························} | ||
| 193 | ·····{1·=>·(-,·Matrix,·Matrix)···································} | ||
| 194 | 192 | o5·=·{0·=>·(diff,·Matrix,·Matrix)································} | |
| 195 | ·····{ | 193 | ·····{1·=>·(diff',·Matrix,·Matrix)·······························} |
| 196 | ·····{ | 194 | ·····{2·=>·(+,·Matrix,·Matrix)···································} |
| 195 | ·····{3·=>·(-,·Matrix,·Matrix)···································} | ||
| 197 | ·····{ | 196 | ·····{4·=>·(contract',·Matrix,·Matrix)···························} |
| 197 | ·····{5·=>·(contract,·Matrix,·Matrix)····························} | ||
| 198 | ·····{6·=>·(markedGB,·Matrix,·Matrix)····························} | 198 | ·····{6·=>·(markedGB,·Matrix,·Matrix)····························} |
| 199 | ·····{7·=>·(Hom,·Matrix,·Matrix)·································} | 199 | ·····{7·=>·(Hom,·Matrix,·Matrix)·································} |
| 200 | ·····{8·=>·(==,·Matrix,·Matrix)··································} | 200 | ·····{8·=>·(==,·Matrix,·Matrix)··································} |
| 201 | ·····{9·=>·(*,·Matrix,·Matrix)···································} | 201 | ·····{9·=>·(*,·Matrix,·Matrix)···································} |
| 202 | ·····{10·=>·(|,·Matrix,·Matrix)··································} | 202 | ·····{10·=>·(|,·Matrix,·Matrix)··································} |
| 203 | ·····{11·=>·(||,·Matrix,·Matrix)·································} | 203 | ·····{11·=>·(||,·Matrix,·Matrix)·································} |
| 204 | ·····{12·=>·(subquotient,·Matrix,·Matrix)························} | 204 | ·····{12·=>·(subquotient,·Matrix,·Matrix)························} |
| Offset 214, 18 lines modified | Offset 214, 18 lines modified | ||
| 214 | ·····{21·=>·(quotient',·Matrix,·Matrix)··························} | 214 | ·····{21·=>·(quotient',·Matrix,·Matrix)··························} |
| 215 | ·····{22·=>·(quotient,·Matrix,·Matrix)···························} | 215 | ·····{22·=>·(quotient,·Matrix,·Matrix)···························} |
| 216 | ·····{23·=>·(remainder',·Matrix,·Matrix)·························} | 216 | ·····{23·=>·(remainder',·Matrix,·Matrix)·························} |
| 217 | ·····{24·=>·(remainder,·Matrix,·Matrix)··························} | 217 | ·····{24·=>·(remainder,·Matrix,·Matrix)··························} |
| 218 | ·····{25·=>·(%,·Matrix,·Matrix)··································} | 218 | ·····{25·=>·(%,·Matrix,·Matrix)··································} |
| 219 | ·····{26·=>·(pushout,·Matrix,·Matrix)····························} | 219 | ·····{26·=>·(pushout,·Matrix,·Matrix)····························} |
| 220 | ·····{27·=>·(solve,·Matrix,·Matrix)······························} | 220 | ·····{27·=>·(solve,·Matrix,·Matrix)······························} |
| 221 | ·····{28·=>·(intersection,·Matrix,·Matrix)·······················} | ||
| 222 | ·····{29·=>·(tensor,·Matrix,·Matrix)·····························} | ||
| 223 | ·····{30·=>·(intersection,·Matrix,·Matrix,·Matrix,·Matrix)·······} | ||
| 224 | ·····{ | 221 | ·····{28·=>·(pullback,·Matrix,·Matrix)···························} |
| 222 | ·····{29·=>·(intersection,·Matrix,·Matrix,·Matrix,·Matrix)·······} | ||
| 223 | ·····{30·=>·(tensor,·Matrix,·Matrix)·····························} | ||
| 224 | ·····{31·=>·(intersection,·Matrix,·Matrix)·······················} | ||
| 225 | ·····{32·=>·(substitute,·Matrix,·Matrix)·························} | 225 | ·····{32·=>·(substitute,·Matrix,·Matrix)·························} |
| 226 | ·····{33·=>·(checkDegrees,·Matrix,·Matrix)·······················} | 226 | ·····{33·=>·(checkDegrees,·Matrix,·Matrix)·······················} |
| 227 | ·····{34·=>·(isIsomorphic,·Matrix,·Matrix)·······················} | 227 | ·····{34·=>·(isIsomorphic,·Matrix,·Matrix)·······················} |
| 228 | ·····{35·=>·(coneFromVData,·Matrix,·Matrix)······················} | 228 | ·····{35·=>·(coneFromVData,·Matrix,·Matrix)······················} |
| 229 | ·····{36·=>·(coneFromHData,·Matrix,·Matrix)······················} | 229 | ·····{36·=>·(coneFromHData,·Matrix,·Matrix)······················} |
| 230 | ·····{37·=>·(fan,·Matrix,·Matrix,·List)··························} | 230 | ·····{37·=>·(fan,·Matrix,·Matrix,·List)··························} |
| 231 | ·····{38·=>·(fan,·Matrix,·Matrix,·Sequence)······················} | 231 | ·····{38·=>·(fan,·Matrix,·Matrix,·Sequence)······················} |
| Offset 16, 34 lines modified | Offset 16, 34 lines modified | ||
| 16 | o1·=·{0·=>·(==,·BettiTally,·BettiTally)···························} | 16 | o1·=·{0·=>·(==,·BettiTally,·BettiTally)···························} |
| 17 | ·····{1·=>·(++,·BettiTally,·BettiTally)···························} | 17 | ·····{1·=>·(++,·BettiTally,·BettiTally)···························} |
| 18 | ·····{2·=>·(**,·BettiTally,·BettiTally)···························} | 18 | ·····{2·=>·(**,·BettiTally,·BettiTally)···························} |
| 19 | ·····{3·=>·(SPACE,·BettiTally,·Array)·····························} | 19 | ·····{3·=>·(SPACE,·BettiTally,·Array)·····························} |
| 20 | ·····{4·=>·(SPACE,·BettiTally,·ZZ)································} | 20 | ·····{4·=>·(SPACE,·BettiTally,·ZZ)································} |
| 21 | ·····{5·=>·(lift,·BettiTally,·ZZ)·································} | 21 | ·····{5·=>·(lift,·BettiTally,·ZZ)·································} |
| 22 | ·····{6·=>·(*,·QQ,·BettiTally)····································} | ||
| 23 | ·····{ | 22 | ·····{6·=>·(*,·ZZ,·BettiTally)····································} |
| 23 | ·····{7·=>·(*,·QQ,·BettiTally)····································} | ||
| 24 | ·····{8·=>·(multigraded,·BettiTally)······························} | 24 | ·····{8·=>·(multigraded,·BettiTally)······························} |
| 25 | ·····{9·=>·(net,·BettiTally)······································} | 25 | ·····{9·=>·(net,·BettiTally)······································} |
| 26 | ·····{10·=>·(texMath,·BettiTally)·································} | 26 | ·····{10·=>·(texMath,·BettiTally)·································} |
| 27 | ·····{11·=>·(betti,·BettiTally)···································} | 27 | ·····{11·=>·(betti,·BettiTally)···································} |
| 28 | ·····{12·=>·(pdim,·BettiTally)····································} | 28 | ·····{12·=>·(pdim,·BettiTally)····································} |
| 29 | ·····{13·=>·(poincare,·BettiTally)································} | 29 | ·····{13·=>·(poincare,·BettiTally)································} |
| 30 | ·····{14·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················} | 30 | ·····{14·=>·(hilbertPolynomial,·ZZ,·BettiTally)···················} |
| 31 | ·····{15·=>·(degree,·BettiTally)··································} | 31 | ·····{15·=>·(degree,·BettiTally)··································} |
| 32 | ·····{16·=>·(hilbertSeries,·ZZ,·BettiTally)·······················} | 32 | ·····{16·=>·(hilbertSeries,·ZZ,·BettiTally)·······················} |
| 33 | ·····{17·=>·(^,·Ring,·BettiTally)·································} | 33 | ·····{17·=>·(^,·Ring,·BettiTally)·································} |
| 34 | ·····{18·=>·(regularity,·BettiTally)······························} | 34 | ·····{18·=>·(regularity,·BettiTally)······························} |
| 35 | ·····{19·=>·(mathML,·BettiTally)··································} | 35 | ·····{19·=>·(mathML,·BettiTally)··································} |
| 36 | ·····{20·=>·(dual,·BettiTally)····································} | ||
| 37 | ·····{2 | 36 | ·····{20·=>·(codim,·BettiTally)···································} |
| 37 | ·····{21·=>·(truncate,·BettiTally,·ZZ,·ZZ)························} | ||
| 38 | ·····{22·=>·(truncate,·BettiTally,·InfiniteNumber | 38 | ·····{22·=>·(truncate,·BettiTally,·ZZ,·InfiniteNumber)············} |
| 39 | ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············} | 39 | ·····{23·=>·(truncate,·BettiTally,·InfiniteNumber,·ZZ)············} |
| 40 | ·····{24·=>·(truncate,·BettiTally,· | 40 | ·····{24·=>·(truncate,·BettiTally,·InfiniteNumber,·InfiniteNumber)} |
| 41 | ·····{25·=>·( | 41 | ·····{25·=>·(dual,·BettiTally)····································} |
| 42 | o1·:·NumberedVerticalList | 42 | o1·:·NumberedVerticalList |
| 43 | i2·:·methods·resolution | 43 | i2·:·methods·resolution |
| 44 | o2·=·{0·=>·(resolution,·Ideal)·} | 44 | o2·=·{0·=>·(resolution,·Ideal)·} |
| 45 | ·····{1·=>·(resolution,·Module)} | 45 | ·····{1·=>·(resolution,·Module)} |
| 46 | ·····{2·=>·(resolution,·Matrix)} | 46 | ·····{2·=>·(resolution,·Matrix)} |
| Offset 85, 20 lines modified | Offset 85, 20 lines modified | ||
| 85 | ····*·Inputs: | 85 | ····*·Inputs: |
| 86 | ··········o·X,·a·_\x8t_\x8y_\x8p_\x8e | 86 | ··········o·X,·a·_\x8t_\x8y_\x8p_\x8e |
| 87 | ··········o·Y,·a·_\x8t_\x8y_\x8p_\x8e | 87 | ··········o·Y,·a·_\x8t_\x8y_\x8p_\x8e |
| 88 | ····*·Outputs: | 88 | ····*·Outputs: |
| 89 | ··········o·a·_\x8v_\x8e_\x8r_\x8t_\x8i_\x8c_\x8a_\x8l_\x8·_\x8l_\x8i_\x8s_\x8t·of·those·methods·associated·with | 89 | ··········o·a·_\x8v_\x8e_\x8r_\x8t_\x8i_\x8c_\x8a_\x8l_\x8·_\x8l_\x8i_\x8s_\x8t·of·those·methods·associated·with |
| 90 | i5·:·methods(·Matrix,·Matrix·) | 90 | i5·:·methods(·Matrix,·Matrix·) |
| 91 | o5·=·{0·=>·(contract,·Matrix,·Matrix)····························} | ||
| 92 | ·····{1·=>·(-,·Matrix,·Matrix)···································} | ||
| 93 | 91 | o5·=·{0·=>·(diff,·Matrix,·Matrix)································} | |
| 94 | ·····{ | 92 | ·····{1·=>·(diff',·Matrix,·Matrix)·······························} |
| 95 | ·····{ | 93 | ·····{2·=>·(+,·Matrix,·Matrix)···································} |
| 94 | ·····{3·=>·(-,·Matrix,·Matrix)···································} | ||
| 96 | ·····{ | 95 | ·····{4·=>·(contract',·Matrix,·Matrix)···························} |
| 96 | ·····{5·=>·(contract,·Matrix,·Matrix)····························} | ||
| 97 | ·····{6·=>·(markedGB,·Matrix,·Matrix)····························} | 97 | ·····{6·=>·(markedGB,·Matrix,·Matrix)····························} |
| 98 | ·····{7·=>·(Hom,·Matrix,·Matrix)·································} | 98 | ·····{7·=>·(Hom,·Matrix,·Matrix)·································} |
| 99 | ·····{8·=>·(==,·Matrix,·Matrix)··································} | 99 | ·····{8·=>·(==,·Matrix,·Matrix)··································} |
| 100 | ·····{9·=>·(*,·Matrix,·Matrix)···································} | 100 | ·····{9·=>·(*,·Matrix,·Matrix)···································} |
| 101 | ·····{10·=>·(|,·Matrix,·Matrix)··································} | 101 | ·····{10·=>·(|,·Matrix,·Matrix)··································} |
| 102 | ·····{11·=>·(||,·Matrix,·Matrix)·································} | 102 | ·····{11·=>·(||,·Matrix,·Matrix)·································} |
| 103 | ·····{12·=>·(subquotient,·Matrix,·Matrix)························} | 103 | ·····{12·=>·(subquotient,·Matrix,·Matrix)························} |
| Offset 113, 18 lines modified | Offset 113, 18 lines modified | ||
| 113 | ·····{21·=>·(quotient',·Matrix,·Matrix)··························} | 113 | ·····{21·=>·(quotient',·Matrix,·Matrix)··························} |
| 114 | ·····{22·=>·(quotient,·Matrix,·Matrix)···························} | 114 | ·····{22·=>·(quotient,·Matrix,·Matrix)···························} |
| 115 | ·····{23·=>·(remainder',·Matrix,·Matrix)·························} | 115 | ·····{23·=>·(remainder',·Matrix,·Matrix)·························} |
| 116 | ·····{24·=>·(remainder,·Matrix,·Matrix)··························} | 116 | ·····{24·=>·(remainder,·Matrix,·Matrix)··························} |
| 117 | ·····{25·=>·(%,·Matrix,·Matrix)··································} | 117 | ·····{25·=>·(%,·Matrix,·Matrix)··································} |
| 118 | ·····{26·=>·(pushout,·Matrix,·Matrix)····························} | 118 | ·····{26·=>·(pushout,·Matrix,·Matrix)····························} |
| 119 | ·····{27·=>·(solve,·Matrix,·Matrix)······························} | 119 | ·····{27·=>·(solve,·Matrix,·Matrix)······························} |
| 120 | ·····{28·=>·(intersection,·Matrix,·Matrix)·······················} | ||
| 121 | ·····{29·=>·(tensor,·Matrix,·Matrix)·····························} | ||
| 122 | ·····{30·=>·(intersection,·Matrix,·Matrix,·Matrix,·Matrix)·······} | ||
| 123 | ·····{ | 120 | ·····{28·=>·(pullback,·Matrix,·Matrix)···························} |
| 121 | ·····{29·=>·(intersection,·Matrix,·Matrix,·Matrix,·Matrix)·······} | ||
| 122 | ·····{30·=>·(tensor,·Matrix,·Matrix)·····························} | ||
| 123 | ·····{31·=>·(intersection,·Matrix,·Matrix)·······················} | ||
| 124 | ·····{32·=>·(substitute,·Matrix,·Matrix)·························} | 124 | ·····{32·=>·(substitute,·Matrix,·Matrix)·························} |
| 125 | ·····{33·=>·(checkDegrees,·Matrix,·Matrix)·······················} | 125 | ·····{33·=>·(checkDegrees,·Matrix,·Matrix)·······················} |
| 126 | ·····{34·=>·(isIsomorphic,·Matrix,·Matrix)·······················} | 126 | ·····{34·=>·(isIsomorphic,·Matrix,·Matrix)·······················} |
| 127 | ·····{35·=>·(coneFromVData,·Matrix,·Matrix)······················} | 127 | ·····{35·=>·(coneFromVData,·Matrix,·Matrix)······················} |
| 128 | ·····{36·=>·(coneFromHData,·Matrix,·Matrix)······················} | 128 | ·····{36·=>·(coneFromHData,·Matrix,·Matrix)······················} |
| 129 | ·····{37·=>·(fan,·Matrix,·Matrix,·List)··························} | 129 | ·····{37·=>·(fan,·Matrix,·Matrix,·List)··························} |
| 130 | ·····{38·=>·(fan,·Matrix,·Matrix,·Sequence)······················} | 130 | ·····{38·=>·(fan,·Matrix,·Matrix,·Sequence)······················} |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | o2·=·S | 97 | o2·=·S |
| 98 | o2·:·PolynomialRing</code></pre> | 98 | o2·:·PolynomialRing</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·minimalBetti·I | 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·minimalBetti·I |
| 102 | ·--· | 102 | ·--·2.19295s·elapsed |
| 103 | ············0··1···2···3···4····5···6···7···8··9·10 | 103 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 104 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 104 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 105 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 105 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 106 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 106 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 107 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 107 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 108 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 108 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·I·=·ideal·I_*; | 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·I·=·ideal·I_*; |
| 123 | o4·:·Ideal·of·S</code></pre> | 123 | o4·:·Ideal·of·S</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) | 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) |
| 127 | ·--·. | 127 | ·--·.801544s·elapsed |
| 128 | ············0··1···2···3···4····5···6···7 | 128 | ············0··1···2···3···4····5···6···7 |
| 129 | o5·=·total:·1·35·140·385·819·1080·735·196 | 129 | o5·=·total:·1·35·140·385·819·1080·735·196 |
| 130 | ·········0:·1··.···.···.···.····.···.···. | 130 | ·········0:·1··.···.···.···.····.···.···. |
| 131 | ·········1:·.·35·140·189··84····.···.···. | 131 | ·········1:·.·35·140·189··84····.···.···. |
| 132 | ·········2:·.··.···.·196·735·1080·735·196 | 132 | ·········2:·.··.···.·196·735·1080·735·196 |
| Offset 138, 15 lines modified | Offset 138, 15 lines modified | ||
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal·I_*; | 139 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal·I_*; |
| 140 | o6·:·Ideal·of·S</code></pre> | 140 | o6·:·Ideal·of·S</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) | 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) |
| 144 | ·--·.0 | 144 | ·--·.0304048s·elapsed |
| 145 | ············0··1···2···3··4 | 145 | ············0··1···2···3··4 |
| 146 | o7·=·total:·1·35·140·189·84 | 146 | o7·=·total:·1·35·140·189·84 |
| 147 | ·········0:·1··.···.···.··. | 147 | ·········0:·1··.···.···.··. |
| 148 | ·········1:·.·35·140·189·84 | 148 | ·········1:·.·35·140·189·84 |
| 149 | o7·:·BettiTally</code></pre> | 149 | o7·:·BettiTally</code></pre> |
| Offset 154, 15 lines modified | Offset 154, 15 lines modified | ||
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i8·:·I·=·ideal·I_*; | 155 | <td>··············<pre><code·class="language-macaulay2">i8·:·I·=·ideal·I_*; |
| 156 | o8·:·Ideal·of·S</code></pre> | 156 | o8·:·Ideal·of·S</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) | 159 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) |
| 160 | ·--·1. | 160 | ·--·1.69004s·elapsed |
| 161 | ············0··1···2···3···4····5 | 161 | ············0··1···2···3···4····5 |
| 162 | o9·=·total:·1·35·140·385·819·1080 | 162 | o9·=·total:·1·35·140·385·819·1080 |
| 163 | ·········0:·1··.···.···.···.····. | 163 | ·········0:·1··.···.···.···.····. |
| 164 | ·········1:·.·35·140·189··84····. | 164 | ·········1:·.·35·140·189··84····. |
| 165 | ·········2:·.··.···.·196·735·1080 | 165 | ·········2:·.··.···.·196·735·1080 |
| Offset 44, 15 lines modified | Offset 44, 15 lines modified | ||
| 44 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 | 44 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 |
| 45 | i2·:·S·=·ring·I | 45 | i2·:·S·=·ring·I |
| 46 | o2·=·S | 46 | o2·=·S |
| 47 | o2·:·PolynomialRing | 47 | o2·:·PolynomialRing |
| 48 | i3·:·elapsedTime·C·=·minimalBetti·I | 48 | i3·:·elapsedTime·C·=·minimalBetti·I |
| 49 | ·--· | 49 | ·--·2.19295s·elapsed |
| 50 | ············0··1···2···3···4····5···6···7···8··9·10 | 50 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 51 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 51 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 52 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 52 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 53 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 53 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 54 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 54 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 55 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 55 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 61, 40 lines modified | Offset 61, 40 lines modified | ||
| 61 | o3·:·BettiTally | 61 | o3·:·BettiTally |
| 62 | One·can·compute·smaller·parts·of·the·Betti·table,·by·using·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·and/or | 62 | One·can·compute·smaller·parts·of·the·Betti·table,·by·using·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·and/or |
| 63 | _\x8L_\x8e_\x8n_\x8g_\x8t_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t. | 63 | _\x8L_\x8e_\x8n_\x8g_\x8t_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t. |
| 64 | i4·:·I·=·ideal·I_*; | 64 | i4·:·I·=·ideal·I_*; |
| 65 | o4·:·Ideal·of·S | 65 | o4·:·Ideal·of·S |
| 66 | i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) | 66 | i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) |
| 67 | ·--·. | 67 | ·--·.801544s·elapsed |
| 68 | ············0··1···2···3···4····5···6···7 | 68 | ············0··1···2···3···4····5···6···7 |
| 69 | o5·=·total:·1·35·140·385·819·1080·735·196 | 69 | o5·=·total:·1·35·140·385·819·1080·735·196 |
| 70 | ·········0:·1··.···.···.···.····.···.···. | 70 | ·········0:·1··.···.···.···.····.···.···. |
| 71 | ·········1:·.·35·140·189··84····.···.···. | 71 | ·········1:·.·35·140·189··84····.···.···. |
| 72 | ·········2:·.··.···.·196·735·1080·735·196 | 72 | ·········2:·.··.···.·196·735·1080·735·196 |
| 73 | o5·:·BettiTally | 73 | o5·:·BettiTally |
| 74 | i6·:·I·=·ideal·I_*; | 74 | i6·:·I·=·ideal·I_*; |
| 75 | o6·:·Ideal·of·S | 75 | o6·:·Ideal·of·S |
| 76 | i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) | 76 | i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) |
| 77 | ·--·.0 | 77 | ·--·.0304048s·elapsed |
| 78 | ············0··1···2···3··4 | 78 | ············0··1···2···3··4 |
| 79 | o7·=·total:·1·35·140·189·84 | 79 | o7·=·total:·1·35·140·189·84 |
| 80 | ·········0:·1··.···.···.··. | 80 | ·········0:·1··.···.···.··. |
| 81 | ·········1:·.·35·140·189·84 | 81 | ·········1:·.·35·140·189·84 |
| 82 | o7·:·BettiTally | 82 | o7·:·BettiTally |
| 83 | i8·:·I·=·ideal·I_*; | 83 | i8·:·I·=·ideal·I_*; |
| 84 | o8·:·Ideal·of·S | 84 | o8·:·Ideal·of·S |
| 85 | i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) | 85 | i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) |
| 86 | ·--·1. | 86 | ·--·1.69004s·elapsed |
| 87 | ············0··1···2···3···4····5 | 87 | ············0··1···2···3···4····5 |
| 88 | o9·=·total:·1·35·140·385·819·1080 | 88 | o9·=·total:·1·35·140·385·819·1080 |
| 89 | ·········0:·1··.···.···.···.····. | 89 | ·········0:·1··.···.···.···.····. |
| 90 | ·········1:·.·35·140·189··84····. | 90 | ·········1:·.·35·140·189··84····. |
| 91 | ·········2:·.··.···.·196·735·1080 | 91 | ·········2:·.··.···.·196·735·1080 |
| Offset 70, 28 lines modified | Offset 70, 28 lines modified | ||
| 70 | ······<div> | 70 | ······<div> |
| 71 | ········<h2>Description</h2> | 71 | ········<h2>Description</h2> |
| 72 | ········<p>Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the·last·must·already·exist.</p> | 72 | ········<p>Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the·last·must·already·exist.</p> |
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName()·|·"/" | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName()·|·"/" |
| 76 | o1·=·/tmp/M2- | 76 | o1·=·/tmp/M2-3499710-0/0/</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·mkdir·p</code></pre> | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·mkdir·p</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·isDirectory·p | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·isDirectory·p |
| 83 | o3·=·true</code></pre> | 83 | o3·=·true</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close |
| 87 | o4·=·/tmp/M2- | 87 | o4·=·/tmp/M2-3499710-0/0/foo |
| 88 | o4·:·File</code></pre> | 88 | o4·:·File</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn |
| 92 | o5·=·hi·there</code></pre> | 92 | o5·=·hi·there</code></pre> |
| Offset 12, 22 lines modified | Offset 12, 22 lines modified | ||
| 12 | ····*·Consequences: | 12 | ····*·Consequences: |
| 13 | ··········o·a·directory·will·be·created·at·the·path·p | 13 | ··········o·a·directory·will·be·created·at·the·path·p |
| 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 14 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 15 | Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the | 15 | Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the |
| 16 | last·must·already·exist. | 16 | last·must·already·exist. |
| 17 | i1·:·p·=·temporaryFileName()·|·"/" | 17 | i1·:·p·=·temporaryFileName()·|·"/" |
| 18 | o1·=·/tmp/M2- | 18 | o1·=·/tmp/M2-3499710-0/0/ |
| 19 | i2·:·mkdir·p | 19 | i2·:·mkdir·p |
| 20 | i3·:·isDirectory·p | 20 | i3·:·isDirectory·p |
| 21 | o3·=·true | 21 | o3·=·true |
| 22 | i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close | 22 | i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close |
| 23 | o4·=·/tmp/M2- | 23 | o4·=·/tmp/M2-3499710-0/0/foo |
| 24 | o4·:·File | 24 | o4·:·File |
| 25 | i5·:·get·fn | 25 | i5·:·get·fn |
| 26 | o5·=·hi·there | 26 | o5·=·hi·there |
| 27 | i6·:·removeFile·fn | 27 | i6·:·removeFile·fn |
| 28 | i7·:·removeDirectory·p | 28 | i7·:·removeDirectory·p |
| Offset 85, 42 lines modified | Offset 85, 42 lines modified | ||
| 85 | ······</div> | 85 | ······</div> |
| 86 | ······<div> | 86 | ······<div> |
| 87 | ········<h2>Description</h2> | 87 | ········<h2>Description</h2> |
| 88 | ········<table·class="examples"> | 88 | ········<table·class="examples"> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() | 90 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() |
| 91 | o1·=·/tmp/M2- | 91 | o1·=·/tmp/M2-3498163-0/0</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() |
| 95 | o2·=·/tmp/M2- | 95 | o2·=·/tmp/M2-3498163-0/1</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close |
| 99 | o3·=·/tmp/M2- | 99 | o3·=·/tmp/M2-3498163-0/0 |
| 100 | o3·:·File</code></pre> | 100 | o3·:·File</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·moveFile(src,dst,Verbose=>true) | 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·moveFile(src,dst,Verbose=>true) |
| 104 | --moving:·/tmp/M2- | 104 | --moving:·/tmp/M2-3498163-0/0·->·/tmp/M2-3498163-0/1</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst |
| 108 | o5·=·hi·there</code></pre> | 108 | o5·=·hi·there</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·bak·=·moveFile(dst,Verbose=>true) | 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·bak·=·moveFile(dst,Verbose=>true) |
| 112 | --backup·file·created:·/tmp/M2- | 112 | --backup·file·created:·/tmp/M2-3498163-0/1.bak |
| 113 | o6·=·/tmp/M2- | 113 | o6·=·/tmp/M2-3498163-0/1.bak</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i7·:·removeFile·bak</code></pre> | 116 | <td>··············<pre><code·class="language-macaulay2">i7·:·removeFile·bak</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ········</table> | 118 | ········</table> |
| 119 | ······</div> | 119 | ······</div> |
| 120 | ······<div> | 120 | ······<div> |
| Offset 21, 31 lines modified | Offset 21, 31 lines modified | ||
| 21 | ··········o·the·name·of·the·backup·file·if·one·was·created,·or·_\x8n_\x8u_\x8l_\x8l | 21 | ··········o·the·name·of·the·backup·file·if·one·was·created,·or·_\x8n_\x8u_\x8l_\x8l |
| 22 | ····*·Consequences: | 22 | ····*·Consequences: |
| 23 | ··········o·the·file·will·be·moved·by·creating·a·new·link·to·the·file·and | 23 | ··········o·the·file·will·be·moved·by·creating·a·new·link·to·the·file·and |
| 24 | ············removing·the·old·one | 24 | ············removing·the·old·one |
| 25 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 26 | i1·:·src·=·temporaryFileName() | 26 | i1·:·src·=·temporaryFileName() |
| 27 | o1·=·/tmp/M2- | 27 | o1·=·/tmp/M2-3498163-0/0 |
| 28 | i2·:·dst·=·temporaryFileName() | 28 | i2·:·dst·=·temporaryFileName() |
| 29 | o2·=·/tmp/M2- | 29 | o2·=·/tmp/M2-3498163-0/1 |
| 30 | i3·:·src·<<·"hi·there"·<<·close | 30 | i3·:·src·<<·"hi·there"·<<·close |
| 31 | o3·=·/tmp/M2- | 31 | o3·=·/tmp/M2-3498163-0/0 |
| 32 | o3·:·File | 32 | o3·:·File |
| 33 | i4·:·moveFile(src,dst,Verbose=>true) | 33 | i4·:·moveFile(src,dst,Verbose=>true) |
| 34 | --moving:·/tmp/M2- | 34 | --moving:·/tmp/M2-3498163-0/0·->·/tmp/M2-3498163-0/1 |
| 35 | i5·:·get·dst | 35 | i5·:·get·dst |
| 36 | o5·=·hi·there | 36 | o5·=·hi·there |
| 37 | i6·:·bak·=·moveFile(dst,Verbose=>true) | 37 | i6·:·bak·=·moveFile(dst,Verbose=>true) |
| 38 | --backup·file·created:·/tmp/M2- | 38 | --backup·file·created:·/tmp/M2-3498163-0/1.bak |
| 39 | o6·=·/tmp/M2- | 39 | o6·=·/tmp/M2-3498163-0/1.bak |
| 40 | i7·:·removeFile·bak | 40 | i7·:·removeFile·bak |
| 41 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 41 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 42 | ····*·_\x8c_\x8o_\x8p_\x8y_\x8F_\x8i_\x8l_\x8e | 42 | ····*·_\x8c_\x8o_\x8p_\x8y_\x8F_\x8i_\x8l_\x8e |
| 43 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 43 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 44 | ····*·moveFile(String) | 44 | ····*·moveFile(String) |
| 45 | ····*·_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e_\x8(_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8,_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8) | 45 | ····*·_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e_\x8(_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8,_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8) |
| Offset 43, 15 lines modified | Offset 43, 15 lines modified | ||
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>nanosleep·--·sleep·for·a·given·number·of·nanoseconds</h1> | 44 | ······<h1>nanosleep·--·sleep·for·a·given·number·of·nanoseconds</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | <span·class="tt">nanosleep·n</span>·--·sleeps·for·<span·class="tt">n</span>·nanoseconds.········<table·class="examples"> | 47 | <span·class="tt">nanosleep·n</span>·--·sleeps·for·<span·class="tt">n</span>·nanoseconds.········<table·class="examples"> |
| 48 | ··········<tr> | 48 | ··········<tr> |
| 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nanosleep·500000000 | 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nanosleep·500000000 |
| 50 | ·--·.5000 | 50 | ·--·.500108s·elapsed |
| 51 | o1·=·0</code></pre> | 51 | o1·=·0</code></pre> |
| 52 | </td>··········</tr> | 52 | </td>··········</tr> |
| 53 | ········</table> | 53 | ········</table> |
| 54 | ······</div> | 54 | ······</div> |
| 55 | ······<div> | 55 | ······<div> |
| 56 | ········<h2>See·also</h2> | 56 | ········<h2>See·also</h2> |
| Offset 4, 14 lines modified | Offset 4, 14 lines modified | ||
| 4 | [q···················] | 4 | [q···················] |
| 5 | _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c | 5 | _\x8n_\x8e_\x8x_\x8t·|·_\x8p_\x8r_\x8e_\x8v_\x8i_\x8o_\x8u_\x8s·|·_\x8f_\x8o_\x8r_\x8w_\x8a_\x8r_\x8d·|·_\x8b_\x8a_\x8c_\x8k_\x8w_\x8a_\x8r_\x8d·|·_\x8u_\x8p·|·_\x8i_\x8n_\x8d_\x8e_\x8x·|·_\x8t_\x8o_\x8c |
| 6 | =============================================================================== | 6 | =============================================================================== |
| 7 | *\x8**\x8**\x8**\x8**\x8**\x8*·n\x8na\x8an\x8no\x8os\x8sl\x8le\x8ee\x8ep\x8p·-\x8--\x8-·s\x8sl\x8le\x8ee\x8ep\x8p·f\x8fo\x8or\x8r·a\x8a·g\x8gi\x8iv\x8ve\x8en\x8n·n\x8nu\x8um\x8mb\x8be\x8er\x8r·o\x8of\x8f·n\x8na\x8an\x8no\x8os\x8se\x8ec\x8co\x8on\x8nd\x8ds\x8s·*\x8**\x8**\x8**\x8**\x8**\x8* | 7 | *\x8**\x8**\x8**\x8**\x8**\x8*·n\x8na\x8an\x8no\x8os\x8sl\x8le\x8ee\x8ep\x8p·-\x8--\x8-·s\x8sl\x8le\x8ee\x8ep\x8p·f\x8fo\x8or\x8r·a\x8a·g\x8gi\x8iv\x8ve\x8en\x8n·n\x8nu\x8um\x8mb\x8be\x8er\x8r·o\x8of\x8f·n\x8na\x8an\x8no\x8os\x8se\x8ec\x8co\x8on\x8nd\x8ds\x8s·*\x8**\x8**\x8**\x8**\x8**\x8* |
| 8 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 8 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 9 | nanosleep·n·--·sleeps·for·n·nanoseconds. | 9 | nanosleep·n·--·sleeps·for·n·nanoseconds. |
| 10 | i1·:·elapsedTime·nanosleep·500000000 | 10 | i1·:·elapsedTime·nanosleep·500000000 |
| 11 | ·--·.5000 | 11 | ·--·.500108s·elapsed |
| 12 | o1·=·0 | 12 | o1·=·0 |
| 13 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 13 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 14 | ····*·_\x8s_\x8l_\x8e_\x8e_\x8p·--·sleep·for·a·while | 14 | ····*·_\x8s_\x8l_\x8e_\x8e_\x8p·--·sleep·for·a·while |
| 15 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 16 | The·object·_\x8n_\x8a_\x8n_\x8o_\x8s_\x8l_\x8e_\x8e_\x8p·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 16 | The·object·_\x8n_\x8a_\x8n_\x8o_\x8s_\x8l_\x8e_\x8e_\x8p·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
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| 60 | ········</div> | 60 | ········</div> |
| 61 | ········<table·class="examples"> | 61 | ········<table·class="examples"> |
| 62 | ··········<tr> | 62 | ··········<tr> |
| 63 | <td>··············<pre><code·class="language-macaulay2">i2·:·L·=·random·toList·(1..10000);</code></pre> | 63 | <td>··············<pre><code·class="language-macaulay2">i2·:·L·=·random·toList·(1..10000);</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); | 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); |
| 67 | ·--·. | 67 | ·--·.900132s·elapsed</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); | 70 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); |
| 71 | ·--·. | 71 | ·--·.239973s·elapsed</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ········</table> | 73 | ········</table> |
| 74 | ········<div> | 74 | ········<div> |
| 75 | ··········<p>You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.</p> | 75 | ··········<p>You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.</p> |
| 76 | ··········<p>Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is·not·"thread·safe",·meaning·they·make·modifications·to·memory·without·ensuring·the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can·slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and·mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists.·Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be·thread·safe.</p> | 76 | ··········<p>Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is·not·"thread·safe",·meaning·they·make·modifications·to·memory·without·ensuring·the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can·slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and·mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists.·Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be·thread·safe.</p> |
| 77 | ··········<p>The·rest·of·this·document·describes·how·to·control·parallel·tasks·more·directly.</p> | 77 | ··········<p>The·rest·of·this·document·describes·how·to·control·parallel·tasks·more·directly.</p> |
| 78 | ··········<p>The·task·system·schedules·functions·and·inputs·to·run·on·a·preset·number·of·threads.·The·number·of·threads·to·be·used·is·given·by·the·variable·<a·title="the·current·maximum·number·of·simultaneously·running·tasks"·href="_allowable__Threads.html">allowableThreads</a>,·and·may·be·examined·and·changed·as·follows.·(<a·title="the·current·maximum·number·of·simultaneously·running·tasks"·href="_allowable__Threads.html">allowableThreads</a>·is·temporarily·increased·if·necessary·inside·<a·title="apply·a·function·to·each·element·in·parallel"·href="_parallel__Apply.html">parallelApply</a>.)</p> | 78 | ··········<p>The·task·system·schedules·functions·and·inputs·to·run·on·a·preset·number·of·threads.·The·number·of·threads·to·be·used·is·given·by·the·variable·<a·title="the·current·maximum·number·of·simultaneously·running·tasks"·href="_allowable__Threads.html">allowableThreads</a>,·and·may·be·examined·and·changed·as·follows.·(<a·title="the·current·maximum·number·of·simultaneously·running·tasks"·href="_allowable__Threads.html">allowableThreads</a>·is·temporarily·increased·if·necessary·inside·<a·title="apply·a·function·to·each·element·in·parallel"·href="_parallel__Apply.html">parallelApply</a>.)</p> |
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| 129 | ········<div> | 129 | ········<div> |
| 130 | ··········<p>Note·that·<a·title="schedule·a·task·for·execution"·href="_schedule.html">schedule</a>·returns·a·task,·not·the·result·of·the·computation,·which·will·be·accessible·only·after·the·task·has·completed·the·computation.</p> | 130 | ··········<p>Note·that·<a·title="schedule·a·task·for·execution"·href="_schedule.html">schedule</a>·returns·a·task,·not·the·result·of·the·computation,·which·will·be·accessible·only·after·the·task·has·completed·the·computation.</p> |
| 131 | ········</div> | 131 | ········</div> |
| 132 | ········<table·class="examples"> | 132 | ········<table·class="examples"> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i12·:·t | 134 | <td>··············<pre><code·class="language-macaulay2">i12·:·t |
| 135 | o12·=·<<task,· | 135 | o12·=·<<task,·running>> |
| 136 | o12·:·Task</code></pre> | 136 | o12·:·Task</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| 139 | ········<div> | 139 | ········<div> |
| 140 | ··········<p>Use·<a·title="whether·a·file·has·data·available·for·reading"·href="_is__Ready_lp__File_rp.html">isReady</a>·to·check·whether·the·result·is·available·yet.</p> | 140 | ··········<p>Use·<a·title="whether·a·file·has·data·available·for·reading"·href="_is__Ready_lp__File_rp.html">isReady</a>·to·check·whether·the·result·is·available·yet.</p> |
| 141 | ········</div> | 141 | ········</div> |
| Offset 17, 17 lines modified | Offset 17, 17 lines modified | ||
| 17 | big·computation.·If·the·list·is·long,·it·will·be·split·into·chunks·for·each | 17 | big·computation.·If·the·list·is·long,·it·will·be·split·into·chunks·for·each |
| 18 | core,·reducing·the·overhead.·But·the·speedup·is·still·limited·by·the·different | 18 | core,·reducing·the·overhead.·But·the·speedup·is·still·limited·by·the·different |
| 19 | threads·competing·for·memory,·including·cpu·caches;·it·is·like·running | 19 | threads·competing·for·memory,·including·cpu·caches;·it·is·like·running |
| 20 | Macaulay2·on·a·computer·that·is·running·other·big·programs·at·the·same·time.·We | 20 | Macaulay2·on·a·computer·that·is·running·other·big·programs·at·the·same·time.·We |
| 21 | can·see·this·using·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e. | 21 | can·see·this·using·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e. |
| 22 | i2·:·L·=·random·toList·(1..10000); | 22 | i2·:·L·=·random·toList·(1..10000); |
| 23 | i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); | 23 | i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); |
| 24 | ·--·. | 24 | ·--·.900132s·elapsed |
| 25 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); | 25 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); |
| 26 | ·--·. | 26 | ·--·.239973s·elapsed |
| 27 | You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up. | 27 | You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up. |
| 28 | Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is | 28 | Warning:·Threads·computing·in·parallel·can·give·wrong·answers·if·their·code·is |
| 29 | not·"thread·safe",·meaning·they·make·modifications·to·memory·without·ensuring | 29 | not·"thread·safe",·meaning·they·make·modifications·to·memory·without·ensuring |
| 30 | the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can | 30 | the·modifications·get·safely·communicated·to·other·threads.·(Thread·safety·can |
| 31 | slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and | 31 | slow·computations·some.)·Currently,·modifications·to·Macaulay2·variables·and |
| 32 | mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists. | 32 | mutable·hash·tables·are·thread·safe,·but·not·changes·inside·mutable·lists. |
| 33 | Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be | 33 | Also,·access·to·external·libraries·such·as·singular,·etc.,·may·not·currently·be |
| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | o11·=·<<task,·created>> | 67 | o11·=·<<task,·created>> |
| 68 | o11·:·Task | 68 | o11·:·Task |
| 69 | Note·that·_\x8s_\x8c_\x8h_\x8e_\x8d_\x8u_\x8l_\x8e·returns·a·task,·not·the·result·of·the·computation,·which | 69 | Note·that·_\x8s_\x8c_\x8h_\x8e_\x8d_\x8u_\x8l_\x8e·returns·a·task,·not·the·result·of·the·computation,·which |
| 70 | will·be·accessible·only·after·the·task·has·completed·the·computation. | 70 | will·be·accessible·only·after·the·task·has·completed·the·computation. |
| 71 | i12·:·t | 71 | i12·:·t |
| 72 | o12·=·<<task,· | 72 | o12·=·<<task,·running>> |
| 73 | o12·:·Task | 73 | o12·:·Task |
| 74 | Use·_\x8i_\x8s_\x8R_\x8e_\x8a_\x8d_\x8y·to·check·whether·the·result·is·available·yet. | 74 | Use·_\x8i_\x8s_\x8R_\x8e_\x8a_\x8d_\x8y·to·check·whether·the·result·is·available·yet. |
| 75 | i13·:·isReady·t | 75 | i13·:·isReady·t |
| 76 | o13·=·false | 76 | o13·=·false |
| 77 | To·wait·for·the·result·and·then·retrieve·it,·use·_\x8t_\x8a_\x8s_\x8k_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t. | 77 | To·wait·for·the·result·and·then·retrieve·it,·use·_\x8t_\x8a_\x8s_\x8k_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t. |
| Offset 123, 15 lines modified | Offset 123, 15 lines modified | ||
| 123 | o3·=·S | 123 | o3·=·S |
| 124 | o3·:·PolynomialRing</code></pre> | 124 | o3·:·PolynomialRing</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalBetti·I | 127 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalBetti·I |
| 128 | ·--· | 128 | ·--·2.57235s·elapsed |
| 129 | ············0··1···2···3···4····5···6···7···8··9·10 | 129 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 130 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 130 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 131 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 131 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 132 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 132 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 133 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 133 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 134 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 134 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
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| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i5·:·I·=·ideal·I_*; | 143 | <td>··············<pre><code·class="language-macaulay2">i5·:·I·=·ideal·I_*; |
| 144 | o5·:·Ideal·of·S</code></pre> | 144 | o5·:·Ideal·of·S</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) | 147 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) |
| 148 | ·--· | 148 | ·--·2.70669s·elapsed |
| 149 | ············0··1···2···3···4····5···6···7···8··9·10 | 149 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 150 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 150 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 151 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 151 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 152 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 152 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 153 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 153 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 154 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 154 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
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| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i8·:·numTBBThreads·=·1 | 167 | <td>··············<pre><code·class="language-macaulay2">i8·:·numTBBThreads·=·1 |
| 168 | o8·=·1</code></pre> | 168 | o8·=·1</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·minimalBetti(I) | 171 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·minimalBetti(I) |
| 172 | ·--· | 172 | ·--·2.6306s·elapsed |
| 173 | ············0··1···2···3···4····5···6···7···8··9·10 | 173 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 174 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 174 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 175 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 175 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 176 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 176 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 177 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 177 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 178 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 178 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
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| 199 | ··········<tr> | 199 | ··········<tr> |
| 200 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal·I_*; | 200 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal·I_*; |
| 201 | o12·:·Ideal·of·S</code></pre> | 201 | o12·:·Ideal·of·S</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 204 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 205 | ·--· | 205 | ·--·2.44039s·elapsed |
| 206 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 | 206 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 207 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S | 207 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S |
| 208 | ·································································································· | 208 | ·································································································· |
| 209 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 | 209 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 |
| 210 | o13·:·Complex</code></pre> | 210 | o13·:·Complex</code></pre> |
| Offset 220, 15 lines modified | Offset 220, 15 lines modified | ||
| 220 | ··········<tr> | 220 | ··········<tr> |
| 221 | <td>··············<pre><code·class="language-macaulay2">i15·:·I·=·ideal·I_*; | 221 | <td>··············<pre><code·class="language-macaulay2">i15·:·I·=·ideal·I_*; |
| 222 | o15·:·Ideal·of·S</code></pre> | 222 | o15·:·Ideal·of·S</code></pre> |
| 223 | </td>··········</tr> | 223 | </td>··········</tr> |
| 224 | ··········<tr> | 224 | ··········<tr> |
| 225 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 225 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 226 | ·--· | 226 | ·--·2.62356s·elapsed |
| 227 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 | 227 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 228 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S | 228 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S |
| 229 | ·································································································· | 229 | ·································································································· |
| 230 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 | 230 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 |
| 231 | o16·:·Complex</code></pre> | 231 | o16·:·Complex</code></pre> |
| Offset 253, 15 lines modified | Offset 253, 15 lines modified | ||
| 253 | ··········<tr> | 253 | ··········<tr> |
| 254 | <td>··············<pre><code·class="language-macaulay2">i19·:·I·=·ideal·random(S^1,·S^{4:-5}); | 254 | <td>··············<pre><code·class="language-macaulay2">i19·:·I·=·ideal·random(S^1,·S^{4:-5}); |
| 255 | o19·:·Ideal·of·S</code></pre> | 255 | o19·:·Ideal·of·S</code></pre> |
| 256 | </td>··········</tr> | 256 | </td>··········</tr> |
| 257 | ··········<tr> | 257 | ··········<tr> |
| 258 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 258 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 259 | ·--· | 259 | ·--·4.30019s·elapsed |
| 260 | ··············1······108 | 260 | ··············1······108 |
| 261 | o20·:·Matrix·S··<--·S</code></pre> | 261 | o20·:·Matrix·S··<--·S</code></pre> |
| 262 | </td>··········</tr> | 262 | </td>··········</tr> |
| 263 | ··········<tr> | 263 | ··········<tr> |
| 264 | <td>··············<pre><code·class="language-macaulay2">i21·:·numTBBThreads·=·1 | 264 | <td>··············<pre><code·class="language-macaulay2">i21·:·numTBBThreads·=·1 |
| Offset 270, 15 lines modified | Offset 270, 15 lines modified | ||
| 270 | ··········<tr> | 270 | ··········<tr> |
| 271 | <td>··············<pre><code·class="language-macaulay2">i22·:·I·=·ideal·I_*; | 271 | <td>··············<pre><code·class="language-macaulay2">i22·:·I·=·ideal·I_*; |
| 272 | o22·:·Ideal·of·S</code></pre> | 272 | o22·:·Ideal·of·S</code></pre> |
| 273 | </td>··········</tr> | 273 | </td>··········</tr> |
| 274 | ··········<tr> | 274 | ··········<tr> |
| 275 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 275 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 276 | ·--· | 276 | ·--·10.041s·elapsed |
| 277 | ··············1······108 | 277 | ··············1······108 |
| 278 | o23·:·Matrix·S··<--·S</code></pre> | 278 | o23·:·Matrix·S··<--·S</code></pre> |
| 279 | </td>··········</tr> | 279 | </td>··········</tr> |
| 280 | ··········<tr> | 280 | ··········<tr> |
| 281 | <td>··············<pre><code·class="language-macaulay2">i24·:·numTBBThreads·=·10 | 281 | <td>··············<pre><code·class="language-macaulay2">i24·:·numTBBThreads·=·10 |
| Offset 287, 15 lines modified | Offset 287, 15 lines modified | ||
| 287 | ··········<tr> | 287 | ··········<tr> |
| 288 | <td>··············<pre><code·class="language-macaulay2">i25·:·I·=·ideal·I_*; | 288 | <td>··············<pre><code·class="language-macaulay2">i25·:·I·=·ideal·I_*; |
| 289 | o25·:·Ideal·of·S</code></pre> | 289 | o25·:·Ideal·of·S</code></pre> |
| 290 | </td>··········</tr> | 290 | </td>··········</tr> |
| 291 | ··········<tr> | 291 | ··········<tr> |
| 292 | <td>··············<pre><code·class="language-macaulay2">i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 292 | <td>··············<pre><code·class="language-macaulay2">i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 293 | ·--· | 293 | ·--·4.87683s·elapsed |
| 294 | ··············1······108 | 294 | ··············1······108 |
| 295 | o26·:·Matrix·S··<--·S</code></pre> | 295 | o26·:·Matrix·S··<--·S</code></pre> |
| 296 | </td>··········</tr> | 296 | </td>··········</tr> |
| 297 | ········</table> | 297 | ········</table> |
| 298 | ········<div> | 298 | ········<div> |
| 299 | ··········<p>For·Groebner·basis·computation·in·associative·algebras,·ParallelizeByDegree·is·not·relevant.··In·this·case,·use·<span·class="tt">numTBBThreads</span>·to·control·the·amount·of·parallelism.</p> | 299 | ··········<p>For·Groebner·basis·computation·in·associative·algebras,·ParallelizeByDegree·is·not·relevant.··In·this·case,·use·<span·class="tt">numTBBThreads</span>·to·control·the·amount·of·parallelism.</p> |
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| Offset 92, 30 lines modified | Offset 92, 30 lines modified | ||
| 92 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 | 92 | 0,5···1,5···2,5···3,5···4,5···0,6···1,6···2,6···3,6···4,6···5,6 |
| 93 | i3·:·S·=·ring·I | 93 | i3·:·S·=·ring·I |
| 94 | o3·=·S | 94 | o3·=·S |
| 95 | o3·:·PolynomialRing | 95 | o3·:·PolynomialRing |
| 96 | i4·:·elapsedTime·minimalBetti·I | 96 | i4·:·elapsedTime·minimalBetti·I |
| 97 | ·--· | 97 | ·--·2.57235s·elapsed |
| 98 | ············0··1···2···3···4····5···6···7···8··9·10 | 98 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 99 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 99 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 100 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 100 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 101 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 101 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 102 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 102 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 103 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 103 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| 104 | ·········4:·.··.···.···.···.····.···.···.···.··.··1 | 104 | ·········4:·.··.···.···.···.····.···.···.···.··.··1 |
| 105 | o4·:·BettiTally | 105 | o4·:·BettiTally |
| 106 | i5·:·I·=·ideal·I_*; | 106 | i5·:·I·=·ideal·I_*; |
| 107 | o5·:·Ideal·of·S | 107 | o5·:·Ideal·of·S |
| 108 | i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) | 108 | i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) |
| 109 | ·--· | 109 | ·--·2.70669s·elapsed |
| 110 | ············0··1···2···3···4····5···6···7···8··9·10 | 110 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 111 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 111 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 112 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 112 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 113 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 113 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 114 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 114 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 115 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 115 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 125, 15 lines modified | Offset 125, 15 lines modified | ||
| 125 | i7·:·I·=·ideal·I_*; | 125 | i7·:·I·=·ideal·I_*; |
| 126 | o7·:·Ideal·of·S | 126 | o7·:·Ideal·of·S |
| 127 | i8·:·numTBBThreads·=·1 | 127 | i8·:·numTBBThreads·=·1 |
| 128 | o8·=·1 | 128 | o8·=·1 |
| 129 | i9·:·elapsedTime·minimalBetti(I) | 129 | i9·:·elapsedTime·minimalBetti(I) |
| 130 | ·--· | 130 | ·--·2.6306s·elapsed |
| 131 | ············0··1···2···3···4····5···6···7···8··9·10 | 131 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 132 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 132 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 133 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 133 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 134 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 134 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 135 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 135 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 136 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 136 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 148, 15 lines modified | Offset 148, 15 lines modified | ||
| 148 | i11·:·numTBBThreads·=·0 | 148 | i11·:·numTBBThreads·=·0 |
| 149 | o11·=·0 | 149 | o11·=·0 |
| 150 | i12·:·I·=·ideal·I_*; | 150 | i12·:·I·=·ideal·I_*; |
| 151 | o12·:·Ideal·of·S | 151 | o12·:·Ideal·of·S |
| 152 | i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 152 | i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 153 | ·--· | 153 | ·--·2.44039s·elapsed |
| 154 | ·······1······35······241······841······1781······2464······2294······1432 | 154 | ·······1······35······241······841······1781······2464······2294······1432 |
| 155 | 576······135······14 | 155 | 576······135······14 |
| 156 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<- | 156 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<- |
| 157 | -·S····<--·S····<--·S | 157 | -·S····<--·S····<--·S |
| Offset 167, 15 lines modified | Offset 167, 15 lines modified | ||
| 167 | i14·:·numTBBThreads·=·1 | 167 | i14·:·numTBBThreads·=·1 |
| 168 | o14·=·1 | 168 | o14·=·1 |
| 169 | i15·:·I·=·ideal·I_*; | 169 | i15·:·I·=·ideal·I_*; |
| 170 | o15·:·Ideal·of·S | 170 | o15·:·Ideal·of·S |
| 171 | i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 171 | i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 172 | ·--· | 172 | ·--·2.62356s·elapsed |
| 173 | ·······1······35······241······841······1781······2464······2294······1432 | 173 | ·······1······35······241······841······1781······2464······2294······1432 |
| 174 | 576······135······14 | 174 | 576······135······14 |
| 175 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<- | 175 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<- |
| 176 | -·S····<--·S····<--·S | 176 | -·S····<--·S····<--·S |
| Offset 194, 37 lines modified | Offset 194, 37 lines modified | ||
| 194 | o18·=·S | 194 | o18·=·S |
| 195 | o18·:·PolynomialRing | 195 | o18·:·PolynomialRing |
| 196 | i19·:·I·=·ideal·random(S^1,·S^{4:-5}); | 196 | i19·:·I·=·ideal·random(S^1,·S^{4:-5}); |
| 197 | o19·:·Ideal·of·S | 197 | o19·:·Ideal·of·S |
| 198 | i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 198 | i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 199 | ·--· | 199 | ·--·4.30019s·elapsed |
| 200 | ··············1······108 | 200 | ··············1······108 |
| 201 | o20·:·Matrix·S··<--·S | 201 | o20·:·Matrix·S··<--·S |
| 202 | i21·:·numTBBThreads·=·1 | 202 | i21·:·numTBBThreads·=·1 |
| 203 | o21·=·1 | 203 | o21·=·1 |
| 204 | i22·:·I·=·ideal·I_*; | 204 | i22·:·I·=·ideal·I_*; |
| 205 | o22·:·Ideal·of·S | 205 | o22·:·Ideal·of·S |
| 206 | i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 206 | i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 207 | ·--· | 207 | ·--·10.041s·elapsed |
| 208 | ··············1······108 | 208 | ··············1······108 |
| 209 | o23·:·Matrix·S··<--·S | 209 | o23·:·Matrix·S··<--·S |
| 210 | i24·:·numTBBThreads·=·10 | 210 | i24·:·numTBBThreads·=·10 |
| 211 | o24·=·10 | 211 | o24·=·10 |
| 212 | i25·:·I·=·ideal·I_*; | 212 | i25·:·I·=·ideal·I_*; |
| 213 | o25·:·Ideal·of·S | 213 | o25·:·Ideal·of·S |
| 214 | i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 214 | i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 215 | ·--· | 215 | ·--·4.87683s·elapsed |
| 216 | ··············1······108 | 216 | ··············1······108 |
| 217 | o26·:·Matrix·S··<--·S | 217 | o26·:·Matrix·S··<--·S |
| 218 | For·Groebner·basis·computation·in·associative·algebras,·ParallelizeByDegree·is | 218 | For·Groebner·basis·computation·in·associative·algebras,·ParallelizeByDegree·is |
| 219 | not·relevant.·In·this·case,·use·numTBBThreads·to·control·the·amount·of | 219 | not·relevant.·In·this·case,·use·numTBBThreads·to·control·the·amount·of |
| 220 | parallelism. | 220 | parallelism. |
| 221 | i27·:·needsPackage·"AssociativeAlgebras" | 221 | i27·:·needsPackage·"AssociativeAlgebras" |
| Offset 245, 15 lines modified | Offset 245, 15 lines modified | ||
| 245 | ···············2·························2·························2 | 245 | ···············2·························2·························2 |
| 246 | o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·) | 246 | o30·=·ideal·(5a··+·2b*c·+·3c*b,·3a*c·+·5b··+·2c*a,·2a*b·+·3b*a·+·5c·) |
| 247 | ················ZZ | 247 | ················ZZ |
| 248 | o30·:·Ideal·of·---<|a,·b,·c|> | 248 | o30·:·Ideal·of·---<|a,·b,·c|> |
| 249 | ···············101 | 249 | ···············101 |
| 250 | i31·:·elapsedTime·NCGB(I,·22); | 250 | i31·:·elapsedTime·NCGB(I,·22); |
| 251 | ·--· | 251 | ·--·1.12137s·elapsed |
| 252 | ···············ZZ············1·······ZZ············148 | 252 | ···············ZZ············1·······ZZ············148 |
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| Offset 314, 34 lines modified | Offset 314, 34 lines modified | ||
| 314 | ··········<tr> | 314 | ··········<tr> |
| 315 | <td>··············<pre><code·class="language-macaulay2">i27·:·gbTrace·=·3 | 315 | <td>··············<pre><code·class="language-macaulay2">i27·:·gbTrace·=·3 |
| 316 | o27·=·3</code></pre> | 316 | o27·=·3</code></pre> |
| 317 | </td>··········</tr> | 317 | </td>··········</tr> |
| 318 | ··········<tr> | 318 | ··········<tr> |
| 319 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·poincare·I | 319 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·poincare·I |
| 320 | ·--·used·0.00 | 320 | ·--·used·0.00361402s·(cpu);·1.2253e-05s·(thread);·0s·(gc) |
| 321 | ············3·····6····9 | 321 | ············3·····6····9 |
| 322 | o28·=·1·-·3T··+·3T··-·T | 322 | o28·=·1·-·3T··+·3T··-·T |
| 323 | o28·:·ZZ[T]</code></pre> | 323 | o28·:·ZZ[T]</code></pre> |
| 324 | </td>··········</tr> | 324 | </td>··········</tr> |
| 325 | ··········<tr> | 325 | ··········<tr> |
| 326 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·gens·gb·I; | 326 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·gens·gb·I; |
| 327 | ···--·registering·gb·19·at·0x7f | 327 | ···--·registering·gb·19·at·0x7f1ed7243e00 |
| 328 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11 | 328 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of·(nonminimal)·gb·elements·=·11 |
| 329 | ···--·number·of·monomials················=·4186 | 329 | ···--·number·of·monomials················=·4186 |
| 330 | ···--·#reduction·steps·=·38 | 330 | ···--·#reduction·steps·=·38 |
| 331 | ···--·#spairs·done·=·11 | 331 | ···--·#spairs·done·=·11 |
| 332 | ···--·ncalls·=·10 | 332 | ···--·ncalls·=·10 |
| 333 | ···--·nloop·=·29 | 333 | ···--·nloop·=·29 |
| 334 | ···--·nsaved·=·0 | 334 | ···--·nsaved·=·0 |
| 335 | ···--··--·used·0.0 | 335 | ···--··--·used·0.0123727s·(cpu);·0.0157315s·(thread);·0s·(gc) |
| 336 | ··············1······11 | 336 | ··············1······11 |
| 337 | o29·:·Matrix·R··<--·R</code></pre> | 337 | o29·:·Matrix·R··<--·R</code></pre> |
| 338 | </td>··········</tr> | 338 | </td>··········</tr> |
| 339 | ········</table> | 339 | ········</table> |
| 340 | ········<div> | 340 | ········<div> |
| 341 | ··········<p>In·this·case,·the·savings·is·minimal,·but·often·it·can·be·dramatic.·Another·important·situation·is·to·compute·a·Gröbner·basis·using·a·different·monomial·order.</p> | 341 | ··········<p>In·this·case,·the·savings·is·minimal,·but·often·it·can·be·dramatic.·Another·important·situation·is·to·compute·a·Gröbner·basis·using·a·different·monomial·order.</p> |
| Offset 349, 39 lines modified | Offset 349, 39 lines modified | ||
| 349 | ········<table·class="examples"> | 349 | ········<table·class="examples"> |
| 350 | ··········<tr> | 350 | ··········<tr> |
| 351 | <td>··············<pre><code·class="language-macaulay2">i30·:·R·=·QQ[a..d];</code></pre> | 351 | <td>··············<pre><code·class="language-macaulay2">i30·:·R·=·QQ[a..d];</code></pre> |
| 352 | </td>··········</tr> | 352 | </td>··········</tr> |
| 353 | ··········<tr> | 353 | ··········<tr> |
| 354 | <td>··············<pre><code·class="language-macaulay2">i31·:·I·=·ideal·random(R^1,·R^{3:-3}); | 354 | <td>··············<pre><code·class="language-macaulay2">i31·:·I·=·ideal·random(R^1,·R^{3:-3}); |
| 355 | ···--·registering·gb·20·at·0x7f | 355 | ···--·registering·gb·20·at·0x7f1ed7243c40 |
| 356 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 | 356 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 |
| 357 | ···--·number·of·monomials················=·0 | 357 | ···--·number·of·monomials················=·0 |
| 358 | ···--·#reduction·steps·=·0 | 358 | ···--·#reduction·steps·=·0 |
| 359 | ···--·#spairs·done·=·0 | 359 | ···--·#spairs·done·=·0 |
| 360 | ···--·ncalls·=·0 | 360 | ···--·ncalls·=·0 |
| 361 | ···--·nloop·=·0 | 361 | ···--·nloop·=·0 |
| 362 | ···--·nsaved·=·0 | 362 | ···--·nsaved·=·0 |
| 363 | ···--· | 363 | ···--· |
| 364 | o31·:·Ideal·of·R</code></pre> | 364 | o31·:·Ideal·of·R</code></pre> |
| 365 | </td>··········</tr> | 365 | </td>··········</tr> |
| 366 | ··········<tr> | 366 | ··········<tr> |
| 367 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·p·=·poincare·I | 367 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·p·=·poincare·I |
| 368 | ···--·registering·gb·21·at·0x7f | 368 | ···--·registering·gb·21·at·0x7f1ed72438c0 |
| 369 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11 | 369 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11 |
| 370 | ···--·number·of·monomials················=·267 | 370 | ···--·number·of·monomials················=·267 |
| 371 | ···--·#reduction·steps·=·236 | 371 | ···--·#reduction·steps·=·236 |
| 372 | ···--·#spairs·done·=·30 | 372 | ···--·#spairs·done·=·30 |
| 373 | ···--·ncalls·=·10 | 373 | ···--·ncalls·=·10 |
| 374 | ···--·nloop·=·20 | 374 | ···--·nloop·=·20 |
| 375 | ···--·nsaved·=·0 | 375 | ···--·nsaved·=·0 |
| 376 | ···--··--·used·0.00 | 376 | ···--··--·used·0.0079994s·(cpu);·0.00685187s·(thread);·0s·(gc) |
| 377 | ············3·····6····9 | 377 | ············3·····6····9 |
| 378 | o32·=·1·-·3T··+·3T··-·T | 378 | o32·=·1·-·3T··+·3T··-·T |
| 379 | o32·:·ZZ[T]</code></pre> | 379 | o32·:·ZZ[T]</code></pre> |
| 380 | </td>··········</tr> | 380 | </td>··········</tr> |
| 381 | ··········<tr> | 381 | ··········<tr> |
| Offset 436, 27 lines modified | Offset 436, 27 lines modified | ||
| 436 | <td>··············<pre><code·class="language-macaulay2">i36·:·gbTrace·=·3 | 436 | <td>··············<pre><code·class="language-macaulay2">i36·:·gbTrace·=·3 |
| 437 | o36·=·3</code></pre> | 437 | o36·=·3</code></pre> |
| 438 | </td>··········</tr> | 438 | </td>··········</tr> |
| 439 | ··········<tr> | 439 | ··········<tr> |
| 440 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·gens·gb·J; | 440 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·gens·gb·J; |
| 441 | ···--·registering·gb·22·at·0x7f | 441 | ···--·registering·gb·22·at·0x7f1ed7243700 |
| 442 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m | 442 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9}(3,9)m |
| 443 | ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m | 443 | ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m |
| 444 | ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m | 444 | ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m{24}(1,3)m |
| 445 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39 | 445 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39 |
| 446 | ···--·number·of·monomials················=·1051 | 446 | ···--·number·of·monomials················=·1051 |
| 447 | ···--·#reduction·steps·=·284 | 447 | ···--·#reduction·steps·=·284 |
| 448 | ···--·#spairs·done·=·53 | 448 | ···--·#spairs·done·=·53 |
| 449 | ···--·ncalls·=·46 | 449 | ···--·ncalls·=·46 |
| 450 | ···--·nloop·=·54 | 450 | ···--·nloop·=·54 |
| 451 | ···--·nsaved·=·0 | 451 | ···--·nsaved·=·0 |
| 452 | ···--··--·used·0.0 | 452 | ···--··--·used·0.0639807s·(cpu);·0.066879s·(thread);·0s·(gc) |
| 453 | ··············1······39 | 453 | ··············1······39 |
| 454 | o37·:·Matrix·S··<--·S</code></pre> | 454 | o37·:·Matrix·S··<--·S</code></pre> |
| 455 | </td>··········</tr> | 455 | </td>··········</tr> |
| 456 | ··········<tr> | 456 | ··········<tr> |
| 457 | <td>··············<pre><code·class="language-macaulay2">i38·:·selectInSubring(1,·gens·gb·J) | 457 | <td>··············<pre><code·class="language-macaulay2">i38·:·selectInSubring(1,·gens·gb·J) |
| Offset 179, 66 lines modified | Offset 179, 66 lines modified | ||
| 179 | o26·=·1·-·3T··+·3T··-·T | 179 | o26·=·1·-·3T··+·3T··-·T |
| 180 | o26·:·ZZ[T] | 180 | o26·:·ZZ[T] |
| 181 | i27·:·gbTrace·=·3 | 181 | i27·:·gbTrace·=·3 |
| 182 | o27·=·3 | 182 | o27·=·3 |
| 183 | i28·:·time·poincare·I | 183 | i28·:·time·poincare·I |
| 184 | ·--·used·0.00 | 184 | ·--·used·0.00361402s·(cpu);·1.2253e-05s·(thread);·0s·(gc) |
| 185 | ············3·····6····9 | 185 | ············3·····6····9 |
| 186 | o28·=·1·-·3T··+·3T··-·T | 186 | o28·=·1·-·3T··+·3T··-·T |
| 187 | o28·:·ZZ[T] | 187 | o28·:·ZZ[T] |
| 188 | i29·:·time·gens·gb·I; | 188 | i29·:·time·gens·gb·I; |
| 189 | ···--·registering·gb·19·at·0x7f | 189 | ···--·registering·gb·19·at·0x7f1ed7243e00 |
| 190 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of | 190 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(2,6)mm{7}(1,4)m{8}(0,2)number·of |
| 191 | (nonminimal)·gb·elements·=·11 | 191 | (nonminimal)·gb·elements·=·11 |
| 192 | ···--·number·of·monomials················=·4186 | 192 | ···--·number·of·monomials················=·4186 |
| 193 | ···--·#reduction·steps·=·38 | 193 | ···--·#reduction·steps·=·38 |
| 194 | ···--·#spairs·done·=·11 | 194 | ···--·#spairs·done·=·11 |
| 195 | ···--·ncalls·=·10 | 195 | ···--·ncalls·=·10 |
| 196 | ···--·nloop·=·29 | 196 | ···--·nloop·=·29 |
| 197 | ···--·nsaved·=·0 | 197 | ···--·nsaved·=·0 |
| 198 | ···--··--·used·0.0 | 198 | ···--··--·used·0.0123727s·(cpu);·0.0157315s·(thread);·0s·(gc) |
| 199 | ··············1······11 | 199 | ··············1······11 |
| 200 | o29·:·Matrix·R··<--·R | 200 | o29·:·Matrix·R··<--·R |
| 201 | In·this·case,·the·savings·is·minimal,·but·often·it·can·be·dramatic.·Another | 201 | In·this·case,·the·savings·is·minimal,·but·often·it·can·be·dramatic.·Another |
| 202 | important·situation·is·to·compute·a·Gröbner·basis·using·a·different·monomial | 202 | important·situation·is·to·compute·a·Gröbner·basis·using·a·different·monomial |
| 203 | order. | 203 | order. |
| 204 | i30·:·R·=·QQ[a..d]; | 204 | i30·:·R·=·QQ[a..d]; |
| 205 | i31·:·I·=·ideal·random(R^1,·R^{3:-3}); | 205 | i31·:·I·=·ideal·random(R^1,·R^{3:-3}); |
| 206 | ···--·registering·gb·20·at·0x7f | 206 | ···--·registering·gb·20·at·0x7f1ed7243c40 |
| 207 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 | 207 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 |
| 208 | ···--·number·of·monomials················=·0 | 208 | ···--·number·of·monomials················=·0 |
| 209 | ···--·#reduction·steps·=·0 | 209 | ···--·#reduction·steps·=·0 |
| 210 | ···--·#spairs·done·=·0 | 210 | ···--·#spairs·done·=·0 |
| 211 | ···--·ncalls·=·0 | 211 | ···--·ncalls·=·0 |
| 212 | ···--·nloop·=·0 | 212 | ···--·nloop·=·0 |
| 213 | ···--·nsaved·=·0 | 213 | ···--·nsaved·=·0 |
| 214 | ···-- | 214 | ···-- |
| 215 | o31·:·Ideal·of·R | 215 | o31·:·Ideal·of·R |
| 216 | i32·:·time·p·=·poincare·I | 216 | i32·:·time·p·=·poincare·I |
| 217 | ···--·registering·gb·21·at·0x7f | 217 | ···--·registering·gb·21·at·0x7f1ed72438c0 |
| 218 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of | 218 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of |
| 219 | (nonminimal)·gb·elements·=·11 | 219 | (nonminimal)·gb·elements·=·11 |
| 220 | ···--·number·of·monomials················=·267 | 220 | ···--·number·of·monomials················=·267 |
| 221 | ···--·#reduction·steps·=·236 | 221 | ···--·#reduction·steps·=·236 |
| 222 | ···--·#spairs·done·=·30 | 222 | ···--·#spairs·done·=·30 |
| 223 | ···--·ncalls·=·10 | 223 | ···--·ncalls·=·10 |
| 224 | ···--·nloop·=·20 | 224 | ···--·nloop·=·20 |
| 225 | ···--·nsaved·=·0 | 225 | ···--·nsaved·=·0 |
| 226 | ···--··--·used·0.00 | 226 | ···--··--·used·0.0079994s·(cpu);·0.00685187s·(thread);·0s·(gc) |
| 227 | ············3·····6····9 | 227 | ············3·····6····9 |
| 228 | o32·=·1·-·3T··+·3T··-·T | 228 | o32·=·1·-·3T··+·3T··-·T |
| 229 | o32·:·ZZ[T] | 229 | o32·:·ZZ[T] |
| 230 | i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2] | 230 | i33·:·S·=·QQ[a..d,·MonomialOrder·=>·Eliminate·2] |
| Offset 283, 30 lines modified | Offset 283, 30 lines modified | ||
| 283 | o35·:·ZZ[T] | 283 | o35·:·ZZ[T] |
| 284 | i36·:·gbTrace·=·3 | 284 | i36·:·gbTrace·=·3 |
| 285 | o36·=·3 | 285 | o36·=·3 |
| 286 | i37·:·time·gens·gb·J; | 286 | i37·:·time·gens·gb·J; |
| 287 | ···--·registering·gb·22·at·0x7f | 287 | ···--·registering·gb·22·at·0x7f1ed7243700 |
| 288 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9} | 288 | ···--·[gb]{3}(3,3)mmm{4}(2,2)mm{5}(3,3)mmm{6}(3,7)mmm{7}(3,8)mmm{8}(3,9)mmm{9} |
| 289 | (3,9)m | 289 | (3,9)m |
| 290 | ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m | 290 | ···--·mm{10}(2,8)mm{11}(1,5)m{12}(1,3)m{13}(1,3)m{14}(1,3)m{15}(1,3)m{16}(1,3)m |
| 291 | ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m | 291 | ···--·{17}(1,3)m{18}(1,3)m{19}(1,3)m{20}(1,3)m{21}(1,3)m{22}(1,3)m{23}(1,3)m |
| 292 | {24}(1,3)m | 292 | {24}(1,3)m |
| 293 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements | 293 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements |
| 294 | =·39 | 294 | =·39 |
| 295 | ···--·number·of·monomials················=·1051 | 295 | ···--·number·of·monomials················=·1051 |
| 296 | ···--·#reduction·steps·=·284 | 296 | ···--·#reduction·steps·=·284 |
| 297 | ···--·#spairs·done·=·53 | 297 | ···--·#spairs·done·=·53 |
| 298 | ···--·ncalls·=·46 | 298 | ···--·ncalls·=·46 |
| 299 | ···--·nloop·=·54 | 299 | ···--·nloop·=·54 |
| 300 | ···--·nsaved·=·0 | 300 | ···--·nsaved·=·0 |
| 301 | ···--··--·used·0.0 | 301 | ···--··--·used·0.0639807s·(cpu);·0.066879s·(thread);·0s·(gc) |
| 302 | ··············1······39 | 302 | ··············1······39 |
| 303 | o37·:·Matrix·S··<--·S | 303 | o37·:·Matrix·S··<--·S |
| 304 | i38·:·selectInSubring(1,·gens·gb·J) | 304 | i38·:·selectInSubring(1,·gens·gb·J) |
| 305 | o38·=·|·243873059890414515367459726418219472801881021280016638460434780718278 | 305 | o38·=·|·243873059890414515367459726418219472801881021280016638460434780718278 |
| 306 | ······----------------------------------------------------------------------- | 306 | ······----------------------------------------------------------------------- |
| Offset 61, 15 lines modified | Offset 61, 15 lines modified | ||
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | ········<table·class="examples"> | 64 | ········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·processID() | 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·processID() |
| 67 | o1·=· | 67 | o1·=·3485508</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ········</table> | 69 | ········</table> |
| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>See·also</h2> | 72 | ········<h2>See·also</h2> |
| 73 | ········<ul> | 73 | ········<ul> |
| 74 | ··········<li> | 74 | ··········<li> |
| Offset 9, 13 lines modified | Offset 9, 13 lines modified | ||
| 9 | ····*···Usage: | 9 | ····*···Usage: |
| 10 | ············processID() | 10 | ············processID() |
| 11 | ····*·Outputs: | 11 | ····*·Outputs: |
| 12 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·identifier·of·the·current·Macaulay2·process | 12 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·process·identifier·of·the·current·Macaulay2·process |
| 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 14 | i1·:·processID() | 14 | i1·:·processID() |
| 15 | o1·=· | 15 | o1·=·3485508 |
| 16 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 16 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 17 | ····*·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·the·process·group·identifier | 17 | ····*·_\x8g_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·the·process·group·identifier |
| 18 | ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier | 18 | ····*·_\x8s_\x8e_\x8t_\x8G_\x8r_\x8o_\x8u_\x8p_\x8I_\x8D·--·set·the·process·group·identifier |
| 19 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 19 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 20 | The·object·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 20 | The·object·_\x8p_\x8r_\x8o_\x8c_\x8e_\x8s_\x8s_\x8I_\x8D·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 59 | ······123····110····13 | 59 | ······123····110····13 |
| 60 | o2·=·x····+·x····+·x···+·1 | 60 | o2·=·x····+·x····+·x···+·1 |
| 61 | o2·:·R</code></pre> | 61 | o2·:·R</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·factor·f | 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·factor·f |
| 65 | ·--·used·0.00 | 65 | ·--·used·0.00402279s·(cpu);·0.00401581s·(thread);·0s·(gc) |
| 66 | ··············2········2·······2·······2·······2·······4·····3······2············4·····3·····2············4·····3·····2············10·····8·····6·····4······2·······10·····8······6·····4······2·······10······8····6····4·····2·······10······8·····6·····4······2·······10······8·····6·····4·····2·······10······8·····6······4·····2·······10······8·····6·····4······2·······10······8·····6······4·····2·······10·····8····6····4······2·······10·····8······6·····4······2 | 66 | ··············2········2·······2·······2·······2·······4·····3······2············4·····3·····2············4·····3·····2············10·····8·····6·····4······2·······10·····8······6·····4······2·······10······8····6····4·····2·······10······8·····6·····4······2·······10······8·····6·····4·····2·······10······8·····6······4·····2·······10······8·····6·····4······2·······10······8·····6······4·····2·······10·····8····6····4······2·······10·····8······6·····4······2 |
| 67 | o3·=·(x·+·1)(x··-·15)(x··+·8)(x··+·4)(x··+·2)(x··+·1)(x··-·4x··+·11x··-·4x·+·1)(x··-·6x··-·2x··-·6x·+·1)(x··+·9x··-·4x··+·9x·+·1)(x···-·5x··-·8x··-·4x··-·13x··+·1)(x···-·9x··+·15x··-·2x··+·10x··+·1)(x···-·10x··-·x··-·x··+·9x··+·1)(x···-·11x··-·8x··-·4x··+·11x··+·1)(x···-·13x··-·4x··-·8x··-·5x··+·1)(x···+·13x··-·2x··+·15x··+·5x··+·1)(x···+·11x··-·4x··-·8x··-·11x··+·1)(x···+·10x··-·2x··+·15x··-·9x··+·1)(x···+·9x··-·x··-·x··-·10x··+·1)(x···+·5x··+·15x··-·2x··+·13x··+·1) | 67 | o3·=·(x·+·1)(x··-·15)(x··+·8)(x··+·4)(x··+·2)(x··+·1)(x··-·4x··+·11x··-·4x·+·1)(x··-·6x··-·2x··-·6x·+·1)(x··+·9x··-·4x··+·9x·+·1)(x···-·5x··-·8x··-·4x··-·13x··+·1)(x···-·9x··+·15x··-·2x··+·10x··+·1)(x···-·10x··-·x··-·x··+·9x··+·1)(x···-·11x··-·8x··-·4x··+·11x··+·1)(x···-·13x··-·4x··-·8x··-·5x··+·1)(x···+·13x··-·2x··+·15x··+·5x··+·1)(x···+·11x··-·4x··-·8x··-·11x··+·1)(x···+·10x··-·2x··+·15x··-·9x··+·1)(x···+·9x··-·x··-·x··-·10x··+·1)(x···+·5x··+·15x··-·2x··+·13x··+·1) |
| 68 | o3·:·Expression·of·class·Product</code></pre> | 68 | o3·:·Expression·of·class·Product</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| Offset 92, 16 lines modified | Offset 92, 16 lines modified | ||
| 92 | o6·:·FunctionClosure</code></pre> | 92 | o6·:·FunctionClosure</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·i·to·10·do·(g();h();h())</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·i·to·10·do·(g();h();h())</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i8·:·profileSummary | 98 | <td>··············<pre><code·class="language-macaulay2">i8·:·profileSummary |
| 99 | g:·11·times,·used·.0 | 99 | g:·11·times,·used·.0393458·seconds |
| 100 | h:·22·times,·used·.0 | 100 | h:·22·times,·used·.0787814·seconds</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ········</table> | 102 | ········</table> |
| 103 | ······</div> | 103 | ······</div> |
| 104 | ······<div·class="waystouse"> | 104 | ······<div·class="waystouse"> |
| 105 | ········<h2>Ways·to·use·<span·class="tt">profile</span>:</h2> | 105 | ········<h2>Ways·to·use·<span·class="tt">profile</span>:</h2> |
| 106 | ········<ul> | 106 | ········<ul> |
| 107 | ··········<li> | 107 | ··········<li> |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i2·:·f·=·(x^110+1)*(x^13+1) | 17 | i2·:·f·=·(x^110+1)*(x^13+1) |
| 18 | ······123····110····13 | 18 | ······123····110····13 |
| 19 | o2·=·x····+·x····+·x···+·1 | 19 | o2·=·x····+·x····+·x···+·1 |
| 20 | o2·:·R | 20 | o2·:·R |
| 21 | i3·:·time·factor·f | 21 | i3·:·time·factor·f |
| 22 | ·--·used·0.00 | 22 | ·--·used·0.00402279s·(cpu);·0.00401581s·(thread);·0s·(gc) |
| 23 | ··············2········2·······2·······2·······2·······4·····3······2 | 23 | ··············2········2·······2·······2·······2·······4·····3······2 |
| 24 | 4·····3·····2············4·····3·····2············10·····8·····6·····4······2 | 24 | 4·····3·····2············4·····3·····2············10·····8·····6·····4······2 |
| 25 | 10·····8······6·····4······2·······10······8····6····4·····2·······10······8 | 25 | 10·····8······6·····4······2·······10······8····6····4·····2·······10······8 |
| 26 | 6·····4······2·······10······8·····6·····4·····2·······10······8·····6······4 | 26 | 6·····4······2·······10······8·····6·····4·····2·······10······8·····6······4 |
| 27 | 2·······10······8·····6·····4······2·······10······8·····6······4·····2 | 27 | 2·······10······8·····6·····4······2·······10······8·····6······4·····2 |
| 28 | 10·····8····6····4······2·······10·····8······6·····4······2 | 28 | 10·····8····6····4······2·······10·····8······6·····4······2 |
| Offset 50, 14 lines modified | Offset 50, 14 lines modified | ||
| 50 | i6·:·h·=·profile("h",·()·->·factor·f) | 50 | i6·:·h·=·profile("h",·()·->·factor·f) |
| 51 | o6·=·h | 51 | o6·=·h |
| 52 | o6·:·FunctionClosure | 52 | o6·:·FunctionClosure |
| 53 | i7·:·for·i·to·10·do·(g();h();h()) | 53 | i7·:·for·i·to·10·do·(g();h();h()) |
| 54 | i8·:·profileSummary | 54 | i8·:·profileSummary |
| 55 | g:·11·times,·used·.0 | 55 | g:·11·times,·used·.0393458·seconds |
| 56 | h:·22·times,·used·.0 | 56 | h:·22·times,·used·.0787814·seconds |
| 57 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pr\x8ro\x8of\x8fi\x8il\x8le\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8* | 57 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pr\x8ro\x8of\x8fi\x8il\x8le\x8e:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 58 | ····*·profile(Function) | 58 | ····*·profile(Function) |
| 59 | ····*·profile(String,Function) | 59 | ····*·profile(String,Function) |
| 60 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 60 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 61 | The·object·_\x8p_\x8r_\x8o_\x8f_\x8i_\x8l_\x8e·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 61 | The·object·_\x8p_\x8r_\x8o_\x8f_\x8i_\x8l_\x8e·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | o5·=·(2,·10) | 90 | o5·=·(2,·10) |
| 91 | o5·:·Sequence</code></pre> | 91 | o5·:·Sequence</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·randomKRationalPoint(I) | 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·randomKRationalPoint(I) |
| 95 | ·--·used·0. | 95 | ·--·used·0.112493s·(cpu);·0.0977693s·(thread);·0s·(gc) |
| 96 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) | 96 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) |
| 97 | ·············2······3···1·····3···0·····3 | 97 | ·············2······3···1·····3···0·····3 |
| 98 | o6·:·Ideal·of·R</code></pre> | 98 | o6·:·Ideal·of·R</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | o9·=·(3,·10) | 114 | o9·=·(3,·10) |
| 115 | o9·:·Sequence</code></pre> | 115 | o9·:·Sequence</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·randomKRationalPoint(I) | 118 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·randomKRationalPoint(I) |
| 119 | ·--·used·0. | 119 | ·--·used·0.348078s·(cpu);·0.305079s·(thread);·0s·(gc) |
| 120 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) | 120 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) |
| 121 | ··············4······5···3······5···2·····5···1······5···0······5 | 121 | ··············4······5···3······5···2·····5···1······5···0······5 |
| 122 | o10·:·Ideal·of·R</code></pre> | 122 | o10·:·Ideal·of·R</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ········</table> | 124 | ········</table> |
| Offset 148, 15 lines modified | Offset 148, 15 lines modified | ||
| 148 | <td>··············<pre><code·class="language-macaulay2">i14·:·I=ideal·random(n,R); | 148 | <td>··············<pre><code·class="language-macaulay2">i14·:·I=ideal·random(n,R); |
| 149 | o14·:·Ideal·of·R</code></pre> | 149 | o14·:·Ideal·of·R</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c); | 152 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c); |
| 153 | ·····················#select(degs,d->d==1))),f->f>0)) | 153 | ·····················#select(degs,d->d==1))),f->f>0)) |
| 154 | ·--·used· | 154 | ·--·used·3.34962s·(cpu);·1.918s·(thread);·0s·(gc) |
| 155 | o15·=·58</code></pre> | 155 | o15·=·58</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ········</table> | 157 | ········</table> |
| 158 | ······</div> | 158 | ······</div> |
| 159 | ······<div·class="waystouse"> | 159 | ······<div·class="waystouse"> |
| 160 | ········<h2>Ways·to·use·<span·class="tt">randomKRationalPoint</span>:</h2> | 160 | ········<h2>Ways·to·use·<span·class="tt">randomKRationalPoint</span>:</h2> |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | o4·:·Ideal·of·R | 30 | o4·:·Ideal·of·R |
| 31 | i5·:·codim·I,·degree·I | 31 | i5·:·codim·I,·degree·I |
| 32 | o5·=·(2,·10) | 32 | o5·=·(2,·10) |
| 33 | o5·:·Sequence | 33 | o5·:·Sequence |
| 34 | i6·:·time·randomKRationalPoint(I) | 34 | i6·:·time·randomKRationalPoint(I) |
| 35 | ·--·used·0. | 35 | ·--·used·0.112493s·(cpu);·0.0977693s·(thread);·0s·(gc) |
| 36 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) | 36 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) |
| 37 | ·············2······3···1·····3···0·····3 | 37 | ·············2······3···1·····3···0·····3 |
| 38 | o6·:·Ideal·of·R | 38 | o6·:·Ideal·of·R |
| 39 | i7·:·R=kk[x_0..x_5]; | 39 | i7·:·R=kk[x_0..x_5]; |
| 40 | i8·:·I=minors(3,random(R^5,R^{3:-1})); | 40 | i8·:·I=minors(3,random(R^5,R^{3:-1})); |
| Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
| 46 | o8·:·Ideal·of·R | 46 | o8·:·Ideal·of·R |
| 47 | i9·:·codim·I,·degree·I | 47 | i9·:·codim·I,·degree·I |
| 48 | o9·=·(3,·10) | 48 | o9·=·(3,·10) |
| 49 | o9·:·Sequence | 49 | o9·:·Sequence |
| 50 | i10·:·time·randomKRationalPoint(I) | 50 | i10·:·time·randomKRationalPoint(I) |
| 51 | ·--·used·0. | 51 | ·--·used·0.348078s·(cpu);·0.305079s·(thread);·0s·(gc) |
| 52 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) | 52 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) |
| 53 | ··············4······5···3······5···2·····5···1······5···0······5 | 53 | ··············4······5···3······5···2·····5···1······5···0······5 |
| 54 | o10·:·Ideal·of·R | 54 | o10·:·Ideal·of·R |
| 55 | The·claim·that·$63·\%$·of·the·intersections·contain·a·K-rational·point·can·be | 55 | The·claim·that·$63·\%$·of·the·intersections·contain·a·K-rational·point·can·be |
| 56 | experimentally·tested: | 56 | experimentally·tested: |
| Offset 70, 14 lines modified | Offset 70, 14 lines modified | ||
| 70 | o13·:·RR·(of·precision·53) | 70 | o13·:·RR·(of·precision·53) |
| 71 | i14·:·I=ideal·random(n,R); | 71 | i14·:·I=ideal·random(n,R); |
| 72 | o14·:·Ideal·of·R | 72 | o14·:·Ideal·of·R |
| 73 | i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c- | 73 | i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c- |
| 74 | >degree·c); | 74 | >degree·c); |
| 75 | ·····················#select(degs,d->d==1))),f->f>0)) | 75 | ·····················#select(degs,d->d==1))),f->f>0)) |
| 76 | ·--·used· | 76 | ·--·used·3.34962s·(cpu);·1.918s·(thread);·0s·(gc) |
| 77 | o15·=·58 | 77 | o15·=·58 |
| 78 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mK\x8KR\x8Ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lP\x8Po\x8oi\x8in\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 78 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mK\x8KR\x8Ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lP\x8Po\x8oi\x8in\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 79 | ····*·randomKRationalPoint(Ideal) | 79 | ····*·randomKRationalPoint(Ideal) |
| 80 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 80 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 81 | The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 81 | The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8K_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8P_\x8o_\x8i_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 67, 32 lines modified | Offset 67, 32 lines modified | ||
| 67 | ······</div> | 67 | ······</div> |
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | ········<table·class="examples"> | 70 | ········<table·class="examples"> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() |
| 73 | o1·=·/tmp/M2- | 73 | o1·=·/tmp/M2-3506286-0/0</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir |
| 77 | o2·=·/tmp/M2- | 77 | o2·=·/tmp/M2-3506286-0/0</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close |
| 81 | o3·=·/tmp/M2- | 81 | o3·=·/tmp/M2-3506286-0/0/foo |
| 82 | o3·:·File</code></pre> | 82 | o3·:·File</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·readDirectory·dir | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·readDirectory·dir |
| 86 | o4·=·{ | 86 | o4·=·{foo,·.,·..} |
| 87 | o4·:·List</code></pre> | 87 | o4·:·List</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre> | 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| Offset 11, 26 lines modified | Offset 11, 26 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory | 12 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory |
| 13 | ····*·Outputs: | 13 | ····*·Outputs: |
| 14 | ··········o·a·_\x8l_\x8i_\x8s_\x8t,·the·list·of·filenames·stored·in·the·directory | 14 | ··········o·a·_\x8l_\x8i_\x8s_\x8t,·the·list·of·filenames·stored·in·the·directory |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·dir·=·temporaryFileName() | 16 | i1·:·dir·=·temporaryFileName() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3506286-0/0 |
| 18 | i2·:·makeDirectory·dir | 18 | i2·:·makeDirectory·dir |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-3506286-0/0 |
| 20 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close | 20 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close |
| 21 | o3·=·/tmp/M2- | 21 | o3·=·/tmp/M2-3506286-0/0/foo |
| 22 | o3·:·File | 22 | o3·:·File |
| 23 | i4·:·readDirectory·dir | 23 | i4·:·readDirectory·dir |
| 24 | o4·=·{ | 24 | o4·=·{foo,·.,·..} |
| 25 | o4·:·List | 25 | o4·:·List |
| 26 | i5·:·removeFile·fn | 26 | i5·:·removeFile·fn |
| 27 | i6·:·removeDirectory·dir | 27 | i6·:·removeDirectory·dir |
| 28 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 28 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 29 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·remove·a·directory | 29 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·remove·a·directory |
| 30 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file | 30 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file |
| Offset 44, 20 lines modified | Offset 44, 20 lines modified | ||
| 44 | ······<h1>reading·files</h1> | 44 | ······<h1>reading·files</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have·access·to.··For·example,·it·might·be·a·polynomial·produced·by·another·program.··The·function·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a·single·string.··We·illustrate·this·here·with·a·file·whose·name·is·<span·class="tt">expression</span>.········<p></p> | 46 | Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have·access·to.··For·example,·it·might·be·a·polynomial·produced·by·another·program.··The·function·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a·single·string.··We·illustrate·this·here·with·a·file·whose·name·is·<span·class="tt">expression</span>.········<p></p> |
| 47 | First·we·create·the·file·by·writing·the·desired·text·to·it.········<table·class="examples"> | 47 | First·we·create·the·file·by·writing·the·desired·text·to·it.········<table·class="examples"> |
| 48 | ··········<tr> | 48 | ··········<tr> |
| 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 50 | o1·=·/tmp/M2- | 50 | o1·=·/tmp/M2-3502046-0/0</code></pre> |
| 51 | </td>··········</tr> | 51 | </td>··········</tr> |
| 52 | ··········<tr> | 52 | ··········<tr> |
| 53 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"·<<·endl·<<·close | 53 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3"·<<·endl·<<·close |
| 54 | o2·=·/tmp/M2- | 54 | o2·=·/tmp/M2-3502046-0/0 |
| 55 | o2·:·File</code></pre> | 55 | o2·:·File</code></pre> |
| 56 | </td>··········</tr> | 56 | </td>··········</tr> |
| 57 | ········</table> | 57 | ········</table> |
| 58 | Now·we·get·the·contents·of·the·file,·as·a·single·string.········<table·class="examples"> | 58 | Now·we·get·the·contents·of·the·file,·as·a·single·string.········<table·class="examples"> |
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·get·fn | 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·get·fn |
| Offset 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | ········</table> | 96 | ········</table> |
| 97 | Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create·such·a·file.········<table·class="examples"> | 97 | Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create·such·a·file.········<table·class="examples"> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i7·:·fn·<<·"sample·=·2^100 | 99 | <td>··············<pre><code·class="language-macaulay2">i7·:·fn·<<·"sample·=·2^100 |
| 100 | ·····print·sample | 100 | ·····print·sample |
| 101 | ·····"·<<·close | 101 | ·····"·<<·close |
| 102 | o7·=·/tmp/M2- | 102 | o7·=·/tmp/M2-3502046-0/0 |
| 103 | o7·:·File</code></pre> | 103 | o7·:·File</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ········</table> | 105 | ········</table> |
| 106 | Now·verify·that·it·contains·the·desired·text·with·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>.········<table·class="examples"> | 106 | Now·verify·that·it·contains·the·desired·text·with·<a·title="get·the·contents·of·a·file"·href="_get.html">get</a>.········<table·class="examples"> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i8·:·get·fn | 108 | <td>··············<pre><code·class="language-macaulay2">i8·:·get·fn |
| Offset 7, 20 lines modified | Offset 7, 20 lines modified | ||
| 7 | Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have | 7 | Sometimes·a·file·will·contain·a·single·expression·whose·value·you·wish·to·have |
| 8 | access·to.·For·example,·it·might·be·a·polynomial·produced·by·another·program. | 8 | access·to.·For·example,·it·might·be·a·polynomial·produced·by·another·program. |
| 9 | The·function·_\x8g_\x8e_\x8t·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a | 9 | The·function·_\x8g_\x8e_\x8t·can·be·used·to·obtain·the·entire·contents·of·a·file·as·a |
| 10 | single·string.·We·illustrate·this·here·with·a·file·whose·name·is·expression. | 10 | single·string.·We·illustrate·this·here·with·a·file·whose·name·is·expression. |
| 11 | First·we·create·the·file·by·writing·the·desired·text·to·it. | 11 | First·we·create·the·file·by·writing·the·desired·text·to·it. |
| 12 | i1·:·fn·=·temporaryFileName() | 12 | i1·:·fn·=·temporaryFileName() |
| 13 | o1·=·/tmp/M2- | 13 | o1·=·/tmp/M2-3502046-0/0 |
| 14 | i2·:·fn·<< | 14 | i2·:·fn·<< |
| 15 | "z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3" | 15 | "z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2+8*y^3" |
| 16 | <<·endl·<<·close | 16 | <<·endl·<<·close |
| 17 | o2·=·/tmp/M2- | 17 | o2·=·/tmp/M2-3502046-0/0 |
| 18 | o2·:·File | 18 | o2·:·File |
| 19 | Now·we·get·the·contents·of·the·file,·as·a·single·string. | 19 | Now·we·get·the·contents·of·the·file,·as·a·single·string. |
| 20 | i3·:·get·fn | 20 | i3·:·get·fn |
| 21 | o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2 | 21 | o3·=·z^6+3*x*z^4+6*y*z^4+3*x^2*z^2+12*x*y*z^2+12*y^2*z^2+x^3+6*x^2*y+12*x*y^2 |
| 22 | ·····+8*y^3 | 22 | ·····+8*y^3 |
| Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
| 50 | o6·:·Expression·of·class·Product | 50 | o6·:·Expression·of·class·Product |
| 51 | Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create | 51 | Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create |
| 52 | such·a·file. | 52 | such·a·file. |
| 53 | i7·:·fn·<<·"sample·=·2^100 | 53 | i7·:·fn·<<·"sample·=·2^100 |
| 54 | ·····print·sample | 54 | ·····print·sample |
| 55 | ·····"·<<·close | 55 | ·····"·<<·close |
| 56 | o7·=·/tmp/M2- | 56 | o7·=·/tmp/M2-3502046-0/0 |
| 57 | o7·:·File | 57 | o7·:·File |
| 58 | Now·verify·that·it·contains·the·desired·text·with·_\x8g_\x8e_\x8t. | 58 | Now·verify·that·it·contains·the·desired·text·with·_\x8g_\x8e_\x8t. |
| 59 | i8·:·get·fn | 59 | i8·:·get·fn |
| 60 | o8·=·sample·=·2^100 | 60 | o8·=·sample·=·2^100 |
| 61 | ·····print·sample | 61 | ·····print·sample |
| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | ······</div> | 67 | ······</div> |
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | ········<table·class="examples"> | 70 | ········<table·class="examples"> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName·() | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName·() |
| 73 | o1·=·/tmp/M2- | 73 | o1·=·/tmp/M2-3507307-0/0</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile·("foo",·p)</code></pre> | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile·("foo",·p)</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·readlink·p | 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·readlink·p |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·file | 12 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·file |
| 13 | ····*·Outputs: | 13 | ····*·Outputs: |
| 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·symbolic·link | 14 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e,·whether·fn·is·the·path·to·a·symbolic·link |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·p·=·temporaryFileName·() | 16 | i1·:·p·=·temporaryFileName·() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3507307-0/0 |
| 18 | i2·:·symlinkFile·("foo",·p) | 18 | i2·:·symlinkFile·("foo",·p) |
| 19 | i3·:·readlink·p | 19 | i3·:·readlink·p |
| 20 | o3·=·foo | 20 | o3·=·foo |
| 21 | i4·:·removeFile·p | 21 | i4·:·removeFile·p |
| 22 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 22 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 23 | The·object·_\x8r_\x8e_\x8a_\x8d_\x8l_\x8i_\x8n_\x8k·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 23 | The·object·_\x8r_\x8e_\x8a_\x8d_\x8l_\x8i_\x8n_\x8k·is·a·_\x8c_\x8o_\x8m_\x8p_\x8i_\x8l_\x8e_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 67, 59 lines modified | Offset 67, 59 lines modified | ||
| 67 | ······</div> | 67 | ······</div> |
| 68 | ······<div> | 68 | ······<div> |
| 69 | ········<h2>Description</h2> | 69 | ········<h2>Description</h2> |
| 70 | ········<table·class="examples"> | 70 | ········<table·class="examples"> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·realpath·"." | 72 | <td>··············<pre><code·class="language-macaulay2">i1·:·realpath·"." |
| 73 | o1·=·/tmp/M2- | 73 | o1·=·/tmp/M2-3485508-0/83-rundir/</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·p·=·temporaryFileName() | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·p·=·temporaryFileName() |
| 77 | o2·=·/tmp/M2- | 77 | o2·=·/tmp/M2-3507339-0/0</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·q·=·temporaryFileName() | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·q·=·temporaryFileName() |
| 81 | o3·=·/tmp/M2- | 81 | o3·=·/tmp/M2-3507339-0/1</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·symlinkFile(p,q)</code></pre> | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·symlinkFile(p,q)</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·p·<<·close | 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·p·<<·close |
| 88 | o5·=·/tmp/M2- | 88 | o5·=·/tmp/M2-3507339-0/0 |
| 89 | o5·:·File</code></pre> | 89 | o5·:·File</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·readlink·q | 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·readlink·q |
| 93 | o6·=·/tmp/M2- | 93 | o6·=·/tmp/M2-3507339-0/0</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·realpath·q | 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·realpath·q |
| 97 | o7·=·/tmp/M2- | 97 | o7·=·/tmp/M2-3507339-0/0</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i8·:·removeFile·p</code></pre> | 100 | <td>··············<pre><code·class="language-macaulay2">i8·:·removeFile·p</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i9·:·removeFile·q</code></pre> | 103 | <td>··············<pre><code·class="language-macaulay2">i9·:·removeFile·q</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ········</table> | 105 | ········</table> |
| 106 | ········<p>The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.</p> | 106 | ········<p>The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.</p> |
| 107 | ········<table·class="examples"> | 107 | ········<table·class="examples"> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i10·:·realpath·"" | 109 | <td>··············<pre><code·class="language-macaulay2">i10·:·realpath·"" |
| 110 | o10·=·/tmp/M2- | 110 | o10·=·/tmp/M2-3485508-0/83-rundir/</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ······</div> | 113 | ······</div> |
| 114 | ······<div> | 114 | ······<div> |
| 115 | ········<h2>Caveat</h2> | 115 | ········<h2>Caveat</h2> |
| 116 | Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to·the·user.·Terminal·slashes·will·be·dropped.··Warning:·under·most·operating·systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of·the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain·circumstances,·return·a·relative·path·when·given·a·relative·path.······</div> | 116 | Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to·the·user.·Terminal·slashes·will·be·dropped.··Warning:·under·most·operating·systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of·the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain·circumstances,·return·a·relative·path·when·given·a·relative·path.······</div> |
| 117 | ······<div> | 117 | ······<div> |
| Offset 13, 39 lines modified | Offset 13, 39 lines modified | ||
| 13 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename,·or·path·to·a·file | 13 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename,·or·path·to·a·file |
| 14 | ····*·Outputs: | 14 | ····*·Outputs: |
| 15 | ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·pathname·to·fn·passing·through·no·symbolic·links,·and | 15 | ··········o·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·pathname·to·fn·passing·through·no·symbolic·links,·and |
| 16 | ············ending·with·a·slash·if·fn·refers·to·a·directory | 16 | ············ending·with·a·slash·if·fn·refers·to·a·directory |
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | i1·:·realpath·"." | 18 | i1·:·realpath·"." |
| 19 | o1·=·/tmp/M2- | 19 | o1·=·/tmp/M2-3485508-0/83-rundir/ |
| 20 | i2·:·p·=·temporaryFileName() | 20 | i2·:·p·=·temporaryFileName() |
| 21 | o2·=·/tmp/M2- | 21 | o2·=·/tmp/M2-3507339-0/0 |
| 22 | i3·:·q·=·temporaryFileName() | 22 | i3·:·q·=·temporaryFileName() |
| 23 | o3·=·/tmp/M2- | 23 | o3·=·/tmp/M2-3507339-0/1 |
| 24 | i4·:·symlinkFile(p,q) | 24 | i4·:·symlinkFile(p,q) |
| 25 | i5·:·p·<<·close | 25 | i5·:·p·<<·close |
| 26 | o5·=·/tmp/M2- | 26 | o5·=·/tmp/M2-3507339-0/0 |
| 27 | o5·:·File | 27 | o5·:·File |
| 28 | i6·:·readlink·q | 28 | i6·:·readlink·q |
| 29 | o6·=·/tmp/M2- | 29 | o6·=·/tmp/M2-3507339-0/0 |
| 30 | i7·:·realpath·q | 30 | i7·:·realpath·q |
| 31 | o7·=·/tmp/M2- | 31 | o7·=·/tmp/M2-3507339-0/0 |
| 32 | i8·:·removeFile·p | 32 | i8·:·removeFile·p |
| 33 | i9·:·removeFile·q | 33 | i9·:·removeFile·q |
| 34 | The·empty·string·is·interpreted·as·a·reference·to·the·current·directory. | 34 | The·empty·string·is·interpreted·as·a·reference·to·the·current·directory. |
| 35 | i10·:·realpath·"" | 35 | i10·:·realpath·"" |
| 36 | o10·=·/tmp/M2- | 36 | o10·=·/tmp/M2-3485508-0/83-rundir/ |
| 37 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 37 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 38 | Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to | 38 | Every·component·of·the·path·must·exist·in·the·file·system·and·be·accessible·to |
| 39 | the·user.·Terminal·slashes·will·be·dropped.·Warning:·under·most·operating | 39 | the·user.·Terminal·slashes·will·be·dropped.·Warning:·under·most·operating |
| 40 | systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of | 40 | systems,·the·value·returned·is·an·absolute·path·(one·starting·at·the·root·of |
| 41 | the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain | 41 | the·file·system),·but·under·Solaris,·this·system·call·may,·in·certain |
| 42 | circumstances,·return·a·relative·path·when·given·a·relative·path. | 42 | circumstances,·return·a·relative·path·when·given·a·relative·path. |
| 43 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 43 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 73, 22 lines modified | Offset 73, 22 lines modified | ||
| 73 | ········<h2>Description</h2> | 73 | ········<h2>Description</h2> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--"))</code></pre> | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--"))</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·collectGarbage()· | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·collectGarbage()· |
| 80 | --finalization:·(1)[4]:·--·finalizing·sequence·#5·-- | ||
| 81 | --finalization:·( | 80 | --finalization:·(1)[3]:·--·finalizing·sequence·#4·-- |
| 82 | --finalization:·(3)[2]:·--·finalizing·sequence·#3·-- | ||
| 83 | --finalization:·(4)[7]:·--·finalizing·sequence·#8·-- | ||
| 84 | --finalization:·(5)[0]:·--·finalizing·sequence·#1·-- | ||
| 85 | --finalization:·( | 81 | --finalization:·(2)[6]:·--·finalizing·sequence·#7·-- |
| 82 | --finalization:·(3)[1]:·--·finalizing·sequence·#2·-- | ||
| 86 | --finalization:·( | 83 | --finalization:·(4)[5]:·--·finalizing·sequence·#6·-- |
| 84 | --finalization:·(5)[2]:·--·finalizing·sequence·#3·-- | ||
| 85 | --finalization:·(6)[0]:·--·finalizing·sequence·#1·-- | ||
| 86 | --finalization:·(7)[7]:·--·finalizing·sequence·#8·-- | ||
| 87 | --finalization:·(8)[ | 87 | --finalization:·(8)[4]:·--·finalizing·sequence·#5·--</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| 90 | ······</div> | 90 | ······</div> |
| 91 | ······<div> | 91 | ······<div> |
| 92 | ········<h2>Caveat</h2> | 92 | ········<h2>Caveat</h2> |
| 93 | This·function·should·mainly·be·used·for·debugging.··Having·a·large·number·of·finalizers·might·degrade·the·performance·of·the·program.··Moreover,·registering·two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for·finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the·chain·being·freed,·even·if·nothing·else·points·to·any·of·them.······</div> | 93 | This·function·should·mainly·be·used·for·debugging.··Having·a·large·number·of·finalizers·might·degrade·the·performance·of·the·program.··Moreover,·registering·two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for·finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the·chain·being·freed,·even·if·nothing·else·points·to·any·of·them.······</div> |
| 94 | ······<div> | 94 | ······<div> |
| Offset 15, 22 lines modified | Offset 15, 22 lines modified | ||
| 15 | ····*·Consequences: | 15 | ····*·Consequences: |
| 16 | ··········o·A·finalizer·is·registered·with·the·garbage·collector·to·print·a | 16 | ··········o·A·finalizer·is·registered·with·the·garbage·collector·to·print·a |
| 17 | ············string·when·that·object·is·collected·as·garbage | 17 | ············string·when·that·object·is·collected·as·garbage |
| 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 18 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 19 | i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"- | 19 | i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"- |
| 20 | -·finalizing·sequence·#"|i|"·--")) | 20 | -·finalizing·sequence·#"|i|"·--")) |
| 21 | i2·:·collectGarbage() | 21 | i2·:·collectGarbage() |
| 22 | --finalization:·(1)[4]:·--·finalizing·sequence·#5·-- | ||
| 23 | --finalization:·( | 22 | --finalization:·(1)[3]:·--·finalizing·sequence·#4·-- |
| 24 | --finalization:·(3)[2]:·--·finalizing·sequence·#3·-- | ||
| 25 | --finalization:·(4)[7]:·--·finalizing·sequence·#8·-- | ||
| 26 | --finalization:·(5)[0]:·--·finalizing·sequence·#1·-- | ||
| 27 | --finalization:·( | 23 | --finalization:·(2)[6]:·--·finalizing·sequence·#7·-- |
| 28 | --finalization:·(7)[5]:·--·finalizing·sequence·#6·-- | ||
| 29 | --finalization:·( | 24 | --finalization:·(3)[1]:·--·finalizing·sequence·#2·-- |
| 25 | --finalization:·(4)[5]:·--·finalizing·sequence·#6·-- | ||
| 26 | --finalization:·(5)[2]:·--·finalizing·sequence·#3·-- | ||
| 27 | --finalization:·(6)[0]:·--·finalizing·sequence·#1·-- | ||
| 28 | --finalization:·(7)[7]:·--·finalizing·sequence·#8·-- | ||
| 29 | --finalization:·(8)[4]:·--·finalizing·sequence·#5·-- | ||
| 30 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 31 | This·function·should·mainly·be·used·for·debugging.·Having·a·large·number·of | 31 | This·function·should·mainly·be·used·for·debugging.·Having·a·large·number·of |
| 32 | finalizers·might·degrade·the·performance·of·the·program.·Moreover,·registering | 32 | finalizers·might·degrade·the·performance·of·the·program.·Moreover,·registering |
| 33 | two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for | 33 | two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for |
| 34 | finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the | 34 | finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the |
| 35 | chain·being·freed,·even·if·nothing·else·points·to·any·of·them. | 35 | chain·being·freed,·even·if·nothing·else·points·to·any·of·them. |
| 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 69, 25 lines modified | Offset 69, 25 lines modified | ||
| 69 | ······</div> | 69 | ······</div> |
| 70 | ······<div> | 70 | ······<div> |
| 71 | ········<h2>Description</h2> | 71 | ········<h2>Description</h2> |
| 72 | ········<table·class="examples"> | 72 | ········<table·class="examples"> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() | 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() |
| 75 | o1·=·/tmp/M2- | 75 | o1·=·/tmp/M2-3499826-0/0</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir |
| 79 | o2·=·/tmp/M2- | 79 | o2·=·/tmp/M2-3499826-0/0</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·readDirectory·dir | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·readDirectory·dir |
| 83 | o3·=·{. | 83 | o3·=·{.,·..} |
| 84 | o3·:·List</code></pre> | 84 | o3·:·List</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·removeDirectory·dir</code></pre> | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·removeDirectory·dir</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| Offset 11, 21 lines modified | Offset 11, 21 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory | 12 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·filename·or·path·to·a·directory |
| 13 | ····*·Consequences: | 13 | ····*·Consequences: |
| 14 | ··········o·the·directory·is·removed | 14 | ··········o·the·directory·is·removed |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·dir·=·temporaryFileName() | 16 | i1·:·dir·=·temporaryFileName() |
| 17 | o1·=·/tmp/M2- | 17 | o1·=·/tmp/M2-3499826-0/0 |
| 18 | i2·:·makeDirectory·dir | 18 | i2·:·makeDirectory·dir |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-3499826-0/0 |
| 20 | i3·:·readDirectory·dir | 20 | i3·:·readDirectory·dir |
| 21 | o3·=·{. | 21 | o3·=·{.,·..} |
| 22 | o3·:·List | 22 | o3·:·List |
| 23 | i4·:·removeDirectory·dir | 23 | i4·:·removeDirectory·dir |
| 24 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 25 | ····*·_\x8r_\x8e_\x8a_\x8d_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·read·the·contents·of·a·directory | 25 | ····*·_\x8r_\x8e_\x8a_\x8d_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·read·the·contents·of·a·directory |
| 26 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·make·a·directory | 26 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·make·a·directory |
| 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 62, 20 lines modified | Offset 62, 20 lines modified | ||
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·external·programs.·Currently,·this·makes·a·difference·only·under·Microsoft·Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that·are·not·part·of·Cygwin.··Fortunately,·programs·compiled·under·Cygwin·know·were·to·look·for·files·whose·paths·start·with·something·like·<span·class="tt">C:/</span>,·so·it·is·safe·always·to·concatenate·with·the·value·of·<a·href="_root__Path.html">rootPath</a>,·even·when·it·is·unknown·whether·the·external·program·has·been·compiled·under·Cygwin.</p> | 64 | ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·external·programs.·Currently,·this·makes·a·difference·only·under·Microsoft·Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that·are·not·part·of·Cygwin.··Fortunately,·programs·compiled·under·Cygwin·know·were·to·look·for·files·whose·paths·start·with·something·like·<span·class="tt">C:/</span>,·so·it·is·safe·always·to·concatenate·with·the·value·of·<a·href="_root__Path.html">rootPath</a>,·even·when·it·is·unknown·whether·the·external·program·has·been·compiled·under·Cygwin.</p> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 68 | o1·=·/tmp/M2- | 68 | o1·=·/tmp/M2-3486057-0/0</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootPath·|·fn | 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootPath·|·fn |
| 72 | o2·=·/tmp/M2- | 72 | o2·=·/tmp/M2-3486057-0/0</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ········</table> | 74 | ········</table> |
| 75 | ······</div> | 75 | ······</div> |
| 76 | ······<div> | 76 | ······<div> |
| 77 | ········<h2>See·also</h2> | 77 | ········<h2>See·also</h2> |
| 78 | ········<ul> | 78 | ········<ul> |
| 79 | ··········<li> | 79 | ··········<li> |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that | 16 | Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that |
| 17 | are·not·part·of·Cygwin.·Fortunately,·programs·compiled·under·Cygwin·know·were | 17 | are·not·part·of·Cygwin.·Fortunately,·programs·compiled·under·Cygwin·know·were |
| 18 | to·look·for·files·whose·paths·start·with·something·like·C:/,·so·it·is·safe | 18 | to·look·for·files·whose·paths·start·with·something·like·C:/,·so·it·is·safe |
| 19 | always·to·concatenate·with·the·value·of·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h,·even·when·it·is·unknown | 19 | always·to·concatenate·with·the·value·of·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h,·even·when·it·is·unknown |
| 20 | whether·the·external·program·has·been·compiled·under·Cygwin. | 20 | whether·the·external·program·has·been·compiled·under·Cygwin. |
| 21 | i1·:·fn·=·temporaryFileName() | 21 | i1·:·fn·=·temporaryFileName() |
| 22 | o1·=·/tmp/M2- | 22 | o1·=·/tmp/M2-3486057-0/0 |
| 23 | i2·:·rootPath·|·fn | 23 | i2·:·rootPath·|·fn |
| 24 | o2·=·/tmp/M2- | 24 | o2·=·/tmp/M2-3486057-0/0 |
| 25 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I | 26 | ····*·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I |
| 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 28 | The·object·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g. | 28 | The·object·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g. |
| Offset 62, 20 lines modified | Offset 62, 20 lines modified | ||
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·an·external·browser.·Currently,·this·makes·a·difference·only·under·Microsoft·Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that·are·not·part·of·Cygwin.··Fortunately,·programs·compiled·under·Cygwin·know·were·to·look·for·files·whose·paths·start·with·something·like·<span·class="tt">C:/</span>,·so·it·is·safe·always·to·concatenate·with·the·value·of·<a·href="_root__Path.html">rootPath</a>,·even·when·it·is·unknown·whether·the·external·program·has·been·compiled·under·Cygwin.</p> | 64 | ········<p>This·string·may·be·concatenated·with·an·absolute·path·to·get·one·understandable·by·an·external·browser.·Currently,·this·makes·a·difference·only·under·Microsoft·Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that·are·not·part·of·Cygwin.··Fortunately,·programs·compiled·under·Cygwin·know·were·to·look·for·files·whose·paths·start·with·something·like·<span·class="tt">C:/</span>,·so·it·is·safe·always·to·concatenate·with·the·value·of·<a·href="_root__Path.html">rootPath</a>,·even·when·it·is·unknown·whether·the·external·program·has·been·compiled·under·Cygwin.</p> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 68 | o1·=·/tmp/M2- | 68 | o1·=·/tmp/M2-3506000-0/0</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootURI·|·fn | 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootURI·|·fn |
| 72 | o2·=·file:///tmp/M2- | 72 | o2·=·file:///tmp/M2-3506000-0/0</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ········</table> | 74 | ········</table> |
| 75 | ······</div> | 75 | ······</div> |
| 76 | ······<div> | 76 | ······<div> |
| 77 | ········<h2>See·also</h2> | 77 | ········<h2>See·also</h2> |
| 78 | ········<ul> | 78 | ········<ul> |
| 79 | ··········<li> | 79 | ··········<li> |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that | 16 | Windows·with·Cygwin,·but·there·it's·crucial·for·those·external·programs·that |
| 17 | are·not·part·of·Cygwin.·Fortunately,·programs·compiled·under·Cygwin·know·were | 17 | are·not·part·of·Cygwin.·Fortunately,·programs·compiled·under·Cygwin·know·were |
| 18 | to·look·for·files·whose·paths·start·with·something·like·C:/,·so·it·is·safe | 18 | to·look·for·files·whose·paths·start·with·something·like·C:/,·so·it·is·safe |
| 19 | always·to·concatenate·with·the·value·of·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h,·even·when·it·is·unknown | 19 | always·to·concatenate·with·the·value·of·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h,·even·when·it·is·unknown |
| 20 | whether·the·external·program·has·been·compiled·under·Cygwin. | 20 | whether·the·external·program·has·been·compiled·under·Cygwin. |
| 21 | i1·:·fn·=·temporaryFileName() | 21 | i1·:·fn·=·temporaryFileName() |
| 22 | o1·=·/tmp/M2- | 22 | o1·=·/tmp/M2-3506000-0/0 |
| 23 | i2·:·rootURI·|·fn | 23 | i2·:·rootURI·|·fn |
| 24 | o2·=·file:///tmp/M2- | 24 | o2·=·file:///tmp/M2-3506000-0/0 |
| 25 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h | 26 | ····*·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h |
| 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 28 | The·object·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g. | 28 | The·object·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g. |
| Offset 74, 20 lines modified | Offset 74, 20 lines modified | ||
| 74 | ·····························1 | 74 | ·····························1 |
| 75 | o4·:·R-module,·submodule·of·R</code></pre> | 75 | o4·:·R-module,·submodule·of·R</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i5·:·f·=·temporaryFileName() | 78 | <td>··············<pre><code·class="language-macaulay2">i5·:·f·=·temporaryFileName() |
| 79 | o5·=·/tmp/M2- | 79 | o5·=·/tmp/M2-3505340-0/0</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i6·:·f·<<·toString·(p,m,M)·<<·close | 82 | <td>··············<pre><code·class="language-macaulay2">i6·:·f·<<·toString·(p,m,M)·<<·close |
| 83 | o6·=·/tmp/M2- | 83 | o6·=·/tmp/M2-3505340-0/0 |
| 84 | o6·:·File</code></pre> | 84 | o6·:·File</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i7·:·get·f | 87 | <td>··············<pre><code·class="language-macaulay2">i7·:·get·f |
| 88 | o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2, | 88 | o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2, |
| Offset 28, 18 lines modified | Offset 28, 18 lines modified | ||
| 28 | o4·=·image·|·x2·x2-y2·xyz7·| | 28 | o4·=·image·|·x2·x2-y2·xyz7·| |
| 29 | ·····························1 | 29 | ·····························1 |
| 30 | o4·:·R-module,·submodule·of·R | 30 | o4·:·R-module,·submodule·of·R |
| 31 | i5·:·f·=·temporaryFileName() | 31 | i5·:·f·=·temporaryFileName() |
| 32 | o5·=·/tmp/M2- | 32 | o5·=·/tmp/M2-3505340-0/0 |
| 33 | i6·:·f·<<·toString·(p,m,M)·<<·close | 33 | i6·:·f·<<·toString·(p,m,M)·<<·close |
| 34 | o6·=·/tmp/M2- | 34 | o6·=·/tmp/M2-3505340-0/0 |
| 35 | o6·:·File | 35 | o6·:·File |
| 36 | i7·:·get·f | 36 | i7·:·get·f |
| 37 | o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2, | 37 | o7·=·(x^3-3*x^2*y+3*x*y^2-y^3-3*x^2+6*x*y-3*y^2+3*x-3*y-1,matrix·{{x^2, |
| 38 | ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}}) | 38 | ·····x^2-y^2,·x*y*z^7}},image·matrix·{{x^2,·x^2-y^2,·x*y*z^7}}) |
| 39 | i8·:·(p',m',M')·=·value·get·f | 39 | i8·:·(p',m',M')·=·value·get·f |
| Offset 320, 19 lines modified | Offset 320, 19 lines modified | ||
| 320 | <td>··············<pre><code·class="language-macaulay2">i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;</code></pre> | 320 | <td>··············<pre><code·class="language-macaulay2">i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;</code></pre> |
| 321 | </td>··········</tr> | 321 | </td>··········</tr> |
| 322 | ··········<tr> | 322 | ··········<tr> |
| 323 | <td>··············<pre><code·class="language-macaulay2">i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;</code></pre> | 323 | <td>··············<pre><code·class="language-macaulay2">i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;</code></pre> |
| 324 | </td>··········</tr> | 324 | </td>··········</tr> |
| 325 | ··········<tr> | 325 | ··········<tr> |
| 326 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·X·=·solve(A,B); | 326 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·X·=·solve(A,B); |
| 327 | ·--·used·0.000 | 327 | ·--·used·0.000648597s·(cpu);·0.000642826s·(thread);·0s·(gc)</code></pre> |
| 328 | </td>··········</tr> | 328 | </td>··········</tr> |
| 329 | ··········<tr> | 329 | ··········<tr> |
| 330 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·X·=·solve(A,B,·MaximalRank=>true); | 330 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 331 | ·--·used· | 331 | ·--·used·0.00013313s·(cpu);·0.00013318s·(thread);·0s·(gc)</code></pre> |
| 332 | </td>··········</tr> | 332 | </td>··········</tr> |
| 333 | ··········<tr> | 333 | ··········<tr> |
| 334 | <td>··············<pre><code·class="language-macaulay2">i32·:·norm(A*X-B) | 334 | <td>··············<pre><code·class="language-macaulay2">i32·:·norm(A*X-B) |
| 335 | o32·=·5.111850690840453e-15 | 335 | o32·=·5.111850690840453e-15 |
| 336 | o32·:·RR·(of·precision·53)</code></pre> | 336 | o32·:·RR·(of·precision·53)</code></pre> |
| Offset 353, 19 lines modified | Offset 353, 19 lines modified | ||
| 353 | <td>··············<pre><code·class="language-macaulay2">i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;</code></pre> | 353 | <td>··············<pre><code·class="language-macaulay2">i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;</code></pre> |
| 354 | </td>··········</tr> | 354 | </td>··········</tr> |
| 355 | ··········<tr> | 355 | ··········<tr> |
| 356 | <td>··············<pre><code·class="language-macaulay2">i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;</code></pre> | 356 | <td>··············<pre><code·class="language-macaulay2">i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;</code></pre> |
| 357 | </td>··········</tr> | 357 | </td>··········</tr> |
| 358 | ··········<tr> | 358 | ··········<tr> |
| 359 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·X·=·solve(A,B); | 359 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·X·=·solve(A,B); |
| 360 | ·--·used·0.1 | 360 | ·--·used·0.152198s·(cpu);·0.151826s·(thread);·0s·(gc)</code></pre> |
| 361 | </td>··········</tr> | 361 | </td>··········</tr> |
| 362 | ··········<tr> | 362 | ··········<tr> |
| 363 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·X·=·solve(A,B,·MaximalRank=>true); | 363 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 364 | ·--·used·0.1 | 364 | ·--·used·0.161831s·(cpu);·0.161927s·(thread);·0s·(gc)</code></pre> |
| 365 | </td>··········</tr> | 365 | </td>··········</tr> |
| 366 | ··········<tr> | 366 | ··········<tr> |
| 367 | <td>··············<pre><code·class="language-macaulay2">i40·:·norm(A*X-B) | 367 | <td>··············<pre><code·class="language-macaulay2">i40·:·norm(A*X-B) |
| 368 | o40·=·1.491578274689709814082355885932e-28 | 368 | o40·=·1.491578274689709814082355885932e-28 |
| 369 | o40·:·RR·(of·precision·100)</code></pre> | 369 | o40·:·RR·(of·precision·100)</code></pre> |
| Offset 195, 33 lines modified | Offset 195, 33 lines modified | ||
| 195 | i24·:·printingPrecision·=·4; | 195 | i24·:·printingPrecision·=·4; |
| 196 | i25·:·N·=·40 | 196 | i25·:·N·=·40 |
| 197 | o25·=·40 | 197 | o25·=·40 |
| 198 | i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A; | 198 | i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A; |
| 199 | i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B; | 199 | i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B; |
| 200 | i30·:·time·X·=·solve(A,B); | 200 | i30·:·time·X·=·solve(A,B); |
| 201 | ·--·used·0.000 | 201 | ·--·used·0.000648597s·(cpu);·0.000642826s·(thread);·0s·(gc) |
| 202 | i31·:·time·X·=·solve(A,B,·MaximalRank=>true); | 202 | i31·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 203 | ·--·used· | 203 | ·--·used·0.00013313s·(cpu);·0.00013318s·(thread);·0s·(gc) |
| 204 | i32·:·norm(A*X-B) | 204 | i32·:·norm(A*X-B) |
| 205 | o32·=·5.111850690840453e-15 | 205 | o32·=·5.111850690840453e-15 |
| 206 | o32·:·RR·(of·precision·53) | 206 | o32·:·RR·(of·precision·53) |
| 207 | Over·higher·precision·RR·or·CC,·these·routines·will·be·much·slower·than·the | 207 | Over·higher·precision·RR·or·CC,·these·routines·will·be·much·slower·than·the |
| 208 | lower·precision·lapack·routines. | 208 | lower·precision·lapack·routines. |
| 209 | i33·:·N·=·100 | 209 | i33·:·N·=·100 |
| 210 | o33·=·100 | 210 | o33·=·100 |
| 211 | i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A; | 211 | i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A; |
| 212 | i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B; | 212 | i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B; |
| 213 | i38·:·time·X·=·solve(A,B); | 213 | i38·:·time·X·=·solve(A,B); |
| 214 | ·--·used·0.1 | 214 | ·--·used·0.152198s·(cpu);·0.151826s·(thread);·0s·(gc) |
| 215 | i39·:·time·X·=·solve(A,B,·MaximalRank=>true); | 215 | i39·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 216 | ·--·used·0.1 | 216 | ·--·used·0.161831s·(cpu);·0.161927s·(thread);·0s·(gc) |
| 217 | i40·:·norm(A*X-B) | 217 | i40·:·norm(A*X-B) |
| 218 | o40·=·1.491578274689709814082355885932e-28 | 218 | o40·=·1.491578274689709814082355885932e-28 |
| 219 | o40·:·RR·(of·precision·100) | 219 | o40·:·RR·(of·precision·100) |
| 220 | Giving·the·option·ClosestFit=>true,·in·the·case·when·the·field·is·RR·or·CC, | 220 | Giving·the·option·ClosestFit=>true,·in·the·case·when·the·field·is·RR·or·CC, |
| 221 | uses·a·least·squares·algorithm·to·find·a·best·fit·solution. | 221 | uses·a·least·squares·algorithm·to·find·a·best·fit·solution. |
| Offset 53, 14 lines modified | Offset 53, 24 lines modified | ||
| 53 | <span><a·title="an·optional·argument"·href="___Syzygies.html">Syzygies</a>·--·an·optional·argument</span>··········</li> | 53 | <span><a·title="an·optional·argument"·href="___Syzygies.html">Syzygies</a>·--·an·optional·argument</span>··········</li> |
| 54 | ········</ul> | 54 | ········</ul> |
| 55 | ········<h4>Symbols·used·as·an·option·name</h4> | 55 | ········<h4>Symbols·used·as·an·option·name</h4> |
| 56 | ········<ul> | 56 | ········<ul> |
| 57 | ··········<li> | 57 | ··········<li> |
| 58 | <span><a·title="an·optional·argument"·href="___Threads.html">Threads</a>·--·an·optional·argument</span>··········</li> | 58 | <span><a·title="an·optional·argument"·href="___Threads.html">Threads</a>·--·an·optional·argument</span>··········</li> |
| 59 | ··········<li> | 59 | ··········<li> |
| 60 | <span><a·title="an·optional·argument"·href="___Strategy.html">Strategy</a>·--·an·optional·argument</span>··········</li> | ||
| 61 | ··········<li> | ||
| 62 | <span><a·title="an·optional·argument"·href="___Basis__Element__Limit.html">BasisElementLimit</a>·--·an·optional·argument</span>··········</li> | ||
| 63 | ··········<li> | ||
| 64 | <span><a·title="an·optional·argument"·href="___Degree__Limit.html">DegreeLimit</a>·--·an·optional·argument</span>··········</li> | ||
| 65 | ··········<li> | ||
| 66 | <span><a·title="an·optional·argument"·href="___Pair__Limit.html">PairLimit</a>·--·an·optional·argument</span>··········</li> | ||
| 67 | ··········<li> | ||
| 68 | <span><a·title="an·optional·argument"·href="___Generic.html">Generic</a>·--·an·optional·argument</span>··········</li> | ||
| 69 | ··········<li> | ||
| 60 | <span><a·title="an·optional·argument"·href="___Degree__Group.html">DegreeGroup</a>·--·an·optional·argument</span>··········</li> | 70 | <span><a·title="an·optional·argument"·href="___Degree__Group.html">DegreeGroup</a>·--·an·optional·argument</span>··········</li> |
| 61 | ··········<li> | 71 | ··········<li> |
| 62 | <span><a·title="an·optional·argument"·href="___Variables.html">Variables</a>·--·an·optional·argument</span>··········</li> | 72 | <span><a·title="an·optional·argument"·href="___Variables.html">Variables</a>·--·an·optional·argument</span>··········</li> |
| 63 | ··········<li> | 73 | ··········<li> |
| 64 | <span><a·title="an·optional·argument"·href="___Degree__Lift.html">DegreeLift</a>·--·an·optional·argument</span>··········</li> | 74 | <span><a·title="an·optional·argument"·href="___Degree__Lift.html">DegreeLift</a>·--·an·optional·argument</span>··········</li> |
| 65 | ··········<li> | 75 | ··········<li> |
| 66 | <span><a·title="an·optional·argument"·href="___Variable__Base__Name.html">VariableBaseName</a>·--·an·optional·argument</span>··········</li> | 76 | <span><a·title="an·optional·argument"·href="___Variable__Base__Name.html">VariableBaseName</a>·--·an·optional·argument</span>··········</li> |
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| 81 | ··········<li> | 91 | ··········<li> |
| 82 | <span><a·title="an·optional·argument"·href="___Constants.html">Constants</a>·--·an·optional·argument</span>··········</li> | 92 | <span><a·title="an·optional·argument"·href="___Constants.html">Constants</a>·--·an·optional·argument</span>··········</li> |
| 83 | ··········<li> | 93 | ··········<li> |
| 84 | <span><a·title="an·optional·argument"·href="___Skew__Commutative.html">SkewCommutative</a>·--·an·optional·argument</span>··········</li> | 94 | <span><a·title="an·optional·argument"·href="___Skew__Commutative.html">SkewCommutative</a>·--·an·optional·argument</span>··········</li> |
| 85 | ··········<li> | 95 | ··········<li> |
| 86 | <span><a·title="an·optional·argument"·href="___Degree__Map.html">DegreeMap</a>·--·an·optional·argument</span>··········</li> | 96 | <span><a·title="an·optional·argument"·href="___Degree__Map.html">DegreeMap</a>·--·an·optional·argument</span>··········</li> |
| 87 | ··········<li> | 97 | ··········<li> |
| 88 | <span><a·title="an·optional·argument"·href="___Generic.html">Generic</a>·--·an·optional·argument</span>··········</li> | ||
| 89 | ··········<li> | ||
| 90 | <span><a·title="an·optional·argument"·href="___Strategy.html">Strategy</a>·--·an·optional·argument</span>··········</li> | ||
| 91 | ··········<li> | ||
| 92 | <span><a·title="an·optional·argument"·href="___Degree__Limit.html">DegreeLimit</a>·--·an·optional·argument</span>··········</li> | ||
| 93 | ··········<li> | ||
| 94 | <span><a·title="an·optional·argument"·href="___Verbosity.html">Verbosity</a>·--·an·optional·argument</span>··········</li> | 98 | <span><a·title="an·optional·argument"·href="___Verbosity.html">Verbosity</a>·--·an·optional·argument</span>··········</li> |
| 95 | ··········<li> | 99 | ··········<li> |
| 96 | <span><a·title="an·optional·argument"·href="___Basis__Element__Limit.html">BasisElementLimit</a>·--·an·optional·argument</span>··········</li> | ||
| 97 | ··········<li> | ||
| 98 | <span><a·title="an·optional·argument"·href="___ | 100 | <span><a·title="an·optional·argument"·href="___Codimension__Limit.html">CodimensionLimit</a>·--·an·optional·argument</span>··········</li> |
| 99 | ··········<li> | 101 | ··········<li> |
| 100 | <span><a·title="an·optional·argument"·href="___Verify.html">Verify</a>·--·an·optional·argument</span>··········</li> | 102 | <span><a·title="an·optional·argument"·href="___Verify.html">Verify</a>·--·an·optional·argument</span>··········</li> |
| 101 | ··········<li> | 103 | ··········<li> |
| 102 | <span><a·title="an·optional·argument"·href="___Codimension__Limit.html">CodimensionLimit</a>·--·an·optional·argument</span>··········</li> | ||
| 103 | ··········<li> | ||
| 104 | <span><a·title="an·optional·argument"·href="___Coefficient__Ring.html">CoefficientRing</a>·--·an·optional·argument</span>··········</li> | 104 | <span><a·title="an·optional·argument"·href="___Coefficient__Ring.html">CoefficientRing</a>·--·an·optional·argument</span>··········</li> |
| 105 | ··········<li> | 105 | ··········<li> |
| 106 | <span><a·title="an·optional·argument"·href="___Follow__Links.html">FollowLinks</a>·--·an·optional·argument</span>··········</li> | 106 | <span><a·title="an·optional·argument"·href="___Follow__Links.html">FollowLinks</a>·--·an·optional·argument</span>··········</li> |
| 107 | ··········<li> | 107 | ··········<li> |
| 108 | <span><a·title="an·optional·argument"·href="___Exclude.html">Exclude</a>·--·an·optional·argument</span>··········</li> | 108 | <span><a·title="an·optional·argument"·href="___Exclude.html">Exclude</a>·--·an·optional·argument</span>··········</li> |
| 109 | ··········<li> | 109 | ··········<li> |
| 110 | <span><a·title="an·optional·argument"·href="___Install__Prefix.html">InstallPrefix</a>·--·an·optional·argument</span>··········</li> | 110 | <span><a·title="an·optional·argument"·href="___Install__Prefix.html">InstallPrefix</a>·--·an·optional·argument</span>··········</li> |
| Offset 6, 36 lines modified | Offset 6, 36 lines modified | ||
| 6 | =============================================================================== | 6 | =============================================================================== |
| 7 | *\x8**\x8**\x8**\x8**\x8**\x8*·s\x8sy\x8ym\x8mb\x8bo\x8ol\x8ls\x8s·u\x8us\x8se\x8ed\x8d·a\x8as\x8s·t\x8th\x8he\x8e·n\x8na\x8am\x8me\x8e·o\x8or\x8r·v\x8va\x8al\x8lu\x8ue\x8e·o\x8of\x8f·a\x8an\x8n·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·*\x8**\x8**\x8**\x8**\x8**\x8* | 7 | *\x8**\x8**\x8**\x8**\x8**\x8*·s\x8sy\x8ym\x8mb\x8bo\x8ol\x8ls\x8s·u\x8us\x8se\x8ed\x8d·a\x8as\x8s·t\x8th\x8he\x8e·n\x8na\x8am\x8me\x8e·o\x8or\x8r·v\x8va\x8al\x8lu\x8ue\x8e·o\x8of\x8f·a\x8an\x8n·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·*\x8**\x8**\x8**\x8**\x8**\x8* |
| 8 | *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8* | 8 | *\x8**\x8**\x8**\x8*·M\x8Me\x8en\x8nu\x8u·*\x8**\x8**\x8**\x8* |
| 9 | *\x8**\x8**\x8*·S\x8Sy\x8ym\x8mb\x8bo\x8ol\x8ls\x8s·u\x8us\x8se\x8ed\x8d·a\x8as\x8s·a\x8an\x8n·o\x8op\x8pt\x8ti\x8io\x8on\x8n·n\x8na\x8am\x8me\x8e·o\x8or\x8r·v\x8va\x8al\x8lu\x8ue\x8e·*\x8**\x8**\x8* | 9 | *\x8**\x8**\x8*·S\x8Sy\x8ym\x8mb\x8bo\x8ol\x8ls\x8s·u\x8us\x8se\x8ed\x8d·a\x8as\x8s·a\x8an\x8n·o\x8op\x8pt\x8ti\x8io\x8on\x8n·n\x8na\x8am\x8me\x8e·o\x8or\x8r·v\x8va\x8al\x8lu\x8ue\x8e·*\x8**\x8**\x8* |
| 10 | ····*·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·--·an·optional·argument | 10 | ····*·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·--·an·optional·argument |
| 11 | *\x8**\x8**\x8*·S\x8Sy\x8ym\x8mb\x8bo\x8ol\x8ls\x8s·u\x8us\x8se\x8ed\x8d·a\x8as\x8s·a\x8an\x8n·o\x8op\x8pt\x8ti\x8io\x8on\x8n·n\x8na\x8am\x8me\x8e·*\x8**\x8**\x8* | 11 | *\x8**\x8**\x8*·S\x8Sy\x8ym\x8mb\x8bo\x8ol\x8ls\x8s·u\x8us\x8se\x8ed\x8d·a\x8as\x8s·a\x8an\x8n·o\x8op\x8pt\x8ti\x8io\x8on\x8n·n\x8na\x8am\x8me\x8e·*\x8**\x8**\x8* |
| 12 | ····*·_\x8T_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s·--·an·optional·argument | 12 | ····*·_\x8T_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s·--·an·optional·argument |
| 13 | ····*·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument | ||
| 14 | ····*·_\x8B_\x8a_\x8s_\x8i_\x8s_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 15 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 16 | ····*·_\x8P_\x8a_\x8i_\x8r_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 17 | ····*·_\x8G_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c·--·an·optional·argument | ||
| 13 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8G_\x8r_\x8o_\x8u_\x8p·--·an·optional·argument | 18 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8G_\x8r_\x8o_\x8u_\x8p·--·an·optional·argument |
| 14 | ····*·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8s·--·an·optional·argument | 19 | ····*·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8s·--·an·optional·argument |
| 15 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8f_\x8t·--·an·optional·argument | 20 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8f_\x8t·--·an·optional·argument |
| 16 | ····*·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8B_\x8a_\x8s_\x8e_\x8N_\x8a_\x8m_\x8e·--·an·optional·argument | 21 | ····*·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8B_\x8a_\x8s_\x8e_\x8N_\x8a_\x8m_\x8e·--·an·optional·argument |
| 17 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8R_\x8a_\x8n_\x8k·--·an·optional·argument | 22 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8R_\x8a_\x8n_\x8k·--·an·optional·argument |
| 18 | ····*·_\x8I_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8s·--·an·optional·argument | 23 | ····*·_\x8I_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8s·--·an·optional·argument |
| 19 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·an·optional·argument | 24 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·an·optional·argument |
| 20 | ····*·_\x8J_\x8o_\x8i_\x8n·--·an·optional·argument | 25 | ····*·_\x8J_\x8o_\x8i_\x8n·--·an·optional·argument |
| 21 | ····*·_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8S_\x8i_\x8z_\x8e·--·an·optional·argument | 26 | ····*·_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8S_\x8i_\x8z_\x8e·--·an·optional·argument |
| 22 | ····*·_\x8L_\x8o_\x8c_\x8a_\x8l·--·an·optional·argument | 27 | ····*·_\x8L_\x8o_\x8c_\x8a_\x8l·--·an·optional·argument |
| 23 | ····*·_\x8H_\x8e_\x8f_\x8t·--·an·optional·argument | 28 | ····*·_\x8H_\x8e_\x8f_\x8t·--·an·optional·argument |
| 24 | ····*·_\x8C_\x8o_\x8n_\x8s_\x8t_\x8a_\x8n_\x8t_\x8s·--·an·optional·argument | 29 | ····*·_\x8C_\x8o_\x8n_\x8s_\x8t_\x8a_\x8n_\x8t_\x8s·--·an·optional·argument |
| 25 | ····*·_\x8S_\x8k_\x8e_\x8w_\x8C_\x8o_\x8m_\x8m_\x8u_\x8t_\x8a_\x8t_\x8i_\x8v_\x8e·--·an·optional·argument | 30 | ····*·_\x8S_\x8k_\x8e_\x8w_\x8C_\x8o_\x8m_\x8m_\x8u_\x8t_\x8a_\x8t_\x8i_\x8v_\x8e·--·an·optional·argument |
| 26 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p·--·an·optional·argument | 31 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p·--·an·optional·argument |
| 27 | ····*·_\x8G_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c·--·an·optional·argument | ||
| 28 | ····*·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument | ||
| 29 | ····*·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 30 | ····*·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8i_\x8t_\x8y·--·an·optional·argument | 32 | ····*·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8i_\x8t_\x8y·--·an·optional·argument |
| 31 | ····*·_\x8B_\x8a_\x8s_\x8i_\x8s_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 32 | ····*·_\x8P_\x8a_\x8i_\x8r_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 33 | ····*·_\x8V_\x8e_\x8r_\x8i_\x8f_\x8y·--·an·optional·argument | ||
| 34 | ····*·_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | 33 | ····*·_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument |
| 34 | ····*·_\x8V_\x8e_\x8r_\x8i_\x8f_\x8y·--·an·optional·argument | ||
| 35 | ····*·_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8R_\x8i_\x8n_\x8g·--·an·optional·argument | 35 | ····*·_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8R_\x8i_\x8n_\x8g·--·an·optional·argument |
| 36 | ····*·_\x8F_\x8o_\x8l_\x8l_\x8o_\x8w_\x8L_\x8i_\x8n_\x8k_\x8s·--·an·optional·argument | 36 | ····*·_\x8F_\x8o_\x8l_\x8l_\x8o_\x8w_\x8L_\x8i_\x8n_\x8k_\x8s·--·an·optional·argument |
| 37 | ····*·_\x8E_\x8x_\x8c_\x8l_\x8u_\x8d_\x8e·--·an·optional·argument | 37 | ····*·_\x8E_\x8x_\x8c_\x8l_\x8u_\x8d_\x8e·--·an·optional·argument |
| 38 | ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8P_\x8r_\x8e_\x8f_\x8i_\x8x·--·an·optional·argument | 38 | ····*·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8P_\x8r_\x8e_\x8f_\x8i_\x8x·--·an·optional·argument |
| 39 | ····*·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8y_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument | 39 | ····*·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8y_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument |
| 40 | ····*·_\x8C_\x8h_\x8a_\x8n_\x8g_\x8e_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument | 40 | ····*·_\x8C_\x8h_\x8a_\x8n_\x8g_\x8e_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument |
| 41 | ····*·_\x8M_\x8i_\x8n_\x8i_\x8m_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument | 41 | ····*·_\x8M_\x8i_\x8n_\x8i_\x8m_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument |
| Offset 85, 73 lines modified | Offset 85, 73 lines modified | ||
| 85 | ······</div> | 85 | ······</div> |
| 86 | ······<div> | 86 | ······<div> |
| 87 | ········<h2>Description</h2> | 87 | ········<h2>Description</h2> |
| 88 | ········<table·class="examples"> | 88 | ········<table·class="examples"> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" | 90 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" |
| 91 | o1·=·/tmp/M2- | 91 | o1·=·/tmp/M2-3502392-0/0/</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" |
| 95 | o2·=·/tmp/M2- | 95 | o2·=·/tmp/M2-3502392-0/1/</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/") | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/") |
| 99 | o3·=·/tmp/M2- | 99 | o3·=·/tmp/M2-3502392-0/0/a/</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/") | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/") |
| 103 | o4·=·/tmp/M2- | 103 | o4·=·/tmp/M2-3502392-0/0/b/</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/") | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/") |
| 107 | o5·=·/tmp/M2- | 107 | o5·=·/tmp/M2-3502392-0/0/b/c/</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close | 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 111 | o6·=·/tmp/M2- | 111 | o6·=·/tmp/M2-3502392-0/0/a/f |
| 112 | o6·:·File</code></pre> | 112 | o6·:·File</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close | 115 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 116 | o7·=·/tmp/M2- | 116 | o7·=·/tmp/M2-3502392-0/0/a/g |
| 117 | o7·:·File</code></pre> | 117 | o7·:·File</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 120 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 121 | o8·=·/tmp/M2- | 121 | o8·=·/tmp/M2-3502392-0/0/b/c/g |
| 122 | o8·:·File</code></pre> | 122 | o8·:·File</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i9·:·symlinkDirectory(src,dst,Verbose=>true) | 125 | <td>··············<pre><code·class="language-macaulay2">i9·:·symlinkDirectory(src,dst,Verbose=>true) |
| 126 | --symlinking:·../../../0/b/c/g·->·/tmp/M2- | 126 | --symlinking:·../../../0/b/c/g·->·/tmp/M2-3502392-0/1/b/c/g |
| 127 | --symlinking:·../../0/a/ | 127 | --symlinking:·../../0/a/g·->·/tmp/M2-3502392-0/1/a/g |
| 128 | --symlinking:·../../0/a/ | 128 | --symlinking:·../../0/a/f·->·/tmp/M2-3502392-0/1/a/f</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·(dst|"b/c/g") | 131 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·(dst|"b/c/g") |
| 132 | o10·=·ho·there</code></pre> | 132 | o10·=·ho·there</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) | 135 | <td>··············<pre><code·class="language-macaulay2">i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) |
| 136 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2- | 136 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-3502392-0/1/b/c/g |
| 137 | --unsymlinking:·../../0/a/ | 137 | --unsymlinking:·../../0/a/g·->·/tmp/M2-3502392-0/1/a/g |
| 138 | --unsymlinking:·../../0/a/ | 138 | --unsymlinking:·../../0/a/f·->·/tmp/M2-3502392-0/1/a/f</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ········</table> | 140 | ········</table> |
| 141 | Now·we·remove·the·files·and·directories·we·created.········<table·class="examples"> | 141 | Now·we·remove·the·files·and·directories·we·created.········<table·class="examples"> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 143 | <td>··············<pre><code·class="language-macaulay2">i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 144 | o12·=·rm | 144 | o12·=·rm |
| Offset 31, 53 lines modified | Offset 31, 53 lines modified | ||
| 31 | ··········o·The·directory·tree·rooted·at·src·is·duplicated·by·a·directory·tree | 31 | ··········o·The·directory·tree·rooted·at·src·is·duplicated·by·a·directory·tree |
| 32 | ············rooted·at·dst.·The·files·in·the·source·tree·are·represented·by | 32 | ············rooted·at·dst.·The·files·in·the·source·tree·are·represented·by |
| 33 | ············relative·symbolic·links·in·the·destination·tree·to·the·original | 33 | ············relative·symbolic·links·in·the·destination·tree·to·the·original |
| 34 | ············files·in·the·source·tree. | 34 | ············files·in·the·source·tree. |
| 35 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 35 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 36 | i1·:·src·=·temporaryFileName()·|·"/" | 36 | i1·:·src·=·temporaryFileName()·|·"/" |
| 37 | o1·=·/tmp/M2- | 37 | o1·=·/tmp/M2-3502392-0/0/ |
| 38 | i2·:·dst·=·temporaryFileName()·|·"/" | 38 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 39 | o2·=·/tmp/M2- | 39 | o2·=·/tmp/M2-3502392-0/1/ |
| 40 | i3·:·makeDirectory·(src|"a/") | 40 | i3·:·makeDirectory·(src|"a/") |
| 41 | o3·=·/tmp/M2- | 41 | o3·=·/tmp/M2-3502392-0/0/a/ |
| 42 | i4·:·makeDirectory·(src|"b/") | 42 | i4·:·makeDirectory·(src|"b/") |
| 43 | o4·=·/tmp/M2- | 43 | o4·=·/tmp/M2-3502392-0/0/b/ |
| 44 | i5·:·makeDirectory·(src|"b/c/") | 44 | i5·:·makeDirectory·(src|"b/c/") |
| 45 | o5·=·/tmp/M2- | 45 | o5·=·/tmp/M2-3502392-0/0/b/c/ |
| 46 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 46 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 47 | o6·=·/tmp/M2- | 47 | o6·=·/tmp/M2-3502392-0/0/a/f |
| 48 | o6·:·File | 48 | o6·:·File |
| 49 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 49 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 50 | o7·=·/tmp/M2- | 50 | o7·=·/tmp/M2-3502392-0/0/a/g |
| 51 | o7·:·File | 51 | o7·:·File |
| 52 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 52 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 53 | o8·=·/tmp/M2- | 53 | o8·=·/tmp/M2-3502392-0/0/b/c/g |
| 54 | o8·:·File | 54 | o8·:·File |
| 55 | i9·:·symlinkDirectory(src,dst,Verbose=>true) | 55 | i9·:·symlinkDirectory(src,dst,Verbose=>true) |
| 56 | --symlinking:·../../../0/b/c/g·->·/tmp/M2- | 56 | --symlinking:·../../../0/b/c/g·->·/tmp/M2-3502392-0/1/b/c/g |
| 57 | --symlinking:·../../0/a/f·->·/tmp/M2-1763448-0/1/a/f | ||
| 58 | --symlinking:·../../0/a/g·->·/tmp/M2- | 57 | --symlinking:·../../0/a/g·->·/tmp/M2-3502392-0/1/a/g |
| 58 | --symlinking:·../../0/a/f·->·/tmp/M2-3502392-0/1/a/f | ||
| 59 | i10·:·get·(dst|"b/c/g") | 59 | i10·:·get·(dst|"b/c/g") |
| 60 | o10·=·ho·there | 60 | o10·=·ho·there |
| 61 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) | 61 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) |
| 62 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2- | 62 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-3502392-0/1/b/c/g |
| 63 | --unsymlinking:·../../0/a/f·->·/tmp/M2-1763448-0/1/a/f | ||
| 64 | --unsymlinking:·../../0/a/g·->·/tmp/M2- | 63 | --unsymlinking:·../../0/a/g·->·/tmp/M2-3502392-0/1/a/g |
| 64 | --unsymlinking:·../../0/a/f·->·/tmp/M2-3502392-0/1/a/f | ||
| 65 | Now·we·remove·the·files·and·directories·we·created. | 65 | Now·we·remove·the·files·and·directories·we·created. |
| 66 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 66 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 67 | o12·=·rm | 67 | o12·=·rm |
| 68 | o12·:·FunctionClosure | 68 | o12·:·FunctionClosure |
| 69 | i13·:·scan(reverse·findFiles·src,·rm) | 69 | i13·:·scan(reverse·findFiles·src,·rm) |
| Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>Description</h2> | 73 | ········<h2>Description</h2> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 77 | o1·=·/tmp/M2- | 77 | o1·=·/tmp/M2-3502663-0/0</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile("qwert",·fn)</code></pre> | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile("qwert",·fn)</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileExists·fn | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileExists·fn |
| Offset 13, 15 lines modified | Offset 13, 15 lines modified | ||
| 13 | ··········o·dst,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g | 13 | ··········o·dst,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g |
| 14 | ····*·Consequences: | 14 | ····*·Consequences: |
| 15 | ··········o·a·symbolic·link·at·the·location·in·the·directory·tree·specified·by | 15 | ··········o·a·symbolic·link·at·the·location·in·the·directory·tree·specified·by |
| 16 | ············dst·is·created,·pointing·to·src | 16 | ············dst·is·created,·pointing·to·src |
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | i1·:·fn·=·temporaryFileName() | 18 | i1·:·fn·=·temporaryFileName() |
| 19 | o1·=·/tmp/M2- | 19 | o1·=·/tmp/M2-3502663-0/0 |
| 20 | i2·:·symlinkFile("qwert",·fn) | 20 | i2·:·symlinkFile("qwert",·fn) |
| 21 | i3·:·fileExists·fn | 21 | i3·:·fileExists·fn |
| 22 | o3·=·false | 22 | o3·=·false |
| 23 | i4·:·readlink·fn | 23 | i4·:·readlink·fn |
| 24 | o4·=·qwert | 24 | o4·=·qwert |
| Offset 61, 20 lines modified | Offset 61, 20 lines modified | ||
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>Description</h2> | 63 | ········<h2>Description</h2> |
| 64 | The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no·collision·with·existing·files·will·occur.··The·files·will·be·removed·when·the·program·terminates,·unless·it·terminates·as·the·result·of·an·error.········<table·class="examples"> | 64 | The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no·collision·with·existing·files·will·occur.··The·files·will·be·removed·when·the·program·terminates,·unless·it·terminates·as·the·result·of·an·error.········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·temporaryFileName·()·|·".tex" | 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·temporaryFileName·()·|·".tex" |
| 67 | o1·=·/tmp/M2- | 67 | o1·=·/tmp/M2-3518772-0/0.tex</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i2·:·temporaryFileName·()·|·".html" | 70 | <td>··············<pre><code·class="language-macaulay2">i2·:·temporaryFileName·()·|·".html" |
| 71 | o2·=·/tmp/M2- | 71 | o2·=·/tmp/M2-3518772-0/1.html</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ········</table> | 73 | ········</table> |
| 74 | ········<p>This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a·directory·on·the·same·drive·called·<span·class="tt">/tmp</span>.</p> | 74 | ········<p>This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a·directory·on·the·same·drive·called·<span·class="tt">/tmp</span>.</p> |
| 75 | ········<p>If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may·be·necessary·to·concatenate·it·with·<a·href="_root__Path.html">rootPath</a>·or·<a·href="_root__U__R__I.html">rootURI</a>·to·enable·the·external·program·to·find·the·file.</p> | 75 | ········<p>If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may·be·necessary·to·concatenate·it·with·<a·href="_root__Path.html">rootPath</a>·or·<a·href="_root__U__R__I.html">rootURI</a>·to·enable·the·external·program·to·find·the·file.</p> |
| 76 | ········<p>The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable·<span·class="tt">TMPDIR</span>,·if·it·has·one.</p> | 76 | ········<p>The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable·<span·class="tt">TMPDIR</span>,·if·it·has·one.</p> |
| 77 | ········<p>If·<a·title="fork·the·process"·href="_fork.html">fork</a>·is·used,·then·the·parent·and·child·Macaulay2·processes·will·each·remove·their·own·temporary·files·upon·termination,·with·the·parent·removing·any·files·created·before·<a·title="fork·the·process"·href="_fork.html">fork</a>·was·called.</p> | 77 | ········<p>If·<a·title="fork·the·process"·href="_fork.html">fork</a>·is·used,·then·the·parent·and·child·Macaulay2·processes·will·each·remove·their·own·temporary·files·upon·termination,·with·the·parent·removing·any·files·created·before·<a·title="fork·the·process"·href="_fork.html">fork</a>·was·called.</p> |
| 78 | ······</div> | 78 | ······</div> |
| Offset 12, 18 lines modified | Offset 12, 18 lines modified | ||
| 12 | ··········o·a·unique·temporary·file·name. | 12 | ··········o·a·unique·temporary·file·name. |
| 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 13 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 14 | The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no | 14 | The·file·name·is·so·unique·that·even·with·various·suffixes·appended,·no |
| 15 | collision·with·existing·files·will·occur.·The·files·will·be·removed·when·the | 15 | collision·with·existing·files·will·occur.·The·files·will·be·removed·when·the |
| 16 | program·terminates,·unless·it·terminates·as·the·result·of·an·error. | 16 | program·terminates,·unless·it·terminates·as·the·result·of·an·error. |
| 17 | i1·:·temporaryFileName·()·|·".tex" | 17 | i1·:·temporaryFileName·()·|·".tex" |
| 18 | o1·=·/tmp/M2- | 18 | o1·=·/tmp/M2-3518772-0/0.tex |
| 19 | i2·:·temporaryFileName·()·|·".html" | 19 | i2·:·temporaryFileName·()·|·".html" |
| 20 | o2·=·/tmp/M2- | 20 | o2·=·/tmp/M2-3518772-0/1.html |
| 21 | This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a | 21 | This·function·will·work·under·Unix,·and·also·under·Windows·if·you·have·a |
| 22 | directory·on·the·same·drive·called·/tmp. | 22 | directory·on·the·same·drive·called·/tmp. |
| 23 | If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may | 23 | If·the·name·of·the·temporary·file·will·be·given·to·an·external·program,·it·may |
| 24 | be·necessary·to·concatenate·it·with·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·or·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·to·enable·the·external | 24 | be·necessary·to·concatenate·it·with·_\x8r_\x8o_\x8o_\x8t_\x8P_\x8a_\x8t_\x8h·or·_\x8r_\x8o_\x8o_\x8t_\x8U_\x8R_\x8I·to·enable·the·external |
| 25 | program·to·find·the·file. | 25 | program·to·find·the·file. |
| 26 | The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable | 26 | The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable |
| 27 | TMPDIR,·if·it·has·one. | 27 | TMPDIR,·if·it·has·one. |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | ········</ul> | 54 | ········</ul> |
| 55 | ······</div> | 55 | ······</div> |
| 56 | ······<div> | 56 | ······<div> |
| 57 | ········<h2>Description</h2> | 57 | ········<h2>Description</h2> |
| 58 | <span·class="tt">time·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·cpu·time·used,·and·returns·the·value·of·<span·class="tt">e</span>.··The·time·used·by·the·the·current·thread·and·garbage·collection·during·the·evaluation·of·<span·class="tt">e</span>·is·also·shown.········<table·class="examples"> | 58 | <span·class="tt">time·e</span>·evaluates·<span·class="tt">e</span>,·prints·the·amount·of·cpu·time·used,·and·returns·the·value·of·<span·class="tt">e</span>.··The·time·used·by·the·the·current·thread·and·garbage·collection·during·the·evaluation·of·<span·class="tt">e</span>·is·also·shown.········<table·class="examples"> |
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·3^30 | 60 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·3^30 |
| 61 | ·--·used· | 61 | ·--·used·2.1891e-05s·(cpu);·7.263e-06s·(thread);·0s·(gc) |
| 62 | o1·=·205891132094649</code></pre> | 62 | o1·=·205891132094649</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ········</table> | 64 | ········</table> |
| 65 | ······</div> | 65 | ······</div> |
| 66 | ······<div> | 66 | ······<div> |
| 67 | ········<h2>See·also</h2> | 67 | ········<h2>See·also</h2> |
| Offset 8, 15 lines modified | Offset 8, 15 lines modified | ||
| 8 | ····*···Usage: | 8 | ····*···Usage: |
| 9 | ············time·e | 9 | ············time·e |
| 10 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 10 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 11 | time·e·evaluates·e,·prints·the·amount·of·cpu·time·used,·and·returns·the·value | 11 | time·e·evaluates·e,·prints·the·amount·of·cpu·time·used,·and·returns·the·value |
| 12 | of·e.·The·time·used·by·the·the·current·thread·and·garbage·collection·during·the | 12 | of·e.·The·time·used·by·the·the·current·thread·and·garbage·collection·during·the |
| 13 | evaluation·of·e·is·also·shown. | 13 | evaluation·of·e·is·also·shown. |
| 14 | i1·:·time·3^30 | 14 | i1·:·time·3^30 |
| 15 | ·--·used· | 15 | ·--·used·2.1891e-05s·(cpu);·7.263e-06s·(thread);·0s·(gc) |
| 16 | o1·=·205891132094649 | 16 | o1·=·205891132094649 |
| 17 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 18 | ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation | 18 | ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation |
| 19 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began | 19 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began |
| 20 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed | 20 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed |
| 21 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed | 21 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed |
| Offset 46, 22 lines modified | Offset 46, 22 lines modified | ||
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | <span·class="tt">timing·e</span>·evaluates·<span·class="tt">e</span>·and·returns·a·list·of·type·<a·title="the·class·of·all·timing·results"·href="___Time.html">Time</a>·of·the·form·<span·class="tt">{t,v}</span>,·where·<span·class="tt">t</span>·is·the·number·of·seconds·of·cpu·timing·used,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p> | 47 | <span·class="tt">timing·e</span>·evaluates·<span·class="tt">e</span>·and·returns·a·list·of·type·<a·title="the·class·of·all·timing·results"·href="___Time.html">Time</a>·of·the·form·<span·class="tt">{t,v}</span>,·where·<span·class="tt">t</span>·is·the·number·of·seconds·of·cpu·timing·used,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p> |
| 48 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples"> | 48 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples"> |
| 49 | ··········<tr> | 49 | ··········<tr> |
| 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·timing·3^30 | 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·timing·3^30 |
| 51 | o1·=·205891132094649 | 51 | o1·=·205891132094649 |
| 52 | ·····--·.00001 | 52 | ·····--·.000015199·seconds |
| 53 | o1·:·Time</code></pre> | 53 | o1·:·Time</code></pre> |
| 54 | </td>··········</tr> | 54 | </td>··········</tr> |
| 55 | ··········<tr> | 55 | ··········<tr> |
| 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·oo | 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·oo |
| 57 | o2·=·Time{.00001 | 57 | o2·=·Time{.000015199,·205891132094649}</code></pre> |
| 58 | </td>··········</tr> | 58 | </td>··········</tr> |
| 59 | ········</table> | 59 | ········</table> |
| 60 | ······</div> | 60 | ······</div> |
| 61 | ······<div> | 61 | ······<div> |
| 62 | ········<h2>See·also</h2> | 62 | ········<h2>See·also</h2> |
| 63 | ········<ul> | 63 | ········<ul> |
| 64 | ··········<li> | 64 | ··········<li> |
| Offset 9, 20 lines modified | Offset 9, 20 lines modified | ||
| 9 | is·the·number·of·seconds·of·cpu·timing·used,·and·v·is·the·value·of·the | 9 | is·the·number·of·seconds·of·cpu·timing·used,·and·v·is·the·value·of·the |
| 10 | expression. | 10 | expression. |
| 11 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing | 11 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing |
| 12 | separately·in·a·comment·below·the·computed·value. | 12 | separately·in·a·comment·below·the·computed·value. |
| 13 | i1·:·timing·3^30 | 13 | i1·:·timing·3^30 |
| 14 | o1·=·205891132094649 | 14 | o1·=·205891132094649 |
| 15 | ·····--·.00001 | 15 | ·····--·.000015199·seconds |
| 16 | o1·:·Time | 16 | o1·:·Time |
| 17 | i2·:·peek·oo | 17 | i2·:·peek·oo |
| 18 | o2·=·Time{.00001 | 18 | o2·=·Time{.000015199,·205891132094649} |
| 19 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 19 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 20 | ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results | 20 | ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results |
| 21 | ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation | 21 | ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation |
| 22 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began | 22 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began |
| 23 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed | 23 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation·using·time·elapsed |
| 24 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed | 24 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed |
| 25 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | ···············"memtailor·version"·=>·1.0 | 98 | ···············"memtailor·version"·=>·1.0 |
| 99 | ···············"mpfi·version"·=>·1.5.4 | 99 | ···············"mpfi·version"·=>·1.5.4 |
| 100 | ···············"mpfr·version"·=>·4.2.1 | 100 | ···············"mpfr·version"·=>·4.2.1 |
| 101 | ···············"mpsolve·version"·=>·3.2.1 | 101 | ···············"mpsolve·version"·=>·3.2.1 |
| 102 | ···············"mysql·version"·=>·not·present | 102 | ···············"mysql·version"·=>·not·present |
| 103 | ···············"normaliz·version"·=>·3.10.4 | 103 | ···············"normaliz·version"·=>·3.10.4 |
| 104 | ···············"ntl·version"·=>·11.5.1 | 104 | ···············"ntl·version"·=>·11.5.1 |
| 105 | ···············"operating·system·release"·=>·6.1 | 105 | ···············"operating·system·release"·=>·6.10.11+bpo-amd64 |
| 106 | ···············"operating·system"·=>·Linux | 106 | ···············"operating·system"·=>·Linux |
| 107 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic·Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition·FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth·Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements·LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings·SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone·ChainComplexExtras·Varieties·Schubert2·PushForward·LocalRings·PruneComplex·BoijSoederberg·BGG·Bruns·InvolutiveBases·ConwayPolynomials·EdgeIdeals·FourTiTwo·StatePolytope·Polyhedra·Truncations·Polymake·gfanInterface·PieriMaps·Normaliz·Posets·XML·OpenMath·SCSCP·RationalPoints·MapleInterface·ConvexInterface·SRdeformations·NumericalAlgebraicGeometry·BeginningMacaulay2·FormalGroupLaws·Graphics·WeylGroups·HodgeIntegrals·Cyclotomic·Binomials·Kronecker·Nauty·ToricVectorBundles·ModuleDeformations·PHCpack·SimplicialDecomposability·BooleanGB·AdjointIdeal·Parametrization·Serialization·NAGtypes·NormalToricVarieties·DGAlgebras·Graphs·GraphicalModels·BIBasis·KustinMiller·Units·NautyGraphs·VersalDeformations·CharacteristicClasses·RandomIdeals·RandomObjects·RandomPlaneCurves·RandomSpaceCurves·RandomGenus14Curves·RandomCanonicalCurves·RandomCurves·TensorComplexes·MonomialAlgebras·QthPower·EliminationMatrices·EllipticIntegrals·Triplets·CompleteIntersectionResolutions·EagonResolution·MCMApproximations·MultiplierIdeals·InvariantRing·QuillenSuslin·EnumerationCurves·Book3264Examples·Divisor·EllipticCurves·HighestWeights·MinimalPrimes·Bertini·TorAlgebra·Permanents·BinomialEdgeIdeals·TateOnProducts·LatticePolytopes·FiniteFittingIdeals·HigherCIOperators·LieTypes·ConformalBlocks·M0nbar·AnalyzeSheafOnP1·MultiplierIdealsDim2·RunExternalM2·NumericalSchubertCalculus·ToricTopology·Cremona·Resultants·VectorFields·SLPexpressions·Miura·ResidualIntersections·Visualize·EquivariantGB·ExampleSystems·RationalMaps·FastMinors·RandomPoints·SwitchingFields·SpectralSequences·SectionRing·OldPolyhedra·OldToricVectorBundles·K3Carpets·ChainComplexOperations·NumericalCertification·PhylogeneticTrees·MonodromySolver·ReactionNetworks·PackageCitations·NumericSolutions·GradedLieAlgebras·InverseSystems·Pullback·EngineTests·SVDComplexes·RandomComplexes·CohomCalg·Topcom·Triangulations·ReflexivePolytopesDB·AbstractToricVarieties·Licenses·TestIdeals·FrobeniusThresholds·Seminormalization·AlgebraicSplines·TriangularSets·Chordal·Tropical·SymbolicPowers·Complexes·GroebnerWalk·RandomMonomialIdeals·Matroids·NumericalImplicitization·NonminimalComplexes·CoincidentRootLoci·RelativeCanonicalResolution·RandomCurvesOverVerySmallFiniteFields·StronglyStableIdeals·SLnEquivariantMatrices·CorrespondenceScrolls·NCAlgebra·SpaceCurves·ExteriorIdeals·ToricInvariants·SegreClasses·SemidefiniteProgramming·SumsOfSquares·MultiGradedRationalMap·AssociativeAlgebras·VirtualResolutions·Quasidegrees·DiffAlg·DeterminantalRepresentations·FGLM·SpechtModule·SchurComplexes·SimplicialPosets·SlackIdeals·PositivityToricBundles·SparseResultants·DecomposableSparseSystems·MixedMultiplicity·PencilsOfQuadrics·ThreadedGB·AdjunctionForSurfaces·VectorGraphics·GKMVarieties·MonomialIntegerPrograms·NoetherianOperators·Hadamard·StatGraphs·GraphicalModelsMLE·EigenSolver·MultiplicitySequence·ResolutionsOfStanleyReisnerRings·NumericalLinearAlgebra·ResLengthThree·MonomialOrbits·MultiprojectiveVarieties·SpecialFanoFourfolds·RationalPoints2·SuperLinearAlgebra·SubalgebraBases·AInfinity·LinearTruncations·ThinSincereQuivers·Python·BettiCharacters·Jets·FunctionFieldDesingularization·HomotopyLieAlgebra·TSpreadIdeals·RealRoots·ExteriorModules·K3Surfaces·GroebnerStrata·QuaternaryQuartics·CotangentSchubert·OnlineLookup·MergeTeX·Probability·Isomorphism·CodingTheory·WhitneyStratifications·JSON·ForeignFunctions·GeometricDecomposability·PseudomonomialPrimaryDecomposition·PolyominoIdeals·MatchingFields·CellularResolutions·SagbiGbDetection·A1BrouwerDegrees·QuadraticIdealExamplesByRoos·TerraciniLoci·MatrixSchubert·RInterface·OIGroebnerBases·PlaneCurveLinearSeries·Valuations·SchurVeronese·VNumber·TropicalToric·MultigradedBGG·AbstractSimplicialComplexes·MultigradedImplicitization·Msolve·Permutations·SCMAlgebras·NumericalSemigroups | 107 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic·Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition·FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth·Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements·LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings·SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone·ChainComplexExtras·Varieties·Schubert2·PushForward·LocalRings·PruneComplex·BoijSoederberg·BGG·Bruns·InvolutiveBases·ConwayPolynomials·EdgeIdeals·FourTiTwo·StatePolytope·Polyhedra·Truncations·Polymake·gfanInterface·PieriMaps·Normaliz·Posets·XML·OpenMath·SCSCP·RationalPoints·MapleInterface·ConvexInterface·SRdeformations·NumericalAlgebraicGeometry·BeginningMacaulay2·FormalGroupLaws·Graphics·WeylGroups·HodgeIntegrals·Cyclotomic·Binomials·Kronecker·Nauty·ToricVectorBundles·ModuleDeformations·PHCpack·SimplicialDecomposability·BooleanGB·AdjointIdeal·Parametrization·Serialization·NAGtypes·NormalToricVarieties·DGAlgebras·Graphs·GraphicalModels·BIBasis·KustinMiller·Units·NautyGraphs·VersalDeformations·CharacteristicClasses·RandomIdeals·RandomObjects·RandomPlaneCurves·RandomSpaceCurves·RandomGenus14Curves·RandomCanonicalCurves·RandomCurves·TensorComplexes·MonomialAlgebras·QthPower·EliminationMatrices·EllipticIntegrals·Triplets·CompleteIntersectionResolutions·EagonResolution·MCMApproximations·MultiplierIdeals·InvariantRing·QuillenSuslin·EnumerationCurves·Book3264Examples·Divisor·EllipticCurves·HighestWeights·MinimalPrimes·Bertini·TorAlgebra·Permanents·BinomialEdgeIdeals·TateOnProducts·LatticePolytopes·FiniteFittingIdeals·HigherCIOperators·LieTypes·ConformalBlocks·M0nbar·AnalyzeSheafOnP1·MultiplierIdealsDim2·RunExternalM2·NumericalSchubertCalculus·ToricTopology·Cremona·Resultants·VectorFields·SLPexpressions·Miura·ResidualIntersections·Visualize·EquivariantGB·ExampleSystems·RationalMaps·FastMinors·RandomPoints·SwitchingFields·SpectralSequences·SectionRing·OldPolyhedra·OldToricVectorBundles·K3Carpets·ChainComplexOperations·NumericalCertification·PhylogeneticTrees·MonodromySolver·ReactionNetworks·PackageCitations·NumericSolutions·GradedLieAlgebras·InverseSystems·Pullback·EngineTests·SVDComplexes·RandomComplexes·CohomCalg·Topcom·Triangulations·ReflexivePolytopesDB·AbstractToricVarieties·Licenses·TestIdeals·FrobeniusThresholds·Seminormalization·AlgebraicSplines·TriangularSets·Chordal·Tropical·SymbolicPowers·Complexes·GroebnerWalk·RandomMonomialIdeals·Matroids·NumericalImplicitization·NonminimalComplexes·CoincidentRootLoci·RelativeCanonicalResolution·RandomCurvesOverVerySmallFiniteFields·StronglyStableIdeals·SLnEquivariantMatrices·CorrespondenceScrolls·NCAlgebra·SpaceCurves·ExteriorIdeals·ToricInvariants·SegreClasses·SemidefiniteProgramming·SumsOfSquares·MultiGradedRationalMap·AssociativeAlgebras·VirtualResolutions·Quasidegrees·DiffAlg·DeterminantalRepresentations·FGLM·SpechtModule·SchurComplexes·SimplicialPosets·SlackIdeals·PositivityToricBundles·SparseResultants·DecomposableSparseSystems·MixedMultiplicity·PencilsOfQuadrics·ThreadedGB·AdjunctionForSurfaces·VectorGraphics·GKMVarieties·MonomialIntegerPrograms·NoetherianOperators·Hadamard·StatGraphs·GraphicalModelsMLE·EigenSolver·MultiplicitySequence·ResolutionsOfStanleyReisnerRings·NumericalLinearAlgebra·ResLengthThree·MonomialOrbits·MultiprojectiveVarieties·SpecialFanoFourfolds·RationalPoints2·SuperLinearAlgebra·SubalgebraBases·AInfinity·LinearTruncations·ThinSincereQuivers·Python·BettiCharacters·Jets·FunctionFieldDesingularization·HomotopyLieAlgebra·TSpreadIdeals·RealRoots·ExteriorModules·K3Surfaces·GroebnerStrata·QuaternaryQuartics·CotangentSchubert·OnlineLookup·MergeTeX·Probability·Isomorphism·CodingTheory·WhitneyStratifications·JSON·ForeignFunctions·GeometricDecomposability·PseudomonomialPrimaryDecomposition·PolyominoIdeals·MatchingFields·CellularResolutions·SagbiGbDetection·A1BrouwerDegrees·QuadraticIdealExamplesByRoos·TerraciniLoci·MatrixSchubert·RInterface·OIGroebnerBases·PlaneCurveLinearSeries·Valuations·SchurVeronese·VNumber·TropicalToric·MultigradedBGG·AbstractSimplicialComplexes·MultigradedImplicitization·Msolve·Permutations·SCMAlgebras·NumericalSemigroups |
| 108 | ···············"pointer·size"·=>·8 | 108 | ···············"pointer·size"·=>·8 |
| 109 | ···············"python·version"·=>·3.12.7 | 109 | ···············"python·version"·=>·3.12.7 |
| 110 | ···············"readline·version"·=>·8.2 | 110 | ···············"readline·version"·=>·8.2 |
| 111 | ···············"scscp·version"·=>·not·present | 111 | ···············"scscp·version"·=>·not·present |
| 112 | ···············"tbb·version"·=>·2021.12 | 112 | ···············"tbb·version"·=>·2021.12 |
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| 66 | ···············"mpfr·version"·=>·4.2.1 | 66 | ···············"mpfr·version"·=>·4.2.1 |
| 67 | ···············"mpsolve·version"·=>·3.2.1 | 67 | ···············"mpsolve·version"·=>·3.2.1 |
| 68 | ···············"mysql·version"·=>·not·present | 68 | ···············"mysql·version"·=>·not·present |
| 69 | ···············"normaliz·version"·=>·3.10.4 | 69 | ···············"normaliz·version"·=>·3.10.4 |
| 70 | ···············"ntl·version"·=>·11.5.1 | 70 | ···············"ntl·version"·=>·11.5.1 |
| 71 | ···············"operating·system·release"·=>·6.1 | 71 | ···············"operating·system·release"·=>·6.10.11+bpo-amd64 |
| 72 | ···············"operating·system"·=>·Linux | 72 | ···············"operating·system"·=>·Linux |
| 73 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic | 73 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic |
| 74 | Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition | 74 | Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition |
| 75 | FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth | 75 | FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth |
| 76 | Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements | 76 | Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements |
| 77 | LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings | 77 | LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings |
| 78 | SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone | 78 | SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone |
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| 2051 | ····*·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l_\x8s_\x8·_\x8u_\x8s_\x8e_\x8d_\x8·_\x8a_\x8s_\x8·_\x8t_\x8h_\x8e_\x8·_\x8n_\x8a_\x8m_\x8e_\x8·_\x8o_\x8r_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e_\x8·_\x8o_\x8f_\x8·_\x8a_\x8n_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8a_\x8r_\x8g_\x8u_\x8m_\x8e_\x8n_\x8t | 2051 | ····*·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l_\x8s_\x8·_\x8u_\x8s_\x8e_\x8d_\x8·_\x8a_\x8s_\x8·_\x8t_\x8h_\x8e_\x8·_\x8n_\x8a_\x8m_\x8e_\x8·_\x8o_\x8r_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e_\x8·_\x8o_\x8f_\x8·_\x8a_\x8n_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8a_\x8r_\x8g_\x8u_\x8m_\x8e_\x8n_\x8t |
| 2052 | ··········o·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·--·an·optional·argument | 2052 | ··········o·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·--·an·optional·argument |
| 2053 | ··········o·_\x8T_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s·--·an·optional·argument | 2053 | ··········o·_\x8T_\x8h_\x8r_\x8e_\x8a_\x8d_\x8s·--·an·optional·argument |
| 2054 | ··········o·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument | ||
| 2055 | ··········o·_\x8B_\x8a_\x8s_\x8i_\x8s_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 2056 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 2057 | ··········o·_\x8P_\x8a_\x8i_\x8r_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 2058 | ··········o·_\x8G_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c·--·an·optional·argument | ||
| 2054 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8G_\x8r_\x8o_\x8u_\x8p·--·an·optional·argument | 2059 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8G_\x8r_\x8o_\x8u_\x8p·--·an·optional·argument |
| 2055 | ··········o·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8s·--·an·optional·argument | 2060 | ··········o·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8s·--·an·optional·argument |
| 2056 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8f_\x8t·--·an·optional·argument | 2061 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8f_\x8t·--·an·optional·argument |
| 2057 | ··········o·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8B_\x8a_\x8s_\x8e_\x8N_\x8a_\x8m_\x8e·--·an·optional·argument | 2062 | ··········o·_\x8V_\x8a_\x8r_\x8i_\x8a_\x8b_\x8l_\x8e_\x8B_\x8a_\x8s_\x8e_\x8N_\x8a_\x8m_\x8e·--·an·optional·argument |
| 2058 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8R_\x8a_\x8n_\x8k·--·an·optional·argument | 2063 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8R_\x8a_\x8n_\x8k·--·an·optional·argument |
| 2059 | ··········o·_\x8I_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8s·--·an·optional·argument | 2064 | ··········o·_\x8I_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8s·--·an·optional·argument |
| 2060 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·an·optional·argument | 2065 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s·--·an·optional·argument |
| 2061 | ··········o·_\x8J_\x8o_\x8i_\x8n·--·an·optional·argument | 2066 | ··········o·_\x8J_\x8o_\x8i_\x8n·--·an·optional·argument |
| 2062 | ··········o·_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8S_\x8i_\x8z_\x8e·--·an·optional·argument | 2067 | ··········o·_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8S_\x8i_\x8z_\x8e·--·an·optional·argument |
| 2063 | ··········o·_\x8L_\x8o_\x8c_\x8a_\x8l·--·an·optional·argument | 2068 | ··········o·_\x8L_\x8o_\x8c_\x8a_\x8l·--·an·optional·argument |
| 2064 | ··········o·_\x8H_\x8e_\x8f_\x8t·--·an·optional·argument | 2069 | ··········o·_\x8H_\x8e_\x8f_\x8t·--·an·optional·argument |
| 2065 | ··········o·_\x8C_\x8o_\x8n_\x8s_\x8t_\x8a_\x8n_\x8t_\x8s·--·an·optional·argument | 2070 | ··········o·_\x8C_\x8o_\x8n_\x8s_\x8t_\x8a_\x8n_\x8t_\x8s·--·an·optional·argument |
| 2066 | ··········o·_\x8S_\x8k_\x8e_\x8w_\x8C_\x8o_\x8m_\x8m_\x8u_\x8t_\x8a_\x8t_\x8i_\x8v_\x8e·--·an·optional·argument | 2071 | ··········o·_\x8S_\x8k_\x8e_\x8w_\x8C_\x8o_\x8m_\x8m_\x8u_\x8t_\x8a_\x8t_\x8i_\x8v_\x8e·--·an·optional·argument |
| 2067 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p·--·an·optional·argument | 2072 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p·--·an·optional·argument |
| 2068 | ··········o·_\x8G_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c·--·an·optional·argument | ||
| 2069 | ··········o·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument | ||
| 2070 | ··········o·_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 2071 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8i_\x8t_\x8y·--·an·optional·argument | 2073 | ··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8i_\x8t_\x8y·--·an·optional·argument |
| 2072 | ··········o·_\x8B_\x8a_\x8s_\x8i_\x8s_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 2073 | ··········o·_\x8P_\x8a_\x8i_\x8r_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | ||
| 2074 | ··········o·_\x8V_\x8e_\x8r_\x8i_\x8f_\x8y·--·an·optional·argument | ||
| 2075 | ··········o·_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument | 2074 | ··········o·_\x8C_\x8o_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8L_\x8i_\x8m_\x8i_\x8t·--·an·optional·argument |
| 2075 | ··········o·_\x8V_\x8e_\x8r_\x8i_\x8f_\x8y·--·an·optional·argument | ||
| 2076 | ··········o·_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8R_\x8i_\x8n_\x8g·--·an·optional·argument | 2076 | ··········o·_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8R_\x8i_\x8n_\x8g·--·an·optional·argument |
| 2077 | ··········o·_\x8F_\x8o_\x8l_\x8l_\x8o_\x8w_\x8L_\x8i_\x8n_\x8k_\x8s·--·an·optional·argument | 2077 | ··········o·_\x8F_\x8o_\x8l_\x8l_\x8o_\x8w_\x8L_\x8i_\x8n_\x8k_\x8s·--·an·optional·argument |
| 2078 | ··········o·_\x8E_\x8x_\x8c_\x8l_\x8u_\x8d_\x8e·--·an·optional·argument | 2078 | ··········o·_\x8E_\x8x_\x8c_\x8l_\x8u_\x8d_\x8e·--·an·optional·argument |
| 2079 | ··········o·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8P_\x8r_\x8e_\x8f_\x8i_\x8x·--·an·optional·argument | 2079 | ··········o·_\x8I_\x8n_\x8s_\x8t_\x8a_\x8l_\x8l_\x8P_\x8r_\x8e_\x8f_\x8i_\x8x·--·an·optional·argument |
| 2080 | ··········o·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8y_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument | 2080 | ··········o·_\x8S_\x8y_\x8z_\x8y_\x8g_\x8y_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument |
| 2081 | ··········o·_\x8C_\x8h_\x8a_\x8n_\x8g_\x8e_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument | 2081 | ··········o·_\x8C_\x8h_\x8a_\x8n_\x8g_\x8e_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument |
| 2082 | ··········o·_\x8M_\x8i_\x8n_\x8i_\x8m_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument | 2082 | ··········o·_\x8M_\x8i_\x8n_\x8i_\x8m_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·an·optional·argument |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=5 | 7 | #:len=5 |
| 8 | c3RvcmU= | 8 | c3RvcmU= |
| 9 | #:len=651 | 9 | #:len=651 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU3RvcmUgcmVzdWx0IG9mIGEgTWFwbGUg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU3RvcmUgcmVzdWx0IG9mIGEgTWFwbGUg |
| 11 | Y29tcHV0YXRpb24gaW4gYSBmaWxlLiIsIERlc2NyaXB0aW9uID0+IDE6KERJVntQQVJBe1RFWHsi | 11 | Y29tcHV0YXRpb24gaW4gYSBmaWxlLiIsIERlc2NyaXB0aW9uID0+IDE6KERJVntQQVJBe1RFWHsi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | Z2F1c3NJZGVhbChSaW5nLExpc3Qp | 8 | Z2F1c3NJZGVhbChSaW5nLExpc3Qp |
| 9 | #:len=239 | 9 | #:len=239 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjE4LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjE4LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhnYXVzc0lkZWFsLFJpbmcsTGlzdCksImdhdXNzSWRl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhnYXVzc0lkZWFsLFJpbmcsTGlzdCksImdhdXNzSWRl |
| Offset 70, 15 lines modified | Offset 70, 15 lines modified | ||
| 70 | ·····|···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2|···1,2,2,2·2,2,2,1····1,2,2,1·2,2,2,2| | 70 | ·····|···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2|···1,2,2,2·2,2,2,1····1,2,2,1·2,2,2,2| |
| 71 | ·····+-------------------------------------+-------------------------------------+ | 71 | ·····+-------------------------------------+-------------------------------------+ |
| 72 | ·····|-·p·······p········+·p·······p·······|-·p·······p········+·p·······p·······| | 72 | ·····|-·p·······p········+·p·······p·······|-·p·······p········+·p·······p·······| |
| 73 | ·····|···1,1,2,1·1,2,1,1····1,1,1,1·1,2,2,1|···1,1,2,2·1,2,1,2····1,1,1,2·1,2,2,2| | 73 | ·····|···1,1,2,1·1,2,1,1····1,1,1,1·1,2,2,1|···1,1,2,2·1,2,1,2····1,1,1,2·1,2,2,2| |
| 74 | ·····+-------------------------------------+-------------------------------------+ | 74 | ·····+-------------------------------------+-------------------------------------+ |
| 75 | i8·:·time·netList·primaryDecomposition·J | 75 | i8·:·time·netList·primaryDecomposition·J |
| 76 | ·--·used·2. | 76 | ·--·used·2.84146s·(cpu);·1.41215s·(thread);·0s·(gc) |
| 77 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 77 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 78 | o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| | 78 | o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| |
| 79 | ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| | 79 | ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| |
| 80 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 80 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 81 | ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| | 81 | ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| |
| 82 | ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| | 82 | ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| |
| Offset 139, 15 lines modified | Offset 139, 15 lines modified | ||
| 139 | ········</table> | 139 | ········</table> |
| 140 | ········<div> | 140 | ········<div> |
| 141 | ··········<p>This·ideal·has·5·primary·components.··The·first·is·the·one·that·has·statistical·significance.·The·significance·of·the·other·components·is·still·poorly·understood.</p> | 141 | ··········<p>This·ideal·has·5·primary·components.··The·first·is·the·one·that·has·statistical·significance.·The·significance·of·the·other·components·is·still·poorly·understood.</p> |
| 142 | ········</div> | 142 | ········</div> |
| 143 | ········<table·class="examples"> | 143 | ········<table·class="examples"> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·netList·primaryDecomposition·J | 145 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·netList·primaryDecomposition·J |
| 146 | ·--·used·2. | 146 | ·--·used·2.84146s·(cpu);·1.41215s·(thread);·0s·(gc) |
| 147 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 147 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 148 | o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| | 148 | o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| |
| 149 | ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| | 149 | ·····|········1,2,2,2···1,2,2,1···1,2,1,2···1,2,1,1···1,1,2,2·2,1,2,1····1,1,2,1·2,1,2,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| |
| 150 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 150 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 151 | ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| | 151 | ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| |
| 152 | ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| | 152 | ·····|········1,2,2,2···1,2,2,1···1,1,2,2···1,1,2,1···1,2,1,2·2,2,1,1····1,2,1,1·2,2,1,2···1,1,1,2·2,1,1,1····1,1,1,1·2,1,1,2··························································································································································································································································································································································································································································································································································································································································································································································| |
| Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | 1,2,2,2| | 102 | 1,2,2,2| |
| 103 | ·····+-------------------------------------+----------------------------------- | 103 | ·····+-------------------------------------+----------------------------------- |
| 104 | --+ | 104 | --+ |
| 105 | This·ideal·has·5·primary·components.·The·first·is·the·one·that·has·statistical | 105 | This·ideal·has·5·primary·components.·The·first·is·the·one·that·has·statistical |
| 106 | significance.·The·significance·of·the·other·components·is·still·poorly | 106 | significance.·The·significance·of·the·other·components·is·still·poorly |
| 107 | understood. | 107 | understood. |
| 108 | i8·:·time·netList·primaryDecomposition·J | 108 | i8·:·time·netList·primaryDecomposition·J |
| 109 | ·--·used·2. | 109 | ·--·used·2.84146s·(cpu);·1.41215s·(thread);·0s·(gc) |
| 110 | ·····+------------------------------------------------------------------------- | 110 | ·····+------------------------------------------------------------------------- |
| 111 | ------------------------------------------------------------------------------- | 111 | ------------------------------------------------------------------------------- |
| 112 | ------------------------------------------------------------------------------- | 112 | ------------------------------------------------------------------------------- |
| 113 | ------------------------------------------------------------------------------- | 113 | ------------------------------------------------------------------------------- |
| 114 | ------------------------------------------------------------------------------- | 114 | ------------------------------------------------------------------------------- |
| 115 | ------------------------------------------------------------------------------- | 115 | ------------------------------------------------------------------------------- |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=24 | 7 | #:len=24 |
| 8 | YWxnZWJyYWljTWF0cm9pZENpcmN1aXRz | 8 | YWxnZWJyYWljTWF0cm9pZENpcmN1aXRz |
| 9 | #:len=1461 | 9 | #:len=1461 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVGhlIGJhc2VzIG9mIHRoZSBhbGdlYnJh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVGhlIGJhc2VzIG9mIHRoZSBhbGdlYnJh |
| 11 | aWMgbWF0cm9pZCIsICJsaW5lbnVtIiA9PiAyMTIxLCBJbnB1dHMgPT4ge1NQQU57VFR7IkwifSwi | 11 | aWMgbWF0cm9pZCIsICJsaW5lbnVtIiA9PiAyMTIxLCBJbnB1dHMgPT4ge1NQQU57VFR7IkwifSwi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | aXNBU01VbmlvbihMaXN0KQ== | 8 | aXNBU01VbmlvbihMaXN0KQ== |
| 9 | #:len=285 | 9 | #:len=285 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTA2MSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTA2MSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNBU01VbmlvbixMaXN0KSwiaXNBU01VbmlvbihM | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNBU01VbmlvbixMaXN0KSwiaXNBU01VbmlvbihM |
| Offset 212, 17 lines modified | Offset 212, 17 lines modified | ||
| 212 | ······|·1·-1·1·| | 212 | ······|·1·-1·1·| |
| 213 | ······|·0·1··0·| | 213 | ······|·0·1··0·| |
| 214 | ···············3·······3 | 214 | ···············3·······3 |
| 215 | o22·:·Matrix·ZZ··<--·ZZ | 215 | o22·:·Matrix·ZZ··<--·ZZ |
| 216 | i23·:·time·schubertRegularity·B | 216 | i23·:·time·schubertRegularity·B |
| 217 | ·--·used·0.069 | 217 | ·--·used·0.0869039s·(cpu);·0.0437993s·(thread);·0s·(gc) |
| 218 | o23·=·1 | 218 | o23·=·1 |
| 219 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B | 219 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B |
| 220 | ·--·used·0.0 | 220 | ·--·used·0.0114717s·(cpu);·0.0131226s·(thread);·0s·(gc) |
| 221 | o24·=·1 | 221 | o24·=·1 |
| 222 | i25·:· | 222 | i25·:· |
| Offset 166, 17 lines modified | Offset 166, 17 lines modified | ||
| 166 | ······z···z···z···,·z···z···z····-·z···z···,·z···z···z····-·z···z···) | 166 | ······z···z···z···,·z···z···z····-·z···z···,·z···z···z····-·z···z···) |
| 167 | ·······1,2·1,3·2,4···1,2·1,4·2,2····1,2·2,4···1,2·1,3·2,2····1,2·2,3 | 167 | ·······1,2·1,3·2,4···1,2·1,4·2,2····1,2·2,4···1,2·1,3·2,2····1,2·2,3 |
| 168 | o14·:·Ideal·of·QQ[z···..z···] | 168 | o14·:·Ideal·of·QQ[z···..z···] |
| 169 | ···················1,1···5,5 | 169 | ···················1,1···5,5 |
| 170 | i15·:·time·schubertRegularity·p | 170 | i15·:·time·schubertRegularity·p |
| 171 | ·--·used·0.00 | 171 | ·--·used·0.00131745s·(cpu);·0.000238768s·(thread);·0s·(gc) |
| 172 | o15·=·5 | 172 | o15·=·5 |
| 173 | i16·:·time·regularity·comodule·I | 173 | i16·:·time·regularity·comodule·I |
| 174 | ·--·used·0.01 | 174 | ·--·used·0.0104067s·(cpu);·0.0122539s·(thread);·0s·(gc) |
| 175 | o16·=·5 | 175 | o16·=·5 |
| 176 | i17·:· | 176 | i17·:· |
| Offset 3, 25 lines modified | Offset 3, 25 lines modified | ||
| 3 | i1·:·w·=·{2,1,4,3} | 3 | i1·:·w·=·{2,1,4,3} |
| 4 | o1·=·{2,·1,·4,·3} | 4 | o1·=·{2,·1,·4,·3} |
| 5 | o1·:·List | 5 | o1·:·List |
| 6 | i2·:·time·grothendieckPolynomial·w | 6 | i2·:·time·grothendieckPolynomial·w |
| 7 | ·--·used·0.003 | 7 | ·--·used·0.00399946s·(cpu);·0.00389768s·(thread);·0s·(gc) |
| 8 | ······2········2······2···············2 | 8 | ······2········2······2···············2 |
| 9 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 9 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 10 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 10 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 11 | o2·:·QQ[x·..x·] | 11 | o2·:·QQ[x·..x·] |
| 12 | ·········1···4 | 12 | ·········1···4 |
| 13 | i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") | 13 | i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") |
| 14 | ·--·used·0.00 | 14 | ·--·used·0.000401262s·(cpu);·0.00165842s·(thread);·0s·(gc) |
| 15 | ······2········2······2···············2 | 15 | ······2········2······2···············2 |
| 16 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 16 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 17 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 17 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 18 | o3·:·QQ[x·..x·] | 18 | o3·:·QQ[x·..x·] |
| 19 | ·········1···4 | 19 | ·········1···4 |
| Offset 333, 21 lines modified | Offset 333, 21 lines modified | ||
| 333 | ········</table> | 333 | ········</table> |
| 334 | ········<div> | 334 | ········<div> |
| 335 | ··········<p>Additionally,·this·package·facilitates·the·investigating·homological·invariants·of·ASM·ideals·efficiently·by·computing·the·associated·invariants·for·their·antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17].·Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and·projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal·initial·ideals·by·[CV20].</p> | 335 | ··········<p>Additionally,·this·package·facilitates·the·investigating·homological·invariants·of·ASM·ideals·efficiently·by·computing·the·associated·invariants·for·their·antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17].·Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and·projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal·initial·ideals·by·[CV20].</p> |
| 336 | ········</div> | 336 | ········</div> |
| 337 | ········<table·class="examples"> | 337 | ········<table·class="examples"> |
| 338 | ··········<tr> | 338 | ··········<tr> |
| 339 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·schubertRegularity·B | 339 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·schubertRegularity·B |
| 340 | ·--·used·0.069 | 340 | ·--·used·0.0869039s·(cpu);·0.0437993s·(thread);·0s·(gc) |
| 341 | o23·=·1</code></pre> | 341 | o23·=·1</code></pre> |
| 342 | </td>··········</tr> | 342 | </td>··········</tr> |
| 343 | ··········<tr> | 343 | ··········<tr> |
| 344 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B | 344 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B |
| 345 | ·--·used·0.0 | 345 | ·--·used·0.0114717s·(cpu);·0.0131226s·(thread);·0s·(gc) |
| 346 | o24·=·1</code></pre> | 346 | o24·=·1</code></pre> |
| 347 | </td>··········</tr> | 347 | </td>··········</tr> |
| 348 | ········</table> | 348 | ········</table> |
| 349 | ········<div> | 349 | ········<div> |
| 350 | ··········<h2>Functions·for·investigating·ASM·varieties</h2> | 350 | ··········<h2>Functions·for·investigating·ASM·varieties</h2> |
| 351 | ········</div> | 351 | ········</div> |
| Offset 241, 19 lines modified | Offset 241, 19 lines modified | ||
| 241 | Additionally,·this·package·facilitates·the·investigating·homological·invariants | 241 | Additionally,·this·package·facilitates·the·investigating·homological·invariants |
| 242 | of·ASM·ideals·efficiently·by·computing·the·associated·invariants·for·their | 242 | of·ASM·ideals·efficiently·by·computing·the·associated·invariants·for·their |
| 243 | antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17]. | 243 | antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17]. |
| 244 | Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and | 244 | Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and |
| 245 | projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal | 245 | projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal |
| 246 | initial·ideals·by·[CV20]. | 246 | initial·ideals·by·[CV20]. |
| 247 | i23·:·time·schubertRegularity·B | 247 | i23·:·time·schubertRegularity·B |
| 248 | ·--·used·0.069 | 248 | ·--·used·0.0869039s·(cpu);·0.0437993s·(thread);·0s·(gc) |
| 249 | o23·=·1 | 249 | o23·=·1 |
| 250 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B | 250 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B |
| 251 | ·--·used·0.0 | 251 | ·--·used·0.0114717s·(cpu);·0.0131226s·(thread);·0s·(gc) |
| 252 | o24·=·1 | 252 | o24·=·1 |
| 253 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·A\x8AS\x8SM\x8M·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 253 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·A\x8AS\x8SM\x8M·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 254 | ····*·_\x8i_\x8s_\x8P_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·whether·a·matrix·is·a·partial·alternating·sign | 254 | ····*·_\x8i_\x8s_\x8P_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·whether·a·matrix·is·a·partial·alternating·sign |
| 255 | ······matrix | 255 | ······matrix |
| 256 | ····*·_\x8p_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8T_\x8o_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·extend·a·partial·alternating·sign·matrix·to·an | 256 | ····*·_\x8p_\x8a_\x8r_\x8t_\x8i_\x8a_\x8l_\x8A_\x8S_\x8M_\x8T_\x8o_\x8A_\x8S_\x8M_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·extend·a·partial·alternating·sign·matrix·to·an |
| 257 | ······alternating·sign·matrix | 257 | ······alternating·sign·matrix |
| Offset 268, 21 lines modified | Offset 268, 21 lines modified | ||
| 268 | ········</table> | 268 | ········</table> |
| 269 | ········<div> | 269 | ········<div> |
| 270 | ··········<p>Finally,·this·package·contains·functions·for·investigating·homological·invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial·algorithms·produced·in·[PSW21].</p> | 270 | ··········<p>Finally,·this·package·contains·functions·for·investigating·homological·invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial·algorithms·produced·in·[PSW21].</p> |
| 271 | ········</div> | 271 | ········</div> |
| 272 | ········<table·class="examples"> | 272 | ········<table·class="examples"> |
| 273 | ··········<tr> | 273 | ··········<tr> |
| 274 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·schubertRegularity·p | 274 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·schubertRegularity·p |
| 275 | ·--·used·0.00 | 275 | ·--·used·0.00131745s·(cpu);·0.000238768s·(thread);·0s·(gc) |
| 276 | o15·=·5</code></pre> | 276 | o15·=·5</code></pre> |
| 277 | </td>··········</tr> | 277 | </td>··········</tr> |
| 278 | ··········<tr> | 278 | ··········<tr> |
| 279 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·regularity·comodule·I | 279 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·regularity·comodule·I |
| 280 | ·--·used·0.01 | 280 | ·--·used·0.0104067s·(cpu);·0.0122539s·(thread);·0s·(gc) |
| 281 | o16·=·5</code></pre> | 281 | o16·=·5</code></pre> |
| 282 | </td>··········</tr> | 282 | </td>··········</tr> |
| 283 | ········</table> | 283 | ········</table> |
| 284 | ········<div> | 284 | ········<div> |
| 285 | ··········<h2>Functions·for·investigating·matrix·Schubert·varieties</h2> | 285 | ··········<h2>Functions·for·investigating·matrix·Schubert·varieties</h2> |
| 286 | ········</div> | 286 | ········</div> |
| Offset 532, 19 lines modified | Offset 532, 19 lines modified | ||
| 532 | o14·:·Ideal·of·QQ[z···..z···] | 532 | o14·:·Ideal·of·QQ[z···..z···] |
| 533 | ···················1,1···5,5 | 533 | ···················1,1···5,5 |
| 534 | Finally,·this·package·contains·functions·for·investigating·homological | 534 | Finally,·this·package·contains·functions·for·investigating·homological |
| 535 | invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial | 535 | invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial |
| 536 | algorithms·produced·in·[PSW21]. | 536 | algorithms·produced·in·[PSW21]. |
| 537 | i15·:·time·schubertRegularity·p | 537 | i15·:·time·schubertRegularity·p |
| 538 | ·--·used·0.00 | 538 | ·--·used·0.00131745s·(cpu);·0.000238768s·(thread);·0s·(gc) |
| 539 | o15·=·5 | 539 | o15·=·5 |
| 540 | i16·:·time·regularity·comodule·I | 540 | i16·:·time·regularity·comodule·I |
| 541 | ·--·used·0.01 | 541 | ·--·used·0.0104067s·(cpu);·0.0122539s·(thread);·0s·(gc) |
| 542 | o16·=·5 | 542 | o16·=·5 |
| 543 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·m\x8ma\x8at\x8tr\x8ri\x8ix\x8x·S\x8Sc\x8ch\x8hu\x8ub\x8be\x8er\x8rt\x8t·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 543 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·f\x8fo\x8or\x8r·i\x8in\x8nv\x8ve\x8es\x8st\x8ti\x8ig\x8ga\x8at\x8ti\x8in\x8ng\x8g·m\x8ma\x8at\x8tr\x8ri\x8ix\x8x·S\x8Sc\x8ch\x8hu\x8ub\x8be\x8er\x8rt\x8t·v\x8va\x8ar\x8ri\x8ie\x8et\x8ti\x8ie\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 544 | ····*·_\x8a_\x8n_\x8t_\x8i_\x8D_\x8i_\x8a_\x8g_\x8I_\x8n_\x8i_\x8t_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·the·(unique)·antidiagonal·initial·ideal·of | 544 | ····*·_\x8a_\x8n_\x8t_\x8i_\x8D_\x8i_\x8a_\x8g_\x8I_\x8n_\x8i_\x8t_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·the·(unique)·antidiagonal·initial·ideal·of |
| 545 | ······an·ASM·ideal | 545 | ······an·ASM·ideal |
| 546 | ····*·_\x8r_\x8a_\x8n_\x8k_\x8T_\x8a_\x8b_\x8l_\x8e_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·a·table·of·rank·conditions·that·determines·a | 546 | ····*·_\x8r_\x8a_\x8n_\x8k_\x8T_\x8a_\x8b_\x8l_\x8e_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·a·table·of·rank·conditions·that·determines·a |
| 547 | ······Schubert·determinantal·ideal·or,·more·generally,·an·alternating·sign | 547 | ······Schubert·determinantal·ideal·or,·more·generally,·an·alternating·sign |
| Offset 77, 26 lines modified | Offset 77, 26 lines modified | ||
| 77 | o1·=·{2,·1,·4,·3} | 77 | o1·=·{2,·1,·4,·3} |
| 78 | o1·:·List</code></pre> | 78 | o1·:·List</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·grothendieckPolynomial·w | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·grothendieckPolynomial·w |
| 82 | ·--·used·0.003 | 82 | ·--·used·0.00399946s·(cpu);·0.00389768s·(thread);·0s·(gc) |
| 83 | ······2········2······2···············2 | 83 | ······2········2······2···············2 |
| 84 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 84 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 85 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 85 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 86 | o2·:·QQ[x·..x·] | 86 | o2·:·QQ[x·..x·] |
| 87 | ·········1···4</code></pre> | 87 | ·········1···4</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") |
| 91 | ·--·used·0.00 | 91 | ·--·used·0.000401262s·(cpu);·0.00165842s·(thread);·0s·(gc) |
| 92 | ······2········2······2···············2 | 92 | ······2········2······2···············2 |
| 93 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 93 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 94 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 94 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 95 | o3·:·QQ[x·..x·] | 95 | o3·:·QQ[x·..x·] |
| 96 | ·········1···4</code></pre> | 96 | ·········1···4</code></pre> |
| Offset 19, 24 lines modified | Offset 19, 24 lines modified | ||
| 19 | PipeDream. | 19 | PipeDream. |
| 20 | i1·:·w·=·{2,1,4,3} | 20 | i1·:·w·=·{2,1,4,3} |
| 21 | o1·=·{2,·1,·4,·3} | 21 | o1·=·{2,·1,·4,·3} |
| 22 | o1·:·List | 22 | o1·:·List |
| 23 | i2·:·time·grothendieckPolynomial·w | 23 | i2·:·time·grothendieckPolynomial·w |
| 24 | ·--·used·0.003 | 24 | ·--·used·0.00399946s·(cpu);·0.00389768s·(thread);·0s·(gc) |
| 25 | ······2········2······2···············2 | 25 | ······2········2······2···············2 |
| 26 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 26 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 27 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 27 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 28 | o2·:·QQ[x·..x·] | 28 | o2·:·QQ[x·..x·] |
| 29 | ·········1···4 | 29 | ·········1···4 |
| 30 | i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") | 30 | i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") |
| 31 | ·--·used·0.00 | 31 | ·--·used·0.000401262s·(cpu);·0.00165842s·(thread);·0s·(gc) |
| 32 | ······2········2······2···············2 | 32 | ······2········2······2···············2 |
| 33 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 33 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 34 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 34 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 35 | o3·:·QQ[x·..x·] | 35 | o3·:·QQ[x·..x·] |
| 36 | ·········1···4 | 36 | ·········1···4 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=24 | 7 | #:len=24 |
| 8 | ZmxhdHMoTWF0cm9pZCxaWixTdHJpbmcp | 8 | ZmxhdHMoTWF0cm9pZCxaWixTdHJpbmcp |
| 9 | #:len=255 | 9 | #:len=255 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzOSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzOSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZmxhdHMsTWF0cm9pZCxaWixTdHJpbmcpLCJmbGF0 | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZmxhdHMsTWF0cm9pZCxaWixTdHJpbmcpLCJmbGF0 |
| Offset 51, 20 lines modified | Offset 51, 20 lines modified | ||
| 51 | i9·:·keys·R10.cache | 51 | i9·:·keys·R10.cache |
| 52 | o9·=·{groundSet,·rankFunction,·storedRepresentation} | 52 | o9·=·{groundSet,·rankFunction,·storedRepresentation} |
| 53 | o9·:·List | 53 | o9·:·List |
| 54 | i10·:·time·isWellDefined·R10 | 54 | i10·:·time·isWellDefined·R10 |
| 55 | ·--·used·0.1 | 55 | ·--·used·0.1312s·(cpu);·0.0687818s·(thread);·0s·(gc) |
| 56 | o10·=·true | 56 | o10·=·true |
| 57 | i11·:·time·fVector·R10 | 57 | i11·:·time·fVector·R10 |
| 58 | ·--·used·0. | 58 | ·--·used·0.124413s·(cpu);·0.0561926s·(thread);·0s·(gc) |
| 59 | o11·=·HashTable{0·=>·1·} | 59 | o11·=·HashTable{0·=>·1·} |
| 60 | ················1·=>·10 | 60 | ················1·=>·10 |
| 61 | ················2·=>·45 | 61 | ················2·=>·45 |
| 62 | ················3·=>·75 | 62 | ················3·=>·75 |
| 63 | ················4·=>·30 | 63 | ················4·=>·30 |
| 64 | ················5·=>·1 | 64 | ················5·=>·1 |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats, | 76 | o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats, |
| 77 | ······----------------------------------------------------------------------- | 77 | ······----------------------------------------------------------------------- |
| 78 | ······groundSet,·dual,·storedRepresentation} | 78 | ······groundSet,·dual,·storedRepresentation} |
| 79 | o12·:·List | 79 | o12·:·List |
| 80 | i13·:·time·fVector·R10 | 80 | i13·:·time·fVector·R10 |
| 81 | ·--·used·0.0003 | 81 | ·--·used·0.000326823s·(cpu);·0.000166662s·(thread);·0s·(gc) |
| 82 | o13·=·HashTable{0·=>·1·} | 82 | o13·=·HashTable{0·=>·1·} |
| 83 | ················1·=>·10 | 83 | ················1·=>·10 |
| 84 | ················2·=>·45 | 84 | ················2·=>·45 |
| 85 | ················3·=>·75 | 85 | ················3·=>·75 |
| 86 | ················4·=>·30 | 86 | ················4·=>·30 |
| 87 | ················5·=>·1 | 87 | ················5·=>·1 |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i2·:·U25·=·uniformMatroid(2,5) | 9 | i2·:·U25·=·uniformMatroid(2,5) |
| 10 | o2·=·a·"matroid"·of·rank·2·on·5·elements | 10 | o2·=·a·"matroid"·of·rank·2·on·5·elements |
| 11 | o2·:·Matroid | 11 | o2·:·Matroid |
| 12 | i3·:·elapsedTime·L·=·allMinors(V,·U25); | 12 | i3·:·elapsedTime·L·=·allMinors(V,·U25); |
| 13 | ·--·.1 | 13 | ·--·.194677s·elapsed |
| 14 | i4·:·#L | 14 | i4·:·#L |
| 15 | o4·=·64 | 15 | o4·=·64 |
| 16 | i5·:·netList·L_{0..4} | 16 | i5·:·netList·L_{0..4} |
| Offset 33, 14 lines modified | Offset 33, 14 lines modified | ||
| 33 | i6·:·F7·=·specificMatroid·"fano" | 33 | i6·:·F7·=·specificMatroid·"fano" |
| 34 | o6·=·a·"matroid"·of·rank·3·on·7·elements | 34 | o6·=·a·"matroid"·of·rank·3·on·7·elements |
| 35 | o6·:·Matroid | 35 | o6·:·Matroid |
| 36 | i7·:·time·autF7·=·getIsos(F7,·F7); | 36 | i7·:·time·autF7·=·getIsos(F7,·F7); |
| 37 | ·--·used·0.1 | 37 | ·--·used·0.190702s·(cpu);·0.0665948s·(thread);·0s·(gc) |
| 38 | i8·:·#autF7 | 38 | i8·:·#autF7 |
| 39 | o8·=·168 | 39 | o8·=·168 |
| 40 | i9·:· | 40 | i9·:· |
| Offset 9, 12 lines modified | Offset 9, 12 lines modified | ||
| 9 | o1·:·Sequence | 9 | o1·:·Sequence |
| 10 | i2·:·hasMinor(M4,·uniformMatroid(2,4)) | 10 | i2·:·hasMinor(M4,·uniformMatroid(2,4)) |
| 11 | o2·=·false | 11 | o2·=·false |
| 12 | i3·:·time·hasMinor(M6,·M5) | 12 | i3·:·time·hasMinor(M6,·M5) |
| 13 | ·--·used·1. | 13 | ·--·used·1.43113s·(cpu);·1.03938s·(thread);·0s·(gc) |
| 14 | o3·=·true | 14 | o3·=·true |
| 15 | i4·:· | 15 | i4·:· |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7}) | 19 | i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7}) |
| 20 | o4·=·a·"matroid"·of·rank·4·on·10·elements | 20 | o4·=·a·"matroid"·of·rank·4·on·10·elements |
| 21 | o4·:·Matroid | 21 | o4·:·Matroid |
| 22 | i5·:·time·isomorphism(M5,·minorM6) | 22 | i5·:·time·isomorphism(M5,·minorM6) |
| 23 | ·--·used·0.0 | 23 | ·--·used·0.00792864s·(cpu);·0.0110556s·(thread);·0s·(gc) |
| 24 | o5·=·HashTable{0·=>·1} | 24 | o5·=·HashTable{0·=>·1} |
| 25 | ···············1·=>·0 | 25 | ···············1·=>·0 |
| 26 | ···············2·=>·3 | 26 | ···············2·=>·3 |
| 27 | ···············3·=>·2 | 27 | ···············3·=>·2 |
| 28 | ···············4·=>·6 | 28 | ···············4·=>·6 |
| 29 | ···············5·=>·5 | 29 | ···············5·=>·5 |
| Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
| 56 | i7·:·N·=·relabel·M6 | 56 | i7·:·N·=·relabel·M6 |
| 57 | o7·=·a·"matroid"·of·rank·5·on·15·elements | 57 | o7·=·a·"matroid"·of·rank·5·on·15·elements |
| 58 | o7·:·Matroid | 58 | o7·:·Matroid |
| 59 | i8·:·time·phi·=·isomorphism(N,M6) | 59 | i8·:·time·phi·=·isomorphism(N,M6) |
| 60 | ·--·used· | 60 | ·--·used·4.02587s·(cpu);·2.42909s·(thread);·0s·(gc) |
| 61 | o8·=·HashTable{0·=>·11·} | 61 | o8·=·HashTable{0·=>·11·} |
| 62 | ···············1·=>·0 | 62 | ···············1·=>·0 |
| 63 | ···············2·=>·1 | 63 | ···············2·=>·1 |
| 64 | ···············3·=>·6 | 64 | ···············3·=>·6 |
| 65 | ···············4·=>·9 | 65 | ···············4·=>·9 |
| 66 | ···············5·=>·8 | 66 | ···············5·=>·8 |
| Offset 37, 15 lines modified | Offset 37, 15 lines modified | ||
| 37 | o7·:·Matroid | 37 | o7·:·Matroid |
| 38 | i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) | 38 | i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) |
| 39 | o9·=·true | 39 | o9·=·true |
| 40 | i10·:·time·quickIsomorphismTest(M0,·M1) | 40 | i10·:·time·quickIsomorphismTest(M0,·M1) |
| 41 | ·--·used·0.000 | 41 | ·--·used·0.000926748s·(cpu);·0.000376285s·(thread);·0s·(gc) |
| 42 | o10·=·false | 42 | o10·=·false |
| 43 | i11·:·value·oo·===·false | 43 | i11·:·value·oo·===·false |
| 44 | o11·=·true | 44 | o11·=·true |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | i5·:·keys·M.cache | 35 | i5·:·keys·M.cache |
| 36 | o5·=·{groundSet,·rankFunction,·storedRepresentation} | 36 | o5·=·{groundSet,·rankFunction,·storedRepresentation} |
| 37 | o5·:·List | 37 | o5·:·List |
| 38 | i6·:·elapsedTime·fVector·M | 38 | i6·:·elapsedTime·fVector·M |
| 39 | ·--·.0 | 39 | ·--·.0741733s·elapsed |
| 40 | o6·=·HashTable{0·=>·1·} | 40 | o6·=·HashTable{0·=>·1·} |
| 41 | ···············1·=>·6 | 41 | ···············1·=>·6 |
| 42 | ···············2·=>·15 | 42 | ···············2·=>·15 |
| 43 | ···············3·=>·20 | 43 | ···············3·=>·20 |
| 44 | ···············4·=>·1 | 44 | ···············4·=>·1 |
| Offset 122, 21 lines modified | Offset 122, 21 lines modified | ||
| 122 | o9·=·{groundSet,·rankFunction,·storedRepresentation} | 122 | o9·=·{groundSet,·rankFunction,·storedRepresentation} |
| 123 | o9·:·List</code></pre> | 123 | o9·:·List</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isWellDefined·R10 | 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isWellDefined·R10 |
| 127 | ·--·used·0.1 | 127 | ·--·used·0.1312s·(cpu);·0.0687818s·(thread);·0s·(gc) |
| 128 | o10·=·true</code></pre> | 128 | o10·=·true</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·fVector·R10 | 131 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·fVector·R10 |
| 132 | ·--·used·0. | 132 | ·--·used·0.124413s·(cpu);·0.0561926s·(thread);·0s·(gc) |
| 133 | o11·=·HashTable{0·=>·1·} | 133 | o11·=·HashTable{0·=>·1·} |
| 134 | ················1·=>·10 | 134 | ················1·=>·10 |
| 135 | ················2·=>·45 | 135 | ················2·=>·45 |
| 136 | ················3·=>·75 | 136 | ················3·=>·75 |
| 137 | ················4·=>·30 | 137 | ················4·=>·30 |
| 138 | ················5·=>·1 | 138 | ················5·=>·1 |
| Offset 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | ······----------------------------------------------------------------------- | 150 | ······----------------------------------------------------------------------- |
| 151 | ······groundSet,·dual,·storedRepresentation} | 151 | ······groundSet,·dual,·storedRepresentation} |
| 152 | o12·:·List</code></pre> | 152 | o12·:·List</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·fVector·R10 | 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·fVector·R10 |
| 156 | ·--·used·0.0003 | 156 | ·--·used·0.000326823s·(cpu);·0.000166662s·(thread);·0s·(gc) |
| 157 | o13·=·HashTable{0·=>·1·} | 157 | o13·=·HashTable{0·=>·1·} |
| 158 | ················1·=>·10 | 158 | ················1·=>·10 |
| 159 | ················2·=>·45 | 159 | ················2·=>·45 |
| 160 | ················3·=>·75 | 160 | ················3·=>·75 |
| 161 | ················4·=>·30 | 161 | ················4·=>·30 |
| 162 | ················5·=>·1 | 162 | ················5·=>·1 |
| Offset 71, 19 lines modified | Offset 71, 19 lines modified | ||
| 71 | o8·:·Matroid | 71 | o8·:·Matroid |
| 72 | i9·:·keys·R10.cache | 72 | i9·:·keys·R10.cache |
| 73 | o9·=·{groundSet,·rankFunction,·storedRepresentation} | 73 | o9·=·{groundSet,·rankFunction,·storedRepresentation} |
| 74 | o9·:·List | 74 | o9·:·List |
| 75 | i10·:·time·isWellDefined·R10 | 75 | i10·:·time·isWellDefined·R10 |
| 76 | ·--·used·0.1 | 76 | ·--·used·0.1312s·(cpu);·0.0687818s·(thread);·0s·(gc) |
| 77 | o10·=·true | 77 | o10·=·true |
| 78 | i11·:·time·fVector·R10 | 78 | i11·:·time·fVector·R10 |
| 79 | ·--·used·0. | 79 | ·--·used·0.124413s·(cpu);·0.0561926s·(thread);·0s·(gc) |
| 80 | o11·=·HashTable{0·=>·1·} | 80 | o11·=·HashTable{0·=>·1·} |
| 81 | ················1·=>·10 | 81 | ················1·=>·10 |
| 82 | ················2·=>·45 | 82 | ················2·=>·45 |
| 83 | ················3·=>·75 | 83 | ················3·=>·75 |
| 84 | ················4·=>·30 | 84 | ················4·=>·30 |
| 85 | ················5·=>·1 | 85 | ················5·=>·1 |
| Offset 93, 15 lines modified | Offset 93, 15 lines modified | ||
| 93 | o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats, | 93 | o12·=·{hyperplanes,·flatsRelationsTable,·rankFunction,·ideal,·ranks,·flats, |
| 94 | ······----------------------------------------------------------------------- | 94 | ······----------------------------------------------------------------------- |
| 95 | ······groundSet,·dual,·storedRepresentation} | 95 | ······groundSet,·dual,·storedRepresentation} |
| 96 | o12·:·List | 96 | o12·:·List |
| 97 | i13·:·time·fVector·R10 | 97 | i13·:·time·fVector·R10 |
| 98 | ·--·used·0.0003 | 98 | ·--·used·0.000326823s·(cpu);·0.000166662s·(thread);·0s·(gc) |
| 99 | o13·=·HashTable{0·=>·1·} | 99 | o13·=·HashTable{0·=>·1·} |
| 100 | ················1·=>·10 | 100 | ················1·=>·10 |
| 101 | ················2·=>·45 | 101 | ················2·=>·45 |
| 102 | ················3·=>·75 | 102 | ················3·=>·75 |
| 103 | ················4·=>·30 | 103 | ················4·=>·30 |
| 104 | ················5·=>·1 | 104 | ················5·=>·1 |
| Offset 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | o2·=·a·"matroid"·of·rank·2·on·5·elements | 88 | o2·=·a·"matroid"·of·rank·2·on·5·elements |
| 89 | o2·:·Matroid</code></pre> | 89 | o2·:·Matroid</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·L·=·allMinors(V,·U25); | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·L·=·allMinors(V,·U25); |
| 93 | ·--·.1 | 93 | ·--·.194677s·elapsed</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·#L | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·#L |
| 97 | o4·=·64</code></pre> | 97 | o4·=·64</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| Offset 28, 15 lines modified | Offset 28, 15 lines modified | ||
| 28 | o1·:·Matroid | 28 | o1·:·Matroid |
| 29 | i2·:·U25·=·uniformMatroid(2,5) | 29 | i2·:·U25·=·uniformMatroid(2,5) |
| 30 | o2·=·a·"matroid"·of·rank·2·on·5·elements | 30 | o2·=·a·"matroid"·of·rank·2·on·5·elements |
| 31 | o2·:·Matroid | 31 | o2·:·Matroid |
| 32 | i3·:·elapsedTime·L·=·allMinors(V,·U25); | 32 | i3·:·elapsedTime·L·=·allMinors(V,·U25); |
| 33 | ·--·.1 | 33 | ·--·.194677s·elapsed |
| 34 | i4·:·#L | 34 | i4·:·#L |
| 35 | o4·=·64 | 35 | o4·=·64 |
| 36 | i5·:·netList·L_{0..4} | 36 | i5·:·netList·L_{0..4} |
| 37 | ·····+----------+-------+ | 37 | ·····+----------+-------+ |
| 38 | o5·=·|set·{5,·3}|set·{2}| | 38 | o5·=·|set·{5,·3}|set·{2}| |
| Offset 123, 15 lines modified | Offset 123, 15 lines modified | ||
| 123 | o6·=·a·"matroid"·of·rank·3·on·7·elements | 123 | o6·=·a·"matroid"·of·rank·3·on·7·elements |
| 124 | o6·:·Matroid</code></pre> | 124 | o6·:·Matroid</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·autF7·=·getIsos(F7,·F7); | 127 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·autF7·=·getIsos(F7,·F7); |
| 128 | ·--·used·0.1 | 128 | ·--·used·0.190702s·(cpu);·0.0665948s·(thread);·0s·(gc)</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i8·:·#autF7 | 131 | <td>··············<pre><code·class="language-macaulay2">i8·:·#autF7 |
| 132 | o8·=·168</code></pre> | 132 | o8·=·168</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ········</table> | 134 | ········</table> |
| Offset 52, 15 lines modified | Offset 52, 15 lines modified | ||
| 52 | symmetric·group·S_7: | 52 | symmetric·group·S_7: |
| 53 | i6·:·F7·=·specificMatroid·"fano" | 53 | i6·:·F7·=·specificMatroid·"fano" |
| 54 | o6·=·a·"matroid"·of·rank·3·on·7·elements | 54 | o6·=·a·"matroid"·of·rank·3·on·7·elements |
| 55 | o6·:·Matroid | 55 | o6·:·Matroid |
| 56 | i7·:·time·autF7·=·getIsos(F7,·F7); | 56 | i7·:·time·autF7·=·getIsos(F7,·F7); |
| 57 | ·--·used·0.1 | 57 | ·--·used·0.190702s·(cpu);·0.0665948s·(thread);·0s·(gc) |
| 58 | i8·:·#autF7 | 58 | i8·:·#autF7 |
| 59 | o8·=·168 | 59 | o8·=·168 |
| 60 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 60 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 61 | ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between | 61 | ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between |
| 62 | ······isomorphic·matroids | 62 | ······isomorphic·matroids |
| 63 | ····*·_\x8q_\x8u_\x8i_\x8c_\x8k_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8T_\x8e_\x8s_\x8t·--·quick·checks·for·isomorphism·between·matroids | 63 | ····*·_\x8q_\x8u_\x8i_\x8c_\x8k_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8T_\x8e_\x8s_\x8t·--·quick·checks·for·isomorphism·between·matroids |
| Offset 94, 15 lines modified | Offset 94, 15 lines modified | ||
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·hasMinor(M4,·uniformMatroid(2,4)) | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·hasMinor(M4,·uniformMatroid(2,4)) |
| 96 | o2·=·false</code></pre> | 96 | o2·=·false</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·hasMinor(M6,·M5) | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·hasMinor(M6,·M5) |
| 100 | ·--·used·1. | 100 | ·--·used·1.43113s·(cpu);·1.03938s·(thread);·0s·(gc) |
| 101 | o3·=·true</code></pre> | 101 | o3·=·true</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ········</table> | 103 | ········</table> |
| 104 | ······</div> | 104 | ······</div> |
| 105 | ······<div> | 105 | ······<div> |
| 106 | ········<h2>See·also</h2> | 106 | ········<h2>See·also</h2> |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | ·····elements,·a·"matroid"·of·rank·5·on·15·elements) | 35 | ·····elements,·a·"matroid"·of·rank·5·on·15·elements) |
| 36 | o1·:·Sequence | 36 | o1·:·Sequence |
| 37 | i2·:·hasMinor(M4,·uniformMatroid(2,4)) | 37 | i2·:·hasMinor(M4,·uniformMatroid(2,4)) |
| 38 | o2·=·false | 38 | o2·=·false |
| 39 | i3·:·time·hasMinor(M6,·M5) | 39 | i3·:·time·hasMinor(M6,·M5) |
| 40 | ·--·used·1. | 40 | ·--·used·1.43113s·(cpu);·1.03938s·(thread);·0s·(gc) |
| 41 | o3·=·true | 41 | o3·=·true |
| 42 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 42 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 43 | ····*·_\x8m_\x8i_\x8n_\x8o_\x8r·--·minor·of·matroid | 43 | ····*·_\x8m_\x8i_\x8n_\x8o_\x8r·--·minor·of·matroid |
| 44 | ····*·_\x8i_\x8s_\x8B_\x8i_\x8n_\x8a_\x8r_\x8y·--·whether·a·matroid·is·representable·over·F_2 | 44 | ····*·_\x8i_\x8s_\x8B_\x8i_\x8n_\x8a_\x8r_\x8y·--·whether·a·matroid·is·representable·over·F_2 |
| 45 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ha\x8as\x8sM\x8Mi\x8in\x8no\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 45 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8ha\x8as\x8sM\x8Mi\x8in\x8no\x8or\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 46 | ····*·hasMinor(Matroid,Matroid) | 46 | ····*·hasMinor(Matroid,Matroid) |
| Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | o4·=·a·"matroid"·of·rank·4·on·10·elements | 102 | o4·=·a·"matroid"·of·rank·4·on·10·elements |
| 103 | o4·:·Matroid</code></pre> | 103 | o4·:·Matroid</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isomorphism(M5,·minorM6) | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isomorphism(M5,·minorM6) |
| 107 | ·--·used·0.0 | 107 | ·--·used·0.00792864s·(cpu);·0.0110556s·(thread);·0s·(gc) |
| 108 | o5·=·HashTable{0·=>·1} | 108 | o5·=·HashTable{0·=>·1} |
| 109 | ···············1·=>·0 | 109 | ···············1·=>·0 |
| 110 | ···············2·=>·3 | 110 | ···············2·=>·3 |
| 111 | ···············3·=>·2 | 111 | ···············3·=>·2 |
| 112 | ···············4·=>·6 | 112 | ···············4·=>·6 |
| 113 | ···············5·=>·5 | 113 | ···············5·=>·5 |
| Offset 142, 15 lines modified | Offset 142, 15 lines modified | ||
| 142 | o7·=·a·"matroid"·of·rank·5·on·15·elements | 142 | o7·=·a·"matroid"·of·rank·5·on·15·elements |
| 143 | o7·:·Matroid</code></pre> | 143 | o7·:·Matroid</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·phi·=·isomorphism(N,M6) | 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·phi·=·isomorphism(N,M6) |
| 147 | ·--·used· | 147 | ·--·used·4.02587s·(cpu);·2.42909s·(thread);·0s·(gc) |
| 148 | o8·=·HashTable{0·=>·11·} | 148 | o8·=·HashTable{0·=>·11·} |
| 149 | ···············1·=>·0 | 149 | ···············1·=>·0 |
| 150 | ···············2·=>·1 | 150 | ···············2·=>·1 |
| 151 | ···············3·=>·6 | 151 | ···············3·=>·6 |
| 152 | ···············4·=>·9 | 152 | ···············4·=>·9 |
| 153 | ···············5·=>·8 | 153 | ···············5·=>·8 |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | o3·:·Sequence | 35 | o3·:·Sequence |
| 36 | i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7}) | 36 | i4·:·minorM6·=·minor(M6,·set{8},·set{4,5,6,7}) |
| 37 | o4·=·a·"matroid"·of·rank·4·on·10·elements | 37 | o4·=·a·"matroid"·of·rank·4·on·10·elements |
| 38 | o4·:·Matroid | 38 | o4·:·Matroid |
| 39 | i5·:·time·isomorphism(M5,·minorM6) | 39 | i5·:·time·isomorphism(M5,·minorM6) |
| 40 | ·--·used·0.0 | 40 | ·--·used·0.00792864s·(cpu);·0.0110556s·(thread);·0s·(gc) |
| 41 | o5·=·HashTable{0·=>·1} | 41 | o5·=·HashTable{0·=>·1} |
| 42 | ···············1·=>·0 | 42 | ···············1·=>·0 |
| 43 | ···············2·=>·3 | 43 | ···············2·=>·3 |
| 44 | ···············3·=>·2 | 44 | ···············3·=>·2 |
| 45 | ···············4·=>·6 | 45 | ···············4·=>·6 |
| 46 | ···············5·=>·5 | 46 | ···············5·=>·5 |
| Offset 69, 15 lines modified | Offset 69, 15 lines modified | ||
| 69 | o6·:·HashTable | 69 | o6·:·HashTable |
| 70 | i7·:·N·=·relabel·M6 | 70 | i7·:·N·=·relabel·M6 |
| 71 | o7·=·a·"matroid"·of·rank·5·on·15·elements | 71 | o7·=·a·"matroid"·of·rank·5·on·15·elements |
| 72 | o7·:·Matroid | 72 | o7·:·Matroid |
| 73 | i8·:·time·phi·=·isomorphism(N,M6) | 73 | i8·:·time·phi·=·isomorphism(N,M6) |
| 74 | ·--·used· | 74 | ·--·used·4.02587s·(cpu);·2.42909s·(thread);·0s·(gc) |
| 75 | o8·=·HashTable{0·=>·11·} | 75 | o8·=·HashTable{0·=>·11·} |
| 76 | ···············1·=>·0 | 76 | ···············1·=>·0 |
| 77 | ···············2·=>·1 | 77 | ···············2·=>·1 |
| 78 | ···············3·=>·6 | 78 | ···············3·=>·6 |
| 79 | ···············4·=>·9 | 79 | ···············4·=>·9 |
| 80 | ···············5·=>·8 | 80 | ···············5·=>·8 |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) | 122 | <td>··············<pre><code·class="language-macaulay2">i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) |
| 123 | o9·=·true</code></pre> | 123 | o9·=·true</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·quickIsomorphismTest(M0,·M1) | 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·quickIsomorphismTest(M0,·M1) |
| 127 | ·--·used·0.000 | 127 | ·--·used·0.000926748s·(cpu);·0.000376285s·(thread);·0s·(gc) |
| 128 | o10·=·false</code></pre> | 128 | o10·=·false</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i11·:·value·oo·===·false | 131 | <td>··············<pre><code·class="language-macaulay2">i11·:·value·oo·===·false |
| 132 | o11·=·true</code></pre> | 132 | o11·=·true</code></pre> |
| Offset 52, 15 lines modified | Offset 52, 15 lines modified | ||
| 52 | o7·=·a·"matroid"·of·rank·7·on·11·elements | 52 | o7·=·a·"matroid"·of·rank·7·on·11·elements |
| 53 | o7·:·Matroid | 53 | o7·:·Matroid |
| 54 | i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) | 54 | i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) |
| 55 | o9·=·true | 55 | o9·=·true |
| 56 | i10·:·time·quickIsomorphismTest(M0,·M1) | 56 | i10·:·time·quickIsomorphismTest(M0,·M1) |
| 57 | ·--·used·0.000 | 57 | ·--·used·0.000926748s·(cpu);·0.000376285s·(thread);·0s·(gc) |
| 58 | o10·=·false | 58 | o10·=·false |
| 59 | i11·:·value·oo·===·false | 59 | i11·:·value·oo·===·false |
| 60 | o11·=·true | 60 | o11·=·true |
| 61 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 61 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 62 | ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between | 62 | ····*·_\x8i_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8,_\x8M_\x8a_\x8t_\x8r_\x8o_\x8i_\x8d_\x8)·--·computes·an·isomorphism·between |
| Offset 116, 15 lines modified | Offset 116, 15 lines modified | ||
| 116 | o5·=·{groundSet,·rankFunction,·storedRepresentation} | 116 | o5·=·{groundSet,·rankFunction,·storedRepresentation} |
| 117 | o5·:·List</code></pre> | 117 | o5·:·List</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·fVector·M | 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·fVector·M |
| 121 | ·--·.0 | 121 | ·--·.0741733s·elapsed |
| 122 | o6·=·HashTable{0·=>·1·} | 122 | o6·=·HashTable{0·=>·1·} |
| 123 | ···············1·=>·6 | 123 | ···············1·=>·6 |
| 124 | ···············2·=>·15 | 124 | ···············2·=>·15 |
| 125 | ···············3·=>·20 | 125 | ···············3·=>·20 |
| 126 | ···············4·=>·1 | 126 | ···············4·=>·1 |
| Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
| 49 | o4·:·Matrix·QQ··<--·QQ | 49 | o4·:·Matrix·QQ··<--·QQ |
| 50 | i5·:·keys·M.cache | 50 | i5·:·keys·M.cache |
| 51 | o5·=·{groundSet,·rankFunction,·storedRepresentation} | 51 | o5·=·{groundSet,·rankFunction,·storedRepresentation} |
| 52 | o5·:·List | 52 | o5·:·List |
| 53 | i6·:·elapsedTime·fVector·M | 53 | i6·:·elapsedTime·fVector·M |
| 54 | ·--·.0 | 54 | ·--·.0741733s·elapsed |
| 55 | o6·=·HashTable{0·=>·1·} | 55 | o6·=·HashTable{0·=>·1·} |
| 56 | ···············1·=>·6 | 56 | ···············1·=>·6 |
| 57 | ···············2·=>·15 | 57 | ···············2·=>·15 |
| 58 | ···············3·=>·20 | 58 | ···············3·=>·20 |
| 59 | ···············4·=>·1 | 59 | ···············4·=>·1 |
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| 8 | ZGVjb21wb3NlKElkZWFsLFN0cmF0ZWd5PT4uLi4p | 8 | ZGVjb21wb3NlKElkZWFsLFN0cmF0ZWd5PT4uLi4p |
| 9 | #:len=285 | 9 | #:len=285 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzEwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzEwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1soZGVjb21wb3NlLElkZWFsKSxTdHJhdGVneV0sImRl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1soZGVjb21wb3NlLElkZWFsKSxTdHJhdGVneV0sImRl |
| Offset 5, 16 lines modified | Offset 5, 16 lines modified | ||
| 5 | i2·:·R·=·ZZ/101[w..z]; | 5 | i2·:·R·=·ZZ/101[w..z]; |
| 6 | i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2); | 6 | i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2); |
| 7 | o3·:·Ideal·of·R | 7 | o3·:·Ideal·of·R |
| 8 | i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); | 8 | i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); |
| 9 | ··Strategy:·Linear············(time·0 | 9 | ··Strategy:·Linear············(time·.000444413)··#primes·=·0·#prunedViaCodim·=·0 |
| 10 | ··Strategy:·Birational········(time·.0 | 10 | ··Strategy:·Birational········(time·.013333)···#primes·=·0·#prunedViaCodim·=·0 |
| 11 | ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0 | 11 | ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0 |
| 12 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes... | 12 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes... |
| 13 | ·--··Time·taken·:·0 | 13 | ·--··Time·taken·:·0 |
| 14 | ·--·.0 | 14 | ·--·.0288672s·elapsed |
| 15 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0 | 15 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0 |
| 16 | i5·:· | 16 | i5·:· |
| Offset 30, 21 lines modified | Offset 30, 21 lines modified | ||
| 30 | ·············2········2···3·····2 | 30 | ·············2········2···3·····2 |
| 31 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) | 31 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) |
| 32 | o5·:·Ideal·of·R | 32 | o5·:·Ideal·of·R |
| 33 | i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) | 33 | i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) |
| 34 | ·--·.000 | 34 | ·--·.000789931s·elapsed |
| 35 | o6·=·ideal·(a,·b,·c) | 35 | o6·=·ideal·(a,·b,·c) |
| 36 | o6·:·Ideal·of·R | 36 | o6·:·Ideal·of·R |
| 37 | i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) | 37 | i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) |
| 38 | ·--·.0 | 38 | ·--·.0155863s·elapsed |
| 39 | o7·=·ideal·(c,·b,·a) | 39 | o7·=·ideal·(c,·b,·a) |
| 40 | o7·:·Ideal·of·R | 40 | o7·:·Ideal·of·R |
| 41 | i8·:· | 41 | i8·:· |
| Offset 29, 22 lines modified | Offset 29, 22 lines modified | ||
| 29 | o5·=·840 | 29 | o5·=·840 |
| 30 | i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 | 30 | i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 |
| 31 | o6·=·true | 31 | o6·=·true |
| 32 | i7·:·elapsedTime·radicalContainment(x_0,·I) | 32 | i7·:·elapsedTime·radicalContainment(x_0,·I) |
| 33 | ·--·. | 33 | ·--·.111395s·elapsed |
| 34 | o7·=·true | 34 | o7·=·true |
| 35 | i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") | 35 | i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") |
| 36 | ·--·.00 | 36 | ·--·.002157s·elapsed |
| 37 | o8·=·true | 37 | o8·=·true |
| 38 | i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") | 38 | i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") |
| 39 | ·--·.001 | 39 | ·--·.00189982s·elapsed |
| 40 | o9·=·false | 40 | o9·=·false |
| 41 | i10·:· | 41 | i10·:· |
| Offset 58, 20 lines modified | Offset 58, 20 lines modified | ||
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2); | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2); |
| 60 | o3·:·Ideal·of·R</code></pre> | 60 | o3·:·Ideal·of·R</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ··········<tr> | 62 | ··········<tr> |
| 63 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); | 63 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); |
| 64 | ··Strategy:·Linear············(time·0 | 64 | ··Strategy:·Linear············(time·.000444413)··#primes·=·0·#prunedViaCodim·=·0 |
| 65 | ··Strategy:·Birational········(time·.0 | 65 | ··Strategy:·Birational········(time·.013333)···#primes·=·0·#prunedViaCodim·=·0 |
| 66 | ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0 | 66 | ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0 |
| 67 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes... | 67 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes... |
| 68 | ·--··Time·taken·:·0 | 68 | ·--··Time·taken·:·0 |
| 69 | ·--·.0 | 69 | ·--·.0288672s·elapsed |
| 70 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0</code></pre> | 70 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ········</table> | 72 | ········</table> |
| 73 | ······</div> | 73 | ······</div> |
| 74 | ······<div> | 74 | ······<div> |
| 75 | ········<h2>See·also</h2> | 75 | ········<h2>See·also</h2> |
| 76 | ········<ul> | 76 | ········<ul> |
| Offset 11, 20 lines modified | Offset 11, 21 lines modified | ||
| 11 | i1·:·debug·MinimalPrimes | 11 | i1·:·debug·MinimalPrimes |
| 12 | i2·:·R·=·ZZ/101[w..z]; | 12 | i2·:·R·=·ZZ/101[w..z]; |
| 13 | i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2); | 13 | i3·:·I·=·ideal(w*x^2-42*y*z,·x^6+12*w*y+x^3*z,·w^2-47*x^4*z-47*x*z^2); |
| 14 | o3·:·Ideal·of·R | 14 | o3·:·Ideal·of·R |
| 15 | i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid | 15 | i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid |
| 16 | {Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); | 16 | {Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); |
| 17 | ··Strategy:·Linear············(time·0 | 17 | ··Strategy:·Linear············(time·.000444413)··#primes·=·0·#prunedViaCodim·= |
| 18 | 0 | ||
| 18 | ··Strategy:·Birational········(time·.0 | 19 | ··Strategy:·Birational········(time·.013333)···#primes·=·0·#prunedViaCodim·=·0 |
| 19 | ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0 | 20 | ··Strategy:·Factorization·····(time·0)·········#primes·=·0·#prunedViaCodim·=·0 |
| 20 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and | 21 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and |
| 21 | selecting·minimal·primes... | 22 | selecting·minimal·primes... |
| 22 | ·--··Time·taken·:·0 | 23 | ·--··Time·taken·:·0 |
| 23 | ·--·.0 | 24 | ·--·.0288672s·elapsed |
| 24 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0 | 25 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0 |
| 25 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 26 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n_\x8(_\x8._\x8._\x8._\x8,_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8=_\x8>_\x8._\x8._\x8._\x8) | 27 | ····*·_\x8p_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n_\x8(_\x8._\x8._\x8._\x8,_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y_\x8=_\x8>_\x8._\x8._\x8._\x8) |
| 27 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 28 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 28 | The·object·_\x8H_\x8y_\x8b_\x8r_\x8i_\x8d·is·a·_\x8s_\x8e_\x8l_\x8f_\x8·_\x8i_\x8n_\x8i_\x8t_\x8i_\x8a_\x8l_\x8i_\x8z_\x8i_\x8n_\x8g_\x8·_\x8t_\x8y_\x8p_\x8e,·with·ancestor·classes·_\x8L_\x8i_\x8s_\x8t·< | 29 | The·object·_\x8H_\x8y_\x8b_\x8r_\x8i_\x8d·is·a·_\x8s_\x8e_\x8l_\x8f_\x8·_\x8i_\x8n_\x8i_\x8t_\x8i_\x8a_\x8l_\x8i_\x8z_\x8i_\x8n_\x8g_\x8·_\x8t_\x8y_\x8p_\x8e,·with·ancestor·classes·_\x8L_\x8i_\x8s_\x8t·< |
| 29 | _\x8V_\x8i_\x8s_\x8i_\x8b_\x8l_\x8e_\x8L_\x8i_\x8s_\x8t·<·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8L_\x8i_\x8s_\x8t·<·_\x8T_\x8h_\x8i_\x8n_\x8g. | 30 | _\x8V_\x8i_\x8s_\x8i_\x8b_\x8l_\x8e_\x8L_\x8i_\x8s_\x8t·<·_\x8B_\x8a_\x8s_\x8i_\x8c_\x8L_\x8i_\x8s_\x8t·<·_\x8T_\x8h_\x8i_\x8n_\x8g. |
| Offset 123, 23 lines modified | Offset 123, 23 lines modified | ||
| 123 | ·············2········2···3·····2 | 123 | ·············2········2···3·····2 |
| 124 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) | 124 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) |
| 125 | o5·:·Ideal·of·R</code></pre> | 125 | o5·:·Ideal·of·R</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) | 128 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) |
| 129 | ·--·.000 | 129 | ·--·.000789931s·elapsed |
| 130 | o6·=·ideal·(a,·b,·c) | 130 | o6·=·ideal·(a,·b,·c) |
| 131 | o6·:·Ideal·of·R</code></pre> | 131 | o6·:·Ideal·of·R</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) | 134 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) |
| 135 | ·--·.0 | 135 | ·--·.0155863s·elapsed |
| 136 | o7·=·ideal·(c,·b,·a) | 136 | o7·=·ideal·(c,·b,·a) |
| 137 | o7·:·Ideal·of·R</code></pre> | 137 | o7·:·Ideal·of·R</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ········</table> | 139 | ········</table> |
| 140 | ········<div> | 140 | ········<div> |
| Offset 63, 21 lines modified | Offset 63, 21 lines modified | ||
| 63 | i5·:·I·=·intersect(ideal(a^2,b^2,c),·ideal(a,b^3,c^2)) | 63 | i5·:·I·=·intersect(ideal(a^2,b^2,c),·ideal(a,b^3,c^2)) |
| 64 | ·············2········2···3·····2 | 64 | ·············2········2···3·····2 |
| 65 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) | 65 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) |
| 66 | o5·:·Ideal·of·R | 66 | o5·:·Ideal·of·R |
| 67 | i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) | 67 | i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) |
| 68 | ·--·.000 | 68 | ·--·.000789931s·elapsed |
| 69 | o6·=·ideal·(a,·b,·c) | 69 | o6·=·ideal·(a,·b,·c) |
| 70 | o6·:·Ideal·of·R | 70 | o6·:·Ideal·of·R |
| 71 | i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) | 71 | i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) |
| 72 | ·--·.0 | 72 | ·--·.0155863s·elapsed |
| 73 | o7·=·ideal·(c,·b,·a) | 73 | o7·=·ideal·(c,·b,·a) |
| 74 | o7·:·Ideal·of·R | 74 | o7·:·Ideal·of·R |
| 75 | For·another·example,·see·_\x8P_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n. | 75 | For·another·example,·see·_\x8P_\x8r_\x8i_\x8m_\x8a_\x8r_\x8y_\x8D_\x8e_\x8c_\x8o_\x8m_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8o_\x8n. |
| 76 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 76 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 77 | Eisenbud,·Huneke,·Vasconcelos,·Invent.·Math.·110·207-235·(1992). | 77 | Eisenbud,·Huneke,·Vasconcelos,·Invent.·Math.·110·207-235·(1992). |
| Offset 115, 27 lines modified | Offset 115, 27 lines modified | ||
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 | 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 |
| 117 | o6·=·true</code></pre> | 117 | o6·=·true</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radicalContainment(x_0,·I) | 120 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radicalContainment(x_0,·I) |
| 121 | ·--·. | 121 | ·--·.111395s·elapsed |
| 122 | o7·=·true</code></pre> | 122 | o7·=·true</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") | 125 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") |
| 126 | ·--·.00 | 126 | ·--·.002157s·elapsed |
| 127 | o8·=·true</code></pre> | 127 | o8·=·true</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") | 130 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") |
| 131 | ·--·.001 | 131 | ·--·.00189982s·elapsed |
| 132 | o9·=·false</code></pre> | 132 | o9·=·false</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ········</table> | 134 | ········</table> |
| 135 | ······</div> | 135 | ······</div> |
| 136 | ······<div> | 136 | ······<div> |
| 137 | ········<h2>See·also</h2> | 137 | ········<h2>See·also</h2> |
| Offset 51, 23 lines modified | Offset 51, 23 lines modified | ||
| 51 | i5·:·D·=·product(I_*/degree/sum) | 51 | i5·:·D·=·product(I_*/degree/sum) |
| 52 | o5·=·840 | 52 | o5·=·840 |
| 53 | i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 | 53 | i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 |
| 54 | o6·=·true | 54 | o6·=·true |
| 55 | i7·:·elapsedTime·radicalContainment(x_0,·I) | 55 | i7·:·elapsedTime·radicalContainment(x_0,·I) |
| 56 | ·--·. | 56 | ·--·.111395s·elapsed |
| 57 | o7·=·true | 57 | o7·=·true |
| 58 | i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") | 58 | i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") |
| 59 | ·--·.00 | 59 | ·--·.002157s·elapsed |
| 60 | o8·=·true | 60 | o8·=·true |
| 61 | i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") | 61 | i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") |
| 62 | ·--·.001 | 62 | ·--·.00189982s·elapsed |
| 63 | o9·=·false | 63 | o9·=·false |
| 64 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 64 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 65 | ····*·_\x8r_\x8a_\x8d_\x8i_\x8c_\x8a_\x8l·--·the·radical·of·an·ideal | 65 | ····*·_\x8r_\x8a_\x8d_\x8i_\x8c_\x8a_\x8l·--·the·radical·of·an·ideal |
| 66 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8ad\x8di\x8ic\x8ca\x8al\x8lC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8nm\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 66 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8ad\x8di\x8ic\x8ca\x8al\x8lC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8nm\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 67 | ····*·radicalContainment(Ideal,Ideal) | 67 | ····*·radicalContainment(Ideal,Ideal) |
| 68 | ····*·radicalContainment(RingElement,Ideal) | 68 | ····*·radicalContainment(RingElement,Ideal) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | c2NhbGFyTXVsdGlwbGljYXRpb24= | 8 | c2NhbGFyTXVsdGlwbGljYXRpb24= |
| 9 | #:len=1333 | 9 | #:len=1333 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQWRkIFJlZHVjZWQgSWRlYWwgTXVsdGlw | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQWRkIFJlZHVjZWQgSWRlYWwgTXVsdGlw |
| 11 | bGUgVGltZXMiLCAibGluZW51bSIgPT4gMjAwLCBJbnB1dHMgPT4ge1NQQU57VFR7IkoifSwiLCAi | 11 | bGUgVGltZXMiLCAibGluZW51bSIgPT4gMjAwLCBJbnB1dHMgPT4ge1NQQU57VFR7IkoifSwiLCAi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | bXVsdGlSZWVzSWRlYWwoSWRlYWwp | 8 | bXVsdGlSZWVzSWRlYWwoSWRlYWwp |
| 9 | #:len=280 | 9 | #:len=280 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjA5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjA5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtdWx0aVJlZXNJZGVhbCxJZGVhbCksIm11bHRpUmVl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtdWx0aVJlZXNJZGVhbCxJZGVhbCksIm11bHRpUmVl |
| Offset 57, 29 lines modified | Offset 57, 29 lines modified | ||
| 57 | i9·:·J·=·ideal·vars·U | 57 | i9·:·J·=·ideal·vars·U |
| 58 | o9·=·ideal·(a,·b,·c) | 58 | o9·=·ideal·(a,·b,·c) |
| 59 | o9·:·Ideal·of·U | 59 | o9·:·Ideal·of·U |
| 60 | i10·:·time·multiReesIdeal·J | 60 | i10·:·time·multiReesIdeal·J |
| 61 | ·--·used· | 61 | ·--·used·0.876742s·(cpu);·0.15108s·(thread);·0s·(gc) |
| 62 | ············································································· | 62 | ············································································· |
| 63 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 63 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 64 | ················1······2·····1······2·····1······2·····0······2·····0······2· | 64 | ················1······2·····1······2·····1······2·····0······2·····0······2· |
| 65 | ······----------------------------------------------------------------------- | 65 | ······----------------------------------------------------------------------- |
| 66 | ····················2·················2···2 | 66 | ····················2·················2···2 |
| 67 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 67 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| 68 | ·········0······2···1····0·2···0·1····2···0····1·2 | 68 | ·········0······2···1····0·2···0·1····2···0····1·2 |
| 69 | o10·:·Ideal·of·U[X·..X·] | 69 | o10·:·Ideal·of·U[X·..X·] |
| 70 | ··················0···2 | 70 | ··················0···2 |
| 71 | i11·:·time·multiReesIdeal·(J,·a) | 71 | i11·:·time·multiReesIdeal·(J,·a) |
| 72 | ·--·used·0. | 72 | ·--·used·0.252245s·(cpu);·0.039178s·(thread);·0s·(gc) |
| 73 | ············································································· | 73 | ············································································· |
| 74 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 74 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 75 | ················1······2·····1······2·····1······2·····0······2·····0······2· | 75 | ················1······2·····1······2·····1······2·····0······2·····0······2· |
| 76 | ······----------------------------------------------------------------------- | 76 | ······----------------------------------------------------------------------- |
| 77 | ····················2·················2···2 | 77 | ····················2·················2···2 |
| 78 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 78 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| Offset 157, 30 lines modified | Offset 157, 30 lines modified | ||
| 157 | o9·=·ideal·(a,·b,·c) | 157 | o9·=·ideal·(a,·b,·c) |
| 158 | o9·:·Ideal·of·U</code></pre> | 158 | o9·:·Ideal·of·U</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ··········<tr> | 160 | ··········<tr> |
| 161 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·multiReesIdeal·J | 161 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·multiReesIdeal·J |
| 162 | ·--·used· | 162 | ·--·used·0.876742s·(cpu);·0.15108s·(thread);·0s·(gc) |
| 163 | ············································································· | 163 | ············································································· |
| 164 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 164 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 165 | ················1······2·····1······2·····1······2·····0······2·····0······2· | 165 | ················1······2·····1······2·····1······2·····0······2·····0······2· |
| 166 | ······----------------------------------------------------------------------- | 166 | ······----------------------------------------------------------------------- |
| 167 | ····················2·················2···2 | 167 | ····················2·················2···2 |
| 168 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 168 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| 169 | ·········0······2···1····0·2···0·1····2···0····1·2 | 169 | ·········0······2···1····0·2···0·1····2···0····1·2 |
| 170 | o10·:·Ideal·of·U[X·..X·] | 170 | o10·:·Ideal·of·U[X·..X·] |
| 171 | ··················0···2</code></pre> | 171 | ··················0···2</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·multiReesIdeal·(J,·a) | 174 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·multiReesIdeal·(J,·a) |
| 175 | ·--·used·0. | 175 | ·--·used·0.252245s·(cpu);·0.039178s·(thread);·0s·(gc) |
| 176 | ············································································· | 176 | ············································································· |
| 177 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 177 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 178 | ················1······2·····1······2·····1······2·····0······2·····0······2· | 178 | ················1······2·····1······2·····1······2·····0······2·····0······2· |
| 179 | ······----------------------------------------------------------------------- | 179 | ······----------------------------------------------------------------------- |
| 180 | ····················2·················2···2 | 180 | ····················2·················2···2 |
| 181 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 181 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| Offset 80, 28 lines modified | Offset 80, 28 lines modified | ||
| 80 | i8·:·U·=·T/minors(2,m); | 80 | i8·:·U·=·T/minors(2,m); |
| 81 | i9·:·J·=·ideal·vars·U | 81 | i9·:·J·=·ideal·vars·U |
| 82 | o9·=·ideal·(a,·b,·c) | 82 | o9·=·ideal·(a,·b,·c) |
| 83 | o9·:·Ideal·of·U | 83 | o9·:·Ideal·of·U |
| 84 | i10·:·time·multiReesIdeal·J | 84 | i10·:·time·multiReesIdeal·J |
| 85 | ·--·used· | 85 | ·--·used·0.876742s·(cpu);·0.15108s·(thread);·0s·(gc) |
| 86 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 86 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 87 | ················1······2·····1······2·····1······2·····0······2·····0······2 | 87 | ················1······2·····1······2·····1······2·····0······2·····0······2 |
| 88 | ······----------------------------------------------------------------------- | 88 | ······----------------------------------------------------------------------- |
| 89 | ····················2·················2···2 | 89 | ····················2·················2···2 |
| 90 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 90 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| 91 | ·········0······2···1····0·2···0·1····2···0····1·2 | 91 | ·········0······2···1····0·2···0·1····2···0····1·2 |
| 92 | o10·:·Ideal·of·U[X·..X·] | 92 | o10·:·Ideal·of·U[X·..X·] |
| 93 | ··················0···2 | 93 | ··················0···2 |
| 94 | i11·:·time·multiReesIdeal·(J,·a) | 94 | i11·:·time·multiReesIdeal·(J,·a) |
| 95 | ·--·used·0. | 95 | ·--·used·0.252245s·(cpu);·0.039178s·(thread);·0s·(gc) |
| 96 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 96 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 97 | ················1······2·····1······2·····1······2·····0······2·····0······2 | 97 | ················1······2·····1······2·····1······2·····0······2·····0······2 |
| 98 | ······----------------------------------------------------------------------- | 98 | ······----------------------------------------------------------------------- |
| 99 | ····················2·················2···2 | 99 | ····················2·················2···2 |
| 100 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 100 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=15 | 7 | #:len=15 |
| 8 | ZGVmb3JtTUNNTW9kdWxl | 8 | ZGVmb3JtTUNNTW9kdWxl |
| 9 | #:len=2237 | 9 | #:len=2237 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmVyc2FsIGRlZm9ybWF0aW9uIG9mIE1D | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmVyc2FsIGRlZm9ybWF0aW9uIG9mIE1D |
| 11 | TS1tb2R1bGUgb24gaHlwZXJzdXJmYWNlIiwgRGVzY3JpcHRpb24gPT4gKCJUaGlzIGlzIHRoZSBt | 11 | TS1tb2R1bGUgb24gaHlwZXJzdXJmYWNlIiwgRGVzY3JpcHRpb24gPT4gKCJUaGlzIGlzIHRoZSBt |
| Offset 40, 15 lines modified | Offset 40, 15 lines modified | ||
| 40 | o7·=·image·|·x2·y2·| | 40 | o7·=·image·|·x2·y2·| |
| 41 | ·····························1 | 41 | ·····························1 |
| 42 | o7·:·R-module,·submodule·of·R | 42 | o7·:·R-module,·submodule·of·R |
| 43 | i8·:·(S,N)·=·time·deformMCMModule·N0· | 43 | i8·:·(S,N)·=·time·deformMCMModule·N0· |
| 44 | ·--·used·0. | 44 | ·--·used·0.401488s·(cpu);·0.275615s·(thread);·0s·(gc) |
| 45 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 | 45 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 |
| 46 | ··················{8}·|·xxi_4-y+xi_3······································· | 46 | ··················{8}·|·xxi_4-y+xi_3······································· |
| 47 | ·····------------------------------------------------------------------------ | 47 | ·····------------------------------------------------------------------------ |
| 48 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) | 48 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) |
| 49 | ·····-x2-xxi_2-xi_1···········································| | 49 | ·····-x2-xxi_2-xi_1···········································| |
| Offset 70, 15 lines modified | Offset 70, 15 lines modified | ||
| 70 | o10·=·cokernel·|·x2·y2··| | 70 | o10·=·cokernel·|·x2·y2··| |
| 71 | ···············|·-y·-x2·| | 71 | ···············|·-y·-x2·| |
| 72 | ·····························2 | 72 | ·····························2 |
| 73 | o10·:·R-module,·quotient·of·R | 73 | o10·:·R-module,·quotient·of·R |
| 74 | i11·:·(S',N')·=·time·deformMCMModule·N0' | 74 | i11·:·(S',N')·=·time·deformMCMModule·N0' |
| 75 | ·--·used·0. | 75 | ·--·used·0.538288s·(cpu);·0.404418s·(thread);·0s·(gc) |
| 76 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 | 76 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 |
| 77 | ····················|·xxi_4-y+xi_3······································· | 77 | ····················|·xxi_4-y+xi_3······································· |
| 78 | ······----------------------------------------------------------------------- | 78 | ······----------------------------------------------------------------------- |
| 79 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) | 79 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) |
| 80 | ······-x2-xxi_2-xi_1·····························| | 80 | ······-x2-xxi_2-xi_1·····························| |
| Offset 134, 15 lines modified | Offset 134, 15 lines modified | ||
| 134 | o7·=·image·|·x2·y2·| | 134 | o7·=·image·|·x2·y2·| |
| 135 | ·····························1 | 135 | ·····························1 |
| 136 | o7·:·R-module,·submodule·of·R</code></pre> | 136 | o7·:·R-module,·submodule·of·R</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i8·:·(S,N)·=·time·deformMCMModule·N0· | 139 | <td>··············<pre><code·class="language-macaulay2">i8·:·(S,N)·=·time·deformMCMModule·N0· |
| 140 | ·--·used·0. | 140 | ·--·used·0.401488s·(cpu);·0.275615s·(thread);·0s·(gc) |
| 141 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 | 141 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 |
| 142 | ··················{8}·|·xxi_4-y+xi_3······································· | 142 | ··················{8}·|·xxi_4-y+xi_3······································· |
| 143 | ·····------------------------------------------------------------------------ | 143 | ·····------------------------------------------------------------------------ |
| 144 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) | 144 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) |
| 145 | ·····-x2-xxi_2-xi_1···········································| | 145 | ·····-x2-xxi_2-xi_1···········································| |
| Offset 169, 15 lines modified | Offset 169, 15 lines modified | ||
| 169 | ···············|·-y·-x2·| | 169 | ···············|·-y·-x2·| |
| 170 | ·····························2 | 170 | ·····························2 |
| 171 | o10·:·R-module,·quotient·of·R</code></pre> | 171 | o10·:·R-module,·quotient·of·R</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i11·:·(S',N')·=·time·deformMCMModule·N0' | 174 | <td>··············<pre><code·class="language-macaulay2">i11·:·(S',N')·=·time·deformMCMModule·N0' |
| 175 | ·--·used·0. | 175 | ·--·used·0.538288s·(cpu);·0.404418s·(thread);·0s·(gc) |
| 176 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 | 176 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 |
| 177 | ····················|·xxi_4-y+xi_3······································· | 177 | ····················|·xxi_4-y+xi_3······································· |
| 178 | ······----------------------------------------------------------------------- | 178 | ······----------------------------------------------------------------------- |
| 179 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) | 179 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) |
| 180 | ······-x2-xxi_2-xi_1·····························| | 180 | ······-x2-xxi_2-xi_1·····························| |
| Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
| 71 | i7·:·N0·=·module·ideal·(x^2,y^2) | 71 | i7·:·N0·=·module·ideal·(x^2,y^2) |
| 72 | o7·=·image·|·x2·y2·| | 72 | o7·=·image·|·x2·y2·| |
| 73 | ·····························1 | 73 | ·····························1 |
| 74 | o7·:·R-module,·submodule·of·R | 74 | o7·:·R-module,·submodule·of·R |
| 75 | i8·:·(S,N)·=·time·deformMCMModule·N0 | 75 | i8·:·(S,N)·=·time·deformMCMModule·N0 |
| 76 | ·--·used·0. | 76 | ·--·used·0.401488s·(cpu);·0.275615s·(thread);·0s·(gc) |
| 77 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 | 77 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 |
| 78 | ··················{8}·|·xxi_4-y+xi_3 | 78 | ··················{8}·|·xxi_4-y+xi_3 |
| 79 | ·····------------------------------------------------------------------------ | 79 | ·····------------------------------------------------------------------------ |
| 80 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) | 80 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) |
| 81 | ·····-x2-xxi_2-xi_1···········································| | 81 | ·····-x2-xxi_2-xi_1···········································| |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | o10·=·cokernel·|·x2·y2··| | 104 | o10·=·cokernel·|·x2·y2··| |
| 105 | ···············|·-y·-x2·| | 105 | ···············|·-y·-x2·| |
| 106 | ·····························2 | 106 | ·····························2 |
| 107 | o10·:·R-module,·quotient·of·R | 107 | o10·:·R-module,·quotient·of·R |
| 108 | i11·:·(S',N')·=·time·deformMCMModule·N0' | 108 | i11·:·(S',N')·=·time·deformMCMModule·N0' |
| 109 | ·--·used·0. | 109 | ·--·used·0.538288s·(cpu);·0.404418s·(thread);·0s·(gc) |
| 110 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 | 110 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 |
| 111 | ····················|·xxi_4-y+xi_3 | 111 | ····················|·xxi_4-y+xi_3 |
| 112 | ······----------------------------------------------------------------------- | 112 | ······----------------------------------------------------------------------- |
| 113 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) | 113 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) |
| 114 | ······-x2-xxi_2-xi_1·····························| | 114 | ······-x2-xxi_2-xi_1·····························| |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=46 | 7 | #:len=46 |
| 8 | c3BhcnNlTW9ub2Ryb215U29sdmUoLi4uLE51bWJlck9mUmVwZWF0cz0+Li4uKQ== | 8 | c3BhcnNlTW9ub2Ryb215U29sdmUoLi4uLE51bWJlck9mUmVwZWF0cz0+Li4uKQ== |
| 9 | #:len=345 | 9 | #:len=345 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tzcGFyc2VNb25vZHJvbXlTb2x2ZSxOdW1iZXJPZlJl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tzcGFyc2VNb25vZHJvbXlTb2x2ZSxOdW1iZXJPZlJl |
| Offset 3, 27 lines modified | Offset 3, 27 lines modified | ||
| 3 | i1·:·R·=·CC[a,b,c,d][x,y]; | 3 | i1·:·R·=·CC[a,b,c,d][x,y]; |
| 4 | i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d}; | 4 | i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d}; |
| 5 | i3·:·(p0,·x0)·=·createSeedPair·polys; | 5 | i3·:·(p0,·x0)·=·createSeedPair·polys; |
| 6 | i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) | 6 | i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) |
| 7 | ·--·.00299355s·elapsed | ||
| 8 | ·--·.00263486s·elapsed | ||
| 9 | ·--·.000395392s·elapsed | ||
| 10 | ·--·.00259313s·elapsed | ||
| 11 | ·--·.0466186s·elapsed | ||
| 12 | ·--·.000393678s·elapsed | ||
| 7 | ·--·.002 | 13 | ·--·.00295821s·elapsed |
| 8 | ·--·.0 | 14 | ·--·.00292531s·elapsed |
| 9 | ·--·.000 | 15 | ·--·.000252974s·elapsed |
| 10 | ·--·.00885352s·elapsed | ||
| 11 | ·--·.107761s·elapsed | ||
| 12 | ·--·.000291269s·elapsed | ||
| 13 | ·--·.00228285s·elapsed | ||
| 14 | ·--·.0 | 16 | ·--·.00358438s·elapsed |
| 15 | ·--·.000212932s·elapsed | ||
| 16 | ·--·.00 | 17 | ·--·.00314339s·elapsed |
| 17 | ·--·.002 | 18 | ·--·.000278752s·elapsed |
| 18 | ·--·.000204619s·elapsed | ||
| 19 | --backup·directory·created:·/tmp/M2- | 19 | --backup·directory·created:·/tmp/M2-3704705-0/1 |
| 20 | ··H01:·1 | 20 | ··H01:·1 |
| 21 | ··H10:·1 | 21 | ··H10:·1 |
| 22 | number·of·paths·tracked:·2 | 22 | number·of·paths·tracked:·2 |
| 23 | found·1·points·in·the·fiber·so·far | 23 | found·1·points·in·the·fiber·so·far |
| 24 | ··H01:·1 | 24 | ··H01:·1 |
| 25 | ··H10:·1 | 25 | ··H10:·1 |
| 26 | number·of·paths·tracked:·4 | 26 | number·of·paths·tracked:·4 |
| Offset 96, 27 lines modified | Offset 96, 27 lines modified | ||
| 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·(p0,·x0)·=·createSeedPair·polys;</code></pre> | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·(p0,·x0)·=·createSeedPair·polys;</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) |
| 103 | ·--·.00299355s·elapsed | ||
| 104 | ·--·.00263486s·elapsed | ||
| 105 | ·--·.000395392s·elapsed | ||
| 106 | ·--·.00259313s·elapsed | ||
| 107 | ·--·.0466186s·elapsed | ||
| 108 | ·--·.000393678s·elapsed | ||
| 103 | ·--·.002 | 109 | ·--·.00295821s·elapsed |
| 104 | ·--·.0 | 110 | ·--·.00292531s·elapsed |
| 105 | ·--·.000 | 111 | ·--·.000252974s·elapsed |
| 106 | ·--·.00885352s·elapsed | ||
| 107 | ·--·.107761s·elapsed | ||
| 108 | ·--·.000291269s·elapsed | ||
| 109 | ·--·.00228285s·elapsed | ||
| 110 | ·--·.0 | 112 | ·--·.00358438s·elapsed |
| 111 | ·--·.000212932s·elapsed | ||
| 112 | ·--·.00 | 113 | ·--·.00314339s·elapsed |
| 113 | ·--·.002 | 114 | ·--·.000278752s·elapsed |
| 114 | ·--·.000204619s·elapsed | ||
| 115 | --backup·directory·created:·/tmp/M2- | 115 | --backup·directory·created:·/tmp/M2-3704705-0/1 |
| 116 | ··H01:·1 | 116 | ··H01:·1 |
| 117 | ··H10:·1 | 117 | ··H10:·1 |
| 118 | number·of·paths·tracked:·2 | 118 | number·of·paths·tracked:·2 |
| 119 | found·1·points·in·the·fiber·so·far | 119 | found·1·points·in·the·fiber·so·far |
| 120 | ··H01:·1 | 120 | ··H01:·1 |
| 121 | ··H10:·1 | 121 | ··H10:·1 |
| 122 | number·of·paths·tracked:·4 | 122 | number·of·paths·tracked:·4 |
| Offset 23, 27 lines modified | Offset 23, 27 lines modified | ||
| 23 | ··········o·npaths,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r, | 23 | ··········o·npaths,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r, |
| 24 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 25 | Output·is·verbose.·For·other·dynamic·strategies,·see·_\x8M_\x8o_\x8n_\x8o_\x8d_\x8r_\x8o_\x8m_\x8y_\x8S_\x8o_\x8l_\x8v_\x8e_\x8r_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 25 | Output·is·verbose.·For·other·dynamic·strategies,·see·_\x8M_\x8o_\x8n_\x8o_\x8d_\x8r_\x8o_\x8m_\x8y_\x8S_\x8o_\x8l_\x8v_\x8e_\x8r_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| 26 | i1·:·R·=·CC[a,b,c,d][x,y]; | 26 | i1·:·R·=·CC[a,b,c,d][x,y]; |
| 27 | i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d}; | 27 | i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d}; |
| 28 | i3·:·(p0,·x0)·=·createSeedPair·polys; | 28 | i3·:·(p0,·x0)·=·createSeedPair·polys; |
| 29 | i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) | 29 | i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) |
| 30 | ·--·.00299355s·elapsed | ||
| 31 | ·--·.00263486s·elapsed | ||
| 32 | ·--·.000395392s·elapsed | ||
| 33 | ·--·.00259313s·elapsed | ||
| 34 | ·--·.0466186s·elapsed | ||
| 35 | ·--·.000393678s·elapsed | ||
| 30 | ·--·.002 | 36 | ·--·.00295821s·elapsed |
| 31 | ·--·.0 | 37 | ·--·.00292531s·elapsed |
| 32 | ·--·.000 | 38 | ·--·.000252974s·elapsed |
| 33 | ·--·.00885352s·elapsed | ||
| 34 | ·--·.107761s·elapsed | ||
| 35 | ·--·.000291269s·elapsed | ||
| 36 | ·--·.00228285s·elapsed | ||
| 37 | ·--·.0 | 39 | ·--·.00358438s·elapsed |
| 38 | ·--·.000212932s·elapsed | ||
| 39 | ·--·.00 | 40 | ·--·.00314339s·elapsed |
| 40 | ·--·.002 | 41 | ·--·.000278752s·elapsed |
| 41 | ·--·.000204619s·elapsed | ||
| 42 | --backup·directory·created:·/tmp/M2- | 42 | --backup·directory·created:·/tmp/M2-3704705-0/1 |
| 43 | ··H01:·1 | 43 | ··H01:·1 |
| 44 | ··H10:·1 | 44 | ··H10:·1 |
| 45 | number·of·paths·tracked:·2 | 45 | number·of·paths·tracked:·2 |
| 46 | found·1·points·in·the·fiber·so·far | 46 | found·1·points·in·the·fiber·so·far |
| 47 | ··H01:·1 | 47 | ··H01:·1 |
| 48 | ··H10:·1 | 48 | ··H10:·1 |
| 49 | number·of·paths·tracked:·4 | 49 | number·of·paths·tracked:·4 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=28 | 7 | #:len=28 |
| 8 | ZGVjb21wb3NlSG9tb2dlbmVvdXNNQShMaXN0KQ== | 8 | ZGVjb21wb3NlSG9tb2dlbmVvdXNNQShMaXN0KQ== |
| 9 | #:len=308 | 9 | #:len=308 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTYxMSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTYxMSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZGVjb21wb3NlSG9tb2dlbmVvdXNNQSxMaXN0KSwi | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZGVjb21wb3NlSG9tb2dlbmVvdXNNQSxMaXN0KSwi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | R3JhZGVkQmV0dGlz | 8 | R3JhZGVkQmV0dGlz |
| 9 | #:len=431 | 9 | #:len=431 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtEZXNjcmlwdGlvbiA9PiB7fSwgImxpbmVudW0iID0+IDExNDYs | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtEZXNjcmlwdGlvbiA9PiB7fSwgImxpbmVudW0iID0+IDExNDYs |
| 11 | IHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7IkdyYWRlZEJldHRp | 11 | IHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7IkdyYWRlZEJldHRp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | aGlsYmVydFJlcHJlc2VudGF0aXZlcw== | 8 | aGlsYmVydFJlcHJlc2VudGF0aXZlcw== |
| 9 | #:len=3397 | 9 | #:len=3397 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZCByZXByZXNlbnRhdGl2ZXMgb2Yg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZCByZXByZXNlbnRhdGl2ZXMgb2Yg |
| 11 | bW9ub21pYWwgaWRlYWxzIHVuZGVyIHBlcm11dGF0aW9ucyBvZiB0aGUgdmFyaWFibGVzIiwgImxp | 11 | bW9ub21pYWwgaWRlYWxzIHVuZGVyIHBlcm11dGF0aW9ucyBvZiB0aGUgdmFyaWFibGVzIiwgImxp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | bXNvbHZlUlVSKElkZWFsKQ== | 8 | bXNvbHZlUlVSKElkZWFsKQ== |
| 9 | #:len=227 | 9 | #:len=227 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjM2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjM2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtc29sdmVSVVIsSWRlYWwpLCJtc29sdmVSVVIoSWRl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtc29sdmVSVVIsSWRlYWwpLCJtc29sdmVSVVIoSWRl |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i2·:·I·=·ideal(x,·y,·z) | 9 | i2·:·I·=·ideal(x,·y,·z) |
| 10 | o2·=·ideal·(x,·y,·z) | 10 | o2·=·ideal·(x,·y,·z) |
| 11 | o2·:·Ideal·of·R | 11 | o2·:·Ideal·of·R |
| 12 | i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6) | 12 | i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6) |
| 13 | ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2- | 13 | ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-3824309-0/0-in.ms·-o·/tmp/M2-3824309-0/0-out.ms |
| 14 | ---------------·INPUT·DATA·--------------- | 14 | ---------------·INPUT·DATA·--------------- |
| 15 | #variables·······················3 | 15 | #variables·······················3 |
| 16 | #equations·······················3 | 16 | #equations·······················3 |
| 17 | #invalid·equations···············0 | 17 | #invalid·equations···············0 |
| 18 | field·characteristic·············0 | 18 | field·characteristic·············0 |
| 19 | homogeneous·input?···············1 | 19 | homogeneous·input?···············1 |
| Offset 45, 24 lines modified | Offset 45, 24 lines modified | ||
| 45 | time(rd)··time·of·the·current·f4·round·in·seconds·given | 45 | time(rd)··time·of·the·current·f4·round·in·seconds·given |
| 46 | ··········for·real·and·cpu·time | 46 | ··········for·real·and·cpu·time |
| 47 | -------------------------------------------------------- | 47 | -------------------------------------------------------- |
| 48 | deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu) | 48 | deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu) |
| 49 | ------------------------------------------------------------------------------------------------------ | 49 | ------------------------------------------------------------------------------------------------------ |
| 50 | ------------------------------------------------------------------------------------------------------ | 50 | ------------------------------------------------------------------------------------------------------ |
| 51 | reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.0 | 51 | reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.03·|·0.11········· |
| 52 | ------------------------------------------------------------------------------------------------------ | 52 | ------------------------------------------------------------------------------------------------------ |
| 53 | ----------------·TIMINGS·---------------- | 53 | ----------------·TIMINGS·---------------- |
| 54 | overall(elapsed)········0. | 54 | overall(elapsed)········0.07·sec |
| 55 | overall(cpu)············0. | 55 | overall(cpu)············0.23·sec |
| 56 | select··················0.00·sec···0.0% | 56 | select··················0.00·sec···0.0% |
| 57 | symbolic·prep.··········0.00·sec···0.0% | 57 | symbolic·prep.··········0.00·sec···0.0% |
| 58 | update··················0.0 | 58 | update··················0.04·sec··55.0% |
| 59 | convert·················0.0 | 59 | convert·················0.03·sec··44.7% |
| 60 | linear·algebra··········0.00·sec···0.0% | 60 | linear·algebra··········0.00·sec···0.0% |
| 61 | reduce·gb···············0.00·sec···0.0% | 61 | reduce·gb···············0.00·sec···0.0% |
| 62 | ----------------------------------------- | 62 | ----------------------------------------- |
| 63 | ----------·COMPUTATIONAL·DATA·----------- | 63 | ----------·COMPUTATIONAL·DATA·----------- |
| 64 | size·of·basis·····················3 | 64 | size·of·basis·····················3 |
| 65 | #terms·in·basis···················3 | 65 | #terms·in·basis···················3 |
| Offset 86, 33 lines modified | Offset 86, 33 lines modified | ||
| 86 | multi-mod·overall(elapsed)······0.08·sec | 86 | multi-mod·overall(elapsed)······0.08·sec |
| 87 | learning·phase··················0.00·Gops/sec | 87 | learning·phase··················0.00·Gops/sec |
| 88 | application·phase···············0.00·Gops/sec | 88 | application·phase···············0.00·Gops/sec |
| 89 | ----------------------------------------- | 89 | ----------------------------------------- |
| 90 | multi-modular·steps | 90 | multi-modular·steps |
| 91 | ------------------------------------------------------------------------------------------------------ | 91 | ------------------------------------------------------------------------------------------------------ |
| 92 | {1}{2}<100.00%> | 92 | {1}{2}<100.00%>· |
| 93 | ------------------------------------------------------------------------------------ | ||
| 94 | msolve·overall·time···········0.26·sec·(elapsed)·/··0.88·sec·(cpu) | ||
| 95 | ------------------------------------------------------------------------------------ | ||
| 96 | · | ||
| 97 | ------------------------------------------------------------------------------------------------------ | 93 | ------------------------------------------------------------------------------------------------------ |
| 98 | ----------·COMPUTATIONAL·DATA·----------- | 94 | ----------·COMPUTATIONAL·DATA·----------- |
| 99 | Max·coeff.·bitsize················1 | 95 | Max·coeff.·bitsize················1 |
| 100 | #primes···························3 | 96 | #primes···························3 |
| 101 | #bad·primes·······················0 | 97 | #bad·primes·······················0 |
| 102 | ----------------------------------------- | 98 | ----------------------------------------- |
| 103 | ----------------·TIMINGS·---------------- | 99 | ----------------·TIMINGS·---------------- |
| 104 | CRT·····(elapsed)···············0.00·sec | 100 | CRT·····(elapsed)···············0.00·sec |
| 105 | ratrecon(elapsed)···············0.00·sec | 101 | ratrecon(elapsed)···············0.00·sec |
| 106 | ----------------------------------------- | 102 | ----------------------------------------- |
| 103 | ------------------------------------------------------------------------------------ | ||
| 104 | msolve·overall·time···········0.31·sec·(elapsed)·/··0.95·sec·(cpu) | ||
| 105 | ------------------------------------------------------------------------------------ | ||
| 107 | o3·=·|·z·y·x·| | 106 | o3·=·|·z·y·x·| |
| 108 | ·············1······3 | 107 | ·············1······3 |
| 109 | o3·:·Matrix·R··<--·R | 108 | o3·:·Matrix·R··<--·R |
| 110 | i4·:· | 109 | i4·:· |
| Offset 11, 51 lines modified | Offset 11, 51 lines modified | ||
| 11 | ·············2·······2 | 11 | ·············2·······2 |
| 12 | o2·=·ideal·(x··-·x,·y··-·5) | 12 | o2·=·ideal·(x··-·x,·y··-·5) |
| 13 | o2·:·Ideal·of·R | 13 | o2·:·Ideal·of·R |
| 14 | i3·:·rationalIntervalSols·=·msolveRealSolutions·I | 14 | i3·:·rationalIntervalSols·=·msolveRealSolutions·I |
| 15 | ········ | 15 | ···············1···········1········4801919417··9603838835······4294967295· |
| 16 | o3·=·{{{----------,·----------},·{ | 16 | o3·=·{{{-·----------,·----------},·{----------,·----------}},·{{----------, |
| 17 | ········4294967296··4294967296······4294967296···· | 17 | ··········4294967296··4294967296····2147483648··4294967296······4294967296· |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ··········1···········1··········9603838835····4801919417······4294967295· | ||
| 20 | ·····----------,·----------},·{-·----------,·-·----------}},·{{----------, | ||
| 21 | ·····429496729 | 19 | ·····4294967297····4801919417··9603838835·············1···········1········· |
| 20 | ·····----------},·{----------,·----------}},·{{-·----------,·----------},·{- | ||
| 21 | ·····4294967296····2147483648··4294967296········4294967296··4294967296····· | ||
| 22 | ·····------------------------------------------------------------------------ | 22 | ·····------------------------------------------------------------------------ |
| 23 | ····· | 23 | ·····9603838835····4801919417······4294967295··4294967297······9603838835··· |
| 24 | ·····---------- | 24 | ·····----------,·-·----------}},·{{----------,·----------},·{-·----------,·- |
| 25 | ·····4294967296····2147483648··4294967296 | 25 | ·····4294967296····2147483648······4294967296··4294967296······4294967296··· |
| 26 | ·····------------------------------------------------------------------------ | 26 | ·····------------------------------------------------------------------------ |
| 27 | ······4801919417··9603838835 | ||
| 28 | ·····{----------,·----------}}} | ||
| 29 | ····· | 27 | ·····4801919417 |
| 28 | ·····----------}}} | ||
| 29 | ·····2147483648 | ||
| 30 | o3·:·List | 30 | o3·:·List |
| 31 | i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ) | 31 | i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ) |
| 32 | ·········· | 32 | ··········19207677669·······19207677669·········19207677669········ |
| 33 | o4·=·{{ | 33 | o4·=·{{0,·-----------},·{1,·-----------},·{0,·-·-----------},·{1,·- |
| 34 | ··········· | 34 | ···········8589934592········8589934592··········8589934592········ |
| 35 | ·····------------------------------------------------------------------------ | 35 | ·····------------------------------------------------------------------------ |
| 36 | ·····19207677669 | 36 | ·····19207677669 |
| 37 | ·····-----------}} | 37 | ·····-----------}} |
| 38 | ······8589934592 | 38 | ······8589934592 |
| 39 | o4·:·List | 39 | o4·:·List |
| 40 | i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi) | 40 | i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi) |
| 41 | o5·=·{{[ | 41 | o5·=·{{[-2.32831e-10,2.32831e-10],·[2.23607,2.23607]},·{[1,1], |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·····[ | 43 | ·····[2.23607,2.23607]},·{[-2.32831e-10,2.32831e-10],·[-2.23607,-2.23607]}, |
| 44 | ·····------------------------------------------------------------------------ | 44 | ·····------------------------------------------------------------------------ |
| 45 | ·····{[ | 45 | ·····{[1,1],·[-2.23607,-2.23607]}} |
| 46 | o5·:·List | 46 | o5·:·List |
| 47 | i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10) | 47 | i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10) |
| 48 | o6·=·{{[.999023,1.00098],·[-2.23633,-2.23535]},·{[-.000976562,.000976562], | 48 | o6·=·{{[.999023,1.00098],·[-2.23633,-2.23535]},·{[-.000976562,.000976562], |
| 49 | ·····------------------------------------------------------------------------ | 49 | ·····------------------------------------------------------------------------ |
| Offset 69, 15 lines modified | Offset 69, 15 lines modified | ||
| 69 | o7·=·{{1,·-2.23607},·{0,·-2.23607},·{1,·2.23607},·{0,·2.23607}} | 69 | o7·=·{{1,·-2.23607},·{0,·-2.23607},·{1,·2.23607},·{0,·2.23607}} |
| 70 | o7·:·List | 70 | o7·:·List |
| 71 | i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10) | 71 | i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10) |
| 72 | o8·=·{{ | 72 | o8·=·{{1,·-2.23584},·{0,·-2.23584},·{1,·2.23584},·{0,·2.23584}} |
| 73 | o8·:·List | 73 | o8·:·List |
| 74 | i9·:·I·=·ideal·{(x-1)*x^3,·(y^2-5)^2} | 74 | i9·:·I·=·ideal·{(x-1)*x^3,·(y^2-5)^2} |
| 75 | ·············4····3···4······2 | 75 | ·············4····3···4······2 |
| 76 | o9·=·ideal·(x··-·x·,·y··-·10y··+·25) | 76 | o9·=·ideal·(x··-·x·,·y··-·10y··+·25) |
| Offset 99, 53 lines modified | Offset 99, 53 lines modified | ||
| 99 | o2·=·ideal·(x··-·x,·y··-·5) | 99 | o2·=·ideal·(x··-·x,·y··-·5) |
| 100 | o2·:·Ideal·of·R</code></pre> | 100 | o2·:·Ideal·of·R</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·rationalIntervalSols·=·msolveRealSolutions·I | 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·rationalIntervalSols·=·msolveRealSolutions·I |
| 104 | ········ | 104 | ···············1···········1········4801919417··9603838835······4294967295· |
| 105 | o3·=·{{{----------,·----------},·{ | 105 | o3·=·{{{-·----------,·----------},·{----------,·----------}},·{{----------, |
| 106 | ········4294967296··4294967296······4294967296···· | 106 | ··········4294967296··4294967296····2147483648··4294967296······4294967296· |
| 107 | ·····------------------------------------------------------------------------ | 107 | ·····------------------------------------------------------------------------ |
| 108 | ··········1···········1··········9603838835····4801919417······4294967295· | ||
| 109 | ·····----------,·----------},·{-·----------,·-·----------}},·{{----------, | ||
| 110 | ·····429496729 | 108 | ·····4294967297····4801919417··9603838835·············1···········1········· |
| 109 | ·····----------},·{----------,·----------}},·{{-·----------,·----------},·{- | ||
| 110 | ·····4294967296····2147483648··4294967296········4294967296··4294967296····· | ||
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| 112 | ····· | 112 | ·····9603838835····4801919417······4294967295··4294967297······9603838835··· |
| 113 | ·····---------- | 113 | ·····----------,·-·----------}},·{{----------,·----------},·{-·----------,·- |
| 114 | ·····4294967296····2147483648··4294967296 | 114 | ·····4294967296····2147483648······4294967296··4294967296······4294967296··· |
| 115 | ·····------------------------------------------------------------------------ | 115 | ·····------------------------------------------------------------------------ |
| 116 | ······4801919417··9603838835 | ||
| 117 | ·····{----------,·----------}}} | ||
| 118 | ····· | 116 | ·····4801919417 |
| 117 | ·····----------}}} | ||
| 118 | ·····2147483648 | ||
| 119 | o3·:·List</code></pre> | 119 | o3·:·List</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ) | 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ) |
| 123 | ·········· | 123 | ··········19207677669·······19207677669·········19207677669········ |
| 124 | o4·=·{{ | 124 | o4·=·{{0,·-----------},·{1,·-----------},·{0,·-·-----------},·{1,·- |
| 125 | ··········· | 125 | ···········8589934592········8589934592··········8589934592········ |
| 126 | ·····------------------------------------------------------------------------ | 126 | ·····------------------------------------------------------------------------ |
| 127 | ·····19207677669 | 127 | ·····19207677669 |
| 128 | ·····-----------}} | 128 | ·····-----------}} |
| 129 | ······8589934592 | 129 | ······8589934592 |
| 130 | o4·:·List</code></pre> | 130 | o4·:·List</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi) | 133 | <td>··············<pre><code·class="language-macaulay2">i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi) |
| 134 | o5·=·{{[ | 134 | o5·=·{{[-2.32831e-10,2.32831e-10],·[2.23607,2.23607]},·{[1,1], |
| 135 | ·····------------------------------------------------------------------------ | 135 | ·····------------------------------------------------------------------------ |
| 136 | ·····[ | 136 | ·····[2.23607,2.23607]},·{[-2.32831e-10,2.32831e-10],·[-2.23607,-2.23607]}, |
| 137 | ·····------------------------------------------------------------------------ | 137 | ·····------------------------------------------------------------------------ |
| 138 | ·····{[ | 138 | ·····{[1,1],·[-2.23607,-2.23607]}} |
| 139 | o5·:·List</code></pre> | 139 | o5·:·List</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10) | 142 | <td>··············<pre><code·class="language-macaulay2">i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10) |
| 143 | o6·=·{{[.999023,1.00098],·[-2.23633,-2.23535]},·{[-.000976562,.000976562], | 143 | o6·=·{{[.999023,1.00098],·[-2.23633,-2.23535]},·{[-.000976562,.000976562], |
| Offset 162, 15 lines modified | Offset 162, 15 lines modified | ||
| 162 | o7·=·{{1,·-2.23607},·{0,·-2.23607},·{1,·2.23607},·{0,·2.23607}} | 162 | o7·=·{{1,·-2.23607},·{0,·-2.23607},·{1,·2.23607},·{0,·2.23607}} |
| 163 | o7·:·List</code></pre> | 163 | o7·:·List</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10) | 166 | <td>··············<pre><code·class="language-macaulay2">i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10) |
| 167 | o8·=·{{ | 167 | o8·=·{{1,·-2.23584},·{0,·-2.23584},·{1,·2.23584},·{0,·2.23584}} |
| 168 | o8·:·List</code></pre> | 168 | o8·:·List</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ········</table> | 170 | ········</table> |
| 171 | ········<div> | 171 | ········<div> |
| 172 | ··········<p>Note·in·cases·where·solutions·have·multiplicity·this·is·not·reflected·in·the·output.·While·the·solver·does·not·return·multiplicities,·it·reliably·outputs·the·verified·isolating·intervals·for·multiple·solutions.</p> | 172 | ··········<p>Note·in·cases·where·solutions·have·multiplicity·this·is·not·reflected·in·the·output.·While·the·solver·does·not·return·multiplicities,·it·reliably·outputs·the·verified·isolating·intervals·for·multiple·solutions.</p> |
| 173 | ········</div> | 173 | ········</div> |
| Offset 44, 49 lines modified | Offset 44, 49 lines modified | ||
| 44 | ·············2·······2 | 44 | ·············2·······2 |
| 45 | o2·=·ideal·(x··-·x,·y··-·5) | 45 | o2·=·ideal·(x··-·x,·y··-·5) |
| 46 | o2·:·Ideal·of·R | 46 | o2·:·Ideal·of·R |
| 47 | i3·:·rationalIntervalSols·=·msolveRealSolutions·I | 47 | i3·:·rationalIntervalSols·=·msolveRealSolutions·I |
| 48 | ········4294967295··4294967297······9603838835····4801919417 | ||
| 49 | o3·=·{{{----------,·----------},·{-·----------,·-·----------}},·{{- | ||
| 50 | ········4294967296··4294967296······4294967296····2147483648 | ||
| 51 | ·····------------------------------------------------------------------------ | ||
| 52 | ·········· | 48 | ···············1···········1········4801919417··9603838835······4294967295 |
| 53 | ·· | 49 | o3·=·{{{-·----------,·----------},·{----------,·----------}},·{{----------, |
| 54 | ·····4294967296··4294967296 | 50 | ··········4294967296··4294967296····2147483648··4294967296······4294967296 |
| 55 | ·····------------------------------------------------------------------------ | 51 | ·····------------------------------------------------------------------------ |
| 56 | ·····4294967297····4801919417··9603838835·············1···········1 | 52 | ·····4294967297····4801919417··9603838835·············1···········1 |
| 57 | ·····----------},·{----------,·----------}},·{{-·----------,·----------}, | 53 | ·····----------},·{----------,·----------}},·{{-·----------,·----------},·{- |
| 58 | ·····4294967296····2147483648··4294967296········4294967296··4294967296 | 54 | ·····4294967296····2147483648··4294967296········4294967296··4294967296 |
| 59 | ·····------------------------------------------------------------------------ | 55 | ·····------------------------------------------------------------------------ |
| 60 | ······4801919417··9603838835 | ||
| 61 | ·····{----------,·----------}}} | ||
| 62 | ······ | 56 | ·····9603838835····4801919417······4294967295··4294967297······9603838835 |
| 57 | ·····----------,·-·----------}},·{{----------,·----------},·{-·----------,·- | ||
| 58 | ·····4294967296····2147483648······4294967296··4294967296······4294967296 | ||
| 59 | ·····------------------------------------------------------------------------ | ||
| 60 | ·····4801919417 | ||
| 61 | ·····----------}}} | ||
| 62 | ·····2147483648 | ||
| 63 | o3·:·List | 63 | o3·:·List |
| 64 | i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ) | 64 | i4·:·rationalApproxSols·=·msolveRealSolutions(I,·QQ) |
| 65 | ············19207677669·········19207677669·······19207677669 | ||
| 66 | o4·=·{{1,·-·-----------},·{0,·-·-----------},·{1,·-----------},·{0, | ||
| 67 | ·········· | 65 | ··········19207677669·······19207677669·········19207677669 |
| 66 | o4·=·{{0,·-----------},·{1,·-----------},·{0,·-·-----------},·{1,·- | ||
| 67 | ···········8589934592········8589934592··········8589934592 | ||
| 68 | ·····------------------------------------------------------------------------ | 68 | ·····------------------------------------------------------------------------ |
| 69 | ·····19207677669 | 69 | ·····19207677669 |
| 70 | ·····-----------}} | 70 | ·····-----------}} |
| 71 | ······8589934592 | 71 | ······8589934592 |
| 72 | o4·:·List | 72 | o4·:·List |
| 73 | i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi) | 73 | i5·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi) |
| 74 | o5·=·{{[ | 74 | o5·=·{{[-2.32831e-10,2.32831e-10],·[2.23607,2.23607]},·{[1,1], |
| 75 | ·····------------------------------------------------------------------------ | 75 | ·····------------------------------------------------------------------------ |
| 76 | ·····[ | 76 | ·····[2.23607,2.23607]},·{[-2.32831e-10,2.32831e-10],·[-2.23607,-2.23607]}, |
| 77 | ·····------------------------------------------------------------------------ | 77 | ·····------------------------------------------------------------------------ |
| 78 | ·····{[ | 78 | ·····{[1,1],·[-2.23607,-2.23607]}} |
| 79 | o5·:·List | 79 | o5·:·List |
| 80 | i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10) | 80 | i6·:·floatIntervalSols·=·msolveRealSolutions(I,·RRi_10) |
| 81 | o6·=·{{[.999023,1.00098],·[-2.23633,-2.23535]},·{[-.000976562,.000976562], | 81 | o6·=·{{[.999023,1.00098],·[-2.23633,-2.23535]},·{[-.000976562,.000976562], |
| 82 | ·····------------------------------------------------------------------------ | 82 | ·····------------------------------------------------------------------------ |
| 83 | ·····[-2.23633,-2.23535]},·{[.999023,1.00098],·[2.23535,2.23633]}, | 83 | ·····[-2.23633,-2.23535]},·{[.999023,1.00098],·[2.23535,2.23633]}, |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR) | 97 | i7·:·floatApproxSols·=·msolveRealSolutions(I,·RR) |
| 98 | o7·=·{{1,·-2.23607},·{0,·-2.23607},·{1,·2.23607},·{0,·2.23607}} | 98 | o7·=·{{1,·-2.23607},·{0,·-2.23607},·{1,·2.23607},·{0,·2.23607}} |
| 99 | o7·:·List | 99 | o7·:·List |
| 100 | i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10) | 100 | i8·:·floatApproxSols·=·msolveRealSolutions(I,·RR_10) |
| 101 | o8·=·{{ | 101 | o8·=·{{1,·-2.23584},·{0,·-2.23584},·{1,·2.23584},·{0,·2.23584}} |
| 102 | o8·:·List | 102 | o8·:·List |
| 103 | Note·in·cases·where·solutions·have·multiplicity·this·is·not·reflected·in·the | 103 | Note·in·cases·where·solutions·have·multiplicity·this·is·not·reflected·in·the |
| 104 | output.·While·the·solver·does·not·return·multiplicities,·it·reliably·outputs | 104 | output.·While·the·solver·does·not·return·multiplicities,·it·reliably·outputs |
| 105 | the·verified·isolating·intervals·for·multiple·solutions. | 105 | the·verified·isolating·intervals·for·multiple·solutions. |
| 106 | i9·:·I·=·ideal·{(x-1)*x^3,·(y^2-5)^2} | 106 | i9·:·I·=·ideal·{(x-1)*x^3,·(y^2-5)^2} |
| Offset 66, 15 lines modified | Offset 66, 15 lines modified | ||
| 66 | o2·=·ideal·(x,·y,·z) | 66 | o2·=·ideal·(x,·y,·z) |
| 67 | o2·:·Ideal·of·R</code></pre> | 67 | o2·:·Ideal·of·R</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6) | 70 | <td>··············<pre><code·class="language-macaulay2">i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6) |
| 71 | ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2- | 71 | ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-3824309-0/0-in.ms·-o·/tmp/M2-3824309-0/0-out.ms |
| 72 | ---------------·INPUT·DATA·--------------- | 72 | ---------------·INPUT·DATA·--------------- |
| 73 | #variables·······················3 | 73 | #variables·······················3 |
| 74 | #equations·······················3 | 74 | #equations·······················3 |
| 75 | #invalid·equations···············0 | 75 | #invalid·equations···············0 |
| 76 | field·characteristic·············0 | 76 | field·characteristic·············0 |
| 77 | homogeneous·input?···············1 | 77 | homogeneous·input?···············1 |
| Offset 102, 24 lines modified | Offset 102, 24 lines modified | ||
| 102 | time(rd)··time·of·the·current·f4·round·in·seconds·given | 102 | time(rd)··time·of·the·current·f4·round·in·seconds·given |
| 103 | ··········for·real·and·cpu·time | 103 | ··········for·real·and·cpu·time |
| 104 | -------------------------------------------------------- | 104 | -------------------------------------------------------- |
| 105 | deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu) | 105 | deg·····sel···pairs········mat··········density············new·data·········time(rd)·in·sec·(real|cpu) |
| 106 | ------------------------------------------------------------------------------------------------------ | 106 | ------------------------------------------------------------------------------------------------------ |
| 107 | ------------------------------------------------------------------------------------------------------ | 107 | ------------------------------------------------------------------------------------------------------ |
| 108 | reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.0 | 108 | reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero·········0.03·|·0.11········· |
| 109 | ------------------------------------------------------------------------------------------------------ | 109 | ------------------------------------------------------------------------------------------------------ |
| 110 | ----------------·TIMINGS·---------------- | 110 | ----------------·TIMINGS·---------------- |
| 111 | overall(elapsed)········0. | 111 | overall(elapsed)········0.07·sec |
| 112 | overall(cpu)············0. | 112 | overall(cpu)············0.23·sec |
| 113 | select··················0.00·sec···0.0% | 113 | select··················0.00·sec···0.0% |
| 114 | symbolic·prep.··········0.00·sec···0.0% | 114 | symbolic·prep.··········0.00·sec···0.0% |
| 115 | update··················0.0 | 115 | update··················0.04·sec··55.0% |
| 116 | convert·················0.0 | 116 | convert·················0.03·sec··44.7% |
| 117 | linear·algebra··········0.00·sec···0.0% | 117 | linear·algebra··········0.00·sec···0.0% |
| 118 | reduce·gb···············0.00·sec···0.0% | 118 | reduce·gb···············0.00·sec···0.0% |
| 119 | ----------------------------------------- | 119 | ----------------------------------------- |
| 120 | ----------·COMPUTATIONAL·DATA·----------- | 120 | ----------·COMPUTATIONAL·DATA·----------- |
| 121 | size·of·basis·····················3 | 121 | size·of·basis·····················3 |
| 122 | #terms·in·basis···················3 | 122 | #terms·in·basis···················3 |
| Offset 143, 34 lines modified | Offset 143, 34 lines modified | ||
| 143 | multi-mod·overall(elapsed)······0.08·sec | 143 | multi-mod·overall(elapsed)······0.08·sec |
| 144 | learning·phase··················0.00·Gops/sec | 144 | learning·phase··················0.00·Gops/sec |
| 145 | application·phase···············0.00·Gops/sec | 145 | application·phase···············0.00·Gops/sec |
| 146 | ----------------------------------------- | 146 | ----------------------------------------- |
| 147 | multi-modular·steps | 147 | multi-modular·steps |
| 148 | ------------------------------------------------------------------------------------------------------ | 148 | ------------------------------------------------------------------------------------------------------ |
| 149 | {1}{2}<100.00%> | 149 | {1}{2}<100.00%>· |
| 150 | ------------------------------------------------------------------------------------ | ||
| 151 | msolve·overall·time···········0.26·sec·(elapsed)·/··0.88·sec·(cpu) | ||
| 152 | ------------------------------------------------------------------------------------ | ||
| 153 | · | ||
| 154 | ------------------------------------------------------------------------------------------------------ | 150 | ------------------------------------------------------------------------------------------------------ |
| 155 | ----------·COMPUTATIONAL·DATA·----------- | 151 | ----------·COMPUTATIONAL·DATA·----------- |
| 156 | Max·coeff.·bitsize················1 | 152 | Max·coeff.·bitsize················1 |
| 157 | #primes···························3 | 153 | #primes···························3 |
| 158 | #bad·primes·······················0 | 154 | #bad·primes·······················0 |
| 159 | ----------------------------------------- | 155 | ----------------------------------------- |
| 160 | ----------------·TIMINGS·---------------- | 156 | ----------------·TIMINGS·---------------- |
| 161 | CRT·····(elapsed)···············0.00·sec | 157 | CRT·····(elapsed)···············0.00·sec |
| 162 | ratrecon(elapsed)···············0.00·sec | 158 | ratrecon(elapsed)···············0.00·sec |
| 163 | ----------------------------------------- | 159 | ----------------------------------------- |
| 160 | ------------------------------------------------------------------------------------ | ||
| 161 | msolve·overall·time···········0.31·sec·(elapsed)·/··0.95·sec·(cpu) | ||
| 162 | ------------------------------------------------------------------------------------ | ||
| 164 | o3·=·|·z·y·x·| | 163 | o3·=·|·z·y·x·| |
| 165 | ·············1······3 | 164 | ·············1······3 |
| 166 | o3·:·Matrix·R··<--·R</code></pre> | 165 | o3·:·Matrix·R··<--·R</code></pre> |
| 167 | </td>··········</tr> | 166 | </td>··········</tr> |
| 168 | ········</table> | 167 | ········</table> |
| 169 | ······</div> | 168 | ······</div> |
| Offset 31, 16 lines modified | Offset 31, 16 lines modified | ||
| 31 | o1·:·PolynomialRing | 31 | o1·:·PolynomialRing |
| 32 | i2·:·I·=·ideal(x,·y,·z) | 32 | i2·:·I·=·ideal(x,·y,·z) |
| 33 | o2·=·ideal·(x,·y,·z) | 33 | o2·=·ideal·(x,·y,·z) |
| 34 | o2·:·Ideal·of·R | 34 | o2·:·Ideal·of·R |
| 35 | i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6) | 35 | i3·:·msolveGB(I,·Verbosity·=>·2,·Threads·=>·6) |
| 36 | ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2- | 36 | ·--·running:·/usr/bin/msolve·-g·2·-t·6·-v·2·-f·/tmp/M2-3824309-0/0-in.ms·-o·/ |
| 37 | tmp/M2- | 37 | tmp/M2-3824309-0/0-out.ms |
| 38 | ---------------·INPUT·DATA·--------------- | 38 | ---------------·INPUT·DATA·--------------- |
| 39 | #variables·······················3 | 39 | #variables·······················3 |
| 40 | #equations·······················3 | 40 | #equations·······················3 |
| 41 | #invalid·equations···············0 | 41 | #invalid·equations···············0 |
| 42 | field·characteristic·············0 | 42 | field·characteristic·············0 |
| 43 | homogeneous·input?···············1 | 43 | homogeneous·input?···············1 |
| Offset 72, 25 lines modified | Offset 72, 25 lines modified | ||
| 72 | deg·····sel···pairs········mat··········density············new·data | 72 | deg·····sel···pairs········mat··········density············new·data |
| 73 | time(rd)·in·sec·(real|cpu) | 73 | time(rd)·in·sec·(real|cpu) |
| 74 | ------------------------------------------------------------------------------- | 74 | ------------------------------------------------------------------------------- |
| 75 | ----------------------- | 75 | ----------------------- |
| 76 | ------------------------------------------------------------------------------- | 76 | ------------------------------------------------------------------------------- |
| 77 | ----------------------- | 77 | ----------------------- |
| 78 | reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero | 78 | reduce·final·basis········3·x·3··········33.33%········3·new·······0·zero |
| 79 | 0.0 | 79 | 0.03·|·0.11 |
| 80 | ------------------------------------------------------------------------------- | 80 | ------------------------------------------------------------------------------- |
| 81 | ----------------------- | 81 | ----------------------- |
| 82 | ----------------·TIMINGS·---------------- | 82 | ----------------·TIMINGS·---------------- |
| 83 | overall(elapsed)········0. | 83 | overall(elapsed)········0.07·sec |
| 84 | overall(cpu)············0. | 84 | overall(cpu)············0.23·sec |
| 85 | select··················0.00·sec···0.0% | 85 | select··················0.00·sec···0.0% |
| 86 | symbolic·prep.··········0.00·sec···0.0% | 86 | symbolic·prep.··········0.00·sec···0.0% |
| 87 | update··················0.0 | 87 | update··················0.04·sec··55.0% |
| 88 | convert·················0.0 | 88 | convert·················0.03·sec··44.7% |
| 89 | linear·algebra··········0.00·sec···0.0% | 89 | linear·algebra··········0.00·sec···0.0% |
| 90 | reduce·gb···············0.00·sec···0.0% | 90 | reduce·gb···············0.00·sec···0.0% |
| 91 | ----------------------------------------- | 91 | ----------------------------------------- |
| 92 | ----------·COMPUTATIONAL·DATA·----------- | 92 | ----------·COMPUTATIONAL·DATA·----------- |
| 93 | size·of·basis·····················3 | 93 | size·of·basis·····················3 |
| 94 | #terms·in·basis···················3 | 94 | #terms·in·basis···················3 |
| Offset 116, 21 lines modified | Offset 116, 14 lines modified | ||
| 116 | application·phase···············0.00·Gops/sec | 116 | application·phase···············0.00·Gops/sec |
| 117 | ----------------------------------------- | 117 | ----------------------------------------- |
| 118 | multi-modular·steps | 118 | multi-modular·steps |
| 119 | ------------------------------------------------------------------------------- | 119 | ------------------------------------------------------------------------------- |
| 120 | ----------------------- | 120 | ----------------------- |
| 121 | {1}{2}<100.00%> | 121 | {1}{2}<100.00%> |
| 122 | ------------------------------------------------------------------------------- | ||
| 123 | ----- | ||
| 124 | msolve·overall·time···········0.26·sec·(elapsed)·/··0.88·sec·(cpu) | ||
| 125 | ------------------------------------------------------------------------------- | ||
| 126 | ----- | ||
| 127 | ------------------------------------------------------------------------------- | 122 | ------------------------------------------------------------------------------- |
| 128 | ----------------------- | 123 | ----------------------- |
| 129 | ----------·COMPUTATIONAL·DATA·----------- | 124 | ----------·COMPUTATIONAL·DATA·----------- |
| 130 | Max·coeff.·bitsize················1 | 125 | Max·coeff.·bitsize················1 |
| 131 | #primes···························3 | 126 | #primes···························3 |
| Offset 138, 14 lines modified | Offset 131, 21 lines modified | ||
| 138 | ----------------------------------------- | 131 | ----------------------------------------- |
| 139 | ----------------·TIMINGS·---------------- | 132 | ----------------·TIMINGS·---------------- |
| 140 | CRT·····(elapsed)···············0.00·sec | 133 | CRT·····(elapsed)···············0.00·sec |
| 141 | ratrecon(elapsed)···············0.00·sec | 134 | ratrecon(elapsed)···············0.00·sec |
| 142 | ----------------------------------------- | 135 | ----------------------------------------- |
| 136 | ------------------------------------------------------------------------------- | ||
| 137 | ----- | ||
| 138 | msolve·overall·time···········0.31·sec·(elapsed)·/··0.95·sec·(cpu) | ||
| 139 | ------------------------------------------------------------------------------- | ||
| 140 | ----- | ||
| 143 | o3·=·|·z·y·x·| | 141 | o3·=·|·z·y·x·| |
| 144 | ·············1······3 | 142 | ·············1······3 |
| 145 | o3·:·Matrix·R··<--·R | 143 | o3·:·Matrix·R··<--·R |
| 146 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 144 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 147 | [1]·The·msolve·library:·_\x8h_\x8t_\x8t_\x8p_\x8s_\x8:_\x8/_\x8/_\x8m_\x8s_\x8o_\x8l_\x8v_\x8e_\x8._\x8l_\x8i_\x8p_\x86_\x8._\x8f_\x8r; | 145 | [1]·The·msolve·library:·_\x8h_\x8t_\x8t_\x8p_\x8s_\x8:_\x8/_\x8/_\x8m_\x8s_\x8o_\x8l_\x8v_\x8e_\x8._\x8l_\x8i_\x8p_\x86_\x8._\x8f_\x8r; |
| 148 | *\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8th\x8ho\x8or\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8* | 146 | *\x8**\x8**\x8**\x8**\x8*·A\x8Au\x8ut\x8th\x8ho\x8or\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | ZGVncmVlT2ZNYXAoSWRlYWwp | 8 | ZGVncmVlT2ZNYXAoSWRlYWwp |
| 9 | #:len=283 | 9 | #:len=283 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjk3LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjk3LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhkZWdyZWVPZk1hcCxJZGVhbCksImRlZ3JlZU9mTWFw | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhkZWdyZWVPZk1hcCxJZGVhbCksImRlZ3JlZU9mTWFw |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| Offset 9, 25 lines modified | Offset 9, 25 lines modified | ||
| 9 | i2·:·I·=·ideal"xy,yz,zx" | 9 | i2·:·I·=·ideal"xy,yz,zx" |
| 10 | o2·=·ideal·(x*y,·y*z,·x*z) | 10 | o2·=·ideal·(x*y,·y*z,·x*z) |
| 11 | o2·:·Ideal·of·R | 11 | o2·:·Ideal·of·R |
| 12 | i3·:·elapsedTime·jMult·I | 12 | i3·:·elapsedTime·jMult·I |
| 13 | ·--·.0 | 13 | ·--·.0249853s·elapsed |
| 14 | o3·=·2 | 14 | o3·=·2 |
| 15 | i4·:·elapsedTime·monjMult·I | 15 | i4·:·elapsedTime·monjMult·I |
| 16 | ·--·. | 16 | ·--·.299065s·elapsed |
| 17 | o4·=·2 | 17 | o4·=·2 |
| 18 | i5·:·elapsedTime·multiplicitySequence·I | 18 | i5·:·elapsedTime·multiplicitySequence·I |
| 19 | ·--·. | 19 | ·--·.816704s·elapsed |
| 20 | o5·=·HashTable{2·=>·3} | 20 | o5·=·HashTable{2·=>·3} |
| 21 | ···············3·=>·2 | 21 | ···············3·=>·2 |
| 22 | o5·:·HashTable | 22 | o5·:·HashTable |
| 23 | i6·:· | 23 | i6·:· |
| Offset 10, 12 lines modified | Offset 10, 12 lines modified | ||
| 10 | ·············2········3 | 10 | ·············2········3 |
| 11 | o2·=·ideal·(x·,·x*y,·y·) | 11 | o2·=·ideal·(x·,·x*y,·y·) |
| 12 | o2·:·Ideal·of·R | 12 | o2·:·Ideal·of·R |
| 13 | i3·:·elapsedTime·monAnalyticSpread·I | 13 | i3·:·elapsedTime·monAnalyticSpread·I |
| 14 | ·--·. | 14 | ·--·.23809s·elapsed |
| 15 | o3·=·2 | 15 | o3·=·2 |
| 16 | i4·:· | 16 | i4·:· |
| Offset 13, 17 lines modified | Offset 13, 17 lines modified | ||
| 13 | ·····------------------------------------------------------------------------ | 13 | ·····------------------------------------------------------------------------ |
| 14 | ······10·11···8·12···9·11···10·10···11·9···12·8 | 14 | ······10·11···8·12···9·11···10·10···11·9···12·8 |
| 15 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) | 15 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) |
| 16 | o2·:·Ideal·of·R | 16 | o2·:·Ideal·of·R |
| 17 | i3·:·elapsedTime·monjMult·I | 17 | i3·:·elapsedTime·monjMult·I |
| 18 | ·--·.2 | 18 | ·--·.289065s·elapsed |
| 19 | o3·=·192 | 19 | o3·=·192 |
| 20 | i4·:·elapsedTime·jMult·I | 20 | i4·:·elapsedTime·jMult·I |
| 21 | ·--·1. | 21 | ·--·1.3146s·elapsed |
| 22 | o4·=·192 | 22 | o4·=·192 |
| 23 | i5·:· | 23 | i5·:· |
| Offset 83, 27 lines modified | Offset 83, 27 lines modified | ||
| 83 | o2·=·ideal·(x*y,·y*z,·x*z) | 83 | o2·=·ideal·(x*y,·y*z,·x*z) |
| 84 | o2·:·Ideal·of·R</code></pre> | 84 | o2·:·Ideal·of·R</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·jMult·I | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·jMult·I |
| 88 | ·--·.0 | 88 | ·--·.0249853s·elapsed |
| 89 | o3·=·2</code></pre> | 89 | o3·=·2</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·monjMult·I | 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·monjMult·I |
| 93 | ·--·. | 93 | ·--·.299065s·elapsed |
| 94 | o4·=·2</code></pre> | 94 | o4·=·2</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·multiplicitySequence·I | 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·multiplicitySequence·I |
| 98 | ·--·. | 98 | ·--·.816704s·elapsed |
| 99 | o5·=·HashTable{2·=>·3} | 99 | o5·=·HashTable{2·=>·3} |
| 100 | ···············3·=>·2 | 100 | ···············3·=>·2 |
| 101 | o5·:·HashTable</code></pre> | 101 | o5·:·HashTable</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ········</table> | 103 | ········</table> |
| Offset 21, 23 lines modified | Offset 21, 23 lines modified | ||
| 21 | o1·:·PolynomialRing | 21 | o1·:·PolynomialRing |
| 22 | i2·:·I·=·ideal"xy,yz,zx" | 22 | i2·:·I·=·ideal"xy,yz,zx" |
| 23 | o2·=·ideal·(x*y,·y*z,·x*z) | 23 | o2·=·ideal·(x*y,·y*z,·x*z) |
| 24 | o2·:·Ideal·of·R | 24 | o2·:·Ideal·of·R |
| 25 | i3·:·elapsedTime·jMult·I | 25 | i3·:·elapsedTime·jMult·I |
| 26 | ·--·.0 | 26 | ·--·.0249853s·elapsed |
| 27 | o3·=·2 | 27 | o3·=·2 |
| 28 | i4·:·elapsedTime·monjMult·I | 28 | i4·:·elapsedTime·monjMult·I |
| 29 | ·--·. | 29 | ·--·.299065s·elapsed |
| 30 | o4·=·2 | 30 | o4·=·2 |
| 31 | i5·:·elapsedTime·multiplicitySequence·I | 31 | i5·:·elapsedTime·multiplicitySequence·I |
| 32 | ·--·. | 32 | ·--·.816704s·elapsed |
| 33 | o5·=·HashTable{2·=>·3} | 33 | o5·=·HashTable{2·=>·3} |
| 34 | ···············3·=>·2 | 34 | ···············3·=>·2 |
| 35 | o5·:·HashTable | 35 | o5·:·HashTable |
| 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal | 37 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ·············2········3 | 84 | ·············2········3 |
| 85 | o2·=·ideal·(x·,·x*y,·y·) | 85 | o2·=·ideal·(x·,·x*y,·y·) |
| 86 | o2·:·Ideal·of·R</code></pre> | 86 | o2·:·Ideal·of·R</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monAnalyticSpread·I | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monAnalyticSpread·I |
| 90 | ·--·. | 90 | ·--·.23809s·elapsed |
| 91 | o3·=·2</code></pre> | 91 | o3·=·2</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ········</table> | 93 | ········</table> |
| 94 | ······</div> | 94 | ······</div> |
| 95 | ······<div> | 95 | ······<div> |
| 96 | ········<h2>See·also</h2> | 96 | ········<h2>See·also</h2> |
| Offset 23, 15 lines modified | Offset 23, 15 lines modified | ||
| 23 | i2·:·I·=·ideal"x2,xy,y3" | 23 | i2·:·I·=·ideal"x2,xy,y3" |
| 24 | ·············2········3 | 24 | ·············2········3 |
| 25 | o2·=·ideal·(x·,·x*y,·y·) | 25 | o2·=·ideal·(x·,·x*y,·y·) |
| 26 | o2·:·Ideal·of·R | 26 | o2·:·Ideal·of·R |
| 27 | i3·:·elapsedTime·monAnalyticSpread·I | 27 | i3·:·elapsedTime·monAnalyticSpread·I |
| 28 | ·--·. | 28 | ·--·.23809s·elapsed |
| 29 | o3·=·2 | 29 | o3·=·2 |
| 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 31 | ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal | 31 | ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal |
| 32 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mo\x8on\x8nA\x8An\x8na\x8al\x8ly\x8yt\x8ti\x8ic\x8cS\x8Sp\x8pr\x8re\x8ea\x8ad\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 32 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mo\x8on\x8nA\x8An\x8na\x8al\x8ly\x8yt\x8ti\x8ic\x8cS\x8Sp\x8pr\x8re\x8ea\x8ad\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 33 | ····*·monAnalyticSpread(Ideal) | 33 | ····*·monAnalyticSpread(Ideal) |
| 34 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 34 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 87, 21 lines modified | Offset 87, 21 lines modified | ||
| 87 | ······10·11···8·12···9·11···10·10···11·9···12·8 | 87 | ······10·11···8·12···9·11···10·10···11·9···12·8 |
| 88 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) | 88 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) |
| 89 | o2·:·Ideal·of·R</code></pre> | 89 | o2·:·Ideal·of·R</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monjMult·I | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monjMult·I |
| 93 | ·--·.2 | 93 | ·--·.289065s·elapsed |
| 94 | o3·=·192</code></pre> | 94 | o3·=·192</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jMult·I | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jMult·I |
| 98 | ·--·1. | 98 | ·--·1.3146s·elapsed |
| 99 | o4·=·192</code></pre> | 99 | o4·=·192</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ········</table> | 101 | ········</table> |
| 102 | ······</div> | 102 | ······</div> |
| 103 | ······<div> | 103 | ······<div> |
| 104 | ········<h2>See·also</h2> | 104 | ········<h2>See·also</h2> |
| Offset 25, 19 lines modified | Offset 25, 19 lines modified | ||
| 25 | o2·=·ideal·(x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··, | 25 | o2·=·ideal·(x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··,·x·y··, |
| 26 | ·····------------------------------------------------------------------------ | 26 | ·····------------------------------------------------------------------------ |
| 27 | ······10·11···8·12···9·11···10·10···11·9···12·8 | 27 | ······10·11···8·12···9·11···10·10···11·9···12·8 |
| 28 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) | 28 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) |
| 29 | o2·:·Ideal·of·R | 29 | o2·:·Ideal·of·R |
| 30 | i3·:·elapsedTime·monjMult·I | 30 | i3·:·elapsedTime·monjMult·I |
| 31 | ·--·.2 | 31 | ·--·.289065s·elapsed |
| 32 | o3·=·192 | 32 | o3·=·192 |
| 33 | i4·:·elapsedTime·jMult·I | 33 | i4·:·elapsedTime·jMult·I |
| 34 | ·--·1. | 34 | ·--·1.3146s·elapsed |
| 35 | o4·=·192 | 35 | o4·=·192 |
| 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal | 37 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8p_\x8l_\x8i_\x8c_\x8i_\x8t_\x8y_\x8S_\x8e_\x8q_\x8u_\x8e_\x8n_\x8c_\x8e·--·the·multiplicity·sequence·of·an·ideal |
| 38 | ····*·_\x8j_\x8M_\x8u_\x8l_\x8t·--·the·j-multiplicity·of·an·ideal | 38 | ····*·_\x8j_\x8M_\x8u_\x8l_\x8t·--·the·j-multiplicity·of·an·ideal |
| 39 | ····*·_\x8m_\x8o_\x8n_\x8R_\x8e_\x8d_\x8u_\x8c_\x8t_\x8i_\x8o_\x8n·--·the·minimal·monomial·reduction·of·a·monomial·ideal | 39 | ····*·_\x8m_\x8o_\x8n_\x8R_\x8e_\x8d_\x8u_\x8c_\x8t_\x8i_\x8o_\x8n·--·the·minimal·monomial·reduction·of·a·monomial·ideal |
| 40 | ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal | 40 | ····*·_\x8N_\x8P·--·the·Newton·polyhedron·of·a·monomial·ideal |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=41 | 7 | #:len=41 |
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| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="___Jumping__Divisor.html">next</a>·|·<a·href="___Biggest__J__N.html">previous</a>·|·<a·href="___Jumping__Divisor.html">forward</a>·|·<a·href="___Biggest__J__N.html">backward</a>·|·up·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> | 41 | </form><a·href="___Jumping__Divisor.html">next</a>·|·<a·href="___Biggest__J__N.html">previous</a>·|·<a·href="___Jumping__Divisor.html">forward</a>·|·<a·href="___Biggest__J__N.html">backward</a>·|·up·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>JNandMI·--·HashTable·containing·all·the·information·about·the·Jumping·Numbers</h1> | 44 | ······<h1>JNandMI·--·HashTable·containing·all·the·information·about·the·Jumping·Numbers</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | This·HashTable·contains·all·the·information·about·the·jumping·numbers·that·computes·<a·title=" | 47 | This·HashTable·contains·all·the·information·about·the·jumping·numbers·that·computes·<a·title="multiplier·ideals"·href="../../MultiplierIdeals/html/index.html">MultiplierIdeals</a>.·As·a·key,·it·contains·the·Jumping·Number·and·for·each·Jumping·Number·it·contains·the·multiplicity,·the·divisor·associated·to·the·ideal,·the·Maximal·and·Minimal·Jumping·Divisors·and·(if·it·applies)·the·critical·chains.········<table·class="examples"> |
| 48 | ··········<tr> | 48 | ··········<tr> |
| 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·E·=·matrix({{·-5,··0,··1,··0,··1}, | 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·E·=·matrix({{·-5,··0,··1,··0,··1}, |
| 50 | ················{··0,·-2,··1,··0,··0}, | 50 | ················{··0,·-2,··1,··0,··0}, |
| 51 | ················{··1,··1,·-1,··0,··0}, | 51 | ················{··1,··1,·-1,··0,··0}, |
| 52 | ················{··0,··0,··0,·-2,··1}, | 52 | ················{··0,··0,··0,·-2,··1}, |
| 53 | ················{··1,··0,··0,··1,·-1}}) | 53 | ················{··1,··0,··0,··1,·-1}}) |
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| 1 | <!DOCTYPE·html> | 1 | <!DOCTYPE·html> |
| 2 | <html·lang="en"> | 2 | <html·lang="en"> |
| 3 | ··<head> | 3 | ··<head> |
| 4 | ····<title>MultiplierIdeals·--· | 4 | ····<title>MultiplierIdeals·--·multiplier·ideals</title> |
| 5 | <meta·content="text/html;·charset=utf-8"·http-equiv="Content-Type"><link·type="text/css"·rel="stylesheet"·href="../../../../Macaulay2/Style/doc.css"> | 5 | <meta·content="text/html;·charset=utf-8"·http-equiv="Content-Type"><link·type="text/css"·rel="stylesheet"·href="../../../../Macaulay2/Style/doc.css"> |
| 6 | ····<link·rel="stylesheet"·href="../../../../Macaulay2/Style/katex/katex.min.css"> | 6 | ····<link·rel="stylesheet"·href="../../../../Macaulay2/Style/katex/katex.min.css"> |
| 7 | ····<script·defer="defer"·src="../../../../Macaulay2/Style/katex/katex.min.js"></script> | 7 | ····<script·defer="defer"·src="../../../../Macaulay2/Style/katex/katex.min.js"></script> |
| 8 | ····<script·defer="defer"·src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> | 8 | ····<script·defer="defer"·src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> |
| 9 | ····<script> | 9 | ····<script> |
| 10 | ······var·macros·=·{ | 10 | ······var·macros·=·{ |
| 11 | ··········"\\break":·"\\\\", | 11 | ··········"\\break":·"\\\\", |
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| 125 | o3·:·Type·of·HashTable</code></pre> | 125 | o3·:·Type·of·HashTable</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ········</table> | 127 | ········</table> |
| 128 | ······</div> | 128 | ······</div> |
| 129 | ······<div·class="waystouse"> | 129 | ······<div·class="waystouse"> |
| 130 | ········<h2>For·the·programmer</h2> | 130 | ········<h2>For·the·programmer</h2> |
| 131 | ········<p>The·object·<a·title=" | 131 | ········<p>The·object·<a·title="multiplier·ideals"·href="../../MultiplierIdeals/html/index.html">MultiplierIdeals</a>·is·<span>a·<a·title="the·class·of·all·function·closures"·href="../../Macaulay2Doc/html/___Function__Closure.html">function·closure</a></span>.</p> |
| 132 | ······</div> | 132 | ······</div> |
| 133 | ····</div> | 133 | ····</div> |
| 134 | ··</body> | 134 | ··</body> |
| 135 | </html> | 135 | </html> |
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| 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> | 40 | ··<input·type="hidden"·name="q"·value="site:macaulay2.com/doc"> |
| 41 | </form><a·href="_algorithm.html">next</a>·|·previous·|·<a·href="_algorithm.html">forward</a>·|·backward·|·up·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> | 41 | </form><a·href="_algorithm.html">next</a>·|·previous·|·<a·href="_algorithm.html">forward</a>·|·backward·|·up·|·<a·href="master.html">index</a>·|·<a·href="toc.html">toc</a>······</div> |
| 42 | ····</div> | 42 | ····</div> |
| 43 | <hr>····<div> | 43 | <hr>····<div> |
| 44 | ······<h1>MultiplierIdealsDim2·--·A·package·for·Multiplier·Ideals</h1> | 44 | ······<h1>MultiplierIdealsDim2·--·A·package·for·Multiplier·Ideals</h1> |
| 45 | ······<div> | 45 | ······<div> |
| 46 | ········<h2>Description</h2> | 46 | ········<h2>Description</h2> |
| 47 | <em>MultiplierIdealsDim2</em>·is·a·package·that·contains·several·tools·related·with·the·computations·of·multiplier·ideals.·Given·the·self·intersection·matrix··and·the·divisor·associated·to·this·ideal,·using·the·function·<a·title=" | 47 | <em>MultiplierIdealsDim2</em>·is·a·package·that·contains·several·tools·related·with·the·computations·of·multiplier·ideals.·Given·the·self·intersection·matrix··and·the·divisor·associated·to·this·ideal,·using·the·function·<a·title="multiplier·ideals"·href="../../MultiplierIdeals/html/index.html">MultiplierIdeals</a>,·one·can·compute·the·jumping·numbers·and·their·associated·multiplier·ideals·in·the·interval·(<a·title="Lower·bound·of·the·interval·where·we·want·to·compute·the·JN."·href="___Smallest__J__N.html">SmallestJN</a>,<a·title="Upper·bound·of·the·interval·where·we·want·to·compute·the·JN."·href="___Biggest__J__N.html">BiggestJN</a>]·using·either·the·algorithms·presented·on·[Tuc10],·[AAD14]·or·[AADG14].·However,·if·we·want·to·know·the·multiplicity·of·a·given·number·as·a·jumping·number·for·a·given·ideal,·one·can·use·<a·title="Computes·the·multiplicity·as·a·jumping·number."·href="___Multiplicity__J__N.html">MultiplicityJN</a>.·Another·option·that·this·package·offers·is·to·compute·the·Multiplier·Ideal·associated·to·a·given·number,·thanks·to·the·function·<a·title="Computes·the·multiplier·ideal·of·a·given·number."·href="___Mult__Ideal.html">MultIdeal</a>.·The·package·also·contains·two·extra·functions:·to·compute·the·relative·Canonical·divisor·of·a·resolution·(<a·title="computes·the·relative·canonical·divisor"·href="___Relative__Canonical__Divisor.html">RelativeCanonicalDivisor</a>).·And·to·compute·the·antinef·closure·of·a·given·divisor·(<a·title="Computes·the·antinef·closure·of·a·divisor."·href="___Unloading.html">Unloading</a>).<br><br><b>Literature·</b>········<ul> |
| 48 | ··········<li> | 48 | ··········<li> |
| 49 | [AAD14]·<em>Multiplier·ideals·in·two-dimensional·local·rings·with·rational·singularities</em>·(M.·Alberich-Carramiñana,·J.·Àlvarez·Montaner,·F.·Dachs-Cadefau,·2014).···········</li> | 49 | [AAD14]·<em>Multiplier·ideals·in·two-dimensional·local·rings·with·rational·singularities</em>·(M.·Alberich-Carramiñana,·J.·Àlvarez·Montaner,·F.·Dachs-Cadefau,·2014).···········</li> |
| 50 | ··········<li> | 50 | ··········<li> |
| 51 | [AADG14]·<em>Poincaré·series·of·multiplier·ideals·in·two-dimensional·local·rings·with·rational·singularities</em>·(M.·Alberich-Carramiñana,·J.·Àlvarez·Montaner,·F.·Dachs-Cadefau,·V.·González-Alonso,·2014)···········</li> | 51 | [AADG14]·<em>Poincaré·series·of·multiplier·ideals·in·two-dimensional·local·rings·with·rational·singularities</em>·(M.·Alberich-Carramiñana,·J.·Àlvarez·Montaner,·F.·Dachs-Cadefau,·V.·González-Alonso,·2014)···········</li> |
| 52 | ··········<li> | 52 | ··········<li> |
| 53 | [Tuc10]·<em>·Jumping·numbers·on·algebraic·surfaces·with·rational·singularities</em>·(K.·Tucker,·2010)··········</li> | 53 | [Tuc10]·<em>·Jumping·numbers·on·algebraic·surfaces·with·rational·singularities</em>·(K.·Tucker,·2010)··········</li> |
| 54 | ········</ul> | 54 | ········</ul> |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | dGV4TWF0aChSQVQp | 8 | dGV4TWF0aChSQVQp |
| 9 | #:len=209 | 9 | #:len=209 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDE5OSwgInVuZG9jdW1lbnRlZCIgPT4g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDE5OSwgInVuZG9jdW1lbnRlZCIgPT4g |
| 11 | dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodGV4TWF0 | 11 | dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodGV4TWF0 |
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| 13 | o4·:·ProjectiveVariety,·curve·in·PP^8 | 13 | o4·:·ProjectiveVariety,·curve·in·PP^8 |
| 14 | i5·:·?·X | 14 | i5·:·?·X |
| 15 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15· | 15 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15· |
| 16 | i6·:·time·f·=·X·===>·Y; | 16 | i6·:·time·f·=·X·===>·Y; |
| 17 | ·--·used·3. | 17 | ·--·used·3.92429s·(cpu);·1.79108s·(thread);·0s·(gc) |
| 18 | o6·:·MultirationalMap·(automorphism·of·PP^8) | 18 | o6·:·MultirationalMap·(automorphism·of·PP^8) |
| 19 | i7·:·f·X | 19 | i7·:·f·X |
| 20 | o7·=·Y | 20 | o7·=·Y |
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| 38 | o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 | 38 | o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 |
| 39 | i10·:·W·=·random({{2},{1}},Y); | 39 | i10·:·W·=·random({{2},{1}},Y); |
| 40 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 | 40 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 |
| 41 | i11·:·time·g·=·V·===>·W; | 41 | i11·:·time·g·=·V·===>·W; |
| 42 | ·--·used·5. | 42 | ·--·used·5.77971s·(cpu);·2.04888s·(thread);·0s·(gc) |
| 43 | o11·:·MultirationalMap·(automorphism·of·PP^8) | 43 | o11·:·MultirationalMap·(automorphism·of·PP^8) |
| 44 | i12·:·g||W | 44 | i12·:·g||W |
| 45 | o12·=·multi-rational·map·consisting·of·one·single·rational·map | 45 | o12·=·multi-rational·map·consisting·of·one·single·rational·map |
| 46 | ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2·hypersurfaces·of·degrees·1^1·2^1· | 46 | ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2·hypersurfaces·of·degrees·1^1·2^1· |
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| 129 | o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9 | 129 | o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9 |
| 130 | i16·:·?·Z | 130 | i16·:·?·Z |
| 131 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2 | 131 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2 |
| 132 | i17·:·time·h·=·Z·===>·GG_K(1,4) | 132 | i17·:·time·h·=·Z·===>·GG_K(1,4) |
| 133 | ·--·used·6. | 133 | ·--·used·6.45121s·(cpu);·3.73045s·(thread);·0s·(gc) |
| 134 | o17·=·h | 134 | o17·=·h |
| 135 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9) | 135 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9) |
| 136 | i18·:·h·||·GG_K(1,4) | 136 | i18·:·h·||·GG_K(1,4) |
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| 7 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4) | 7 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4) |
| 8 | i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi)); | 8 | i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi)); |
| 9 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4 | 9 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4 |
| 10 | i4·:·time·X·=·Phi^*·Y; | 10 | i4·:·time·X·=·Phi^*·Y; |
| 11 | ·--·used· | 11 | ·--·used·3.96686s·(cpu);·3.26466s·(thread);·0s·(gc) |
| 12 | o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·) | 12 | o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·) |
| 13 | i5·:·dim·X,·degree·X,·degrees·X | 13 | i5·:·dim·X,·degree·X,·degrees·X |
| 14 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), | 14 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), |
| 15 | ·····------------------------------------------------------------------------ | 15 | ·····------------------------------------------------------------------------ |
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| 11 | o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^7·x·PP^7) | 11 | o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^7·x·PP^7) |
| 12 | i4·:·Z·=·source·Phi; | 12 | i4·:·Z·=·source·Phi; |
| 13 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7 | 13 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7 |
| 14 | i5·:·time·Phi·Z; | 14 | i5·:·time·Phi·Z; |
| 15 | ·--·used·0.3 | 15 | ·--·used·0.322598s·(cpu);·0.130368s·(thread);·0s·(gc) |
| 16 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7 | 16 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7 |
| 17 | i6·:·dim·oo,·degree·oo,·degrees·oo | 17 | i6·:·dim·oo,·degree·oo,·degrees·oo |
| 18 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) | 18 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) |
| 19 | o6·:·Sequence | 19 | o6·:·Sequence |
| 20 | i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) | 20 | i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) |
| 21 | ·--·used· | 21 | ·--·used·2.10094s·(cpu);·1.26521s·(thread);·0s·(gc) |
| 22 | o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3· | 22 | o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3· |
| 23 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7 | 23 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7 |
| 24 | i8·:·dim·oo,·degree·oo,·degrees·oo | 24 | i8·:·dim·oo,·degree·oo,·degrees·oo |
| Offset 11, 22 lines modified | Offset 11, 22 lines modified | ||
| 11 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 11 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 12 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of | 12 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of |
| 13 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 | 13 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 |
| 14 | ·····------------------------------------------------------------------------ | 14 | ·····------------------------------------------------------------------------ |
| 15 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1 | 15 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1 |
| 16 | i4·:·time·degree(Phi,Strategy=>"random·point") | 16 | i4·:·time·degree(Phi,Strategy=>"random·point") |
| 17 | ·--·used· | 17 | ·--·used·4.52399s·(cpu);·2.66659s·(thread);·0s·(gc) |
| 18 | o4·=·2 | 18 | o4·=·2 |
| 19 | i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") | 19 | i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") |
| 20 | ·--·used·0.2 | 20 | ·--·used·0.423067s·(cpu);·0.346634s·(thread);·0s·(gc) |
| 21 | o5·=·2 | 21 | o5·=·2 |
| 22 | i6·:·time·degree·Phi | 22 | i6·:·time·degree·Phi |
| 23 | ·--·used·0. | 23 | ·--·used·0.338524s·(cpu);·0.340681s·(thread);·0s·(gc) |
| 24 | o6·=·2 | 24 | o6·=·2 |
| 25 | i7·:· | 25 | i7·:· |
| Offset 3, 12 lines modified | Offset 3, 12 lines modified | ||
| 3 | i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2}; | 3 | i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2}; |
| 4 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 4 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 5 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4) | 5 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4) |
| 6 | i3·:·time·degree·Phi | 6 | i3·:·time·degree·Phi |
| 7 | ·--·used·0. | 7 | ·--·used·0.80694s·(cpu);·0.488036s·(thread);·0s·(gc) |
| 8 | o3·=·1 | 8 | o3·=·1 |
| 9 | i4·:· | 9 | i4·:· |
| Offset 1, 52 lines modified | Offset 1, 52 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·11533721324852072161 | 1 | --·-*-·M2-comint·-*-·hash:·11533721324852072161 |
| 2 | i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); | 2 | i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); |
| 3 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5) | 3 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5) |
| 4 | i2·:·time·?·Phi | 4 | i2·:·time·?·Phi |
| 5 | ·--·used·0.00 | 5 | ·--·used·0.00100996s·(cpu);·0.000142226s·(thread);·0s·(gc) |
| 6 | o2·=·multi-rational·map·consisting·of·2·rational·maps | 6 | o2·=·multi-rational·map·consisting·of·2·rational·maps |
| 7 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 7 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 8 | ·····target·variety:·PP^4·x·PP^5 | 8 | ·····target·variety:·PP^4·x·PP^5 |
| 9 | ·····------------------------------------------------------------------------ | 9 | ·····------------------------------------------------------------------------ |
| 10 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 | 10 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 |
| 11 | i3·:·image·Phi; | 11 | i3·:·image·Phi; |
| 12 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5 | 12 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5 |
| 13 | i4·:·time·?·Phi | 13 | i4·:·time·?·Phi |
| 14 | ·--·used·0.00 | 14 | ·--·used·0.00188283s·(cpu);·0.000202439s·(thread);·0s·(gc) |
| 15 | o4·=·multi-rational·map·consisting·of·2·rational·maps | 15 | o4·=·multi-rational·map·consisting·of·2·rational·maps |
| 16 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 16 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 17 | ·····target·variety:·PP^4·x·PP^5 | 17 | ·····target·variety:·PP^4·x·PP^5 |
| 18 | ·····dominance:·false | 18 | ·····dominance:·false |
| 19 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 19 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 20 | i5·:·time·describe·Phi | 20 | i5·:·time·describe·Phi |
| 21 | ·--·used· | 21 | ·--·used·1.03358s·(cpu);·0.859667s·(thread);·0s·(gc) |
| 22 | o5·=·multi-rational·map·consisting·of·2·rational·maps | 22 | o5·=·multi-rational·map·consisting·of·2·rational·maps |
| 23 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 23 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 24 | ·····target·variety:·PP^4·x·PP^5 | 24 | ·····target·variety:·PP^4·x·PP^5 |
| 25 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 25 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 26 | ·····dominance:·false | 26 | ·····dominance:·false |
| 27 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 27 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 28 | ·····multidegree:·{51,·51,·51,·51,·51} | 28 | ·····multidegree:·{51,·51,·51,·51,·51} |
| 29 | ·····degree:·1 | 29 | ·····degree:·1 |
| 30 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] | 30 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] |
| 31 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] | 31 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] |
| 32 | ·····coefficient·ring:·ZZ/65521 | 32 | ·····coefficient·ring:·ZZ/65521 |
| 33 | i6·:·time·?·Phi | 33 | i6·:·time·?·Phi |
| 34 | ·--·used·0.00010 | 34 | ·--·used·0.000130775s·(cpu);·0.000423464s·(thread);·0s·(gc) |
| 35 | o6·=·multi-rational·map·consisting·of·2·rational·maps | 35 | o6·=·multi-rational·map·consisting·of·2·rational·maps |
| 36 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 36 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 37 | ·····target·variety:·PP^4·x·PP^5 | 37 | ·····target·variety:·PP^4·x·PP^5 |
| 38 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 38 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 39 | ·····dominance:·false | 39 | ·····dominance:·false |
| 40 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 40 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| Offset 3, 45 lines modified | Offset 3, 45 lines modified | ||
| 3 | i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true) | 3 | i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true) |
| 4 | o1·=·Phi | 4 | o1·=·Phi |
| 5 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) | 5 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) |
| 6 | i2·:·time·(Phi1,Phi2)·=·graph·Phi | 6 | i2·:·time·(Phi1,Phi2)·=·graph·Phi |
| 7 | ·--·used·0.2 | 7 | ·--·used·0.254436s·(cpu);·0.0556115s·(thread);·0s·(gc) |
| 8 | o2·=·(Phi1,·Phi2) | 8 | o2·=·(Phi1,·Phi2) |
| 9 | o2·:·Sequence | 9 | o2·:·Sequence |
| 10 | i3·:·Phi1; | 10 | i3·:·Phi1; |
| 11 | o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4) | 11 | o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4) |
| 12 | i4·:·Phi2; | 12 | i4·:·Phi2; |
| 13 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5) | 13 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5) |
| 14 | i5·:·time·(Phi21,Phi22)·=·graph·Phi2 | 14 | i5·:·time·(Phi21,Phi22)·=·graph·Phi2 |
| 15 | ·--·used·0. | 15 | ·--·used·0.286226s·(cpu);·0.0764986s·(thread);·0s·(gc) |
| 16 | o5·=·(Phi21,·Phi22) | 16 | o5·=·(Phi21,·Phi22) |
| 17 | o5·:·Sequence | 17 | o5·:·Sequence |
| 18 | i6·:·Phi21; | 18 | i6·:·Phi21; |
| 19 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) | 19 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) |
| 20 | i7·:·Phi22; | 20 | i7·:·Phi22; |
| 21 | o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5) | 21 | o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5) |
| 22 | i8·:·time·(Phi211,Phi212)·=·graph·Phi21 | 22 | i8·:·time·(Phi211,Phi212)·=·graph·Phi21 |
| 23 | ·--·used·0.4 | 23 | ·--·used·0.450029s·(cpu);·0.169538s·(thread);·0s·(gc) |
| 24 | o8·=·(Phi211,·Phi212) | 24 | o8·=·(Phi211,·Phi212) |
| 25 | o8·:·Sequence | 25 | o8·:·Sequence |
| 26 | i9·:·Phi211; | 26 | i9·:·Phi211; |
| Offset 11, 25 lines modified | Offset 11, 25 lines modified | ||
| 11 | o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) | 11 | o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) |
| 12 | i4·:·Phi·=·rationalMap·{f,g}; | 12 | i4·:·Phi·=·rationalMap·{f,g}; |
| 13 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4) | 13 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4) |
| 14 | i5·:·time·Z·=·image·Phi; | 14 | i5·:·time·Z·=·image·Phi; |
| 15 | ·--·used·0.3 | 15 | ·--·used·0.324588s·(cpu);·0.121334s·(thread);·0s·(gc) |
| 16 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 | 16 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 |
| 17 | i6·:·dim·Z,·degree·Z,·degrees·Z | 17 | i6·:·dim·Z,·degree·Z,·degrees·Z |
| 18 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) | 18 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) |
| 19 | o6·:·Sequence | 19 | o6·:·Sequence |
| 20 | i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); | 20 | i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); |
| 21 | ·--·used·7. | 21 | ·--·used·7.83072s·(cpu);·2.37175s·(thread);·0s·(gc) |
| 22 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 | 22 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 |
| 23 | i8·:·assert(Z·==·Z') | 23 | i8·:·assert(Z·==·Z') |
| 24 | i9·:· | 24 | i9·:· |
| Offset 4, 25 lines modified | Offset 4, 25 lines modified | ||
| 4 | i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·6 | 4 | i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·6 |
| 5 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2)); | 5 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2)); |
| 6 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4)) | 6 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4)) |
| 7 | i3·:·time·Psi·=·inverse2·Phi; | 7 | i3·:·time·Psi·=·inverse2·Phi; |
| 8 | ·--·used·0.5 | 8 | ·--·used·0.506898s·(cpu);·0.297915s·(thread);·0s·(gc) |
| 9 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6) | 9 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6) |
| 10 | i4·:·assert(Phi·*·Psi·==·1) | 10 | i4·:·assert(Phi·*·Psi·==·1) |
| 11 | i5·:·Phi'·=·Phi·||·Phi; | 11 | i5·:·Phi'·=·Phi·||·Phi; |
| 12 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4)) | 12 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4)) |
| 13 | i6·:·time·Psi'·=·inverse2·Phi'; | 13 | i6·:·time·Psi'·=·inverse2·Phi'; |
| 14 | ·--·used·1. | 14 | ·--·used·1.33918s·(cpu);·0.985739s·(thread);·0s·(gc) |
| 15 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6) | 15 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6) |
| 16 | i7·:·assert(Phi'·*·Psi'·==·1) | 16 | i7·:·assert(Phi'·*·Psi'·==·1) |
| 17 | i8·:· | 17 | i8·:· |
| Offset 7, 33 lines modified | Offset 7, 33 lines modified | ||
| 7 | i2·:·--·we·see·Phi·as·a·dominant·map | 7 | i2·:·--·we·see·Phi·as·a·dominant·map |
| 8 | ·····Phi·=·rationalMap(Phi,image·Phi); | 8 | ·····Phi·=·rationalMap(Phi,image·Phi); |
| 9 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) | 9 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) |
| 10 | i3·:·time·inverse·Phi; | 10 | i3·:·time·inverse·Phi; |
| 11 | ·--·used·0.2 | 11 | ·--·used·0.257598s·(cpu);·0.0683477s·(thread);·0s·(gc) |
| 12 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4) | 12 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4) |
| 13 | i4·:·Psi·=·last·graph·Phi; | 13 | i4·:·Psi·=·last·graph·Phi; |
| 14 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5) | 14 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5) |
| 15 | i5·:·time·inverse·Psi; | 15 | i5·:·time·inverse·Psi; |
| 16 | ·--·used·0.6 | 16 | ·--·used·0.607465s·(cpu);·0.130866s·(thread);·0s·(gc) |
| 17 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) | 17 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) |
| 18 | i6·:·Eta·=·first·graph·Psi; | 18 | i6·:·Eta·=·first·graph·Psi; |
| 19 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) | 19 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) |
| 20 | i7·:·time·inverse·Eta; | 20 | i7·:·time·inverse·Eta; |
| 21 | ·--·used·0. | 21 | ·--·used·0.803872s·(cpu);·0.311077s·(thread);·0s·(gc) |
| 22 | o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5) | 22 | o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5) |
| 23 | i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1) | 23 | i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1) |
| 24 | i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1) | 24 | i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1) |
| Offset 6, 32 lines modified | Offset 6, 32 lines modified | ||
| 6 | o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2) | 6 | o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2) |
| 7 | i3·:·Phi·=·rationalMap·{f,f}; | 7 | i3·:·Phi·=·rationalMap·{f,f}; |
| 8 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2) | 8 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2) |
| 9 | i4·:·time·isIsomorphism·Phi | 9 | i4·:·time·isIsomorphism·Phi |
| 10 | ·--·used·0.00 | 10 | ·--·used·0.0011877s·(cpu);·5.851e-06s·(thread);·0s·(gc) |
| 11 | o4·=·false | 11 | o4·=·false |
| 12 | i5·:·Psi·=·first·graph·Phi; | 12 | i5·:·Psi·=·first·graph·Phi; |
| 13 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3) | 13 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3) |
| 14 | i6·:·time·isIsomorphism·Psi | 14 | i6·:·time·isIsomorphism·Psi |
| 15 | ·--·used·0.7 | 15 | ·--·used·0.734836s·(cpu);·0.209719s·(thread);·0s·(gc) |
| 16 | o6·=·false | 16 | o6·=·false |
| 17 | i7·:·Eta·=·first·graph·Psi; | 17 | i7·:·Eta·=·first·graph·Psi; |
| 18 | o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2) | 18 | o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2) |
| 19 | i8·:·time·isIsomorphism·Eta | 19 | i8·:·time·isIsomorphism·Eta |
| 20 | ·--·used·1. | 20 | ·--·used·1.67145s·(cpu);·0.749711s·(thread);·0s·(gc) |
| 21 | o8·=·true | 21 | o8·=·true |
| 22 | i9·:·assert(o8·and·(not·o6)·and·(not·o4)) | 22 | i9·:·assert(o8·and·(not·o6)·and·(not·o4)) |
| 23 | i10·:· | 23 | i10·:· |
| Offset 3, 24 lines modified | Offset 3, 24 lines modified | ||
| 3 | i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2-a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2}); | 3 | i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2-a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2}); |
| 4 | i2·:·Phi·=·rationalMap·{f,g}; | 4 | i2·:·Phi·=·rationalMap·{f,g}; |
| 5 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2) | 5 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2) |
| 6 | i3·:·time·isMorphism·Phi | 6 | i3·:·time·isMorphism·Phi |
| 7 | ·--·used·0.1 | 7 | ·--·used·0.213266s·(cpu);·0.16531s·(thread);·0s·(gc) |
| 8 | o3·=·false | 8 | o3·=·false |
| 9 | i4·:·time·Psi·=·first·graph·Phi; | 9 | i4·:·time·Psi·=·first·graph·Phi; |
| 10 | ·--·used·0.3 | 10 | ·--·used·0.344549s·(cpu);·0.112859s·(thread);·0s·(gc) |
| 11 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7) | 11 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7) |
| 12 | i5·:·time·isMorphism·Psi | 12 | i5·:·time·isMorphism·Psi |
| 13 | ·--·used· | 13 | ·--·used·3.1136s·(cpu);·2.61896s·(thread);·0s·(gc) |
| 14 | o5·=·true | 14 | o5·=·true |
| 15 | i6·:·assert((not·o3)·and·o5) | 15 | i6·:·assert((not·o3)·and·o5) |
| 16 | i7·:· | 16 | i7·:· |
| Offset 3, 24 lines modified | Offset 3, 24 lines modified | ||
| 3 | i1·:·K·=·ZZ/333331; | 3 | i1·:·K·=·ZZ/333331; |
| 4 | i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 | 4 | i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 |
| 5 | o2·:·ProjectiveVariety,·curve·in·PP^7 | 5 | o2·:·ProjectiveVariety,·curve·in·PP^7 |
| 6 | i3·:·time·f·=·linearlyNormalEmbedding·X; | 6 | i3·:·time·f·=·linearlyNormalEmbedding·X; |
| 7 | ·--·used·0.00 | 7 | ·--·used·0.00854149s·(cpu);·0.00878027s·(thread);·0s·(gc) |
| 8 | o3·:·MultirationalMap·(automorphism·of·X) | 8 | o3·:·MultirationalMap·(automorphism·of·X) |
| 9 | i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^3 | 9 | i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^3 |
| 10 | o4·:·ProjectiveVariety,·curve·in·PP^3 | 10 | o4·:·ProjectiveVariety,·curve·in·PP^3 |
| 11 | i5·:·time·g·=·linearlyNormalEmbedding·Y; | 11 | i5·:·time·g·=·linearlyNormalEmbedding·Y; |
| 12 | ·--·used·0.3 | 12 | ·--·used·0.386421s·(cpu);·0.333963s·(thread);·0s·(gc) |
| 13 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7) | 13 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7) |
| 14 | i6·:·assert(isIsomorphism·g) | 14 | i6·:·assert(isIsomorphism·g) |
| 15 | i7·:·describe·g | 15 | i7·:·describe·g |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2}; | 3 | i1·:·ZZ/300007[x_0..x_3],·f·=·rationalMap·{x_2^2-x_1*x_3,·x_1*x_2-x_0*x_3,·x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3,·x_3^2}; |
| 4 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 4 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 5 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4) | 5 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4) |
| 6 | i3·:·time·multidegree·Phi | 6 | i3·:·time·multidegree·Phi |
| 7 | ·--·used·0. | 7 | ·--·used·0.733566s·(cpu);·0.389721s·(thread);·0s·(gc) |
| 8 | o3·=·{66,·46,·31,·20} | 8 | o3·=·{66,·46,·31,·20} |
| 9 | o3·:·List | 9 | o3·:·List |
| 10 | i4·:·(degree·source·Phi,degree·image·Phi) | 10 | i4·:·(degree·source·Phi,degree·image·Phi) |
| Offset 1, 21 lines modified | Offset 1, 21 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·16199733219210081214 | 1 | --·-*-·M2-comint·-*-·hash:·16199733219210081214 |
| 2 | i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); | 2 | i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); |
| 3 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5) | 3 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5) |
| 4 | i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) | 4 | i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) |
| 5 | ·--·used·0.00 | 5 | ·--·used·0.00127277s·(cpu);·0.00140549s·(thread);·0s·(gc) |
| 6 | ·--·used·0.185899s·(cpu);·0.13238s·(thread);·0s·(gc) | ||
| 6 | ·--·used·0. | 7 | ·--·used·0.204939s·(cpu);·0.141056s·(thread);·0s·(gc) |
| 8 | ·--·used·0.185013s·(cpu);·0.133897s·(thread);·0s·(gc) | ||
| 7 | ·--·used·0.1 | 9 | ·--·used·0.172616s·(cpu);·0.115406s·(thread);·0s·(gc) |
| 8 | ·--·used·0.144896s·(cpu);·0.0945684s·(thread);·0s·(gc) | ||
| 9 | ·--·used·0.124072s·(cpu);·0.0728073s·(thread);·0s·(gc) | ||
| 10 | o2·=·{51,·28,·14,·6,·2} | 10 | o2·=·{51,·28,·14,·6,·2} |
| 11 | o2·:·List | 11 | o2·:·List |
| 12 | i3·:·time·assert(oo·==·multidegree·Phi) | 12 | i3·:·time·assert(oo·==·multidegree·Phi) |
| 13 | ·--·used·0. | 13 | ·--·used·0.249002s·(cpu);·0.0920012s·(thread);·0s·(gc) |
| 14 | i4·:· | 14 | i4·:· |
| Offset 3, 26 lines modified | Offset 3, 26 lines modified | ||
| 3 | i1·:·K·=·ZZ/1000003; | 3 | i1·:·K·=·ZZ/1000003; |
| 4 | i2·:·X·=·PP_K^({1,1,2},{3,2,3}); | 4 | i2·:·X·=·PP_K^({1,1,2},{3,2,3}); |
| 5 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9 | 5 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9 |
| 6 | i3·:·time·p·:=·point·X | 6 | i3·:·time·p·:=·point·X |
| 7 | ·--·used·0. | 7 | ·--·used·0.187477s·(cpu);·0.0366352s·(thread);·0s·(gc) |
| 8 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) | 8 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) |
| 9 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 | 9 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 |
| 10 | i4·:·Y·=·random({2,1,2},X); | 10 | i4·:·Y·=·random({2,1,2},X); |
| 11 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9 | 11 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9 |
| 12 | i5·:·time·q·=·point·Y | 12 | i5·:·time·q·=·point·Y |
| 13 | ·--·used·1. | 13 | ·--·used·1.47449s·(cpu);·0.826538s·(thread);·0s·(gc) |
| 14 | o5·=·q | 14 | o5·=·q |
| 15 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 | 15 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 |
| 16 | i6·:·assert(isSubset(p,X)·and·isSubset(q,Y)) | 16 | i6·:·assert(isSubset(p,X)·and·isSubset(q,Y)) |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) | 15 | o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) |
| 16 | i5·:·Phi·=·rationalMap·{f,g,h}; | 16 | i5·:·Phi·=·rationalMap·{f,g,h}; |
| 17 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4) | 17 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4) |
| 18 | i6·:·time·segre·Phi; | 18 | i6·:·time·segre·Phi; |
| 19 | ·--·used· | 19 | ·--·used·3.7862s·(cpu);·0.785813s·(thread);·0s·(gc) |
| 20 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149) | 20 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149) |
| 21 | i7·:·describe·segre·Phi | 21 | i7·:·describe·segre·Phi |
| 22 | o7·=·rational·map·defined·by·forms·of·degree·6 | 22 | o7·=·rational·map·defined·by·forms·of·degree·6 |
| 23 | ·····source·variety:·PP^4 | 23 | ·····source·variety:·PP^4 |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3) | 3 | i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3) |
| 4 | o1·=·Phi | 4 | o1·=·Phi |
| 5 | o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2) | 5 | o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2) |
| 6 | i2·:·time·describe·Phi | 6 | i2·:·time·describe·Phi |
| 7 | ·--·used·0. | 7 | ·--·used·0.202657s·(cpu);·0.137455s·(thread);·0s·(gc) |
| 8 | o2·=·multi-rational·map·consisting·of·3·rational·maps | 8 | o2·=·multi-rational·map·consisting·of·3·rational·maps |
| 9 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1) | 9 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1) |
| 10 | ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2· | 10 | ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2· |
| 11 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 | 11 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 |
| 12 | ·····dominance:·true | 12 | ·····dominance:·true |
| 13 | ·····multidegree:·{10,·14,·19,·25} | 13 | ·····multidegree:·{10,·14,·19,·25} |
| Offset 94, 15 lines modified | Offset 94, 15 lines modified | ||
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·?·X | 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·?·X |
| 96 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·</code></pre> | 96 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·f·=·X·===>·Y; | 99 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·f·=·X·===>·Y; |
| 100 | ·--·used·3. | 100 | ·--·used·3.92429s·(cpu);·1.79108s·(thread);·0s·(gc) |
| 101 | o6·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> | 101 | o6·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·f·X | 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·f·X |
| 105 | o7·=·Y | 105 | o7·=·Y |
| Offset 124, 15 lines modified | Offset 124, 15 lines modified | ||
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i10·:·W·=·random({{2},{1}},Y); | 125 | <td>··············<pre><code·class="language-macaulay2">i10·:·W·=·random({{2},{1}},Y); |
| 126 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8</code></pre> | 126 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·g·=·V·===>·W; | 129 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·g·=·V·===>·W; |
| 130 | ·--·used·5. | 130 | ·--·used·5.77971s·(cpu);·2.04888s·(thread);·0s·(gc) |
| 131 | o11·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> | 131 | o11·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i12·:·g||W | 134 | <td>··············<pre><code·class="language-macaulay2">i12·:·g||W |
| 135 | o12·=·multi-rational·map·consisting·of·one·single·rational·map | 135 | o12·=·multi-rational·map·consisting·of·one·single·rational·map |
| Offset 223, 15 lines modified | Offset 223, 15 lines modified | ||
| 223 | ··········<tr> | 223 | ··········<tr> |
| 224 | <td>··············<pre><code·class="language-macaulay2">i16·:·?·Z | 224 | <td>··············<pre><code·class="language-macaulay2">i16·:·?·Z |
| 225 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2</code></pre> | 225 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2</code></pre> |
| 226 | </td>··········</tr> | 226 | </td>··········</tr> |
| 227 | ··········<tr> | 227 | ··········<tr> |
| 228 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·h·=·Z·===>·GG_K(1,4) | 228 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·h·=·Z·===>·GG_K(1,4) |
| 229 | ·--·used·6. | 229 | ·--·used·6.45121s·(cpu);·3.73045s·(thread);·0s·(gc) |
| 230 | o17·=·h | 230 | o17·=·h |
| 231 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)</code></pre> | 231 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| 233 | ··········<tr> | 233 | ··········<tr> |
| 234 | <td>··············<pre><code·class="language-macaulay2">i18·:·h·||·GG_K(1,4) | 234 | <td>··············<pre><code·class="language-macaulay2">i18·:·h·||·GG_K(1,4) |
| Offset 34, 15 lines modified | Offset 34, 15 lines modified | ||
| 34 | take(N,-2)); | 34 | take(N,-2)); |
| 35 | o4·:·ProjectiveVariety,·curve·in·PP^8 | 35 | o4·:·ProjectiveVariety,·curve·in·PP^8 |
| 36 | i5·:·?·X | 36 | i5·:·?·X |
| 37 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15 | 37 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15 |
| 38 | i6·:·time·f·=·X·===>·Y; | 38 | i6·:·time·f·=·X·===>·Y; |
| 39 | ·--·used·3. | 39 | ·--·used·3.92429s·(cpu);·1.79108s·(thread);·0s·(gc) |
| 40 | o6·:·MultirationalMap·(automorphism·of·PP^8) | 40 | o6·:·MultirationalMap·(automorphism·of·PP^8) |
| 41 | i7·:·f·X | 41 | i7·:·f·X |
| 42 | o7·=·Y | 42 | o7·=·Y |
| 43 | o7·:·ProjectiveVariety,·curve·in·PP^8 | 43 | o7·:·ProjectiveVariety,·curve·in·PP^8 |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | i9·:·V·=·random({{2},{1}},X); | 54 | i9·:·V·=·random({{2},{1}},X); |
| 55 | o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 | 55 | o9·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 |
| 56 | i10·:·W·=·random({{2},{1}},Y); | 56 | i10·:·W·=·random({{2},{1}},Y); |
| 57 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 | 57 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8 |
| 58 | i11·:·time·g·=·V·===>·W; | 58 | i11·:·time·g·=·V·===>·W; |
| 59 | ·--·used·5. | 59 | ·--·used·5.77971s·(cpu);·2.04888s·(thread);·0s·(gc) |
| 60 | o11·:·MultirationalMap·(automorphism·of·PP^8) | 60 | o11·:·MultirationalMap·(automorphism·of·PP^8) |
| 61 | i12·:·g||W | 61 | i12·:·g||W |
| 62 | o12·=·multi-rational·map·consisting·of·one·single·rational·map | 62 | o12·=·multi-rational·map·consisting·of·one·single·rational·map |
| 63 | ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2 | 63 | ······source·variety:·6-dimensional·subvariety·of·PP^8·cut·out·by·2 |
| 64 | hypersurfaces·of·degrees·1^1·2^1 | 64 | hypersurfaces·of·degrees·1^1·2^1 |
| Offset 145, 15 lines modified | Offset 145, 15 lines modified | ||
| 145 | i15·:·Z·=·projectiveVariety·pfaffians(4,A); | 145 | i15·:·Z·=·projectiveVariety·pfaffians(4,A); |
| 146 | o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9 | 146 | o15·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^9 |
| 147 | i16·:·?·Z | 147 | i16·:·?·Z |
| 148 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2 | 148 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2 |
| 149 | i17·:·time·h·=·Z·===>·GG_K(1,4) | 149 | i17·:·time·h·=·Z·===>·GG_K(1,4) |
| 150 | ·--·used·6. | 150 | ·--·used·6.45121s·(cpu);·3.73045s·(thread);·0s·(gc) |
| 151 | o17·=·h | 151 | o17·=·h |
| 152 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9) | 152 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9) |
| 153 | i18·:·h·||·GG_K(1,4) | 153 | i18·:·h·||·GG_K(1,4) |
| 154 | o18·=·multi-rational·map·consisting·of·one·single·rational·map | 154 | o18·=·multi-rational·map·consisting·of·one·single·rational·map |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi)); | 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi)); |
| 86 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4</code></pre> | 86 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·X·=·Phi^*·Y; | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·X·=·Phi^*·Y; |
| 90 | ·--·used· | 90 | ·--·used·3.96686s·(cpu);·3.26466s·(thread);·0s·(gc) |
| 91 | o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)</code></pre> | 91 | o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension·2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi-degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·dim·X,·degree·X,·degrees·X | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·dim·X,·degree·X,·degrees·X |
| 95 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), | 95 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to | 27 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to |
| 28 | PP^2·x·PP^4) | 28 | PP^2·x·PP^4) |
| 29 | i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random( | 29 | i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random( |
| 30 | {1,1},ring·target·Phi)); | 30 | {1,1},ring·target·Phi)); |
| 31 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4 | 31 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4 |
| 32 | i4·:·time·X·=·Phi^*·Y; | 32 | i4·:·time·X·=·Phi^*·Y; |
| 33 | ·--·used· | 33 | ·--·used·3.96686s·(cpu);·3.26466s·(thread);·0s·(gc) |
| 34 | o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension | 34 | o4·:·ProjectiveVariety,·curve·in·PP^3·x·PP^2·x·PP^4·(subvariety·of·codimension |
| 35 | 2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi- | 35 | 2·in·threefold·in·PP^3·x·PP^2·x·PP^4·cut·out·by·12·hypersurfaces·of·multi- |
| 36 | degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·) | 36 | degrees·(0,0,2)^1·(0,1,1)^2·(1,0,1)^7·(1,1,0)^2·) |
| 37 | i5·:·dim·X,·degree·X,·degrees·X | 37 | i5·:·dim·X,·degree·X,·degrees·X |
| 38 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), | 38 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), |
| Offset 88, 28 lines modified | Offset 88, 28 lines modified | ||
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·Z·=·source·Phi; | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·Z·=·source·Phi; |
| 90 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7</code></pre> | 90 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Phi·Z; | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Phi·Z; |
| 94 | ·--·used·0.3 | 94 | ·--·used·0.322598s·(cpu);·0.130368s·(thread);·0s·(gc) |
| 95 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> | 95 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·oo,·degree·oo,·degrees·oo | 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·oo,·degree·oo,·degrees·oo |
| 99 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) | 99 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) |
| 100 | o6·:·Sequence</code></pre> | 100 | o6·:·Sequence</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) | 103 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) |
| 104 | ·--·used· | 104 | ·--·used·2.10094s·(cpu);·1.26521s·(thread);·0s·(gc) |
| 105 | o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3· | 105 | o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of·multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3· |
| 106 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> | 106 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i8·:·dim·oo,·degree·oo,·degrees·oo | 109 | <td>··············<pre><code·class="language-macaulay2">i8·:·dim·oo,·degree·oo,·degrees·oo |
| Offset 26, 24 lines modified | Offset 26, 24 lines modified | ||
| 26 | o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x | 26 | o3·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 27 | PP^7·to·PP^7·x·PP^7) | 27 | PP^7·to·PP^7·x·PP^7) |
| 28 | i4·:·Z·=·source·Phi; | 28 | i4·:·Z·=·source·Phi; |
| 29 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7 | 29 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7 |
| 30 | i5·:·time·Phi·Z; | 30 | i5·:·time·Phi·Z; |
| 31 | ·--·used·0.3 | 31 | ·--·used·0.322598s·(cpu);·0.130368s·(thread);·0s·(gc) |
| 32 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7 | 32 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7 |
| 33 | i6·:·dim·oo,·degree·oo,·degrees·oo | 33 | i6·:·dim·oo,·degree·oo,·degrees·oo |
| 34 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) | 34 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) |
| 35 | o6·:·Sequence | 35 | o6·:·Sequence |
| 36 | i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) | 36 | i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) |
| 37 | ·--·used· | 37 | ·--·used·2.10094s·(cpu);·1.26521s·(thread);·0s·(gc) |
| 38 | o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of | 38 | o7·=·0-dimensional·subvariety·of·PP^7·x·PP^7·cut·out·by·22·hypersurfaces·of |
| 39 | multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3 | 39 | multi-degrees·(0,1)^5·(0,2)^3·(1,0)^5·(1,1)^6·(2,0)^3 |
| 40 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7 | 40 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7 |
| 41 | i8·:·dim·oo,·degree·oo,·degrees·oo | 41 | i8·:·dim·oo,·degree·oo,·degrees·oo |
| Offset 88, 27 lines modified | Offset 88, 27 lines modified | ||
| 88 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of | 88 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of |
| 89 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 | 89 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 |
| 90 | ·····------------------------------------------------------------------------ | 90 | ·····------------------------------------------------------------------------ |
| 91 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1</code></pre> | 91 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree(Phi,Strategy=>"random·point") | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree(Phi,Strategy=>"random·point") |
| 95 | ·--·used· | 95 | ·--·used·4.52399s·(cpu);·2.66659s·(thread);·0s·(gc) |
| 96 | o4·=·2</code></pre> | 96 | o4·=·2</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") |
| 100 | ·--·used·0.2 | 100 | ·--·used·0.423067s·(cpu);·0.346634s·(thread);·0s·(gc) |
| 101 | o5·=·2</code></pre> | 101 | o5·=·2</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·degree·Phi | 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·degree·Phi |
| 105 | ·--·used·0. | 105 | ·--·used·0.338524s·(cpu);·0.340681s·(thread);·0s·(gc) |
| 106 | o6·=·2</code></pre> | 106 | o6·=·2</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ········<p>Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the·strategy·used.</p> | 109 | ········<p>Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the·strategy·used.</p> |
| 110 | ······</div> | 110 | ······</div> |
| 111 | ······<div> | 111 | ······<div> |
| Offset 28, 23 lines modified | Offset 28, 23 lines modified | ||
| 28 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 28 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 29 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of | 29 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of |
| 30 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 | 30 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 |
| 31 | ·····------------------------------------------------------------------------ | 31 | ·····------------------------------------------------------------------------ |
| 32 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1 | 32 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1 |
| 33 | i4·:·time·degree(Phi,Strategy=>"random·point") | 33 | i4·:·time·degree(Phi,Strategy=>"random·point") |
| 34 | ·--·used· | 34 | ·--·used·4.52399s·(cpu);·2.66659s·(thread);·0s·(gc) |
| 35 | o4·=·2 | 35 | o4·=·2 |
| 36 | i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") | 36 | i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") |
| 37 | ·--·used·0.2 | 37 | ·--·used·0.423067s·(cpu);·0.346634s·(thread);·0s·(gc) |
| 38 | o5·=·2 | 38 | o5·=·2 |
| 39 | i6·:·time·degree·Phi | 39 | i6·:·time·degree·Phi |
| 40 | ·--·used·0. | 40 | ·--·used·0.338524s·(cpu);·0.340681s·(thread);·0s·(gc) |
| 41 | o6·=·2 | 41 | o6·=·2 |
| 42 | Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the | 42 | Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the |
| 43 | strategy·used. | 43 | strategy·used. |
| 44 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 44 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 45 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·multi-rational·map | 45 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·multi-rational·map |
| 46 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map | 46 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8M_\x8a_\x8p_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map |
| Offset 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 79 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> | 79 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·degree·Phi | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·degree·Phi |
| 83 | ·--·used·0. | 83 | ·--·used·0.80694s·(cpu);·0.488036s·(thread);·0s·(gc) |
| 84 | o3·=·1</code></pre> | 84 | o3·=·1</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ········</table> | 86 | ········</table> |
| 87 | ······</div> | 87 | ······</div> |
| 88 | ······<div> | 88 | ······<div> |
| 89 | ········<h2>See·also</h2> | 89 | ········<h2>See·also</h2> |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3, | 19 | x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3, |
| 20 | x_3^2}; | 20 | x_3^2}; |
| 21 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 21 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 22 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to | 22 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to |
| 23 | PP^2·x·PP^4) | 23 | PP^2·x·PP^4) |
| 24 | i3·:·time·degree·Phi | 24 | i3·:·time·degree·Phi |
| 25 | ·--·used·0. | 25 | ·--·used·0.80694s·(cpu);·0.488036s·(thread);·0s·(gc) |
| 26 | o3·=·1 | 26 | o3·=·1 |
| 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 28 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8,_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8)·--·degree·of·a·multi-rational·map·using·a | 28 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8,_\x8O_\x8p_\x8t_\x8i_\x8o_\x8n_\x8)·--·degree·of·a·multi-rational·map·using·a |
| 29 | ······probabilistic·approach | 29 | ······probabilistic·approach |
| 30 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map | 30 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·degree·of·a·rational·map |
| 31 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational | 31 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational |
| Offset 75, 40 lines modified | Offset 75, 40 lines modified | ||
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); |
| 77 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)</code></pre> | 77 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·?·Phi | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·?·Phi |
| 81 | ·--·used·0.00 | 81 | ·--·used·0.00100996s·(cpu);·0.000142226s·(thread);·0s·(gc) |
| 82 | o2·=·multi-rational·map·consisting·of·2·rational·maps | 82 | o2·=·multi-rational·map·consisting·of·2·rational·maps |
| 83 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 83 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 84 | ·····target·variety:·PP^4·x·PP^5 | 84 | ·····target·variety:·PP^4·x·PP^5 |
| 85 | ·····------------------------------------------------------------------------ | 85 | ·····------------------------------------------------------------------------ |
| 86 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8</code></pre> | 86 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·image·Phi; | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·image·Phi; |
| 90 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5</code></pre> | 90 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·?·Phi | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·?·Phi |
| 94 | ·--·used·0.00 | 94 | ·--·used·0.00188283s·(cpu);·0.000202439s·(thread);·0s·(gc) |
| 95 | o4·=·multi-rational·map·consisting·of·2·rational·maps | 95 | o4·=·multi-rational·map·consisting·of·2·rational·maps |
| 96 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 96 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 97 | ·····target·variety:·PP^4·x·PP^5 | 97 | ·····target·variety:·PP^4·x·PP^5 |
| 98 | ·····dominance:·false | 98 | ·····dominance:·false |
| 99 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·</code></pre> | 99 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8·</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·Phi | 102 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·Phi |
| 103 | ·--·used· | 103 | ·--·used·1.03358s·(cpu);·0.859667s·(thread);·0s·(gc) |
| 104 | o5·=·multi-rational·map·consisting·of·2·rational·maps | 104 | o5·=·multi-rational·map·consisting·of·2·rational·maps |
| 105 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 105 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 106 | ·····target·variety:·PP^4·x·PP^5 | 106 | ·····target·variety:·PP^4·x·PP^5 |
| 107 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 107 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 108 | ·····dominance:·false | 108 | ·····dominance:·false |
| 109 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 109 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| Offset 116, 15 lines modified | Offset 116, 15 lines modified | ||
| 116 | ·····degree:·1 | 116 | ·····degree:·1 |
| 117 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] | 117 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] |
| 118 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] | 118 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] |
| 119 | ·····coefficient·ring:·ZZ/65521</code></pre> | 119 | ·····coefficient·ring:·ZZ/65521</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·?·Phi | 122 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·?·Phi |
| 123 | ·--·used·0.00010 | 123 | ·--·used·0.000130775s·(cpu);·0.000423464s·(thread);·0s·(gc) |
| 124 | o6·=·multi-rational·map·consisting·of·2·rational·maps | 124 | o6·=·multi-rational·map·consisting·of·2·rational·maps |
| 125 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 125 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| 126 | ·····target·variety:·PP^4·x·PP^5 | 126 | ·····target·variety:·PP^4·x·PP^5 |
| 127 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 127 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 128 | ·····dominance:·false | 128 | ·····dominance:·false |
| 129 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 129 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· |
| Offset 17, 36 lines modified | Offset 17, 36 lines modified | ||
| 17 | ?·Phi·is·a·lite·version·of·describe·Phi.·The·latter·has·a·different·behavior | 17 | ?·Phi·is·a·lite·version·of·describe·Phi.·The·latter·has·a·different·behavior |
| 18 | than·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8),·since·it·performs·computations. | 18 | than·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8),·since·it·performs·computations. |
| 19 | i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); | 19 | i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); |
| 20 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x | 20 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 21 | PP^5·to·PP^4·x·PP^5) | 21 | PP^5·to·PP^4·x·PP^5) |
| 22 | i2·:·time·?·Phi | 22 | i2·:·time·?·Phi |
| 23 | ·--·used·0.00 | 23 | ·--·used·0.00100996s·(cpu);·0.000142226s·(thread);·0s·(gc) |
| 24 | o2·=·multi-rational·map·consisting·of·2·rational·maps | 24 | o2·=·multi-rational·map·consisting·of·2·rational·maps |
| 25 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 25 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 26 | ·····target·variety:·PP^4·x·PP^5 | 26 | ·····target·variety:·PP^4·x·PP^5 |
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| 28 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 | 28 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 |
| 29 | i3·:·image·Phi; | 29 | i3·:·image·Phi; |
| 30 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5 | 30 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5 |
| 31 | i4·:·time·?·Phi | 31 | i4·:·time·?·Phi |
| 32 | ·--·used·0.00 | 32 | ·--·used·0.00188283s·(cpu);·0.000202439s·(thread);·0s·(gc) |
| 33 | o4·=·multi-rational·map·consisting·of·2·rational·maps | 33 | o4·=·multi-rational·map·consisting·of·2·rational·maps |
| 34 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 34 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 35 | hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 | 35 | hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 |
| 36 | ·····target·variety:·PP^4·x·PP^5 | 36 | ·····target·variety:·PP^4·x·PP^5 |
| 37 | ·····dominance:·false | 37 | ·····dominance:·false |
| 38 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces | 38 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces |
| 39 | of·multi-degrees·(0,2)^1·(1,1)^8 | 39 | of·multi-degrees·(0,2)^1·(1,1)^8 |
| 40 | i5·:·time·describe·Phi | 40 | i5·:·time·describe·Phi |
| 41 | ·--·used· | 41 | ·--·used·1.03358s·(cpu);·0.859667s·(thread);·0s·(gc) |
| 42 | o5·=·multi-rational·map·consisting·of·2·rational·maps | 42 | o5·=·multi-rational·map·consisting·of·2·rational·maps |
| 43 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 43 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 44 | hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 | 44 | hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 |
| 45 | ·····target·variety:·PP^4·x·PP^5 | 45 | ·····target·variety:·PP^4·x·PP^5 |
| 46 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 46 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 47 | ·····dominance:·false | 47 | ·····dominance:·false |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | of·multi-degrees·(0,2)^1·(1,1)^8 | 54 | of·multi-degrees·(0,2)^1·(1,1)^8 |
| 55 | ·····multidegree:·{51,·51,·51,·51,·51} | 55 | ·····multidegree:·{51,·51,·51,·51,·51} |
| 56 | ·····degree:·1 | 56 | ·····degree:·1 |
| 57 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] | 57 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] |
| 58 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] | 58 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] |
| 59 | ·····coefficient·ring:·ZZ/65521 | 59 | ·····coefficient·ring:·ZZ/65521 |
| 60 | i6·:·time·?·Phi | 60 | i6·:·time·?·Phi |
| 61 | ·--·used·0.00010 | 61 | ·--·used·0.000130775s·(cpu);·0.000423464s·(thread);·0s·(gc) |
| 62 | o6·=·multi-rational·map·consisting·of·2·rational·maps | 62 | o6·=·multi-rational·map·consisting·of·2·rational·maps |
| 63 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 63 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 64 | hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 | 64 | hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8 |
| 65 | ·····target·variety:·PP^4·x·PP^5 | 65 | ·····target·variety:·PP^4·x·PP^5 |
| 66 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 66 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 67 | ·····dominance:·false | 67 | ·····dominance:·false |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | o1·=·Phi | 84 | o1·=·Phi |
| 85 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 85 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(Phi1,Phi2)·=·graph·Phi | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(Phi1,Phi2)·=·graph·Phi |
| 89 | ·--·used·0.2 | 89 | ·--·used·0.254436s·(cpu);·0.0556115s·(thread);·0s·(gc) |
| 90 | o2·=·(Phi1,·Phi2) | 90 | o2·=·(Phi1,·Phi2) |
| 91 | o2·:·Sequence</code></pre> | 91 | o2·:·Sequence</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi1; | 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi1; |
| Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi2; | 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi2; |
| 104 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> | 104 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(Phi21,Phi22)·=·graph·Phi2 | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(Phi21,Phi22)·=·graph·Phi2 |
| 108 | ·--·used·0. | 108 | ·--·used·0.286226s·(cpu);·0.0764986s·(thread);·0s·(gc) |
| 109 | o5·=·(Phi21,·Phi22) | 109 | o5·=·(Phi21,·Phi22) |
| 110 | o5·:·Sequence</code></pre> | 110 | o5·:·Sequence</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i6·:·Phi21; | 113 | <td>··············<pre><code·class="language-macaulay2">i6·:·Phi21; |
| Offset 120, 15 lines modified | Offset 120, 15 lines modified | ||
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i7·:·Phi22; | 121 | <td>··············<pre><code·class="language-macaulay2">i7·:·Phi22; |
| 122 | o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)</code></pre> | 122 | o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5)</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·(Phi211,Phi212)·=·graph·Phi21 | 125 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·(Phi211,Phi212)·=·graph·Phi21 |
| 126 | ·--·used·0.4 | 126 | ·--·used·0.450029s·(cpu);·0.169538s·(thread);·0s·(gc) |
| 127 | o8·=·(Phi211,·Phi212) | 127 | o8·=·(Phi211,·Phi212) |
| 128 | o8·:·Sequence</code></pre> | 128 | o8·:·Sequence</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·Phi211; | 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·Phi211; |
| Offset 20, 43 lines modified | Offset 20, 43 lines modified | ||
| 20 | Phi)^-1·*·(last·graph·Phi)·==·Phi·are·always·satisfied. | 20 | Phi)^-1·*·(last·graph·Phi)·==·Phi·are·always·satisfied. |
| 21 | i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true) | 21 | i1·:·Phi·=·rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true) |
| 22 | o1·=·Phi | 22 | o1·=·Phi |
| 23 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) | 23 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) |
| 24 | i2·:·time·(Phi1,Phi2)·=·graph·Phi | 24 | i2·:·time·(Phi1,Phi2)·=·graph·Phi |
| 25 | ·--·used·0.2 | 25 | ·--·used·0.254436s·(cpu);·0.0556115s·(thread);·0s·(gc) |
| 26 | o2·=·(Phi1,·Phi2) | 26 | o2·=·(Phi1,·Phi2) |
| 27 | o2·:·Sequence | 27 | o2·:·Sequence |
| 28 | i3·:·Phi1; | 28 | i3·:·Phi1; |
| 29 | o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 29 | o3·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 30 | PP^5·to·PP^4) | 30 | PP^5·to·PP^4) |
| 31 | i4·:·Phi2; | 31 | i4·:·Phi2; |
| 32 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of | 32 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of |
| 33 | PP^4·x·PP^5·to·hypersurface·in·PP^5) | 33 | PP^4·x·PP^5·to·hypersurface·in·PP^5) |
| 34 | i5·:·time·(Phi21,Phi22)·=·graph·Phi2 | 34 | i5·:·time·(Phi21,Phi22)·=·graph·Phi2 |
| 35 | ·--·used·0. | 35 | ·--·used·0.286226s·(cpu);·0.0764986s·(thread);·0s·(gc) |
| 36 | o5·=·(Phi21,·Phi22) | 36 | o5·=·(Phi21,·Phi22) |
| 37 | o5·:·Sequence | 37 | o5·:·Sequence |
| 38 | i6·:·Phi21; | 38 | i6·:·Phi21; |
| 39 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 39 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 40 | PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) | 40 | PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) |
| 41 | i7·:·Phi22; | 41 | i7·:·Phi22; |
| 42 | o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of | 42 | o7·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of |
| 43 | PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5) | 43 | PP^4·x·PP^5·x·PP^5·to·hypersurface·in·PP^5) |
| 44 | i8·:·time·(Phi211,Phi212)·=·graph·Phi21 | 44 | i8·:·time·(Phi211,Phi212)·=·graph·Phi21 |
| 45 | ·--·used·0.4 | 45 | ·--·used·0.450029s·(cpu);·0.169538s·(thread);·0s·(gc) |
| 46 | o8·=·(Phi211,·Phi212) | 46 | o8·=·(Phi211,·Phi212) |
| 47 | o8·:·Sequence | 47 | o8·:·Sequence |
| 48 | i9·:·Phi211; | 48 | i9·:·Phi211; |
| 49 | o9·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 49 | o9·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| Offset 87, 15 lines modified | Offset 87, 15 lines modified | ||
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi·=·rationalMap·{f,g}; | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi·=·rationalMap·{f,g}; |
| 89 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)</code></pre> | 89 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Z·=·image·Phi; | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Z·=·image·Phi; |
| 93 | ·--·used·0.3 | 93 | ·--·used·0.324588s·(cpu);·0.121334s·(thread);·0s·(gc) |
| 94 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> | 94 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·Z,·degree·Z,·degrees·Z | 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·Z,·degree·Z,·degrees·Z |
| 98 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) | 98 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) |
| Offset 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | o6·:·Sequence</code></pre> | 103 | o6·:·Sequence</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ········</table> | 105 | ········</table> |
| 106 | ········<p>Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as·follows:</p> | 106 | ········<p>Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as·follows:</p> |
| 107 | ········<table·class="examples"> | 107 | ········<table·class="examples"> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); | 109 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); |
| 110 | ·--·used·7. | 110 | ·--·used·7.83072s·(cpu);·2.37175s·(thread);·0s·(gc) |
| 111 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> | 111 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Z·==·Z')</code></pre> | 114 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Z·==·Z')</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ········</table> | 116 | ········</table> |
| Offset 24, 26 lines modified | Offset 24, 26 lines modified | ||
| 24 | 3*x_2^2+2*x_1*x_3+x_0*x_4,·2*x_1*x_2-2*x_0*x_3,·-x_1^2+x_0*x_2}; | 24 | 3*x_2^2+2*x_1*x_3+x_0*x_4,·2*x_1*x_2-2*x_0*x_3,·-x_1^2+x_0*x_2}; |
| 25 | o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) | 25 | o3·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) |
| 26 | i4·:·Phi·=·rationalMap·{f,g}; | 26 | i4·:·Phi·=·rationalMap·{f,g}; |
| 27 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4) | 27 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4) |
| 28 | i5·:·time·Z·=·image·Phi; | 28 | i5·:·time·Z·=·image·Phi; |
| 29 | ·--·used·0.3 | 29 | ·--·used·0.324588s·(cpu);·0.121334s·(thread);·0s·(gc) |
| 30 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 | 30 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 |
| 31 | i6·:·dim·Z,·degree·Z,·degrees·Z | 31 | i6·:·dim·Z,·degree·Z,·degrees·Z |
| 32 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) | 32 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) |
| 33 | o6·:·Sequence | 33 | o6·:·Sequence |
| 34 | Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as | 34 | Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as |
| 35 | follows: | 35 | follows: |
| 36 | i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); | 36 | i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); |
| 37 | ·--·used·7. | 37 | ·--·used·7.83072s·(cpu);·2.37175s·(thread);·0s·(gc) |
| 38 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 | 38 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4 |
| 39 | i8·:·assert(Z·==·Z') | 39 | i8·:·assert(Z·==·Z') |
| 40 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 40 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 41 | ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·direct·image·via·a·multi- | 41 | ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·direct·image·via·a·multi- |
| 42 | ······rational·map | 42 | ······rational·map |
| 43 | ····*·_\x8i_\x8m_\x8a_\x8g_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·closure·of·the·image·of·a·rational·map | 43 | ····*·_\x8i_\x8m_\x8a_\x8g_\x8e_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·closure·of·the·image·of·a·rational·map |
| Offset 78, 29 lines modified | Offset 78, 29 lines modified | ||
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·6 | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·6 |
| 79 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2)); | 79 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2)); |
| 80 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))</code></pre> | 80 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·Psi·=·inverse2·Phi; | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·Psi·=·inverse2·Phi; |
| 84 | ·--·used·0.5 | 84 | ·--·used·0.506898s·(cpu);·0.297915s·(thread);·0s·(gc) |
| 85 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)</code></pre> | 85 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(Phi·*·Psi·==·1)</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(Phi·*·Psi·==·1)</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi'·=·Phi·||·Phi; | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi'·=·Phi·||·Phi; |
| 92 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))</code></pre> | 92 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Psi'·=·inverse2·Phi'; | 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Psi'·=·inverse2·Phi'; |
| 96 | ·--·used·1. | 96 | ·--·used·1.33918s·(cpu);·0.985739s·(thread);·0s·(gc) |
| 97 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)</code></pre> | 97 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(Phi'·*·Psi'·==·1)</code></pre> | 100 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(Phi'·*·Psi'·==·1)</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ········</table> | 102 | ········</table> |
| Offset 25, 23 lines modified | Offset 25, 23 lines modified | ||
| 25 | i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational | 25 | i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational |
| 26 | normal·curve·of·degree·6 | 26 | normal·curve·of·degree·6 |
| 27 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal | 27 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal |
| 28 | PP_K([6],2)); | 28 | PP_K([6],2)); |
| 29 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4)) | 29 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4)) |
| 30 | i3·:·time·Psi·=·inverse2·Phi; | 30 | i3·:·time·Psi·=·inverse2·Phi; |
| 31 | ·--·used·0.5 | 31 | ·--·used·0.506898s·(cpu);·0.297915s·(thread);·0s·(gc) |
| 32 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6) | 32 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6) |
| 33 | i4·:·assert(Phi·*·Psi·==·1) | 33 | i4·:·assert(Phi·*·Psi·==·1) |
| 34 | i5·:·Phi'·=·Phi·||·Phi; | 34 | i5·:·Phi'·=·Phi·||·Phi; |
| 35 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4)) | 35 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4)) |
| 36 | i6·:·time·Psi'·=·inverse2·Phi'; | 36 | i6·:·time·Psi'·=·inverse2·Phi'; |
| 37 | ·--·used·1. | 37 | ·--·used·1.33918s·(cpu);·0.985739s·(thread);·0s·(gc) |
| 38 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6) | 38 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6) |
| 39 | i7·:·assert(Phi'·*·Psi'·==·1) | 39 | i7·:·assert(Phi'·*·Psi'·==·1) |
| 40 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 40 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 41 | ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map | 41 | ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map |
| 42 | ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8<_\x8=_\x8=_\x8>_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·equality·of·multi-rational·maps | 42 | ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8·_\x8<_\x8=_\x8=_\x8>_\x8·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p·--·equality·of·multi-rational·maps |
| 43 | ······with·checks·on·internal·data | 43 | ······with·checks·on·internal·data |
| Offset 84, 37 lines modified | Offset 84, 37 lines modified | ||
| 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·we·see·Phi·as·a·dominant·map | 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·we·see·Phi·as·a·dominant·map |
| 85 | ·····Phi·=·rationalMap(Phi,image·Phi); | 85 | ·····Phi·=·rationalMap(Phi,image·Phi); |
| 86 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 86 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·Phi; | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·Phi; |
| 90 | ·--·used·0.2 | 90 | ·--·used·0.257598s·(cpu);·0.0683477s·(thread);·0s·(gc) |
| 91 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> | 91 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·Psi·=·last·graph·Phi; | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·Psi·=·last·graph·Phi; |
| 95 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> | 95 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·inverse·Psi; | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·inverse·Psi; |
| 99 | ·--·used·0.6 | 99 | ·--·used·0.607465s·(cpu);·0.130866s·(thread);·0s·(gc) |
| 100 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre> | 100 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·Eta·=·first·graph·Psi; | 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·Eta·=·first·graph·Psi; |
| 104 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre> | 104 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·inverse·Eta; | 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·inverse·Eta; |
| 108 | ·--·used·0. | 108 | ·--·used·0.803872s·(cpu);·0.311077s·(thread);·0s·(gc) |
| 109 | o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)</code></pre> | 109 | o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5)</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)</code></pre> | 112 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| Offset 25, 32 lines modified | Offset 25, 32 lines modified | ||
| 25 | o1·:·MultirationalMap·(rational·map·from·PP^4·to·PP^5) | 25 | o1·:·MultirationalMap·(rational·map·from·PP^4·to·PP^5) |
| 26 | i2·:·--·we·see·Phi·as·a·dominant·map | 26 | i2·:·--·we·see·Phi·as·a·dominant·map |
| 27 | ·····Phi·=·rationalMap(Phi,image·Phi); | 27 | ·····Phi·=·rationalMap(Phi,image·Phi); |
| 28 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) | 28 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5) |
| 29 | i3·:·time·inverse·Phi; | 29 | i3·:·time·inverse·Phi; |
| 30 | ·--·used·0.2 | 30 | ·--·used·0.257598s·(cpu);·0.0683477s·(thread);·0s·(gc) |
| 31 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4) | 31 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4) |
| 32 | i4·:·Psi·=·last·graph·Phi; | 32 | i4·:·Psi·=·last·graph·Phi; |
| 33 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 33 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 34 | PP^5·to·hypersurface·in·PP^5) | 34 | PP^5·to·hypersurface·in·PP^5) |
| 35 | i5·:·time·inverse·Psi; | 35 | i5·:·time·inverse·Psi; |
| 36 | ·--·used·0.6 | 36 | ·--·used·0.607465s·(cpu);·0.130866s·(thread);·0s·(gc) |
| 37 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4- | 37 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4- |
| 38 | dimensional·subvariety·of·PP^4·x·PP^5) | 38 | dimensional·subvariety·of·PP^4·x·PP^5) |
| 39 | i6·:·Eta·=·first·graph·Psi; | 39 | i6·:·Eta·=·first·graph·Psi; |
| 40 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 40 | o6·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 41 | PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) | 41 | PP^5·x·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5) |
| 42 | i7·:·time·inverse·Eta; | 42 | i7·:·time·inverse·Eta; |
| 43 | ·--·used·0. | 43 | ·--·used·0.803872s·(cpu);·0.311077s·(thread);·0s·(gc) |
| 44 | o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 44 | o7·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 45 | PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5) | 45 | PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5) |
| 46 | i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1) | 46 | i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1) |
| 47 | i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1) | 47 | i9·:·assert(Psi·*·Psi^-1·==·1·and·Psi^-1·*·Psi·==·1) |
| 48 | i10·:·assert(Eta·*·Eta^-1·==·1·and·Eta^-1·*·Eta·==·1) | 48 | i10·:·assert(Eta·*·Eta^-1·==·1·and·Eta^-1·*·Eta·==·1) |
| 49 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 49 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| Offset 79, 37 lines modified | Offset 79, 37 lines modified | ||
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap·{f,f}; | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap·{f,f}; |
| 81 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)</code></pre> | 81 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isIsomorphism·Phi | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isIsomorphism·Phi |
| 85 | ·--·used·0.00 | 85 | ·--·used·0.0011877s·(cpu);·5.851e-06s·(thread);·0s·(gc) |
| 86 | o4·=·false</code></pre> | 86 | o4·=·false</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·Psi·=·first·graph·Phi; | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·Psi·=·first·graph·Phi; |
| 90 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)</code></pre> | 90 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isIsomorphism·Psi | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isIsomorphism·Psi |
| 94 | ·--·used·0.7 | 94 | ·--·used·0.734836s·(cpu);·0.209719s·(thread);·0s·(gc) |
| 95 | o6·=·false</code></pre> | 95 | o6·=·false</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i7·:·Eta·=·first·graph·Psi; | 98 | <td>··············<pre><code·class="language-macaulay2">i7·:·Eta·=·first·graph·Psi; |
| 99 | o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre> | 99 | o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x·PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isIsomorphism·Eta | 102 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isIsomorphism·Eta |
| 103 | ·--·used·1. | 103 | ·--·used·1.67145s·(cpu);·0.749711s·(thread);·0s·(gc) |
| 104 | o8·=·true</code></pre> | 104 | o8·=·true</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i9·:·assert(o8·and·(not·o6)·and·(not·o4))</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i9·:·assert(o8·and·(not·o6)·and·(not·o4))</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| Offset 18, 31 lines modified | Offset 18, 31 lines modified | ||
| 18 | ·····ZZ/33331[a..d];·f·=·rationalMap·{c^2-b*d,b*c-a*d,b^2-a*c}; | 18 | ·····ZZ/33331[a..d];·f·=·rationalMap·{c^2-b*d,b*c-a*d,b^2-a*c}; |
| 19 | o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2) | 19 | o2·:·RationalMap·(quadratic·rational·map·from·PP^3·to·PP^2) |
| 20 | i3·:·Phi·=·rationalMap·{f,f}; | 20 | i3·:·Phi·=·rationalMap·{f,f}; |
| 21 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2) | 21 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2) |
| 22 | i4·:·time·isIsomorphism·Phi | 22 | i4·:·time·isIsomorphism·Phi |
| 23 | ·--·used·0.00 | 23 | ·--·used·0.0011877s·(cpu);·5.851e-06s·(thread);·0s·(gc) |
| 24 | o4·=·false | 24 | o4·=·false |
| 25 | i5·:·Psi·=·first·graph·Phi; | 25 | i5·:·Psi·=·first·graph·Phi; |
| 26 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to | 26 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to |
| 27 | PP^3) | 27 | PP^3) |
| 28 | i6·:·time·isIsomorphism·Psi | 28 | i6·:·time·isIsomorphism·Psi |
| 29 | ·--·used·0.7 | 29 | ·--·used·0.734836s·(cpu);·0.209719s·(thread);·0s·(gc) |
| 30 | o6·=·false | 30 | o6·=·false |
| 31 | i7·:·Eta·=·first·graph·Psi; | 31 | i7·:·Eta·=·first·graph·Psi; |
| 32 | o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x | 32 | o7·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·x |
| 33 | PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2) | 33 | PP^3·to·threefold·in·PP^3·x·PP^2·x·PP^2) |
| 34 | i8·:·time·isIsomorphism·Eta | 34 | i8·:·time·isIsomorphism·Eta |
| 35 | ·--·used·1. | 35 | ·--·used·1.67145s·(cpu);·0.749711s·(thread);·0s·(gc) |
| 36 | o8·=·true | 36 | o8·=·true |
| 37 | i9·:·assert(o8·and·(not·o6)·and·(not·o4)) | 37 | i9·:·assert(o8·and·(not·o6)·and·(not·o4)) |
| 38 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 38 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 39 | ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map | 39 | ····*·_\x8i_\x8n_\x8v_\x8e_\x8r_\x8s_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·inverse·of·a·birational·map |
| 40 | ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·multi-rational·map·is·a | 40 | ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·multi-rational·map·is·a |
| 41 | ······morphism | 41 | ······morphism |
| Offset 76, 27 lines modified | Offset 76, 27 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·rationalMap·{f,g}; | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·rationalMap·{f,g}; |
| 78 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)</code></pre> | 78 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isMorphism·Phi | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isMorphism·Phi |
| 82 | ·--·used·0.1 | 82 | ·--·used·0.213266s·(cpu);·0.16531s·(thread);·0s·(gc) |
| 83 | o3·=·false</code></pre> | 83 | o3·=·false</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Psi·=·first·graph·Phi; | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Psi·=·first·graph·Phi; |
| 87 | ·--·used·0.3 | 87 | ·--·used·0.344549s·(cpu);·0.112859s·(thread);·0s·(gc) |
| 88 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)</code></pre> | 88 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7)</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isMorphism·Psi | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isMorphism·Psi |
| 92 | ·--·used· | 92 | ·--·used·3.1136s·(cpu);·2.61896s·(thread);·0s·(gc) |
| 93 | o5·=·true</code></pre> | 93 | o5·=·true</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert((not·o3)·and·o5)</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert((not·o3)·and·o5)</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ········</table> | 98 | ········</table> |
| Offset 18, 24 lines modified | Offset 18, 24 lines modified | ||
| 18 | i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2- | 18 | i1·:·ZZ/300007[a..e],·f·=·first·graph·rationalMap·ideal(c^2-b*d,b*c-a*d,b^2- |
| 19 | a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2}); | 19 | a*c,e),·g·=·rationalMap·submatrix(matrix·f,{0..2}); |
| 20 | i2·:·Phi·=·rationalMap·{f,g}; | 20 | i2·:·Phi·=·rationalMap·{f,g}; |
| 21 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x | 21 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 22 | PP^7·to·PP^4·x·PP^2) | 22 | PP^7·to·PP^4·x·PP^2) |
| 23 | i3·:·time·isMorphism·Phi | 23 | i3·:·time·isMorphism·Phi |
| 24 | ·--·used·0.1 | 24 | ·--·used·0.213266s·(cpu);·0.16531s·(thread);·0s·(gc) |
| 25 | o3·=·false | 25 | o3·=·false |
| 26 | i4·:·time·Psi·=·first·graph·Phi; | 26 | i4·:·time·Psi·=·first·graph·Phi; |
| 27 | ·--·used·0.3 | 27 | ·--·used·0.344549s·(cpu);·0.112859s·(thread);·0s·(gc) |
| 28 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x | 28 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 29 | PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7) | 29 | PP^7·x·PP^4·x·PP^2·to·4-dimensional·subvariety·of·PP^4·x·PP^7) |
| 30 | i5·:·time·isMorphism·Psi | 30 | i5·:·time·isMorphism·Psi |
| 31 | ·--·used· | 31 | ·--·used·3.1136s·(cpu);·2.61896s·(thread);·0s·(gc) |
| 32 | o5·=·true | 32 | o5·=·true |
| 33 | i6·:·assert((not·o3)·and·o5) | 33 | i6·:·assert((not·o3)·and·o5) |
| 34 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 34 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 35 | ····*·_\x8i_\x8s_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·birational·map·is·an | 35 | ····*·_\x8i_\x8s_\x8I_\x8s_\x8o_\x8m_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·birational·map·is·an |
| 36 | ······isomorphism | 36 | ······isomorphism |
| 37 | ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·rational·map·is·a·morphism | 37 | ····*·_\x8i_\x8s_\x8M_\x8o_\x8r_\x8p_\x8h_\x8i_\x8s_\x8m_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·whether·a·rational·map·is·a·morphism |
| Offset 74, 26 lines modified | Offset 74, 26 lines modified | ||
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 | 75 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 |
| 76 | o2·:·ProjectiveVariety,·curve·in·PP^7</code></pre> | 76 | o2·:·ProjectiveVariety,·curve·in·PP^7</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·linearlyNormalEmbedding·X; | 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·linearlyNormalEmbedding·X; |
| 80 | ·--·used·0.00 | 80 | ·--·used·0.00854149s·(cpu);·0.00878027s·(thread);·0s·(gc) |
| 81 | o3·:·MultirationalMap·(automorphism·of·X)</code></pre> | 81 | o3·:·MultirationalMap·(automorphism·of·X)</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^3 | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an·isomorphic·projection·of·X·in·PP^3 |
| 85 | o4·:·ProjectiveVariety,·curve·in·PP^3</code></pre> | 85 | o4·:·ProjectiveVariety,·curve·in·PP^3</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·g·=·linearlyNormalEmbedding·Y; | 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·g·=·linearlyNormalEmbedding·Y; |
| 89 | ·--·used·0.3 | 89 | ·--·used·0.386421s·(cpu);·0.333963s·(thread);·0s·(gc) |
| 90 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)</code></pre> | 90 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isIsomorphism·g)</code></pre> | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isIsomorphism·g)</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| Offset 14, 23 lines modified | Offset 14, 23 lines modified | ||
| 14 | ············is·a·linear·projection | 14 | ············is·a·linear·projection |
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | i1·:·K·=·ZZ/333331; | 16 | i1·:·K·=·ZZ/333331; |
| 17 | i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 | 17 | i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 |
| 18 | o2·:·ProjectiveVariety,·curve·in·PP^7 | 18 | o2·:·ProjectiveVariety,·curve·in·PP^7 |
| 19 | i3·:·time·f·=·linearlyNormalEmbedding·X; | 19 | i3·:·time·f·=·linearlyNormalEmbedding·X; |
| 20 | ·--·used·0.00 | 20 | ·--·used·0.00854149s·(cpu);·0.00878027s·(thread);·0s·(gc) |
| 21 | o3·:·MultirationalMap·(automorphism·of·X) | 21 | o3·:·MultirationalMap·(automorphism·of·X) |
| 22 | i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an | 22 | i4·:·Y·=·(rationalMap·{for·i·to·3·list·random(1,ring·ambient·X)})·X;·--·an |
| 23 | isomorphic·projection·of·X·in·PP^3 | 23 | isomorphic·projection·of·X·in·PP^3 |
| 24 | o4·:·ProjectiveVariety,·curve·in·PP^3 | 24 | o4·:·ProjectiveVariety,·curve·in·PP^3 |
| 25 | i5·:·time·g·=·linearlyNormalEmbedding·Y; | 25 | i5·:·time·g·=·linearlyNormalEmbedding·Y; |
| 26 | ·--·used·0.3 | 26 | ·--·used·0.386421s·(cpu);·0.333963s·(thread);·0s·(gc) |
| 27 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7) | 27 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7) |
| 28 | i6·:·assert(isIsomorphism·g) | 28 | i6·:·assert(isIsomorphism·g) |
| 29 | i7·:·describe·g | 29 | i7·:·describe·g |
| 30 | o7·=·multi-rational·map·consisting·of·one·single·rational·map | 30 | o7·=·multi-rational·map·consisting·of·one·single·rational·map |
| 31 | ·····source·variety:·curve·in·PP^3·cut·out·by·6·hypersurfaces·of·degree·4 | 31 | ·····source·variety:·curve·in·PP^3·cut·out·by·6·hypersurfaces·of·degree·4 |
| Offset 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 79 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> | 79 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·multidegree·Phi | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·multidegree·Phi |
| 83 | ·--·used·0. | 83 | ·--·used·0.733566s·(cpu);·0.389721s·(thread);·0s·(gc) |
| 84 | o3·=·{66,·46,·31,·20} | 84 | o3·=·{66,·46,·31,·20} |
| 85 | o3·:·List</code></pre> | 85 | o3·:·List</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·(degree·source·Phi,degree·image·Phi) | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·(degree·source·Phi,degree·image·Phi) |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3, | 20 | x_1^2-x_0*x_2},·g·=·rationalMap·{x_1^2-x_0*x_2,·x_0*x_3,·x_1*x_3,·x_2*x_3, |
| 21 | x_3^2}; | 21 | x_3^2}; |
| 22 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 22 | i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 23 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to | 23 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to |
| 24 | PP^2·x·PP^4) | 24 | PP^2·x·PP^4) |
| 25 | i3·:·time·multidegree·Phi | 25 | i3·:·time·multidegree·Phi |
| 26 | ·--·used·0. | 26 | ·--·used·0.733566s·(cpu);·0.389721s·(thread);·0s·(gc) |
| 27 | o3·=·{66,·46,·31,·20} | 27 | o3·=·{66,·46,·31,·20} |
| 28 | o3·:·List | 28 | o3·:·List |
| 29 | i4·:·(degree·source·Phi,degree·image·Phi) | 29 | i4·:·(degree·source·Phi,degree·image·Phi) |
| 30 | o4·=·(66,·20) | 30 | o4·=·(66,·20) |
| Offset 76, 27 lines modified | Offset 76, 27 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); |
| 78 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)</code></pre> | 78 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) |
| 82 | ·--·used·0.00 | 82 | ·--·used·0.00127277s·(cpu);·0.00140549s·(thread);·0s·(gc) |
| 83 | ·--·used·0.185899s·(cpu);·0.13238s·(thread);·0s·(gc) | ||
| 83 | ·--·used·0. | 84 | ·--·used·0.204939s·(cpu);·0.141056s·(thread);·0s·(gc) |
| 85 | ·--·used·0.185013s·(cpu);·0.133897s·(thread);·0s·(gc) | ||
| 84 | ·--·used·0.1 | 86 | ·--·used·0.172616s·(cpu);·0.115406s·(thread);·0s·(gc) |
| 85 | ·--·used·0.144896s·(cpu);·0.0945684s·(thread);·0s·(gc) | ||
| 86 | ·--·used·0.124072s·(cpu);·0.0728073s·(thread);·0s·(gc) | ||
| 87 | o2·=·{51,·28,·14,·6,·2} | 87 | o2·=·{51,·28,·14,·6,·2} |
| 88 | o2·:·List</code></pre> | 88 | o2·:·List</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·assert(oo·==·multidegree·Phi) | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·assert(oo·==·multidegree·Phi) |
| 92 | ·--·used·0. | 92 | ·--·used·0.249002s·(cpu);·0.0920012s·(thread);·0s·(gc)</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ········</table> | 94 | ········</table> |
| 95 | ······</div> | 95 | ······</div> |
| 96 | ······<div> | 96 | ······<div> |
| 97 | ········<h2>References</h2> | 97 | ········<h2>References</h2> |
| 98 | ArXiv·preprint:·<a·href="https://arxiv.org/abs/2101.04503">Computations·with·rational·maps·between·multi-projective·varieties</a>.······</div> | 98 | ArXiv·preprint:·<a·href="https://arxiv.org/abs/2101.04503">Computations·with·rational·maps·between·multi-projective·varieties</a>.······</div> |
| 99 | ······<div> | 99 | ······<div> |
| Offset 18, 25 lines modified | Offset 18, 25 lines modified | ||
| 18 | This·is·calculated·by·means·of·the·inverse·image·of·an·appropriate·random | 18 | This·is·calculated·by·means·of·the·inverse·image·of·an·appropriate·random |
| 19 | subvariety·of·the·target. | 19 | subvariety·of·the·target. |
| 20 | i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); | 20 | i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); |
| 21 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x | 21 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x |
| 22 | PP^5·to·PP^5) | 22 | PP^5·to·PP^5) |
| 23 | i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) | 23 | i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) |
| 24 | ·--·used·0.00 | 24 | ·--·used·0.00127277s·(cpu);·0.00140549s·(thread);·0s·(gc) |
| 25 | ·--·used·0.185899s·(cpu);·0.13238s·(thread);·0s·(gc) | ||
| 25 | ·--·used·0. | 26 | ·--·used·0.204939s·(cpu);·0.141056s·(thread);·0s·(gc) |
| 27 | ·--·used·0.185013s·(cpu);·0.133897s·(thread);·0s·(gc) | ||
| 26 | ·--·used·0.1 | 28 | ·--·used·0.172616s·(cpu);·0.115406s·(thread);·0s·(gc) |
| 27 | ·--·used·0.144896s·(cpu);·0.0945684s·(thread);·0s·(gc) | ||
| 28 | ·--·used·0.124072s·(cpu);·0.0728073s·(thread);·0s·(gc) | ||
| 29 | o2·=·{51,·28,·14,·6,·2} | 29 | o2·=·{51,·28,·14,·6,·2} |
| 30 | o2·:·List | 30 | o2·:·List |
| 31 | i3·:·time·assert(oo·==·multidegree·Phi) | 31 | i3·:·time·assert(oo·==·multidegree·Phi) |
| 32 | ·--·used·0. | 32 | ·--·used·0.249002s·(cpu);·0.0920012s·(thread);·0s·(gc) |
| 33 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 33 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 34 | ArXiv·preprint:·_\x8C_\x8o_\x8m_\x8p_\x8u_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p_\x8s_\x8·_\x8b_\x8e_\x8t_\x8w_\x8e_\x8e_\x8n_\x8·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e | 34 | ArXiv·preprint:·_\x8C_\x8o_\x8m_\x8p_\x8u_\x8t_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8·_\x8m_\x8a_\x8p_\x8s_\x8·_\x8b_\x8e_\x8t_\x8w_\x8e_\x8e_\x8n_\x8·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e |
| 35 | _\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s. | 35 | _\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s. |
| 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational | 37 | ····*·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8r_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·multi-rational |
| 38 | ······map | 38 | ······map |
| 39 | ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·rational·map | 39 | ····*·_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8D_\x8e_\x8g_\x8r_\x8e_\x8e_\x8s_\x8(_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8p_\x8)·--·projective·degrees·of·a·rational·map |
| Offset 76, 28 lines modified | Offset 76, 28 lines modified | ||
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^({1,1,2},{3,2,3}); | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^({1,1,2},{3,2,3}); |
| 78 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9</code></pre> | 78 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·:=·point·X | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·:=·point·X |
| 82 | ·--·used·0. | 82 | ·--·used·0.187477s·(cpu);·0.0366352s·(thread);·0s·(gc) |
| 83 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) | 83 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) |
| 84 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> | 84 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·Y·=·random({2,1,2},X); | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·Y·=·random({2,1,2},X); |
| 88 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9</code></pre> | 88 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·q·=·point·Y | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·q·=·point·Y |
| 92 | ·--·used·1. | 92 | ·--·used·1.47449s·(cpu);·0.826538s·(thread);·0s·(gc) |
| 93 | o5·=·q | 93 | o5·=·q |
| 94 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> | 94 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))</code></pre> | 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))</code></pre> |
| Offset 15, 25 lines modified | Offset 15, 25 lines modified | ||
| 15 | ··········o·a·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y,·a·random·rational·point·on·$X$ | 15 | ··········o·a·_\x8m_\x8u_\x8l_\x8t_\x8i_\x8-_\x8p_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y,·a·random·rational·point·on·$X$ |
| 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 17 | i1·:·K·=·ZZ/1000003; | 17 | i1·:·K·=·ZZ/1000003; |
| 18 | i2·:·X·=·PP_K^({1,1,2},{3,2,3}); | 18 | i2·:·X·=·PP_K^({1,1,2},{3,2,3}); |
| 19 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9 | 19 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9 |
| 20 | i3·:·time·p·:=·point·X | 20 | i3·:·time·p·:=·point·X |
| 21 | ·--·used·0. | 21 | ·--·used·0.187477s·(cpu);·0.0366352s·(thread);·0s·(gc) |
| 22 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1], | 22 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1], |
| 23 | [3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) | 23 | [3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) |
| 24 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 | 24 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 |
| 25 | i4·:·Y·=·random({2,1,2},X); | 25 | i4·:·Y·=·random({2,1,2},X); |
| 26 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9 | 26 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9 |
| 27 | i5·:·time·q·=·point·Y | 27 | i5·:·time·q·=·point·Y |
| 28 | ·--·used·1. | 28 | ·--·used·1.47449s·(cpu);·0.826538s·(thread);·0s·(gc) |
| 29 | o5·=·q | 29 | o5·=·q |
| 30 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 | 30 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9 |
| 31 | i6·:·assert(isSubset(p,X)·and·isSubset(q,Y)) | 31 | i6·:·assert(isSubset(p,X)·and·isSubset(q,Y)) |
| 32 | The·list·of·homogeneous·coordinates·can·be·obtained·with·the·operator·|-. | 32 | The·list·of·homogeneous·coordinates·can·be·obtained·with·the·operator·|-. |
| 33 | i7·:·|-·p | 33 | i7·:·|-·p |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi·=·rationalMap·{f,g,h}; | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi·=·rationalMap·{f,g,h}; |
| 93 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)</code></pre> | 93 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·segre·Phi; | 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·segre·Phi; |
| 97 | ·--·used· | 97 | ·--·used·3.7862s·(cpu);·0.785813s·(thread);·0s·(gc) |
| 98 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)</code></pre> | 98 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i7·:·describe·segre·Phi | 101 | <td>··············<pre><code·class="language-macaulay2">i7·:·describe·segre·Phi |
| 102 | o7·=·rational·map·defined·by·forms·of·degree·6 | 102 | o7·=·rational·map·defined·by·forms·of·degree·6 |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) | 30 | o4·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^4) |
| 31 | i5·:·Phi·=·rationalMap·{f,g,h}; | 31 | i5·:·Phi·=·rationalMap·{f,g,h}; |
| 32 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x | 32 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x |
| 33 | PP^4) | 33 | PP^4) |
| 34 | i6·:·time·segre·Phi; | 34 | i6·:·time·segre·Phi; |
| 35 | ·--·used· | 35 | ·--·used·3.7862s·(cpu);·0.785813s·(thread);·0s·(gc) |
| 36 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149) | 36 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149) |
| 37 | i7·:·describe·segre·Phi | 37 | i7·:·describe·segre·Phi |
| 38 | o7·=·rational·map·defined·by·forms·of·degree·6 | 38 | o7·=·rational·map·defined·by·forms·of·degree·6 |
| 39 | ·····source·variety:·PP^4 | 39 | ·····source·variety:·PP^4 |
| 40 | ·····target·variety:·PP^149 | 40 | ·····target·variety:·PP^149 |
| Offset 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | o1·=·Phi | 75 | o1·=·Phi |
| 76 | o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre> | 76 | o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to·threefold·in·PP^3·x·PP^2·x·PP^2)</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·Phi | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·Phi |
| 80 | ·--·used·0. | 80 | ·--·used·0.202657s·(cpu);·0.137455s·(thread);·0s·(gc) |
| 81 | o2·=·multi-rational·map·consisting·of·3·rational·maps | 81 | o2·=·multi-rational·map·consisting·of·3·rational·maps |
| 82 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1) | 82 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1) |
| 83 | ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2· | 83 | ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces·of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2· |
| 84 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 | 84 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 |
| 85 | ·····dominance:·true | 85 | ·····dominance:·true |
| 86 | ·····multidegree:·{10,·14,·19,·25} | 86 | ·····multidegree:·{10,·14,·19,·25} |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3) | 16 | i1·:·Phi·=·inverse·first·graph·last·graph·rationalMap·PP_(ZZ/33331)^(1,3) |
| 17 | o1·=·Phi | 17 | o1·=·Phi |
| 18 | o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to | 18 | o1·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·to |
| 19 | threefold·in·PP^3·x·PP^2·x·PP^2) | 19 | threefold·in·PP^3·x·PP^2·x·PP^2) |
| 20 | i2·:·time·describe·Phi | 20 | i2·:·time·describe·Phi |
| 21 | ·--·used·0. | 21 | ·--·used·0.202657s·(cpu);·0.137455s·(thread);·0s·(gc) |
| 22 | o2·=·multi-rational·map·consisting·of·3·rational·maps | 22 | o2·=·multi-rational·map·consisting·of·3·rational·maps |
| 23 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of | 23 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of |
| 24 | multi-degree·(1,1) | 24 | multi-degree·(1,1) |
| 25 | ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces | 25 | ·····target·variety:·threefold·in·PP^3·x·PP^2·x·PP^2·cut·out·by·7·hypersurfaces |
| 26 | of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2 | 26 | of·multi-degrees·(0,1,1)^3·(1,0,1)^2·(1,1,0)^2 |
| 27 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 | 27 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 |
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| 7 | #:len=9 | 7 | #:len=9 |
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | UVEgJSBOQ0dyb2VibmVyQmFzaXM= | 8 | UVEgJSBOQ0dyb2VibmVyQmFzaXM= |
| 9 | #:len=317 | 9 | #:len=317 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTY3MCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTY3MCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ltYm9sICUsUVEsTkNHcm9lYm5lckJhc2lzKSwi | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ltYm9sICUsUVEsTkNHcm9lYm5lckJhc2lzKSwi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=30 | 7 | #:len=30 |
| 8 | Z2VuZXJhdGVSYW5kb21HcmFwaHMoWlosWlosWlop | 8 | Z2VuZXJhdGVSYW5kb21HcmFwaHMoWlosWlosWlop |
| 9 | #:len=275 | 9 | #:len=275 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTExMiwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTExMiwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2VuZXJhdGVSYW5kb21HcmFwaHMsWlosWlosWlop | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2VuZXJhdGVSYW5kb21HcmFwaHMsWlosWlosWlop |
| Offset 26, 22 lines modified | Offset 26, 22 lines modified | ||
| 26 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true}; | 26 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true}; |
| 27 | i8·:·prob·=·n·->·log(n)/n; | 27 | i8·:·prob·=·n·->·log(n)/n; |
| 28 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) | 28 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) |
| 29 | o9·=·( | 29 | o9·=·(70,·79,·89,·93,·93,·95,·97,·98,·95,·99,·97,·94,·98,·96,·96,·98,·99,·97, |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ·····9 | 31 | ·····98,·97,·100,·97,·96,·99,·97,·99,·99,·99,·98) |
| 32 | o9·:·Sequence | 32 | o9·:·Sequence |
| 33 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) | 33 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) |
| 34 | o10·=·( | 34 | o10·=·(14,·8,·8,·6,·4,·4,·5,·1,·1,·3,·2,·2,·1,·0,·0,·1,·1,·1,·2,·0,·0,·0,·3, |
| 35 | ······----------------------------------------------------------------------- | 35 | ······----------------------------------------------------------------------- |
| 36 | ······ | 36 | ······2,·0,·1,·0,·0,·0) |
| 37 | o10·:·Sequence | 37 | o10·:·Sequence |
| 38 | i11·:· | 38 | i11·:· |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 4 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 5 | o1·:·List | 5 | o1·:·List |
| 6 | i2·:·generateRandomGraphs(5,·5) | 6 | i2·:·generateRandomGraphs(5,·5) |
| 7 | o2·=·{D | 7 | o2·=·{DBs,·Df_,·DC?,·DOc,·DZ[} |
| 8 | o2·:·List | 8 | o2·:·List |
| 9 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 9 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 10 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 10 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| Offset 1, 21 lines modified | Offset 1, 21 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1729831171060067675 | 1 | --·-*-·M2-comint·-*-·hash:·1729831171060067675 |
| 2 | i1·:·R·=·QQ[a..e]; | 2 | i1·:·R·=·QQ[a..e]; |
| 3 | i2·:·generateRandomRegularGraphs(R,·3,·2) | 3 | i2·:·generateRandomRegularGraphs(R,·3,·2) |
| 4 | o2·=·{Graph{"edges"·=>·{{ | 4 | o2·=·{Graph{"edges"·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}}, |
| 5 | ············"ring"·=>·R·········································· | 5 | ············"ring"·=>·R·········································· |
| 6 | ············"vertices"·=>·{a,·b,·c,·d,·e}························ | 6 | ············"vertices"·=>·{a,·b,·c,·d,·e}························ |
| 7 | ·····------------------------------------------------------------------------ | 7 | ·····------------------------------------------------------------------------ |
| 8 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}, | 8 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}, |
| 9 | ···········"ring"·=>·R·········································· | 9 | ···········"ring"·=>·R·········································· |
| 10 | ···········"vertices"·=>·{a,·b,·c,·d,·e}························ | 10 | ···········"vertices"·=>·{a,·b,·c,·d,·e}························ |
| 11 | ·····------------------------------------------------------------------------ | 11 | ·····------------------------------------------------------------------------ |
| 12 | ·····Graph{"edges"·=>·{{ | 12 | ·····Graph{"edges"·=>·{{a,·c},·{a,·d},·{b,·d},·{b,·e},·{c,·e}}}} |
| 13 | ···········"ring"·=>·R | 13 | ···········"ring"·=>·R |
| 14 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 14 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 15 | o2·:·List | 15 | o2·:·List |
| 16 | i3·:· | 16 | i3·:· |
| Offset 13, 13 lines modified | Offset 13, 13 lines modified | ||
| 13 | i3·:·graphComplement·"Dhc" | 13 | i3·:·graphComplement·"Dhc" |
| 14 | o3·=·DUW | 14 | o3·=·DUW |
| 15 | i4·:·G·=·generateBipartiteGraphs·7; | 15 | i4·:·G·=·generateBipartiteGraphs·7; |
| 16 | i5·:·time·graphComplement·G; | 16 | i5·:·time·graphComplement·G; |
| 17 | ·--·used·0.000 | 17 | ·--·used·0.000793097s·(cpu);·0.000662963s·(thread);·0s·(gc) |
| 18 | i6·:·time·(graphComplement·\·G); | 18 | i6·:·time·(graphComplement·\·G); |
| 19 | ·--·used·0.1 | 19 | ·--·used·0.146469s·(cpu);·0.0889744s·(thread);·0s·(gc) |
| 20 | i7·:· | 20 | i7·:· |
| Offset 93, 26 lines modified | Offset 93, 26 lines modified | ||
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) | 98 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) |
| 99 | o9·=·( | 99 | o9·=·(70,·79,·89,·93,·93,·95,·97,·98,·95,·99,·97,·94,·98,·96,·96,·98,·99,·97, |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ·····9 | 101 | ·····98,·97,·100,·97,·96,·99,·97,·99,·99,·99,·98) |
| 102 | o9·:·Sequence</code></pre> | 102 | o9·:·Sequence</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) | 105 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) |
| 106 | o10·=·( | 106 | o10·=·(14,·8,·8,·6,·4,·4,·5,·1,·1,·3,·2,·2,·1,·0,·0,·1,·1,·1,·2,·0,·0,·0,·3, |
| 107 | ······----------------------------------------------------------------------- | 107 | ······----------------------------------------------------------------------- |
| 108 | ······ | 108 | ······2,·0,·1,·0,·0,·0) |
| 109 | o10·:·Sequence</code></pre> | 109 | o10·:·Sequence</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| 112 | ······</div> | 112 | ······</div> |
| 113 | ······<div> | 113 | ······<div> |
| 114 | ········<h2>See·also</h2> | 114 | ········<h2>See·also</h2> |
| Offset 38, 25 lines modified | Offset 38, 25 lines modified | ||
| 38 | connected,·at·least·as·$n$·tends·to·infinity. | 38 | connected,·at·least·as·$n$·tends·to·infinity. |
| 39 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=> | 39 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=> |
| 40 | true}; | 40 | true}; |
| 41 | i8·:·prob·=·n·->·log(n)/n; | 41 | i8·:·prob·=·n·->·log(n)/n; |
| 42 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)), | 42 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)), |
| 43 | connected)) | 43 | connected)) |
| 44 | o9·=·( | 44 | o9·=·(70,·79,·89,·93,·93,·95,·97,·98,·95,·99,·97,·94,·98,·96,·96,·98,·99,·97, |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ·····9 | 46 | ·····98,·97,·100,·97,·96,·99,·97,·99,·99,·99,·98) |
| 47 | o9·:·Sequence | 47 | o9·:·Sequence |
| 48 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2), | 48 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2), |
| 49 | connected)) | 49 | connected)) |
| 50 | o10·=·( | 50 | o10·=·(14,·8,·8,·6,·4,·4,·5,·1,·1,·3,·2,·2,·1,·0,·0,·1,·1,·1,·2,·0,·0,·0,·3, |
| 51 | ······----------------------------------------------------------------------- | 51 | ······----------------------------------------------------------------------- |
| 52 | ······ | 52 | ······2,·0,·1,·0,·0,·0) |
| 53 | o10·:·Sequence | 53 | o10·:·Sequence |
| 54 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 54 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 55 | ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with | 55 | ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with |
| 56 | ······filterGraphs·and·countGraphs | 56 | ······filterGraphs·and·countGraphs |
| 57 | ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given | 57 | ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given |
| 58 | ······properties | 58 | ······properties |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 104 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 105 | o1·:·List</code></pre> | 105 | o1·:·List</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) | 108 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) |
| 109 | o2·=·{D | 109 | o2·=·{DBs,·Df_,·DC?,·DOc,·DZ[} |
| 110 | o2·:·List</code></pre> | 110 | o2·:·List</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 113 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 114 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 114 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| Offset 38, 15 lines modified | Offset 38, 15 lines modified | ||
| 38 | i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 38 | i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 39 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 39 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 40 | o1·:·List | 40 | o1·:·List |
| 41 | i2·:·generateRandomGraphs(5,·5) | 41 | i2·:·generateRandomGraphs(5,·5) |
| 42 | o2·=·{D | 42 | o2·=·{DBs,·Df_,·DC?,·DOc,·DZ[} |
| 43 | o2·:·List | 43 | o2·:·List |
| 44 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 44 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 45 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 45 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 46 | o3·:·List | 46 | o3·:·List |
| Offset 89, 23 lines modified | Offset 89, 23 lines modified | ||
| 89 | ········<table·class="examples"> | 89 | ········<table·class="examples"> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[a..e];</code></pre> | 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[a..e];</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomRegularGraphs(R,·3,·2) | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomRegularGraphs(R,·3,·2) |
| 95 | o2·=·{Graph{"edges"·=>·{{ | 95 | o2·=·{Graph{"edges"·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}}, |
| 96 | ············"ring"·=>·R·········································· | 96 | ············"ring"·=>·R·········································· |
| 97 | ············"vertices"·=>·{a,·b,·c,·d,·e}························ | 97 | ············"vertices"·=>·{a,·b,·c,·d,·e}························ |
| 98 | ·····------------------------------------------------------------------------ | 98 | ·····------------------------------------------------------------------------ |
| 99 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}, | 99 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}, |
| 100 | ···········"ring"·=>·R·········································· | 100 | ···········"ring"·=>·R·········································· |
| 101 | ···········"vertices"·=>·{a,·b,·c,·d,·e}························ | 101 | ···········"vertices"·=>·{a,·b,·c,·d,·e}························ |
| 102 | ·····------------------------------------------------------------------------ | 102 | ·····------------------------------------------------------------------------ |
| 103 | ·····Graph{"edges"·=>·{{ | 103 | ·····Graph{"edges"·=>·{{a,·c},·{a,·d},·{b,·d},·{b,·e},·{c,·e}}}} |
| 104 | ···········"ring"·=>·R | 104 | ···········"ring"·=>·R |
| 105 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 105 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 106 | o2·:·List</code></pre> | 106 | o2·:·List</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ······</div> | 109 | ······</div> |
| Offset 25, 23 lines modified | Offset 25, 23 lines modified | ||
| 25 | vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic. | 25 | vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic. |
| 26 | If·a·_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8R_\x8i_\x8n_\x8g·$R$·is·supplied·instead,·then·the·number·of·vertices·is·the | 26 | If·a·_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8R_\x8i_\x8n_\x8g·$R$·is·supplied·instead,·then·the·number·of·vertices·is·the |
| 27 | number·of·generators.·Moreover,·the·nauty-based·strings·are·automatically | 27 | number·of·generators.·Moreover,·the·nauty-based·strings·are·automatically |
| 28 | converted·to·instances·of·the·class·_\x8G_\x8r_\x8a_\x8p_\x8h·in·$R$. | 28 | converted·to·instances·of·the·class·_\x8G_\x8r_\x8a_\x8p_\x8h·in·$R$. |
| 29 | i1·:·R·=·QQ[a..e]; | 29 | i1·:·R·=·QQ[a..e]; |
| 30 | i2·:·generateRandomRegularGraphs(R,·3,·2) | 30 | i2·:·generateRandomRegularGraphs(R,·3,·2) |
| 31 | o2·=·{Graph{"edges"·=>·{{ | 31 | o2·=·{Graph{"edges"·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}}, |
| 32 | ············"ring"·=>·R | 32 | ············"ring"·=>·R |
| 33 | ············"vertices"·=>·{a,·b,·c,·d,·e} | 33 | ············"vertices"·=>·{a,·b,·c,·d,·e} |
| 34 | ·····------------------------------------------------------------------------ | 34 | ·····------------------------------------------------------------------------ |
| 35 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}, | 35 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{a,·d},·{c,·e},·{d,·e}}}, |
| 36 | ···········"ring"·=>·R | 36 | ···········"ring"·=>·R |
| 37 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 37 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····Graph{"edges"·=>·{{ | 39 | ·····Graph{"edges"·=>·{{a,·c},·{a,·d},·{b,·d},·{b,·e},·{c,·e}}}} |
| 40 | ···········"ring"·=>·R | 40 | ···········"ring"·=>·R |
| 41 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 41 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 42 | o2·:·List | 42 | o2·:·List |
| 43 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 43 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 44 | The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with | 44 | The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with |
| 45 | zero·vertices. | 45 | zero·vertices. |
| Offset 113, 19 lines modified | Offset 113, 19 lines modified | ||
| 113 | ········</div> | 113 | ········</div> |
| 114 | ········<table·class="examples"> | 114 | ········<table·class="examples"> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·generateBipartiteGraphs·7;</code></pre> | 116 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·generateBipartiteGraphs·7;</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·graphComplement·G; | 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·graphComplement·G; |
| 120 | ·--·used·0.000 | 120 | ·--·used·0.000793097s·(cpu);·0.000662963s·(thread);·0s·(gc)</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(graphComplement·\·G); | 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(graphComplement·\·G); |
| 124 | ·--·used·0.1 | 124 | ·--·used·0.146469s·(cpu);·0.0889744s·(thread);·0s·(gc)</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ········</table> | 126 | ········</table> |
| 127 | ······</div> | 127 | ······</div> |
| 128 | ······<div> | 128 | ······<div> |
| 129 | ········<h2>See·also</h2> | 129 | ········<h2>See·also</h2> |
| 130 | ········<ul> | 130 | ········<ul> |
| 131 | ··········<li> | 131 | ··········<li> |
| Offset 42, 17 lines modified | Offset 42, 17 lines modified | ||
| 42 | o3·=·DUW | 42 | o3·=·DUW |
| 43 | Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input | 43 | Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input |
| 44 | format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in | 44 | format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in |
| 45 | Graph6·or·Sparse6·format. | 45 | Graph6·or·Sparse6·format. |
| 46 | i4·:·G·=·generateBipartiteGraphs·7; | 46 | i4·:·G·=·generateBipartiteGraphs·7; |
| 47 | i5·:·time·graphComplement·G; | 47 | i5·:·time·graphComplement·G; |
| 48 | ·--·used·0.000 | 48 | ·--·used·0.000793097s·(cpu);·0.000662963s·(thread);·0s·(gc) |
| 49 | i6·:·time·(graphComplement·\·G); | 49 | i6·:·time·(graphComplement·\·G); |
| 50 | ·--·used·0.1 | 50 | ·--·used·0.146469s·(cpu);·0.0889744s·(thread);·0s·(gc) |
| 51 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 51 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 52 | ····*·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8G_\x8r_\x8a_\x8p_\x8h·--·returns·the·complement·of·a·graph·or·hypergraph | 52 | ····*·_\x8c_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8G_\x8r_\x8a_\x8p_\x8h·--·returns·the·complement·of·a·graph·or·hypergraph |
| 53 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 53 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 54 | ····*·graphComplement(Graph) | 54 | ····*·graphComplement(Graph) |
| 55 | ····*·graphComplement(List) | 55 | ····*·graphComplement(List) |
| 56 | ····*·graphComplement(String) | 56 | ····*·graphComplement(String) |
| 57 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 57 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | YWRkRWRnZXMoLi4uLE5vTmV3NUN5Y2xlcz0+Li4uKQ== | 8 | YWRkRWRnZXMoLi4uLE5vTmV3NUN5Y2xlcz0+Li4uKQ== |
| 9 | #:len=261 | 9 | #:len=261 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTkxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTkxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1thZGRFZGdlcyxOb05ldzVDeWNsZXNdLCJhZGRFZGdl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1thZGRFZGdlcyxOb05ldzVDeWNsZXNdLCJhZGRFZGdl |
| Offset 26, 22 lines modified | Offset 26, 22 lines modified | ||
| 26 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true}; | 26 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=>·true}; |
| 27 | i8·:·prob·=·n·->·log(n)/n; | 27 | i8·:·prob·=·n·->·log(n)/n; |
| 28 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) | 28 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) |
| 29 | o9·=·( | 29 | o9·=·(66,·83,·91,·94,·96,·91,·98,·94,·93,·98,·96,·97,·96,·98,·95,·96,·97,·97, |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ·····9 | 31 | ·····98,·96,·100,·98,·99,·99,·98,·98,·99,·97,·99) |
| 32 | o9·:·Sequence | 32 | o9·:·Sequence |
| 33 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) | 33 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) |
| 34 | o10·=·(1 | 34 | o10·=·(15,·7,·5,·6,·2,·2,·4,·4,·2,·2,·0,·1,·0,·1,·0,·2,·1,·0,·1,·0,·1,·0,·0, |
| 35 | ······----------------------------------------------------------------------- | 35 | ······----------------------------------------------------------------------- |
| 36 | ······0,·0,· | 36 | ······0,·0,·0,·0,·0,·0) |
| 37 | o10·:·Sequence | 37 | o10·:·Sequence |
| 38 | i11·:· | 38 | i11·:· |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 4 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 5 | o1·:·List | 5 | o1·:·List |
| 6 | i2·:·generateRandomGraphs(5,·5) | 6 | i2·:·generateRandomGraphs(5,·5) |
| 7 | o2·=·{D | 7 | o2·=·{Dyo,·DmC,·Du?,·Dvs,·DDW} |
| 8 | o2·:·List | 8 | o2·:·List |
| 9 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 9 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 10 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 10 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| Offset 1, 9 lines modified | Offset 1, 9 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1331287392268 | 1 | --·-*-·M2-comint·-*-·hash:·1331287392268 |
| 2 | i1·:·generateRandomRegularGraphs(5,·3,·2) | 2 | i1·:·generateRandomRegularGraphs(5,·3,·2) |
| 3 | o1·=·{D | 3 | o1·=·{D[S,·DYc,·DLo} |
| 4 | o1·:·List | 4 | o1·:·List |
| 5 | i2·:· | 5 | i2·:· |
| Offset 13, 13 lines modified | Offset 13, 13 lines modified | ||
| 13 | ···········4·=>·{2,·1} | 13 | ···········4·=>·{2,·1} |
| 14 | o2·:·Graph | 14 | o2·:·Graph |
| 15 | i3·:·G·=·generateBipartiteGraphs·7; | 15 | i3·:·G·=·generateBipartiteGraphs·7; |
| 16 | i4·:·time·graphComplement·G; | 16 | i4·:·time·graphComplement·G; |
| 17 | ·--·used·0.000 | 17 | ·--·used·0.000859532s·(cpu);·0.00060767s·(thread);·0s·(gc) |
| 18 | i5·:·time·(graphComplement·\·G); | 18 | i5·:·time·(graphComplement·\·G); |
| 19 | ·--·used·0.1 | 19 | ·--·used·0.162242s·(cpu);·0.0936039s·(thread);·0s·(gc) |
| 20 | i6·:· | 20 | i6·:· |
| Offset 93, 26 lines modified | Offset 93, 26 lines modified | ||
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) | 98 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) |
| 99 | o9·=·( | 99 | o9·=·(66,·83,·91,·94,·96,·91,·98,·94,·93,·98,·96,·97,·96,·98,·95,·96,·97,·97, |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ·····9 | 101 | ·····98,·96,·100,·98,·99,·99,·98,·98,·99,·97,·99) |
| 102 | o9·:·Sequence</code></pre> | 102 | o9·:·Sequence</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) | 105 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) |
| 106 | o10·=·(1 | 106 | o10·=·(15,·7,·5,·6,·2,·2,·4,·4,·2,·2,·0,·1,·0,·1,·0,·2,·1,·0,·1,·0,·1,·0,·0, |
| 107 | ······----------------------------------------------------------------------- | 107 | ······----------------------------------------------------------------------- |
| 108 | ······0,·0,· | 108 | ······0,·0,·0,·0,·0,·0) |
| 109 | o10·:·Sequence</code></pre> | 109 | o10·:·Sequence</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| 112 | ······</div> | 112 | ······</div> |
| 113 | ······<div> | 113 | ······<div> |
| 114 | ········<h2>See·also</h2> | 114 | ········<h2>See·also</h2> |
| Offset 38, 25 lines modified | Offset 38, 25 lines modified | ||
| 38 | connected,·at·least·as·$n$·tends·to·infinity. | 38 | connected,·at·least·as·$n$·tends·to·infinity. |
| 39 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=> | 39 | i7·:·connected·=·buildGraphFilter·{"Connectivity"·=>·0,·"NegateConnectivity"·=> |
| 40 | true}; | 40 | true}; |
| 41 | i8·:·prob·=·n·->·log(n)/n; | 41 | i8·:·prob·=·n·->·log(n)/n; |
| 42 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)), | 42 | i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)), |
| 43 | connected)) | 43 | connected)) |
| 44 | o9·=·( | 44 | o9·=·(66,·83,·91,·94,·96,·91,·98,·94,·93,·98,·96,·97,·96,·98,·95,·96,·97,·97, |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ·····9 | 46 | ·····98,·96,·100,·98,·99,·99,·98,·98,·99,·97,·99) |
| 47 | o9·:·Sequence | 47 | o9·:·Sequence |
| 48 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2), | 48 | i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2), |
| 49 | connected)) | 49 | connected)) |
| 50 | o10·=·(1 | 50 | o10·=·(15,·7,·5,·6,·2,·2,·4,·4,·2,·2,·0,·1,·0,·1,·0,·2,·1,·0,·1,·0,·1,·0,·0, |
| 51 | ······----------------------------------------------------------------------- | 51 | ······----------------------------------------------------------------------- |
| 52 | ······0,·0,· | 52 | ······0,·0,·0,·0,·0,·0) |
| 53 | o10·:·Sequence | 53 | o10·:·Sequence |
| 54 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 54 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 55 | ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with | 55 | ····*·_\x8b_\x8u_\x8i_\x8l_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8F_\x8i_\x8l_\x8t_\x8e_\x8r·--·creates·the·appropriate·filter·string·for·use·with |
| 56 | ······filterGraphs·and·countGraphs | 56 | ······filterGraphs·and·countGraphs |
| 57 | ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given | 57 | ····*·_\x8f_\x8i_\x8l_\x8t_\x8e_\x8r_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·filters·(i.e.,·selects)·graphs·in·a·list·for·given |
| 58 | ······properties | 58 | ······properties |
| Offset 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 96 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 97 | o1·:·List</code></pre> | 97 | o1·:·List</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) | 100 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) |
| 101 | o2·=·{D | 101 | o2·=·{Dyo,·DmC,·Du?,·Dvs,·DDW} |
| 102 | o2·:·List</code></pre> | 102 | o2·:·List</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 106 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 106 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| Offset 31, 15 lines modified | Offset 31, 15 lines modified | ||
| 31 | i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 31 | i1·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 32 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 32 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 33 | o1·:·List | 33 | o1·:·List |
| 34 | i2·:·generateRandomGraphs(5,·5) | 34 | i2·:·generateRandomGraphs(5,·5) |
| 35 | o2·=·{D | 35 | o2·=·{Dyo,·DmC,·Du?,·Dvs,·DDW} |
| 36 | o2·:·List | 36 | o2·:·List |
| 37 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 37 | i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 38 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 38 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 39 | o3·:·List | 39 | o3·:·List |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | ········<div> | 80 | ········<div> |
| 81 | ··········<p>This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of·vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.</p> | 81 | ··········<p>This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of·vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic.</p> |
| 82 | ········</div> | 82 | ········</div> |
| 83 | ········<table·class="examples"> | 83 | ········<table·class="examples"> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·generateRandomRegularGraphs(5,·3,·2) | 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·generateRandomRegularGraphs(5,·3,·2) |
| 86 | o1·=·{D | 86 | o1·=·{D[S,·DYc,·DLo} |
| 87 | o1·:·List</code></pre> | 87 | o1·:·List</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| 90 | ······</div> | 90 | ······</div> |
| 91 | ······<div> | 91 | ······<div> |
| 92 | ········<h2>Caveat</h2> | 92 | ········<h2>Caveat</h2> |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | ····*·Outputs: | 19 | ····*·Outputs: |
| 20 | ··········o·G,·a·_\x8l_\x8i_\x8s_\x8t,·the·randomly·generated·regular·graphs | 20 | ··········o·G,·a·_\x8l_\x8i_\x8s_\x8t,·the·randomly·generated·regular·graphs |
| 21 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 21 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 22 | This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of | 22 | This·method·generates·a·specified·number·of·random·graphs·on·a·given·number·of |
| 23 | vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic. | 23 | vertices·with·a·given·regularity.·Note·that·some·graphs·may·be·isomorphic. |
| 24 | i1·:·generateRandomRegularGraphs(5,·3,·2) | 24 | i1·:·generateRandomRegularGraphs(5,·3,·2) |
| 25 | o1·=·{D | 25 | o1·=·{D[S,·DYc,·DLo} |
| 26 | o1·:·List | 26 | o1·:·List |
| 27 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 28 | The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with | 28 | The·number·of·vertices·$n$·must·be·positive·as·nauty·cannot·handle·graphs·with |
| 29 | zero·vertices. | 29 | zero·vertices. |
| 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 31 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8e_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·generates·random·graphs·on·a·given·number·of | 31 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8a_\x8t_\x8e_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8G_\x8r_\x8a_\x8p_\x8h_\x8s·--·generates·random·graphs·on·a·given·number·of |
| Offset 109, 19 lines modified | Offset 109, 19 lines modified | ||
| 109 | ········</div> | 109 | ········</div> |
| 110 | ········<table·class="examples"> | 110 | ········<table·class="examples"> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i3·:·G·=·generateBipartiteGraphs·7;</code></pre> | 112 | <td>··············<pre><code·class="language-macaulay2">i3·:·G·=·generateBipartiteGraphs·7;</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·graphComplement·G; | 115 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·graphComplement·G; |
| 116 | ·--·used·0.000 | 116 | ·--·used·0.000859532s·(cpu);·0.00060767s·(thread);·0s·(gc)</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(graphComplement·\·G); | 119 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(graphComplement·\·G); |
| 120 | ·--·used·0.1 | 120 | ·--·used·0.162242s·(cpu);·0.0936039s·(thread);·0s·(gc)</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ········</table> | 122 | ········</table> |
| 123 | ······</div> | 123 | ······</div> |
| 124 | ······<div·class="waystouse"> | 124 | ······<div·class="waystouse"> |
| 125 | ········<h2>Ways·to·use·<span·class="tt">graphComplement</span>:</h2> | 125 | ········<h2>Ways·to·use·<span·class="tt">graphComplement</span>:</h2> |
| 126 | ········<ul> | 126 | ········<ul> |
| 127 | ··········<li> | 127 | ··········<li> |
| Offset 39, 16 lines modified | Offset 39, 16 lines modified | ||
| 39 | o2·:·Graph | 39 | o2·:·Graph |
| 40 | Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input | 40 | Batch·calls·can·be·performed·considerably·faster·when·using·the·List·input |
| 41 | format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in | 41 | format.·However,·care·should·be·taken·as·the·returned·list·is·entirely·in |
| 42 | Graph6·or·Sparse6·format. | 42 | Graph6·or·Sparse6·format. |
| 43 | i3·:·G·=·generateBipartiteGraphs·7; | 43 | i3·:·G·=·generateBipartiteGraphs·7; |
| 44 | i4·:·time·graphComplement·G; | 44 | i4·:·time·graphComplement·G; |
| 45 | ·--·used·0.000 | 45 | ·--·used·0.000859532s·(cpu);·0.00060767s·(thread);·0s·(gc) |
| 46 | i5·:·time·(graphComplement·\·G); | 46 | i5·:·time·(graphComplement·\·G); |
| 47 | ·--·used·0.1 | 47 | ·--·used·0.162242s·(cpu);·0.0936039s·(thread);·0s·(gc) |
| 48 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* | 48 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·g\x8gr\x8ra\x8ap\x8ph\x8hC\x8Co\x8om\x8mp\x8pl\x8le\x8em\x8me\x8en\x8nt\x8t:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 49 | ····*·graphComplement(Graph) | 49 | ····*·graphComplement(Graph) |
| 50 | ····*·graphComplement(List) | 50 | ····*·graphComplement(List) |
| 51 | ····*·graphComplement(String) | 51 | ····*·graphComplement(String) |
| 52 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 52 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 53 | The·object·_\x8g_\x8r_\x8a_\x8p_\x8h_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 53 | The·object·_\x8g_\x8r_\x8a_\x8p_\x8h_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=38 | 7 | #:len=38 |
| 8 | bm9ldGhlck5vcm1hbGl6YXRpb24oLi4uLFZlcmJvc2U9Pi4uLik= | 8 | bm9ldGhlck5vcm1hbGl6YXRpb24oLi4uLFZlcmJvc2U9Pi4uLik= |
| 9 | #:len=326 | 9 | #:len=326 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzEzLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzEzLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tub2V0aGVyTm9ybWFsaXphdGlvbixWZXJib3NlXSwi | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tub2V0aGVyTm9ybWFsaXphdGlvbixWZXJib3NlXSwi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=32 | 7 | #:len=32 |
| 8 | bm9ldGhlcmlhbk9wZXJhdG9ycyhJZGVhbCxJZGVhbCk= | 8 | bm9ldGhlcmlhbk9wZXJhdG9ycyhJZGVhbCxJZGVhbCk= |
| 9 | #:len=2583 | 9 | #:len=2583 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTm9ldGhlcmlhbiBvcGVyYXRvcnMgb2Yg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiTm9ldGhlcmlhbiBvcGVyYXRvcnMgb2Yg |
| 11 | YSBwcmltYXJ5IGNvbXBvbmVudCIsICJsaW5lbnVtIiA9PiAyNzQ5LCBJbnB1dHMgPT4ge1NQQU57 | 11 | YSBwcmltYXJ5IGNvbXBvbmVudCIsICJsaW5lbnVtIiA9PiAyNzQ5LCBJbnB1dHMgPT4ge1NQQU57 |
| Offset 47, 15 lines modified | Offset 47, 15 lines modified | ||
| 47 | o4·:·Ideal·of·R | 47 | o4·:·Ideal·of·R |
| 48 | i5·:·isPrimary·Q | 48 | i5·:·isPrimary·Q |
| 49 | o5·=·true | 49 | o5·=·true |
| 50 | i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") | 50 | i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") |
| 51 | ·--·. | 51 | ·--·.118048s·elapsed |
| 52 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| | 52 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| |
| 53 | ·····------------------------------------------------------------------------ | 53 | ·····------------------------------------------------------------------------ |
| 54 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} | 54 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} |
| 55 | o6·:·List | 55 | o6·:·List |
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| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·isPrimary·Q | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·isPrimary·Q |
| 104 | o5·=·true</code></pre> | 104 | o5·=·true</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") | 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") |
| 108 | ·--·. | 108 | ·--·.118048s·elapsed |
| 109 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| | 109 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} | 111 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} |
| 112 | o6·:·List</code></pre> | 112 | o6·:·List</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
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| 51 | ·······1·2·3····2·3 | 51 | ·······1·2·3····2·3 |
| 52 | o4·:·Ideal·of·R | 52 | o4·:·Ideal·of·R |
| 53 | i5·:·isPrimary·Q | 53 | i5·:·isPrimary·Q |
| 54 | o5·=·true | 54 | o5·=·true |
| 55 | i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") | 55 | i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") |
| 56 | ·--·. | 56 | ·--·.118048s·elapsed |
| 57 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| | 57 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| |
| 58 | ·····------------------------------------------------------------------------ | 58 | ·····------------------------------------------------------------------------ |
| 59 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} | 59 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} |
| 60 | o6·:·List | 60 | o6·:·List |
| 61 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 61 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=19 | 7 | #:len=19 |
| 8 | Tm9ubWluaW1hbENvbXBsZXhlcw== | 8 | Tm9ubWluaW1hbENvbXBsZXhlcw== |
| 9 | #:len=668 | 9 | #:len=668 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAic3VwcG9ydCBmb3IgY29tcHV0aW5nIGhv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAic3VwcG9ydCBmb3IgY29tcHV0aW5nIGhv |
| 11 | bW9sb2d5LCByYW5rcyBhbmQgU1ZEIGNvbXBsZXhlcywgZnJvbSBhIGNoYWluIGNvbXBsZXggb3Zl | 11 | bW9sb2d5LCByYW5rcyBhbmQgU1ZEIGNvbXBsZXhlcywgZnJvbSBhIGNoYWluIGNvbXBsZXggb3Zl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | VG9yaWNEaXZpc29yID09IFpa | 8 | VG9yaWNEaXZpc29yID09IFpa |
| 9 | #:len=349 | 9 | #:len=349 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTQ0MSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTQ0MSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ltYm9sID09LFRvcmljRGl2aXNvcixaWiksIlRv | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ltYm9sID09LFRvcmljRGl2aXNvcixaWiksIlRv |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1) | 78 | i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1) |
| 79 | o13·=·{1,·2,·3,·3,·2,·1} | 79 | o13·=·{1,·2,·3,·3,·2,·1} |
| 80 | o13·:·List | 80 | o13·:·List |
| 81 | i14·:·Y·=·time·smoothFanoToricVariety(5,100); | 81 | i14·:·Y·=·time·smoothFanoToricVariety(5,100); |
| 82 | ·--·used·0.1 | 82 | ·--·used·0.194045s·(cpu);·0.191751s·(thread);·0s·(gc) |
| 83 | i15·:·A2·=·intersectionRing·Y; | 83 | i15·:·A2·=·intersectionRing·Y; |
| 84 | i16·:·assert·(#·rays·Y·===·numgens·A2) | 84 | i16·:·assert·(#·rays·Y·===·numgens·A2) |
| 85 | i17·:·ideal·A2 | 85 | i17·:·ideal·A2 |
| Offset 110, 19 lines modified | Offset 110, 19 lines modified | ||
| 110 | ········2·················2···2·······················2···2·····························2·············2······················2·····3······2 | 110 | ········2·················2···2·······················2···2·····························2·············2······················2·····3······2 |
| 111 | ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t·t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··) | 111 | ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t·t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··) |
| 112 | ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10····9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10 | 112 | ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10····9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10 |
| 113 | o18·:·QuotientRing | 113 | o18·:·QuotientRing |
| 114 | i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) | 114 | i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) |
| 115 | ·--·used·0.00 | 115 | ·--·used·0.00239499s·(cpu);·0.00103858s·(thread);·0s·(gc) |
| 116 | ·--·used·7.6754e-05s·(cpu);·9.8786e-05s·(thread);·0s·(gc) | ||
| 117 | ·--·used·1.3765e-05s·(cpu);·7.7456e-05s·(thread);·0s·(gc) | ||
| 116 | ·--·used·1. | 118 | ·--·used·1.2513e-05s·(cpu);·9.2404e-05s·(thread);·0s·(gc) |
| 117 | ·--·used·5.929e-06s·(cpu);·4.8773e-05s·(thread);·0s·(gc) | ||
| 118 | ·--·used·5.428e-06s·(cpu);·4.5018e-05s·(thread);·0s·(gc) | ||
| 119 | ·--·used·5.518e-06s·(cpu);·4.662e-05s·(thread);·0s·(gc) | ||
| 120 | ·--·used· | 119 | ·--·used·1.5278e-05s·(cpu);·7.3398e-05s·(thread);·0s·(gc) |
| 120 | ·--·used·9.878e-06s·(cpu);·6.8449e-05s·(thread);·0s·(gc) | ||
| 121 | o19·=·{1,·6,·13,·13,·6,·1} | 121 | o19·=·{1,·6,·13,·13,·6,·1} |
| 122 | o19·:·List | 122 | o19·:·List |
| 123 | i20·:· | 123 | i20·:· |
| Offset 2, 27 lines modified | Offset 2, 27 lines modified | ||
| 2 | i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1)) | 2 | i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1)) |
| 3 | i2·:·setRandomSeed·(currentTime·()); | 3 | i2·:·setRandomSeed·(currentTime·()); |
| 4 | i3·:·a·=·sort·apply·(3,·i·->·random·(7)) | 4 | i3·:·a·=·sort·apply·(3,·i·->·random·(7)) |
| 5 | o3·=·{ | 5 | o3·=·{2,·3,·4} |
| 6 | o3·:·List | 6 | o3·:·List |
| 7 | i4·:·assert·isWellDefined·kleinschmidt·(4,a) | 7 | i4·:·assert·isWellDefined·kleinschmidt·(4,a) |
| 8 | i5·:·q·=·sort·apply·(5,·j·->·random·(1,9)); | 8 | i5·:·q·=·sort·apply·(5,·j·->·random·(1,9)); |
| 9 | i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9)); | 9 | i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9)); |
| 10 | i7·:·q | 10 | i7·:·q |
| 11 | o7·=·{ | 11 | o7·=·{1,·3,·4,·7,·8} |
| 12 | o7·:·List | 12 | o7·:·List |
| 13 | i8·:·assert·isWellDefined·weightedProjectiveSpace·q | 13 | i8·:·assert·isWellDefined·weightedProjectiveSpace·q |
| 14 | i9·:·X·=·new·MutableHashTable; | 14 | i9·:·X·=·new·MutableHashTable; |
| Offset 6, 61 lines modified | Offset 6, 61 lines modified | ||
| 6 | o2·=·5*PP2 | 6 | o2·=·5*PP2 |
| 7 | ··········0 | 7 | ··········0 |
| 8 | o2·:·ToricDivisor·on·PP2 | 8 | o2·:·ToricDivisor·on·PP2 |
| 9 | i3·:·M1·=·elapsedTime·monomials·D1 | 9 | i3·:·M1·=·elapsedTime·monomials·D1 |
| 10 | ·--·.12 | 10 | ·--·.152174s·elapsed |
| 11 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4··· | 11 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4··· |
| 12 | o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·, | 12 | o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·, |
| 13 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2· | 13 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2· |
| 14 | ·····------------------------------------------------------------------------ | 14 | ·····------------------------------------------------------------------------ |
| 15 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 | 15 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 |
| 16 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} | 16 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} |
| 17 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 | 17 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 |
| 18 | o3·:·List | 18 | o3·:·List |
| 19 | i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1)) | 19 | i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1)) |
| 20 | ·--·.001 | 20 | ·--·.00116386s·elapsed |
| 21 | i5·:·FF2·=·hirzebruchSurface·2; | 21 | i5·:·FF2·=·hirzebruchSurface·2; |
| 22 | i6·:·D2·=·2*FF2_0·+·3·*·FF2_1 | 22 | i6·:·D2·=·2*FF2_0·+·3·*·FF2_1 |
| 23 | o6·=·2*FF2··+·3*FF2 | 23 | o6·=·2*FF2··+·3*FF2 |
| 24 | ··········0········1 | 24 | ··········0········1 |
| 25 | o6·:·ToricDivisor·on·FF2 | 25 | o6·:·ToricDivisor·on·FF2 |
| 26 | i7·:·M2·=·elapsedTime·monomials·D2 | 26 | i7·:·M2·=·elapsedTime·monomials·D2 |
| 27 | ·--·.3 | 27 | ·--·.350522s·elapsed |
| 28 | ·······2·····3·2·····3·····2·3 | 28 | ·······2·····3·2·····3·····2·3 |
| 29 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} | 29 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} |
| 30 | ·······1·3···1·2···0·1·2···0·1 | 30 | ·······1·3···1·2···0·1·2···0·1 |
| 31 | o7·:·List | 31 | o7·:·List |
| 32 | i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2)) | 32 | i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2)) |
| 33 | ·--·.00 | 33 | ·--·.00117456s·elapsed |
| 34 | i9·:·X·=·kleinschmidt·(5,·{1,2,3}); | 34 | i9·:·X·=·kleinschmidt·(5,·{1,2,3}); |
| 35 | i10·:·D3·=·3*X_0·+·5*X_1 | 35 | i10·:·D3·=·3*X_0·+·5*X_1 |
| 36 | o10·=·3*X··+·5*X | 36 | o10·=·3*X··+·5*X |
| 37 | ·········0······1 | 37 | ·········0······1 |
| 38 | o10·:·ToricDivisor·on·X | 38 | o10·:·ToricDivisor·on·X |
| 39 | i11·:·m3·=·elapsedTime·#·monomials·D3 | 39 | i11·:·m3·=·elapsedTime·#·monomials·D3 |
| 40 | ·--· | 40 | ·--·40.8838s·elapsed |
| 41 | o11·=·7909 | 41 | o11·=·7909 |
| 42 | i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3)) | 42 | i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3)) |
| 43 | ·--·.02 | 43 | ·--·.0258035s·elapsed |
| 44 | i13·:· | 44 | i13·:· |
| Offset 24, 19 lines modified | Offset 24, 19 lines modified | ||
| 24 | o3·:·List | 24 | o3·:·List |
| 25 | i4·:·X·=·normalToricVariety·F; | 25 | i4·:·X·=·normalToricVariety·F; |
| 26 | i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F) | 26 | i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F) |
| 27 | i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) | 27 | i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) |
| 28 | ·--·used·0.00 | 28 | ·--·used·0.00317488s·(cpu);·6.7567e-05s·(thread);·0s·(gc) |
| 29 | o6·=·X1 | 29 | o6·=·X1 |
| 30 | o6·:·NormalToricVariety | 30 | o6·:·NormalToricVariety |
| 31 | i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}}; | 31 | i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}}; |
| 32 | ·--·used·0. | 32 | ·--·used·0.109675s·(cpu);·0.0580306s·(thread);·0s·(gc) |
| 33 | i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2) | 33 | i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2) |
| 34 | i9·:· | 34 | i9·:· |
| Offset 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | o18·=·|·0·1·0·| | 88 | o18·=·|·0·1·0·| |
| 89 | ······|·0·0·1·| | 89 | ······|·0·0·1·| |
| 90 | ···············2·······3 | 90 | ···············2·······3 |
| 91 | o18·:·Matrix·ZZ··<--·ZZ | 91 | o18·:·Matrix·ZZ··<--·ZZ |
| 92 | i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); | 92 | i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); |
| 93 | ·--·used·0.0 | 93 | ·--·used·0.0959806s·(cpu);·0.0464125s·(thread);·0s·(gc) |
| 94 | i20·:·X2·=·time·normalToricVariety·vertMatrix; | 94 | i20·:·X2·=·time·normalToricVariety·vertMatrix; |
| 95 | ·--·used·0.001 | 95 | ·--·used·0.000130995s·(cpu);·0.00303884s·(thread);·0s·(gc) |
| 96 | i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2) | 96 | i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2) |
| 97 | i22·:· | 97 | i22·:· |
| Offset 181, 15 lines modified | Offset 181, 15 lines modified | ||
| 181 | ········</table> | 181 | ········</table> |
| 182 | ········<div> | 182 | ········<div> |
| 183 | ··········<p>We·end·with·a·slightly·larger·example.</p> | 183 | ··········<p>We·end·with·a·slightly·larger·example.</p> |
| 184 | ········</div> | 184 | ········</div> |
| 185 | ········<table·class="examples"> | 185 | ········<table·class="examples"> |
| 186 | ··········<tr> | 186 | ··········<tr> |
| 187 | <td>··············<pre><code·class="language-macaulay2">i14·:·Y·=·time·smoothFanoToricVariety(5,100); | 187 | <td>··············<pre><code·class="language-macaulay2">i14·:·Y·=·time·smoothFanoToricVariety(5,100); |
| 188 | ·--·used·0.1 | 188 | ·--·used·0.194045s·(cpu);·0.191751s·(thread);·0s·(gc)</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i15·:·A2·=·intersectionRing·Y;</code></pre> | 191 | <td>··············<pre><code·class="language-macaulay2">i15·:·A2·=·intersectionRing·Y;</code></pre> |
| 192 | </td>··········</tr> | 192 | </td>··········</tr> |
| 193 | ··········<tr> | 193 | ··········<tr> |
| 194 | <td>··············<pre><code·class="language-macaulay2">i16·:·assert·(#·rays·Y·===·numgens·A2)</code></pre> | 194 | <td>··············<pre><code·class="language-macaulay2">i16·:·assert·(#·rays·Y·===·numgens·A2)</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| Offset 218, 20 lines modified | Offset 218, 20 lines modified | ||
| 218 | ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t·t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··) | 218 | ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t·t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··) |
| 219 | ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10····9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10 | 219 | ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10····9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10 |
| 220 | o18·:·QuotientRing</code></pre> | 220 | o18·:·QuotientRing</code></pre> |
| 221 | </td>··········</tr> | 221 | </td>··········</tr> |
| 222 | ··········<tr> | 222 | ··········<tr> |
| 223 | <td>··············<pre><code·class="language-macaulay2">i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) | 223 | <td>··············<pre><code·class="language-macaulay2">i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) |
| 224 | ·--·used·0.00 | 224 | ·--·used·0.00239499s·(cpu);·0.00103858s·(thread);·0s·(gc) |
| 225 | ·--·used·7.6754e-05s·(cpu);·9.8786e-05s·(thread);·0s·(gc) | ||
| 226 | ·--·used·1.3765e-05s·(cpu);·7.7456e-05s·(thread);·0s·(gc) | ||
| 225 | ·--·used·1. | 227 | ·--·used·1.2513e-05s·(cpu);·9.2404e-05s·(thread);·0s·(gc) |
| 226 | ·--·used·5.929e-06s·(cpu);·4.8773e-05s·(thread);·0s·(gc) | ||
| 227 | ·--·used·5.428e-06s·(cpu);·4.5018e-05s·(thread);·0s·(gc) | ||
| 228 | ·--·used·5.518e-06s·(cpu);·4.662e-05s·(thread);·0s·(gc) | ||
| 229 | ·--·used· | 228 | ·--·used·1.5278e-05s·(cpu);·7.3398e-05s·(thread);·0s·(gc) |
| 229 | ·--·used·9.878e-06s·(cpu);·6.8449e-05s·(thread);·0s·(gc) | ||
| 230 | o19·=·{1,·6,·13,·13,·6,·1} | 230 | o19·=·{1,·6,·13,·13,·6,·1} |
| 231 | o19·:·List</code></pre> | 231 | o19·:·List</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| 233 | ········</table> | 233 | ········</table> |
| 234 | ······</div> | 234 | ······</div> |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1) | 97 | i13·:·for·i·to·dim·X·list·hilbertFunction·(i,·A1) |
| 98 | o13·=·{1,·2,·3,·3,·2,·1} | 98 | o13·=·{1,·2,·3,·3,·2,·1} |
| 99 | o13·:·List | 99 | o13·:·List |
| 100 | We·end·with·a·slightly·larger·example. | 100 | We·end·with·a·slightly·larger·example. |
| 101 | i14·:·Y·=·time·smoothFanoToricVariety(5,100); | 101 | i14·:·Y·=·time·smoothFanoToricVariety(5,100); |
| 102 | ·--·used·0.1 | 102 | ·--·used·0.194045s·(cpu);·0.191751s·(thread);·0s·(gc) |
| 103 | i15·:·A2·=·intersectionRing·Y; | 103 | i15·:·A2·=·intersectionRing·Y; |
| 104 | i16·:·assert·(#·rays·Y·===·numgens·A2) | 104 | i16·:·assert·(#·rays·Y·===·numgens·A2) |
| 105 | i17·:·ideal·A2 | 105 | i17·:·ideal·A2 |
| 106 | o17·=·ideal·(t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·t··, | 106 | o17·=·ideal·(t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·,·t·t·t··, |
| 107 | ··············2·3···2·5···4·5···3·6···4·6···1·7···7·9···8·9···0·1·10 | 107 | ··············2·3···2·5···4·5···3·6···4·6···1·7···7·9···8·9···0·1·10 |
| 108 | ······----------------------------------------------------------------------- | 108 | ······----------------------------------------------------------------------- |
| Offset 130, 20 lines modified | Offset 130, 20 lines modified | ||
| 130 | ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t | 130 | ······(t··+·t·t·,·t·t··+·t·,·t··+·t·t·,·t·t·,·t·t··+·t·,·t··-·t·t··-·3t·t···+·t |
| 131 | t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··) | 131 | t···+·2t··,·-·t·t··+·t··+·2t·t··,·t·t·,·-·t·t···+·t··,·t·t··) |
| 132 | ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10 | 132 | ········3····3·5···3·5····5···5····5·6···3·6···5·6····6···8····8·9·····8·10 |
| 133 | 9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10 | 133 | 9·10·····10·····8·9····9·····9·10···8·9·····8·10····10···8·10 |
| 134 | o18·:·QuotientRing | 134 | o18·:·QuotientRing |
| 135 | i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) | 135 | i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) |
| 136 | ·--·used·0.00 | 136 | ·--·used·0.00239499s·(cpu);·0.00103858s·(thread);·0s·(gc) |
| 137 | ·--·used·7.6754e-05s·(cpu);·9.8786e-05s·(thread);·0s·(gc) | ||
| 138 | ·--·used·1.3765e-05s·(cpu);·7.7456e-05s·(thread);·0s·(gc) | ||
| 137 | ·--·used·1. | 139 | ·--·used·1.2513e-05s·(cpu);·9.2404e-05s·(thread);·0s·(gc) |
| 138 | ·--·used·5.929e-06s·(cpu);·4.8773e-05s·(thread);·0s·(gc) | ||
| 139 | ·--·used·5.428e-06s·(cpu);·4.5018e-05s·(thread);·0s·(gc) | ||
| 140 | ·--·used·5.518e-06s·(cpu);·4.662e-05s·(thread);·0s·(gc) | ||
| 141 | ·--·used· | 140 | ·--·used·1.5278e-05s·(cpu);·7.3398e-05s·(thread);·0s·(gc) |
| 141 | ·--·used·9.878e-06s·(cpu);·6.8449e-05s·(thread);·0s·(gc) | ||
| 142 | o19·=·{1,·6,·13,·13,·6,·1} | 142 | o19·=·{1,·6,·13,·13,·6,·1} |
| 143 | o19·:·List | 143 | o19·:·List |
| 144 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 144 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 145 | ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8s_\x8h_\x8e_\x8a_\x8v_\x8e_\x8s·--·information·about·coherent·sheaves·and·total | 145 | ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8s_\x8h_\x8e_\x8a_\x8v_\x8e_\x8s·--·information·about·coherent·sheaves·and·total |
| 146 | ······coordinate·rings·(a.k.a.·Cox·rings) | 146 | ······coordinate·rings·(a.k.a.·Cox·rings) |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ········<table·class="examples"> | 100 | ········<table·class="examples"> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i2·:·setRandomSeed·(currentTime·());</code></pre> | 102 | <td>··············<pre><code·class="language-macaulay2">i2·:·setRandomSeed·(currentTime·());</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·a·=·sort·apply·(3,·i·->·random·(7)) | 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·a·=·sort·apply·(3,·i·->·random·(7)) |
| 106 | o3·=·{ | 106 | o3·=·{2,·3,·4} |
| 107 | o3·:·List</code></pre> | 107 | o3·:·List</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert·isWellDefined·kleinschmidt·(4,a)</code></pre> | 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert·isWellDefined·kleinschmidt·(4,a)</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| Offset 118, 15 lines modified | Offset 118, 15 lines modified | ||
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9));</code></pre> | 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j·->·random·(1,9));</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·q | 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·q |
| 124 | o7·=·{ | 124 | o7·=·{1,·3,·4,·7,·8} |
| 125 | o7·:·List</code></pre> | 125 | o7·:·List</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·isWellDefined·weightedProjectiveSpace·q</code></pre> | 128 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·isWellDefined·weightedProjectiveSpace·q</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ········</table> | 130 | ········</table> |
| Offset 31, 24 lines modified | Offset 31, 24 lines modified | ||
| 31 | The·first·examples·illustrate·that·small·projective·spaces·are·well-defined. | 31 | The·first·examples·illustrate·that·small·projective·spaces·are·well-defined. |
| 32 | i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1)) | 32 | i1·:·assert·all·(5,·d·->·isWellDefined·toricProjectiveSpace·(d+1)) |
| 33 | The·second·examples·show·that·a·randomly·selected·Kleinschmidt·toric·variety | 33 | The·second·examples·show·that·a·randomly·selected·Kleinschmidt·toric·variety |
| 34 | and·a·weighted·projective·space·are·also·well-defined. | 34 | and·a·weighted·projective·space·are·also·well-defined. |
| 35 | i2·:·setRandomSeed·(currentTime·()); | 35 | i2·:·setRandomSeed·(currentTime·()); |
| 36 | i3·:·a·=·sort·apply·(3,·i·->·random·(7)) | 36 | i3·:·a·=·sort·apply·(3,·i·->·random·(7)) |
| 37 | o3·=·{ | 37 | o3·=·{2,·3,·4} |
| 38 | o3·:·List | 38 | o3·:·List |
| 39 | i4·:·assert·isWellDefined·kleinschmidt·(4,a) | 39 | i4·:·assert·isWellDefined·kleinschmidt·(4,a) |
| 40 | i5·:·q·=·sort·apply·(5,·j·->·random·(1,9)); | 40 | i5·:·q·=·sort·apply·(5,·j·->·random·(1,9)); |
| 41 | i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j | 41 | i6·:·while·not·all·(subsets·(q,#q-1),·s·->·gcd·s·===·1)·do·q·=·sort·apply·(5,·j |
| 42 | ->·random·(1,9)); | 42 | ->·random·(1,9)); |
| 43 | i7·:·q | 43 | i7·:·q |
| 44 | o7·=·{ | 44 | o7·=·{1,·3,·4,·7,·8} |
| 45 | o7·:·List | 45 | o7·:·List |
| 46 | i8·:·assert·isWellDefined·weightedProjectiveSpace·q | 46 | i8·:·assert·isWellDefined·weightedProjectiveSpace·q |
| 47 | The·next·ten·examples·illustrate·various·ways·that·two·lists·can·fail·to·define | 47 | The·next·ten·examples·illustrate·various·ways·that·two·lists·can·fail·to·define |
| 48 | a·normal·toric·variety.·By·making·the·current·debugging·level·greater·than·one, | 48 | a·normal·toric·variety.·By·making·the·current·debugging·level·greater·than·one, |
| 49 | one·gets·some·addition·information·about·the·nature·of·the·failure. | 49 | one·gets·some·addition·information·about·the·nature·of·the·failure. |
| 50 | i9·:·X·=·new·MutableHashTable; | 50 | i9·:·X·=·new·MutableHashTable; |
| Offset 94, 29 lines modified | Offset 94, 29 lines modified | ||
| 94 | o2·=·5*PP2 | 94 | o2·=·5*PP2 |
| 95 | ··········0 | 95 | ··········0 |
| 96 | o2·:·ToricDivisor·on·PP2</code></pre> | 96 | o2·:·ToricDivisor·on·PP2</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·M1·=·elapsedTime·monomials·D1 | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·M1·=·elapsedTime·monomials·D1 |
| 100 | ·--·.12 | 100 | ·--·.152174s·elapsed |
| 101 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4··· | 101 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4··· |
| 102 | o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·, | 102 | o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·, |
| 103 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2· | 103 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2· |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 | 105 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 |
| 106 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} | 106 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} |
| 107 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 | 107 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 |
| 108 | o3·:·List</code></pre> | 108 | o3·:·List</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1)) | 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1)) |
| 112 | ·--·.001 | 112 | ·--·.00116386s·elapsed</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ········</table> | 114 | ········</table> |
| 115 | ········<div> | 115 | ········<div> |
| 116 | ··········<p>Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.</p> | 116 | ··········<p>Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.</p> |
| 117 | ········</div> | 117 | ········</div> |
| 118 | ········<table·class="examples"> | 118 | ········<table·class="examples"> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| Offset 128, 46 lines modified | Offset 128, 46 lines modified | ||
| 128 | o6·=·2*FF2··+·3*FF2 | 128 | o6·=·2*FF2··+·3*FF2 |
| 129 | ··········0········1 | 129 | ··········0········1 |
| 130 | o6·:·ToricDivisor·on·FF2</code></pre> | 130 | o6·:·ToricDivisor·on·FF2</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i7·:·M2·=·elapsedTime·monomials·D2 | 133 | <td>··············<pre><code·class="language-macaulay2">i7·:·M2·=·elapsedTime·monomials·D2 |
| 134 | ·--·.3 | 134 | ·--·.350522s·elapsed |
| 135 | ·······2·····3·2·····3·····2·3 | 135 | ·······2·····3·2·····3·····2·3 |
| 136 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} | 136 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} |
| 137 | ·······1·3···1·2···0·1·2···0·1 | 137 | ·······1·3···1·2···0·1·2···0·1 |
| 138 | o7·:·List</code></pre> | 138 | o7·:·List</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2)) | 141 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2)) |
| 142 | ·--·.00 | 142 | ·--·.00117456s·elapsed</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i9·:·X·=·kleinschmidt·(5,·{1,2,3});</code></pre> | 145 | <td>··············<pre><code·class="language-macaulay2">i9·:·X·=·kleinschmidt·(5,·{1,2,3});</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i10·:·D3·=·3*X_0·+·5*X_1 | 148 | <td>··············<pre><code·class="language-macaulay2">i10·:·D3·=·3*X_0·+·5*X_1 |
| 149 | o10·=·3*X··+·5*X | 149 | o10·=·3*X··+·5*X |
| 150 | ·········0······1 | 150 | ·········0······1 |
| 151 | o10·:·ToricDivisor·on·X</code></pre> | 151 | o10·:·ToricDivisor·on·X</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i11·:·m3·=·elapsedTime·#·monomials·D3 | 154 | <td>··············<pre><code·class="language-macaulay2">i11·:·m3·=·elapsedTime·#·monomials·D3 |
| 155 | ·--· | 155 | ·--·40.8838s·elapsed |
| 156 | o11·=·7909</code></pre> | 156 | o11·=·7909</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3)) | 159 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3)) |
| 160 | ·--·.02 | 160 | ·--·.0258035s·elapsed</code></pre> |
| 161 | </td>··········</tr> | 161 | </td>··········</tr> |
| 162 | ········</table> | 162 | ········</table> |
| 163 | ········<div> | 163 | ········<div> |
| 164 | ··········<p>By·exploiting·<a·title="computes·the·lattice·points·of·a·polytope"·href="../../Polyhedra/html/_lattice__Points.html">latticePoints</a>,·this·method·function·avoids·using·the·<a·title="basis·or·generating·set·of·all·or·part·of·a·ring,·ideal·or·module"·href="../../Macaulay2Doc/html/_basis.html">basis</a>·function.</p> | 164 | ··········<p>By·exploiting·<a·title="computes·the·lattice·points·of·a·polytope"·href="../../Polyhedra/html/_lattice__Points.html">latticePoints</a>,·this·method·function·avoids·using·the·<a·title="basis·or·generating·set·of·all·or·part·of·a·ring,·ideal·or·module"·href="../../Macaulay2Doc/html/_basis.html">basis</a>·function.</p> |
| 165 | ········</div> | 165 | ········</div> |
| 166 | ······</div> | 166 | ······</div> |
| 167 | ······<div> | 167 | ······<div> |
| Offset 28, 61 lines modified | Offset 28, 61 lines modified | ||
| 28 | i2·:·D1·=·5*PP2_0 | 28 | i2·:·D1·=·5*PP2_0 |
| 29 | o2·=·5*PP2 | 29 | o2·=·5*PP2 |
| 30 | ··········0 | 30 | ··········0 |
| 31 | o2·:·ToricDivisor·on·PP2 | 31 | o2·:·ToricDivisor·on·PP2 |
| 32 | i3·:·M1·=·elapsedTime·monomials·D1 | 32 | i3·:·M1·=·elapsedTime·monomials·D1 |
| 33 | ·--·.12 | 33 | ·--·.152174s·elapsed |
| 34 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4 | 34 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4 |
| 35 | o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·, | 35 | o3·=·{x·,·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·,·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·x·, |
| 36 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2 | 36 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2 |
| 37 | ·····------------------------------------------------------------------------ | 37 | ·····------------------------------------------------------------------------ |
| 38 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 | 38 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 |
| 39 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} | 39 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} |
| 40 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 | 40 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 |
| 41 | o3·:·List | 41 | o3·:·List |
| 42 | i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring | 42 | i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring |
| 43 | variety·D1)) | 43 | variety·D1)) |
| 44 | ·--·.001 | 44 | ·--·.00116386s·elapsed |
| 45 | Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting. | 45 | Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting. |
| 46 | i5·:·FF2·=·hirzebruchSurface·2; | 46 | i5·:·FF2·=·hirzebruchSurface·2; |
| 47 | i6·:·D2·=·2*FF2_0·+·3·*·FF2_1 | 47 | i6·:·D2·=·2*FF2_0·+·3·*·FF2_1 |
| 48 | o6·=·2*FF2··+·3*FF2 | 48 | o6·=·2*FF2··+·3*FF2 |
| 49 | ··········0········1 | 49 | ··········0········1 |
| 50 | o6·:·ToricDivisor·on·FF2 | 50 | o6·:·ToricDivisor·on·FF2 |
| 51 | i7·:·M2·=·elapsedTime·monomials·D2 | 51 | i7·:·M2·=·elapsedTime·monomials·D2 |
| 52 | ·--·.3 | 52 | ·--·.350522s·elapsed |
| 53 | ·······2·····3·2·····3·····2·3 | 53 | ·······2·····3·2·····3·····2·3 |
| 54 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} | 54 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} |
| 55 | ·······1·3···1·2···0·1·2···0·1 | 55 | ·······1·3···1·2···0·1·2···0·1 |
| 56 | o7·:·List | 56 | o7·:·List |
| 57 | i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring | 57 | i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring |
| 58 | variety·D2)) | 58 | variety·D2)) |
| 59 | ·--·.00 | 59 | ·--·.00117456s·elapsed |
| 60 | i9·:·X·=·kleinschmidt·(5,·{1,2,3}); | 60 | i9·:·X·=·kleinschmidt·(5,·{1,2,3}); |
| 61 | i10·:·D3·=·3*X_0·+·5*X_1 | 61 | i10·:·D3·=·3*X_0·+·5*X_1 |
| 62 | o10·=·3*X··+·5*X | 62 | o10·=·3*X··+·5*X |
| 63 | ·········0······1 | 63 | ·········0······1 |
| 64 | o10·:·ToricDivisor·on·X | 64 | o10·:·ToricDivisor·on·X |
| 65 | i11·:·m3·=·elapsedTime·#·monomials·D3 | 65 | i11·:·m3·=·elapsedTime·#·monomials·D3 |
| 66 | ·--· | 66 | ·--·40.8838s·elapsed |
| 67 | o11·=·7909 | 67 | o11·=·7909 |
| 68 | i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety | 68 | i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety |
| 69 | D3)) | 69 | D3)) |
| 70 | ·--·.02 | 70 | ·--·.0258035s·elapsed |
| 71 | By·exploiting·_\x8l_\x8a_\x8t_\x8t_\x8i_\x8c_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s,·this·method·function·avoids·using·the·_\x8b_\x8a_\x8s_\x8i_\x8s | 71 | By·exploiting·_\x8l_\x8a_\x8t_\x8t_\x8i_\x8c_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s,·this·method·function·avoids·using·the·_\x8b_\x8a_\x8s_\x8i_\x8s |
| 72 | function. | 72 | function. |
| 73 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 73 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 74 | ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8d_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8s·--·information·about·toric·divisors·and·their | 74 | ····*·_\x8w_\x8o_\x8r_\x8k_\x8i_\x8n_\x8g_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8d_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r_\x8s·--·information·about·toric·divisors·and·their |
| 75 | ······related·groups | 75 | ······related·groups |
| 76 | ····*·_\x8r_\x8i_\x8n_\x8g_\x8(_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·make·the·total·coordinate·ring·(a.k.a.·Cox | 76 | ····*·_\x8r_\x8i_\x8n_\x8g_\x8(_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·make·the·total·coordinate·ring·(a.k.a.·Cox |
| 77 | ······ring) | 77 | ······ring) |
| Offset 120, 23 lines modified | Offset 120, 23 lines modified | ||
| 120 | ········</table> | 120 | ········</table> |
| 121 | ········<div> | 121 | ········<div> |
| 122 | ··········<p>The·recommended·method·for·creating·a·<a·title="the·class·of·all·normal·toric·varieties"·href="___Normal__Toric__Variety.html">NormalToricVariety</a>·from·a·fan·is·<a·title="make·a·normal·toric·variety"·href="_normal__Toric__Variety_lp__List_cm__List_rp.html">normalToricVariety(List,List)</a>.··In·fact,·this·package·avoids·using·objects·from·the·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·package·whenever·possible.···Here·is·a·trivial·example,·namely·projective·2-space,·illustrating·the·substantial·increase·in·time·resulting·from·the·use·of·a·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·fan.</p> | 122 | ··········<p>The·recommended·method·for·creating·a·<a·title="the·class·of·all·normal·toric·varieties"·href="___Normal__Toric__Variety.html">NormalToricVariety</a>·from·a·fan·is·<a·title="make·a·normal·toric·variety"·href="_normal__Toric__Variety_lp__List_cm__List_rp.html">normalToricVariety(List,List)</a>.··In·fact,·this·package·avoids·using·objects·from·the·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·package·whenever·possible.···Here·is·a·trivial·example,·namely·projective·2-space,·illustrating·the·substantial·increase·in·time·resulting·from·the·use·of·a·<a·title="for·computations·with·convex·polyhedra,·cones,·and·fans"·href="../../Polyhedra/html/index.html">Polyhedra</a>·fan.</p> |
| 123 | ········</div> | 123 | ········</div> |
| 124 | ········<table·class="examples"> | 124 | ········<table·class="examples"> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) | 126 | <td>··············<pre><code·class="language-macaulay2">i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) |
| 127 | ·--·used·0.00 | 127 | ·--·used·0.00317488s·(cpu);·6.7567e-05s·(thread);·0s·(gc) |
| 128 | o6·=·X1 | 128 | o6·=·X1 |
| 129 | o6·:·NormalToricVariety</code></pre> | 129 | o6·:·NormalToricVariety</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}}; | 132 | <td>··············<pre><code·class="language-macaulay2">i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull·matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}}; |
| 133 | ·--·used·0. | 133 | ·--·used·0.109675s·(cpu);·0.0580306s·(thread);·0s·(gc)</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)</code></pre> | 136 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| 139 | ······</div> | 139 | ······</div> |
| 140 | ······<div> | 140 | ······<div> |
| Offset 49, 22 lines modified | Offset 49, 22 lines modified | ||
| 49 | i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F) | 49 | i5·:·assert·(transpose·matrix·rays·X·==·rays·F·and·max·X·==·sort·maxCones·F) |
| 50 | The·recommended·method·for·creating·a·_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·from·a·fan·is | 50 | The·recommended·method·for·creating·a·_\x8N_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·from·a·fan·is |
| 51 | _\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8L_\x8i_\x8s_\x8t_\x8,_\x8L_\x8i_\x8s_\x8t_\x8).·In·fact,·this·package·avoids·using·objects·from | 51 | _\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8L_\x8i_\x8s_\x8t_\x8,_\x8L_\x8i_\x8s_\x8t_\x8).·In·fact,·this·package·avoids·using·objects·from |
| 52 | the·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·package·whenever·possible.·Here·is·a·trivial·example,·namely | 52 | the·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·package·whenever·possible.·Here·is·a·trivial·example,·namely |
| 53 | projective·2-space,·illustrating·the·substantial·increase·in·time·resulting | 53 | projective·2-space,·illustrating·the·substantial·increase·in·time·resulting |
| 54 | from·the·use·of·a·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·fan. | 54 | from·the·use·of·a·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·fan. |
| 55 | i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) | 55 | i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) |
| 56 | ·--·used·0.00 | 56 | ·--·used·0.00317488s·(cpu);·6.7567e-05s·(thread);·0s·(gc) |
| 57 | o6·=·X1 | 57 | o6·=·X1 |
| 58 | o6·:·NormalToricVariety | 58 | o6·:·NormalToricVariety |
| 59 | i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull | 59 | i7·:·X2·=·time·normalToricVariety·fan·{posHull·matrix·{{-1,1},{-1,0}},·posHull |
| 60 | matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}}; | 60 | matrix·{{1,0},{0,1}},·posHull·matrix{{-1,0},{-1,1}}}; |
| 61 | ·--·used·0. | 61 | ·--·used·0.109675s·(cpu);·0.0580306s·(thread);·0s·(gc) |
| 62 | i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2) | 62 | i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2) |
| 63 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 63 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 64 | ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors | 64 | ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors |
| 65 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·make·a·normal·toric·variety | 65 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·make·a·normal·toric·variety |
| 66 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 66 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 67 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8F_\x8a_\x8n_\x8)·--·make·a·normal·toric·variety·from·a·'Polyhedra' | 67 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8F_\x8a_\x8n_\x8)·--·make·a·normal·toric·variety·from·a·'Polyhedra' |
| 68 | ······fan | 68 | ······fan |
| Offset 202, 19 lines modified | Offset 202, 19 lines modified | ||
| 202 | ······|·0·0·1·| | 202 | ······|·0·0·1·| |
| 203 | ···············2·······3 | 203 | ···············2·······3 |
| 204 | o18·:·Matrix·ZZ··<--·ZZ</code></pre> | 204 | o18·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 205 | </td>··········</tr> | 205 | </td>··········</tr> |
| 206 | ··········<tr> | 206 | ··········<tr> |
| 207 | <td>··············<pre><code·class="language-macaulay2">i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); | 207 | <td>··············<pre><code·class="language-macaulay2">i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); |
| 208 | ·--·used·0.0 | 208 | ·--·used·0.0959806s·(cpu);·0.0464125s·(thread);·0s·(gc)</code></pre> |
| 209 | </td>··········</tr> | 209 | </td>··········</tr> |
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i20·:·X2·=·time·normalToricVariety·vertMatrix; | 211 | <td>··············<pre><code·class="language-macaulay2">i20·:·X2·=·time·normalToricVariety·vertMatrix; |
| 212 | ·--·used·0.001 | 212 | ·--·used·0.000130995s·(cpu);·0.00303884s·(thread);·0s·(gc)</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ··········<tr> | 214 | ··········<tr> |
| 215 | <td>··············<pre><code·class="language-macaulay2">i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)</code></pre> | 215 | <td>··············<pre><code·class="language-macaulay2">i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)</code></pre> |
| 216 | </td>··········</tr> | 216 | </td>··········</tr> |
| 217 | ········</table> | 217 | ········</table> |
| 218 | ······</div> | 218 | ······</div> |
| 219 | ······<div> | 219 | ······<div> |
| Offset 103, 17 lines modified | Offset 103, 17 lines modified | ||
| 103 | o18·=·|·0·1·0·| | 103 | o18·=·|·0·1·0·| |
| 104 | ······|·0·0·1·| | 104 | ······|·0·0·1·| |
| 105 | ···············2·······3 | 105 | ···············2·······3 |
| 106 | o18·:·Matrix·ZZ··<--·ZZ | 106 | o18·:·Matrix·ZZ··<--·ZZ |
| 107 | i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); | 107 | i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); |
| 108 | ·--·used·0.0 | 108 | ·--·used·0.0959806s·(cpu);·0.0464125s·(thread);·0s·(gc) |
| 109 | i20·:·X2·=·time·normalToricVariety·vertMatrix; | 109 | i20·:·X2·=·time·normalToricVariety·vertMatrix; |
| 110 | ·--·used·0.001 | 110 | ·--·used·0.000130995s·(cpu);·0.00303884s·(thread);·0s·(gc) |
| 111 | i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2) | 111 | i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2) |
| 112 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 112 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 113 | ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors | 113 | ····*·_\x8m_\x8a_\x8k_\x8i_\x8n_\x8g_\x8·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8·_\x8t_\x8o_\x8r_\x8i_\x8c_\x8·_\x8v_\x8a_\x8r_\x8i_\x8e_\x8t_\x8i_\x8e_\x8s·--·information·about·the·basic·constructors |
| 114 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·make·a·normal·toric·variety·from·a·polytope | 114 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·make·a·normal·toric·variety·from·a·polytope |
| 115 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 115 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 116 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8o_\x8n_\x8)·--·make·a·normal·toric·variety·from·a | 116 | ····*·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8T_\x8o_\x8r_\x8i_\x8c_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8(_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8o_\x8n_\x8)·--·make·a·normal·toric·variety·from·a |
| 117 | ······'Polyhedra'·polyhedron | 117 | ······'Polyhedra'·polyhedron |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=32 | 7 | #:len=32 |
| 8 | aW50Y2xNb25JZGVhbChJZGVhbCxSaW5nRWxlbWVudCk= | 8 | aW50Y2xNb25JZGVhbChJZGVhbCxSaW5nRWxlbWVudCk= |
| 9 | #:len=2753 | 9 | #:len=2753 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
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| 8 | am9yZGFuRm9ybShNYXRyaXgp | 8 | am9yZGFuRm9ybShNYXRyaXgp |
| 9 | #:len=263 | 9 | #:len=263 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODE0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODE0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=43 | 7 | #:len=43 |
| 8 | aXNTdWJzZXQoTnVtZXJpY2FsVmFyaWV0eSxOdW1lcmljYWxWYXJpZXR5KQ== | 8 | aXNTdWJzZXQoTnVtZXJpY2FsVmFyaWV0eSxOdW1lcmljYWxWYXJpZXR5KQ== |
| 9 | #:len=1173 | 9 | #:len=1173 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hlY2sgY29udGFpbm1lbnQiLCAibGlu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hlY2sgY29udGFpbm1lbnQiLCAibGlu |
| 11 | ZW51bSIgPT4gNzg5LCBJbnB1dHMgPT4ge1NQQU57VFR7IlYifSwiLCAiLCIgb3IgIixTUEFOeyJh | 11 | ZW51bSIgPT4gNzg5LCBJbnB1dHMgPT4ge1NQQU57VFR7IlYifSwiLCAiLCIgb3IgIixTUEFOeyJh |
| Offset 16, 14 lines modified | Offset 16, 14 lines modified | ||
| 16 | ······3······2 | 16 | ······3······2 |
| 17 | o3·=·x··-·36x··+·431x·-·1716 | 17 | o3·=·x··-·36x··+·431x·-·1716 |
| 18 | o3·:·R | 18 | o3·:·R |
| 19 | i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}},·Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" | 19 | i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}},·Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" |
| 20 | sh:·1:·bertini:·not·found | 20 | sh:·line·1:·bertini:·command·not·found |
| 21 | true | 21 | true |
| 22 | o4·=·need·to·install·Bertini·to·run·these·lines | 22 | o4·=·need·to·install·Bertini·to·run·these·lines |
| 23 | i5·:· | 23 | i5·:· |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ······3······2 | 100 | ······3······2 |
| 101 | o3·=·x··-·36x··+·431x·-·1716 | 101 | o3·=·x··-·36x··+·431x·-·1716 |
| 102 | o3·:·R</code></pre> | 102 | o3·:·R</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}},·Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}},·Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" |
| 106 | sh:·1:·bertini:·not·found | 106 | sh:·line·1:·bertini:·command·not·found |
| 107 | true | 107 | true |
| 108 | o4·=·need·to·install·Bertini·to·run·these·lines</code></pre> | 108 | o4·=·need·to·install·Bertini·to·run·these·lines</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ········</table> | 110 | ········</table> |
| 111 | ······</div> | 111 | ······</div> |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | ······3······2 | 35 | ······3······2 |
| 36 | o3·=·x··-·36x··+·431x·-·1716 | 36 | o3·=·x··-·36x··+·431x·-·1716 |
| 37 | o3·:·R | 37 | o3·:·R |
| 38 | i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}}, | 38 | i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}}, |
| 39 | Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" | 39 | Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" |
| 40 | sh:·1:·bertini:·not·found | 40 | sh:·line·1:·bertini:·command·not·found |
| 41 | true | 41 | true |
| 42 | o4·=·need·to·install·Bertini·to·run·these·lines | 42 | o4·=·need·to·install·Bertini·to·run·these·lines |
| 43 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 43 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 44 | Available·only·with·Software=>BERTINI·at·the·moment... | 44 | Available·only·with·Software=>BERTINI·at·the·moment... |
| 45 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 45 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=23 | 7 | #:len=23 |
| 8 | aW50ZXJ2YWxDQ2koUlJpLE51bWJlcik= | 8 | aW50ZXJ2YWxDQ2koUlJpLE51bWJlcik= |
| 9 | #:len=261 | 9 | #:len=261 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDQsICJ1bmRvY3VtZW50ZWQiID0+IHRy | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDQsICJ1bmRvY3VtZW50ZWQiID0+IHRy |
| 11 | dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KGludGVydmFs | 11 | dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KGludGVydmFs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=42 | 7 | #:len=42 |
| 8 | bnVtZXJpY2FsSGlsYmVydEZ1bmN0aW9uKFJpbmdNYXAsSWRlYWwsWlop | 8 | bnVtZXJpY2FsSGlsYmVydEZ1bmN0aW9uKFJpbmdNYXAsSWRlYWwsWlop |
| 9 | #:len=367 | 9 | #:len=367 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDUwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDUwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhudW1lcmljYWxIaWxiZXJ0RnVuY3Rpb24sUmluZ01h | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhudW1lcmljYWxIaWxiZXJ0RnVuY3Rpb24sUmluZ01h |
| Offset 23, 19 lines modified | Offset 23, 19 lines modified | ||
| 23 | --·warning:·experimental·computation·over·inexact·field·begun | 23 | --·warning:·experimental·computation·over·inexact·field·begun |
| 24 | --··········results·not·reliable·(one·warning·given·per·session) | 24 | --··········results·not·reliable·(one·warning·given·per·session) |
| 25 | o4·=·true | 25 | o4·=·true |
| 26 | i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) | 26 | i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) |
| 27 | Sampling·image·points·... | 27 | Sampling·image·points·... |
| 28 | ·····--·used·.0074 | 28 | ·····--·used·.00874157·seconds |
| 29 | Creating·interpolation·matrix·... | 29 | Creating·interpolation·matrix·... |
| 30 | ·····--·used·.00 | 30 | ·····--·used·.00695187·seconds |
| 31 | Performing·normalization·preconditioning·... | 31 | Performing·normalization·preconditioning·... |
| 32 | ·····--·used·.00399 | 32 | ·····--·used·.00399949·seconds |
| 33 | Computing·numerical·kernel·... | 33 | Computing·numerical·kernel·... |
| 34 | ·····--·used·0·seconds | 34 | ·····--·used·0·seconds |
| 35 | o5·=·a·"numerical·interpolation·table",·indicating | 35 | o5·=·a·"numerical·interpolation·table",·indicating |
| 36 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 | 36 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 |
| 37 | o5·:·NumericalInterpolationTable | 37 | o5·:·NumericalInterpolationTable |
| Offset 13, 17 lines modified | Offset 13, 17 lines modified | ||
| 13 | o2·=·|·s3·s2t·st2·t3·| | 13 | o2·=·|·s3·s2t·st2·t3·| |
| 14 | ·············1······4 | 14 | ·············1······4 |
| 15 | o2·:·Matrix·R··<--·R | 15 | o2·:·Matrix·R··<--·R |
| 16 | i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) | 16 | i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) |
| 17 | Sampling·image·points·... | 17 | Sampling·image·points·... |
| 18 | ·····--·used·.00 | 18 | ·····--·used·.00532185·seconds |
| 19 | Creating·interpolation·matrix·... | 19 | Creating·interpolation·matrix·... |
| 20 | ·····--·used·.00 | 20 | ·····--·used·.00400877·seconds |
| 21 | Performing·normalization·preconditioning·... | 21 | Performing·normalization·preconditioning·... |
| 22 | ·····--·used·0·seconds | 22 | ·····--·used·0·seconds |
| 23 | Computing·numerical·kernel·... | 23 | Computing·numerical·kernel·... |
| 24 | ·····--·used·0·seconds | 24 | ·····--·used·0·seconds |
| 25 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| | 25 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| |
| Offset 13, 40 lines modified | Offset 13, 40 lines modified | ||
| 13 | o2·=·|·s3·s2t·st2·t3·| | 13 | o2·=·|·s3·s2t·st2·t3·| |
| 14 | ·············1······4 | 14 | ·············1······4 |
| 15 | o2·:·Matrix·R··<--·R | 15 | o2·:·Matrix·R··<--·R |
| 16 | i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) | 16 | i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) |
| 17 | Sampling·image·points·... | 17 | Sampling·image·points·... |
| 18 | ·····--·used·.0 | 18 | ·····--·used·.0112647·seconds |
| 19 | Creating·interpolation·matrix·... | 19 | Creating·interpolation·matrix·... |
| 20 | ·····--·used·.00 | 20 | ·····--·used·.00950867·seconds |
| 21 | Performing·normalization·preconditioning·... | 21 | Performing·normalization·preconditioning·... |
| 22 | ·····--·used·.0 | 22 | ·····--·used·.0103907·seconds |
| 23 | Computing·numerical·kernel·... | 23 | Computing·numerical·kernel·... |
| 24 | ·····--·used·.00 | 24 | ·····--·used·.000928911·seconds |
| 25 | o3·=·a·"numerical·interpolation·table",·indicating | 25 | o3·=·a·"numerical·interpolation·table",·indicating |
| 26 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 | 26 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 |
| 27 | o3·:·NumericalInterpolationTable | 27 | o3·:·NumericalInterpolationTable |
| 28 | i4·:·R·=·CC[x_(1,1)..x_(2,4)]; | 28 | i4·:·R·=·CC[x_(1,1)..x_(2,4)]; |
| 29 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; | 29 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; |
| 30 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); | 30 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); |
| 31 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) | 31 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) |
| 32 | Creating·interpolation·matrix·... | 32 | Creating·interpolation·matrix·... |
| 33 | ·····--·used·.003 | 33 | ·····--·used·.00378994·seconds |
| 34 | Performing·normalization·preconditioning·... | 34 | Performing·normalization·preconditioning·... |
| 35 | ·····--·used·.00 | 35 | ·····--·used·.00816177·seconds |
| 36 | Computing·numerical·kernel·... | 36 | Computing·numerical·kernel·... |
| 37 | ·····--·used· | 37 | ·····--·used·0·seconds |
| 38 | o7·=·a·"numerical·interpolation·table",·indicating | 38 | o7·=·a·"numerical·interpolation·table",·indicating |
| 39 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 | 39 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 |
| 40 | o7·:·NumericalInterpolationTable | 40 | o7·:·NumericalInterpolationTable |
| 41 | i8·:· | 41 | i8·:· |
| Offset 22, 12 lines modified | Offset 22, 12 lines modified | ||
| 22 | --·warning:·experimental·computation·over·inexact·field·begun | 22 | --·warning:·experimental·computation·over·inexact·field·begun |
| 23 | --··········results·not·reliable·(one·warning·given·per·session) | 23 | --··········results·not·reliable·(one·warning·given·per·session) |
| 24 | ·············1······70 | 24 | ·············1······70 |
| 25 | o8·:·Matrix·R··<--·R | 25 | o8·:·Matrix·R··<--·R |
| 26 | i9·:·time·numericalImageDim(F,·ideal·0_R) | 26 | i9·:·time·numericalImageDim(F,·ideal·0_R) |
| 27 | ·--·used·0.05 | 27 | ·--·used·0.0537996s·(cpu);·0.0529546s·(thread);·0s·(gc) |
| 28 | o9·=·69 | 28 | o9·=·69 |
| 29 | i10·:· | 29 | i10·:· |
| Offset 31, 15 lines modified | Offset 31, 15 lines modified | ||
| 31 | o5·:·Ideal·of·R | 31 | o5·:·Ideal·of·R |
| 32 | i6·:·I·=·I1·+·I2; | 32 | i6·:·I·=·I1·+·I2; |
| 33 | o6·:·Ideal·of·R | 33 | o6·:·Ideal·of·R |
| 34 | i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) | 34 | i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) |
| 35 | ·--·.5 | 35 | ·--·.54158s·elapsed |
| 36 | o7·=·p | 36 | o7·=·p |
| 37 | o7·:·Point | 37 | o7·:·Point |
| 38 | i8·:·matrix·pack(5,·p#Coordinates) | 38 | i8·:·matrix·pack(5,·p#Coordinates) |
| Offset 89, 19 lines modified | Offset 89, 19 lines modified | ||
| 89 | --··········results·not·reliable·(one·warning·given·per·session) | 89 | --··········results·not·reliable·(one·warning·given·per·session) |
| 90 | o4·=·true</code></pre> | 90 | o4·=·true</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) |
| 94 | Sampling·image·points·... | 94 | Sampling·image·points·... |
| 95 | ·····--·used·.0074 | 95 | ·····--·used·.00874157·seconds |
| 96 | Creating·interpolation·matrix·... | 96 | Creating·interpolation·matrix·... |
| 97 | ·····--·used·.00 | 97 | ·····--·used·.00695187·seconds |
| 98 | Performing·normalization·preconditioning·... | 98 | Performing·normalization·preconditioning·... |
| 99 | ·····--·used·.00399 | 99 | ·····--·used·.00399949·seconds |
| 100 | Computing·numerical·kernel·... | 100 | Computing·numerical·kernel·... |
| 101 | ·····--·used·0·seconds | 101 | ·····--·used·0·seconds |
| 102 | o5·=·a·"numerical·interpolation·table",·indicating | 102 | o5·=·a·"numerical·interpolation·table",·indicating |
| 103 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 | 103 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 |
| 104 | o5·:·NumericalInterpolationTable</code></pre> | 104 | o5·:·NumericalInterpolationTable</code></pre> |
| Offset 36, 19 lines modified | Offset 36, 19 lines modified | ||
| 36 | ==·0 | 36 | ==·0 |
| 37 | --·warning:·experimental·computation·over·inexact·field·begun | 37 | --·warning:·experimental·computation·over·inexact·field·begun |
| 38 | --··········results·not·reliable·(one·warning·given·per·session) | 38 | --··········results·not·reliable·(one·warning·given·per·session) |
| 39 | o4·=·true | 39 | o4·=·true |
| 40 | i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) | 40 | i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) |
| 41 | Sampling·image·points·... | 41 | Sampling·image·points·... |
| 42 | ·····--·used·.0074 | 42 | ·····--·used·.00874157·seconds |
| 43 | Creating·interpolation·matrix·... | 43 | Creating·interpolation·matrix·... |
| 44 | ·····--·used·.00 | 44 | ·····--·used·.00695187·seconds |
| 45 | Performing·normalization·preconditioning·... | 45 | Performing·normalization·preconditioning·... |
| 46 | ·····--·used·.00399 | 46 | ·····--·used·.00399949·seconds |
| 47 | Computing·numerical·kernel·... | 47 | Computing·numerical·kernel·... |
| 48 | ·····--·used·0·seconds | 48 | ·····--·used·0·seconds |
| 49 | o5·=·a·"numerical·interpolation·table",·indicating | 49 | o5·=·a·"numerical·interpolation·table",·indicating |
| 50 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 | 50 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 |
| 51 | o5·:·NumericalInterpolationTable | 51 | o5·:·NumericalInterpolationTable |
| Offset 105, 17 lines modified | Offset 105, 17 lines modified | ||
| 105 | ·············1······4 | 105 | ·············1······4 |
| 106 | o2·:·Matrix·R··<--·R</code></pre> | 106 | o2·:·Matrix·R··<--·R</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) | 109 | <td>··············<pre><code·class="language-macaulay2">i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) |
| 110 | Sampling·image·points·... | 110 | Sampling·image·points·... |
| 111 | ·····--·used·.00 | 111 | ·····--·used·.00532185·seconds |
| 112 | Creating·interpolation·matrix·... | 112 | Creating·interpolation·matrix·... |
| 113 | ·····--·used·.00 | 113 | ·····--·used·.00400877·seconds |
| 114 | Performing·normalization·preconditioning·... | 114 | Performing·normalization·preconditioning·... |
| 115 | ·····--·used·0·seconds | 115 | ·····--·used·0·seconds |
| 116 | Computing·numerical·kernel·... | 116 | Computing·numerical·kernel·... |
| 117 | ·····--·used·0·seconds | 117 | ·····--·used·0·seconds |
| 118 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| | 118 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| |
| Offset 41, 17 lines modified | Offset 41, 17 lines modified | ||
| 41 | o2·=·|·s3·s2t·st2·t3·| | 41 | o2·=·|·s3·s2t·st2·t3·| |
| 42 | ·············1······4 | 42 | ·············1······4 |
| 43 | o2·:·Matrix·R··<--·R | 43 | o2·:·Matrix·R··<--·R |
| 44 | i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) | 44 | i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) |
| 45 | Sampling·image·points·... | 45 | Sampling·image·points·... |
| 46 | ·····--·used·.00 | 46 | ·····--·used·.00532185·seconds |
| 47 | Creating·interpolation·matrix·... | 47 | Creating·interpolation·matrix·... |
| 48 | ·····--·used·.00 | 48 | ·····--·used·.00400877·seconds |
| 49 | Performing·normalization·preconditioning·... | 49 | Performing·normalization·preconditioning·... |
| 50 | ·····--·used·0·seconds | 50 | ·····--·used·0·seconds |
| 51 | Computing·numerical·kernel·... | 51 | Computing·numerical·kernel·... |
| 52 | ·····--·used·0·seconds | 52 | ·····--·used·0·seconds |
| 53 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| | 53 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| |
| Offset 114, 21 lines modified | Offset 114, 21 lines modified | ||
| 114 | ·············1······4 | 114 | ·············1······4 |
| 115 | o2·:·Matrix·R··<--·R</code></pre> | 115 | o2·:·Matrix·R··<--·R</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) | 118 | <td>··············<pre><code·class="language-macaulay2">i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) |
| 119 | Sampling·image·points·... | 119 | Sampling·image·points·... |
| 120 | ·····--·used·.0 | 120 | ·····--·used·.0112647·seconds |
| 121 | Creating·interpolation·matrix·... | 121 | Creating·interpolation·matrix·... |
| 122 | ·····--·used·.00 | 122 | ·····--·used·.00950867·seconds |
| 123 | Performing·normalization·preconditioning·... | 123 | Performing·normalization·preconditioning·... |
| 124 | ·····--·used·.0 | 124 | ·····--·used·.0103907·seconds |
| 125 | Computing·numerical·kernel·... | 125 | Computing·numerical·kernel·... |
| 126 | ·····--·used·.00 | 126 | ·····--·used·.000928911·seconds |
| 127 | o3·=·a·"numerical·interpolation·table",·indicating | 127 | o3·=·a·"numerical·interpolation·table",·indicating |
| 128 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 | 128 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 |
| 129 | o3·:·NumericalInterpolationTable</code></pre> | 129 | o3·:·NumericalInterpolationTable</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ········</table> | 131 | ········</table> |
| Offset 146, 19 lines modified | Offset 146, 19 lines modified | ||
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);</code></pre> | 148 | <td>··············<pre><code·class="language-macaulay2">i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);</code></pre> |
| 149 | </td>··········</tr> | 149 | </td>··········</tr> |
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) | 151 | <td>··············<pre><code·class="language-macaulay2">i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) |
| 152 | Creating·interpolation·matrix·... | 152 | Creating·interpolation·matrix·... |
| 153 | ·····--·used·.003 | 153 | ·····--·used·.00378994·seconds |
| 154 | Performing·normalization·preconditioning·... | 154 | Performing·normalization·preconditioning·... |
| 155 | ·····--·used·.00 | 155 | ·····--·used·.00816177·seconds |
| 156 | Computing·numerical·kernel·... | 156 | Computing·numerical·kernel·... |
| 157 | ·····--·used· | 157 | ·····--·used·0·seconds |
| 158 | o7·=·a·"numerical·interpolation·table",·indicating | 158 | o7·=·a·"numerical·interpolation·table",·indicating |
| 159 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 | 159 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 |
| 160 | o7·:·NumericalInterpolationTable</code></pre> | 160 | o7·:·NumericalInterpolationTable</code></pre> |
| 161 | </td>··········</tr> | 161 | </td>··········</tr> |
| 162 | ········</table> | 162 | ········</table> |
| Offset 60, 39 lines modified | Offset 60, 39 lines modified | ||
| 60 | o2·=·|·s3·s2t·st2·t3·| | 60 | o2·=·|·s3·s2t·st2·t3·| |
| 61 | ·············1······4 | 61 | ·············1······4 |
| 62 | o2·:·Matrix·R··<--·R | 62 | o2·:·Matrix·R··<--·R |
| 63 | i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) | 63 | i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) |
| 64 | Sampling·image·points·... | 64 | Sampling·image·points·... |
| 65 | ·····--·used·.0 | 65 | ·····--·used·.0112647·seconds |
| 66 | Creating·interpolation·matrix·... | 66 | Creating·interpolation·matrix·... |
| 67 | ·····--·used·.00 | 67 | ·····--·used·.00950867·seconds |
| 68 | Performing·normalization·preconditioning·... | 68 | Performing·normalization·preconditioning·... |
| 69 | ·····--·used·.0 | 69 | ·····--·used·.0103907·seconds |
| 70 | Computing·numerical·kernel·... | 70 | Computing·numerical·kernel·... |
| 71 | ·····--·used·.00 | 71 | ·····--·used·.000928911·seconds |
| 72 | o3·=·a·"numerical·interpolation·table",·indicating | 72 | o3·=·a·"numerical·interpolation·table",·indicating |
| 73 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 | 73 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 |
| 74 | o3·:·NumericalInterpolationTable | 74 | o3·:·NumericalInterpolationTable |
| 75 | The·following·example·computes·the·dimension·of·Plücker·quadrics·in·the | 75 | The·following·example·computes·the·dimension·of·Plücker·quadrics·in·the |
| 76 | defining·ideal·of·the·Grassmannian·$Gr(2,4)$·of·$P^1$'s·in·$P^3$,·in·the | 76 | defining·ideal·of·the·Grassmannian·$Gr(2,4)$·of·$P^1$'s·in·$P^3$,·in·the |
| 77 | ambient·space·$P^5$. | 77 | ambient·space·$P^5$. |
| 78 | i4·:·R·=·CC[x_(1,1)..x_(2,4)]; | 78 | i4·:·R·=·CC[x_(1,1)..x_(2,4)]; |
| 79 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; | 79 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; |
| 80 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); | 80 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); |
| 81 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) | 81 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) |
| 82 | Creating·interpolation·matrix·... | 82 | Creating·interpolation·matrix·... |
| 83 | ·····--·used·.003 | 83 | ·····--·used·.00378994·seconds |
| 84 | Performing·normalization·preconditioning·... | 84 | Performing·normalization·preconditioning·... |
| 85 | ·····--·used·.00 | 85 | ·····--·used·.00816177·seconds |
| 86 | Computing·numerical·kernel·... | 86 | Computing·numerical·kernel·... |
| 87 | ·····--·used· | 87 | ·····--·used·0·seconds |
| 88 | o7·=·a·"numerical·interpolation·table",·indicating | 88 | o7·=·a·"numerical·interpolation·table",·indicating |
| 89 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 | 89 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 |
| 90 | o7·:·NumericalInterpolationTable | 90 | o7·:·NumericalInterpolationTable |
| 91 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 91 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 92 | ····*·_\x8N_\x8u_\x8m_\x8e_\x8r_\x8i_\x8c_\x8a_\x8l_\x8I_\x8n_\x8t_\x8e_\x8r_\x8p_\x8o_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8T_\x8a_\x8b_\x8l_\x8e·--·the·class·of·all | 92 | ····*·_\x8N_\x8u_\x8m_\x8e_\x8r_\x8i_\x8c_\x8a_\x8l_\x8I_\x8n_\x8t_\x8e_\x8r_\x8p_\x8o_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8T_\x8a_\x8b_\x8l_\x8e·--·the·class·of·all |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 129 | --··········results·not·reliable·(one·warning·given·per·session) | 129 | --··········results·not·reliable·(one·warning·given·per·session) |
| 130 | ·············1······70 | 130 | ·············1······70 |
| 131 | o8·:·Matrix·R··<--·R</code></pre> | 131 | o8·:·Matrix·R··<--·R</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·numericalImageDim(F,·ideal·0_R) | 134 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·numericalImageDim(F,·ideal·0_R) |
| 135 | ·--·used·0.05 | 135 | ·--·used·0.0537996s·(cpu);·0.0529546s·(thread);·0s·(gc) |
| 136 | o9·=·69</code></pre> | 136 | o9·=·69</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| 139 | ······</div> | 139 | ······</div> |
| 140 | ······<div·class="waystouse"> | 140 | ······<div·class="waystouse"> |
| 141 | ········<h2>Ways·to·use·<span·class="tt">numericalImageDim</span>:</h2> | 141 | ········<h2>Ways·to·use·<span·class="tt">numericalImageDim</span>:</h2> |
| Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
| 46 | i8·:·F·=·sum(1..14,·i·->·basis(4,·R,·Variables=>toList(a_(i,1)..a_(i,5)))); | 46 | i8·:·F·=·sum(1..14,·i·->·basis(4,·R,·Variables=>toList(a_(i,1)..a_(i,5)))); |
| 47 | --·warning:·experimental·computation·over·inexact·field·begun | 47 | --·warning:·experimental·computation·over·inexact·field·begun |
| 48 | --··········results·not·reliable·(one·warning·given·per·session) | 48 | --··········results·not·reliable·(one·warning·given·per·session) |
| 49 | ·············1······70 | 49 | ·············1······70 |
| 50 | o8·:·Matrix·R··<--·R | 50 | o8·:·Matrix·R··<--·R |
| 51 | i9·:·time·numericalImageDim(F,·ideal·0_R) | 51 | i9·:·time·numericalImageDim(F,·ideal·0_R) |
| 52 | ·--·used·0.05 | 52 | ·--·used·0.0537996s·(cpu);·0.0529546s·(thread);·0s·(gc) |
| 53 | o9·=·69 | 53 | o9·=·69 |
| 54 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·n\x8nu\x8um\x8me\x8er\x8ri\x8ic\x8ca\x8al\x8lI\x8Im\x8ma\x8ag\x8ge\x8eD\x8Di\x8im\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8* | 54 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·n\x8nu\x8um\x8me\x8er\x8ri\x8ic\x8ca\x8al\x8lI\x8Im\x8ma\x8ag\x8ge\x8eD\x8Di\x8im\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 55 | ····*·numericalImageDim(List,Ideal) | 55 | ····*·numericalImageDim(List,Ideal) |
| 56 | ····*·numericalImageDim(List,Ideal,Point) | 56 | ····*·numericalImageDim(List,Ideal,Point) |
| 57 | ····*·numericalImageDim(Matrix,Ideal) | 57 | ····*·numericalImageDim(Matrix,Ideal) |
| 58 | ····*·numericalImageDim(Matrix,Ideal,Point) | 58 | ····*·numericalImageDim(Matrix,Ideal,Point) |
| Offset 123, 15 lines modified | Offset 123, 15 lines modified | ||
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·I1·+·I2; | 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·I1·+·I2; |
| 125 | o6·:·Ideal·of·R</code></pre> | 125 | o6·:·Ideal·of·R</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) | 128 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) |
| 129 | ·--·.5 | 129 | ·--·.54158s·elapsed |
| 130 | o7·=·p | 130 | o7·=·p |
| 131 | o7·:·Point</code></pre> | 131 | o7·:·Point</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i8·:·matrix·pack(5,·p#Coordinates) | 134 | <td>··············<pre><code·class="language-macaulay2">i8·:·matrix·pack(5,·p#Coordinates) |
| Offset 50, 15 lines modified | Offset 50, 15 lines modified | ||
| 50 | i5·:·I2·=·ideal·apply(entries·transpose·A,·row·->·sum(row,·v·->·v^2)·-·1); | 50 | i5·:·I2·=·ideal·apply(entries·transpose·A,·row·->·sum(row,·v·->·v^2)·-·1); |
| 51 | o5·:·Ideal·of·R | 51 | o5·:·Ideal·of·R |
| 52 | i6·:·I·=·I1·+·I2; | 52 | i6·:·I·=·I1·+·I2; |
| 53 | o6·:·Ideal·of·R | 53 | o6·:·Ideal·of·R |
| 54 | i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) | 54 | i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) |
| 55 | ·--·.5 | 55 | ·--·.54158s·elapsed |
| 56 | o7·=·p | 56 | o7·=·p |
| 57 | o7·:·Point | 57 | o7·:·Point |
| 58 | i8·:·matrix·pack(5,·p#Coordinates) | 58 | i8·:·matrix·pack(5,·p#Coordinates) |
| 59 | o8·=·|·.722359··.289465··-.295808··.591752··-.454678·| | 59 | o8·=·|·.722359··.289465··-.295808··.591752··-.454678·| |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=35 | 7 | #:len=35 |
| 8 | bnVtZXJpY2FsS2VybmVsKC4uLixUb2xlcmFuY2U9Pi4uLik= | 8 | bnVtZXJpY2FsS2VybmVsKC4uLixUb2xlcmFuY2U9Pi4uLik= |
| 9 | #:len=352 | 9 | #:len=352 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjE1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjE1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tudW1lcmljYWxLZXJuZWwsVG9sZXJhbmNlXSwibnVt | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tudW1lcmljYWxLZXJuZWwsVG9sZXJhbmNlXSwibnVt |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=32 | 7 | #:len=32 |
| 8 | UGllcmlSb290Q291bnQoLi4uLFZlcmJvc2U9Pi4uLik= | 8 | UGllcmlSb290Q291bnQoLi4uLFZlcmJvc2U9Pi4uLik= |
| 9 | #:len=334 | 9 | #:len=334 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmVxdWVzdCB2ZXJib3NlIGZlZWRiYWNr | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmVxdWVzdCB2ZXJib3NlIGZlZWRiYWNr |
| 11 | IiwgRGVzY3JpcHRpb24gPT4ge30sICJsaW5lbnVtIiA9PiAzMzMsIHN5bWJvbCBEb2N1bWVudFRh | 11 | IiwgRGVzY3JpcHRpb24gPT4ge30sICJsaW5lbnVtIiA9PiAzMzMsIHN5bWJvbCBEb2N1bWVudFRh |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=37 | 7 | #:len=37 |
| 8 | aGV1cmlzdGljU21vb3RobmVzcyguLi4sVmVyYm9zZT0+Li4uKQ== | 8 | aGV1cmlzdGljU21vb3RobmVzcyguLi4sVmVyYm9zZT0+Li4uKQ== |
| 9 | #:len=320 | 9 | #:len=320 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc0NCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc0NCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaGV1cmlzdGljU21vb3RobmVzcyxWZXJib3NlXSwi | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaGV1cmlzdGljU21vb3RobmVzcyxWZXJib3NlXSwi |
| Offset 14, 35 lines modified | Offset 14, 35 lines modified | ||
| 14 | i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a | 14 | i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a |
| 15 | o5·=·2 | 15 | o5·=·2 |
| 16 | i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true)) | 16 | i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true)) |
| 17 | unfolding | 17 | unfolding |
| 18 | ·--·. | 18 | ·--·.143497s·elapsed |
| 19 | flatteningRelations | 19 | flatteningRelations |
| 20 | ·--·. | 20 | ·--·.103154s·elapsed |
| 21 | next·gb | 21 | next·gb |
| 22 | ·--·.000 | 22 | ·--·.000912131s·elapsed |
| 23 | true | 23 | true |
| 24 | unfolding | 24 | unfolding |
| 25 | ·--·.09 | 25 | ·--·.0998286s·elapsed |
| 26 | flatteningRelations | 26 | flatteningRelations |
| 27 | ·--·.0 | 27 | ·--·.090158s·elapsed |
| 28 | next·gb | 28 | next·gb |
| 29 | ·--·.000 | 29 | ·--·.000639329s·elapsed |
| 30 | true | 30 | true |
| 31 | ·--·. | 31 | ·--·1.21935s·elapsed |
| 32 | o6·=·{} | 32 | o6·=·{} |
| 33 | o6·:·List | 33 | o6·:·List |
| 34 | i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0)) | 34 | i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0)) |
| 35 | ·--·. | 35 | ·--·1.18824s·elapsed |
| 36 | o7·=·{} | 36 | o7·=·{} |
| 37 | o7·:·List | 37 | o7·:·List |
| 38 | i8·:·LL7b=={} | 38 | i8·:·LL7b=={} |
| Offset 75, 22 lines modified | Offset 75, 22 lines modified | ||
| 75 | o10·:·Sequence | 75 | o10·:·Sequence |
| 76 | i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true) | 76 | i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true) |
| 77 | (13,·1) | 77 | (13,·1) |
| 78 | {5,·8,·11,·12} | 78 | {5,·8,·11,·12} |
| 79 | unfolding | 79 | unfolding |
| 80 | ·--·. | 80 | ·--·.24203s·elapsed |
| 81 | flatteningRelations | 81 | flatteningRelations |
| 82 | ·--·.09 | 82 | ·--·.109169s·elapsed |
| 83 | next·gb | 83 | next·gb |
| 84 | ·--·.00 | 84 | ·--·.00120054s·elapsed |
| 85 | true | 85 | true |
| 86 | ·--·. | 86 | ·--·.562357s·elapsed |
| 87 | (5,·8,··all·semigroups·are·smoothable)·--·. | 87 | (5,·8,··all·semigroups·are·smoothable)·--·.592698s·elapsed |
| 88 | o11·=·{} | 88 | o11·=·{} |
| 89 | o11·:·List | 89 | o11·:·List |
| 90 | i12·:·L={6,8,9,11} | 90 | i12·:·L={6,8,9,11} |
| Offset 100, 22 lines modified | Offset 100, 22 lines modified | ||
| 100 | o12·:·List | 100 | o12·:·List |
| 101 | i13·:·genus·L | 101 | i13·:·genus·L |
| 102 | o13·=·8 | 102 | o13·=·8 |
| 103 | i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true) | 103 | i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true) |
| 104 | ·--·.0 | 104 | ·--·.0579553s·elapsed |
| 105 | 6 | 105 | 6 |
| 106 | false | 106 | false |
| 107 | 5 | 107 | 5 |
| 108 | false | 108 | false |
| 109 | 4 | 109 | 4 |
| 110 | decompose | 110 | decompose |
| 111 | ·--·. | 111 | ·--·.259506s·elapsed |
| 112 | number·of·components:·2 | 112 | number·of·components:·2 |
| 113 | support·c,·codim·c:·{(1,·1),·(16,·3)} | 113 | support·c,·codim·c:·{(1,·1),·(16,·3)} |
| 114 | {0,·-1} | 114 | {0,·-1} |
| 115 | o14·=·true | 115 | o14·=·true |
| 116 | i15·:· | 116 | i15·:· |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i3·:·setRandomSeed·"some·singular·and·some·smooth·curves"; | 9 | i3·:·setRandomSeed·"some·singular·and·some·smooth·curves"; |
| 10 | i4·:·elapsedTime·tally·apply(10,i->·( | 10 | i4·:·elapsedTime·tally·apply(10,i->·( |
| 11 | ·············c=minors(2,random(S^2,S^{3:-2})); | 11 | ·············c=minors(2,random(S^2,S^{3:-2})); |
| 12 | ·············c=sub(c,x_0=>1); | 12 | ·············c=sub(c,x_0=>1); |
| 13 | ·············R=kk[support·c];c=sub(c,R); | 13 | ·············R=kk[support·c];c=sub(c,R); |
| 14 | ·············heuristicSmoothness·c)) | 14 | ·············heuristicSmoothness·c)) |
| 15 | ·--· | 15 | ·--·2.87674s·elapsed |
| 16 | o4·=·Tally{false·=>·6} | 16 | o4·=·Tally{false·=>·6} |
| 17 | ···········true·=>·4 | 17 | ···········true·=>·4 |
| 18 | o4·:·Tally | 18 | o4·:·Tally |
| 19 | i5·:· | 19 | i5·:· |
| Offset 7, 17 lines modified | Offset 7, 17 lines modified | ||
| 7 | o1·:·List | 7 | o1·:·List |
| 8 | i2·:·genus·L | 8 | i2·:·genus·L |
| 9 | o2·=·8 | 9 | o2·=·8 |
| 10 | i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0) | 10 | i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0) |
| 11 | ·--·. | 11 | ·--·.830321s·elapsed |
| 12 | o3·=·false | 12 | o3·=·false |
| 13 | i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0) | 13 | i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0) |
| 14 | ·--· | 14 | ·--·3.11095s·elapsed |
| 15 | o4·=·true | 15 | o4·=·true |
| 16 | i5·:· | 16 | i5·:· |
| Offset 7, 12 lines modified | Offset 7, 12 lines modified | ||
| 7 | o1·:·List | 7 | o1·:·List |
| 8 | i2·:·genus·L | 8 | i2·:·genus·L |
| 9 | o2·=·8 | 9 | o2·=·8 |
| 10 | i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15) | 10 | i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15) |
| 11 | ·--· | 11 | ·--·3.49781s·elapsed |
| 12 | o3·=·true | 12 | o3·=·true |
| 13 | i4·:· | 13 | i4·:· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·6860996532851631556 | 1 | --·-*-·M2-comint·-*-·hash:·6860996532851631556 |
| 2 | i1·:·elapsedTime·nonWeierstrassSemigroups(6,7) | 2 | i1·:·elapsedTime·nonWeierstrassSemigroups(6,7) |
| 3 | (6,·7,··all·semigroups·are·smoothable)·--·1. | 3 | (6,·7,··all·semigroups·are·smoothable)·--·1.38825s·elapsed |
| 4 | o1·=·{} | 4 | o1·=·{} |
| 5 | o1·:·List | 5 | o1·:·List |
| 6 | i2·:·LLdifficult={{6,·8,·9,·11}} | 6 | i2·:·LLdifficult={{6,·8,·9,·11}} |
| Offset 14, 61 lines modified | Offset 14, 61 lines modified | ||
| 14 | o2·:·List | 14 | o2·:·List |
| 15 | i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true) | 15 | i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true) |
| 16 | (17,·5) | 16 | (17,·5) |
| 17 | {6,·7,·8,·17} | 17 | {6,·7,·8,·17} |
| 18 | unfolding | 18 | unfolding |
| 19 | ·--·. | 19 | ·--·.40753s·elapsed |
| 20 | flatteningRelations | 20 | flatteningRelations |
| 21 | ·--·.1 | 21 | ·--·.139132s·elapsed |
| 22 | next·gb | 22 | next·gb |
| 23 | ·--·.001 | 23 | ·--·.00168577s·elapsed |
| 24 | true | 24 | true |
| 25 | ·--·. | 25 | ·--·.930714s·elapsed |
| 26 | {6,·7,·9,·17} | 26 | {6,·7,·9,·17} |
| 27 | unfolding | 27 | unfolding |
| 28 | ·--·. | 28 | ·--·.418757s·elapsed |
| 29 | flatteningRelations | 29 | flatteningRelations |
| 30 | ·--·.1 | 30 | ·--·.163901s·elapsed |
| 31 | next·gb | 31 | next·gb |
| 32 | ·--·.00 | 32 | ·--·.00250943s·elapsed |
| 33 | decompose | 33 | decompose |
| 34 | ·--·.1 | 34 | ·--·.170181s·elapsed |
| 35 | number·of·components:·2 | 35 | number·of·components:·2 |
| 36 | support·c,·codim·c:·{(2,·2),·(5,·2)} | 36 | support·c,·codim·c:·{(2,·2),·(5,·2)} |
| 37 | {0,·-1} | 37 | {0,·-1} |
| 38 | ·--·2. | 38 | ·--·2.57433s·elapsed |
| 39 | {6,·8,·9,·10} | 39 | {6,·8,·9,·10} |
| 40 | unfolding | 40 | unfolding |
| 41 | ·--·.0 | 41 | ·--·.092305s·elapsed |
| 42 | flatteningRelations | 42 | flatteningRelations |
| 43 | ·--·.1 | 43 | ·--·.142878s·elapsed |
| 44 | next·gb | 44 | next·gb |
| 45 | ·--·.000 | 45 | ·--·.000401443s·elapsed |
| 46 | true | 46 | true |
| 47 | ·--·. | 47 | ·--·.63324s·elapsed |
| 48 | {6,·8,·10,·11,·13} | 48 | {6,·8,·10,·11,·13} |
| 49 | unfolding | 49 | unfolding |
| 50 | ·--·. | 50 | ·--·.479438s·elapsed |
| 51 | flatteningRelations | 51 | flatteningRelations |
| 52 | ·--·. | 52 | ·--·.203942s·elapsed |
| 53 | next·gb | 53 | next·gb |
| 54 | ·--·.00 | 54 | ·--·.00423436s·elapsed |
| 55 | decompose | 55 | decompose |
| 56 | ·--·. | 56 | ·--·1.03515s·elapsed |
| 57 | number·of·components:·1 | 57 | number·of·components:·1 |
| 58 | support·c,·codim·c:·{(5,·1)} | 58 | support·c,·codim·c:·{(5,·1)} |
| 59 | {-1} | 59 | {-1} |
| 60 | ·--·2.82808s·elapsed | ||
| 60 | ·--· | 61 | ·--·6.96652s·elapsed |
| 61 | ·--·5.13833s·elapsed | ||
| 62 | 0 | 62 | 0 |
| 63 | ·--·.00000 | 63 | ·--·.000003557s·elapsed |
| 64 | ·--· | 64 | ·--·7.00242s·elapsed |
| 65 | {} | 65 | {} |
| 66 | o3·=·{{6,·8,·9,·11}} | 66 | o3·=·{{6,·8,·9,·11}} |
| 67 | o3·:·List | 67 | o3·:·List |
| 68 | i4·:· | 68 | i4·:· |
| Offset 89, 36 lines modified | Offset 89, 36 lines modified | ||
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a |
| 90 | o5·=·2</code></pre> | 90 | o5·=·2</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true)) | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0,Verbose=>true)) |
| 94 | unfolding | 94 | unfolding |
| 95 | ·--·. | 95 | ·--·.143497s·elapsed |
| 96 | flatteningRelations | 96 | flatteningRelations |
| 97 | ·--·. | 97 | ·--·.103154s·elapsed |
| 98 | next·gb | 98 | next·gb |
| 99 | ·--·.000 | 99 | ·--·.000912131s·elapsed |
| 100 | true | 100 | true |
| 101 | unfolding | 101 | unfolding |
| 102 | ·--·.09 | 102 | ·--·.0998286s·elapsed |
| 103 | flatteningRelations | 103 | flatteningRelations |
| 104 | ·--·.0 | 104 | ·--·.090158s·elapsed |
| 105 | next·gb | 105 | next·gb |
| 106 | ·--·.000 | 106 | ·--·.000639329s·elapsed |
| 107 | true | 107 | true |
| 108 | ·--·. | 108 | ·--·1.21935s·elapsed |
| 109 | o6·=·{} | 109 | o6·=·{} |
| 110 | o6·:·List</code></pre> | 110 | o6·:·List</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0)) | 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0)) |
| 114 | ·--·. | 114 | ·--·1.18824s·elapsed |
| 115 | o7·=·{} | 115 | o7·=·{} |
| 116 | o7·:·List</code></pre> | 116 | o7·:·List</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i8·:·LL7b=={} | 119 | <td>··············<pre><code·class="language-macaulay2">i8·:·LL7b=={} |
| Offset 167, 22 lines modified | Offset 167, 22 lines modified | ||
| 167 | o10·:·Sequence</code></pre> | 167 | o10·:·Sequence</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true) | 170 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true) |
| 171 | (13,·1) | 171 | (13,·1) |
| 172 | {5,·8,·11,·12} | 172 | {5,·8,·11,·12} |
| 173 | unfolding | 173 | unfolding |
| 174 | ·--·. | 174 | ·--·.24203s·elapsed |
| 175 | flatteningRelations | 175 | flatteningRelations |
| 176 | ·--·.09 | 176 | ·--·.109169s·elapsed |
| 177 | next·gb | 177 | next·gb |
| 178 | ·--·.00 | 178 | ·--·.00120054s·elapsed |
| 179 | true | 179 | true |
| 180 | ·--·. | 180 | ·--·.562357s·elapsed |
| 181 | (5,·8,··all·semigroups·are·smoothable)·--·. | 181 | (5,·8,··all·semigroups·are·smoothable)·--·.592698s·elapsed |
| 182 | o11·=·{} | 182 | o11·=·{} |
| 183 | o11·:·List</code></pre> | 183 | o11·:·List</code></pre> |
| 184 | </td>··········</tr> | 184 | </td>··········</tr> |
| 185 | ········</table> | 185 | ········</table> |
| Offset 200, 22 lines modified | Offset 200, 22 lines modified | ||
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i13·:·genus·L | 201 | <td>··············<pre><code·class="language-macaulay2">i13·:·genus·L |
| 202 | o13·=·8</code></pre> | 202 | o13·=·8</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true) | 205 | <td>··············<pre><code·class="language-macaulay2">i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true) |
| 206 | ·--·.0 | 206 | ·--·.0579553s·elapsed |
| 207 | 6 | 207 | 6 |
| 208 | false | 208 | false |
| 209 | 5 | 209 | 5 |
| 210 | false | 210 | false |
| 211 | 4 | 211 | 4 |
| 212 | decompose | 212 | decompose |
| 213 | ·--·. | 213 | ·--·.259506s·elapsed |
| 214 | number·of·components:·2 | 214 | number·of·components:·2 |
| 215 | support·c,·codim·c:·{(1,·1),·(16,·3)} | 215 | support·c,·codim·c:·{(1,·1),·(16,·3)} |
| 216 | {0,·-1} | 216 | {0,·-1} |
| 217 | o14·=·true</code></pre> | 217 | o14·=·true</code></pre> |
| 218 | </td>··········</tr> | 218 | </td>··········</tr> |
| 219 | ········</table> | 219 | ········</table> |
| Offset 27, 34 lines modified | Offset 27, 34 lines modified | ||
| 27 | o3·=·39 | 27 | o3·=·39 |
| 28 | i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a | 28 | i4·:·LL7a=select(LL7,L->not·knownExample·L);#LL7a |
| 29 | o5·=·2 | 29 | o5·=·2 |
| 30 | i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup | 30 | i6·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup |
| 31 | (L,0.25,0,Verbose=>true)) | 31 | (L,0.25,0,Verbose=>true)) |
| 32 | unfolding | 32 | unfolding |
| 33 | ·--·. | 33 | ·--·.143497s·elapsed |
| 34 | flatteningRelations | 34 | flatteningRelations |
| 35 | ·--·. | 35 | ·--·.103154s·elapsed |
| 36 | next·gb | 36 | next·gb |
| 37 | ·--·.000 | 37 | ·--·.000912131s·elapsed |
| 38 | true | 38 | true |
| 39 | unfolding | 39 | unfolding |
| 40 | ·--·.09 | 40 | ·--·.0998286s·elapsed |
| 41 | flatteningRelations | 41 | flatteningRelations |
| 42 | ·--·.0 | 42 | ·--·.090158s·elapsed |
| 43 | next·gb | 43 | next·gb |
| 44 | ·--·.000 | 44 | ·--·.000639329s·elapsed |
| 45 | true | 45 | true |
| 46 | ·--·. | 46 | ·--·1.21935s·elapsed |
| 47 | o6·=·{} | 47 | o6·=·{} |
| 48 | o6·:·List | 48 | o6·:·List |
| 49 | i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0)) | 49 | i7·:·elapsedTime·LL7b=select(LL7a,L->not·isSmoothableSemigroup(L,0.25,0)) |
| 50 | ·--·. | 50 | ·--·1.18824s·elapsed |
| 51 | o7·=·{} | 51 | o7·=·{} |
| 52 | o7·:·List | 52 | o7·:·List |
| 53 | i8·:·LL7b=={} | 53 | i8·:·LL7b=={} |
| 54 | o8·=·true | 54 | o8·=·true |
| Offset 93, 22 lines modified | Offset 93, 22 lines modified | ||
| 93 | o10·=·(5,·8) | 93 | o10·=·(5,·8) |
| 94 | o10·:·Sequence | 94 | o10·:·Sequence |
| 95 | i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true) | 95 | i11·:·elapsedTime·nonWeierstrassSemigroups(m,g,Verbose=>true) |
| 96 | (13,·1) | 96 | (13,·1) |
| 97 | {5,·8,·11,·12} | 97 | {5,·8,·11,·12} |
| 98 | unfolding | 98 | unfolding |
| 99 | ·--·. | 99 | ·--·.24203s·elapsed |
| 100 | flatteningRelations | 100 | flatteningRelations |
| 101 | ·--·.09 | 101 | ·--·.109169s·elapsed |
| 102 | next·gb | 102 | next·gb |
| 103 | ·--·.00 | 103 | ·--·.00120054s·elapsed |
| 104 | true | 104 | true |
| 105 | ·--·. | 105 | ·--·.562357s·elapsed |
| 106 | (5,·8,··all·semigroups·are·smoothable)·--·. | 106 | (5,·8,··all·semigroups·are·smoothable)·--·.592698s·elapsed |
| 107 | o11·=·{} | 107 | o11·=·{} |
| 108 | o11·:·List | 108 | o11·:·List |
| 109 | In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further | 109 | In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further |
| 110 | information.·The·first·line,·(13,1),·indicates·that·there·13·semigroups·of | 110 | information.·The·first·line,·(13,1),·indicates·that·there·13·semigroups·of |
| Offset 121, 22 lines modified | Offset 121, 22 lines modified | ||
| 121 | o12·=·{6,·8,·9,·11} | 121 | o12·=·{6,·8,·9,·11} |
| 122 | o12·:·List | 122 | o12·:·List |
| 123 | i13·:·genus·L | 123 | i13·:·genus·L |
| 124 | o13·=·8 | 124 | o13·=·8 |
| 125 | i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true) | 125 | i14·:·isWeierstrassSemigroup(L,0.2,Verbose=>true) |
| 126 | ·--·.0 | 126 | ·--·.0579553s·elapsed |
| 127 | 6 | 127 | 6 |
| 128 | false | 128 | false |
| 129 | 5 | 129 | 5 |
| 130 | false | 130 | false |
| 131 | 4 | 131 | 4 |
| 132 | decompose | 132 | decompose |
| 133 | ·--·. | 133 | ·--·.259506s·elapsed |
| 134 | number·of·components:·2 | 134 | number·of·components:·2 |
| 135 | support·c,·codim·c:·{(1,·1),·(16,·3)} | 135 | support·c,·codim·c:·{(1,·1),·(16,·3)} |
| 136 | {0,·-1} | 136 | {0,·-1} |
| 137 | o14·=·true | 137 | o14·=·true |
| 138 | The·first·integer,·6,·tells·that·in·this·attempt·deformation·parameters·of | 138 | The·first·integer,·6,·tells·that·in·this·attempt·deformation·parameters·of |
| 139 | degree·>=·6·were·used·and·no·smooth·fiber·was·found.·Finally·with·all | 139 | degree·>=·6·were·used·and·no·smooth·fiber·was·found.·Finally·with·all |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·tally·apply(10,i->·( | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·tally·apply(10,i->·( |
| 94 | ·············c=minors(2,random(S^2,S^{3:-2})); | 94 | ·············c=minors(2,random(S^2,S^{3:-2})); |
| 95 | ·············c=sub(c,x_0=>1); | 95 | ·············c=sub(c,x_0=>1); |
| 96 | ·············R=kk[support·c];c=sub(c,R); | 96 | ·············R=kk[support·c];c=sub(c,R); |
| 97 | ·············heuristicSmoothness·c)) | 97 | ·············heuristicSmoothness·c)) |
| 98 | ·--· | 98 | ·--·2.87674s·elapsed |
| 99 | o4·=·Tally{false·=>·6} | 99 | o4·=·Tally{false·=>·6} |
| 100 | ···········true·=>·4 | 100 | ···········true·=>·4 |
| 101 | o4·:·Tally</code></pre> | 101 | o4·:·Tally</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ········</table> | 103 | ········</table> |
| Offset 26, 15 lines modified | Offset 26, 15 lines modified | ||
| 26 | o2·:·PolynomialRing | 26 | o2·:·PolynomialRing |
| 27 | i3·:·setRandomSeed·"some·singular·and·some·smooth·curves"; | 27 | i3·:·setRandomSeed·"some·singular·and·some·smooth·curves"; |
| 28 | i4·:·elapsedTime·tally·apply(10,i->·( | 28 | i4·:·elapsedTime·tally·apply(10,i->·( |
| 29 | ·············c=minors(2,random(S^2,S^{3:-2})); | 29 | ·············c=minors(2,random(S^2,S^{3:-2})); |
| 30 | ·············c=sub(c,x_0=>1); | 30 | ·············c=sub(c,x_0=>1); |
| 31 | ·············R=kk[support·c];c=sub(c,R); | 31 | ·············R=kk[support·c];c=sub(c,R); |
| 32 | ·············heuristicSmoothness·c)) | 32 | ·············heuristicSmoothness·c)) |
| 33 | ·--· | 33 | ·--·2.87674s·elapsed |
| 34 | o4·=·Tally{false·=>·6} | 34 | o4·=·Tally{false·=>·6} |
| 35 | ···········true·=>·4 | 35 | ···········true·=>·4 |
| 36 | o4·:·Tally | 36 | o4·:·Tally |
| 37 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8cS\x8Sm\x8mo\x8oo\x8ot\x8th\x8hn\x8ne\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 37 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·h\x8he\x8eu\x8ur\x8ri\x8is\x8st\x8ti\x8ic\x8cS\x8Sm\x8mo\x8oo\x8ot\x8th\x8hn\x8ne\x8es\x8ss\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 38 | ····*·heuristicSmoothness(Ideal) | 38 | ····*·heuristicSmoothness(Ideal) |
| Offset 95, 21 lines modified | Offset 95, 21 lines modified | ||
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·genus·L | 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·genus·L |
| 97 | o2·=·8</code></pre> | 97 | o2·=·8</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0) | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0) |
| 101 | ·--·. | 101 | ·--·.830321s·elapsed |
| 102 | o3·=·false</code></pre> | 102 | o3·=·false</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0) | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0) |
| 106 | ·--· | 106 | ·--·3.11095s·elapsed |
| 107 | o4·=·true</code></pre> | 107 | o4·=·true</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ······</div> | 110 | ······</div> |
| 111 | ······<div> | 111 | ······<div> |
| 112 | ········<h2>See·also</h2> | 112 | ········<h2>See·also</h2> |
| Offset 30, 19 lines modified | Offset 30, 19 lines modified | ||
| 30 | o1·=·{6,·8,·9,·11} | 30 | o1·=·{6,·8,·9,·11} |
| 31 | o1·:·List | 31 | o1·:·List |
| 32 | i2·:·genus·L | 32 | i2·:·genus·L |
| 33 | o2·=·8 | 33 | o2·=·8 |
| 34 | i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0) | 34 | i3·:·elapsedTime·isSmoothableSemigroup(L,0.30,0) |
| 35 | ·--·. | 35 | ·--·.830321s·elapsed |
| 36 | o3·=·false | 36 | o3·=·false |
| 37 | i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0) | 37 | i4·:·elapsedTime·isSmoothableSemigroup(L,0.14,0) |
| 38 | ·--· | 38 | ·--·3.11095s·elapsed |
| 39 | o4·=·true | 39 | o4·=·true |
| 40 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 40 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 41 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal | 41 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal |
| 42 | ······with·positive·degree·parameters | 42 | ······with·positive·degree·parameters |
| 43 | ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding | 43 | ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding |
| 44 | ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of | 44 | ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of |
| Offset 93, 15 lines modified | Offset 93, 15 lines modified | ||
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·genus·L | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·genus·L |
| 95 | o2·=·8</code></pre> | 95 | o2·=·8</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15) | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15) |
| 99 | ·--· | 99 | ·--·3.49781s·elapsed |
| 100 | o3·=·true</code></pre> | 100 | o3·=·true</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ········</table> | 102 | ········</table> |
| 103 | ······</div> | 103 | ······</div> |
| 104 | ······<div> | 104 | ······<div> |
| 105 | ········<h2>See·also</h2> | 105 | ········<h2>See·also</h2> |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | o1·=·{6,·8,·9,·11} | 30 | o1·=·{6,·8,·9,·11} |
| 31 | o1·:·List | 31 | o1·:·List |
| 32 | i2·:·genus·L | 32 | i2·:·genus·L |
| 33 | o2·=·8 | 33 | o2·=·8 |
| 34 | i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15) | 34 | i3·:·elapsedTime·isWeierstrassSemigroup(L,0.15) |
| 35 | ·--· | 35 | ·--·3.49781s·elapsed |
| 36 | o3·=·true | 36 | o3·=·true |
| 37 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 37 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 38 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal | 38 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8U_\x8n_\x8f_\x8o_\x8l_\x8d_\x8i_\x8n_\x8g·--·Makes·the·universal·homogeneous·unfolding·of·an·ideal |
| 39 | ······with·positive·degree·parameters | 39 | ······with·positive·degree·parameters |
| 40 | ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding | 40 | ····*·_\x8f_\x8l_\x8a_\x8t_\x8t_\x8e_\x8n_\x8i_\x8n_\x8g_\x8R_\x8e_\x8l_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·--·Compute·the·flattening·relations·of·an·unfolding |
| 41 | ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of | 41 | ····*·_\x8g_\x8e_\x8t_\x8F_\x8l_\x8a_\x8t_\x8F_\x8a_\x8m_\x8i_\x8l_\x8y·--·Compute·the·flat·family·depending·on·a·subset·of |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | ········<h2>Description</h2> | 82 | ········<h2>Description</h2> |
| 83 | ········<div> | 83 | ········<div> |
| 84 | ··········<p>We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no·smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In·this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is·particular·heavy·are·excluded.</p> | 84 | ··········<p>We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no·smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In·this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is·particular·heavy·are·excluded.</p> |
| 85 | ········</div> | 85 | ········</div> |
| 86 | ········<table·class="examples"> | 86 | ········<table·class="examples"> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nonWeierstrassSemigroups(6,7) | 88 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nonWeierstrassSemigroups(6,7) |
| 89 | (6,·7,··all·semigroups·are·smoothable)·--·1. | 89 | (6,·7,··all·semigroups·are·smoothable)·--·1.38825s·elapsed |
| 90 | o1·=·{} | 90 | o1·=·{} |
| 91 | o1·:·List</code></pre> | 91 | o1·:·List</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| Offset 101, 61 lines modified | Offset 101, 61 lines modified | ||
| 101 | o2·:·List</code></pre> | 101 | o2·:·List</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true) | 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true) |
| 105 | (17,·5) | 105 | (17,·5) |
| 106 | {6,·7,·8,·17} | 106 | {6,·7,·8,·17} |
| 107 | unfolding | 107 | unfolding |
| 108 | ·--·. | 108 | ·--·.40753s·elapsed |
| 109 | flatteningRelations | 109 | flatteningRelations |
| 110 | ·--·.1 | 110 | ·--·.139132s·elapsed |
| 111 | next·gb | 111 | next·gb |
| 112 | ·--·.001 | 112 | ·--·.00168577s·elapsed |
| 113 | true | 113 | true |
| 114 | ·--·. | 114 | ·--·.930714s·elapsed |
| 115 | {6,·7,·9,·17} | 115 | {6,·7,·9,·17} |
| 116 | unfolding | 116 | unfolding |
| 117 | ·--·. | 117 | ·--·.418757s·elapsed |
| 118 | flatteningRelations | 118 | flatteningRelations |
| 119 | ·--·.1 | 119 | ·--·.163901s·elapsed |
| 120 | next·gb | 120 | next·gb |
| 121 | ·--·.00 | 121 | ·--·.00250943s·elapsed |
| 122 | decompose | 122 | decompose |
| 123 | ·--·.1 | 123 | ·--·.170181s·elapsed |
| 124 | number·of·components:·2 | 124 | number·of·components:·2 |
| 125 | support·c,·codim·c:·{(2,·2),·(5,·2)} | 125 | support·c,·codim·c:·{(2,·2),·(5,·2)} |
| 126 | {0,·-1} | 126 | {0,·-1} |
| 127 | ·--·2. | 127 | ·--·2.57433s·elapsed |
| 128 | {6,·8,·9,·10} | 128 | {6,·8,·9,·10} |
| 129 | unfolding | 129 | unfolding |
| 130 | ·--·.0 | 130 | ·--·.092305s·elapsed |
| 131 | flatteningRelations | 131 | flatteningRelations |
| 132 | ·--·.1 | 132 | ·--·.142878s·elapsed |
| 133 | next·gb | 133 | next·gb |
| 134 | ·--·.000 | 134 | ·--·.000401443s·elapsed |
| 135 | true | 135 | true |
| 136 | ·--·. | 136 | ·--·.63324s·elapsed |
| 137 | {6,·8,·10,·11,·13} | 137 | {6,·8,·10,·11,·13} |
| 138 | unfolding | 138 | unfolding |
| 139 | ·--·. | 139 | ·--·.479438s·elapsed |
| 140 | flatteningRelations | 140 | flatteningRelations |
| 141 | ·--·. | 141 | ·--·.203942s·elapsed |
| 142 | next·gb | 142 | next·gb |
| 143 | ·--·.00 | 143 | ·--·.00423436s·elapsed |
| 144 | decompose | 144 | decompose |
| 145 | ·--·. | 145 | ·--·1.03515s·elapsed |
| 146 | number·of·components:·1 | 146 | number·of·components:·1 |
| 147 | support·c,·codim·c:·{(5,·1)} | 147 | support·c,·codim·c:·{(5,·1)} |
| 148 | {-1} | 148 | {-1} |
| 149 | ·--·2.82808s·elapsed | ||
| 149 | ·--· | 150 | ·--·6.96652s·elapsed |
| 150 | ·--·5.13833s·elapsed | ||
| 151 | 0 | 151 | 0 |
| 152 | ·--·.00000 | 152 | ·--·.000003557s·elapsed |
| 153 | ·--· | 153 | ·--·7.00242s·elapsed |
| 154 | {} | 154 | {} |
| 155 | o3·=·{{6,·8,·9,·11}} | 155 | o3·=·{{6,·8,·9,·11}} |
| 156 | o3·:·List</code></pre> | 156 | o3·:·List</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ········</table> | 158 | ········</table> |
| Offset 22, 76 lines modified | Offset 22, 76 lines modified | ||
| 22 | ············LLdifficult | 22 | ············LLdifficult |
| 23 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 23 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 24 | We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no | 24 | We·test·which·semigroups·of·multiplicity·m·and·genus·g·are·smoothable.·If·no |
| 25 | smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In | 25 | smoothing·was·found·then·L·is·a·candidate·for·a·non·Weierstrass·semigroup.·In |
| 26 | this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is | 26 | this·search·certain·semigroups·L·in·LLdifficult,·where·the·computation·is |
| 27 | particular·heavy·are·excluded. | 27 | particular·heavy·are·excluded. |
| 28 | i1·:·elapsedTime·nonWeierstrassSemigroups(6,7) | 28 | i1·:·elapsedTime·nonWeierstrassSemigroups(6,7) |
| 29 | (6,·7,··all·semigroups·are·smoothable)·--·1. | 29 | (6,·7,··all·semigroups·are·smoothable)·--·1.38825s·elapsed |
| 30 | o1·=·{} | 30 | o1·=·{} |
| 31 | o1·:·List | 31 | o1·:·List |
| 32 | i2·:·LLdifficult={{6,·8,·9,·11}} | 32 | i2·:·LLdifficult={{6,·8,·9,·11}} |
| 33 | o2·=·{{6,·8,·9,·11}} | 33 | o2·=·{{6,·8,·9,·11}} |
| 34 | o2·:·List | 34 | o2·:·List |
| 35 | i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true) | 35 | i3·:·elapsedTime·nonWeierstrassSemigroups(6,8,LLdifficult,Verbose=>true) |
| 36 | (17,·5) | 36 | (17,·5) |
| 37 | {6,·7,·8,·17} | 37 | {6,·7,·8,·17} |
| 38 | unfolding | 38 | unfolding |
| 39 | ·--·. | 39 | ·--·.40753s·elapsed |
| 40 | flatteningRelations | 40 | flatteningRelations |
| 41 | ·--·.1 | 41 | ·--·.139132s·elapsed |
| 42 | next·gb | 42 | next·gb |
| 43 | ·--·.001 | 43 | ·--·.00168577s·elapsed |
| 44 | true | 44 | true |
| 45 | ·--·. | 45 | ·--·.930714s·elapsed |
| 46 | {6,·7,·9,·17} | 46 | {6,·7,·9,·17} |
| 47 | unfolding | 47 | unfolding |
| 48 | ·--·. | 48 | ·--·.418757s·elapsed |
| 49 | flatteningRelations | 49 | flatteningRelations |
| 50 | ·--·.1 | 50 | ·--·.163901s·elapsed |
| 51 | next·gb | 51 | next·gb |
| 52 | ·--·.00 | 52 | ·--·.00250943s·elapsed |
| 53 | decompose | 53 | decompose |
| 54 | ·--·.1 | 54 | ·--·.170181s·elapsed |
| 55 | number·of·components:·2 | 55 | number·of·components:·2 |
| 56 | support·c,·codim·c:·{(2,·2),·(5,·2)} | 56 | support·c,·codim·c:·{(2,·2),·(5,·2)} |
| 57 | {0,·-1} | 57 | {0,·-1} |
| 58 | ·--·2. | 58 | ·--·2.57433s·elapsed |
| 59 | {6,·8,·9,·10} | 59 | {6,·8,·9,·10} |
| 60 | unfolding | 60 | unfolding |
| 61 | ·--·.0 | 61 | ·--·.092305s·elapsed |
| 62 | flatteningRelations | 62 | flatteningRelations |
| 63 | ·--·.1 | 63 | ·--·.142878s·elapsed |
| 64 | next·gb | 64 | next·gb |
| 65 | ·--·.000 | 65 | ·--·.000401443s·elapsed |
| 66 | true | 66 | true |
| 67 | ·--·. | 67 | ·--·.63324s·elapsed |
| 68 | {6,·8,·10,·11,·13} | 68 | {6,·8,·10,·11,·13} |
| 69 | unfolding | 69 | unfolding |
| 70 | ·--·. | 70 | ·--·.479438s·elapsed |
| 71 | flatteningRelations | 71 | flatteningRelations |
| 72 | ·--·. | 72 | ·--·.203942s·elapsed |
| 73 | next·gb | 73 | next·gb |
| 74 | ·--·.00 | 74 | ·--·.00423436s·elapsed |
| 75 | decompose | 75 | decompose |
| 76 | ·--·. | 76 | ·--·1.03515s·elapsed |
| 77 | number·of·components:·1 | 77 | number·of·components:·1 |
| 78 | support·c,·codim·c:·{(5,·1)} | 78 | support·c,·codim·c:·{(5,·1)} |
| 79 | {-1} | 79 | {-1} |
| 80 | ·--·2.82808s·elapsed | ||
| 80 | ·--· | 81 | ·--·6.96652s·elapsed |
| 81 | ·--·5.13833s·elapsed | ||
| 82 | 0 | 82 | 0 |
| 83 | ·--·.00000 | 83 | ·--·.000003557s·elapsed |
| 84 | ·--· | 84 | ·--·7.00242s·elapsed |
| 85 | {} | 85 | {} |
| 86 | o3·=·{{6,·8,·9,·11}} | 86 | o3·=·{{6,·8,·9,·11}} |
| 87 | o3·:·List | 87 | o3·:·List |
| 88 | In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further | 88 | In·the·verbose·mode·we·get·timings·of·various·computation·steps·and·further |
| 89 | information.·The·first·line,·(17,5),·indicates·that·there·17·semigroups·of | 89 | information.·The·first·line,·(17,5),·indicates·that·there·17·semigroups·of |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=29 | 7 | #:len=29 |
| 8 | dG9TdHJpbmcoUG9seW5vbWlhbE9JQWxnZWJyYSk= | 8 | dG9TdHJpbmcoUG9seW5vbWlhbE9JQWxnZWJyYSk= |
| 9 | #:len=1044 | 9 | #:len=1044 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheSBhIHBvbHlub21pYWwgT0kt | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheSBhIHBvbHlub21pYWwgT0kt |
| 11 | YWxnZWJyYSBpbiBjb25kZW5zZWQgZm9ybSIsICJsaW5lbnVtIiA9PiAxNTE2LCBJbnB1dHMgPT4g | 11 | YWxnZWJyYSBpbiBjb25kZW5zZWQgZm9ybSIsICJsaW5lbnVtIiA9PiAxNTE2LCBJbnB1dHMgPT4g |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·C·=·oiRes({b},·1) | 8 | i5·:·time·C·=·oiRes({b},·1) |
| 9 | ·--·used·0.1 | 9 | ·--·used·0.14129s·(cpu);·0.0957502s·(thread);·0s·(gc) |
| 10 | o5·=·0:·(e0,·{2},·{-2}) | 10 | o5·=·0:·(e0,·{2},·{-2}) |
| 11 | ·····1:·(e1,·{4,·4},·{-4,·-4}) | 11 | ·····1:·(e1,·{4,·4},·{-4,·-4}) |
| 12 | o5·:·OIResolution | 12 | o5·:·OIResolution |
| 13 | i6·:·C.dd_0 | 13 | i6·:·C.dd_0 |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·C·=·oiRes({b},·1); | 8 | i5·:·time·C·=·oiRes({b},·1); |
| 9 | ·--·used·0.1 | 9 | ·--·used·0.119386s·(cpu);·0.0866595s·(thread);·0s·(gc) |
| 10 | i6·:·C_0 | 10 | i6·:·C_0 |
| 11 | o6·=·Basis·symbol:·e0 | 11 | o6·=·Basis·symbol:·e0 |
| 12 | ·····Basis·element·widths:·{2} | 12 | ·····Basis·element·widths:·{2} |
| 13 | ·····Degree·shifts:·{-2} | 13 | ·····Degree·shifts:·{-2} |
| 14 | ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 14 | ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 8 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 9 | ·--·used·0. | 9 | ·--·used·0.30971s·(cpu);·0.231062s·(thread);·0s·(gc) |
| 10 | o5·=·0:·(e0,·{2},·{-2}) | 10 | o5·=·0:·(e0,·{2},·{-2}) |
| 11 | ·····1:·(e1,·{4},·{-4}) | 11 | ·····1:·(e1,·{4},·{-4}) |
| 12 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 12 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 13 | o5·:·OIResolution | 13 | o5·:·OIResolution |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·C·=·oiRes({b},·1); | 8 | i5·:·time·C·=·oiRes({b},·1); |
| 9 | ·--·used·0.1 | 9 | ·--·used·0.143174s·(cpu);·0.106642s·(thread);·0s·(gc) |
| 10 | i6·:·describeFull·C | 10 | i6·:·describeFull·C |
| 11 | o6·=·0:·Module:·Basis·symbol:·e0 | 11 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 12 | ················Basis·element·widths:·{2} | 12 | ················Basis·element·widths:·{2} |
| 13 | ················Degree·shifts:·{-2} | 13 | ················Degree·shifts:·{-2} |
| 14 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 14 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| Offset 21, 11 lines modified | Offset 21, 11 lines modified | ||
| 21 | ·····Differential:·Source:·(e0,·{2},·{-2})·Target:·(e,·{1,·1},·{0,·0}) | 21 | ·····Differential:·Source:·(e0,·{2},·{-2})·Target:·(e,·{1,·1},·{0,·0}) |
| 22 | ·····1:·Module:·Basis·symbol:·e1 | 22 | ·····1:·Module:·Basis·symbol:·e1 |
| 23 | ················Basis·element·widths:·{4,·4} | 23 | ················Basis·element·widths:·{4,·4} |
| 24 | ················Degree·shifts:·{-4,·-4} | 24 | ················Degree·shifts:·{-4,·-4} |
| 25 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 25 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| 26 | ················Monomial·order:·Lex | 26 | ················Monomial·order:·Lex |
| 27 | ·····Differential:·Source:·(e1,·{4,·4},·{-4,·-4})·Target:·(e0,·{2},·{-2}) | 27 | ·····Differential:·Source:·(e1,·{4,·4},·{-4,·-4})·Target:·(e0,·{2},·{-2}) |
| 28 | ···················Basis·element·images:·{-x···x···e0···········+·x···x···e0···········+·x···x···e0···········-·x···x···e0 | 28 | ···················Basis·element·images:·{0,·-x···x···e0···········+·x···x···e0···········+·x···x···e0···········-·x···x···e0··········} |
| 29 | ············································2,3·1,1··4,{2,·4},1····2,4·1,1··4,{2,·3},1····2,3·1,2··4,{1,·4},1····2,4·1,2··4,{1,·3},1 | 29 | ···············································2,3·1,1··4,{2,·4},1····2,4·1,1··4,{2,·3},1····2,3·1,2··4,{1,·4},1····2,4·1,2··4,{1,·3},1 |
| 30 | i7·:· | 30 | i7·:· |
| Offset 10, 21 lines modified | Offset 10, 18 lines modified | ||
| 10 | i5·:·C·=·oiRes({b},·2); | 10 | i5·:·C·=·oiRes({b},·2); |
| 11 | i6·:·phi·=·C.dd_1; | 11 | i6·:·phi·=·C.dd_1; |
| 12 | i7·:·describe·phi | 12 | i7·:·describe·phi |
| 13 | o7·=·Source:·(e1,·{5,·5},·{- | 13 | o7·=·Source:·(e1,·{5,·5},·{-4,·-3})·Target:·(e0,·{3},·{-2}) |
| 14 | ·····Basis·element·images:·{ | 14 | ·····Basis·element·images:·{x···x···e0··············-·x···x···e0············· |
| 15 | ······························ | 15 | ·····························2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1 |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ·····x···e0··············-·x···e0·············,·x···x···e0··············- | ||
| 18 | ····· | 17 | ·····-·x···x···e0··············+·x···x···e0·············,·-x···e0········ |
| 18 | ········2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1····2,2··5,{1,·3, | ||
| 19 | ·····------------------------------------------------------------------------ | 19 | ·····------------------------------------------------------------------------ |
| 20 | ··········+·x···e0··············+·x···e0··············-·x···e0·············} | ||
| 21 | ·····5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1····2,3··5,{1,·2,·4},1 | ||
| 20 | ·····x···x···e0··············-·x···x···e0··············+·x···x···e0········ | ||
| 21 | ······2,4·1,1··5,{2,·3,·5},1····2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3, | ||
| 22 | ·····------------------------------------------------------------------------ | ||
| 23 | ·········} | ||
| 24 | ·····5},1 | ||
| 25 | i8·:· | 22 | i8·:· |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·C·=·oiRes({b},·1); | 8 | i5·:·time·C·=·oiRes({b},·1); |
| 9 | ·--·used·0. | 9 | ·--·used·0.129141s·(cpu);·0.0923676s·(thread);·0s·(gc) |
| 10 | i6·:·describe·C | 10 | i6·:·describe·C |
| 11 | o6·=·0:·Module:·Basis·symbol:·e0 | 11 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 12 | ················Basis·element·widths:·{2} | 12 | ················Basis·element·widths:·{2} |
| 13 | ················Degree·shifts:·{-2} | 13 | ················Degree·shifts:·{-2} |
| 14 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 14 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| Offset 10, 19 lines modified | Offset 10, 19 lines modified | ||
| 10 | i5·:·C·=·oiRes({b},·2); | 10 | i5·:·C·=·oiRes({b},·2); |
| 11 | i6·:·phi·=·C.dd_1; | 11 | i6·:·phi·=·C.dd_1; |
| 12 | i7·:·image·phi | 12 | i7·:·image·phi |
| 13 | o7·=·{x···x···e0··············-·x···x···e0··············-·x···x···e0········ | ||
| 14 | 13 | o7·=·{-x···e0··············+·x···e0··············+·x···e0··············- | |
| 14 | ········2,2··5,{1,·3,·5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1·· | ||
| 15 | ·····------------------------------------------------------------------------ | 15 | ·····------------------------------------------------------------------------ |
| 16 | ··········+·x···x···e0·············,·-x···e0··············+·x···e0········ | ||
| 17 | ····· | 16 | ·····x···e0·············,·x···x···e0··············-·x···x···e0··············- |
| 17 | ······2,3··5,{1,·2,·4},1···2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1·· | ||
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ····· | 19 | ·····x···x···e0··············+·x···x···e0·············} |
| 20 | ····· | 20 | ······2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1 |
| 21 | o7·:·List | 21 | o7·:·List |
| 22 | i8·:· | 22 | i8·:· |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) | 8 | i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) |
| 9 | ·--·used·0.2 | 9 | ·--·used·0.28884s·(cpu);·0.208916s·(thread);·0s·(gc) |
| 10 | o5·=·0:·(e0,·{2},·{-2}) | 10 | o5·=·0:·(e0,·{2},·{-2}) |
| 11 | ·····1:·(e1,·{4},·{-4}) | 11 | ·····1:·(e1,·{4},·{-4}) |
| 12 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 12 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 13 | o5·:·OIResolution | 13 | o5·:·OIResolution |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); | 15 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); |
| 16 | i10·:·isOIGB·{b1,·b2} | 16 | i10·:·isOIGB·{b1,·b2} |
| 17 | o10·=·false | 17 | o10·=·false |
| 18 | i11·:·time·B·=·oiGB·{b1,·b2} | 18 | i11·:·time·B·=·oiGB·{b1,·b2} |
| 19 | ·--·used·0.01 | 19 | ·--·used·0.0199799s·(cpu);·0.0196231s·(thread);·0s·(gc) |
| 20 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 20 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 21 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· | 21 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· |
| 22 | ······----------------------------------------------------------------------- | 22 | ······----------------------------------------------------------------------- |
| 23 | ······x···x···x···e···········-·x···x···x···e··········} | 23 | ······x···x···x···e···········-·x···x···x···e··········} |
| 24 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 24 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | i5·:·installGeneratorsInWidth(F,·3); | 11 | i5·:·installGeneratorsInWidth(F,·3); |
| 12 | i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); | 12 | i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); |
| 13 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); | 13 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); |
| 14 | i10·:·time·B·=·oiGB·{b1,·b2} | 14 | i10·:·time·B·=·oiGB·{b1,·b2} |
| 15 | ·--·used·0.02 | 15 | ·--·used·0.0200118s·(cpu);·0.0226442s·(thread);·0s·(gc) |
| 16 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 16 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 17 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· | 17 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· |
| 18 | ······----------------------------------------------------------------------- | 18 | ······----------------------------------------------------------------------- |
| 19 | ······x···x···x···e···········-·x···x···x···e··········} | 19 | ······x···x···x···e···········-·x···x···x···e··········} |
| 20 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 20 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·C·=·oiRes({b},·1); | 8 | i5·:·time·C·=·oiRes({b},·1); |
| 9 | ·--·used·0.1 | 9 | ·--·used·0.120985s·(cpu);·0.0827037s·(thread);·0s·(gc) |
| 10 | i6·:·net·C | 10 | i6·:·net·C |
| 11 | o6·=·0:·(e0,·{2},·{-2}) | 11 | o6·=·0:·(e0,·{2},·{-2}) |
| 12 | ·····1:·(e1,·{4,·4},·{-4,·-4}) | 12 | ·····1:·(e1,·{4,·4},·{-4,·-4}) |
| 13 | i7·:· | 13 | i7·:· |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i4·:·installGeneratorsInWidth(F,·2); | 9 | i4·:·installGeneratorsInWidth(F,·2); |
| 10 | i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); | 10 | i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); |
| 11 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); | 11 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); |
| 12 | i9·:·time·oiGB·{b1,·b2} | 12 | i9·:·time·oiGB·{b1,·b2} |
| 13 | ·--·used·0.02 | 13 | ·--·used·0.0217364s·(cpu);·0.0241287s·(thread);·0s·(gc) |
| 14 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 14 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 15 | ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· | 15 | ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ·····x···x···x···e···········-·x···x···x···e··········} | 17 | ·····x···x···x···e···········-·x···x···x···e··········} |
| 18 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 18 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 5 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 6 | i3·:·installGeneratorsInWidth(F,·2); | 6 | i3·:·installGeneratorsInWidth(F,·2); |
| 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 7 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 8 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 8 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 9 | ·--·used·0. | 9 | ·--·used·0.310541s·(cpu);·0.241663s·(thread);·0s·(gc) |
| 10 | o5·=·0:·(e0,·{2},·{-2}) | 10 | o5·=·0:·(e0,·{2},·{-2}) |
| 11 | ·····1:·(e1,·{4},·{-4}) | 11 | ·····1:·(e1,·{4},·{-4}) |
| 12 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 12 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 13 | o5·:·OIResolution | 13 | o5·:·OIResolution |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i4·:·installGeneratorsInWidth(F,·2); | 9 | i4·:·installGeneratorsInWidth(F,·2); |
| 10 | i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2); | 10 | i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2); |
| 11 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2); | 11 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2); |
| 12 | i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) | 12 | i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) |
| 13 | ·--·used·0.1 | 13 | ·--·used·0.163458s·(cpu);·0.132119s·(thread);·0s·(gc) |
| 14 | ······································································· | 14 | ······································································· |
| 15 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, | 15 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, |
| 16 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2· | 16 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2· |
| 17 | ·····------------------------------------------------------------------------ | 17 | ·····------------------------------------------------------------------------ |
| 18 | ······2··················2 | 18 | ······2··················2 |
| 19 | ·····x···x···e········-·x···x···e·······} | 19 | ·····x···x···e········-·x···x···e·······} |
| Offset 13, 13 lines modified | Offset 13, 13 lines modified | ||
| 13 | ·································4 | 13 | ·································4 |
| 14 | o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2 | 14 | o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2 |
| 15 | ··········2,2···2,1···1,2···1,1 | 15 | ··········2,2···2,1···1,2···1,1 |
| 16 | i5·:·terms·f | 16 | i5·:·terms·f |
| 17 | o5·=·{ | 17 | o5·=·{x···e·······,·-x···e·······,·x···e·······,·-x···e·······} |
| 18 | ······· | 18 | ·······1,1·2,{1},1····1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2 |
| 19 | o5·:·List | 19 | o5·:·List |
| 20 | i6·:· | 20 | i6·:· |
| Offset 87, 49 lines modified | Offset 87, 49 lines modified | ||
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2);</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2);</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·C·=·oiRes({b},·2) | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·C·=·oiRes({b},·2) |
| 92 | o5·=·0:·(e0,·{3},·{-2}) | 92 | o5·=·0:·(e0,·{3},·{-2}) |
| 93 | ·····1:·(e1,·{5,·5},·{- | 93 | ·····1:·(e1,·{5,·5},·{-4,·-3}) |
| 94 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{- | 94 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{-4,·-3,·-3,·-2,·-4,·-5,·-4,·-5,·-5}) |
| 95 | o5·:·OIResolution</code></pre> | 95 | o5·:·OIResolution</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1 | 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1 |
| 99 | o6·=·Source:·(e1,·{5,·5},·{- | 99 | o6·=·Source:·(e1,·{5,·5},·{-4,·-3})·Target:·(e0,·{3},·{-2}) |
| 100 | o6·:·FreeOIModuleMap</code></pre> | 100 | o6·:·FreeOIModuleMap</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i7·:·G·=·getBasisElements·C_1 | 103 | <td>··············<pre><code·class="language-macaulay2">i7·:·G·=·getBasisElements·C_1 |
| 104 | o7·=·{1e1···················,·1e1···················} | 104 | o7·=·{1e1···················,·1e1···················} |
| 105 | ·········5,{1,·2,·3,·4,·5},1·····5,{1,·2,·3,·4,·5},2 | 105 | ·········5,{1,·2,·3,·4,·5},1·····5,{1,·2,·3,·4,·5},2 |
| 106 | o7·:·List</code></pre> | 106 | o7·:·List</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i8·:·phi·G#0 | 109 | <td>··············<pre><code·class="language-macaulay2">i8·:·phi·G#0 |
| 110 | o8·=·-x···e0··············+·x···e0··············+·x···e0··············-·x···e0 | ||
| 111 | ······· | 110 | o8·=·x···x···e0··············-·x···x···e0··············-·x···x···e0··············+·x···x···e0 |
| 111 | ······2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1····2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1 | ||
| 112 | ·····································································10 | 112 | ·····································································10 |
| 113 | o8·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in·width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} | 113 | o8·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in·width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} |
| 114 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1</code></pre> | 114 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i9·:·phi·G#1 | 117 | <td>··············<pre><code·class="language-macaulay2">i9·:·phi·G#1 |
| 118 | o9·=·x···x···e0··············-·x···x···e0··············-·x···x···e0··············+·x···x···e0 | ||
| 119 | 118 | o9·=·-x···e0··············+·x···e0··············+·x···e0··············-·x···e0 | |
| 119 | ·······2,2··5,{1,·3,·5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1····2,3··5,{1,·2,·4},1 | ||
| 120 | ·····································································10 | 120 | ·····································································10 |
| 121 | o9·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in·width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} | 121 | o9·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in·width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} |
| 122 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1</code></pre> | 122 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ········</table> | 124 | ········</table> |
| 125 | ······</div> | 125 | ······</div> |
| Offset 19, 45 lines modified | Offset 19, 45 lines modified | ||
| 19 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 19 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 20 | i2·:·F·=·makeFreeOIModule(e,·{1,2},·P); | 20 | i2·:·F·=·makeFreeOIModule(e,·{1,2},·P); |
| 21 | i3·:·installGeneratorsInWidth(F,·3); | 21 | i3·:·installGeneratorsInWidth(F,·3); |
| 22 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); | 22 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); |
| 23 | i5·:·C·=·oiRes({b},·2) | 23 | i5·:·C·=·oiRes({b},·2) |
| 24 | o5·=·0:·(e0,·{3},·{-2}) | 24 | o5·=·0:·(e0,·{3},·{-2}) |
| 25 | ·····1:·(e1,·{5,·5},·{- | 25 | ·····1:·(e1,·{5,·5},·{-4,·-3}) |
| 26 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{- | 26 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{-4,·-3,·-3,·-2,·-4,·-5,·-4,·-5,·-5}) |
| 27 | o5·:·OIResolution | 27 | o5·:·OIResolution |
| 28 | i6·:·phi·=·C.dd_1 | 28 | i6·:·phi·=·C.dd_1 |
| 29 | o6·=·Source:·(e1,·{5,·5},·{- | 29 | o6·=·Source:·(e1,·{5,·5},·{-4,·-3})·Target:·(e0,·{3},·{-2}) |
| 30 | o6·:·FreeOIModuleMap | 30 | o6·:·FreeOIModuleMap |
| 31 | i7·:·G·=·getBasisElements·C_1 | 31 | i7·:·G·=·getBasisElements·C_1 |
| 32 | o7·=·{1e1···················,·1e1···················} | 32 | o7·=·{1e1···················,·1e1···················} |
| 33 | ·········5,{1,·2,·3,·4,·5},1·····5,{1,·2,·3,·4,·5},2 | 33 | ·········5,{1,·2,·3,·4,·5},1·····5,{1,·2,·3,·4,·5},2 |
| 34 | o7·:·List | 34 | o7·:·List |
| 35 | i8·:·phi·G#0 | 35 | i8·:·phi·G#0 |
| 36 | o8·=·-x···e0··············+·x···e0··············+·x···e0··············-·x···e0 | ||
| 37 | ·······2,2··5,{1,·3,·5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1····2,3 | ||
| 38 | 36 | o8·=·x···x···e0··············-·x···x···e0··············-·x···x···e0 | |
| 37 | +·x···x···e0 | ||
| 38 | ······2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1····2,3·1,2··5,{1,·4, | ||
| 39 | 5},1····2,4·1,2··5,{1,·3,·5},1 | ||
| 39 | ·····································································10 | 40 | ·····································································10 |
| 40 | o8·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in | 41 | o8·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in |
| 41 | width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} | 42 | width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} |
| 42 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1 | 43 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1 |
| 43 | i9·:·phi·G#1 | 44 | i9·:·phi·G#1 |
| 45 | o9·=·-x···e0··············+·x···e0··············+·x···e0··············-·x···e0 | ||
| 46 | ·······2,2··5,{1,·3,·5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1····2,3 | ||
| 47 | 5,{1,·2,·4},1 | ||
| 44 | o9·=·x···x···e0··············-·x···x···e0··············-·x···x···e0 | ||
| 45 | +·x···x···e0 | ||
| 46 | ······2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1····2,3·1,2··5,{1,·4, | ||
| 47 | 5},1····2,4·1,2··5,{1,·3,·5},1 | ||
| 48 | ·····································································10 | 48 | ·····································································10 |
| 49 | o9·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in | 49 | o9·:·(QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···])···in |
| 50 | width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} | 50 | width·5,·degrees·{2,·2,·2,·2,·2,·2,·2,·2,·2,·2} |
| 51 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1 | 51 | ··········2,5···2,4···2,3···2,2···2,1···1,5···1,4···1,3···1,2···1,1 |
| 52 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 52 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 53 | ····*·_\x8F_\x8r_\x8e_\x8e_\x8O_\x8I_\x8M_\x8o_\x8d_\x8u_\x8l_\x8e_\x8M_\x8a_\x8p_\x8·_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h·--·apply·a·free·OI-module·map·to·an·element | 53 | ····*·_\x8F_\x8r_\x8e_\x8e_\x8O_\x8I_\x8M_\x8o_\x8d_\x8u_\x8l_\x8e_\x8M_\x8a_\x8p_\x8·_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h·--·apply·a·free·OI-module·map·to·an·element |
| Offset 58, 15 lines modified | Offset 58, 15 lines modified | ||
| 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 59 | </td>··········</tr> | 59 | </td>··········</tr> |
| 60 | ··········<tr> | 60 | ··········<tr> |
| 61 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 61 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1) | 64 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1) |
| 65 | ·--·used·0.1 | 65 | ·--·used·0.14129s·(cpu);·0.0957502s·(thread);·0s·(gc) |
| 66 | o5·=·0:·(e0,·{2},·{-2}) | 66 | o5·=·0:·(e0,·{2},·{-2}) |
| 67 | ·····1:·(e1,·{4,·4},·{-4,·-4}) | 67 | ·····1:·(e1,·{4,·4},·{-4,·-4}) |
| 68 | o5·:·OIResolution</code></pre> | 68 | o5·:·OIResolution</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | complex,·use·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x.·To·get·the·$n$th·differential·in·an·OI-resolution·C, | 11 | complex,·use·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x.·To·get·the·$n$th·differential·in·an·OI-resolution·C, |
| 12 | use·C.dd_n. | 12 | use·C.dd_n. |
| 13 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 13 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 14 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 14 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 15 | i3·:·installGeneratorsInWidth(F,·2); | 15 | i3·:·installGeneratorsInWidth(F,·2); |
| 16 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 16 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 17 | i5·:·time·C·=·oiRes({b},·1) | 17 | i5·:·time·C·=·oiRes({b},·1) |
| 18 | ·--·used·0.1 | 18 | ·--·used·0.14129s·(cpu);·0.0957502s·(thread);·0s·(gc) |
| 19 | o5·=·0:·(e0,·{2},·{-2}) | 19 | o5·=·0:·(e0,·{2},·{-2}) |
| 20 | ·····1:·(e1,·{4,·4},·{-4,·-4}) | 20 | ·····1:·(e1,·{4,·4},·{-4,·-4}) |
| 21 | o5·:·OIResolution | 21 | o5·:·OIResolution |
| 22 | i6·:·C.dd_0 | 22 | i6·:·C.dd_0 |
| Offset 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 91 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 92 | ·--·used·0.1 | 92 | ·--·used·0.119386s·(cpu);·0.0866595s·(thread);·0s·(gc)</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·C_0 | 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·C_0 |
| 96 | o6·=·Basis·symbol:·e0 | 96 | o6·=·Basis·symbol:·e0 |
| 97 | ·····Basis·element·widths:·{2} | 97 | ·····Basis·element·widths:·{2} |
| 98 | ·····Degree·shifts:·{-2} | 98 | ·····Degree·shifts:·{-2} |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | Returns·the·free·OI-module·of·$C$·in·homological·degree·$n$. | 18 | Returns·the·free·OI-module·of·$C$·in·homological·degree·$n$. |
| 19 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 19 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 20 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 20 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 21 | i3·:·installGeneratorsInWidth(F,·2); | 21 | i3·:·installGeneratorsInWidth(F,·2); |
| 22 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 22 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 23 | i5·:·time·C·=·oiRes({b},·1); | 23 | i5·:·time·C·=·oiRes({b},·1); |
| 24 | ·--·used·0.1 | 24 | ·--·used·0.119386s·(cpu);·0.0866595s·(thread);·0s·(gc) |
| 25 | i6·:·C_0 | 25 | i6·:·C_0 |
| 26 | o6·=·Basis·symbol:·e0 | 26 | o6·=·Basis·symbol:·e0 |
| 27 | ·····Basis·element·widths:·{2} | 27 | ·····Basis·element·widths:·{2} |
| 28 | ·····Degree·shifts:·{-2} | 28 | ·····Degree·shifts:·{-2} |
| 29 | ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 29 | ·····Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| 30 | ·····Monomial·order:·Lex | 30 | ·····Monomial·order:·Lex |
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| 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 58 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 59 | </td>··········</tr> | 59 | </td>··········</tr> |
| 60 | ··········<tr> | 60 | ··········<tr> |
| 61 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 61 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 64 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 65 | ·--·used·0. | 65 | ·--·used·0.30971s·(cpu);·0.231062s·(thread);·0s·(gc) |
| 66 | o5·=·0:·(e0,·{2},·{-2}) | 66 | o5·=·0:·(e0,·{2},·{-2}) |
| 67 | ·····1:·(e1,·{4},·{-4}) | 67 | ·····1:·(e1,·{4},·{-4}) |
| 68 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 68 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 69 | o5·:·OIResolution</code></pre> | 69 | o5·:·OIResolution</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | homological·degree·$n-1$·to·be·minimized.·Therefore,·use·TopNonminimal·=>·true | 11 | homological·degree·$n-1$·to·be·minimized.·Therefore,·use·TopNonminimal·=>·true |
| 12 | for·no·minimization·of·the·basis·in·degree·$n-1$. | 12 | for·no·minimization·of·the·basis·in·degree·$n-1$. |
| 13 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 13 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 14 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 14 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 15 | i3·:·installGeneratorsInWidth(F,·2); | 15 | i3·:·installGeneratorsInWidth(F,·2); |
| 16 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 16 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 17 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 17 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 18 | ·--·used·0. | 18 | ·--·used·0.30971s·(cpu);·0.231062s·(thread);·0s·(gc) |
| 19 | o5·=·0:·(e0,·{2},·{-2}) | 19 | o5·=·0:·(e0,·{2},·{-2}) |
| 20 | ·····1:·(e1,·{4},·{-4}) | 20 | ·····1:·(e1,·{4},·{-4}) |
| 21 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 21 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 22 | o5·:·OIResolution | 22 | o5·:·OIResolution |
| 23 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·T\x8To\x8op\x8pN\x8No\x8on\x8nm\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* | 23 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8un\x8nc\x8ct\x8ti\x8io\x8on\x8ns\x8s·w\x8wi\x8it\x8th\x8h·o\x8op\x8pt\x8ti\x8io\x8on\x8na\x8al\x8l·a\x8ar\x8rg\x8gu\x8um\x8me\x8en\x8nt\x8t·n\x8na\x8am\x8me\x8ed\x8d·T\x8To\x8op\x8pN\x8No\x8on\x8nm\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 88 | ·--·used·0.1 | 88 | ·--·used·0.143174s·(cpu);·0.106642s·(thread);·0s·(gc)</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i6·:·describeFull·C | 91 | <td>··············<pre><code·class="language-macaulay2">i6·:·describeFull·C |
| 92 | o6·=·0:·Module:·Basis·symbol:·e0 | 92 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 93 | ················Basis·element·widths:·{2} | 93 | ················Basis·element·widths:·{2} |
| 94 | ················Degree·shifts:·{-2} | 94 | ················Degree·shifts:·{-2} |
| Offset 98, 16 lines modified | Offset 98, 16 lines modified | ||
| 98 | ·····Differential:·Source:·(e0,·{2},·{-2})·Target:·(e,·{1,·1},·{0,·0}) | 98 | ·····Differential:·Source:·(e0,·{2},·{-2})·Target:·(e,·{1,·1},·{0,·0}) |
| 99 | ·····1:·Module:·Basis·symbol:·e1 | 99 | ·····1:·Module:·Basis·symbol:·e1 |
| 100 | ················Basis·element·widths:·{4,·4} | 100 | ················Basis·element·widths:·{4,·4} |
| 101 | ················Degree·shifts:·{-4,·-4} | 101 | ················Degree·shifts:·{-4,·-4} |
| 102 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 102 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| 103 | ················Monomial·order:·Lex | 103 | ················Monomial·order:·Lex |
| 104 | ·····Differential:·Source:·(e1,·{4,·4},·{-4,·-4})·Target:·(e0,·{2},·{-2}) | 104 | ·····Differential:·Source:·(e1,·{4,·4},·{-4,·-4})·Target:·(e0,·{2},·{-2}) |
| 105 | ···················Basis·element·images:·{-x···x···e0···········+·x···x···e0···········+·x···x···e0···········-·x···x···e0 | 105 | ···················Basis·element·images:·{0,·-x···x···e0···········+·x···x···e0···········+·x···x···e0···········-·x···x···e0··········} |
| 106 | ············································2,3·1,1··4,{2,·4},1····2,4·1,1··4,{2,·3},1····2,3·1,2··4,{1,·4},1····2,4·1,2··4,{1,·3},1</code></pre> | 106 | ···············································2,3·1,1··4,{2,·4},1····2,4·1,1··4,{2,·3},1····2,3·1,2··4,{1,·4},1····2,4·1,2··4,{1,·3},1</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ······</div> | 109 | ······</div> |
| 110 | ······<div·class="waystouse"> | 110 | ······<div·class="waystouse"> |
| 111 | ········<h2>Ways·to·use·<span·class="tt">describeFull</span>:</h2> | 111 | ········<h2>Ways·to·use·<span·class="tt">describeFull</span>:</h2> |
| 112 | ········<ul> | 112 | ········<ul> |
| 113 | ··········<li> | 113 | ··········<li> |
| Offset 15, 30 lines modified | Offset 15, 30 lines modified | ||
| 15 | Displays·the·free·OI-modules·and·describes·the·differentials·of·an·OI- | 15 | Displays·the·free·OI-modules·and·describes·the·differentials·of·an·OI- |
| 16 | resolution. | 16 | resolution. |
| 17 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 17 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 18 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 18 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 19 | i3·:·installGeneratorsInWidth(F,·2); | 19 | i3·:·installGeneratorsInWidth(F,·2); |
| 20 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 20 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 21 | i5·:·time·C·=·oiRes({b},·1); | 21 | i5·:·time·C·=·oiRes({b},·1); |
| 22 | ·--·used·0.1 | 22 | ·--·used·0.143174s·(cpu);·0.106642s·(thread);·0s·(gc) |
| 23 | i6·:·describeFull·C | 23 | i6·:·describeFull·C |
| 24 | o6·=·0:·Module:·Basis·symbol:·e0 | 24 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 25 | ················Basis·element·widths:·{2} | 25 | ················Basis·element·widths:·{2} |
| 26 | ················Degree·shifts:·{-2} | 26 | ················Degree·shifts:·{-2} |
| 27 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 27 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| 28 | ················Monomial·order:·Lex | 28 | ················Monomial·order:·Lex |
| 29 | ·····Differential:·Source:·(e0,·{2},·{-2})·Target:·(e,·{1,·1},·{0,·0}) | 29 | ·····Differential:·Source:·(e0,·{2},·{-2})·Target:·(e,·{1,·1},·{0,·0}) |
| 30 | ·····1:·Module:·Basis·symbol:·e1 | 30 | ·····1:·Module:·Basis·symbol:·e1 |
| 31 | ················Basis·element·widths:·{4,·4} | 31 | ················Basis·element·widths:·{4,·4} |
| 32 | ················Degree·shifts:·{-4,·-4} | 32 | ················Degree·shifts:·{-4,·-4} |
| 33 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 33 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| 34 | ················Monomial·order:·Lex | 34 | ················Monomial·order:·Lex |
| 35 | ·····Differential:·Source:·(e1,·{4,·4},·{-4,·-4})·Target:·(e0,·{2},·{-2}) | 35 | ·····Differential:·Source:·(e1,·{4,·4},·{-4,·-4})·Target:·(e0,·{2},·{-2}) |
| 36 | ···················Basis·element·images:·{-x···x···e0···········+·x···x···e0 | 36 | ···················Basis·element·images:·{0,·-x···x···e0···········+·x···x···e0 |
| 37 | +·x···x···e0···········-·x···x···e0·········· | 37 | +·x···x···e0···········-·x···x···e0··········} |
| 38 | ············································2,3·1,1··4,{2,·4},1····2,4·1,1 | 38 | ···············································2,3·1,1··4,{2,·4},1····2,4·1,1 |
| 39 | {2,·3},1····2,3·1,2··4,{1,·4},1····2,4·1,2··4,{1,·3},1 | 39 | 4,{2,·3},1····2,3·1,2··4,{1,·4},1····2,4·1,2··4,{1,·3},1 |
| 40 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·d\x8de\x8es\x8sc\x8cr\x8ri\x8ib\x8be\x8eF\x8Fu\x8ul\x8ll\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* | 40 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·d\x8de\x8es\x8sc\x8cr\x8ri\x8ib\x8be\x8eF\x8Fu\x8ul\x8ll\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 41 | ····*·describeFull(OIResolution) | 41 | ····*·describeFull(OIResolution) |
| 42 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 42 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 43 | The·object·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8F_\x8u_\x8l_\x8l·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 43 | The·object·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8F_\x8u_\x8l_\x8l·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 90, 26 lines modified | Offset 90, 23 lines modified | ||
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1;</code></pre> | 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1;</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i7·:·describe·phi | 95 | <td>··············<pre><code·class="language-macaulay2">i7·:·describe·phi |
| 96 | o7·=·Source:·(e1,·{5,·5},·{- | 96 | o7·=·Source:·(e1,·{5,·5},·{-4,·-3})·Target:·(e0,·{3},·{-2}) |
| 97 | ·····Basis·element·images:·{ | 97 | ·····Basis·element·images:·{x···x···e0··············-·x···x···e0············· |
| 98 | ······························ | 98 | ·····························2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1 |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ·····x···e0··············-·x···e0·············,·x···x···e0··············- | ||
| 101 | ····· | 100 | ·····-·x···x···e0··············+·x···x···e0·············,·-x···e0········ |
| 101 | ········2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1····2,2··5,{1,·3, | ||
| 102 | ·····------------------------------------------------------------------------ | 102 | ·····------------------------------------------------------------------------ |
| 103 | ··········+·x···e0··············+·x···e0··············-·x···e0·············} | ||
| 104 | ·····5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1····2,3··5,{1,·2,·4},1</code></pre> | ||
| 103 | ·····x···x···e0··············-·x···x···e0··············+·x···x···e0········ | ||
| 104 | ······2,4·1,1··5,{2,·3,·5},1····2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3, | ||
| 105 | ·····------------------------------------------------------------------------ | ||
| 106 | ·········} | ||
| 107 | ·····5},1</code></pre> | ||
| 108 | </td>··········</tr> | 105 | </td>··········</tr> |
| 109 | ········</table> | 106 | ········</table> |
| 110 | ······</div> | 107 | ······</div> |
| 111 | ······<div·class="waystouse"> | 108 | ······<div·class="waystouse"> |
| 112 | ········<h2>Ways·to·use·this·method:</h2> | 109 | ········<h2>Ways·to·use·this·method:</h2> |
| 113 | ········<ul> | 110 | ········<ul> |
| 114 | ··········<li> | 111 | ··········<li> |
| Offset 19, 21 lines modified | Offset 19, 18 lines modified | ||
| 19 | i2·:·F·=·makeFreeOIModule(e,·{1,2},·P); | 19 | i2·:·F·=·makeFreeOIModule(e,·{1,2},·P); |
| 20 | i3·:·installGeneratorsInWidth(F,·3); | 20 | i3·:·installGeneratorsInWidth(F,·3); |
| 21 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); | 21 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); |
| 22 | i5·:·C·=·oiRes({b},·2); | 22 | i5·:·C·=·oiRes({b},·2); |
| 23 | i6·:·phi·=·C.dd_1; | 23 | i6·:·phi·=·C.dd_1; |
| 24 | i7·:·describe·phi | 24 | i7·:·describe·phi |
| 25 | o7·=·Source:·(e1,·{5,·5},·{- | 25 | o7·=·Source:·(e1,·{5,·5},·{-4,·-3})·Target:·(e0,·{3},·{-2}) |
| 26 | ·····Basis·element·images:·{ | 26 | ·····Basis·element·images:·{x···x···e0··············-·x···x···e0 |
| 27 | ······························ | 27 | ·····························2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1 |
| 28 | ·····------------------------------------------------------------------------ | 28 | ·····------------------------------------------------------------------------ |
| 29 | ····· | 29 | ·····-·x···x···e0··············+·x···x···e0·············,·-x···e0 |
| 30 | ······2,3··5,{1,· | 30 | ········2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1····2,2··5,{1,·3, |
| 31 | ·····------------------------------------------------------------------------ | 31 | ·····------------------------------------------------------------------------ |
| 32 | ··········+·x···e0··············+·x···e0··············-·x···e0·············} | ||
| 33 | ·····5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1····2,3··5,{1,·2,·4},1 | ||
| 32 | ·····x···x···e0··············-·x···x···e0··············+·x···x···e0 | ||
| 33 | ······2,4·1,1··5,{2,·3,·5},1····2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3, | ||
| 34 | ·····------------------------------------------------------------------------ | ||
| 35 | ·········} | ||
| 36 | ·····5},1 | ||
| 37 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 34 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 38 | ····*·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8(_\x8F_\x8r_\x8e_\x8e_\x8O_\x8I_\x8M_\x8o_\x8d_\x8u_\x8l_\x8e_\x8M_\x8a_\x8p_\x8)·--·display·a·free·OI-module·map | 35 | ····*·_\x8d_\x8e_\x8s_\x8c_\x8r_\x8i_\x8b_\x8e_\x8(_\x8F_\x8r_\x8e_\x8e_\x8O_\x8I_\x8M_\x8o_\x8d_\x8u_\x8l_\x8e_\x8M_\x8a_\x8p_\x8)·--·display·a·free·OI-module·map |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 90 | ·--·used·0. | 90 | ·--·used·0.129141s·(cpu);·0.0923676s·(thread);·0s·(gc)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·C | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·C |
| 94 | o6·=·0:·Module:·Basis·symbol:·e0 | 94 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 95 | ················Basis·element·widths:·{2} | 95 | ················Basis·element·widths:·{2} |
| 96 | ················Degree·shifts:·{-2} | 96 | ················Degree·shifts:·{-2} |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 15 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 16 | Displays·the·free·OI-modules·and·differentials·of·an·OI-resolution. | 16 | Displays·the·free·OI-modules·and·differentials·of·an·OI-resolution. |
| 17 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 17 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 18 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 18 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 19 | i3·:·installGeneratorsInWidth(F,·2); | 19 | i3·:·installGeneratorsInWidth(F,·2); |
| 20 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 20 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 21 | i5·:·time·C·=·oiRes({b},·1); | 21 | i5·:·time·C·=·oiRes({b},·1); |
| 22 | ·--·used·0. | 22 | ·--·used·0.129141s·(cpu);·0.0923676s·(thread);·0s·(gc) |
| 23 | i6·:·describe·C | 23 | i6·:·describe·C |
| 24 | o6·=·0:·Module:·Basis·symbol:·e0 | 24 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 25 | ················Basis·element·widths:·{2} | 25 | ················Basis·element·widths:·{2} |
| 26 | ················Degree·shifts:·{-2} | 26 | ················Degree·shifts:·{-2} |
| 27 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) | 27 | ················Polynomial·OI-algebra:·(2,·x,·QQ,·RowUpColUp) |
| 28 | ················Monomial·order:·Lex | 28 | ················Monomial·order:·Lex |
| Offset 90, 22 lines modified | Offset 90, 22 lines modified | ||
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1;</code></pre> | 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1;</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i7·:·image·phi | 95 | <td>··············<pre><code·class="language-macaulay2">i7·:·image·phi |
| 96 | o7·=·{x···x···e0··············-·x···x···e0··············-·x···x···e0········ | ||
| 97 | 96 | o7·=·{-x···e0··············+·x···e0··············+·x···e0··············- | |
| 97 | ········2,2··5,{1,·3,·5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1·· | ||
| 98 | ·····------------------------------------------------------------------------ | 98 | ·····------------------------------------------------------------------------ |
| 99 | ··········+·x···x···e0·············,·-x···e0··············+·x···e0········ | ||
| 100 | ····· | 99 | ·····x···e0·············,·x···x···e0··············-·x···x···e0··············- |
| 100 | ······2,3··5,{1,·2,·4},1···2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1·· | ||
| 101 | ·····------------------------------------------------------------------------ | 101 | ·····------------------------------------------------------------------------ |
| 102 | ····· | 102 | ·····x···x···e0··············+·x···x···e0·············} |
| 103 | ····· | 103 | ······2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1 |
| 104 | o7·:·List</code></pre> | 104 | o7·:·List</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | ······</div> | 107 | ······</div> |
| 108 | ······<div·class="waystouse"> | 108 | ······<div·class="waystouse"> |
| 109 | ········<h2>Ways·to·use·this·method:</h2> | 109 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 19, 20 lines modified | Offset 19, 20 lines modified | ||
| 19 | i2·:·F·=·makeFreeOIModule(e,·{1,2},·P); | 19 | i2·:·F·=·makeFreeOIModule(e,·{1,2},·P); |
| 20 | i3·:·installGeneratorsInWidth(F,·3); | 20 | i3·:·installGeneratorsInWidth(F,·3); |
| 21 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); | 21 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); |
| 22 | i5·:·C·=·oiRes({b},·2); | 22 | i5·:·C·=·oiRes({b},·2); |
| 23 | i6·:·phi·=·C.dd_1; | 23 | i6·:·phi·=·C.dd_1; |
| 24 | i7·:·image·phi | 24 | i7·:·image·phi |
| 25 | o7·=·{x···x···e0··············-·x···x···e0··············-·x···x···e0 | ||
| 26 | 25 | o7·=·{-x···e0··············+·x···e0··············+·x···e0··············- | |
| 26 | ········2,2··5,{1,·3,·5},1····2,2··5,{1,·3,·4},1····2,3··5,{1,·2,·5},1 | ||
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| 28 | ·········· | 28 | ·····x···e0·············,·x···x···e0··············-·x···x···e0··············- |
| 29 | ····· | 29 | ······2,3··5,{1,·2,·4},1···2,3·1,1··5,{2,·4,·5},1····2,4·1,1··5,{2,·3,·5},1 |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ····· | 31 | ·····x···x···e0··············+·x···x···e0·············} |
| 32 | ····· | 32 | ······2,3·1,2··5,{1,·4,·5},1····2,4·1,2··5,{1,·3,·5},1 |
| 33 | o7·:·List | 33 | o7·:·List |
| 34 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 34 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 35 | ····*·_\x8i_\x8m_\x8a_\x8g_\x8e_\x8(_\x8F_\x8r_\x8e_\x8e_\x8O_\x8I_\x8M_\x8o_\x8d_\x8u_\x8l_\x8e_\x8M_\x8a_\x8p_\x8)·--·get·the·basis·element·images·of·a·free·OI- | 35 | ····*·_\x8i_\x8m_\x8a_\x8g_\x8e_\x8(_\x8F_\x8r_\x8e_\x8e_\x8O_\x8I_\x8M_\x8o_\x8d_\x8u_\x8l_\x8e_\x8M_\x8a_\x8p_\x8)·--·get·the·basis·element·images·of·a·free·OI- |
| 36 | ······module·map | 36 | ······module·map |
| Offset 87, 15 lines modified | Offset 87, 15 lines modified | ||
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) |
| 94 | ·--·used·0.2 | 94 | ·--·used·0.28884s·(cpu);·0.208916s·(thread);·0s·(gc) |
| 95 | o5·=·0:·(e0,·{2},·{-2}) | 95 | o5·=·0:·(e0,·{2},·{-2}) |
| 96 | ·····1:·(e1,·{4},·{-4}) | 96 | ·····1:·(e1,·{4},·{-4}) |
| 97 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 97 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 98 | o5·:·OIResolution</code></pre> | 98 | o5·:·OIResolution</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| Offset 18, 15 lines modified | Offset 18, 15 lines modified | ||
| 18 | option·must·be·either·true·or·false,·depending·on·whether·one·wants·debug | 18 | option·must·be·either·true·or·false,·depending·on·whether·one·wants·debug |
| 19 | information·printed. | 19 | information·printed. |
| 20 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 20 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 21 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 21 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 22 | i3·:·installGeneratorsInWidth(F,·2); | 22 | i3·:·installGeneratorsInWidth(F,·2); |
| 23 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 23 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 24 | i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) | 24 | i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) |
| 25 | ·--·used·0.2 | 25 | ·--·used·0.28884s·(cpu);·0.208916s·(thread);·0s·(gc) |
| 26 | o5·=·0:·(e0,·{2},·{-2}) | 26 | o5·=·0:·(e0,·{2},·{-2}) |
| 27 | ·····1:·(e1,·{4},·{-4}) | 27 | ·····1:·(e1,·{4},·{-4}) |
| 28 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 28 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 29 | o5·:·OIResolution | 29 | o5·:·OIResolution |
| 30 | i6·:·isComplex·C | 30 | i6·:·isComplex·C |
| Offset 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i10·:·isOIGB·{b1,·b2} | 102 | <td>··············<pre><code·class="language-macaulay2">i10·:·isOIGB·{b1,·b2} |
| 103 | o10·=·false</code></pre> | 103 | o10·=·false</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·B·=·oiGB·{b1,·b2} | 106 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·B·=·oiGB·{b1,·b2} |
| 107 | ·--·used·0.01 | 107 | ·--·used·0.0199799s·(cpu);·0.0196231s·(thread);·0s·(gc) |
| 108 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 108 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 109 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· | 109 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· |
| 110 | ······----------------------------------------------------------------------- | 110 | ······----------------------------------------------------------------------- |
| 111 | ······x···x···x···e···········-·x···x···x···e··········} | 111 | ······x···x···x···e···········-·x···x···x···e··········} |
| 112 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 112 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 25, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | i5·:·installGeneratorsInWidth(F,·3); | 25 | i5·:·installGeneratorsInWidth(F,·3); |
| 26 | i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); | 26 | i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); |
| 27 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); | 27 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); |
| 28 | i10·:·isOIGB·{b1,·b2} | 28 | i10·:·isOIGB·{b1,·b2} |
| 29 | o10·=·false | 29 | o10·=·false |
| 30 | i11·:·time·B·=·oiGB·{b1,·b2} | 30 | i11·:·time·B·=·oiGB·{b1,·b2} |
| 31 | ·--·used·0.01 | 31 | ·--·used·0.0199799s·(cpu);·0.0196231s·(thread);·0s·(gc) |
| 32 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 32 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 33 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3 | 33 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3 |
| 34 | ······----------------------------------------------------------------------- | 34 | ······----------------------------------------------------------------------- |
| 35 | ······x···x···x···e···········-·x···x···x···e··········} | 35 | ······x···x···x···e···········-·x···x···x···e··········} |
| 36 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 36 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre> | 99 | <td>··············<pre><code·class="language-macaulay2">i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·B·=·oiGB·{b1,·b2} | 102 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·B·=·oiGB·{b1,·b2} |
| 103 | ·--·used·0.02 | 103 | ·--·used·0.0200118s·(cpu);·0.0226442s·(thread);·0s·(gc) |
| 104 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 104 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 105 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· | 105 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· |
| 106 | ······----------------------------------------------------------------------- | 106 | ······----------------------------------------------------------------------- |
| 107 | ······x···x···x···e···········-·x···x···x···e··········} | 107 | ······x···x···x···e···········-·x···x···x···e··········} |
| 108 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 108 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 22, 15 lines modified | Offset 22, 15 lines modified | ||
| 22 | i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P); | 22 | i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P); |
| 23 | i3·:·installGeneratorsInWidth(F,·1); | 23 | i3·:·installGeneratorsInWidth(F,·1); |
| 24 | i4·:·installGeneratorsInWidth(F,·2); | 24 | i4·:·installGeneratorsInWidth(F,·2); |
| 25 | i5·:·installGeneratorsInWidth(F,·3); | 25 | i5·:·installGeneratorsInWidth(F,·3); |
| 26 | i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); | 26 | i6·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); |
| 27 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); | 27 | i8·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); |
| 28 | i10·:·time·B·=·oiGB·{b1,·b2} | 28 | i10·:·time·B·=·oiGB·{b1,·b2} |
| 29 | ·--·used·0.02 | 29 | ·--·used·0.0200118s·(cpu);·0.0226442s·(thread);·0s·(gc) |
| 30 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 30 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 31 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3 | 31 | ········1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3 |
| 32 | ······----------------------------------------------------------------------- | 32 | ······----------------------------------------------------------------------- |
| 33 | ······x···x···x···e···········-·x···x···x···e··········} | 33 | ······x···x···x···e···········-·x···x···x···e··········} |
| 34 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 34 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 90 | ·--·used·0.1 | 90 | ·--·used·0.120985s·(cpu);·0.0827037s·(thread);·0s·(gc)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·net·C | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·net·C |
| 94 | o6·=·0:·(e0,·{2},·{-2}) | 94 | o6·=·0:·(e0,·{2},·{-2}) |
| 95 | ·····1:·(e1,·{4,·4},·{-4,·-4})</code></pre> | 95 | ·····1:·(e1,·{4,·4},·{-4,·-4})</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| Offset 16, 14 lines modified | Offset 16, 14 lines modified | ||
| 16 | Displays·the·basis·element·widths·and·degree·shifts·of·the·free·OI-modules·in | 16 | Displays·the·basis·element·widths·and·degree·shifts·of·the·free·OI-modules·in |
| 17 | an·OI-resolution. | 17 | an·OI-resolution. |
| 18 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 18 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 19 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 19 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 20 | i3·:·installGeneratorsInWidth(F,·2); | 20 | i3·:·installGeneratorsInWidth(F,·2); |
| 21 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 21 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 22 | i5·:·time·C·=·oiRes({b},·1); | 22 | i5·:·time·C·=·oiRes({b},·1); |
| 23 | ·--·used·0.1 | 23 | ·--·used·0.120985s·(cpu);·0.0827037s·(thread);·0s·(gc) |
| 24 | i6·:·net·C | 24 | i6·:·net·C |
| 25 | o6·=·0:·(e0,·{2},·{-2}) | 25 | o6·=·0:·(e0,·{2},·{-2}) |
| 26 | ·····1:·(e1,·{4,·4},·{-4,·-4}) | 26 | ·····1:·(e1,·{4,·4},·{-4,·-4}) |
| 27 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 27 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 28 | ····*·_\x8n_\x8e_\x8t_\x8(_\x8O_\x8I_\x8R_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n_\x8)·--·display·an·OI-resolution | 28 | ····*·_\x8n_\x8e_\x8t_\x8(_\x8O_\x8I_\x8R_\x8e_\x8s_\x8o_\x8l_\x8u_\x8t_\x8i_\x8o_\x8n_\x8)·--·display·an·OI-resolution |
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| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);</code></pre> | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2);</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3);</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·oiGB·{b1,·b2} | 110 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·oiGB·{b1,·b2} |
| 111 | ·--·used·0.02 | 111 | ·--·used·0.0217364s·(cpu);·0.0241287s·(thread);·0s·(gc) |
| 112 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 112 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 113 | ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· | 113 | ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3· |
| 114 | ·····------------------------------------------------------------------------ | 114 | ·····------------------------------------------------------------------------ |
| 115 | ·····x···x···x···e···········-·x···x···x···e··········} | 115 | ·····x···x···x···e···········-·x···x···x···e··········} |
| 116 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 116 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 29 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 30 | i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P); | 30 | i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P); |
| 31 | i3·:·installGeneratorsInWidth(F,·1); | 31 | i3·:·installGeneratorsInWidth(F,·1); |
| 32 | i4·:·installGeneratorsInWidth(F,·2); | 32 | i4·:·installGeneratorsInWidth(F,·2); |
| 33 | i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); | 33 | i5·:·use·F_1;·b1·=·x_(1,1)*e_(1,{1},1)+x_(2,1)*e_(1,{1},2); |
| 34 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); | 34 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},2)+x_(2,2)*x_(2,1)*e_(2,{1,2},3); |
| 35 | i9·:·time·oiGB·{b1,·b2} | 35 | i9·:·time·oiGB·{b1,·b2} |
| 36 | ·--·used·0.02 | 36 | ·--·used·0.0217364s·(cpu);·0.0241287s·(thread);·0s·(gc) |
| 37 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 37 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 38 | ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3 | 38 | ·······1,1·1,{1},1····2,1·1,{1},2···1,2·1,1·2,{2},2····2,2·2,1·2,{1,·2},3 |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ·····x···x···x···e···········-·x···x···x···e··········} | 40 | ·····x···x···x···e···········-·x···x···x···e··········} |
| 41 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 41 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> | 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2);</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 112 | ·--·used·0. | 112 | ·--·used·0.310541s·(cpu);·0.241663s·(thread);·0s·(gc) |
| 113 | o5·=·0:·(e0,·{2},·{-2}) | 113 | o5·=·0:·(e0,·{2},·{-2}) |
| 114 | ·····1:·(e1,·{4},·{-4}) | 114 | ·····1:·(e1,·{4},·{-4}) |
| 115 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 115 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 116 | o5·:·OIResolution</code></pre> | 116 | o5·:·OIResolution</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| Offset 34, 15 lines modified | Offset 34, 15 lines modified | ||
| 34 | Therefore,·use·TopNonminimal·=>·true·for·no·minimization·of·the·basis·in·degree | 34 | Therefore,·use·TopNonminimal·=>·true·for·no·minimization·of·the·basis·in·degree |
| 35 | $n-1$. | 35 | $n-1$. |
| 36 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 36 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 37 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); | 37 | i2·:·F·=·makeFreeOIModule(e,·{1,1},·P); |
| 38 | i3·:·installGeneratorsInWidth(F,·2); | 38 | i3·:·installGeneratorsInWidth(F,·2); |
| 39 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); | 39 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(2,1)*e_(2,{1},2); |
| 40 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 40 | i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 41 | ·--·used·0. | 41 | ·--·used·0.310541s·(cpu);·0.241663s·(thread);·0s·(gc) |
| 42 | o5·=·0:·(e0,·{2},·{-2}) | 42 | o5·=·0:·(e0,·{2},·{-2}) |
| 43 | ·····1:·(e1,·{4},·{-4}) | 43 | ·····1:·(e1,·{4},·{-4}) |
| 44 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 44 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 45 | o5·:·OIResolution | 45 | o5·:·OIResolution |
| 46 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·o\x8oi\x8iR\x8Re\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 46 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·o\x8oi\x8iR\x8Re\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 93, 15 lines modified | Offset 93, 15 lines modified | ||
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2);</code></pre> | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2);</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2);</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) | 99 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) |
| 100 | ·--·used·0.1 | 100 | ·--·used·0.163458s·(cpu);·0.132119s·(thread);·0s·(gc) |
| 101 | ······································································· | 101 | ······································································· |
| 102 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, | 102 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, |
| 103 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2· | 103 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2· |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ······2··················2 | 105 | ······2··················2 |
| 106 | ·····x···x···e········-·x···x···e·······} | 106 | ·····x···x···e········-·x···x···e·······} |
| Offset 21, 15 lines modified | Offset 21, 15 lines modified | ||
| 21 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); | 21 | i1·:·P·=·makePolynomialOIAlgebra(2,·x,·QQ); |
| 22 | i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P); | 22 | i2·:·F·=·makeFreeOIModule(e,·{1,1,2},·P); |
| 23 | i3·:·installGeneratorsInWidth(F,·1); | 23 | i3·:·installGeneratorsInWidth(F,·1); |
| 24 | i4·:·installGeneratorsInWidth(F,·2); | 24 | i4·:·installGeneratorsInWidth(F,·2); |
| 25 | i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2); | 25 | i5·:·use·F_1;·b1·=·x_(2,1)*e_(1,{1},2)+x_(1,1)*e_(1,{1},2); |
| 26 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2); | 26 | i7·:·use·F_2;·b2·=·x_(1,2)*x_(1,1)*e_(2,{2},1)+x_(2,2)*x_(1,2)*e_(2,{2},2); |
| 27 | i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) | 27 | i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) |
| 28 | ·--·used·0.1 | 28 | ·--·used·0.163458s·(cpu);·0.132119s·(thread);·0s·(gc) |
| 29 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, | 29 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, |
| 30 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2 | 30 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2 |
| 31 | ·····------------------------------------------------------------------------ | 31 | ·····------------------------------------------------------------------------ |
| 32 | ······2··················2 | 32 | ······2··················2 |
| 33 | ·····x···x···e········-·x···x···e·······} | 33 | ·····x···x···e········-·x···x···e·······} |
| Offset 91, 16 lines modified | Offset 91, 16 lines modified | ||
| 91 | ·································4 | 91 | ·································4 |
| 92 | o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2 | 92 | o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2 |
| 93 | ··········2,2···2,1···1,2···1,1</code></pre> | 93 | ··········2,2···2,1···1,2···1,1</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·terms·f | 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·terms·f |
| 97 | o5·=·{ | 97 | o5·=·{x···e·······,·-x···e·······,·x···e·······,·-x···e·······} |
| 98 | ······· | 98 | ·······1,1·2,{1},1····1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2 |
| 99 | o5·:·List</code></pre> | 99 | o5·:·List</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ········</table> | 101 | ········</table> |
| 102 | ······</div> | 102 | ······</div> |
| 103 | ······<div> | 103 | ······<div> |
| 104 | ········<h2>Caveat</h2> | 104 | ········<h2>Caveat</h2> |
| Offset 25, 16 lines modified | Offset 25, 16 lines modified | ||
| 25 | ·······1,2·2,{2},1····1,1·2,{1},1····2,2·2,{2},2····2,1·2,{1},2 | 25 | ·······1,2·2,{2},1····1,1·2,{1},1····2,2·2,{2},2····2,1·2,{1},2 |
| 26 | ·································4 | 26 | ·································4 |
| 27 | o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2 | 27 | o4·:·(QQ[x···,·x···,·x···,·x···])··in·width·2 |
| 28 | ··········2,2···2,1···1,2···1,1 | 28 | ··········2,2···2,1···1,2···1,1 |
| 29 | i5·:·terms·f | 29 | i5·:·terms·f |
| 30 | o5·=·{ | 30 | o5·=·{x···e·······,·-x···e·······,·x···e·······,·-x···e·······} |
| 31 | ······· | 31 | ·······1,1·2,{1},1····1,2·2,{2},1···2,1·2,{1},2····2,2·2,{2},2 |
| 32 | o5·:·List | 32 | o5·:·List |
| 33 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 33 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 34 | The·list·of·terms·need·not·be·in·order.·To·find·the·lead·term·of·an·element, | 34 | The·list·of·terms·need·not·be·in·order.·To·find·the·lead·term·of·an·element, |
| 35 | see·_\x8l_\x8e_\x8a_\x8d_\x8T_\x8e_\x8r_\x8m_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8). | 35 | see·_\x8l_\x8e_\x8a_\x8d_\x8T_\x8e_\x8r_\x8m_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8). |
| 36 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·_\x8t_\x8e_\x8r_\x8m_\x8s_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8)·--·get·the·terms·of·an·element·of·a·free·OI-module | 37 | ····*·_\x8t_\x8e_\x8r_\x8m_\x8s_\x8(_\x8V_\x8e_\x8c_\x8t_\x8o_\x8r_\x8I_\x8n_\x8W_\x8i_\x8d_\x8t_\x8h_\x8)·--·get·the·terms·of·an·element·of·a·free·OI-module |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | bWF4Q29uZXM= | 8 | bWF4Q29uZXM= |
| 9 | #:len=1120 | 9 | #:len=1120 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheXMgdGhlIGdlbmVyYXRpbmcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheXMgdGhlIGdlbmVyYXRpbmcg |
| 11 | Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gNTIzMiwgSW5wdXRzID0+IHtTUEFOe1RUeyJG | 11 | Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gNTIzMiwgSW5wdXRzID0+IHtTUEFOe1RUeyJG |
| Offset 27, 13 lines modified | Offset 27, 13 lines modified | ||
| 27 | ·········}} | 27 | ·········}} |
| 28 | ·····=>·0 | 28 | ·····=>·0 |
| 29 | o2·:·List | 29 | o2·:·List |
| 30 | i3·:·apply(L,vertices) | 30 | i3·:·apply(L,vertices) |
| 31 | o3·=·{|·-1· | 31 | o3·=·{|·-1·-1·|,·|·1··1·|,·|·-1·1·|,·|·-1·1··|} |
| 32 | ······|·-1· | 32 | ······|·-1·1··|··|·-1·1·|··|·1··1·|··|·-1·-1·| |
| 33 | o3·:·List | 33 | o3·:·List |
| 34 | i4·:· | 34 | i4·:· |
| Offset 28, 16 lines modified | Offset 28, 16 lines modified | ||
| 28 | ······top·dimension·of·the·cones·=>·2 | 28 | ······top·dimension·of·the·cones·=>·2 |
| 29 | o3·:·Fan | 29 | o3·:·Fan |
| 30 | i4·:·apply(maxCones·F1,rays) | 30 | i4·:·apply(maxCones·F1,rays) |
| 31 | o4·=·{|·1·-1·|,·|·0·-1·|,·|·1·0·|,·|·0·0·|,·|·1·0·|,·|·-1·0·|} | 31 | o4·=·{|·1·-1·|,·|·0·-1·|,·|·1·0·|,·|·0·0·|,·|·1·0·|,·|·-1·0·|} |
| 32 | ······|·0·-1·|··|·1·-1·|··|·0· | 32 | ······|·0·-1·|··|·1·-1·|··|·0·0·|··|·1·0·|··|·0·1·|··|·-1·0·| |
| 33 | ······|·0·-1·|··|·0·-1·|··|·0· | 33 | ······|·0·-1·|··|·0·-1·|··|·0·1·|··|·0·1·|··|·0·0·|··|·-1·1·| |
| 34 | o4·:·List | 34 | o4·:·List |
| 35 | i5·:·PC·=·polyhedralComplex·hypercube·3 | 35 | i5·:·PC·=·polyhedralComplex·hypercube·3 |
| 36 | o5·=·{ambient·dimension·=>·3·············} | 36 | o5·=·{ambient·dimension·=>·3·············} |
| 37 | ······number·of·generating·polyhedra·=>·1 | 37 | ······number·of·generating·polyhedra·=>·1 |
| Offset 51, 18 lines modified | Offset 51, 18 lines modified | ||
| 51 | ······number·of·generating·polyhedra·=>·6 | 51 | ······number·of·generating·polyhedra·=>·6 |
| 52 | ······top·dimension·of·the·polyhedra·=>·2 | 52 | ······top·dimension·of·the·polyhedra·=>·2 |
| 53 | o6·:·PolyhedralComplex | 53 | o6·:·PolyhedralComplex |
| 54 | i7·:·apply(maxPolyhedra·PC1,vertices) | 54 | i7·:·apply(maxPolyhedra·PC1,vertices) |
| 55 | o7·=·{|·-1· | 55 | o7·=·{|·-1·1··-1·1·|,·|·1··1··1··1·|,·|·-1·1··-1·1··|,·|·-1·1··-1·1·|,·|·-1 |
| 56 | ······|· | 56 | ······|·1··1··1··1·|··|·-1·1··-1·1·|··|·-1·-1·-1·-1·|··|·-1·-1·1··1·|··|·-1 |
| 57 | ······|·-1·-1·1··1· | 57 | ······|·-1·-1·1··1·|··|·-1·-1·1··1·|··|·-1·-1·1··1··|··|·1··1··1··1·|··|·-1 |
| 58 | ·····------------------------------------------------------------------------ | 58 | ·····------------------------------------------------------------------------ |
| 59 | ·····1··-1·1·|,·|·-1· | 59 | ·····1··-1·1··|,·|·-1·-1·-1·-1·|} |
| 60 | ·····-1·1··1··|··|·-1·1··-1·1··| | ||
| 60 | ·····-1·1· | 61 | ·····-1·-1·-1·|··|·-1·-1·1··1··| |
| 61 | ·····1··1··1·|··|·-1·-1·-1·-1·| | ||
| 62 | o7·:·List | 62 | o7·:·List |
| 63 | i8·:· | 63 | i8·:· |
| Offset 99, 16 lines modified | Offset 99, 16 lines modified | ||
| 99 | ·····=>·0 | 99 | ·····=>·0 |
| 100 | o2·:·List</code></pre> | 100 | o2·:·List</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·apply(L,vertices) | 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·apply(L,vertices) |
| 104 | o3·=·{|·-1· | 104 | o3·=·{|·-1·-1·|,·|·1··1·|,·|·-1·1·|,·|·-1·1··|} |
| 105 | ······|·-1· | 105 | ······|·-1·1··|··|·-1·1·|··|·1··1·|··|·-1·-1·| |
| 106 | o3·:·List</code></pre> | 106 | o3·:·List</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ······</div> | 109 | ······</div> |
| 110 | ······<div·class="waystouse"> | 110 | ······<div·class="waystouse"> |
| 111 | ········<h2>For·the·programmer</h2> | 111 | ········<h2>For·the·programmer</h2> |
| Offset 42, 13 lines modified | Offset 42, 13 lines modified | ||
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·········}} | 43 | ·········}} |
| 44 | ·····=>·0 | 44 | ·····=>·0 |
| 45 | o2·:·List | 45 | o2·:·List |
| 46 | i3·:·apply(L,vertices) | 46 | i3·:·apply(L,vertices) |
| 47 | o3·=·{|·-1· | 47 | o3·=·{|·-1·-1·|,·|·1··1·|,·|·-1·1·|,·|·-1·1··|} |
| 48 | ······|·-1· | 48 | ······|·-1·1··|··|·-1·1·|··|·1··1·|··|·-1·-1·| |
| 49 | o3·:·List | 49 | o3·:·List |
| 50 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 50 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 51 | The·object·_\x8m_\x8a_\x8x_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 51 | The·object·_\x8m_\x8a_\x8x_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 107, 16 lines modified | Offset 107, 16 lines modified | ||
| 107 | o3·:·Fan</code></pre> | 107 | o3·:·Fan</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·apply(maxCones·F1,rays) | 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·apply(maxCones·F1,rays) |
| 111 | o4·=·{|·1·-1·|,·|·0·-1·|,·|·1·0·|,·|·0·0·|,·|·1·0·|,·|·-1·0·|} | 111 | o4·=·{|·1·-1·|,·|·0·-1·|,·|·1·0·|,·|·0·0·|,·|·1·0·|,·|·-1·0·|} |
| 112 | ······|·0·-1·|··|·1·-1·|··|·0· | 112 | ······|·0·-1·|··|·1·-1·|··|·0·0·|··|·1·0·|··|·0·1·|··|·-1·0·| |
| 113 | ······|·0·-1·|··|·0·-1·|··|·0· | 113 | ······|·0·-1·|··|·0·-1·|··|·0·1·|··|·0·1·|··|·0·0·|··|·-1·1·| |
| 114 | o4·:·List</code></pre> | 114 | o4·:·List</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ········</table> | 116 | ········</table> |
| 117 | ········<p></p> | 117 | ········<p></p> |
| 118 | For·a·<a·title="the·class·of·all·polyhedral·complexes"·href="___Polyhedral__Complex.html">PolyhedralComplex</a><span·class="tt">·PC</span>·and·an·integer·<span·class="tt">k</span>·between·0·and·the·dimension·of·<span·class="tt">PC</span>,·<span·class="tt">skeleton</span>·computes·the·<span·class="tt">k</span>-skeleton·of·the·<a·title="the·class·of·all·polyhedral·complexes"·href="___Polyhedral__Complex.html">PolyhedralComplex</a>·<span·class="tt">PC</span>,·i.e.·the·<a·title="the·class·of·all·polyhedral·complexes"·href="___Polyhedral__Complex.html">PolyhedralComplex</a>·<span·class="tt">PC1</span>·generated·by·all·polyhedra·of·dimension·<span·class="tt">k</span>·in·<span·class="tt">PC</span>.········<table·class="examples"> | 118 | For·a·<a·title="the·class·of·all·polyhedral·complexes"·href="___Polyhedral__Complex.html">PolyhedralComplex</a><span·class="tt">·PC</span>·and·an·integer·<span·class="tt">k</span>·between·0·and·the·dimension·of·<span·class="tt">PC</span>,·<span·class="tt">skeleton</span>·computes·the·<span·class="tt">k</span>-skeleton·of·the·<a·title="the·class·of·all·polyhedral·complexes"·href="___Polyhedral__Complex.html">PolyhedralComplex</a>·<span·class="tt">PC</span>,·i.e.·the·<a·title="the·class·of·all·polyhedral·complexes"·href="___Polyhedral__Complex.html">PolyhedralComplex</a>·<span·class="tt">PC1</span>·generated·by·all·polyhedra·of·dimension·<span·class="tt">k</span>·in·<span·class="tt">PC</span>.········<table·class="examples"> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| Offset 136, 21 lines modified | Offset 136, 21 lines modified | ||
| 136 | ······top·dimension·of·the·polyhedra·=>·2 | 136 | ······top·dimension·of·the·polyhedra·=>·2 |
| 137 | o6·:·PolyhedralComplex</code></pre> | 137 | o6·:·PolyhedralComplex</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i7·:·apply(maxPolyhedra·PC1,vertices) | 140 | <td>··············<pre><code·class="language-macaulay2">i7·:·apply(maxPolyhedra·PC1,vertices) |
| 141 | o7·=·{|·-1· | 141 | o7·=·{|·-1·1··-1·1·|,·|·1··1··1··1·|,·|·-1·1··-1·1··|,·|·-1·1··-1·1·|,·|·-1 |
| 142 | ······|· | 142 | ······|·1··1··1··1·|··|·-1·1··-1·1·|··|·-1·-1·-1·-1·|··|·-1·-1·1··1·|··|·-1 |
| 143 | ······|·-1·-1·1··1· | 143 | ······|·-1·-1·1··1·|··|·-1·-1·1··1·|··|·-1·-1·1··1··|··|·1··1··1··1·|··|·-1 |
| 144 | ·····------------------------------------------------------------------------ | 144 | ·····------------------------------------------------------------------------ |
| 145 | ·····1··-1·1·|,·|·-1· | 145 | ·····1··-1·1··|,·|·-1·-1·-1·-1·|} |
| 146 | ·····-1·1··1··|··|·-1·1··-1·1··| | ||
| 146 | ·····-1·1· | 147 | ·····-1·-1·-1·|··|·-1·-1·1··1··| |
| 147 | ·····1··1··1·|··|·-1·-1·-1·-1·| | ||
| 148 | o7·:·List</code></pre> | 148 | o7·:·List</code></pre> |
| 149 | </td>··········</tr> | 149 | </td>··········</tr> |
| 150 | ········</table> | 150 | ········</table> |
| 151 | ······</div> | 151 | ······</div> |
| 152 | ······<div·class="waystouse"> | 152 | ······<div·class="waystouse"> |
| 153 | ········<h2>For·the·programmer</h2> | 153 | ········<h2>For·the·programmer</h2> |
| Offset 45, 16 lines modified | Offset 45, 16 lines modified | ||
| 45 | ······number·of·rays·=>·4 | 45 | ······number·of·rays·=>·4 |
| 46 | ······top·dimension·of·the·cones·=>·2 | 46 | ······top·dimension·of·the·cones·=>·2 |
| 47 | o3·:·Fan | 47 | o3·:·Fan |
| 48 | i4·:·apply(maxCones·F1,rays) | 48 | i4·:·apply(maxCones·F1,rays) |
| 49 | o4·=·{|·1·-1·|,·|·0·-1·|,·|·1·0·|,·|·0·0·|,·|·1·0·|,·|·-1·0·|} | 49 | o4·=·{|·1·-1·|,·|·0·-1·|,·|·1·0·|,·|·0·0·|,·|·1·0·|,·|·-1·0·|} |
| 50 | ······|·0·-1·|··|·1·-1·|··|·0· | 50 | ······|·0·-1·|··|·1·-1·|··|·0·0·|··|·1·0·|··|·0·1·|··|·-1·0·| |
| 51 | ······|·0·-1·|··|·0·-1·|··|·0· | 51 | ······|·0·-1·|··|·0·-1·|··|·0·1·|··|·0·1·|··|·0·0·|··|·-1·1·| |
| 52 | o4·:·List | 52 | o4·:·List |
| 53 | For·a·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·PC·and·an·integer·k·between·0·and·the·dimension·of·PC, | 53 | For·a·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·PC·and·an·integer·k·between·0·and·the·dimension·of·PC, |
| 54 | skeleton·computes·the·k-skeleton·of·the·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·PC,·i.e.·the | 54 | skeleton·computes·the·k-skeleton·of·the·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·PC,·i.e.·the |
| 55 | _\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·PC1·generated·by·all·polyhedra·of·dimension·k·in·PC. | 55 | _\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·PC1·generated·by·all·polyhedra·of·dimension·k·in·PC. |
| 56 | i5·:·PC·=·polyhedralComplex·hypercube·3 | 56 | i5·:·PC·=·polyhedralComplex·hypercube·3 |
| Offset 68, 18 lines modified | Offset 68, 18 lines modified | ||
| 68 | o6·=·{ambient·dimension·=>·3·············} | 68 | o6·=·{ambient·dimension·=>·3·············} |
| 69 | ······number·of·generating·polyhedra·=>·6 | 69 | ······number·of·generating·polyhedra·=>·6 |
| 70 | ······top·dimension·of·the·polyhedra·=>·2 | 70 | ······top·dimension·of·the·polyhedra·=>·2 |
| 71 | o6·:·PolyhedralComplex | 71 | o6·:·PolyhedralComplex |
| 72 | i7·:·apply(maxPolyhedra·PC1,vertices) | 72 | i7·:·apply(maxPolyhedra·PC1,vertices) |
| 73 | o7·=·{|·-1· | 73 | o7·=·{|·-1·1··-1·1·|,·|·1··1··1··1·|,·|·-1·1··-1·1··|,·|·-1·1··-1·1·|,·|·-1 |
| 74 | ······|· | 74 | ······|·1··1··1··1·|··|·-1·1··-1·1·|··|·-1·-1·-1·-1·|··|·-1·-1·1··1·|··|·-1 |
| 75 | ······|·-1·-1·1··1· | 75 | ······|·-1·-1·1··1·|··|·-1·-1·1··1·|··|·-1·-1·1··1··|··|·1··1··1··1·|··|·-1 |
| 76 | ·····------------------------------------------------------------------------ | 76 | ·····------------------------------------------------------------------------ |
| 77 | ·····1··-1·1·|,·|·-1· | 77 | ·····1··-1·1··|,·|·-1·-1·-1·-1·|} |
| 78 | ·····-1·1··1··|··|·-1·1··-1·1··| | ||
| 78 | ·····-1·1· | 79 | ·····-1·-1·-1·|··|·-1·-1·1··1··| |
| 79 | ·····1··1··1·|··|·-1·-1·-1·-1·| | ||
| 80 | o7·:·List | 80 | o7·:·List |
| 81 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 81 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 82 | The·object·_\x8s_\x8k_\x8e_\x8l_\x8e_\x8t_\x8o_\x8n·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 82 | The·object·_\x8s_\x8k_\x8e_\x8l_\x8e_\x8t_\x8o_\x8n·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=23 | 7 | #:len=23 |
| 8 | ZHVhbChUb3JpY1ZlY3RvckJ1bmRsZSk= | 8 | ZHVhbChUb3JpY1ZlY3RvckJ1bmRsZSk= |
| 9 | #:len=1522 | 9 | #:len=1522 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=4 | 7 | #:len=4 |
| 8 | b2Vpcw== | 8 | b2Vpcw== |
| 9 | #:len=753 | 9 | #:len=753 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | T3Blbk1hdGg= | 8 | T3Blbk1hdGg= |
| 9 | #:len=478 | 9 | #:len=478 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=34 | 7 | #:len=34 |
| 8 | ZmFjdG9yV2l0bmVzc1NldCguLi4sVmVyYm9zZT0+Li4uKQ== | 8 | ZmFjdG9yV2l0bmVzc1NldCguLi4sVmVyYm9zZT0+Li4uKQ== |
| 9 | #:len=595 | 9 | #:len=595 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAib3B0aW9uIHRvIHNwZWNpZnkgd2hldGhl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAib3B0aW9uIHRvIHNwZWNpZnkgd2hldGhl |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | UGFja2FnZUNpdGF0aW9ucw== | 8 | UGFja2FnZUNpdGF0aW9ucw== |
| 9 | #:len=1928 | 9 | #:len=1928 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZhY2lsaXRhdGluZyBj | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZhY2lsaXRhdGluZyBj |
| 11 | aXRhdGlvbiBvZiBNYWNhdWxheTIgcGFja2FnZXMiLCAibGluZW51bSIgPT4gMjY4LCBTZWVBbHNv | 11 | aXRhdGlvbiBvZiBNYWNhdWxheTIgcGFja2FnZXMiLCAibGluZW51bSIgPT4gMjY4LCBTZWVBbHNv |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | c2Vjb25kRnVuY3Rpb24= | 8 | c2Vjb25kRnVuY3Rpb24= |
| 9 | #:len=379 | 9 | #:len=379 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBzaWxseSBzZWNvbmQgZnVuY3Rpb24i | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBzaWxseSBzZWNvbmQgZnVuY3Rpb24i |
| 11 | LCBEZXNjcmlwdGlvbiA9PiAoIlRoaXMgZnVuY3Rpb24gaXMgcHJvdmlkZWQgYnkgdGhlIHBhY2th | 11 | LCBEZXNjcmlwdGlvbiA9PiAoIlRoaXMgZnVuY3Rpb24gaXMgcHJvdmlkZWQgYnkgdGhlIHBhY2th |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | cGFyYW1ldHJpemVDb25pYw== | 8 | cGFyYW1ldHJpemVDb25pYw== |
| 9 | #:len=1904 | 9 | #:len=1904 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3B0aW9uIHdoZXRoZXIgdG8gcmF0aW9u | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiT3B0aW9uIHdoZXRoZXIgdG8gcmF0aW9u |
| 11 | YWxseSBwYXJhbWV0cml6ZSBjb25pY3MuIiwgImxpbmVudW0iID0+IDE2ODYsICJmaWxlbmFtZSIg | 11 | YWxseSBwYXJhbWV0cml6ZSBjb25pY3MuIiwgImxpbmVudW0iID0+IDE2ODYsICJmaWxlbmFtZSIg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | Y2hhckFuYWx5emVy | 8 | Y2hhckFuYWx5emVy |
| 9 | #:len=752 | 9 | #:len=752 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBsZXhpY2FsIGFuYWx5emVyIHRoYXQg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBsZXhpY2FsIGFuYWx5emVyIHRoYXQg |
| 11 | cHJvdmlkZXMgY2hhcmFjdGVycyBmcm9tIGEgc3RyaW5nIG9uZSBhdCBhIHRpbWUiLCAibGluZW51 | 11 | cHJvdmlkZXMgY2hhcmFjdGVycyBmcm9tIGEgc3RyaW5nIG9uZSBhdCBhIHRpbWUiLCAibGluZW51 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=30 | 7 | #:len=30 |
| 8 | cmFuZG9tRXh0ZW5zaW9uKE1hdHJpeCxNYXRyaXgp | 8 | cmFuZG9tRXh0ZW5zaW9uKE1hdHJpeCxNYXRyaXgp |
| 9 | #:len=301 | 9 | #:len=301 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzE5Nywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzE5Nywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmFuZG9tRXh0ZW5zaW9uLE1hdHJpeCxNYXRyaXgp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmFuZG9tRXh0ZW5zaW9uLE1hdHJpeCxNYXRyaXgp |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | i3·:·g=3 | 41 | i3·:·g=3 |
| 42 | o3·=·3 | 42 | o3·=·3 |
| 43 | i4·:·kk=·ZZ/101; | 43 | i4·:·kk=·ZZ/101; |
| 44 | i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g); | 44 | i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g); |
| 45 | ·--· | 45 | ·--·1.20671s·elapsed |
| 46 | i6·:·M=cliffordModule(Mu1,Mu2,R) | 46 | i6·:·M=cliffordModule(Mu1,Mu2,R) |
| 47 | o6·=·CliffordModule{...6...} | 47 | o6·=·CliffordModule{...6...} |
| 48 | o6·:·CliffordModule | 48 | o6·:·CliffordModule |
| Offset 67, 30 lines modified | Offset 67, 30 lines modified | ||
| 67 | ··········m12=randomExtension(m1.yAction,m2.yAction); | 67 | ··········m12=randomExtension(m1.yAction,m2.yAction); |
| 68 | ··········V·=·vectorBundleOnE·m12; | 68 | ··········V·=·vectorBundleOnE·m12; |
| 69 | ··········Ul=tensorProduct(Mor,V); | 69 | ··········Ul=tensorProduct(Mor,V); |
| 70 | ··········Ul1=tensorProduct(Mor1,V); | 70 | ··········Ul1=tensorProduct(Mor1,V); |
| 71 | ··········d0=unique·degrees·target·Ul.yAction; | 71 | ··········d0=unique·degrees·target·Ul.yAction; |
| 72 | ··········d1=unique·degrees·target·Ul1.yAction; | 72 | ··········d1=unique·degrees·target·Ul1.yAction; |
| 73 | ··········#d1·>=3·or·#d0·>=3)·do·(); | 73 | ··········#d1·>=3·or·#d0·>=3)·do·(); |
| 74 | ·--·.3 | 74 | ·--·.351805s·elapsed |
| 75 | i12·:·betti·Ul.yAction,·betti·Ul1.yAction | 75 | i12·:·betti·Ul.yAction,·betti·Ul1.yAction |
| 76 | ···············0··1··········0··1 | 76 | ···············0··1··········0··1 |
| 77 | o12·=·(total:·32·32,·total:·32·32) | 77 | o12·=·(total:·32·32,·total:·32·32) |
| 78 | ··········-4:·16··.·····-2:·32··. | 78 | ··········-4:·16··.·····-2:·32··. |
| 79 | ··········-3:·16··.·····-1:··.··. | 79 | ··········-3:·16··.·····-1:··.··. |
| 80 | ··········-2:··.··.······0:··.··. | 80 | ··········-2:··.··.······0:··.··. |
| 81 | ··········-1:··.·16······1:··.·32 | 81 | ··········-1:··.·16······1:··.·32 |
| 82 | ···········0:··.·16 | 82 | ···········0:··.·16 |
| 83 | o12·:·Sequence | 83 | o12·:·Sequence |
| 84 | i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators | 84 | i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators |
| 85 | ·--·1 | 85 | ·--·15.8888s·elapsed |
| 86 | i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S)); | 86 | i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S)); |
| 87 | ··············32······32 | 87 | ··············32······32 |
| 88 | o14·:·Matrix·S···<--·S | 88 | o14·:·Matrix·S···<--·S |
| 89 | i15·:·r=2 | 89 | i15·:·r=2 |
| Offset 45, 30 lines modified | Offset 45, 30 lines modified | ||
| 45 | i11·:·M=cliffordModule(Mu1,Mu2,R) | 45 | i11·:·M=cliffordModule(Mu1,Mu2,R) |
| 46 | o11·=·CliffordModule{...6...} | 46 | o11·=·CliffordModule{...6...} |
| 47 | o11·:·CliffordModule | 47 | o11·:·CliffordModule |
| 48 | i12·:·elapsedTime·Ulr·=·searchUlrich(M,S); | 48 | i12·:·elapsedTime·Ulr·=·searchUlrich(M,S); |
| 49 | ·--·. | 49 | ·--·.710483s·elapsed |
| 50 | i13·:·betti·res·Ulr | 50 | i13·:·betti·res·Ulr |
| 51 | ·············0··1·2 | 51 | ·············0··1·2 |
| 52 | o13·=·total:·8·16·8 | 52 | o13·=·total:·8·16·8 |
| 53 | ··········0:·8·16·8 | 53 | ··········0:·8·16·8 |
| 54 | o13·:·BettiTally | 54 | o13·:·BettiTally |
| 55 | i14·:·ann·Ulr·==·ideal·qs | 55 | i14·:·ann·Ulr·==·ideal·qs |
| 56 | o14·=·true | 56 | o14·=·true |
| 57 | i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3); | 57 | i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3); |
| 58 | ·--·1. | 58 | ·--·1.83737s·elapsed |
| 59 | i16·:·betti·res·Ulr3 | 59 | i16·:·betti·res·Ulr3 |
| 60 | ··············0··1··2 | 60 | ··············0··1··2 |
| 61 | o16·=·total:·12·24·12 | 61 | o16·=·total:·12·24·12 |
| 62 | ··········0:·12·24·12 | 62 | ··········0:·12·24·12 |
| Offset 120, 15 lines modified | Offset 120, 15 lines modified | ||
| 120 | o3·=·3</code></pre> | 120 | o3·=·3</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·kk=·ZZ/101;</code></pre> | 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·kk=·ZZ/101;</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g); | 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g); |
| 127 | ·--· | 127 | ·--·1.20671s·elapsed</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i6·:·M=cliffordModule(Mu1,Mu2,R) | 130 | <td>··············<pre><code·class="language-macaulay2">i6·:·M=cliffordModule(Mu1,Mu2,R) |
| 131 | o6·=·CliffordModule{...6...} | 131 | o6·=·CliffordModule{...6...} |
| 132 | o6·:·CliffordModule</code></pre> | 132 | o6·:·CliffordModule</code></pre> |
| Offset 152, 15 lines modified | Offset 152, 15 lines modified | ||
| 152 | ··········m12=randomExtension(m1.yAction,m2.yAction); | 152 | ··········m12=randomExtension(m1.yAction,m2.yAction); |
| 153 | ··········V·=·vectorBundleOnE·m12; | 153 | ··········V·=·vectorBundleOnE·m12; |
| 154 | ··········Ul=tensorProduct(Mor,V); | 154 | ··········Ul=tensorProduct(Mor,V); |
| 155 | ··········Ul1=tensorProduct(Mor1,V); | 155 | ··········Ul1=tensorProduct(Mor1,V); |
| 156 | ··········d0=unique·degrees·target·Ul.yAction; | 156 | ··········d0=unique·degrees·target·Ul.yAction; |
| 157 | ··········d1=unique·degrees·target·Ul1.yAction; | 157 | ··········d1=unique·degrees·target·Ul1.yAction; |
| 158 | ··········#d1·>=3·or·#d0·>=3)·do·(); | 158 | ··········#d1·>=3·or·#d0·>=3)·do·(); |
| 159 | ·--·.3 | 159 | ·--·.351805s·elapsed</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| 162 | <td>··············<pre><code·class="language-macaulay2">i12·:·betti·Ul.yAction,·betti·Ul1.yAction | 162 | <td>··············<pre><code·class="language-macaulay2">i12·:·betti·Ul.yAction,·betti·Ul1.yAction |
| 163 | ···············0··1··········0··1 | 163 | ···············0··1··········0··1 |
| 164 | o12·=·(total:·32·32,·total:·32·32) | 164 | o12·=·(total:·32·32,·total:·32·32) |
| 165 | ··········-4:·16··.·····-2:·32··. | 165 | ··········-4:·16··.·····-2:·32··. |
| Offset 169, 15 lines modified | Offset 169, 15 lines modified | ||
| 169 | ··········-1:··.·16······1:··.·32 | 169 | ··········-1:··.·16······1:··.·32 |
| 170 | ···········0:··.·16 | 170 | ···········0:··.·16 |
| 171 | o12·:·Sequence</code></pre> | 171 | o12·:·Sequence</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators | 174 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the·actions·of·generators |
| 175 | ·--·1 | 175 | ·--·15.8888s·elapsed</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ··········<tr> | 177 | ··········<tr> |
| 178 | <td>··············<pre><code·class="language-macaulay2">i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S)); | 178 | <td>··············<pre><code·class="language-macaulay2">i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S)); |
| 179 | ··············32······32 | 179 | ··············32······32 |
| 180 | o14·:·Matrix·S···<--·S</code></pre> | 180 | o14·:·Matrix·S···<--·S</code></pre> |
| 181 | </td>··········</tr> | 181 | </td>··········</tr> |
| Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
| 56 | ············--·will·give·an·Ulrich·bundle,·with·betti·table | 56 | ············--·will·give·an·Ulrich·bundle,·with·betti·table |
| 57 | ············--·16·32·16 | 57 | ············--·16·32·16 |
| 58 | i3·:·g=3 | 58 | i3·:·g=3 |
| 59 | o3·=·3 | 59 | o3·=·3 |
| 60 | i4·:·kk=·ZZ/101; | 60 | i4·:·kk=·ZZ/101; |
| 61 | i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g); | 61 | i5·:·elapsedTime·(S,qq,R,u,·M1,M2,·Mu1,·Mu2)=randomNicePencil(kk,g); |
| 62 | ·--· | 62 | ·--·1.20671s·elapsed |
| 63 | i6·:·M=cliffordModule(Mu1,Mu2,R) | 63 | i6·:·M=cliffordModule(Mu1,Mu2,R) |
| 64 | o6·=·CliffordModule{...6...} | 64 | o6·=·CliffordModule{...6...} |
| 65 | o6·:·CliffordModule | 65 | o6·:·CliffordModule |
| 66 | i7·:·Mor·=·vectorBundleOnE·M.evenCenter; | 66 | i7·:·Mor·=·vectorBundleOnE·M.evenCenter; |
| 67 | i8·:·Mor1=·vectorBundleOnE·M.oddCenter; | 67 | i8·:·Mor1=·vectorBundleOnE·M.oddCenter; |
| Offset 76, 29 lines modified | Offset 76, 29 lines modified | ||
| 76 | ··········m12=randomExtension(m1.yAction,m2.yAction); | 76 | ··········m12=randomExtension(m1.yAction,m2.yAction); |
| 77 | ··········V·=·vectorBundleOnE·m12; | 77 | ··········V·=·vectorBundleOnE·m12; |
| 78 | ··········Ul=tensorProduct(Mor,V); | 78 | ··········Ul=tensorProduct(Mor,V); |
| 79 | ··········Ul1=tensorProduct(Mor1,V); | 79 | ··········Ul1=tensorProduct(Mor1,V); |
| 80 | ··········d0=unique·degrees·target·Ul.yAction; | 80 | ··········d0=unique·degrees·target·Ul.yAction; |
| 81 | ··········d1=unique·degrees·target·Ul1.yAction; | 81 | ··········d1=unique·degrees·target·Ul1.yAction; |
| 82 | ··········#d1·>=3·or·#d0·>=3)·do·(); | 82 | ··········#d1·>=3·or·#d0·>=3)·do·(); |
| 83 | ·--·.3 | 83 | ·--·.351805s·elapsed |
| 84 | i12·:·betti·Ul.yAction,·betti·Ul1.yAction | 84 | i12·:·betti·Ul.yAction,·betti·Ul1.yAction |
| 85 | ···············0··1··········0··1 | 85 | ···············0··1··········0··1 |
| 86 | o12·=·(total:·32·32,·total:·32·32) | 86 | o12·=·(total:·32·32,·total:·32·32) |
| 87 | ··········-4:·16··.·····-2:·32··. | 87 | ··········-4:·16··.·····-2:·32··. |
| 88 | ··········-3:·16··.·····-1:··.··. | 88 | ··········-3:·16··.·····-1:··.··. |
| 89 | ··········-2:··.··.······0:··.··. | 89 | ··········-2:··.··.······0:··.··. |
| 90 | ··········-1:··.·16······1:··.·32 | 90 | ··········-1:··.·16······1:··.·32 |
| 91 | ···········0:··.·16 | 91 | ···········0:··.·16 |
| 92 | o12·:·Sequence | 92 | o12·:·Sequence |
| 93 | i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the | 93 | i13·:·elapsedTime·Ul·=·tensorProduct(M,V);·--·the·heaviest·part·computing·the |
| 94 | actions·of·generators | 94 | actions·of·generators |
| 95 | ·--·1 | 95 | ·--·15.8888s·elapsed |
| 96 | i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S)); | 96 | i14·:·M1Ul=sum(#Ul.oddOperators,i->S_i*sub(Ul.oddOperators_i,S)); |
| 97 | ··············32······32 | 97 | ··············32······32 |
| 98 | o14·:·Matrix·S···<--·S | 98 | o14·:·Matrix·S···<--·S |
| 99 | i15·:·r=2 | 99 | i15·:·r=2 |
| 100 | o15·=·2 | 100 | o15·=·2 |
| Offset 139, 15 lines modified | Offset 139, 15 lines modified | ||
| 139 | o11·=·CliffordModule{...6...} | 139 | o11·=·CliffordModule{...6...} |
| 140 | o11·:·CliffordModule</code></pre> | 140 | o11·:·CliffordModule</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·Ulr·=·searchUlrich(M,S); | 143 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·Ulr·=·searchUlrich(M,S); |
| 144 | ·--·. | 144 | ·--·.710483s·elapsed</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i13·:·betti·res·Ulr | 147 | <td>··············<pre><code·class="language-macaulay2">i13·:·betti·res·Ulr |
| 148 | ·············0··1·2 | 148 | ·············0··1·2 |
| 149 | o13·=·total:·8·16·8 | 149 | o13·=·total:·8·16·8 |
| 150 | ··········0:·8·16·8 | 150 | ··········0:·8·16·8 |
| Offset 157, 15 lines modified | Offset 157, 15 lines modified | ||
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i14·:·ann·Ulr·==·ideal·qs | 158 | <td>··············<pre><code·class="language-macaulay2">i14·:·ann·Ulr·==·ideal·qs |
| 159 | o14·=·true</code></pre> | 159 | o14·=·true</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| 162 | <td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3); | 162 | <td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3); |
| 163 | ·--·1. | 163 | ·--·1.83737s·elapsed</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i16·:·betti·res·Ulr3 | 166 | <td>··············<pre><code·class="language-macaulay2">i16·:·betti·res·Ulr3 |
| 167 | ··············0··1··2 | 167 | ··············0··1··2 |
| 168 | o16·=·total:·12·24·12 | 168 | o16·=·total:·12·24·12 |
| 169 | ··········0:·12·24·12 | 169 | ··········0:·12·24·12 |
| Offset 64, 27 lines modified | Offset 64, 27 lines modified | ||
| 64 | o10·:·Matrix·S··<--·S | 64 | o10·:·Matrix·S··<--·S |
| 65 | i11·:·M=cliffordModule(Mu1,Mu2,R) | 65 | i11·:·M=cliffordModule(Mu1,Mu2,R) |
| 66 | o11·=·CliffordModule{...6...} | 66 | o11·=·CliffordModule{...6...} |
| 67 | o11·:·CliffordModule | 67 | o11·:·CliffordModule |
| 68 | i12·:·elapsedTime·Ulr·=·searchUlrich(M,S); | 68 | i12·:·elapsedTime·Ulr·=·searchUlrich(M,S); |
| 69 | ·--·. | 69 | ·--·.710483s·elapsed |
| 70 | i13·:·betti·res·Ulr | 70 | i13·:·betti·res·Ulr |
| 71 | ·············0··1·2 | 71 | ·············0··1·2 |
| 72 | o13·=·total:·8·16·8 | 72 | o13·=·total:·8·16·8 |
| 73 | ··········0:·8·16·8 | 73 | ··········0:·8·16·8 |
| 74 | o13·:·BettiTally | 74 | o13·:·BettiTally |
| 75 | i14·:·ann·Ulr·==·ideal·qs | 75 | i14·:·ann·Ulr·==·ideal·qs |
| 76 | o14·=·true | 76 | o14·=·true |
| 77 | i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3); | 77 | i15·:·elapsedTime·Ulr3·=·searchUlrich(M,S,3); |
| 78 | ·--·1. | 78 | ·--·1.83737s·elapsed |
| 79 | i16·:·betti·res·Ulr3 | 79 | i16·:·betti·res·Ulr3 |
| 80 | ··············0··1··2 | 80 | ··············0··1··2 |
| 81 | o16·=·total:·12·24·12 | 81 | o16·=·total:·12·24·12 |
| 82 | ··········0:·12·24·12 | 82 | ··········0:·12·24·12 |
| 83 | o16·:·BettiTally | 83 | o16·:·BettiTally |
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| 9 | #:len=2848 | 9 | #:len=2848 |
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| 11 | dmFyaWFudHMgb2YgYSBncm91cC1iYXNlZCBwaHlsb2dlbmV0aWMgbW9kZWwiLCAibGluZW51bSIg | 11 | dmFyaWFudHMgb2YgYSBncm91cC1iYXNlZCBwaHlsb2dlbmV0aWMgbW9kZWwiLCAibGluZW51bSIg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | c3RhbmRhcmRUYWJsZWF1eChaWixMaXN0KQ== | 8 | c3RhbmRhcmRUYWJsZWF1eChaWixMaXN0KQ== |
| 9 | #:len=268 | 9 | #:len=268 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTA1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTA1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzdGFuZGFyZFRhYmxlYXV4LFpaLExpc3QpLCJzdGFu | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzdGFuZGFyZFRhYmxlYXV4LFpaLExpc3QpLCJzdGFu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=27 | 7 | #:len=27 |
| 8 | YWRkaXRpb24oSWRlYWwsSWRlYWwsSWRlYWwp | 8 | YWRkaXRpb24oSWRlYWwsSWRlYWwsSWRlYWwp |
| 9 | #:len=295 | 9 | #:len=295 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGRpdGlvbixJZGVhbCxJZGVhbCxJZGVhbCksImFk | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhZGRpdGlvbixJZGVhbCxJZGVhbCxJZGVhbCksImFk |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=24 | 7 | #:len=24 |
| 8 | cmFuZG9tUG9pbnRzTWF0KFJpbmcsWlop | 8 | cmFuZG9tUG9pbnRzTWF0KFJpbmcsWlop |
| 9 | #:len=255 | 9 | #:len=255 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODc0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODc0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyYW5kb21Qb2ludHNNYXQsUmluZyxaWiksInJhbmRv | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhyYW5kb21Qb2ludHNNYXQsUmluZyxaWiksInJhbmRv |
| Offset 66, 17 lines modified | Offset 66, 17 lines modified | ||
| 66 | i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3} | 66 | i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3} |
| 67 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} | 67 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} |
| 68 | o9·:·List | 68 | o9·:·List |
| 69 | i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); | 69 | i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); |
| 70 | ·--· | 70 | ·--·3.12009s·elapsed |
| 71 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); | 71 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); |
| 72 | ·--· | 72 | ·--·4.4746s·elapsed |
| 73 | i12·:·G==H | 73 | i12·:·G==H |
| 74 | o12·=·true | 74 | o12·=·true |
| 75 | i13·:· | 75 | i13·:· |
| Offset 162, 19 lines modified | Offset 162, 19 lines modified | ||
| 162 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} | 162 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} |
| 163 | o9·:·List</code></pre> | 163 | o9·:·List</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); | 166 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); |
| 167 | ·--· | 167 | ·--·3.12009s·elapsed</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); | 170 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); |
| 171 | ·--· | 171 | ·--·4.4746s·elapsed</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i12·:·G==H | 174 | <td>··············<pre><code·class="language-macaulay2">i12·:·G==H |
| 175 | o12·=·true</code></pre> | 175 | o12·=·true</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ········</table> | 177 | ········</table> |
| Offset 82, 17 lines modified | Offset 82, 17 lines modified | ||
| 82 | o8·:·Matrix·K··<--·K | 82 | o8·:·Matrix·K··<--·K |
| 83 | i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3} | 83 | i9·:·mults·=·{1,2,3,1,2,3,1,2,3,1,2,3} |
| 84 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} | 84 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} |
| 85 | o9·:·List | 85 | o9·:·List |
| 86 | i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); | 86 | i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); |
| 87 | ·--· | 87 | ·--·3.12009s·elapsed |
| 88 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); | 88 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); |
| 89 | ·--· | 89 | ·--·4.4746s·elapsed |
| 90 | i12·:·G==H | 90 | i12·:·G==H |
| 91 | o12·=·true | 91 | o12·=·true |
| 92 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 92 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 93 | For·reduced·points,·this·function·may·be·a·bit·slower·than·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s. | 93 | For·reduced·points,·this·function·may·be·a·bit·slower·than·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s. |
| 94 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 94 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 95 | ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8F_\x8a_\x8t_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s_\x8B_\x8y_\x8I_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8,_\x8L_\x8i_\x8s_\x8t_\x8,_\x8R_\x8i_\x8n_\x8g_\x8)·--·computes·ideal·of·fat | 95 | ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8F_\x8a_\x8t_\x8P_\x8o_\x8i_\x8n_\x8t_\x8s_\x8B_\x8y_\x8I_\x8n_\x8t_\x8e_\x8r_\x8s_\x8e_\x8c_\x8t_\x8i_\x8o_\x8n_\x8(_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8,_\x8L_\x8i_\x8s_\x8t_\x8,_\x8R_\x8i_\x8n_\x8g_\x8)·--·computes·ideal·of·fat |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | bWF4Q29uZXM= | 8 | bWF4Q29uZXM= |
| 9 | #:len=1185 | 9 | #:len=1185 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheXMgdGhlIGdlbmVyYXRpbmcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZGlzcGxheXMgdGhlIGdlbmVyYXRpbmcg |
| 11 | Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gODQzLCBJbnB1dHMgPT4ge1NQQU57VFR7IkYi | 11 | Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gODQzLCBJbnB1dHMgPT4ge1NQQU57VFR7IkYi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | UG9seW1ha2U= | 8 | UG9seW1ha2U= |
| 9 | #:len=610 | 9 | #:len=610 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZvciBpbnRlcmZhY2lu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwYWNrYWdlIGZvciBpbnRlcmZhY2lu |
| 11 | ZyB3aXRoIHBvbHltYWtlIiwgRGVzY3JpcHRpb24gPT4gKEVNeyJQb2x5bWFrZSJ9LCIgaXMgYSBw | 11 | ZyB3aXRoIHBvbHltYWtlIiwgRGVzY3JpcHRpb24gPT4gKEVNeyJQb2x5bWFrZSJ9LCIgaXMgYSBw |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | cG9seW9JZGVhbChMaXN0KQ== | 8 | cG9seW9JZGVhbChMaXN0KQ== |
| 9 | #:len=256 | 9 | #:len=256 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwb2x5b0lkZWFsLExpc3QpLCJwb2x5b0lkZWFsKExp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwb2x5b0lkZWFsLExpc3QpLCJwb2x5b0lkZWFsKExp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=17 | 7 | #:len=17 |
| 8 | bWF4aW1hbEFudGljaGFpbnM= | 8 | bWF4aW1hbEFudGljaGFpbnM= |
| 9 | #:len=1127 | 9 | #:len=1127 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYWxsIG1heGltYWwgYW50 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYWxsIG1heGltYWwgYW50 |
| 11 | aWNoYWlucyBvZiBhIHBvc2V0IiwgImxpbmVudW0iID0+IDQ4NzgsIElucHV0cyA9PiB7U1BBTntU | 11 | aWNoYWlucyBvZiBhIHBvc2V0IiwgImxpbmVudW0iID0+IDQ4NzgsIElucHV0cyA9PiB7U1BBTntU |
| Offset 31, 27 lines modified | Offset 31, 27 lines modified | ||
| 31 | o5·=·CacheTable{name·=>·P} | 31 | o5·=·CacheTable{name·=>·P} |
| 32 | i6·:·C·==·P | 32 | i6·:·C·==·P |
| 33 | o6·=·true | 33 | o6·=·true |
| 34 | i7·:·time·isDistributive·C | 34 | i7·:·time·isDistributive·C |
| 35 | ·--·used· | 35 | ·--·used·1.7132e-05s·(cpu);·5.56e-06s·(thread);·0s·(gc) |
| 36 | o7·=·true | 36 | o7·=·true |
| 37 | i8·:·time·isDistributive·P | 37 | i8·:·time·isDistributive·P |
| 38 | ·--·used·4. | 38 | ·--·used·4.97271s·(cpu);·3.46374s·(thread);·0s·(gc) |
| 39 | o8·=·true | 39 | o8·=·true |
| 40 | i9·:·C'·=·dual·C; | 40 | i9·:·C'·=·dual·C; |
| 41 | i10·:·time·isDistributive·C' | 41 | i10·:·time·isDistributive·C' |
| 42 | ·--·used·0.000 | 42 | ·--·used·0.00022398s·(cpu);·4.248e-06s·(thread);·0s·(gc) |
| 43 | o10·=·true | 43 | o10·=·true |
| 44 | i11·:·peek·C'.cache | 44 | i11·:·peek·C'.cache |
| 45 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································} | 45 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································} |
| 46 | ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4},·{6,·5},·{7,·6},·{8,·7},·{9,·8}} | 46 | ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4},·{6,·5},·{7,·6},·{8,·7},·{9,·8}} |
| Offset 7, 22 lines modified | Offset 7, 22 lines modified | ||
| 7 | o2·=·Partition{4,·2} | 7 | o2·=·Partition{4,·2} |
| 8 | o2·:·Partition | 8 | o2·:·Partition |
| 9 | i3·:·D·=·dominanceLattice·6; | 9 | i3·:·D·=·dominanceLattice·6; |
| 10 | i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") | 10 | i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") |
| 11 | ·--·used·0. | 11 | ·--·used·0.283607s·(cpu);·0.165089s·(thread);·0s·(gc) |
| 12 | o4·=·Partition{9,·2} | 12 | o4·=·Partition{9,·2} |
| 13 | o4·:·Partition | 13 | o4·:·Partition |
| 14 | i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") | 14 | i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") |
| 15 | ·--·used· | 15 | ·--·used·6.5843e-05s·(cpu);·9.859e-06s·(thread);·0s·(gc) |
| 16 | o5·=·Partition{9,·2} | 16 | o5·=·Partition{9,·2} |
| 17 | o5·:·Partition | 17 | o5·:·Partition |
| 18 | i6·:·greeneKleitmanPartition·chain·10 | 18 | i6·:·greeneKleitmanPartition·chain·10 |
| Offset 87, 35 lines modified | Offset 87, 35 lines modified | ||
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i6·:·C·==·P | 88 | <td>··············<pre><code·class="language-macaulay2">i6·:·C·==·P |
| 89 | o6·=·true</code></pre> | 89 | o6·=·true</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDistributive·C | 92 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDistributive·C |
| 93 | ·--·used· | 93 | ·--·used·1.7132e-05s·(cpu);·5.56e-06s·(thread);·0s·(gc) |
| 94 | o7·=·true</code></pre> | 94 | o7·=·true</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isDistributive·P | 97 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isDistributive·P |
| 98 | ·--·used·4. | 98 | ·--·used·4.97271s·(cpu);·3.46374s·(thread);·0s·(gc) |
| 99 | o8·=·true</code></pre> | 99 | o8·=·true</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ········</table> | 101 | ········</table> |
| 102 | ········<div> | 102 | ········<div> |
| 103 | ··········<p>We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive·lattice.··Other·information·is·copied·when·possible.</p> | 103 | ··········<p>We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive·lattice.··Other·information·is·copied·when·possible.</p> |
| 104 | ········</div> | 104 | ········</div> |
| 105 | ········<table·class="examples"> | 105 | ········<table·class="examples"> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i9·:·C'·=·dual·C;</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i9·:·C'·=·dual·C;</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isDistributive·C' | 110 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isDistributive·C' |
| 111 | ·--·used·0.000 | 111 | ·--·used·0.00022398s·(cpu);·4.248e-06s·(thread);·0s·(gc) |
| 112 | o10·=·true</code></pre> | 112 | o10·=·true</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i11·:·peek·C'.cache | 115 | <td>··············<pre><code·class="language-macaulay2">i11·:·peek·C'.cache |
| 116 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································} | 116 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································} |
| Offset 41, 26 lines modified | Offset 41, 26 lines modified | ||
| 41 | i5·:·peek·P.cache | 41 | i5·:·peek·P.cache |
| 42 | o5·=·CacheTable{name·=>·P} | 42 | o5·=·CacheTable{name·=>·P} |
| 43 | i6·:·C·==·P | 43 | i6·:·C·==·P |
| 44 | o6·=·true | 44 | o6·=·true |
| 45 | i7·:·time·isDistributive·C | 45 | i7·:·time·isDistributive·C |
| 46 | ·--·used· | 46 | ·--·used·1.7132e-05s·(cpu);·5.56e-06s·(thread);·0s·(gc) |
| 47 | o7·=·true | 47 | o7·=·true |
| 48 | i8·:·time·isDistributive·P | 48 | i8·:·time·isDistributive·P |
| 49 | ·--·used·4. | 49 | ·--·used·4.97271s·(cpu);·3.46374s·(thread);·0s·(gc) |
| 50 | o8·=·true | 50 | o8·=·true |
| 51 | We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive | 51 | We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive |
| 52 | lattice.·Other·information·is·copied·when·possible. | 52 | lattice.·Other·information·is·copied·when·possible. |
| 53 | i9·:·C'·=·dual·C; | 53 | i9·:·C'·=·dual·C; |
| 54 | i10·:·time·isDistributive·C' | 54 | i10·:·time·isDistributive·C' |
| 55 | ·--·used·0.000 | 55 | ·--·used·0.00022398s·(cpu);·4.248e-06s·(thread);·0s·(gc) |
| 56 | o10·=·true | 56 | o10·=·true |
| 57 | i11·:·peek·C'.cache | 57 | i11·:·peek·C'.cache |
| 58 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}} | 58 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}} |
| 59 | } | 59 | } |
| 60 | ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4}, | 60 | ·················coveringRelations·=>·{{1,·0},·{2,·1},·{3,·2},·{4,·3},·{5,·4}, |
| Offset 95, 23 lines modified | Offset 95, 23 lines modified | ||
| 95 | ········</div> | 95 | ········</div> |
| 96 | ········<table·class="examples"> | 96 | ········<table·class="examples"> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·D·=·dominanceLattice·6;</code></pre> | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·D·=·dominanceLattice·6;</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") |
| 102 | ·--·used·0. | 102 | ·--·used·0.283607s·(cpu);·0.165089s·(thread);·0s·(gc) |
| 103 | o4·=·Partition{9,·2} | 103 | o4·=·Partition{9,·2} |
| 104 | o4·:·Partition</code></pre> | 104 | o4·:·Partition</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") |
| 108 | ·--·used· | 108 | ·--·used·6.5843e-05s·(cpu);·9.859e-06s·(thread);·0s·(gc) |
| 109 | o5·=·Partition{9,·2} | 109 | o5·=·Partition{9,·2} |
| 110 | o5·:·Partition</code></pre> | 110 | o5·:·Partition</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ········<div> | 113 | ········<div> |
| Offset 29, 21 lines modified | Offset 29, 21 lines modified | ||
| 29 | o2·:·Partition | 29 | o2·:·Partition |
| 30 | The·conjugate·of·$l$·has·the·same·property,·but·with·chains·replaced·by | 30 | The·conjugate·of·$l$·has·the·same·property,·but·with·chains·replaced·by |
| 31 | _\x8a_\x8n_\x8t_\x8i_\x8c_\x8h_\x8a_\x8i_\x8n_\x8s.·Because·of·this,·it·is·often·better·to·count·via·antichains·instead | 31 | _\x8a_\x8n_\x8t_\x8i_\x8c_\x8h_\x8a_\x8i_\x8n_\x8s.·Because·of·this,·it·is·often·better·to·count·via·antichains·instead |
| 32 | of·chains.·This·can·be·done·by·passing·"antichains"·as·the·Strategy. | 32 | of·chains.·This·can·be·done·by·passing·"antichains"·as·the·Strategy. |
| 33 | i3·:·D·=·dominanceLattice·6; | 33 | i3·:·D·=·dominanceLattice·6; |
| 34 | i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") | 34 | i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") |
| 35 | ·--·used·0. | 35 | ·--·used·0.283607s·(cpu);·0.165089s·(thread);·0s·(gc) |
| 36 | o4·=·Partition{9,·2} | 36 | o4·=·Partition{9,·2} |
| 37 | o4·:·Partition | 37 | o4·:·Partition |
| 38 | i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") | 38 | i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") |
| 39 | ·--·used· | 39 | ·--·used·6.5843e-05s·(cpu);·9.859e-06s·(thread);·0s·(gc) |
| 40 | o5·=·Partition{9,·2} | 40 | o5·=·Partition{9,·2} |
| 41 | o5·:·Partition | 41 | o5·:·Partition |
| 42 | The·Greene-Kleitman·partition·of·the·$n$·_\x8c_\x8h_\x8a_\x8i_\x8n·is·the·partition·of·$n$·with·$1$ | 42 | The·Greene-Kleitman·partition·of·the·$n$·_\x8c_\x8h_\x8a_\x8i_\x8n·is·the·partition·of·$n$·with·$1$ |
| 43 | part. | 43 | part. |
| 44 | i6·:·greeneKleitmanPartition·chain·10 | 44 | i6·:·greeneKleitmanPartition·chain·10 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | ZHJhd1BhcmxpYW1lbnQyRHRpa3o= | 8 | ZHJhd1BhcmxpYW1lbnQyRHRpa3o= |
| 9 | #:len=2626 | 9 | #:len=2626 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmlzdWFsaXNlcyB0aGUgcGFybGlhbWVu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmlzdWFsaXNlcyB0aGUgcGFybGlhbWVu |
| 11 | dCBvZiBwb2x5dG9wZXMgZm9yIGEgdmVjdG9yIGJ1bmRsZSBvbiBhIHRvcmljIHN1cmZhY2UgdXNp | 11 | dCBvZiBwb2x5dG9wZXMgZm9yIGEgdmVjdG9yIGJ1bmRsZSBvbiBhIHRvcmljIHN1cmZhY2UgdXNp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=35 | 7 | #:len=35 |
| 8 | cHJpbWFyeUNvbXBvbmVudCguLi4sU3RyYXRlZ3k9Pi4uLik= | 8 | cHJpbWFyeUNvbXBvbmVudCguLi4sU3RyYXRlZ3k9Pi4uLik= |
| 9 | #:len=316 | 9 | #:len=316 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzQ5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzQ5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1twcmltYXJ5Q29tcG9uZW50LFN0cmF0ZWd5XSwicHJp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1twcmltYXJ5Q29tcG9uZW50LFN0cmF0ZWd5XSwicHJp |
| Offset 24, 35 lines modified | Offset 24, 35 lines modified | ||
| 24 | ··············|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 24 | ··············|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 25 | ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 25 | ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 26 | ····························3 | 26 | ····························3 |
| 27 | o3·:·R-module,·quotient·of·R | 27 | o3·:·R-module,·quotient·of·R |
| 28 | i4·:·elapsedTime·kernelOfLocalization(M,·I1) | 28 | i4·:·elapsedTime·kernelOfLocalization(M,·I1) |
| 29 | ·--·.1 | 29 | ·--·.199533s·elapsed |
| 30 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) | 30 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 31 | ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 31 | ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 32 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 32 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 33 | ·······························3 | 33 | ·······························3 |
| 34 | o4·:·R-module,·subquotient·of·R | 34 | o4·:·R-module,·subquotient·of·R |
| 35 | i5·:·elapsedTime·kernelOfLocalization(M,·I2) | 35 | i5·:·elapsedTime·kernelOfLocalization(M,·I2) |
| 36 | ·--·.01 | 36 | ·--·.0171701s·elapsed |
| 37 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) | 37 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 38 | ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 38 | ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 39 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 39 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 40 | ·······························3 | 40 | ·······························3 |
| 41 | o5·:·R-module,·subquotient·of·R | 41 | o5·:·R-module,·subquotient·of·R |
| 42 | i6·:·elapsedTime·kernelOfLocalization(M,·I3) | 42 | i6·:·elapsedTime·kernelOfLocalization(M,·I3) |
| 43 | ·--·.0 | 43 | ·--·.0451606s·elapsed |
| 44 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) | 44 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 45 | ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 45 | ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 46 | ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 46 | ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 47 | ·······························3 | 47 | ·······························3 |
| 48 | o6·:·R-module,·subquotient·of·R | 48 | o6·:·R-module,·subquotient·of·R |
| Offset 13, 15 lines modified | Offset 13, 15 lines modified | ||
| 13 | ·····------------------------------------------------------------------------ | 13 | ·····------------------------------------------------------------------------ |
| 14 | ·····x·x·) | 14 | ·····x·x·) |
| 15 | ······0·4 | 15 | ······0·4 |
| 16 | o2·:·Ideal·of·R | 16 | o2·:·Ideal·of·R |
| 17 | i3·:·elapsedTime·regSeqInIdeal·I | 17 | i3·:·elapsedTime·regSeqInIdeal·I |
| 18 | ·--·.0 | 18 | ·--·.0924602s·elapsed |
| 19 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) | 19 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) |
| 20 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 | 20 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 |
| 21 | o3·:·Ideal·of·R | 21 | o3·:·Ideal·of·R |
| 22 | i4·:·R·=·QQ[h,l,s,x,y,z] | 22 | i4·:·R·=·QQ[h,l,s,x,y,z] |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | o5·:·Ideal·of·R | 41 | o5·:·Ideal·of·R |
| 42 | i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 | 42 | i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 |
| 43 | o6·=·true | 43 | o6·=·true |
| 44 | i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) | 44 | i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) |
| 45 | ·--·.0 | 45 | ·--·.0123894s·elapsed |
| 46 | ···················2················3····2·····2····8····3····2·····2 | 46 | ···················2················3····2·····2····8····3····2·····2 |
| 47 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) | 47 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) |
| 48 | o7·:·Ideal·of·R | 48 | o7·:·Ideal·of·R |
| 49 | i8·:· | 49 | i8·:· |
| Offset 101, 37 lines modified | Offset 101, 37 lines modified | ||
| 101 | ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 101 | ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 102 | ····························3 | 102 | ····························3 |
| 103 | o3·:·R-module,·quotient·of·R</code></pre> | 103 | o3·:·R-module,·quotient·of·R</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·kernelOfLocalization(M,·I1) | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·kernelOfLocalization(M,·I1) |
| 107 | ·--·.1 | 107 | ·--·.199533s·elapsed |
| 108 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) | 108 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 109 | ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 109 | ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 110 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 110 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 111 | ·······························3 | 111 | ·······························3 |
| 112 | o4·:·R-module,·subquotient·of·R</code></pre> | 112 | o4·:·R-module,·subquotient·of·R</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·kernelOfLocalization(M,·I2) | 115 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·kernelOfLocalization(M,·I2) |
| 116 | ·--·.01 | 116 | ·--·.0171701s·elapsed |
| 117 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) | 117 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 118 | ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 118 | ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 119 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 119 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 120 | ·······························3 | 120 | ·······························3 |
| 121 | o5·:·R-module,·subquotient·of·R</code></pre> | 121 | o5·:·R-module,·subquotient·of·R</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·kernelOfLocalization(M,·I3) | 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·kernelOfLocalization(M,·I3) |
| 125 | ·--·.0 | 125 | ·--·.0451606s·elapsed |
| 126 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) | 126 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 127 | ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 127 | ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 128 | ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 128 | ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 129 | ·······························3 | 129 | ·······························3 |
| 130 | o6·:·R-module,·subquotient·of·R</code></pre> | 130 | o6·:·R-module,·subquotient·of·R</code></pre> |
| Offset 42, 39 lines modified | Offset 42, 39 lines modified | ||
| 42 | | | 42 | | |
| 43 | ··············|·0············0·············0············0··············x_1^5- | 43 | ··············|·0············0·············0············0··············x_1^5- |
| 44 | x_0x_2^4·| | 44 | x_0x_2^4·| |
| 45 | ····························3 | 45 | ····························3 |
| 46 | o3·:·R-module,·quotient·of·R | 46 | o3·:·R-module,·quotient·of·R |
| 47 | i4·:·elapsedTime·kernelOfLocalization(M,·I1) | 47 | i4·:·elapsedTime·kernelOfLocalization(M,·I1) |
| 48 | ·--·.1 | 48 | ·--·.199533s·elapsed |
| 49 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0 | 49 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0 |
| 50 | 0··············|) | 50 | 0··············|) |
| 51 | ··················|·1·0·|··|·0············0·············0············x_1^3- | 51 | ··················|·1·0·|··|·0············0·············0············x_1^3- |
| 52 | x_0x_2^2·0··············| | 52 | x_0x_2^2·0··············| |
| 53 | ··················|·0·1·|··|·0············0·············0············0 | 53 | ··················|·0·1·|··|·0············0·············0············0 |
| 54 | x_1^5-x_0x_2^4·| | 54 | x_1^5-x_0x_2^4·| |
| 55 | ·······························3 | 55 | ·······························3 |
| 56 | o4·:·R-module,·subquotient·of·R | 56 | o4·:·R-module,·subquotient·of·R |
| 57 | i5·:·elapsedTime·kernelOfLocalization(M,·I2) | 57 | i5·:·elapsedTime·kernelOfLocalization(M,·I2) |
| 58 | ·--·.01 | 58 | ·--·.0171701s·elapsed |
| 59 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0 | 59 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0 |
| 60 | 0··············|) | 60 | 0··············|) |
| 61 | ··················|·0·0·|··|·0············0·············0············x_1^3- | 61 | ··················|·0·0·|··|·0············0·············0············x_1^3- |
| 62 | x_0x_2^2·0··············| | 62 | x_0x_2^2·0··············| |
| 63 | ··················|·0·1·|··|·0············0·············0············0 | 63 | ··················|·0·1·|··|·0············0·············0············0 |
| 64 | x_1^5-x_0x_2^4·| | 64 | x_1^5-x_0x_2^4·| |
| 65 | ·······························3 | 65 | ·······························3 |
| 66 | o5·:·R-module,·subquotient·of·R | 66 | o5·:·R-module,·subquotient·of·R |
| 67 | i6·:·elapsedTime·kernelOfLocalization(M,·I3) | 67 | i6·:·elapsedTime·kernelOfLocalization(M,·I3) |
| 68 | ·--·.0 | 68 | ·--·.0451606s·elapsed |
| 69 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0 | 69 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0 |
| 70 | 0··············|) | 70 | 0··············|) |
| 71 | ··················|·0·1·|··|·0············0·············0············x_1^3- | 71 | ··················|·0·1·|··|·0············0·············0············x_1^3- |
| 72 | x_0x_2^2·0··············| | 72 | x_0x_2^2·0··············| |
| 73 | ··················|·0·0·|··|·0············0·············0············0 | 73 | ··················|·0·0·|··|·0············0·············0············0 |
| 74 | x_1^5-x_0x_2^4·| | 74 | x_1^5-x_0x_2^4·| |
| Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | ·····x·x·) | 102 | ·····x·x·) |
| 103 | ······0·4 | 103 | ······0·4 |
| 104 | o2·:·Ideal·of·R</code></pre> | 104 | o2·:·Ideal·of·R</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·regSeqInIdeal·I | 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·regSeqInIdeal·I |
| 108 | ·--·.0 | 108 | ·--·.0924602s·elapsed |
| 109 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) | 109 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) |
| 110 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 | 110 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 |
| 111 | o3·:·Ideal·of·R</code></pre> | 111 | o3·:·Ideal·of·R</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ········</table> | 113 | ········</table> |
| Offset 140, 15 lines modified | Offset 140, 15 lines modified | ||
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 | 141 | <td>··············<pre><code·class="language-macaulay2">i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 |
| 142 | o6·=·true</code></pre> | 142 | o6·=·true</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) | 145 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) |
| 146 | ·--·.0 | 146 | ·--·.0123894s·elapsed |
| 147 | ···················2················3····2·····2····8····3····2·····2 | 147 | ···················2················3····2·····2····8····3····2·····2 |
| 148 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) | 148 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) |
| 149 | o7·:·Ideal·of·R</code></pre> | 149 | o7·:·Ideal·of·R</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ········</table> | 151 | ········</table> |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | ·············2·7···0·7···3·6···2·6···1·6···0·6···2·5···0·5···3·4···2·4···1·4 | 41 | ·············2·7···0·7···3·6···2·6···1·6···0·6···2·5···0·5···3·4···2·4···1·4 |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·····x·x·) | 43 | ·····x·x·) |
| 44 | ······0·4 | 44 | ······0·4 |
| 45 | o2·:·Ideal·of·R | 45 | o2·:·Ideal·of·R |
| 46 | i3·:·elapsedTime·regSeqInIdeal·I | 46 | i3·:·elapsedTime·regSeqInIdeal·I |
| 47 | ·--·.0 | 47 | ·--·.0924602s·elapsed |
| 48 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) | 48 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) |
| 49 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 | 49 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 |
| 50 | o3·:·Ideal·of·R | 50 | o3·:·Ideal·of·R |
| 51 | If·I·is·the·unit·ideal,·then·an·ideal·of·variables·of·the·ring·is·returned. | 51 | If·I·is·the·unit·ideal,·then·an·ideal·of·variables·of·the·ring·is·returned. |
| 52 | If·the·codimension·of·I·is·already·known,·then·one·can·specify·this,·along·with | 52 | If·the·codimension·of·I·is·already·known,·then·one·can·specify·this,·along·with |
| Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
| 71 | ·····l·,·s·) | 71 | ·····l·,·s·) |
| 72 | o5·:·Ideal·of·R | 72 | o5·:·Ideal·of·R |
| 73 | i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 | 73 | i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 |
| 74 | o6·=·true | 74 | o6·=·true |
| 75 | i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) | 75 | i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) |
| 76 | ·--·.0 | 76 | ·--·.0123894s·elapsed |
| 77 | ···················2················3····2·····2····8····3····2·····2 | 77 | ···················2················3····2·····2····8····3····2·····2 |
| 78 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) | 78 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) |
| 79 | o7·:·Ideal·of·R | 79 | o7·:·Ideal·of·R |
| 80 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 80 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 81 | ····*·_\x8r_\x8a_\x8d_\x8i_\x8c_\x8a_\x8l·--·the·radical·of·an·ideal | 81 | ····*·_\x8r_\x8a_\x8d_\x8i_\x8c_\x8a_\x8l·--·the·radical·of·an·ideal |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | dERpc3RyaWJ1dGlvbihOdW1iZXIp | 8 | dERpc3RyaWJ1dGlvbihOdW1iZXIp |
| 9 | #:len=261 | 9 | #:len=261 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 6 | #·End·of·header | 6 | #·End·of·header |
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| 9 | #:len=276 | 9 | #:len=276 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| Offset 4, 12 lines modified | Offset 4, 12 lines modified | ||
| 4 | o1·=·range(0,·3) | 4 | o1·=·range(0,·3) |
| 5 | o1·:·PythonObject·of·class·range | 5 | o1·:·PythonObject·of·class·range |
| 6 | i2·:·i·=·iterator·x | 6 | i2·:·i·=·iterator·x |
| 7 | o2·=·<range_iterator·object·at·0x7f | 7 | o2·=·<range_iterator·object·at·0x7f3ba9cfdc50> |
| 8 | o2·:·PythonObject·of·class·range_iterator | 8 | o2·:·PythonObject·of·class·range_iterator |
| 9 | i3·:· | 9 | i3·:· |
| Offset 4, 15 lines modified | Offset 4, 15 lines modified | ||
| 4 | o1·=·range(0,·3) | 4 | o1·=·range(0,·3) |
| 5 | o1·:·PythonObject·of·class·range | 5 | o1·:·PythonObject·of·class·range |
| 6 | i2·:·i·=·iterator·x | 6 | i2·:·i·=·iterator·x |
| 7 | o2·=·<range_iterator·object·at·0x7f | 7 | o2·=·<range_iterator·object·at·0x7fd7371f9da0> |
| 8 | o2·:·PythonObject·of·class·range_iterator | 8 | o2·:·PythonObject·of·class·range_iterator |
| 9 | i3·:·next·i | 9 | i3·:·next·i |
| 10 | o3·=·0 | 10 | o3·=·0 |
| Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | o12·=·m2sqrt | 72 | o12·=·m2sqrt |
| 73 | o12·:·FunctionClosure | 73 | o12·:·FunctionClosure |
| 74 | i13·:·pysqrt·=·toPython·m2sqrt | 74 | i13·:·pysqrt·=·toPython·m2sqrt |
| 75 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f | 75 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f67445f9f50> |
| 76 | o13·:·PythonObject·of·class·builtin_function_or_method | 76 | o13·:·PythonObject·of·class·builtin_function_or_method |
| 77 | i14·:·pysqrt·2 | 77 | i14·:·pysqrt·2 |
| 78 | calling·Macaulay2·code·from·Python! | 78 | calling·Macaulay2·code·from·Python! |
| 79 | o14·=·1.4142135623730951 | 79 | o14·=·1.4142135623730951 |
| Offset 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | o1·=·range(0,·3) | 79 | o1·=·range(0,·3) |
| 80 | o1·:·PythonObject·of·class·range</code></pre> | 80 | o1·:·PythonObject·of·class·range</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x |
| 84 | o2·=·<range_iterator·object·at·0x7f | 84 | o2·=·<range_iterator·object·at·0x7f3ba9cfdc50> |
| 85 | o2·:·PythonObject·of·class·range_iterator</code></pre> | 85 | o2·:·PythonObject·of·class·range_iterator</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ········</table> | 87 | ········</table> |
| 88 | ······</div> | 88 | ······</div> |
| 89 | ······<div> | 89 | ······<div> |
| 90 | ········<h2>See·also</h2> | 90 | ········<h2>See·also</h2> |
| Offset 18, 14 lines modified | Offset 18, 14 lines modified | ||
| 18 | i1·:·x·=·pythonValue·"range(3)" | 18 | i1·:·x·=·pythonValue·"range(3)" |
| 19 | o1·=·range(0,·3) | 19 | o1·=·range(0,·3) |
| 20 | o1·:·PythonObject·of·class·range | 20 | o1·:·PythonObject·of·class·range |
| 21 | i2·:·i·=·iterator·x | 21 | i2·:·i·=·iterator·x |
| 22 | o2·=·<range_iterator·object·at·0x7f | 22 | o2·=·<range_iterator·object·at·0x7f3ba9cfdc50> |
| 23 | o2·:·PythonObject·of·class·range_iterator | 23 | o2·:·PythonObject·of·class·range_iterator |
| 24 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 25 | ····*·_\x8n_\x8e_\x8x_\x8t_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·retrieve·the·next·item·from·a·python·iterator | 25 | ····*·_\x8n_\x8e_\x8x_\x8t_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·retrieve·the·next·item·from·a·python·iterator |
| 26 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 26 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 27 | ····*·_\x8i_\x8t_\x8e_\x8r_\x8a_\x8t_\x8o_\x8r_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·get·iterator·of·iterable·python·object | 27 | ····*·_\x8i_\x8t_\x8e_\x8r_\x8a_\x8t_\x8o_\x8r_\x8(_\x8P_\x8y_\x8t_\x8h_\x8o_\x8n_\x8O_\x8b_\x8j_\x8e_\x8c_\x8t_\x8)·--·get·iterator·of·iterable·python·object |
| Offset 73, 15 lines modified | Offset 73, 15 lines modified | ||
| 73 | o1·=·range(0,·3) | 73 | o1·=·range(0,·3) |
| 74 | o1·:·PythonObject·of·class·range</code></pre> | 74 | o1·:·PythonObject·of·class·range</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x |
| 78 | o2·=·<range_iterator·object·at·0x7f | 78 | o2·=·<range_iterator·object·at·0x7fd7371f9da0> |
| 79 | o2·:·PythonObject·of·class·range_iterator</code></pre> | 79 | o2·:·PythonObject·of·class·range_iterator</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·next·i | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·next·i |
| 83 | o3·=·0 | 83 | o3·=·0 |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i1·:·x·=·pythonValue·"range(3)" | 17 | i1·:·x·=·pythonValue·"range(3)" |
| 18 | o1·=·range(0,·3) | 18 | o1·=·range(0,·3) |
| 19 | o1·:·PythonObject·of·class·range | 19 | o1·:·PythonObject·of·class·range |
| 20 | i2·:·i·=·iterator·x | 20 | i2·:·i·=·iterator·x |
| 21 | o2·=·<range_iterator·object·at·0x7f | 21 | o2·=·<range_iterator·object·at·0x7fd7371f9da0> |
| 22 | o2·:·PythonObject·of·class·range_iterator | 22 | o2·:·PythonObject·of·class·range_iterator |
| 23 | i3·:·next·i | 23 | i3·:·next·i |
| 24 | o3·=·0 | 24 | o3·=·0 |
| 25 | o3·:·PythonObject·of·class·int | 25 | o3·:·PythonObject·of·class·int |
| Offset 156, 15 lines modified | Offset 156, 15 lines modified | ||
| 156 | o12·=·m2sqrt | 156 | o12·=·m2sqrt |
| 157 | o12·:·FunctionClosure</code></pre> | 157 | o12·:·FunctionClosure</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i13·:·pysqrt·=·toPython·m2sqrt | 160 | <td>··············<pre><code·class="language-macaulay2">i13·:·pysqrt·=·toPython·m2sqrt |
| 161 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f | 161 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f67445f9f50> |
| 162 | o13·:·PythonObject·of·class·builtin_function_or_method</code></pre> | 162 | o13·:·PythonObject·of·class·builtin_function_or_method</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i14·:·pysqrt·2 | 165 | <td>··············<pre><code·class="language-macaulay2">i14·:·pysqrt·2 |
| 166 | calling·Macaulay2·code·from·Python! | 166 | calling·Macaulay2·code·from·Python! |
| Offset 73, 15 lines modified | Offset 73, 15 lines modified | ||
| 73 | ··········sqrt·x) | 73 | ··········sqrt·x) |
| 74 | o12·=·m2sqrt | 74 | o12·=·m2sqrt |
| 75 | o12·:·FunctionClosure | 75 | o12·:·FunctionClosure |
| 76 | i13·:·pysqrt·=·toPython·m2sqrt | 76 | i13·:·pysqrt·=·toPython·m2sqrt |
| 77 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f | 77 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f67445f9f50> |
| 78 | o13·:·PythonObject·of·class·builtin_function_or_method | 78 | o13·:·PythonObject·of·class·builtin_function_or_method |
| 79 | i14·:·pysqrt·2 | 79 | i14·:·pysqrt·2 |
| 80 | calling·Macaulay2·code·from·Python! | 80 | calling·Macaulay2·code·from·Python! |
| 81 | o14·=·1.4142135623730951 | 81 | o14·=·1.4142135623730951 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 6 | #·End·of·header | 6 | #·End·of·header |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 9 | #:len=3881 | 9 | #:len=3881 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgcXVhc2lkZWdyZWUg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgcXVhc2lkZWdyZWUg |
| 11 | c2V0cyBvZiBsb2NhbCBjb2hvbW9sb2d5IG1vZHVsZXMiLCAibGluZW51bSIgPT4gNzczLCBJbnB1 | 11 | c2V0cyBvZiBsb2NhbCBjb2hvbW9sb2d5IG1vZHVsZXMiLCAibGluZW51bSIgPT4gNzczLCBJbnB1 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=4 | 7 | #:len=4 |
| 8 | W1FRXQ== | 8 | W1FRXQ== |
| 9 | #:len=544 | 9 | #:len=544 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUXVhdGVybmFyeSBRdWFydGljIEZvcm1z | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUXVhdGVybmFyeSBRdWFydGljIEZvcm1z |
| 11 | IGFuZCBHb3JlbnN0ZWluIHJpbmdzIChLYXB1c3RrYSwgS2FwdXN0a2EsIFJhbmVzdGFkLCBTY2hl | 11 | IGFuZCBHb3JlbnN0ZWluIHJpbmdzIChLYXB1c3RrYSwgS2FwdXN0a2EsIFJhbmVzdGFkLCBTY2hl |
| Offset 179, 15 lines modified | Offset 179, 15 lines modified | ||
| 179 | i21·:·L·=·trim·groebnerStratum·F; | 179 | i21·:·L·=·trim·groebnerStratum·F; |
| 180 | o21·:·Ideal·of·T | 180 | o21·:·Ideal·of·T |
| 181 | i22·:·assert(dim·L·==·18) | 181 | i22·:·assert(dim·L·==·18) |
| 182 | i23·:·elapsedTime·isPrime·L | 182 | i23·:·elapsedTime·isPrime·L |
| 183 | ·--·3. | 183 | ·--·3.01112s·elapsed |
| 184 | o23·=·true | 184 | o23·=·true |
| 185 | i24·:·I·=·pointsIdeal·randomPoints(S,·6) | 185 | i24·:·I·=·pointsIdeal·randomPoints(S,·6) |
| 186 | ·····························2······························2···2·········· | 186 | ·····························2······························2···2·········· |
| 187 | o24·=·ideal·(a*c·-·7b*c·-·49c··+·40a*d·-·42b*d·+·12c*d·+·28d·,·b··-·36b*c·- | 187 | o24·=·ideal·(a*c·-·7b*c·-·49c··+·40a*d·-·42b*d·+·12c*d·+·28d·,·b··-·36b*c·- |
| Offset 301, 15 lines modified | Offset 301, 15 lines modified | ||
| 301 | o38·=·true | 301 | o38·=·true |
| 302 | i39·:·L441·=·trim(L·+·ideal·M1); | 302 | i39·:·L441·=·trim(L·+·ideal·M1); |
| 303 | o39·:·Ideal·of·T | 303 | o39·:·Ideal·of·T |
| 304 | i40·:·elapsedTime·compsL441·=·decompose·L441; | 304 | i40·:·elapsedTime·compsL441·=·decompose·L441; |
| 305 | ·--· | 305 | ·--·2.25783s·elapsed |
| 306 | i41·:·#compsL441 | 306 | i41·:·#compsL441 |
| 307 | o41·=·2 | 307 | o41·=·2 |
| 308 | i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16. | 308 | i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16. |
| Offset 319, 37 lines modified | Offset 319, 37 lines modified | ||
| 319 | i43·:·compsL441/dim·==·{16,·14} | 319 | i43·:·compsL441/dim·==·{16,·14} |
| 320 | o43·=·true | 320 | o43·=·true |
| 321 | i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 | 321 | i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 |
| 322 | o44·=·|·0· | 322 | o44·=·|·-40·-4·-40·44·-22·-50·-30·13·-1·-16·45·-23·29·19·14·23·-21·19·14·29·6 |
| 323 | ······----------------------------------------------------------------------- | 323 | ······----------------------------------------------------------------------- |
| 324 | ······10· | 324 | ······10·-32·18·-22·37·34·15·5·-10·-29·26·49·-50·45·-28·| |
| 325 | ···············1·······36 | 325 | ···············1·······36 |
| 326 | o44·:·Matrix·kk··<--·kk | 326 | o44·:·Matrix·kk··<--·kk |
| 327 | i45·:·Fa·=·sub(F,·(vars·S)·|·pta) | 327 | i45·:·Fa·=·sub(F,·(vars·S)·|·pta) |
| 328 | ··············2·············2·········································· | 328 | ··············2··············2······························2··············· |
| 329 | o45·=·ideal·(a··+· | 329 | o45·=·ideal·(a··+·14b*c·-·16c··-·23a*d·-·50b*d·-·40c*d·-·40d·,·a*b·-·22b*c·+ |
| 330 | ······----------------------------------------------------------------------- | 330 | ······----------------------------------------------------------------------- |
| 331 | ········· | 331 | ·········2··························2···2··············2·················· |
| 332 | ······4 | 332 | ······14c··+·6a*d·+·29b*d·-·c*d·-·4d·,·b··+·45b*c·+·15c··+·49a*d·+·10b*d·+ |
| 333 | ······----------------------------------------------------------------------- | 333 | ······----------------------------------------------------------------------- |
| 334 | ········· | 334 | ·················2···················2·····························2·····2·· |
| 335 | ······3 | 335 | ······23c*d·-·30d·,·a*c·+·26b*c·+·37c··+·5a*d·+·29b*d·+·19c*d·-·22d·,·b*c··- |
| 336 | ······----------------------------------------------------------------------- | 336 | ······----------------------------------------------------------------------- |
| 337 | ··········· | 337 | ···················2·········2········2········2······3···3················2· |
| 338 | ······ | 338 | ······10b*c*d·-·32c·d·+·34a*d··-·21b*d··+·45c*d··+·44d·,·c··-·28b*c*d·-·29c·d |
| 339 | ······----------------------------------------------------------------------- | 339 | ······----------------------------------------------------------------------- |
| 340 | ·············2········2·····3 | 340 | ·············2········2········2······3 |
| 341 | ······+·1 | 341 | ······-·50a*d··+·18b*d··+·19c*d··+·13d·) |
| 342 | o45·:·Ideal·of·S | 342 | o45·:·Ideal·of·S |
| 343 | i46·:·betti·res·Fa | 343 | i46·:·betti·res·Fa |
| 344 | ·············0·1·2·3 | 344 | ·············0·1·2·3 |
| 345 | o46·=·total:·1·6·8·3 | 345 | o46·=·total:·1·6·8·3 |
| Offset 357, 40 lines modified | Offset 357, 40 lines modified | ||
| 357 | ··········1:·.·4·4·1 | 357 | ··········1:·.·4·4·1 |
| 358 | ··········2:·.·2·4·2 | 358 | ··········2:·.·2·4·2 |
| 359 | o46·:·BettiTally | 359 | o46·:·BettiTally |
| 360 | i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point | 360 | i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point |
| 361 | ······+-------------------------------------------------------------------------------------------------------+ | 361 | ······+------------------------------------------------------------------------------------------------------------+ |
| 362 | o47·=·|ideal·(c·+· | 362 | o47·=·|ideal·(c·+·5d,·b·-·33d,·a·-·21d)············································································| |
| 363 | ······+-------------------------------------------------------------------------------------------------------+ | 363 | ······+------------------------------------------------------------------------------------------------------------+ |
| 364 | ······|······································2·············2··················································| | 364 | ······|······································2··············2······················································| |
| 365 | ······|ideal·(b· | 365 | ······|ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,·c··+·49c*d·+·42d·)·····················································| |
| 366 | ······+-------------------------------------------------------------------------------------------------------+ | 366 | ······+------------------------------------------------------------------------------------------------------------+ |
| 367 | ······|·····························2·····················2························2···2····················2·| | 367 | ······|·····························2······················2···························2···2·····················2·| |
| 368 | ······|ideal·(a· | 368 | ······|ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+·27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)| |
| 369 | ······+-------------------------------------------------------------------------------------------------------+ | 369 | ······+------------------------------------------------------------------------------------------------------------+ |
| 370 | i48·:·CFa·=·minimalPrimes·Fa | 370 | i48·:·CFa·=·minimalPrimes·Fa |
| 371 | ········································································· | 371 | ············································································· |
| 372 | o48·=·{ideal·(c·+· | 372 | o48·=·{ideal·(c·+·5d,·b·-·33d,·a·-·21d),·ideal·(b·+·45c·+·49d,·a·-·22c·-·26d, |
| 373 | ······----------------------------------------------------------------------- | 373 | ······----------------------------------------------------------------------- |
| 374 | ······· | 374 | ·······2··············2································2·················· |
| 375 | ······ | 375 | ······c··+·49c*d·+·42d·),·ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+ |
| 376 | ······----------------------------------------------------------------------- | 376 | ······----------------------------------------------------------------------- |
| 377 | ·········2························2···2····················2 | 377 | ·········2···························2···2·····················2 |
| 378 | ······ | 378 | ······27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)} |
| 379 | o48·:·List | 379 | o48·:·List |
| 380 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. | 380 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. |
| 381 | o49·=·b· | 381 | o49·=·b·+·45c·+·49d |
| 382 | o49·:·S | 382 | o49·:·S |
| 383 | i50·:·CFa/degree | 383 | i50·:·CFa/degree |
| 384 | o50·=·{1,·2,·3} | 384 | o50·=·{1,·2,·3} |
| Offset 404, 37 lines modified | Offset 404, 37 lines modified | ||
| 404 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of·the·5·points | 404 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of·the·5·points |
| 405 | o52·=·2 | 405 | o52·=·2 |
| 406 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 | 406 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 |
| 407 | o53·=·|· | 407 | o53·=·|·31·42·28·25·19·3·43·-7·-3·-42·-29·-29·14·2·50·5·36·-13·-42·47·13·31 |
| 408 | ······----------------------------------------------------------------------- | 408 | ······----------------------------------------------------------------------- |
| 409 | ······- | 409 | ······-37·-23·-24·-4·38·-29·-23·21·17·9·0·21·-9·-47·| |
| 410 | ···············1·······36 | 410 | ···············1·······36 |
| 411 | o53·:·Matrix·kk··<--·kk | 411 | o53·:·Matrix·kk··<--·kk |
| 412 | i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) | 412 | i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) |
| Max diff block lines reached; 19580/27119 bytes (72.20%) of diff not shown. | |||
| Offset 291, 15 lines modified | Offset 291, 15 lines modified | ||
| 291 | o21·:·Ideal·of·T</code></pre> | 291 | o21·:·Ideal·of·T</code></pre> |
| 292 | </td>··········</tr> | 292 | </td>··········</tr> |
| 293 | ··········<tr> | 293 | ··········<tr> |
| 294 | <td>··············<pre><code·class="language-macaulay2">i22·:·assert(dim·L·==·18)</code></pre> | 294 | <td>··············<pre><code·class="language-macaulay2">i22·:·assert(dim·L·==·18)</code></pre> |
| 295 | </td>··········</tr> | 295 | </td>··········</tr> |
| 296 | ··········<tr> | 296 | ··········<tr> |
| 297 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·L | 297 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·L |
| 298 | ·--·3. | 298 | ·--·3.01112s·elapsed |
| 299 | o23·=·true</code></pre> | 299 | o23·=·true</code></pre> |
| 300 | </td>··········</tr> | 300 | </td>··········</tr> |
| 301 | ········</table> | 301 | ········</table> |
| 302 | ········<div> | 302 | ········<div> |
| 303 | ··········<h2>The·Schreyer·resolution·and·minimal·Betti·numbers</h2> | 303 | ··········<h2>The·Schreyer·resolution·and·minimal·Betti·numbers</h2> |
| 304 | ········</div> | 304 | ········</div> |
| Offset 469, 15 lines modified | Offset 469, 15 lines modified | ||
| 469 | ··········<tr> | 469 | ··········<tr> |
| 470 | <td>··············<pre><code·class="language-macaulay2">i39·:·L441·=·trim(L·+·ideal·M1); | 470 | <td>··············<pre><code·class="language-macaulay2">i39·:·L441·=·trim(L·+·ideal·M1); |
| 471 | o39·:·Ideal·of·T</code></pre> | 471 | o39·:·Ideal·of·T</code></pre> |
| 472 | </td>··········</tr> | 472 | </td>··········</tr> |
| 473 | ··········<tr> | 473 | ··········<tr> |
| 474 | <td>··············<pre><code·class="language-macaulay2">i40·:·elapsedTime·compsL441·=·decompose·L441; | 474 | <td>··············<pre><code·class="language-macaulay2">i40·:·elapsedTime·compsL441·=·decompose·L441; |
| 475 | ·--· | 475 | ·--·2.25783s·elapsed</code></pre> |
| 476 | </td>··········</tr> | 476 | </td>··········</tr> |
| 477 | ··········<tr> | 477 | ··········<tr> |
| 478 | <td>··············<pre><code·class="language-macaulay2">i41·:·#compsL441 | 478 | <td>··············<pre><code·class="language-macaulay2">i41·:·#compsL441 |
| 479 | o41·=·2</code></pre> | 479 | o41·=·2</code></pre> |
| 480 | </td>··········</tr> | 480 | </td>··········</tr> |
| 481 | ··········<tr> | 481 | ··········<tr> |
| Offset 496, 38 lines modified | Offset 496, 38 lines modified | ||
| 496 | ········<div> | 496 | ········<div> |
| 497 | ··········<p>Both·components·are·rational,·and·here·are·random·points,·one·on·each·component:</p> | 497 | ··········<p>Both·components·are·rational,·and·here·are·random·points,·one·on·each·component:</p> |
| 498 | ········</div> | 498 | ········</div> |
| 499 | ········<table·class="examples"> | 499 | ········<table·class="examples"> |
| 500 | ··········<tr> | 500 | ··········<tr> |
| 501 | <td>··············<pre><code·class="language-macaulay2">i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 | 501 | <td>··············<pre><code·class="language-macaulay2">i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 |
| 502 | o44·=·|·0· | 502 | o44·=·|·-40·-4·-40·44·-22·-50·-30·13·-1·-16·45·-23·29·19·14·23·-21·19·14·29·6 |
| 503 | ······----------------------------------------------------------------------- | 503 | ······----------------------------------------------------------------------- |
| 504 | ······10· | 504 | ······10·-32·18·-22·37·34·15·5·-10·-29·26·49·-50·45·-28·| |
| 505 | ···············1·······36 | 505 | ···············1·······36 |
| 506 | o44·:·Matrix·kk··<--·kk</code></pre> | 506 | o44·:·Matrix·kk··<--·kk</code></pre> |
| 507 | </td>··········</tr> | 507 | </td>··········</tr> |
| 508 | ··········<tr> | 508 | ··········<tr> |
| 509 | <td>··············<pre><code·class="language-macaulay2">i45·:·Fa·=·sub(F,·(vars·S)·|·pta) | 509 | <td>··············<pre><code·class="language-macaulay2">i45·:·Fa·=·sub(F,·(vars·S)·|·pta) |
| 510 | ··············2·············2·········································· | 510 | ··············2··············2······························2··············· |
| 511 | o45·=·ideal·(a··+· | 511 | o45·=·ideal·(a··+·14b*c·-·16c··-·23a*d·-·50b*d·-·40c*d·-·40d·,·a*b·-·22b*c·+ |
| 512 | ······----------------------------------------------------------------------- | 512 | ······----------------------------------------------------------------------- |
| 513 | ········· | 513 | ·········2··························2···2··············2·················· |
| 514 | ······4 | 514 | ······14c··+·6a*d·+·29b*d·-·c*d·-·4d·,·b··+·45b*c·+·15c··+·49a*d·+·10b*d·+ |
| 515 | ······----------------------------------------------------------------------- | 515 | ······----------------------------------------------------------------------- |
| 516 | ········· | 516 | ·················2···················2·····························2·····2·· |
| 517 | ······3 | 517 | ······23c*d·-·30d·,·a*c·+·26b*c·+·37c··+·5a*d·+·29b*d·+·19c*d·-·22d·,·b*c··- |
| 518 | ······----------------------------------------------------------------------- | 518 | ······----------------------------------------------------------------------- |
| 519 | ··········· | 519 | ···················2·········2········2········2······3···3················2· |
| 520 | ······ | 520 | ······10b*c*d·-·32c·d·+·34a*d··-·21b*d··+·45c*d··+·44d·,·c··-·28b*c*d·-·29c·d |
| 521 | ······----------------------------------------------------------------------- | 521 | ······----------------------------------------------------------------------- |
| 522 | ·············2········2·····3 | 522 | ·············2········2········2······3 |
| 523 | ······+·1 | 523 | ······-·50a*d··+·18b*d··+·19c*d··+·13d·) |
| 524 | o45·:·Ideal·of·S</code></pre> | 524 | o45·:·Ideal·of·S</code></pre> |
| 525 | </td>··········</tr> | 525 | </td>··········</tr> |
| 526 | ··········<tr> | 526 | ··········<tr> |
| 527 | <td>··············<pre><code·class="language-macaulay2">i46·:·betti·res·Fa | 527 | <td>··············<pre><code·class="language-macaulay2">i46·:·betti·res·Fa |
| 528 | ·············0·1·2·3 | 528 | ·············0·1·2·3 |
| Offset 537, 42 lines modified | Offset 537, 42 lines modified | ||
| 537 | ··········2:·.·2·4·2 | 537 | ··········2:·.·2·4·2 |
| 538 | o46·:·BettiTally</code></pre> | 538 | o46·:·BettiTally</code></pre> |
| 539 | </td>··········</tr> | 539 | </td>··········</tr> |
| 540 | ··········<tr> | 540 | ··········<tr> |
| 541 | <td>··············<pre><code·class="language-macaulay2">i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point | 541 | <td>··············<pre><code·class="language-macaulay2">i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point |
| 542 | ······+-------------------------------------------------------------------------------------------------------+ | 542 | ······+------------------------------------------------------------------------------------------------------------+ |
| 543 | o47·=·|ideal·(c·+· | 543 | o47·=·|ideal·(c·+·5d,·b·-·33d,·a·-·21d)············································································| |
| 544 | ······+-------------------------------------------------------------------------------------------------------+ | 544 | ······+------------------------------------------------------------------------------------------------------------+ |
| 545 | ······|······································2·············2··················································| | 545 | ······|······································2··············2······················································| |
| 546 | ······|ideal·(b· | 546 | ······|ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,·c··+·49c*d·+·42d·)·····················································| |
| 547 | ······+-------------------------------------------------------------------------------------------------------+ | 547 | ······+------------------------------------------------------------------------------------------------------------+ |
| 548 | ······|·····························2·····················2························2···2····················2·| | 548 | ······|·····························2······················2···························2···2·····················2·| |
| 549 | ······|ideal·(a· | 549 | ······|ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+·27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)| |
| 550 | ······+-------------------------------------------------------------------------------------------------------+</code></pre> | 550 | ······+------------------------------------------------------------------------------------------------------------+</code></pre> |
| 551 | </td>··········</tr> | 551 | </td>··········</tr> |
| 552 | ··········<tr> | 552 | ··········<tr> |
| 553 | <td>··············<pre><code·class="language-macaulay2">i48·:·CFa·=·minimalPrimes·Fa | 553 | <td>··············<pre><code·class="language-macaulay2">i48·:·CFa·=·minimalPrimes·Fa |
| 554 | ········································································· | 554 | ············································································· |
| 555 | o48·=·{ideal·(c·+· | 555 | o48·=·{ideal·(c·+·5d,·b·-·33d,·a·-·21d),·ideal·(b·+·45c·+·49d,·a·-·22c·-·26d, |
| 556 | ······----------------------------------------------------------------------- | 556 | ······----------------------------------------------------------------------- |
| 557 | ······· | 557 | ·······2··············2································2·················· |
| 558 | ······ | 558 | ······c··+·49c*d·+·42d·),·ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+ |
| 559 | ······----------------------------------------------------------------------- | 559 | ······----------------------------------------------------------------------- |
| 560 | ·········2························2···2····················2 | 560 | ·········2···························2···2·····················2 |
| 561 | ······ | 561 | ······27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)} |
| 562 | o48·:·List</code></pre> | 562 | o48·:·List</code></pre> |
| 563 | </td>··········</tr> | 563 | </td>··········</tr> |
| 564 | ··········<tr> | 564 | ··········<tr> |
| 565 | <td>··············<pre><code·class="language-macaulay2">i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. | 565 | <td>··············<pre><code·class="language-macaulay2">i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. |
| 566 | o49·=·b· | 566 | o49·=·b·+·45c·+·49d |
| 567 | o49·:·S</code></pre> | 567 | o49·:·S</code></pre> |
| 568 | </td>··········</tr> | 568 | </td>··········</tr> |
| 569 | ··········<tr> | 569 | ··········<tr> |
| 570 | <td>··············<pre><code·class="language-macaulay2">i50·:·CFa/degree | 570 | <td>··············<pre><code·class="language-macaulay2">i50·:·CFa/degree |
| 571 | o50·=·{1,·2,·3} | 571 | o50·=·{1,·2,·3} |
| Offset 592, 38 lines modified | Offset 592, 38 lines modified | ||
| 592 | o52·=·2</code></pre> | 592 | o52·=·2</code></pre> |
| 593 | </td>··········</tr> | 593 | </td>··········</tr> |
| 594 | ········</table> | 594 | ········</table> |
| 595 | ········<table·class="examples"> | 595 | ········<table·class="examples"> |
| 596 | ··········<tr> | 596 | ··········<tr> |
| 597 | <td>··············<pre><code·class="language-macaulay2">i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 | 597 | <td>··············<pre><code·class="language-macaulay2">i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 |
| 598 | o53·=·|· | 598 | o53·=·|·31·42·28·25·19·3·43·-7·-3·-42·-29·-29·14·2·50·5·36·-13·-42·47·13·31 |
| 599 | ······----------------------------------------------------------------------- | 599 | ······----------------------------------------------------------------------- |
| 600 | ······- | 600 | ······-37·-23·-24·-4·38·-29·-23·21·17·9·0·21·-9·-47·| |
| 601 | ···············1·······36 | 601 | ···············1·······36 |
| 602 | o53·:·Matrix·kk··<--·kk</code></pre> | 602 | o53·:·Matrix·kk··<--·kk</code></pre> |
| Max diff block lines reached; 21526/29915 bytes (71.96%) of diff not shown. | |||
| Offset 250, 15 lines modified | Offset 250, 15 lines modified | ||
| 250 | ······|······31·········33········32·······34········35········36····| | 250 | ······|······31·········33········32·······34········35········36····| |
| 251 | ······+--------------------------------------------------------------+ | 251 | ······+--------------------------------------------------------------+ |
| 252 | i21·:·L·=·trim·groebnerStratum·F; | 252 | i21·:·L·=·trim·groebnerStratum·F; |
| 253 | o21·:·Ideal·of·T | 253 | o21·:·Ideal·of·T |
| 254 | i22·:·assert(dim·L·==·18) | 254 | i22·:·assert(dim·L·==·18) |
| 255 | i23·:·elapsedTime·isPrime·L | 255 | i23·:·elapsedTime·isPrime·L |
| 256 | ·--·3. | 256 | ·--·3.01112s·elapsed |
| 257 | o23·=·true | 257 | o23·=·true |
| 258 | *\x8**\x8**\x8**\x8**\x8*·T\x8Th\x8he\x8e·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·r\x8re\x8es\x8so\x8ol\x8lu\x8ut\x8ti\x8io\x8on\x8n·a\x8an\x8nd\x8d·m\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l·B\x8Be\x8et\x8tt\x8ti\x8i·n\x8nu\x8um\x8mb\x8be\x8er\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8* | 258 | *\x8**\x8**\x8**\x8**\x8*·T\x8Th\x8he\x8e·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·r\x8re\x8es\x8so\x8ol\x8lu\x8ut\x8ti\x8io\x8on\x8n·a\x8an\x8nd\x8d·m\x8mi\x8in\x8ni\x8im\x8ma\x8al\x8l·B\x8Be\x8et\x8tt\x8ti\x8i·n\x8nu\x8um\x8mb\x8be\x8er\x8rs\x8s·*\x8**\x8**\x8**\x8**\x8* |
| 259 | Schreyer's·construction·of·a·nonminimal·free·resolution·starts·with·a·Groebner | 259 | Schreyer's·construction·of·a·nonminimal·free·resolution·starts·with·a·Groebner |
| 260 | basis.·First,·one·constructs·the·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·f\x8fr\x8ra\x8am\x8me\x8e·(see·La·Scala,·Stillman).·This | 260 | basis.·First,·one·constructs·the·S\x8Sc\x8ch\x8hr\x8re\x8ey\x8ye\x8er\x8r·f\x8fr\x8ra\x8am\x8me\x8e·(see·La·Scala,·Stillman).·This |
| 261 | is·determined·solely·from·the·initial·ideal·$J$·and·its·minimal·generators·(but | 261 | is·determined·solely·from·the·initial·ideal·$J$·and·its·minimal·generators·(but |
| 262 | depends·on·some·choices·of·ordering,·but·otherwise·is·combinatorial).·This | 262 | depends·on·some·choices·of·ordering,·but·otherwise·is·combinatorial).·This |
| Offset 414, 15 lines modified | Offset 414, 15 lines modified | ||
| 414 | We·now·compute·the·locus·in·$V(L)$·where·the·Betti·diagram·has·no·cancellation. | 414 | We·now·compute·the·locus·in·$V(L)$·where·the·Betti·diagram·has·no·cancellation. |
| 415 | This·is·a·closed·subscheme·of·$V(L)$,·which·is·a·closed·subscheme·of·the | 415 | This·is·a·closed·subscheme·of·$V(L)$,·which·is·a·closed·subscheme·of·the |
| 416 | Hilbert·scheme.·Notice·that·there·are·two·components. | 416 | Hilbert·scheme.·Notice·that·there·are·two·components. |
| 417 | i39·:·L441·=·trim(L·+·ideal·M1); | 417 | i39·:·L441·=·trim(L·+·ideal·M1); |
| 418 | o39·:·Ideal·of·T | 418 | o39·:·Ideal·of·T |
| 419 | i40·:·elapsedTime·compsL441·=·decompose·L441; | 419 | i40·:·elapsedTime·compsL441·=·decompose·L441; |
| 420 | ·--· | 420 | ·--·2.25783s·elapsed |
| 421 | i41·:·#compsL441 | 421 | i41·:·#compsL441 |
| 422 | o41·=·2 | 422 | o41·=·2 |
| 423 | i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16. | 423 | i42·:·compsL441/dim·--·two·components,·of·dimensions·14·and·16. |
| 424 | o42·=·{16,·14} | 424 | o42·=·{16,·14} |
| Offset 430, 36 lines modified | Offset 430, 36 lines modified | ||
| 430 | i43·:·compsL441/dim·==·{16,·14} | 430 | i43·:·compsL441/dim·==·{16,·14} |
| 431 | o43·=·true | 431 | o43·=·true |
| 432 | Both·components·are·rational,·and·here·are·random·points,·one·on·each | 432 | Both·components·are·rational,·and·here·are·random·points,·one·on·each |
| 433 | component: | 433 | component: |
| 434 | i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 | 434 | i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 |
| 435 | o44·=·|·0· | 435 | o44·=·|·-40·-4·-40·44·-22·-50·-30·13·-1·-16·45·-23·29·19·14·23·-21·19·14·29·6 |
| 436 | ······----------------------------------------------------------------------- | 436 | ······----------------------------------------------------------------------- |
| 437 | ······10· | 437 | ······10·-32·18·-22·37·34·15·5·-10·-29·26·49·-50·45·-28·| |
| 438 | ···············1·······36 | 438 | ···············1·······36 |
| 439 | o44·:·Matrix·kk··<--·kk | 439 | o44·:·Matrix·kk··<--·kk |
| 440 | i45·:·Fa·=·sub(F,·(vars·S)·|·pta) | 440 | i45·:·Fa·=·sub(F,·(vars·S)·|·pta) |
| 441 | ··············2············· | 441 | ··············2··············2······························2 |
| 442 | o45·=·ideal·(a··+· | 442 | o45·=·ideal·(a··+·14b*c·-·16c··-·23a*d·-·50b*d·-·40c*d·-·40d·,·a*b·-·22b*c·+ |
| 443 | ······----------------------------------------------------------------------- | 443 | ······----------------------------------------------------------------------- |
| 444 | ·································2···2··············2 | 444 | ·········2··························2···2··············2 |
| 445 | ······4 | 445 | ······14c··+·6a*d·+·29b*d·-·c*d·-·4d·,·b··+·45b*c·+·15c··+·49a*d·+·10b*d·+ |
| 446 | ······----------------------------------------------------------------------- | 446 | ······----------------------------------------------------------------------- |
| 447 | ·········2···················2 | 447 | ·················2···················2·····························2·····2 |
| 448 | ······3 | 448 | ······23c*d·-·30d·,·a*c·+·26b*c·+·37c··+·5a*d·+·29b*d·+·19c*d·-·22d·,·b*c··- |
| 449 | ······----------------------------------------------------------------------- | 449 | ······----------------------------------------------------------------------- |
| 450 | ··········· | 450 | ···················2·········2········2········2······3···3················2 |
| 451 | ······ | 451 | ······10b*c*d·-·32c·d·+·34a*d··-·21b*d··+·45c*d··+·44d·,·c··-·28b*c*d·-·29c·d |
| 452 | ······----------------------------------------------------------------------- | 452 | ······----------------------------------------------------------------------- |
| 453 | ·············2········2·····3 | 453 | ·············2········2········2······3 |
| 454 | ······+·1 | 454 | ······-·50a*d··+·18b*d··+·19c*d··+·13d·) |
| 455 | o45·:·Ideal·of·S | 455 | o45·:·Ideal·of·S |
| 456 | i46·:·betti·res·Fa | 456 | i46·:·betti·res·Fa |
| 457 | ·············0·1·2·3 | 457 | ·············0·1·2·3 |
| 458 | o46·=·total:·1·6·8·3 | 458 | o46·=·total:·1·6·8·3 |
| 459 | ··········0:·1·.·.·. | 459 | ··········0:·1·.·.·. |
| Offset 467, 46 lines modified | Offset 467, 46 lines modified | ||
| 467 | ··········2:·.·2·4·2 | 467 | ··········2:·.·2·4·2 |
| 468 | o46·:·BettiTally | 468 | o46·:·BettiTally |
| 469 | i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another | 469 | i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another |
| 470 | point | 470 | point |
| 471 | ······+------------------------------------------------------------------------ | 471 | ······+------------------------------------------------------------------------ |
| 472 | -------------------------------+ | 472 | ------------------------------------+ |
| 473 | o47·=·|ideal·(c·+· | 473 | o47·=·|ideal·(c·+·5d,·b·-·33d,·a·-·21d) |
| 474 | | | 474 | | |
| 475 | ······+------------------------------------------------------------------------ | 475 | ······+------------------------------------------------------------------------ |
| 476 | -------------------------------+ | 476 | ------------------------------------+ |
| 477 | ······|······································2·············2 | 477 | ······|······································2··············2 |
| 478 | | | 478 | | |
| 479 | ······|ideal·(b· | 479 | ······|ideal·(b·+·45c·+·49d,·a·-·22c·-·26d,·c··+·49c*d·+·42d·) |
| 480 | | | 480 | | |
| 481 | ······+------------------------------------------------------------------------ | 481 | ······+------------------------------------------------------------------------ |
| 482 | -------------------------------+ | 482 | ------------------------------------+ |
| 483 | ······|·····························2·····················2 | 483 | ······|·····························2······················2 |
| 484 | 2···2····················2·| | 484 | 2···2·····················2·| |
| 485 | ······|ideal·(a· | 485 | ······|ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+·27d·,·b*c·-·30b*d·+ |
| 486 | +·6d·,·b··-·b*d·-· | 486 | 16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)| |
| 487 | ······+------------------------------------------------------------------------ | 487 | ······+------------------------------------------------------------------------ |
| 488 | -------------------------------+ | 488 | ------------------------------------+ |
| 489 | i48·:·CFa·=·minimalPrimes·Fa | 489 | i48·:·CFa·=·minimalPrimes·Fa |
| 490 | o48·=·{ideal·(c·+· | 490 | o48·=·{ideal·(c·+·5d,·b·-·33d,·a·-·21d),·ideal·(b·+·45c·+·49d,·a·-·22c·-·26d, |
| 491 | ······----------------------------------------------------------------------- | 491 | ······----------------------------------------------------------------------- |
| 492 | ······· | 492 | ·······2··············2································2 |
| 493 | ······ | 493 | ······c··+·49c*d·+·42d·),·ideal·(a·+·26b·+·37c·+·36d,·c··-·21b*d·+·43c*d·+ |
| 494 | ······----------------------------------------------------------------------- | 494 | ······----------------------------------------------------------------------- |
| 495 | ·········2························2···2····················2 | 495 | ·········2···························2···2·····················2 |
| 496 | ······ | 496 | ······27d·,·b*c·-·30b*d·+·16c*d·+·26d·,·b··-·3b*d·-·24c*d·-·36d·)} |
| 497 | o48·:·List | 497 | o48·:·List |
| 498 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. | 498 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. |
| 499 | o49·=·b· | 499 | o49·=·b·+·45c·+·49d |
| 500 | o49·:·S | 500 | o49·:·S |
| 501 | i50·:·CFa/degree | 501 | i50·:·CFa/degree |
| 502 | o50·=·{1,·2,·3} | 502 | o50·=·{1,·2,·3} |
| 503 | o50·:·List | 503 | o50·:·List |
| Offset 517, 124 lines modified | Offset 517, 206 lines modified | ||
| 517 | o51·:·List | 517 | o51·:·List |
| 518 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of | 518 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of |
| 519 | the·5·points | 519 | the·5·points |
| 520 | o52·=·2 | 520 | o52·=·2 |
| 521 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 | 521 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 |
| 522 | o53·=·|· | 522 | o53·=·|·31·42·28·25·19·3·43·-7·-3·-42·-29·-29·14·2·50·5·36·-13·-42·47·13·31 |
| 523 | ······----------------------------------------------------------------------- | 523 | ······----------------------------------------------------------------------- |
| 524 | ······- | 524 | ······-37·-23·-24·-4·38·-29·-23·21·17·9·0·21·-9·-47·| |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 9 | #:len=251 | 9 | #:len=251 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhOZXdGcm9tTWV0aG9kLFJPYmplY3QsQ0MpLCJuZXcg | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhOZXdGcm9tTWV0aG9kLFJPYmplY3QsQ0MpLCJuZXcg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | cmFuZG9tQ2Fub25pY2FsQ3VydmU= | 8 | cmFuZG9tQ2Fub25pY2FsQ3VydmU= |
| 9 | #:len=218 | 9 | #:len=218 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzAsICJ1bmRvY3VtZW50ZWQiID0+IHRy | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzAsICJ1bmRvY3VtZW50ZWQiID0+IHRy |
| 11 | dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7InJhbmRvbUNh | 11 | dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7InJhbmRvbUNh |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·g=14; | 5 | i2·:·g=14; |
| 6 | i3·:·FF=ZZ/10007; | 6 | i3·:·FF=ZZ/10007; |
| 7 | i4·:·R=FF[x_0..x_(g-1)]; | 7 | i4·:·R=FF[x_0..x_(g-1)]; |
| 8 | i5·:·time·betti(I=(random·canonicalCurve)(g,R)) | 8 | i5·:·time·betti(I=(random·canonicalCurve)(g,R)) |
| 9 | ·--·used·5. | 9 | ·--·used·5.83595s·(cpu);·4.66384s·(thread);·0s·(gc) |
| 10 | ············0··1 | 10 | ············0··1 |
| 11 | o5·=·total:·1·66 | 11 | o5·=·total:·1·66 |
| 12 | ·········0:·1··. | 12 | ·········0:·1··. |
| 13 | ·········1:·.·66 | 13 | ·········1:·.·66 |
| 14 | o5·:·BettiTally | 14 | o5·:·BettiTally |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·FF=ZZ/10007;</code></pre> | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·FF=ZZ/10007;</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·R=FF[x_0..x_(g-1)];</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·R=FF[x_0..x_(g-1)];</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·betti(I=(random·canonicalCurve)(g,R)) | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·betti(I=(random·canonicalCurve)(g,R)) |
| 90 | ·--·used·5. | 90 | ·--·used·5.83595s·(cpu);·4.66384s·(thread);·0s·(gc) |
| 91 | ············0··1 | 91 | ············0··1 |
| 92 | o5·=·total:·1·66 | 92 | o5·=·total:·1·66 |
| 93 | ·········0:·1··. | 93 | ·········0:·1··. |
| 94 | ·········1:·.·66 | 94 | ·········1:·.·66 |
| 95 | o5·:·BettiTally</code></pre> | 95 | o5·:·BettiTally</code></pre> |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | Compute·a·random·canonical·curve·of·genus·$g·\le{}·14$,·based·on·the·proofs·of | 17 | Compute·a·random·canonical·curve·of·genus·$g·\le{}·14$,·based·on·the·proofs·of |
| 18 | unirationality·of·$M_g$·by·Severi,·Sernesi,·Chang-Ran·and·Verra. | 18 | unirationality·of·$M_g$·by·Severi,·Sernesi,·Chang-Ran·and·Verra. |
| 19 | i1·:·setRandomSeed·"alpha"; | 19 | i1·:·setRandomSeed·"alpha"; |
| 20 | i2·:·g=14; | 20 | i2·:·g=14; |
| 21 | i3·:·FF=ZZ/10007; | 21 | i3·:·FF=ZZ/10007; |
| 22 | i4·:·R=FF[x_0..x_(g-1)]; | 22 | i4·:·R=FF[x_0..x_(g-1)]; |
| 23 | i5·:·time·betti(I=(random·canonicalCurve)(g,R)) | 23 | i5·:·time·betti(I=(random·canonicalCurve)(g,R)) |
| 24 | ·--·used·5. | 24 | ·--·used·5.83595s·(cpu);·4.66384s·(thread);·0s·(gc) |
| 25 | ············0··1 | 25 | ············0··1 |
| 26 | o5·=·total:·1·66 | 26 | o5·=·total:·1·66 |
| 27 | ·········0:·1··. | 27 | ·········0:·1··. |
| 28 | ·········1:·.·66 | 28 | ·········1:·.·66 |
| 29 | o5·:·BettiTally | 29 | o5·:·BettiTally |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=26 | 7 | #:len=26 |
| 8 | bWF4aW1hbEVudHJ5KENoYWluQ29tcGxleCk= | 8 | bWF4aW1hbEVudHJ5KENoYWluQ29tcGxleCk= |
| 9 | #:len=280 | 9 | #:len=280 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtYXhpbWFsRW50cnksQ2hhaW5Db21wbGV4KSwibWF4 | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtYXhpbWFsRW50cnksQ2hhaW5Db21wbGV4KSwibWF4 |
| Offset 6, 42 lines modified | Offset 6, 42 lines modified | ||
| 6 | o2·=·(10,·20) | 6 | o2·=·(10,·20) |
| 7 | o2·:·Sequence | 7 | o2·:·Sequence |
| 8 | i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) | 8 | i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) |
| 9 | o3·=·({5,·2.91596e52,·9},· | 9 | o3·=·({5,·2.91596e52,·9},·0,·0) |
| 10 | o3·:·Sequence | 10 | o3·:·Sequence |
| 11 | i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) | 11 | i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) |
| 12 | o4·=·({50,·2.30853e454,·98},·.00 | 12 | o4·=·({50,·2.30853e454,·98},·.00799572,·.0432257) |
| 13 | o4·:·Sequence | 13 | o4·:·Sequence |
| 14 | i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) | 14 | i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) |
| 15 | o5·=·{{.00 | 15 | o5·=·{{.0072652,·.011516},·{.00537036,·.00688168},·{.00821387,·.00777908}, |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ·····{.00 | 17 | ·····{.00800066,·.0119758},·{.0583988,·.0167532},·{.00532297,·.0185107}, |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ·····{.00 | 19 | ·····{.00763111,·.00799873},·{.00400122,·.00799659},·{.00796115,·.0039934}, |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ·····{.00400 | 21 | ·····{.00400694,·.0119988}} |
| 22 | o5·:·List | 22 | o5·:·List |
| 23 | i6·:·1/10*sum(L,t->t_0) | 23 | i6·:·1/10*sum(L,t->t_0) |
| 24 | o6·=·.0 | 24 | o6·=·.01161723120000007 |
| 25 | o6·:·RR·(of·precision·53) | 25 | o6·:·RR·(of·precision·53) |
| 26 | i7·:·1/10*sum(L,t->t_1) | 26 | i7·:·1/10*sum(L,t->t_1) |
| 27 | o7·=·.00 | 27 | o7·=·.01054038820000001 |
| 28 | o7·:·RR·(of·precision·53) | 28 | o7·:·RR·(of·precision·53) |
| 29 | i8·:· | 29 | i8·:· |
| Offset 92, 49 lines modified | Offset 92, 49 lines modified | ||
| 92 | o2·=·(10,·20) | 92 | o2·=·(10,·20) |
| 93 | o2·:·Sequence</code></pre> | 93 | o2·:·Sequence</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) |
| 97 | o3·=·({5,·2.91596e52,·9},· | 97 | o3·=·({5,·2.91596e52,·9},·0,·0) |
| 98 | o3·:·Sequence</code></pre> | 98 | o3·:·Sequence</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) |
| 102 | o4·=·({50,·2.30853e454,·98},·.00 | 102 | o4·=·({50,·2.30853e454,·98},·.00799572,·.0432257) |
| 103 | o4·:·Sequence</code></pre> | 103 | o4·:·Sequence</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) | 106 | <td>··············<pre><code·class="language-macaulay2">i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) |
| 107 | o5·=·{{.00 | 107 | o5·=·{{.0072652,·.011516},·{.00537036,·.00688168},·{.00821387,·.00777908}, |
| 108 | ·····------------------------------------------------------------------------ | 108 | ·····------------------------------------------------------------------------ |
| 109 | ·····{.00 | 109 | ·····{.00800066,·.0119758},·{.0583988,·.0167532},·{.00532297,·.0185107}, |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ·····{.00 | 111 | ·····{.00763111,·.00799873},·{.00400122,·.00799659},·{.00796115,·.0039934}, |
| 112 | ·····------------------------------------------------------------------------ | 112 | ·····------------------------------------------------------------------------ |
| 113 | ·····{.00400 | 113 | ·····{.00400694,·.0119988}} |
| 114 | o5·:·List</code></pre> | 114 | o5·:·List</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i6·:·1/10*sum(L,t->t_0) | 117 | <td>··············<pre><code·class="language-macaulay2">i6·:·1/10*sum(L,t->t_0) |
| 118 | o6·=·.0 | 118 | o6·=·.01161723120000007 |
| 119 | o6·:·RR·(of·precision·53)</code></pre> | 119 | o6·:·RR·(of·precision·53)</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i7·:·1/10*sum(L,t->t_1) | 122 | <td>··············<pre><code·class="language-macaulay2">i7·:·1/10*sum(L,t->t_1) |
| 123 | o7·=·.00 | 123 | o7·=·.01054038820000001 |
| 124 | o7·:·RR·(of·precision·53)</code></pre> | 124 | o7·:·RR·(of·precision·53)</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ········</table> | 126 | ········</table> |
| 127 | ······</div> | 127 | ······</div> |
| 128 | ······<div·class="waystouse"> | 128 | ······<div·class="waystouse"> |
| 129 | ········<h2>Ways·to·use·<span·class="tt">testTimeForLLLonSyzygies</span>:</h2> | 129 | ········<h2>Ways·to·use·<span·class="tt">testTimeForLLLonSyzygies</span>:</h2> |
| Offset 25, 40 lines modified | Offset 25, 40 lines modified | ||
| 25 | i2·:·r=10,n=20 | 25 | i2·:·r=10,n=20 |
| 26 | o2·=·(10,·20) | 26 | o2·=·(10,·20) |
| 27 | o2·:·Sequence | 27 | o2·:·Sequence |
| 28 | i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) | 28 | i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) |
| 29 | o3·=·({5,·2.91596e52,·9},· | 29 | o3·=·({5,·2.91596e52,·9},·0,·0) |
| 30 | o3·:·Sequence | 30 | o3·:·Sequence |
| 31 | i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) | 31 | i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) |
| 32 | o4·=·({50,·2.30853e454,·98},·.00 | 32 | o4·=·({50,·2.30853e454,·98},·.00799572,·.0432257) |
| 33 | o4·:·Sequence | 33 | o4·:·Sequence |
| 34 | i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) | 34 | i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) |
| 35 | o5·=·{{.00 | 35 | o5·=·{{.0072652,·.011516},·{.00537036,·.00688168},·{.00821387,·.00777908}, |
| 36 | ·····------------------------------------------------------------------------ | 36 | ·····------------------------------------------------------------------------ |
| 37 | ·····{.00 | 37 | ·····{.00800066,·.0119758},·{.0583988,·.0167532},·{.00532297,·.0185107}, |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····{.00 | 39 | ·····{.00763111,·.00799873},·{.00400122,·.00799659},·{.00796115,·.0039934}, |
| 40 | ·····------------------------------------------------------------------------ | 40 | ·····------------------------------------------------------------------------ |
| 41 | ·····{.00400 | 41 | ·····{.00400694,·.0119988}} |
| 42 | o5·:·List | 42 | o5·:·List |
| 43 | i6·:·1/10*sum(L,t->t_0) | 43 | i6·:·1/10*sum(L,t->t_0) |
| 44 | o6·=·.0 | 44 | o6·=·.01161723120000007 |
| 45 | o6·:·RR·(of·precision·53) | 45 | o6·:·RR·(of·precision·53) |
| 46 | i7·:·1/10*sum(L,t->t_1) | 46 | i7·:·1/10*sum(L,t->t_1) |
| 47 | o7·=·.00 | 47 | o7·=·.01054038820000001 |
| 48 | o7·:·RR·(of·precision·53) | 48 | o7·:·RR·(of·precision·53) |
| 49 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8te\x8es\x8st\x8tT\x8Ti\x8im\x8me\x8eF\x8Fo\x8or\x8rL\x8LL\x8LL\x8Lo\x8on\x8nS\x8Sy\x8yz\x8zy\x8yg\x8gi\x8ie\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 49 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8te\x8es\x8st\x8tT\x8Ti\x8im\x8me\x8eF\x8Fo\x8or\x8rL\x8LL\x8LL\x8Lo\x8on\x8nS\x8Sy\x8yz\x8zy\x8yg\x8gi\x8ie\x8es\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 50 | ····*·testTimeForLLLonSyzygies(ZZ,ZZ) | 50 | ····*·testTimeForLLLonSyzygies(ZZ,ZZ) |
| 51 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 51 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 52 | The·object·_\x8t_\x8e_\x8s_\x8t_\x8T_\x8i_\x8m_\x8e_\x8F_\x8o_\x8r_\x8L_\x8L_\x8L_\x8o_\x8n_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 52 | The·object·_\x8t_\x8e_\x8s_\x8t_\x8T_\x8i_\x8m_\x8e_\x8F_\x8o_\x8r_\x8L_\x8L_\x8L_\x8o_\x8n_\x8S_\x8y_\x8z_\x8y_\x8g_\x8i_\x8e_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | UmFuZG9tQ3VydmVz | 8 | UmFuZG9tQ3VydmVz |
| 9 | #:len=775 | 9 | #:len=775 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmFuZG9tIGN1cnZlcyIsIERlc2NyaXB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmFuZG9tIGN1cnZlcyIsIERlc2NyaXB0 |
| 11 | aW9uID0+IDE6KERJVntQQVJBe1RFWHsiVGhpcyBwYWNrYWdlIGxvYWRzIHRoZSAifSxUT3tuZXcg | 11 | aW9uID0+IDE6KERJVntQQVJBe1RFWHsiVGhpcyBwYWNrYWdlIGxvYWRzIHRoZSAifSxUT3tuZXcg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=46 | 7 | #:len=46 |
| 8 | c21vb3RoQ2Fub25pY2FsQ3VydmVHZW51czE1KC4uLixQcmludGluZz0+Li4uKQ== | 8 | c21vb3RoQ2Fub25pY2FsQ3VydmVHZW51czE1KC4uLixQcmludGluZz0+Li4uKQ== |
| 9 | #:len=370 | 9 | #:len=370 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTI4Nywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTI4Nywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc21vb3RoQ2Fub25pY2FsQ3VydmVHZW51czE1LFBy | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc21vb3RoQ2Fub25pY2FsQ3VydmVHZW51czE1LFBy |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·11549527689790345152 | 1 | --·-*-·M2-comint·-*-·hash:·11549527689790345152 |
| 2 | i1·:·time·ICan·=·smoothCanonicalCurve(11,5); | 2 | i1·:·time·ICan·=·smoothCanonicalCurve(11,5); |
| 3 | ·--·used·1. | 3 | ·--·used·1.46557s·(cpu);·1.10562s·(thread);·0s·(gc) |
| 4 | ··············ZZ | 4 | ··············ZZ |
| 5 | o1·:·Ideal·of·--[t·..t··] | 5 | o1·:·Ideal·of·--[t·..t··] |
| 6 | ···············5··0···10 | 6 | ···············5··0···10 |
| 7 | i2·:·(dim·ICan,·genus·ICan,·degree·ICan) | 7 | i2·:·(dim·ICan,·genus·ICan,·degree·ICan) |
| Offset 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ··········<p>For·g=15·the·curves·are·constructed·via·matrix·factorizations.</p> | 85 | ··········<p>For·g=15·the·curves·are·constructed·via·matrix·factorizations.</p> |
| 86 | ··········<p>If·the·option·<span·class="tt">Printing</span>·is·set·to·<span·class="tt">true</span>·then·printings·about·the·current·step·in·the·construction·are·displayed.</p> | 86 | ··········<p>If·the·option·<span·class="tt">Printing</span>·is·set·to·<span·class="tt">true</span>·then·printings·about·the·current·step·in·the·construction·are·displayed.</p> |
| 87 | ··········<p></p> | 87 | ··········<p></p> |
| 88 | ········</div> | 88 | ········</div> |
| 89 | ········<table·class="examples"> | 89 | ········<table·class="examples"> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·ICan·=·smoothCanonicalCurve(11,5); | 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·ICan·=·smoothCanonicalCurve(11,5); |
| 92 | ·--·used·1. | 92 | ·--·used·1.46557s·(cpu);·1.10562s·(thread);·0s·(gc) |
| 93 | ··············ZZ | 93 | ··············ZZ |
| 94 | o1·:·Ideal·of·--[t·..t··] | 94 | o1·:·Ideal·of·--[t·..t··] |
| 95 | ···············5··0···10</code></pre> | 95 | ···············5··0···10</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i2·:·(dim·ICan,·genus·ICan,·degree·ICan) | 98 | <td>··············<pre><code·class="language-macaulay2">i2·:·(dim·ICan,·genus·ICan,·degree·ICan) |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | For·g<=10·the·curves·are·constructed·via·plane·models. | 30 | For·g<=10·the·curves·are·constructed·via·plane·models. |
| 31 | For·g<=13·the·curves·are·constructed·via·space·models. | 31 | For·g<=13·the·curves·are·constructed·via·space·models. |
| 32 | For·g=14·the·curves·are·constructed·by·Verra's·method. | 32 | For·g=14·the·curves·are·constructed·by·Verra's·method. |
| 33 | For·g=15·the·curves·are·constructed·via·matrix·factorizations. | 33 | For·g=15·the·curves·are·constructed·via·matrix·factorizations. |
| 34 | If·the·option·Printing·is·set·to·true·then·printings·about·the·current·step·in | 34 | If·the·option·Printing·is·set·to·true·then·printings·about·the·current·step·in |
| 35 | the·construction·are·displayed. | 35 | the·construction·are·displayed. |
| 36 | i1·:·time·ICan·=·smoothCanonicalCurve(11,5); | 36 | i1·:·time·ICan·=·smoothCanonicalCurve(11,5); |
| 37 | ·--·used·1. | 37 | ·--·used·1.46557s·(cpu);·1.10562s·(thread);·0s·(gc) |
| 38 | ··············ZZ | 38 | ··············ZZ |
| 39 | o1·:·Ideal·of·--[t·..t··] | 39 | o1·:·Ideal·of·--[t·..t··] |
| 40 | ···············5··0···10 | 40 | ···············5··0···10 |
| 41 | i2·:·(dim·ICan,·genus·ICan,·degree·ICan) | 41 | i2·:·(dim·ICan,·genus·ICan,·degree·ICan) |
| 42 | o2·=·(2,·11,·20) | 42 | o2·=·(2,·11,·20) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | Y2Fub25pY2FsQ3VydmVHZW51czE0 | 8 | Y2Fub25pY2FsQ3VydmVHZW51czE0 |
| 9 | #:len=1011 | 9 | #:len=1011 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBhIHJhbmRvbSBjdXJ2ZSBv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBhIHJhbmRvbSBjdXJ2ZSBv |
| 11 | ZiBnZW51cyAxNCBpbiBpdHMgY2Fub25pY2FsIGVtYmVkZGluZyIsICJsaW5lbnVtIiA9PiAyMDEs | 11 | ZiBnZW51cyAxNCBpbiBpdHMgY2Fub25pY2FsIGVtYmVkZGluZyIsICJsaW5lbnVtIiA9PiAyMDEs |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·setRandomSeed("alpha"); | 3 | i1·:·setRandomSeed("alpha"); |
| 4 | i2·:·FF=ZZ/10007; | 4 | i2·:·FF=ZZ/10007; |
| 5 | i3·:·S=FF[x_0..x_6]; | 5 | i3·:·S=FF[x_0..x_6]; |
| 6 | i4·:·time·I=randomCurveGenus14Degree18inP6(S); | 6 | i4·:·time·I=randomCurveGenus14Degree18inP6(S); |
| 7 | ·--·used·1. | 7 | ·--·used·1.4448s·(cpu);·1.28118s·(thread);·0s·(gc) |
| 8 | o4·:·Ideal·of·S | 8 | o4·:·Ideal·of·S |
| 9 | i5·:·betti·res·I | 9 | i5·:·betti·res·I |
| 10 | ············0··1··2··3··4·5 | 10 | ············0··1··2··3··4·5 |
| 11 | o5·=·total:·1·13·45·56·25·2 | 11 | o5·=·total:·1·13·45·56·25·2 |
| Offset 87, 15 lines modified | Offset 87, 15 lines modified | ||
| 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·FF=ZZ/10007;</code></pre> | 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·FF=ZZ/10007;</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=FF[x_0..x_6];</code></pre> | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=FF[x_0..x_6];</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I=randomCurveGenus14Degree18inP6(S); | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I=randomCurveGenus14Degree18inP6(S); |
| 94 | ·--·used·1. | 94 | ·--·used·1.4448s·(cpu);·1.28118s·(thread);·0s·(gc) |
| 95 | o4·:·Ideal·of·S</code></pre> | 95 | o4·:·Ideal·of·S</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·betti·res·I | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·betti·res·I |
| 99 | ············0··1··2··3··4·5 | 99 | ············0··1··2··3··4·5 |
| Offset 28, 15 lines modified | Offset 28, 15 lines modified | ||
| 28 | the·unirationality·of·$M_{14}$.·It·proves·the·unirationality·of·$M_{14}$·for | 28 | the·unirationality·of·$M_{14}$.·It·proves·the·unirationality·of·$M_{14}$·for |
| 29 | fields·of·the·chosen·finite·characteristic·10007,·for·fields·of·characteristic | 29 | fields·of·the·chosen·finite·characteristic·10007,·for·fields·of·characteristic |
| 30 | 0·by·semi-continuity,·and,·hence,·for·all·but·finitely·many·primes·$p$. | 30 | 0·by·semi-continuity,·and,·hence,·for·all·but·finitely·many·primes·$p$. |
| 31 | i1·:·setRandomSeed("alpha"); | 31 | i1·:·setRandomSeed("alpha"); |
| 32 | i2·:·FF=ZZ/10007; | 32 | i2·:·FF=ZZ/10007; |
| 33 | i3·:·S=FF[x_0..x_6]; | 33 | i3·:·S=FF[x_0..x_6]; |
| 34 | i4·:·time·I=randomCurveGenus14Degree18inP6(S); | 34 | i4·:·time·I=randomCurveGenus14Degree18inP6(S); |
| 35 | ·--·used·1. | 35 | ·--·used·1.4448s·(cpu);·1.28118s·(thread);·0s·(gc) |
| 36 | o4·:·Ideal·of·S | 36 | o4·:·Ideal·of·S |
| 37 | i5·:·betti·res·I | 37 | i5·:·betti·res·I |
| 38 | ············0··1··2··3··4·5 | 38 | ············0··1··2··3··4·5 |
| 39 | o5·=·total:·1·13·45·56·25·2 | 39 | o5·=·total:·1·13·45·56·25·2 |
| 40 | ·········0:·1··.··.··.··.·. | 40 | ·········0:·1··.··.··.··.·. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | cmFuZG9tU2hlbGxhYmxlSWRlYWxDaGFpbg== | 8 | cmFuZG9tU2hlbGxhYmxlSWRlYWxDaGFpbg== |
| 9 | #:len=1807 | 9 | #:len=1807 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUHJvZHVjZXMgYSBjaGFpbiBvZiBpZGVh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiUHJvZHVjZXMgYSBjaGFpbiBvZiBpZGVh |
| 11 | bHMgZnJvbSBhIHJhbmRvbSBzaGVsbGluZyIsICJsaW5lbnVtIiA9PiA3NjksIElucHV0cyA9PiB7 | 11 | bHMgZnJvbSBhIHJhbmRvbSBzaGVsbGluZyIsICJsaW5lbnVtIiA9PiA3NjksIElucHV0cyA9PiB7 |
| Offset 1, 23 lines modified | Offset 1, 22 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·9542801742429495161 | 1 | --·-*-·M2-comint·-*-·hash:·9542801742429495161 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1765916196 |
| 4 | i2·:·kk=ZZ/101; | 4 | i2·:·kk=ZZ/101; |
| 5 | i3·:·S=kk[vars(0..5)]; | 5 | i3·:·S=kk[vars(0..5)]; |
| 6 | i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) | 6 | i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) |
| 7 | ·--·used·1. | 7 | ·--·used·1.59865s·(cpu);·1.21867s·(thread);·0s·(gc) |
| 8 | o4·=·Tally{4·=>· | 8 | o4·=·Tally{4·=>·54·} |
| 9 | ···········5·=>· | 9 | ···········5·=>·197 |
| 10 | ···········6·=>·16 | 10 | ···········6·=>·167 |
| 11 | ···········7·=>· | 11 | ···········7·=>·66 |
| 12 | ···········8·=>·1 | 12 | ···········8·=>·16 |
| 13 | ···········9·=>·2 | ||
| 14 | o4·:·Tally | 13 | o4·:·Tally |
| 15 | i5·:· | 14 | i5·:· |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·5959465567197821046 | 1 | --·-*-·M2-comint·-*-·hash:·5959465567197821046 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1765916242 |
| 4 | i2·:·kk=ZZ/101 | 4 | i2·:·kk=ZZ/101 |
| 5 | o2·=·kk | 5 | o2·=·kk |
| 6 | o2·:·QuotientRing | 6 | o2·:·QuotientRing |
| Offset 14, 13 lines modified | Offset 14, 13 lines modified | ||
| 14 | o3·=·S | 14 | o3·=·S |
| 15 | o3·:·PolynomialRing | 15 | o3·:·PolynomialRing |
| 16 | i4·:·randomMonomial(3,S) | 16 | i4·:·randomMonomial(3,S) |
| 17 | ······ | 17 | ······2 |
| 18 | o4·=· | 18 | o4·=·a·b |
| 19 | o4·:·S | 19 | o4·:·S |
| 20 | i5·:· | 20 | i5·:· |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·8876340562021865447 | 1 | --·-*-·M2-comint·-*-·hash:·8876340562021865447 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1765916312 |
| 4 | i2·:·kk=ZZ/101 | 4 | i2·:·kk=ZZ/101 |
| 5 | o2·=·kk | 5 | o2·=·kk |
| 6 | o2·:·QuotientRing | 6 | o2·:·QuotientRing |
| Offset 27, 12 lines modified | Offset 27, 12 lines modified | ||
| 27 | o5·=·ideal(a*d*e) | 27 | o5·=·ideal(a*d*e) |
| 28 | o5·:·Ideal·of·S | 28 | o5·:·Ideal·of·S |
| 29 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) | 29 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) |
| 30 | o6·=·ideal·( | 30 | o6·=·ideal·(b*c,·a*b,·a*e,·b*e,·c*e) |
| 31 | o6·:·Ideal·of·S | 31 | o6·:·Ideal·of·S |
| 32 | i7·:· | 32 | i7·:· |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·10504911213508281315 | 1 | --·-*-·M2-comint·-*-·hash:·10504911213508281315 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1765916292 |
| 4 | i2·:·S=ZZ/2[vars(0..3)] | 4 | i2·:·S=ZZ/2[vars(0..3)] |
| 5 | o2·=·S | 5 | o2·=·S |
| 6 | o2·:·PolynomialRing | 6 | o2·:·PolynomialRing |
| Offset 14, 17 lines modified | Offset 14, 17 lines modified | ||
| 14 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) | 14 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) |
| 15 | o3·:·MonomialIdeal·of·S | 15 | o3·:·MonomialIdeal·of·S |
| 16 | i4·:·randomSquareFreeStep·J | 16 | i4·:·randomSquareFreeStep·J |
| 17 | o4·=·{monomialIdeal·(a*b,·a*c*d,·b | 17 | o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*d),·{a*b,·a*c,·a*d,·b*d},·{c*d,·b*c, |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ····· | 19 | ·····a}} |
| 20 | o4·:·List | 20 | o4·:·List |
| 21 | i5·:·setRandomSeed(1) | 21 | i5·:·setRandomSeed(1) |
| 22 | o5·=·1 | 22 | o5·=·1 |
| Offset 37, 15 lines modified | Offset 37, 15 lines modified | ||
| 37 | i7·:·J·=·monomialIdeal·0_S | 37 | i7·:·J·=·monomialIdeal·0_S |
| 38 | o7·=·monomialIdeal·() | 38 | o7·=·monomialIdeal·() |
| 39 | o7·:·MonomialIdeal·of·S | 39 | o7·:·MonomialIdeal·of·S |
| 40 | i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01)); | 40 | i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01)); |
| 41 | ·--·used· | 41 | ·--·used·3.82083s·(cpu);·2.65245s·(thread);·0s·(gc) |
| 42 | i9·:·#T | 42 | i9·:·#T |
| 43 | o9·=·168 | 43 | o9·=·168 |
| 44 | i10·:·T | 44 | i10·:·T |
| Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | ········<div> | 72 | ········<div> |
| 73 | ··········<p>Chooses·a·random·monomial.</p> | 73 | ··········<p>Chooses·a·random·monomial.</p> |
| 74 | ········</div> | 74 | ········</div> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 78 | o1·=·17 | 78 | o1·=·1765916242</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 |
| 82 | o2·=·kk | 82 | o2·=·kk |
| 83 | o2·:·QuotientRing</code></pre> | 83 | o2·:·QuotientRing</code></pre> |
| Offset 91, 16 lines modified | Offset 91, 16 lines modified | ||
| 91 | o3·=·S | 91 | o3·=·S |
| 92 | o3·:·PolynomialRing</code></pre> | 92 | o3·:·PolynomialRing</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomMonomial(3,S) | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomMonomial(3,S) |
| 96 | ······ | 96 | ······2 |
| 97 | o4·=· | 97 | o4·=·a·b |
| 98 | o4·:·S</code></pre> | 98 | o4·:·S</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ········</table> | 100 | ········</table> |
| 101 | ······</div> | 101 | ······</div> |
| 102 | ······<div> | 102 | ······<div> |
| 103 | ········<h2>See·also</h2> | 103 | ········<h2>See·also</h2> |
| Offset 13, 29 lines modified | Offset 13, 29 lines modified | ||
| 13 | ··········o·S,·a·_\x8r_\x8i_\x8n_\x8g,·polynomial·ring | 13 | ··········o·S,·a·_\x8r_\x8i_\x8n_\x8g,·polynomial·ring |
| 14 | ····*·Outputs: | 14 | ····*·Outputs: |
| 15 | ··········o·m,·a·_\x8r_\x8i_\x8n_\x8g_\x8·_\x8e_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t,·monomial·of·S | 15 | ··········o·m,·a·_\x8r_\x8i_\x8n_\x8g_\x8·_\x8e_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t,·monomial·of·S |
| 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 17 | Chooses·a·random·monomial. | 17 | Chooses·a·random·monomial. |
| 18 | i1·:·setRandomSeed(currentTime()) | 18 | i1·:·setRandomSeed(currentTime()) |
| 19 | o1·=·17 | 19 | o1·=·1765916242 |
| 20 | i2·:·kk=ZZ/101 | 20 | i2·:·kk=ZZ/101 |
| 21 | o2·=·kk | 21 | o2·=·kk |
| 22 | o2·:·QuotientRing | 22 | o2·:·QuotientRing |
| 23 | i3·:·S=kk[a,b,c] | 23 | i3·:·S=kk[a,b,c] |
| 24 | o3·=·S | 24 | o3·=·S |
| 25 | o3·:·PolynomialRing | 25 | o3·:·PolynomialRing |
| 26 | i4·:·randomMonomial(3,S) | 26 | i4·:·randomMonomial(3,S) |
| 27 | ······ | 27 | ······2 |
| 28 | o4·=· | 28 | o4·=·a·b |
| 29 | o4·:·S | 29 | o4·:·S |
| 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 31 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·monomial·ideal·with·given·degree·generators | 31 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·monomial·ideal·with·given·degree·generators |
| 32 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8q_\x8u_\x8a_\x8r_\x8e_\x8F_\x8r_\x8e_\x8e_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·square-free·monomial·ideal·with | 32 | ····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8q_\x8u_\x8a_\x8r_\x8e_\x8F_\x8r_\x8e_\x8e_\x8M_\x8o_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8I_\x8d_\x8e_\x8a_\x8l·--·random·square-free·monomial·ideal·with |
| 33 | ······given·degree·generators | 33 | ······given·degree·generators |
| 34 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* | 34 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mM\x8Mo\x8on\x8no\x8om\x8mi\x8ia\x8al\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | ········<div> | 72 | ········<div> |
| 73 | ··········<p>Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees·specified·by·the·list·or·sequence·L.</p> | 73 | ··········<p>Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees·specified·by·the·list·or·sequence·L.</p> |
| 74 | ········</div> | 74 | ········</div> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 78 | o1·=·17 | 78 | o1·=·1765916312</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 |
| 82 | o2·=·kk | 82 | o2·=·kk |
| 83 | o2·:·QuotientRing</code></pre> | 83 | o2·:·QuotientRing</code></pre> |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | o5·=·ideal(a*d*e) | 106 | o5·=·ideal(a*d*e) |
| 107 | o5·:·Ideal·of·S</code></pre> | 107 | o5·:·Ideal·of·S</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·randomSquareFreeMonomialIdeal(5:2,·S) | 110 | <td>··············<pre><code·class="language-macaulay2">i6·:·randomSquareFreeMonomialIdeal(5:2,·S) |
| 111 | o6·=·ideal·( | 111 | o6·=·ideal·(b*c,·a*b,·a*e,·b*e,·c*e) |
| 112 | o6·:·Ideal·of·S</code></pre> | 112 | o6·:·Ideal·of·S</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ········</table> | 114 | ········</table> |
| 115 | ······</div> | 115 | ······</div> |
| 116 | ······<div> | 116 | ······<div> |
| 117 | ········<h2>Caveat</h2> | 117 | ········<h2>Caveat</h2> |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | ··········o·I,·an·_\x8i_\x8d_\x8e_\x8a_\x8l,·square-free·monomial·ideal·with·generators·of | 15 | ··········o·I,·an·_\x8i_\x8d_\x8e_\x8a_\x8l,·square-free·monomial·ideal·with·generators·of |
| 16 | ············specified·degrees | 16 | ············specified·degrees |
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees | 18 | Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees |
| 19 | specified·by·the·list·or·sequence·L. | 19 | specified·by·the·list·or·sequence·L. |
| 20 | i1·:·setRandomSeed(currentTime()) | 20 | i1·:·setRandomSeed(currentTime()) |
| 21 | o1·=·17 | 21 | o1·=·1765916312 |
| 22 | i2·:·kk=ZZ/101 | 22 | i2·:·kk=ZZ/101 |
| 23 | o2·=·kk | 23 | o2·=·kk |
| 24 | o2·:·QuotientRing | 24 | o2·:·QuotientRing |
| 25 | i3·:·S=kk[a..e] | 25 | i3·:·S=kk[a..e] |
| Offset 39, 15 lines modified | Offset 39, 15 lines modified | ||
| 39 | low·degree·gens·generated·everything | 39 | low·degree·gens·generated·everything |
| 40 | o5·=·ideal(a*d*e) | 40 | o5·=·ideal(a*d*e) |
| 41 | o5·:·Ideal·of·S | 41 | o5·:·Ideal·of·S |
| 42 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) | 42 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) |
| 43 | o6·=·ideal·( | 43 | o6·=·ideal·(b*c,·a*b,·a*e,·b*e,·c*e) |
| 44 | o6·:·Ideal·of·S | 44 | o6·:·Ideal·of·S |
| 45 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 45 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 46 | The·ideal·is·constructed·degree·by·degree,·starting·from·the·lowest·degree | 46 | The·ideal·is·constructed·degree·by·degree,·starting·from·the·lowest·degree |
| 47 | specified.·If·there·are·not·enough·monomials·of·the·next·specified·degree·that | 47 | specified.·If·there·are·not·enough·monomials·of·the·next·specified·degree·that |
| 48 | are·not·already·in·the·ideal,·the·function·prints·a·warning·and·returns·an | 48 | are·not·already·in·the·ideal,·the·function·prints·a·warning·and·returns·an |
| 49 | ideal·containing·all·the·generators·of·that·degree. | 49 | ideal·containing·all·the·generators·of·that·degree. |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | ··········<p>With·probability·p·the·routine·takes·the·Alexander·dual·of·I;·the·default·value·of·p·is·.05,·and·it·can·be·set·with·the·option·AlexanderProbility.</p> | 82 | ··········<p>With·probability·p·the·routine·takes·the·Alexander·dual·of·I;·the·default·value·of·p·is·.05,·and·it·can·be·set·with·the·option·AlexanderProbility.</p> |
| 83 | ··········<p>Otherwise·uses·the·Metropolis·algorithm·to·produce·a·random·walk·on·the·space·of·square-free·ideals.·Note·that·there·are·a·LOT·of·square-free·ideals;·these·are·the·Dedekind·numbers,·and·the·sequence·(with·1,2,3,4,5,6,7,8·variables)·begins·3,6,20,168,7581,·7828354,·2414682040998,·56130437228687557907788.·(see·the·Online·Encyclopedia·of·Integer·Sequences·for·more·information).·Given·I·in·a·polynomial·ring·S,·we·make·a·list·ISocgens·of·the·square-free·minimal·monomial·generators·of·the·socle·of·S/(squares+I)·and·a·list·of·minimal·generators·Igens·of·I.·A·candidate·"next"·ideal·J·is·formed·as·follows:·We·choose·randomly·from·the·union·of·these·lists;·if·a·socle·element·is·chosen,·it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square-free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is·then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the·similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random·RR·<·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1].</p> | 83 | ··········<p>Otherwise·uses·the·Metropolis·algorithm·to·produce·a·random·walk·on·the·space·of·square-free·ideals.·Note·that·there·are·a·LOT·of·square-free·ideals;·these·are·the·Dedekind·numbers,·and·the·sequence·(with·1,2,3,4,5,6,7,8·variables)·begins·3,6,20,168,7581,·7828354,·2414682040998,·56130437228687557907788.·(see·the·Online·Encyclopedia·of·Integer·Sequences·for·more·information).·Given·I·in·a·polynomial·ring·S,·we·make·a·list·ISocgens·of·the·square-free·minimal·monomial·generators·of·the·socle·of·S/(squares+I)·and·a·list·of·minimal·generators·Igens·of·I.·A·candidate·"next"·ideal·J·is·formed·as·follows:·We·choose·randomly·from·the·union·of·these·lists;·if·a·socle·element·is·chosen,·it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square-free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is·then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the·similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random·RR·<·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1].</p> |
| 84 | ········</div> | 84 | ········</div> |
| 85 | ········<table·class="examples"> | 85 | ········<table·class="examples"> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 87 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 88 | o1·=·17 | 88 | o1·=·1765916292</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·S=ZZ/2[vars(0..3)] | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·S=ZZ/2[vars(0..3)] |
| 92 | o2·=·S | 92 | o2·=·S |
| 93 | o2·:·PolynomialRing</code></pre> | 93 | o2·:·PolynomialRing</code></pre> |
| Offset 101, 17 lines modified | Offset 101, 17 lines modified | ||
| 101 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) | 101 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) |
| 102 | o3·:·MonomialIdeal·of·S</code></pre> | 102 | o3·:·MonomialIdeal·of·S</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomSquareFreeStep·J | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomSquareFreeStep·J |
| 106 | o4·=·{monomialIdeal·(a*b,·a*c*d,·b | 106 | o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*d),·{a*b,·a*c,·a*d,·b*d},·{c*d,·b*c, |
| 107 | ·····------------------------------------------------------------------------ | 107 | ·····------------------------------------------------------------------------ |
| 108 | ····· | 108 | ·····a}} |
| 109 | o4·:·List</code></pre> | 109 | o4·:·List</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| 112 | ········<div> | 112 | ········<div> |
| 113 | ··········<p>With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less·than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000·takes·about·2·seconds.</p> | 113 | ··········<p>With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less·than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000·takes·about·2·seconds.</p> |
| 114 | ········</div> | 114 | ········</div> |
| Offset 133, 15 lines modified | Offset 133, 15 lines modified | ||
| 133 | o7·=·monomialIdeal·() | 133 | o7·=·monomialIdeal·() |
| 134 | o7·:·MonomialIdeal·of·S</code></pre> | 134 | o7·:·MonomialIdeal·of·S</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01)); | 137 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01)); |
| 138 | ·--·used· | 138 | ·--·used·3.82083s·(cpu);·2.65245s·(thread);·0s·(gc)</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i9·:·#T | 141 | <td>··············<pre><code·class="language-macaulay2">i9·:·#T |
| 142 | o9·=·168</code></pre> | 142 | o9·=·168</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| Offset 37, 30 lines modified | Offset 37, 30 lines modified | ||
| 37 | it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square- | 37 | it's·added·to·I;·if·a·minimal·generator·is·chosen,·it's·replaced·by·the·square- |
| 38 | free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is | 38 | free·part·of·the·maximal·ideal·times·it.·the·chance·of·making·the·given·move·is |
| 39 | then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the | 39 | then·1/(#ISocgens+#Igens),·and·the·chance·of·making·the·move·back·would·be·the |
| 40 | similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random | 40 | similar·quantity·for·J,·so·we·make·the·move·or·not·depending·on·whether·random |
| 41 | RR·<·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1]. | 41 | RR·<·(nJ+nSocJ)/(nI+nSocI)·or·not;·here·random·RR·is·a·random·number·in·[0,1]. |
| 42 | i1·:·setRandomSeed(currentTime()) | 42 | i1·:·setRandomSeed(currentTime()) |
| 43 | o1·=·17 | 43 | o1·=·1765916292 |
| 44 | i2·:·S=ZZ/2[vars(0..3)] | 44 | i2·:·S=ZZ/2[vars(0..3)] |
| 45 | o2·=·S | 45 | o2·=·S |
| 46 | o2·:·PolynomialRing | 46 | o2·:·PolynomialRing |
| 47 | i3·:·J·=·monomialIdeal"ab,ad,·bcd" | 47 | i3·:·J·=·monomialIdeal"ab,ad,·bcd" |
| 48 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) | 48 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) |
| 49 | o3·:·MonomialIdeal·of·S | 49 | o3·:·MonomialIdeal·of·S |
| 50 | i4·:·randomSquareFreeStep·J | 50 | i4·:·randomSquareFreeStep·J |
| 51 | o4·=·{monomialIdeal·(a*b,·a*c*d,·b | 51 | o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*d),·{a*b,·a*c,·a*d,·b*d},·{c*d,·b*c, |
| 52 | ·····------------------------------------------------------------------------ | 52 | ·····------------------------------------------------------------------------ |
| 53 | ····· | 53 | ·····a}} |
| 54 | o4·:·List | 54 | o4·:·List |
| 55 | With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less | 55 | With·4·variables·and·168·possible·monomial·ideals,·a·run·of·5000·takes·less |
| 56 | than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000 | 56 | than·6·seconds·on·a·reasonably·fast·machine.·With·10·variables·a·run·of·1000 |
| 57 | takes·about·2·seconds. | 57 | takes·about·2·seconds. |
| 58 | i5·:·setRandomSeed(1) | 58 | i5·:·setRandomSeed(1) |
| Offset 73, 15 lines modified | Offset 73, 15 lines modified | ||
| 73 | i7·:·J·=·monomialIdeal·0_S | 73 | i7·:·J·=·monomialIdeal·0_S |
| 74 | o7·=·monomialIdeal·() | 74 | o7·=·monomialIdeal·() |
| 75 | o7·:·MonomialIdeal·of·S | 75 | o7·:·MonomialIdeal·of·S |
| 76 | i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs | 76 | i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs |
| 77 | (J,AlexanderProbability·=>·.01)); | 77 | (J,AlexanderProbability·=>·.01)); |
| 78 | ·--·used· | 78 | ·--·used·3.82083s·(cpu);·2.65245s·(thread);·0s·(gc) |
| 79 | i9·:·#T | 79 | i9·:·#T |
| 80 | o9·=·168 | 80 | o9·=·168 |
| 81 | i10·:·T | 81 | i10·:·T |
| 82 | o10·=·Tally{monomialIdeal·()·=>·45····························} | 82 | o10·=·Tally{monomialIdeal·()·=>·45····························} |
| 83 | ············monomialIdeal·(a*b*c,·a*b*d)·=>·33 | 83 | ············monomialIdeal·(a*b*c,·a*b*d)·=>·33 |
| Offset 47, 32 lines modified | Offset 47, 31 lines modified | ||
| 47 | ········<div> | 47 | ········<div> |
| 48 | ··········<p>This·package·can·be·used·to·make·experiments,·trying·many·ideals,·perhaps·over·small·fields.·For·example...what·would·you·expect·the·regularities·of·"typical"·monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a·bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a·second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done·conveniently.</p> | 48 | ··········<p>This·package·can·be·used·to·make·experiments,·trying·many·ideals,·perhaps·over·small·fields.·For·example...what·would·you·expect·the·regularities·of·"typical"·monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a·bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a·second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done·conveniently.</p> |
| 49 | ········</div> | 49 | ········</div> |
| 50 | ········<table·class="examples"> | 50 | ········<table·class="examples"> |
| 51 | ··········<tr> | 51 | ··········<tr> |
| 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 53 | o1·=·17 | 53 | o1·=·1765916196</code></pre> |
| 54 | </td>··········</tr> | 54 | </td>··········</tr> |
| 55 | ··········<tr> | 55 | ··········<tr> |
| 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101;</code></pre> | 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101;</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=kk[vars(0..5)];</code></pre> | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=kk[vars(0..5)];</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ··········<tr> | 61 | ··········<tr> |
| 62 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) | 62 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) |
| 63 | ·--·used·1. | 63 | ·--·used·1.59865s·(cpu);·1.21867s·(thread);·0s·(gc) |
| 64 | o4·=·Tally{4·=>· | 64 | o4·=·Tally{4·=>·54·} |
| 65 | ···········5·=>· | 65 | ···········5·=>·197 |
| 66 | ···········6·=>·16 | 66 | ···········6·=>·167 |
| 67 | ···········7·=>· | 67 | ···········7·=>·66 |
| 68 | ···········8·=>·1 | 68 | ···········8·=>·16 |
| 69 | ···········9·=>·2 | ||
| 70 | o4·:·Tally</code></pre> | 69 | o4·:·Tally</code></pre> |
| 71 | </td>··········</tr> | 70 | </td>··········</tr> |
| 72 | ········</table> | 71 | ········</table> |
| 73 | ········<div> | 72 | ········<div> |
| 74 | ··········<p>How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial·ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal"·above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger·numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see·some·other,·more·elaborate·ways·to·search.</p> | 73 | ··········<p>How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial·ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal"·above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger·numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see·some·other,·more·elaborate·ways·to·search.</p> |
| 75 | ········</div> | 74 | ········</div> |
| Offset 10, 26 lines modified | Offset 10, 25 lines modified | ||
| 10 | small·fields.·For·example...what·would·you·expect·the·regularities·of·"typical" | 10 | small·fields.·For·example...what·would·you·expect·the·regularities·of·"typical" |
| 11 | monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a | 11 | monomial·ideals·with·10·generators·of·degree·3·in·6·variables·to·be?·Try·a |
| 12 | bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a | 12 | bunch·of·examples·--·it's·fast.·Here·we·do·only·500·--·this·takes·about·a |
| 13 | second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done | 13 | second·on·a·fast·machine·--·but·with·a·little·patience,·thousands·can·be·done |
| 14 | conveniently. | 14 | conveniently. |
| 15 | i1·:·setRandomSeed(currentTime()) | 15 | i1·:·setRandomSeed(currentTime()) |
| 16 | o1·=·17 | 16 | o1·=·1765916196 |
| 17 | i2·:·kk=ZZ/101; | 17 | i2·:·kk=ZZ/101; |
| 18 | i3·:·S=kk[vars(0..5)]; | 18 | i3·:·S=kk[vars(0..5)]; |
| 19 | i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) | 19 | i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) |
| 20 | ·--·used·1. | 20 | ·--·used·1.59865s·(cpu);·1.21867s·(thread);·0s·(gc) |
| 21 | o4·=·Tally{4·=>· | 21 | o4·=·Tally{4·=>·54·} |
| 22 | ···········5·=>· | 22 | ···········5·=>·197 |
| 23 | ···········6·=>·16 | 23 | ···········6·=>·167 |
| 24 | ···········7·=>· | 24 | ···········7·=>·66 |
| 25 | ···········8·=>·1 | 25 | ···········8·=>·16 |
| 26 | ···········9·=>·2 | ||
| 27 | o4·:·Tally | 26 | o4·:·Tally |
| 28 | How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial | 27 | How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial |
| 29 | ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal" | 28 | ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal" |
| 30 | above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger | 29 | above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger |
| 31 | numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see | 30 | numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see |
| 32 | some·other,·more·elaborate·ways·to·search. | 31 | some·other,·more·elaborate·ways·to·search. |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=46 | 7 | #:len=46 |
| 8 | ZmluZEFOb25aZXJvTWlub3IoLi4uLFBvaW50Q2hlY2tBdHRlbXB0cz0+Li4uKQ== | 8 | ZmluZEFOb25aZXJvTWlub3IoLi4uLFBvaW50Q2hlY2tBdHRlbXB0cz0+Li4uKQ== |
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| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbZmluZEFOb25aZXJvTWlub3IsUG9pbnRDaGVja0F0 | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbZmluZEFOb25aZXJvTWlub3IsUG9pbnRDaGVja0F0 |
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| 5 | i2·:·S=kk[y_0..y_8]; | 5 | i2·:·S=kk[y_0..y_8]; |
| 6 | i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; | 6 | i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; |
| 7 | o3·:·Ideal·of·S | 7 | o3·:·Ideal·of·S |
| 8 | i4·:·elapsedTime·dimViaBezout(I) | 8 | i4·:·elapsedTime·dimViaBezout(I) |
| 9 | ·--·1. | 9 | ·--·1.28118s·elapsed |
| 10 | o4·=·4 | 10 | o4·=·4 |
| 11 | i5·:·elapsedTime·dim·I | 11 | i5·:·elapsedTime·dim·I |
| 12 | ·--· | 12 | ·--·4.16029s·elapsed |
| 13 | o5·=·4 | 13 | o5·=·4 |
| 14 | i6·:· | 14 | i6·:· |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | i8·:·i·=·0; | 35 | i8·:·i·=·0; |
| 36 | i9·:·J·=·I; | 36 | i9·:·J·=·I; |
| 37 | o9·:·Ideal·of·T | 37 | o9·:·Ideal·of·T |
| 38 | i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·); | 38 | i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·); |
| 39 | ·--·1. | 39 | ·--·1.96594s·elapsed |
| 40 | i11·:·dim·J | 40 | i11·:·dim·J |
| 41 | o11·=·1 | 41 | o11·=·1 |
| 42 | i12·:·i | 42 | i12·:·i |
| Offset 27, 24 lines modified | Offset 27, 24 lines modified | ||
| 27 | i6·:·S=ZZ/103[y_0..y_30]; | 27 | i6·:·S=ZZ/103[y_0..y_30]; |
| 28 | i7·:·I=minors(2,random(S^3,S^{3:-1})); | 28 | i7·:·I=minors(2,random(S^3,S^{3:-1})); |
| 29 | o7·:·Ideal·of·S | 29 | o7·:·Ideal·of·S |
| 30 | i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable) | 30 | i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable) |
| 31 | ·--·3. | 31 | ·--·3.51404s·elapsed |
| 32 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, | 32 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, |
| 33 | ·····------------------------------------------------------------------------ | 33 | ·····------------------------------------------------------------------------ |
| 34 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} | 34 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} |
| 35 | o8·:·List | 35 | o8·:·List |
| 36 | i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose) | 36 | i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose) |
| 37 | ·--· | 37 | ·--·2.2213s·elapsed |
| 38 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, | 38 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} | 40 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} |
| 41 | o9·:·List | 41 | o9·:·List |
| Offset 94, 21 lines modified | Offset 94, 21 lines modified | ||
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; |
| 96 | o3·:·Ideal·of·S</code></pre> | 96 | o3·:·Ideal·of·S</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·dimViaBezout(I) | 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·dimViaBezout(I) |
| 100 | ·--·1. | 100 | ·--·1.28118s·elapsed |
| 101 | o4·=·4</code></pre> | 101 | o4·=·4</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·dim·I | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·dim·I |
| 105 | ·--· | 105 | ·--·4.16029s·elapsed |
| 106 | o5·=·4</code></pre> | 106 | o5·=·4</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ········<div> | 109 | ········<div> |
| 110 | ··········<p>The·user·may·set·the·<span·class="tt">MinimumFieldSize</span>·to·ensure·that·the·field·being·worked·over·is·big·enough.··For·instance,·there·are·relatively·few·linear·spaces·over·a·field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided.··If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on·ambient·ring.</p> | 110 | ··········<p>The·user·may·set·the·<span·class="tt">MinimumFieldSize</span>·to·ensure·that·the·field·being·worked·over·is·big·enough.··For·instance,·there·are·relatively·few·linear·spaces·over·a·field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided.··If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on·ambient·ring.</p> |
| 111 | ········</div> | 111 | ········</div> |
| Offset 33, 19 lines modified | Offset 33, 19 lines modified | ||
| 33 | examples,·the·built·in·dim·function·is·much·faster. | 33 | examples,·the·built·in·dim·function·is·much·faster. |
| 34 | i1·:·kk=ZZ/101; | 34 | i1·:·kk=ZZ/101; |
| 35 | i2·:·S=kk[y_0..y_8]; | 35 | i2·:·S=kk[y_0..y_8]; |
| 36 | i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; | 36 | i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; |
| 37 | o3·:·Ideal·of·S | 37 | o3·:·Ideal·of·S |
| 38 | i4·:·elapsedTime·dimViaBezout(I) | 38 | i4·:·elapsedTime·dimViaBezout(I) |
| 39 | ·--·1. | 39 | ·--·1.28118s·elapsed |
| 40 | o4·=·4 | 40 | o4·=·4 |
| 41 | i5·:·elapsedTime·dim·I | 41 | i5·:·elapsedTime·dim·I |
| 42 | ·--· | 42 | ·--·4.16029s·elapsed |
| 43 | o5·=·4 | 43 | o5·=·4 |
| 44 | The·user·may·set·the·MinimumFieldSize·to·ensure·that·the·field·being·worked | 44 | The·user·may·set·the·MinimumFieldSize·to·ensure·that·the·field·being·worked |
| 45 | over·is·big·enough.·For·instance,·there·are·relatively·few·linear·spaces·over·a | 45 | over·is·big·enough.·For·instance,·there·are·relatively·few·linear·spaces·over·a |
| 46 | field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided. | 46 | field·of·characteristic·2,·and·this·can·cause·incorrect·results·to·be·provided. |
| 47 | If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on | 47 | If·no·size·is·provided,·the·function·tries·to·guess·a·good·size·based·on |
| 48 | ambient·ring. | 48 | ambient·ring. |
| Offset 149, 15 lines modified | Offset 149, 15 lines modified | ||
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i9·:·J·=·I; | 150 | <td>··············<pre><code·class="language-macaulay2">i9·:·J·=·I; |
| 151 | o9·:·Ideal·of·T</code></pre> | 151 | o9·:·Ideal·of·T</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·); | 154 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·); |
| 155 | ·--·1. | 155 | ·--·1.96594s·elapsed</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim·J | 158 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim·J |
| 159 | o11·=·1</code></pre> | 159 | o11·=·1</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | o7·:·Matrix·T··<--·T | 80 | o7·:·Matrix·T··<--·T |
| 81 | i8·:·i·=·0; | 81 | i8·:·i·=·0; |
| 82 | i9·:·J·=·I; | 82 | i9·:·J·=·I; |
| 83 | o9·:·Ideal·of·T | 83 | o9·:·Ideal·of·T |
| 84 | i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·= | 84 | i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·= |
| 85 | extendIdealByNonZeroMinor(4,·M,·J))·); | 85 | extendIdealByNonZeroMinor(4,·M,·J))·); |
| 86 | ·--·1. | 86 | ·--·1.96594s·elapsed |
| 87 | i11·:·dim·J | 87 | i11·:·dim·J |
| 88 | o11·=·1 | 88 | o11·=·1 |
| 89 | i12·:·i | 89 | i12·:·i |
| 90 | o12·=·4 | 90 | o12·=·4 |
| 91 | In·this·particular·example,·there·tend·to·be·about·5·associated·primes·when | 91 | In·this·particular·example,·there·tend·to·be·about·5·associated·primes·when |
| Offset 141, 25 lines modified | Offset 141, 25 lines modified | ||
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i7·:·I=minors(2,random(S^3,S^{3:-1})); | 142 | <td>··············<pre><code·class="language-macaulay2">i7·:·I=minors(2,random(S^3,S^{3:-1})); |
| 143 | o7·:·Ideal·of·S</code></pre> | 143 | o7·:·Ideal·of·S</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable) | 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable) |
| 147 | ·--·3. | 147 | ·--·3.51404s·elapsed |
| 148 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, | 148 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, |
| 149 | ·····------------------------------------------------------------------------ | 149 | ·····------------------------------------------------------------------------ |
| 150 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} | 150 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} |
| 151 | o8·:·List</code></pre> | 151 | o8·:·List</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose) | 154 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose) |
| 155 | ·--· | 155 | ·--·2.2213s·elapsed |
| 156 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, | 156 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, |
| 157 | ·····------------------------------------------------------------------------ | 157 | ·····------------------------------------------------------------------------ |
| 158 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} | 158 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} |
| 159 | o9·:·List</code></pre> | 159 | o9·:·List</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| Offset 67, 24 lines modified | Offset 67, 24 lines modified | ||
| 67 | first·in·rings·with·more·variables. | 67 | first·in·rings·with·more·variables. |
| 68 | i6·:·S=ZZ/103[y_0..y_30]; | 68 | i6·:·S=ZZ/103[y_0..y_30]; |
| 69 | i7·:·I=minors(2,random(S^3,S^{3:-1})); | 69 | i7·:·I=minors(2,random(S^3,S^{3:-1})); |
| 70 | o7·:·Ideal·of·S | 70 | o7·:·Ideal·of·S |
| 71 | i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection, | 71 | i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection, |
| 72 | DecompositionStrategy=>MultiplicationTable) | 72 | DecompositionStrategy=>MultiplicationTable) |
| 73 | ·--·3. | 73 | ·--·3.51404s·elapsed |
| 74 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, | 74 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, |
| 75 | ·····------------------------------------------------------------------------ | 75 | ·····------------------------------------------------------------------------ |
| 76 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} | 76 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} |
| 77 | o8·:·List | 77 | o8·:·List |
| 78 | i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection, | 78 | i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection, |
| 79 | DecompositionStrategy=>Decompose) | 79 | DecompositionStrategy=>Decompose) |
| 80 | ·--· | 80 | ·--·2.2213s·elapsed |
| 81 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, | 81 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, |
| 82 | ·····------------------------------------------------------------------------ | 82 | ·····------------------------------------------------------------------------ |
| 83 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} | 83 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} |
| 84 | o9·:·List | 84 | o9·:·List |
| 85 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mP\x8Po\x8oi\x8in\x8nt\x8ts\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 85 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mP\x8Po\x8oi\x8in\x8nt\x8ts\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=38 | 7 | #:len=38 |
| 8 | a25vd25VbmlyYXRpb25hbENvbXBvbmVudE9mU3BhY2VDdXJ2ZXM= | 8 | a25vd25VbmlyYXRpb25hbENvbXBvbmVudE9mU3BhY2VDdXJ2ZXM= |
| 9 | #:len=2298 | 9 | #:len=2298 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hlY2sgd2hldGhlciB0aGVyZSBpcyBh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hlY2sgd2hldGhlciB0aGVyZSBpcyBh |
| 11 | IHVuaXJhdGlvbmFsIGNvbnN0cnVjdGlvbiBmb3IgYSBjb21wb25lbnQgb2YgdGhlIEhpbGJlcnQg | 11 | IHVuaXJhdGlvbmFsIGNvbnN0cnVjdGlvbiBmb3IgYSBjb21wb25lbnQgb2YgdGhlIEhpbGJlcnQg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=46 | 7 | #:len=46 |
| 8 | aXNCaXJhdGlvbmFsT250b0ltYWdlKC4uLixBc3N1bWVEb21pbmFudD0+Li4uKQ== | 8 | aXNCaXJhdGlvbmFsT250b0ltYWdlKC4uLixBc3N1bWVEb21pbmFudD0+Li4uKQ== |
| 9 | #:len=321 | 9 | #:len=321 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgwNywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgwNywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaXNCaXJhdGlvbmFsT250b0ltYWdlLEFzc3VtZURv | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaXNCaXJhdGlvbmFsT250b0ltYWdlLEFzc3VtZURv |
| Offset 49, 15 lines modified | Offset 49, 15 lines modified | ||
| 49 | i12·:·Q=QQ[x,y,z,t,u]; | 49 | i12·:·Q=QQ[x,y,z,t,u]; |
| 50 | i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}}); | 50 | i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}}); |
| 51 | o13·:·RingMap·Q·<--·Q | 51 | o13·:·RingMap·Q·<--·Q |
| 52 | i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) | 52 | i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) |
| 53 | ·--·used·2. | 53 | ·--·used·2.17546s·(cpu);·0.576108s·(thread);·0s·(gc) |
| 54 | ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124 | 54 | ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124 |
| 55 | o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u} | 55 | o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u} |
| 56 | o14·:·RationalMapping | 56 | o14·:·RationalMapping |
| 57 | i15·:·R=QQ[x,y,z,t]/(z-2*t); | 57 | i15·:·R=QQ[x,y,z,t]/(z-2*t); |
| Offset 171, 15 lines modified | Offset 171, 15 lines modified | ||
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}}); | 172 | <td>··············<pre><code·class="language-macaulay2">i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}}); |
| 173 | o13·:·RingMap·Q·<--·Q</code></pre> | 173 | o13·:·RingMap·Q·<--·Q</code></pre> |
| 174 | </td>··········</tr> | 174 | </td>··········</tr> |
| 175 | ··········<tr> | 175 | ··········<tr> |
| 176 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) | 176 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) |
| 177 | ·--·used·2. | 177 | ·--·used·2.17546s·(cpu);·0.576108s·(thread);·0s·(gc) |
| 178 | ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124 | 178 | ································125···124······120·5····124····100·25·····104·20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120········8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6··········28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70·11···········48·65·12···········52·60·13···········56·55·14···········60·50·15···········64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25·20·········84·20·21········88·15·22·······92·10·23······96·5·24····100·25·····24·100········28·95··········32·90·2·········36·85·3··········40·80·4··········44·75·5···········48·70·6···········52·65·7···········56·60·8···········60·55·9···········64·50·10···········68·45·11···········72·40·12···········76·35·13···········80·30·14··········84·25·15··········88·20·16·········92·15·17········96·10·18········100·5·19······104·20·······48·75·2·······52·70···2········56·65·2·2········60·60·3·2·········64·55·4·2·········68·50·5·2·········72·45·6·2·········76·40·7·2·········80·35·8·2·········84·30·9·2·········88·25·10·2·········92·20·11·2········96·15·12·2········100·10·13·2·······104·5·14·2······108·15·2······72·50·3·······76·45···3·······80·40·2·3········84·35·3·3········88·30·4·3········92·25·5·3········96·20·6·3········100·15·7·3·······104·10·8·3·······108·5·9·3······112·10·3·····96·25·4······100·20···4······104·15·2·4······108·10·3·4······112·5·4·4·····116·5·4····120·5····124 |
| 179 | o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u} | 179 | o14·=·Proj·Q·-·-·-·>·Proj·Q···{x···,·x···y,·-·x···y··+·x···z,·x···y···-·5x···y··z·+·10x···y··z··-·10x···y··z··+·5x···y·z··-·x···z··+·x···t,·-·y····+·25x·y···z·-·300x·y···z··+·2300x··y···z··-·12650x··y···z··+·53130x··y···z··-·177100x··y··z··+·480700x··y··z··-·1081575x··y··z··+·2042975x··y··z··-·3268760x··y··z···+·4457400x··y··z···-·5200300x··y··z···+·5200300x··y··z···-·4457400x··y··z···+·3268760x··y··z···-·2042975x··y··z···+·1081575x··y··z···-·480700x··y··z···+·177100x··y··z···-·53130x··y··z···+·12650x··y··z···-·2300x··y··z···+·300x··y··z···-·25x··y·z···+·x···z···-·5x··y···t·+·100x··y··z*t·-·950x··y··z·t·+·5700x··y··z·t·-·24225x··y··z·t·+·77520x··y··z·t·-·193800x··y··z·t·+·387600x··y··z·t·-·629850x··y··z·t·+·839800x··y··z·t·-·923780x··y··z··t·+·839800x··y··z··t·-·629850x··y··z··t·+·387600x··y··z··t·-·193800x··y··z··t·+·77520x··y··z··t·-·24225x··y··z··t·+·5700x··y··z··t·-·950x··y··z··t·+·100x···y·z··t·-·5x···z··t·-·10x··y··t··+·150x··y··z*t··-·1050x··y··z·t··+·4550x··y··z·t··-·13650x··y··z·t··+·30030x··y··z·t··-·50050x··y··z·t··+·64350x··y··z·t··-·64350x··y··z·t··+·50050x··y··z·t··-·30030x··y··z··t··+·13650x··y··z··t··-·4550x··y··z··t··+·1050x···y··z··t··-·150x···y·z··t··+·10x···z··t··-·10x··y··t··+·100x··y··z*t··-·450x··y··z·t··+·1200x··y··z·t··-·2100x··y··z·t··+·2520x··y··z·t··-·2100x··y··z·t··+·1200x···y··z·t··-·450x···y··z·t··+·100x···y·z·t··-·10x···z··t··-·5x··y··t··+·25x···y··z*t··-·50x···y··z·t··+·50x···y··z·t··-·25x···y·z·t··+·5x···z·t··-·x···t··+·x···u} |
| 180 | o14·:·RationalMapping</code></pre> | 180 | o14·:·RationalMapping</code></pre> |
| 181 | </td>··········</tr> | 181 | </td>··········</tr> |
| 182 | ········</table> | 182 | ········</table> |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | o11·:·Ideal·of·blowUpSubvar | 95 | o11·:·Ideal·of·blowUpSubvar |
| 96 | The·next·example·is·a·birational·map·on·$\mathbb{P}^4$. | 96 | The·next·example·is·a·birational·map·on·$\mathbb{P}^4$. |
| 97 | i12·:·Q=QQ[x,y,z,t,u]; | 97 | i12·:·Q=QQ[x,y,z,t,u]; |
| 98 | i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}}); | 98 | i13·:·phi=map(Q,Q,matrix{{x^5,y*x^4,z*x^4+y^5,t*x^4+z^5,u*x^4+t^5}}); |
| 99 | o13·:·RingMap·Q·<--·Q | 99 | o13·:·RingMap·Q·<--·Q |
| 100 | i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) | 100 | i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) |
| 101 | ·--·used·2. | 101 | ·--·used·2.17546s·(cpu);·0.576108s·(thread);·0s·(gc) |
| 102 | ································125···124······120·5····124····100·25·····104 | 102 | ································125···124······120·5····124····100·25·····104 |
| 103 | 20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120 | 103 | 20·······108·15·2······112·10·3·····116·5·4····120·5····124······125······4·120 |
| 104 | 8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6 | 104 | 8·115·2········12·110·3·········16·105·4·········20·100·5··········24·95·6 |
| 105 | 28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70 | 105 | 28·90·7···········32·85·8···········36·80·9···········40·75·10···········44·70 |
| 106 | 11···········48·65·12···········52·60·13···········56·55·14···········60·50·15 | 106 | 11···········48·65·12···········52·60·13···········56·55·14···········60·50·15 |
| 107 | 64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25 | 107 | 64·45·16···········68·40·17··········72·35·18··········76·30·19·········80·25 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | U29ydEdlbnM= | 8 | U29ydEdlbnM= |
| 9 | #:len=246 | 9 | #:len=246 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg3LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg3LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJTb3J0R2VucyIsIlNvcnRHZW5zIiwiUmF0aW9uYWxQ | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJTb3J0R2VucyIsIlNvcnRHZW5zIiwiUmF0aW9uYWxQ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | bmV0KFByb2plY3RpdmVQb2ludCk= | 8 | bmV0KFByb2plY3RpdmVQb2ludCk= |
| 9 | #:len=205 | 9 | #:len=205 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTcsICJ1bmRvY3VtZW50ZWQiID0+IHRy | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTcsICJ1bmRvY3VtZW50ZWQiID0+IHRy |
| 11 | dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KG5ldCxQcm9q | 11 | dWUsIHN5bWJvbCBEb2N1bWVudFRhZyA9PiBuZXcgRG9jdW1lbnRUYWcgZnJvbSB7KG5ldCxQcm9q |
| Offset 48, 15 lines modified | Offset 48, 15 lines modified | ||
| 48 | ·············0····1····2····3····4····5····6····7····8····9····10 | 48 | ·············0····1····2····3····4····5····6····7····8····9····10 |
| 49 | ················ZZ | 49 | ················ZZ |
| 50 | o13·:·Ideal·of·---[u·..u··] | 50 | o13·:·Ideal·of·---[u·..u··] |
| 51 | ···············101··0···10 | 51 | ···············101··0···10 |
| 52 | i14·:·time·rationalPoints(I,·Amount·=>·true) | 52 | i14·:·time·rationalPoints(I,·Amount·=>·true) |
| 53 | ·--·used·0.00 | 53 | ·--·used·0.00399733s·(cpu);·0.00340968s·(thread);·0s·(gc) |
| 54 | o14·=·110462212541120451001 | 54 | o14·=·110462212541120451001 |
| 55 | i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z); | 55 | i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z); |
| 56 | o16·:·Ideal·of·QQ[x..z] | 56 | o16·:·Ideal·of·QQ[x..z] |
| Offset 141, 24 lines modified | Offset 141, 24 lines modified | ||
| 141 | o30·:·Ideal·of·R | 141 | o30·:·Ideal·of·R |
| 142 | i31·:·nodes·=·I·+·ideal·jacobian·I; | 142 | i31·:·nodes·=·I·+·ideal·jacobian·I; |
| 143 | o31·:·Ideal·of·R | 143 | o31·:·Ideal·of·R |
| 144 | i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); | 144 | i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); |
| 145 | ·--·used· | 145 | ·--·used·1.33427s·(cpu);·0.892937s·(thread);·0s·(gc) |
| 146 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25) | 146 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25) |
| 147 | i33·:·#oo | 147 | i33·:·#oo |
| 148 | o33·=·31 | 148 | o33·=·31 |
| 149 | i34·:·nodes'·=·baseChange_32003·nodes; | 149 | i34·:·nodes'·=·baseChange_32003·nodes; |
| 150 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w] | 150 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w] |
| 151 | i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) | 151 | i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) |
| 152 | ·--·used·0. | 152 | ·--·used·0.442493s·(cpu);·0.248235s·(thread);·0s·(gc) |
| 153 | o35·=·31 | 153 | o35·=·31 |
| 154 | i36·:· | 154 | i36·:· |
| Offset 167, 15 lines modified | Offset 167, 15 lines modified | ||
| 167 | ················ZZ | 167 | ················ZZ |
| 168 | o13·:·Ideal·of·---[u·..u··] | 168 | o13·:·Ideal·of·---[u·..u··] |
| 169 | ···············101··0···10</code></pre> | 169 | ···············101··0···10</code></pre> |
| 170 | </td>··········</tr> | 170 | </td>··········</tr> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalPoints(I,·Amount·=>·true) | 172 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalPoints(I,·Amount·=>·true) |
| 173 | ·--·used·0.00 | 173 | ·--·used·0.00399733s·(cpu);·0.00340968s·(thread);·0s·(gc) |
| 174 | o14·=·110462212541120451001</code></pre> | 174 | o14·=·110462212541120451001</code></pre> |
| 175 | </td>··········</tr> | 175 | </td>··········</tr> |
| 176 | ········</table> | 176 | ········</table> |
| 177 | ········<div> | 177 | ········<div> |
| 178 | ··········<h3>Over·number·fields</h3> | 178 | ··········<h3>Over·number·fields</h3> |
| 179 | ········</div> | 179 | ········</div> |
| Offset 308, 15 lines modified | Offset 308, 15 lines modified | ||
| 308 | ··········<tr> | 308 | ··········<tr> |
| 309 | <td>··············<pre><code·class="language-macaulay2">i31·:·nodes·=·I·+·ideal·jacobian·I; | 309 | <td>··············<pre><code·class="language-macaulay2">i31·:·nodes·=·I·+·ideal·jacobian·I; |
| 310 | o31·:·Ideal·of·R</code></pre> | 310 | o31·:·Ideal·of·R</code></pre> |
| 311 | </td>··········</tr> | 311 | </td>··········</tr> |
| 312 | ··········<tr> | 312 | ··········<tr> |
| 313 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); | 313 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); |
| 314 | ·--·used· | 314 | ·--·used·1.33427s·(cpu);·0.892937s·(thread);·0s·(gc) |
| 315 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)</code></pre> | 315 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)</code></pre> |
| 316 | </td>··········</tr> | 316 | </td>··········</tr> |
| 317 | ··········<tr> | 317 | ··········<tr> |
| 318 | <td>··············<pre><code·class="language-macaulay2">i33·:·#oo | 318 | <td>··············<pre><code·class="language-macaulay2">i33·:·#oo |
| 319 | o33·=·31</code></pre> | 319 | o33·=·31</code></pre> |
| 320 | </td>··········</tr> | 320 | </td>··········</tr> |
| Offset 328, 15 lines modified | Offset 328, 15 lines modified | ||
| 328 | ··········<tr> | 328 | ··········<tr> |
| 329 | <td>··············<pre><code·class="language-macaulay2">i34·:·nodes'·=·baseChange_32003·nodes; | 329 | <td>··············<pre><code·class="language-macaulay2">i34·:·nodes'·=·baseChange_32003·nodes; |
| 330 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]</code></pre> | 330 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]</code></pre> |
| 331 | </td>··········</tr> | 331 | </td>··········</tr> |
| 332 | ··········<tr> | 332 | ··········<tr> |
| 333 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) | 333 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) |
| 334 | ·--·used·0. | 334 | ·--·used·0.442493s·(cpu);·0.248235s·(thread);·0s·(gc) |
| 335 | o35·=·31</code></pre> | 335 | o35·=·31</code></pre> |
| 336 | </td>··········</tr> | 336 | </td>··········</tr> |
| 337 | ········</table> | 337 | ········</table> |
| 338 | ······</div> | 338 | ······</div> |
| 339 | ······<div> | 339 | ······<div> |
| 340 | ········<h2>Caveat</h2> | 340 | ········<h2>Caveat</h2> |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | o13·=·ideal(u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··) | 90 | o13·=·ideal(u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··+·u··) |
| 91 | ·············0····1····2····3····4····5····6····7····8····9····10 | 91 | ·············0····1····2····3····4····5····6····7····8····9····10 |
| 92 | ················ZZ | 92 | ················ZZ |
| 93 | o13·:·Ideal·of·---[u·..u··] | 93 | o13·:·Ideal·of·---[u·..u··] |
| 94 | ···············101··0···10 | 94 | ···············101··0···10 |
| 95 | i14·:·time·rationalPoints(I,·Amount·=>·true) | 95 | i14·:·time·rationalPoints(I,·Amount·=>·true) |
| 96 | ·--·used·0.00 | 96 | ·--·used·0.00399733s·(cpu);·0.00340968s·(thread);·0s·(gc) |
| 97 | o14·=·110462212541120451001 | 97 | o14·=·110462212541120451001 |
| 98 | *\x8**\x8**\x8**\x8*·O\x8Ov\x8ve\x8er\x8r·n\x8nu\x8um\x8mb\x8be\x8er\x8r·f\x8fi\x8ie\x8el\x8ld\x8ds\x8s·*\x8**\x8**\x8**\x8* | 98 | *\x8**\x8**\x8**\x8*·O\x8Ov\x8ve\x8er\x8r·n\x8nu\x8um\x8mb\x8be\x8er\x8r·f\x8fi\x8ie\x8el\x8ld\x8ds\x8s·*\x8**\x8**\x8**\x8* |
| 99 | Over·a·number·field·one·can·use·the·option·Bound·to·specify·a·maximal | 99 | Over·a·number·field·one·can·use·the·option·Bound·to·specify·a·maximal |
| 100 | multiplicative·height·given·by·$(x_0:\dots:x_n)\mapsto·\prod_{v}\max_i|x_i|_v·^ | 100 | multiplicative·height·given·by·$(x_0:\dots:x_n)\mapsto·\prod_{v}\max_i|x_i|_v·^ |
| 101 | {d_v/d}$·(this·is·also·available·as·a·method·_\x8g_\x8l_\x8o_\x8b_\x8a_\x8l_\x8H_\x8e_\x8i_\x8g_\x8h_\x8t). | 101 | {d_v/d}$·(this·is·also·available·as·a·method·_\x8g_\x8l_\x8o_\x8b_\x8a_\x8l_\x8H_\x8e_\x8i_\x8g_\x8h_\x8t). |
| 102 | i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z); | 102 | i15·:·QQ[x,y,z];·I·=·homogenize(ideal(y^2-x*(x-1)*(x-2)*(x-5)*(x-6)),·z); |
| Offset 197, 25 lines modified | Offset 197, 25 lines modified | ||
| 197 | (2z-qw)(4(x2+y2-z2)+(1+3(5-q2))w2)2"; | 197 | (2z-qw)(4(x2+y2-z2)+(1+3(5-q2))w2)2"; |
| 198 | o30·:·Ideal·of·R | 198 | o30·:·Ideal·of·R |
| 199 | i31·:·nodes·=·I·+·ideal·jacobian·I; | 199 | i31·:·nodes·=·I·+·ideal·jacobian·I; |
| 200 | o31·:·Ideal·of·R | 200 | o31·:·Ideal·of·R |
| 201 | i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); | 201 | i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); |
| 202 | ·--·used· | 202 | ·--·used·1.33427s·(cpu);·0.892937s·(thread);·0s·(gc) |
| 203 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25) | 203 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25) |
| 204 | i33·:·#oo | 204 | i33·:·#oo |
| 205 | o33·=·31 | 205 | o33·=·31 |
| 206 | Still·it·runs·a·lot·faster·when·reduced·to·a·positive·characteristic. | 206 | Still·it·runs·a·lot·faster·when·reduced·to·a·positive·characteristic. |
| 207 | i34·:·nodes'·=·baseChange_32003·nodes; | 207 | i34·:·nodes'·=·baseChange_32003·nodes; |
| 208 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w] | 208 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w] |
| 209 | i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) | 209 | i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) |
| 210 | ·--·used·0. | 210 | ·--·used·0.442493s·(cpu);·0.248235s·(thread);·0s·(gc) |
| 211 | o35·=·31 | 211 | o35·=·31 |
| 212 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 212 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 213 | For·a·number·field·other·than·QQ,·the·enumeration·of·elements·with·bounded | 213 | For·a·number·field·other·than·QQ,·the·enumeration·of·elements·with·bounded |
| 214 | height·depends·on·an·algorithm·by·DoyleâKrumm,·which·is·currently·only | 214 | height·depends·on·an·algorithm·by·DoyleâKrumm,·which·is·currently·only |
| 215 | implemented·in·Sage. | 215 | implemented·in·Sage. |
| 216 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lP\x8Po\x8oi\x8in\x8nt\x8ts\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 216 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8at\x8ti\x8io\x8on\x8na\x8al\x8lP\x8Po\x8oi\x8in\x8nt\x8ts\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=30 | 7 | #:len=30 |
| 8 | bW9kaWZpY2F0aW9uT2ZUd29TdWJzdHJhdGVzSCgp | 8 | bW9kaWZpY2F0aW9uT2ZUd29TdWJzdHJhdGVzSCgp |
| 9 | #:len=344 | 9 | #:len=344 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20gezE6KG1vZGlmaWNhdGlvbk9mVHdvU3Vic3RyYXRlc0gp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20gezE6KG1vZGlmaWNhdGlvbk9mVHdvU3Vic3RyYXRlc0gp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | U3lsdmVzdGVyQ291bnQ= | 8 | U3lsdmVzdGVyQ291bnQ= |
| 9 | #:len=2145 | 9 | #:len=2145 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGRpZmZlcmVuY2UgaW4gdmFyaWF0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGRpZmZlcmVuY2UgaW4gdmFyaWF0 |
| 11 | aW9ucyBvZiB0aGUgU3lsdmVzdGVyIHNlcXVlbmNlIG9mIHR3byByYXRpb25hbCB1bml2YXJpYXRl | 11 | aW9ucyBvZiB0aGUgU3lsdmVzdGVyIHNlcXVlbmNlIG9mIHR3byByYXRpb25hbCB1bml2YXJpYXRl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | aXNMaW5lYXJUeXBlKE1vZHVsZSk= | 8 | aXNMaW5lYXJUeXBlKE1vZHVsZSk= |
| 9 | #:len=257 | 9 | #:len=257 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIxMCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTIxMCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNMaW5lYXJUeXBlLE1vZHVsZSksImlzTGluZWFy | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNMaW5lYXJUeXBlLE1vZHVsZSksImlzTGluZWFy |
| Offset 331, 15 lines modified | Offset 331, 15 lines modified | ||
| 331 | ···············2·2····2···2·············2·2····2 | 331 | ···············2·2····2···2·············2·2····2 |
| 332 | ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·) | 332 | ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·) |
| 333 | ·········2·1···0······1···0·0·····1·2···0·0····2 | 333 | ·········2·1···0······1···0·0·····1·2···0·0····2 |
| 334 | o47·:·Ideal·of·B2 | 334 | o47·:·Ideal·of·B2 |
| 335 | i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; | 335 | i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; |
| 336 | ·--·used·0. | 336 | ·--·used·0.894145s·(cpu);·0.781388s·(thread);·0s·(gc) |
| 337 | ·················ZZ | 337 | ·················ZZ |
| 338 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] | 338 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] |
| 339 | ···············32003··0···2···0···1 | 339 | ···············32003··0···2···0···1 |
| 340 | i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) | 340 | i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) |
| Offset 57, 15 lines modified | Offset 57, 15 lines modified | ||
| 57 | o5·:·Matrix·S··<--·S | 57 | o5·:·Matrix·S··<--·S |
| 58 | i6·:·I·=·minors(n-1,·M); | 58 | i6·:·I·=·minors(n-1,·M); |
| 59 | o6·:·Ideal·of·S | 59 | o6·:·Ideal·of·S |
| 60 | i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. | 60 | i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. |
| 61 | ·--·used·1. | 61 | ·--·used·1.4722s·(cpu);·0.737097s·(thread);·0s·(gc) |
| 62 | o7·:·Ideal·of·S[w·..w·] | 62 | o7·:·Ideal·of·S[w·..w·] |
| 63 | ·················0···4 | 63 | ·················0···4 |
| 64 | i8·:·kk·=·ZZ/101; | 64 | i8·:·kk·=·ZZ/101; |
| 65 | i9·:·S·=·kk[x,y,z]; | 65 | i9·:·S·=·kk[x,y,z]; |
| Offset 76, 19 lines modified | Offset 76, 19 lines modified | ||
| 76 | o10·:·Matrix·S··<--·S | 76 | o10·:·Matrix·S··<--·S |
| 77 | i11·:·I·=·minors(3,m); | 77 | i11·:·I·=·minors(3,m); |
| 78 | o11·:·Ideal·of·S | 78 | o11·:·Ideal·of·S |
| 79 | i12·:·time·reesIdeal·(I,·I_0); | 79 | i12·:·time·reesIdeal·(I,·I_0); |
| 80 | ·--·used·1. | 80 | ·--·used·1.48784s·(cpu);·1.07755s·(thread);·0s·(gc) |
| 81 | o12·:·Ideal·of·S[w·..w·] | 81 | o12·:·Ideal·of·S[w·..w·] |
| 82 | ··················0···3 | 82 | ··················0···3 |
| 83 | i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); | 83 | i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); |
| 84 | ·--·used·1. | 84 | ·--·used·1.37532s·(cpu);·1.16911s·(thread);·0s·(gc) |
| 85 | o13·:·Ideal·of·S[w·..w·] | 85 | o13·:·Ideal·of·S[w·..w·] |
| 86 | ··················0···3 | 86 | ··················0···3 |
| 87 | i14·:· | 87 | i14·:· |
| Offset 13, 21 lines modified | Offset 13, 21 lines modified | ||
| 13 | ················3····2 | 13 | ················3····2 |
| 14 | ·····-·x·x·x·,·x··-·x·x·) | 14 | ·····-·x·x·x·,·x··-·x·x·) |
| 15 | ········0·2·4···1····0·4 | 15 | ········0·2·4···1····0·4 |
| 16 | o3·:·Ideal·of·S | 16 | o3·:·Ideal·of·S |
| 17 | i4·:·time·V1·=·reesIdeal·i; | 17 | i4·:·time·V1·=·reesIdeal·i; |
| 18 | ·--·used·1. | 18 | ·--·used·1.39373s·(cpu);·0.17256s·(thread);·0s·(gc) |
| 19 | o4·:·Ideal·of·S[w·..w·] | 19 | o4·:·Ideal·of·S[w·..w·] |
| 20 | ·················0···6 | 20 | ·················0···6 |
| 21 | i5·:·time·V2·=·reesIdeal(i,i_0); | 21 | i5·:·time·V2·=·reesIdeal(i,i_0); |
| 22 | ·--·used·0. | 22 | ·--·used·0.703406s·(cpu);·0.206379s·(thread);·0s·(gc) |
| 23 | o5·:·Ideal·of·S[w·..w·] | 23 | o5·:·Ideal·of·S[w·..w·] |
| 24 | ·················0···6 | 24 | ·················0···6 |
| 25 | i6·:·S=kk[a,b,c] | 25 | i6·:·S=kk[a,b,c] |
| 26 | o6·=·S | 26 | o6·=·S |
| Offset 47, 21 lines modified | Offset 47, 21 lines modified | ||
| 47 | ·············2········2 | 47 | ·············2········2 |
| 48 | o8·=·ideal·(a·,·a*b,·b·) | 48 | o8·=·ideal·(a·,·a*b,·b·) |
| 49 | o8·:·Ideal·of·S | 49 | o8·:·Ideal·of·S |
| 50 | i9·:·time·I1·=·reesIdeal·i; | 50 | i9·:·time·I1·=·reesIdeal·i; |
| 51 | ·--·used·0.8 | 51 | ·--·used·0.840277s·(cpu);·0.1411s·(thread);·0s·(gc) |
| 52 | o9·:·Ideal·of·S[w·..w·] | 52 | o9·:·Ideal·of·S[w·..w·] |
| 53 | ·················0···2 | 53 | ·················0···2 |
| 54 | i10·:·time·I2·=·reesIdeal(i,i_0); | 54 | i10·:·time·I2·=·reesIdeal(i,i_0); |
| 55 | ·--·used·0.2 | 55 | ·--·used·0.254048s·(cpu);·0.0289345s·(thread);·0s·(gc) |
| 56 | o10·:·Ideal·of·S[w·..w·] | 56 | o10·:·Ideal·of·S[w·..w·] |
| 57 | ··················0···2 | 57 | ··················0···2 |
| 58 | i11·:·transpose·gens·I1 | 58 | i11·:·transpose·gens·I1 |
| 59 | o11·=·{-1,·-3}·|·aw_1-bw_2····| | 59 | o11·=·{-1,·-3}·|·aw_1-bw_2····| |
| Offset 485, 15 lines modified | Offset 485, 15 lines modified | ||
| 485 | ········</table> | 485 | ········</table> |
| 486 | ········<div> | 486 | ········<div> |
| 487 | ··········<p>We·compute·the·singular·locus·once·again:</p> | 487 | ··········<p>We·compute·the·singular·locus·once·again:</p> |
| 488 | ········</div> | 488 | ········</div> |
| 489 | ········<table·class="examples"> | 489 | ········<table·class="examples"> |
| 490 | ··········<tr> | 490 | ··········<tr> |
| 491 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; | 491 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; |
| 492 | ·--·used·0. | 492 | ·--·used·0.894145s·(cpu);·0.781388s·(thread);·0s·(gc) |
| 493 | ·················ZZ | 493 | ·················ZZ |
| 494 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] | 494 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] |
| 495 | ···············32003··0···2···0···1</code></pre> | 495 | ···············32003··0···2···0···1</code></pre> |
| 496 | </td>··········</tr> | 496 | </td>··········</tr> |
| 497 | ··········<tr> | 497 | ··········<tr> |
| 498 | <td>··············<pre><code·class="language-macaulay2">i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) | 498 | <td>··············<pre><code·class="language-macaulay2">i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) |
| Offset 325, 15 lines modified | Offset 325, 15 lines modified | ||
| 325 | ···············2·2····2···2·············2·2····2 | 325 | ···············2·2····2···2·············2·2····2 |
| 326 | ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·) | 326 | ······-·p·w·,·p·y··-·p·,·p·w·y·-·p·p·,·p·w··-·p·) |
| 327 | ·········2·1···0······1···0·0·····1·2···0·0····2 | 327 | ·········2·1···0······1···0·0·····1·2···0·0····2 |
| 328 | o47·:·Ideal·of·B2 | 328 | o47·:·Ideal·of·B2 |
| 329 | We·compute·the·singular·locus·once·again: | 329 | We·compute·the·singular·locus·once·again: |
| 330 | i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; | 330 | i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; |
| 331 | ·--·used·0. | 331 | ·--·used·0.894145s·(cpu);·0.781388s·(thread);·0s·(gc) |
| 332 | ·················ZZ | 332 | ·················ZZ |
| 333 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] | 333 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] |
| 334 | ···············32003··0···2···0···1 | 334 | ···············32003··0···2···0···1 |
| 335 | i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) | 335 | i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) |
| 336 | o49·=·ideal·1 | 336 | o49·=·ideal·1 |
| Offset 138, 15 lines modified | Offset 138, 15 lines modified | ||
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·minors(n-1,·M); | 139 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·minors(n-1,·M); |
| 140 | o6·:·Ideal·of·S</code></pre> | 140 | o6·:·Ideal·of·S</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. | 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. |
| 144 | ·--·used·1. | 144 | ·--·used·1.4722s·(cpu);·0.737097s·(thread);·0s·(gc) |
| 145 | o7·:·Ideal·of·S[w·..w·] | 145 | o7·:·Ideal·of·S[w·..w·] |
| 146 | ·················0···4</code></pre> | 146 | ·················0···4</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i8·:·kk·=·ZZ/101;</code></pre> | 149 | <td>··············<pre><code·class="language-macaulay2">i8·:·kk·=·ZZ/101;</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| Offset 162, 22 lines modified | Offset 162, 22 lines modified | ||
| 162 | ··········<tr> | 162 | ··········<tr> |
| 163 | <td>··············<pre><code·class="language-macaulay2">i11·:·I·=·minors(3,m); | 163 | <td>··············<pre><code·class="language-macaulay2">i11·:·I·=·minors(3,m); |
| 164 | o11·:·Ideal·of·S</code></pre> | 164 | o11·:·Ideal·of·S</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·reesIdeal·(I,·I_0); | 167 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·reesIdeal·(I,·I_0); |
| 168 | ·--·used·1. | 168 | ·--·used·1.48784s·(cpu);·1.07755s·(thread);·0s·(gc) |
| 169 | o12·:·Ideal·of·S[w·..w·] | 169 | o12·:·Ideal·of·S[w·..w·] |
| 170 | ··················0···3</code></pre> | 170 | ··················0···3</code></pre> |
| 171 | </td>··········</tr> | 171 | </td>··········</tr> |
| 172 | ··········<tr> | 172 | ··········<tr> |
| 173 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); | 173 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); |
| 174 | ·--·used·1. | 174 | ·--·used·1.37532s·(cpu);·1.16911s·(thread);·0s·(gc) |
| 175 | o13·:·Ideal·of·S[w·..w·] | 175 | o13·:·Ideal·of·S[w·..w·] |
| 176 | ··················0···3</code></pre> | 176 | ··················0···3</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ········</table> | 178 | ········</table> |
| 179 | ······</div> | 179 | ······</div> |
| 180 | ······<div> | 180 | ······<div> |
| Offset 86, 34 lines modified | Offset 86, 34 lines modified | ||
| 86 | ·············5······4 | 86 | ·············5······4 |
| 87 | o5·:·Matrix·S··<--·S | 87 | o5·:·Matrix·S··<--·S |
| 88 | i6·:·I·=·minors(n-1,·M); | 88 | i6·:·I·=·minors(n-1,·M); |
| 89 | o6·:·Ideal·of·S | 89 | o6·:·Ideal·of·S |
| 90 | i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. | 90 | i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. |
| 91 | ·--·used·1. | 91 | ·--·used·1.4722s·(cpu);·0.737097s·(thread);·0s·(gc) |
| 92 | o7·:·Ideal·of·S[w·..w·] | 92 | o7·:·Ideal·of·S[w·..w·] |
| 93 | ·················0···4 | 93 | ·················0···4 |
| 94 | i8·:·kk·=·ZZ/101; | 94 | i8·:·kk·=·ZZ/101; |
| 95 | i9·:·S·=·kk[x,y,z]; | 95 | i9·:·S·=·kk[x,y,z]; |
| 96 | i10·:·m·=·random(S^3,·S^{4:-2}); | 96 | i10·:·m·=·random(S^3,·S^{4:-2}); |
| 97 | ··············3······4 | 97 | ··············3······4 |
| 98 | o10·:·Matrix·S··<--·S | 98 | o10·:·Matrix·S··<--·S |
| 99 | i11·:·I·=·minors(3,m); | 99 | i11·:·I·=·minors(3,m); |
| 100 | o11·:·Ideal·of·S | 100 | o11·:·Ideal·of·S |
| 101 | i12·:·time·reesIdeal·(I,·I_0); | 101 | i12·:·time·reesIdeal·(I,·I_0); |
| 102 | ·--·used·1. | 102 | ·--·used·1.48784s·(cpu);·1.07755s·(thread);·0s·(gc) |
| 103 | o12·:·Ideal·of·S[w·..w·] | 103 | o12·:·Ideal·of·S[w·..w·] |
| 104 | ··················0···3 | 104 | ··················0···3 |
| 105 | i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); | 105 | i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); |
| 106 | ·--·used·1. | 106 | ·--·used·1.37532s·(cpu);·1.16911s·(thread);·0s·(gc) |
| 107 | o13·:·Ideal·of·S[w·..w·] | 107 | o13·:·Ideal·of·S[w·..w·] |
| 108 | ··················0···3 | 108 | ··················0···3 |
| 109 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 109 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 110 | ····*·_\x8s_\x8y_\x8m_\x8m_\x8e_\x8t_\x8r_\x8i_\x8c_\x8A_\x8l_\x8g_\x8e_\x8b_\x8r_\x8a_\x8I_\x8d_\x8e_\x8a_\x8l·--·Ideal·of·the·symmetric·algebra·of·an·ideal·or | 110 | ····*·_\x8s_\x8y_\x8m_\x8m_\x8e_\x8t_\x8r_\x8i_\x8c_\x8A_\x8l_\x8g_\x8e_\x8b_\x8r_\x8a_\x8I_\x8d_\x8e_\x8a_\x8l·--·Ideal·of·the·symmetric·algebra·of·an·ideal·or |
| 111 | ······module | 111 | ······module |
| 112 | ····*·_\x8j_\x8a_\x8c_\x8o_\x8b_\x8i_\x8a_\x8n_\x8D_\x8u_\x8a_\x8l·--·Computes·the·'jacobian·dual',·part·of·a·method·of·finding | 112 | ····*·_\x8j_\x8a_\x8c_\x8o_\x8b_\x8i_\x8a_\x8n_\x8D_\x8u_\x8a_\x8l·--·Computes·the·'jacobian·dual',·part·of·a·method·of·finding |
| Offset 113, 22 lines modified | Offset 113, 22 lines modified | ||
| 113 | ·····-·x·x·x·,·x··-·x·x·) | 113 | ·····-·x·x·x·,·x··-·x·x·) |
| 114 | ········0·2·4···1····0·4 | 114 | ········0·2·4···1····0·4 |
| 115 | o3·:·Ideal·of·S</code></pre> | 115 | o3·:·Ideal·of·S</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·V1·=·reesIdeal·i; | 118 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·V1·=·reesIdeal·i; |
| 119 | ·--·used·1. | 119 | ·--·used·1.39373s·(cpu);·0.17256s·(thread);·0s·(gc) |
| 120 | o4·:·Ideal·of·S[w·..w·] | 120 | o4·:·Ideal·of·S[w·..w·] |
| 121 | ·················0···6</code></pre> | 121 | ·················0···6</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·V2·=·reesIdeal(i,i_0); | 124 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·V2·=·reesIdeal(i,i_0); |
| 125 | ·--·used·0. | 125 | ·--·used·0.703406s·(cpu);·0.206379s·(thread);·0s·(gc) |
| 126 | o5·:·Ideal·of·S[w·..w·] | 126 | o5·:·Ideal·of·S[w·..w·] |
| 127 | ·················0···6</code></pre> | 127 | ·················0···6</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ········</table> | 129 | ········</table> |
| 130 | ········<div> | 130 | ········<div> |
| 131 | ··········<p>The·following·example·shows·how·we·handle·degrees</p> | 131 | ··········<p>The·following·example·shows·how·we·handle·degrees</p> |
| Offset 157, 22 lines modified | Offset 157, 22 lines modified | ||
| 157 | ·············2········2 | 157 | ·············2········2 |
| 158 | o8·=·ideal·(a·,·a*b,·b·) | 158 | o8·=·ideal·(a·,·a*b,·b·) |
| 159 | o8·:·Ideal·of·S</code></pre> | 159 | o8·:·Ideal·of·S</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| 162 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·I1·=·reesIdeal·i; | 162 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·I1·=·reesIdeal·i; |
| 163 | ·--·used·0.8 | 163 | ·--·used·0.840277s·(cpu);·0.1411s·(thread);·0s·(gc) |
| 164 | o9·:·Ideal·of·S[w·..w·] | 164 | o9·:·Ideal·of·S[w·..w·] |
| 165 | ·················0···2</code></pre> | 165 | ·················0···2</code></pre> |
| 166 | </td>··········</tr> | 166 | </td>··········</tr> |
| 167 | ··········<tr> | 167 | ··········<tr> |
| 168 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·I2·=·reesIdeal(i,i_0); | 168 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·I2·=·reesIdeal(i,i_0); |
| 169 | ·--·used·0.2 | 169 | ·--·used·0.254048s·(cpu);·0.0289345s·(thread);·0s·(gc) |
| 170 | o10·:·Ideal·of·S[w·..w·] | 170 | o10·:·Ideal·of·S[w·..w·] |
| 171 | ··················0···2</code></pre> | 171 | ··················0···2</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i11·:·transpose·gens·I1 | 174 | <td>··············<pre><code·class="language-macaulay2">i11·:·transpose·gens·I1 |
| Offset 52, 20 lines modified | Offset 52, 20 lines modified | ||
| 52 | ·····------------------------------------------------------------------------ | 52 | ·····------------------------------------------------------------------------ |
| 53 | ················3····2 | 53 | ················3····2 |
| 54 | ·····-·x·x·x·,·x··-·x·x·) | 54 | ·····-·x·x·x·,·x··-·x·x·) |
| 55 | ········0·2·4···1····0·4 | 55 | ········0·2·4···1····0·4 |
| 56 | o3·:·Ideal·of·S | 56 | o3·:·Ideal·of·S |
| 57 | i4·:·time·V1·=·reesIdeal·i; | 57 | i4·:·time·V1·=·reesIdeal·i; |
| 58 | ·--·used·1. | 58 | ·--·used·1.39373s·(cpu);·0.17256s·(thread);·0s·(gc) |
| 59 | o4·:·Ideal·of·S[w·..w·] | 59 | o4·:·Ideal·of·S[w·..w·] |
| 60 | ·················0···6 | 60 | ·················0···6 |
| 61 | i5·:·time·V2·=·reesIdeal(i,i_0); | 61 | i5·:·time·V2·=·reesIdeal(i,i_0); |
| 62 | ·--·used·0. | 62 | ·--·used·0.703406s·(cpu);·0.206379s·(thread);·0s·(gc) |
| 63 | o5·:·Ideal·of·S[w·..w·] | 63 | o5·:·Ideal·of·S[w·..w·] |
| 64 | ·················0···6 | 64 | ·················0···6 |
| 65 | The·following·example·shows·how·we·handle·degrees | 65 | The·following·example·shows·how·we·handle·degrees |
| 66 | i6·:·S=kk[a,b,c] | 66 | i6·:·S=kk[a,b,c] |
| 67 | o6·=·S | 67 | o6·=·S |
| Offset 82, 20 lines modified | Offset 82, 20 lines modified | ||
| 82 | i8·:·i=minors(2,m) | 82 | i8·:·i=minors(2,m) |
| 83 | ·············2········2 | 83 | ·············2········2 |
| 84 | o8·=·ideal·(a·,·a*b,·b·) | 84 | o8·=·ideal·(a·,·a*b,·b·) |
| 85 | o8·:·Ideal·of·S | 85 | o8·:·Ideal·of·S |
| 86 | i9·:·time·I1·=·reesIdeal·i; | 86 | i9·:·time·I1·=·reesIdeal·i; |
| 87 | ·--·used·0.8 | 87 | ·--·used·0.840277s·(cpu);·0.1411s·(thread);·0s·(gc) |
| 88 | o9·:·Ideal·of·S[w·..w·] | 88 | o9·:·Ideal·of·S[w·..w·] |
| 89 | ·················0···2 | 89 | ·················0···2 |
| 90 | i10·:·time·I2·=·reesIdeal(i,i_0); | 90 | i10·:·time·I2·=·reesIdeal(i,i_0); |
| 91 | ·--·used·0.2 | 91 | ·--·used·0.254048s·(cpu);·0.0289345s·(thread);·0s·(gc) |
| 92 | o10·:·Ideal·of·S[w·..w·] | 92 | o10·:·Ideal·of·S[w·..w·] |
| 93 | ··················0···2 | 93 | ··················0···2 |
| 94 | i11·:·transpose·gens·I1 | 94 | i11·:·transpose·gens·I1 |
| 95 | o11·=·{-1,·-3}·|·aw_1-bw_2····| | 95 | o11·=·{-1,·-3}·|·aw_1-bw_2····| |
| 96 | ······{-1,·-3}·|·aw_0-bw_1····| | 96 | ······{-1,·-3}·|·aw_0-bw_1····| |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:14·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=7 | 7 | #:len=7 |
| 8 | S1NFbnRyeQ== | 8 | S1NFbnRyeQ== |
| 9 | #:len=2433 | 9 | #:len=2433 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZW50cnkgZnJvbSB0aGUgS3JldXpl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZW50cnkgZnJvbSB0aGUgS3JldXpl |
| 11 | ci1Ta2Fya2UgZGF0YWJhc2Ugb2YgZGltZW5zaW9uIDMgYW5kIDQgcmVmbGV4aXZlIHBvbHl0b3Bl | 11 | ci1Ta2Fya2UgZGF0YWJhc2Ugb2YgZGltZW5zaW9uIDMgYW5kIDQgcmVmbGV4aXZlIHBvbHl0b3Bl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=10 | 7 | #:len=10 |
| 8 | UmVndWxhcml0eQ== | 8 | UmVndWxhcml0eQ== |
| 9 | #:len=797 | 9 | #:len=797 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBDYXN0ZWxudW92by1NdW1m | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBDYXN0ZWxudW92by1NdW1m |
| 11 | b3JkIHJlZ3VsYXJpdHkgb2YgYSBob21vZ2VuZW91cyBpZGVhbCIsIERlc2NyaXB0aW9uID0+IChQ | 11 | b3JkIHJlZ3VsYXJpdHkgb2YgYSBob21vZ2VuZW91cyBpZGVhbCIsIERlc2NyaXB0aW9uID0+IChQ |
| Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
| 71 | ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·) | 71 | ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·) |
| 72 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 | 72 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 |
| 73 | o7·:·Ideal·of·R | 73 | o7·:·Ideal·of·R |
| 74 | i8·:·benchmark·"mRegularity·I1" | 74 | i8·:·benchmark·"mRegularity·I1" |
| 75 | o8·=·.1 | 75 | o8·=·.1866235718461538 |
| 76 | o8·:·RR·(of·precision·53) | 76 | o8·:·RR·(of·precision·53) |
| 77 | i9·:·R·=·QQ[x_0..x_5] | 77 | i9·:·R·=·QQ[x_0..x_5] |
| 78 | o9·=·R | 78 | o9·=·R |
| Offset 87, 17 lines modified | Offset 87, 17 lines modified | ||
| 87 | i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,·x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3); | 87 | i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,·x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3); |
| 88 | o10·:·Ideal·of·R | 88 | o10·:·Ideal·of·R |
| 89 | i11·:·benchmark·"·mRegularity·I2" | 89 | i11·:·benchmark·"·mRegularity·I2" |
| 90 | o11·=·.0 | 90 | o11·=·.05633935880952379 |
| 91 | o11·:·RR·(of·precision·53) | 91 | o11·:·RR·(of·precision·53) |
| 92 | i12·:·time·regularity·I2·· | 92 | i12·:·time·regularity·I2·· |
| 93 | ·--·used·0.00 | 93 | ·--·used·0.00401012s·(cpu);·0.00248955s·(thread);·0s·(gc) |
| 94 | o12·=·4 | 94 | o12·=·4 |
| 95 | i13·:· | 95 | i13·:· |
| Offset 165, 15 lines modified | Offset 165, 15 lines modified | ||
| 165 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 | 165 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 |
| 166 | o7·:·Ideal·of·R</code></pre> | 166 | o7·:·Ideal·of·R</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i8·:·benchmark·"mRegularity·I1" | 169 | <td>··············<pre><code·class="language-macaulay2">i8·:·benchmark·"mRegularity·I1" |
| 170 | o8·=·.1 | 170 | o8·=·.1866235718461538 |
| 171 | o8·:·RR·(of·precision·53)</code></pre> | 171 | o8·:·RR·(of·precision·53)</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ········</table> | 173 | ········</table> |
| 174 | ········<p>This·is·an·example·where·regularity·is·faster·than·mRegularity.</p> | 174 | ········<p>This·is·an·example·where·regularity·is·faster·than·mRegularity.</p> |
| 175 | ········<table·class="examples"> | 175 | ········<table·class="examples"> |
| 176 | ··········<tr> | 176 | ··········<tr> |
| Offset 187, 21 lines modified | Offset 187, 21 lines modified | ||
| 187 | <td>··············<pre><code·class="language-macaulay2">i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,·x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3); | 187 | <td>··············<pre><code·class="language-macaulay2">i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5,·x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3); |
| 188 | o10·:·Ideal·of·R</code></pre> | 188 | o10·:·Ideal·of·R</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i11·:·benchmark·"·mRegularity·I2" | 191 | <td>··············<pre><code·class="language-macaulay2">i11·:·benchmark·"·mRegularity·I2" |
| 192 | o11·=·.0 | 192 | o11·=·.05633935880952379 |
| 193 | o11·:·RR·(of·precision·53)</code></pre> | 193 | o11·:·RR·(of·precision·53)</code></pre> |
| 194 | </td>··········</tr> | 194 | </td>··········</tr> |
| 195 | ··········<tr> | 195 | ··········<tr> |
| 196 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·regularity·I2·· | 196 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·regularity·I2·· |
| 197 | ·--·used·0.00 | 197 | ·--·used·0.00401012s·(cpu);·0.00248955s·(thread);·0s·(gc) |
| 198 | o12·=·4</code></pre> | 198 | o12·=·4</code></pre> |
| 199 | </td>··········</tr> | 199 | </td>··········</tr> |
| 200 | ········</table> | 200 | ········</table> |
| 201 | ········<p>This·symbol·is·provided·by·the·package·Regularity.</p> | 201 | ········<p>This·symbol·is·provided·by·the·package·Regularity.</p> |
| 202 | ······</div> | 202 | ······</div> |
| 203 | ······<div> | 203 | ······<div> |
| Offset 95, 34 lines modified | Offset 95, 34 lines modified | ||
| 95 | ··············3····2········2············3····3······2 | 95 | ··············3····2········2············3····3······2 |
| 96 | ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·) | 96 | ·····x·x·x·,·x··+·x·x··-·x·x··-·x·x·x·,·x··+·x··-·x·x·) |
| 97 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 | 97 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 |
| 98 | o7·:·Ideal·of·R | 98 | o7·:·Ideal·of·R |
| 99 | i8·:·benchmark·"mRegularity·I1" | 99 | i8·:·benchmark·"mRegularity·I1" |
| 100 | o8·=·.1 | 100 | o8·=·.1866235718461538 |
| 101 | o8·:·RR·(of·precision·53) | 101 | o8·:·RR·(of·precision·53) |
| 102 | This·is·an·example·where·regularity·is·faster·than·mRegularity. | 102 | This·is·an·example·where·regularity·is·faster·than·mRegularity. |
| 103 | i9·:·R·=·QQ[x_0..x_5] | 103 | i9·:·R·=·QQ[x_0..x_5] |
| 104 | o9·=·R | 104 | o9·=·R |
| 105 | o9·:·PolynomialRing | 105 | o9·:·PolynomialRing |
| 106 | i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5, | 106 | i10·:·I2·=·ideal·(·x_0^2+x_5^2,·x_0^2+x_0*x_3+x_4^2,·x_0^2+x_0*x_5+x_2*x_5, |
| 107 | x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3); | 107 | x_0^2-x_0*x_3-x_3*x_5,·x_0^2-x_3*x_4,·x_0*x_3); |
| 108 | o10·:·Ideal·of·R | 108 | o10·:·Ideal·of·R |
| 109 | i11·:·benchmark·"·mRegularity·I2" | 109 | i11·:·benchmark·"·mRegularity·I2" |
| 110 | o11·=·.0 | 110 | o11·=·.05633935880952379 |
| 111 | o11·:·RR·(of·precision·53) | 111 | o11·:·RR·(of·precision·53) |
| 112 | i12·:·time·regularity·I2 | 112 | i12·:·time·regularity·I2 |
| 113 | ·--·used·0.00 | 113 | ·--·used·0.00401012s·(cpu);·0.00248955s·(thread);·0s·(gc) |
| 114 | o12·=·4 | 114 | o12·=·4 |
| 115 | This·symbol·is·provided·by·the·package·Regularity. | 115 | This·symbol·is·provided·by·the·package·Regularity. |
| 116 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 116 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 117 | ····*·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y·--·compute·the·Castelnuovo-Mumford·regularity | 117 | ····*·_\x8r_\x8e_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8t_\x8y·--·compute·the·Castelnuovo-Mumford·regularity |
| 118 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8ri\x8it\x8ty\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* | 118 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·m\x8mR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8ri\x8it\x8ty\x8y:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 119 | ····*·mRegularity(Ideal) | 119 | ····*·mRegularity(Ideal) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | Y2Fub25pY2FsTXVsdGlwbGllcnM= | 8 | Y2Fub25pY2FsTXVsdGlwbGllcnM= |
| 9 | #:len=1705 | 9 | #:len=1705 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIGNhbm9uaWNhbCBt | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIGNhbm9uaWNhbCBt |
| 11 | dWx0aXBsaWVycyBvZiBhIHJhdGlvbmFsIGN1cnZlcyB3aXRoIG5vZGVzIiwgImxpbmVudW0iID0+ | 11 | dWx0aXBsaWVycyBvZiBhIHJhdGlvbmFsIGN1cnZlcyB3aXRoIG5vZGVzIiwgImxpbmVudW0iID0+ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | bXVsdFRhYmxlT25lVHdvKFJpbmcp | 8 | bXVsdFRhYmxlT25lVHdvKFJpbmcp |
| 9 | #:len=273 | 9 | #:len=273 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjMwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjMwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtdWx0VGFibGVPbmVUd28sUmluZyksIm11bHRUYWJs | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtdWx0VGFibGVPbmVUd28sUmluZyksIm11bHRUYWJs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=15 | 7 | #:len=15 |
| 8 | Z2VuZXJpY1Jlc2lkdWFs | 8 | Z2VuZXJpY1Jlc2lkdWFs |
| 9 | #:len=1739 | 9 | #:len=1739 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgZ2VuZXJpYyByZXNpZHVh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgZ2VuZXJpYyByZXNpZHVh |
| 11 | bCBpbnRlcnNlY3Rpb25zIG9mIGFuIGlkZWFsIiwgImxpbmVudW0iID0+IDg4NiwgSW5wdXRzID0+ | 11 | bCBpbnRlcnNlY3Rpb25zIG9mIGFuIGlkZWFsIiwgImxpbmVudW0iID0+IDg4NiwgSW5wdXRzID0+ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=41 | 7 | #:len=41 |
| 8 | YmFyeWNlbnRyaWNTdWJkaXZpc2lvbihTaW1wbGljaWFsQ29tcGxleCk= | 8 | YmFyeWNlbnRyaWNTdWJkaXZpc2lvbihTaW1wbGljaWFsQ29tcGxleCk= |
| 9 | #:len=381 | 9 | #:len=381 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzI4LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzI4LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhiYXJ5Y2VudHJpY1N1YmRpdmlzaW9uLFNpbXBsaWNp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhiYXJ5Y2VudHJpY1N1YmRpdmlzaW9uLFNpbXBsaWNp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=35 | 7 | #:len=35 |
| 8 | aHVyd2l0ekZvcm0oLi4uLFNpbmd1bGFyTG9jdXM9Pi4uLik= | 8 | aHVyd2l0ekZvcm0oLi4uLFNpbmd1bGFyTG9jdXM9Pi4uLik= |
| 9 | #:len=277 | 9 | #:len=277 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMzMCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMzMCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaHVyd2l0ekZvcm0sU2luZ3VsYXJMb2N1c10sImh1 | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaHVyd2l0ekZvcm0sU2luZ3VsYXJMb2N1c10sImh1 |
| Offset 5, 18 lines modified | Offset 5, 18 lines modified | ||
| 5 | o2·=·ideal(x·x··-·x·x·) | 5 | o2·=·ideal(x·x··-·x·x·) |
| 6 | ············0·1····2·3 | 6 | ············0·1····2·3 |
| 7 | o2·:·Ideal·of·QQ[x·..x·] | 7 | o2·:·Ideal·of·QQ[x·..x·] |
| 8 | ··················0···3 | 8 | ··················0···3 |
| 9 | i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); | 9 | i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); |
| 10 | ·--·used·0.0 | 10 | ·--·used·0.0990359s·(cpu);·0.063335s·(thread);·0s·(gc) |
| 11 | i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) | 11 | i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) |
| 12 | ·--·used·0.04 | 12 | ·--·used·0.0492793s·(cpu);·0.0525106s·(thread);·0s·(gc) |
| 13 | ··········································································· | 13 | ··········································································· |
| 14 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 14 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 15 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3· | 15 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3· |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ············································································ | 17 | ············································································ |
| 18 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· | 18 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· |
| Offset 37, 17 lines modified | Offset 37, 17 lines modified | ||
| 37 | ··············································2···2 | 37 | ··············································2···2 |
| 38 | ·····4x···x···x···x····-·2x···x···x···x····+·x···x···)) | 38 | ·····4x···x···x···x····-·2x···x···x···x····+·x···x···)) |
| 39 | ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,3 | 39 | ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,3 |
| 40 | o4·:·Sequence | 40 | o4·:·Sequence |
| 41 | i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); | 41 | i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); |
| 42 | ·--·used·0.10 | 42 | ·--·used·0.101765s·(cpu);·0.0724443s·(thread);·0s·(gc) |
| 43 | i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1')) | 43 | i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1')) |
| 44 | i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); | 44 | i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); |
| 45 | ·--·used·0.1 | 45 | ·--·used·0.119894s·(cpu);·0.0829232s·(thread);·0s·(gc) |
| 46 | i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2')) | 46 | i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2')) |
| 47 | i9·:· | 47 | i9·:· |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·) | 9 | o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·) |
| 10 | ·············0····1····2····3···0·1····1·2····2·3 | 10 | ·············0····1····2····3···0·1····1·2····2·3 |
| 11 | o2·:·Ideal·of·P3 | 11 | o2·:·Ideal·of·P3 |
| 12 | i3·:·--·Chow·equations·of·C | 12 | i3·:·--·Chow·equations·of·C |
| 13 | ·····time·eqsC·=·chowEquations·chowForm·C | 13 | ·····time·eqsC·=·chowEquations·chowForm·C |
| 14 | ·--·used·0. | 14 | ·--·used·0.102316s·(cpu);·0.0627419s·(thread);·0s·(gc) |
| 15 | ·············2·2····2·2····2·2····4················2······2·2···2······ | 15 | ·············2·2····2·2····2·2····4················2······2·2···2······ |
| 16 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ | 16 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ |
| 17 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3·· | 17 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3·· |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ······2········3···········2·········2······3···3·········2··········2····2·2 | 19 | ······2········3···········2·········2······3···3·········2··········2····2·2 |
| 20 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x· | 20 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x· |
| Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·) | 72 | o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·) |
| 73 | ·············1····0·2···2····0·1·3···1·2····0·3 | 73 | ·············1····0·2···2····0·1·3···1·2····0·3 |
| 74 | o5·:·Ideal·of·P3 | 74 | o5·:·Ideal·of·P3 |
| 75 | i6·:·--·Chow·equations·of·D | 75 | i6·:·--·Chow·equations·of·D |
| 76 | ·····time·eqsD·=·chowEquations·chowForm·D | 76 | ·····time·eqsD·=·chowEquations·chowForm·D |
| 77 | ·--·used·0.0 | 77 | ·--·used·0.0448864s·(cpu);·0.0442736s·(thread);·0s·(gc) |
| 78 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2· | 78 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2· |
| 79 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, | 79 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, |
| 80 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3· | 80 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3· |
| 81 | ·····------------------------------------------------------------------------ | 81 | ·····------------------------------------------------------------------------ |
| 82 | ··········2······3·2···3········3·2···4·········2·········2·2·······3···· | 82 | ··········2······3·2···3········3·2···4·········2·········2·2·······3···· |
| 83 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- | 83 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- |
| Offset 117, 24 lines modified | Offset 117, 24 lines modified | ||
| 117 | o9·=·ideal(x·x··+·x·x·) | 117 | o9·=·ideal(x·x··+·x·x·) |
| 118 | ············0·1····2·3 | 118 | ············0·1····2·3 |
| 119 | o9·:·Ideal·of·P3 | 119 | o9·:·Ideal·of·P3 |
| 120 | i10·:·--·tangential·Chow·forms·of·Q | 120 | i10·:·--·tangential·Chow·forms·of·Q |
| 121 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2)) | 121 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2)) |
| 122 | ·--·used·0. | 122 | ·--·used·0.1563s·(cpu);·0.114285s·(thread);·0s·(gc) |
| 123 | ·····················2······························2 | 123 | ·····················2······························2 |
| 124 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ | 124 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ |
| 125 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3·· | 125 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3·· |
| 126 | ······----------------------------------------------------------------------- | 126 | ······----------------------------------------------------------------------- |
| 127 | ······x·····x·····) | 127 | ······x·····x·····) |
| 128 | ·······0,2,3·1,2,3 | 128 | ·······0,2,3·1,2,3 |
| 129 | o10·:·Sequence | 129 | o10·:·Sequence |
| 130 | i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2)) | 130 | i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2)) |
| 131 | ·--·used·0. | 131 | ·--·used·0.113608s·(cpu);·0.0785367s·(thread);·0s·(gc) |
| 132 | o11·=·true | 132 | o11·=·true |
| 133 | i12·:· | 133 | i12·:· |
| Offset 16, 15 lines modified | Offset 16, 15 lines modified | ||
| 16 | ···············ZZ | 16 | ···············ZZ |
| 17 | o2·:·Ideal·of·----[x·..x·] | 17 | o2·:·Ideal·of·----[x·..x·] |
| 18 | ··············3331··0···5 | 18 | ··············3331··0···5 |
| 19 | i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian) | 19 | i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian) |
| 20 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) | 20 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) |
| 21 | ·--·used·4. | 21 | ·--·used·4.8072s·(cpu);·4.60683s·(thread);·0s·(gc) |
| 22 | ······4···············2··············2·····2···············2············ | 22 | ······4···············2··············2·····2···············2············ |
| 23 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ | 23 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ |
| 24 | ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5·· | 24 | ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5·· |
| 25 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 26 | ······2·····2··············2······································· | 26 | ······2·····2··············2······································· |
| 27 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ | 27 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ |
| Offset 143, 19 lines modified | Offset 143, 19 lines modified | ||
| 143 | ··········································································································································································································································································································································································································································································································································································································································································································································································3331··0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4···0,1,5···0,2,5···1,2,5···0,3,5···1,3,5···2,3,5···0,4,5···1,4,5···2,4,5···3,4,5 | 143 | ··········································································································································································································································································································································································································································································································································································································································································································································································3331··0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4···0,1,5···0,2,5···1,2,5···0,3,5···1,3,5···2,3,5···0,4,5···1,4,5···2,4,5···3,4,5 |
| 144 | o3·:·------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 144 | o3·:·------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 145 | ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····) | 145 | ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····) |
| 146 | ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 | 146 | ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 |
| 147 | i4·:·--·equivalently·(but·faster)... | 147 | i4·:·--·equivalently·(but·faster)... |
| 148 | ·····time·assert(ChowV·===·chowForm·f) | 148 | ·····time·assert(ChowV·===·chowForm·f) |
| 149 | ·--·used· | 149 | ·--·used·1.07888s·(cpu);·0.994322s·(thread);·0s·(gc) |
| 150 | i5·:·--·X-resultant·of·V | 150 | i5·:·--·X-resultant·of·V |
| 151 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; | 151 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; |
| 152 | ·--·used·0.1 | 152 | ·--·used·0.184919s·(cpu);·0.150657s·(thread);·0s·(gc) |
| 153 | i6·:·--·three·generic·ternary·quadrics | 153 | i6·:·--·three·generic·ternary·quadrics |
| 154 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) | 154 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) |
| 155 | ·········2···············2························2·····2···············2·· | 155 | ·········2···············2························2·····2···············2·· |
| 156 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ | 156 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ |
| 157 | ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1·· | 157 | ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1·· |
| Offset 164, 12 lines modified | Offset 164, 12 lines modified | ||
| 164 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} | 164 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 165 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 165 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 166 | o6·:·List | 166 | o6·:·List |
| 167 | i7·:·--·resultant·of·the·three·forms | 167 | i7·:·--·resultant·of·the·three·forms |
| 168 | ·····time·resF·=·resultant·F; | 168 | ·····time·resF·=·resultant·F; |
| 169 | ·--·used·0.1 | 169 | ·--·used·0.167678s·(cpu);·0.132508s·(thread);·0s·(gc) |
| 170 | i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres)) | 170 | i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres)) |
| 171 | i9·:· | 171 | i9·:· |
| Offset 4, 30 lines modified | Offset 4, 30 lines modified | ||
| 4 | ········2··············2 | 4 | ········2··············2 |
| 5 | o2·=·a*x··+·b*x*y·+·c*y | 5 | o2·=·a*x··+·b*x*y·+·c*y |
| 6 | o2·:·ZZ[a..c][x..y] | 6 | o2·:·ZZ[a..c][x..y] |
| 7 | i3·:·time·discriminant·F | 7 | i3·:·time·discriminant·F |
| 8 | ·--·used·0.00 | 8 | ·--·used·0.0100446s·(cpu);·0.00907116s·(thread);·0s·(gc) |
| 9 | ········2 | 9 | ········2 |
| 10 | o3·=·-·b··+·4a*c | 10 | o3·=·-·b··+·4a*c |
| 11 | o3·:·ZZ[a..c] | 11 | o3·:·ZZ[a..c] |
| 12 | i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^3 | 12 | i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^3 |
| 13 | ········3······2·········2······3 | 13 | ········3······2·········2······3 |
| 14 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y | 14 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y |
| 15 | o5·:·ZZ[a..d][x..y] | 15 | o5·:·ZZ[a..d][x..y] |
| 16 | i6·:·time·discriminant·F | 16 | i6·:·time·discriminant·F |
| 17 | ·--·used·0.0 | 17 | ·--·used·0.0558115s·(cpu);·0.0267675s·(thread);·0s·(gc) |
| 18 | ········2·2·······3·····3···················2·2 | 18 | ········2·2·······3·····3···················2·2 |
| 19 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d | 19 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d |
| 20 | o6·:·ZZ[a..d] | 20 | o6·:·ZZ[a..d] |
| 21 | i7·:·x=symbol·x;·R=ZZ/331[x_0..x_3] | 21 | i7·:·x=symbol·x;·R=ZZ/331[x_0..x_3] |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 59 | ················4········3······4·············4········3······4 | 59 | ················4········3······4·············4········3······4 |
| 60 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x | 60 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x |
| 61 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 | 61 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 |
| 62 | o12·:·R' | 62 | o12·:·R' |
| 63 | i13·:·time·D=discriminant·pencil | 63 | i13·:·time·D=discriminant·pencil |
| 64 | ·--·used·0. | 64 | ·--·used·0.389589s·(cpu);·0.390219s·(thread);·0s·(gc) |
| 65 | ···········108······106·2·······102·6······100·8·······98·10·······96·12·· | 65 | ···········108······106·2·······102·6······100·8·······98·10·······96·12·· |
| 66 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ | 66 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ |
| 67 | ···········0········0···1·······0···1······0···1·······0··1········0··1··· | 67 | ···········0········0···1·······0···1······0···1·······0··1········0··1··· |
| 68 | ······----------------------------------------------------------------------- | 68 | ······----------------------------------------------------------------------- |
| 69 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24·· | 69 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24·· |
| 70 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ | 70 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ |
| Offset 9, 25 lines modified | Offset 9, 25 lines modified | ||
| 9 | ·····x·x·) | 9 | ·····x·x·) |
| 10 | ······0·3 | 10 | ······0·3 |
| 11 | o1·:·Ideal·of·QQ[x·..x·] | 11 | o1·:·Ideal·of·QQ[x·..x·] |
| 12 | ··················0···5 | 12 | ··················0···5 |
| 13 | i2·:·time·V'·=·dualVariety·V | 13 | i2·:·time·V'·=·dualVariety·V |
| 14 | ·--·used·0.1 | 14 | ·--·used·0.183516s·(cpu);·0.144563s·(thread);·0s·(gc) |
| 15 | ············2·················2····2 | 15 | ············2·················2····2 |
| 16 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) | 16 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) |
| 17 | ············2·3····1·2·4····0·4····1·5·····0·3·5 | 17 | ············2·3····1·2·4····0·4····1·5·····0·3·5 |
| 18 | o2·:·Ideal·of·QQ[x·..x·] | 18 | o2·:·Ideal·of·QQ[x·..x·] |
| 19 | ··················0···5 | 19 | ··················0···5 |
| 20 | i3·:·time·V·==·dualVariety·V' | 20 | i3·:·time·V·==·dualVariety·V' |
| 21 | ·--·used·0.1 | 21 | ·--·used·0.158401s·(cpu);·0.135101s·(thread);·0s·(gc) |
| 22 | o3·=·true | 22 | o3·=·true |
| 23 | i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331) | 23 | i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331) |
| 24 | ········3······2··········2······3······2···················2··········2·· | 24 | ········3······2··········2······3······2···················2··········2·· |
| 25 | o4·=·a·x··+·a·x·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x·x··+·a·x·x··+·a·x·x··+ | 25 | o4·=·a·x··+·a·x·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x·x··+·a·x·x··+·a·x·x··+ |
| Offset 38, 22 lines modified | Offset 38, 22 lines modified | ||
| 38 | ······8·1·2····9·2 | 38 | ······8·1·2····9·2 |
| 39 | ······ZZ | 39 | ······ZZ |
| 40 | o4·:·----[a·..a·][x·..x·] | 40 | o4·:·----[a·..a·][x·..x·] |
| 41 | ·····3331··0···9···0···2 | 41 | ·····3331··0···9···0···2 |
| 42 | i5·:·time·discF·=·ideal·discriminant·F; | 42 | i5·:·time·discF·=·ideal·discriminant·F; |
| 43 | ·--·used·0.0 | 43 | ·--·used·0.0559319s·(cpu);·0.055454s·(thread);·0s·(gc) |
| 44 | ···············ZZ | 44 | ···············ZZ |
| 45 | o5·:·Ideal·of·----[a·..a·] | 45 | o5·:·Ideal·of·----[a·..a·] |
| 46 | ··············3331··0···9 | 46 | ··············3331··0···9 |
| 47 | i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); | 47 | i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); |
| 48 | ·--·used·0. | 48 | ·--·used·0.713257s·(cpu);·0.674457s·(thread);·0s·(gc) |
| 49 | ···············ZZ | 49 | ···············ZZ |
| 50 | o6·:·Ideal·of·----[x·..x·] | 50 | o6·:·Ideal·of·----[x·..x·] |
| 51 | ··············3331··0···9 | 51 | ··············3331··0···9 |
| 52 | i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) | 52 | i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) |
| Offset 6, 15 lines modified | Offset 6, 15 lines modified | ||
| 6 | o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·) | 6 | o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·) |
| 7 | ·············2····1·3···1·2····0·3···1····0·2 | 7 | ·············2····1·3···1·2····0·3···1····0·2 |
| 8 | o1·:·Ideal·of·QQ[x·..x·] | 8 | o1·:·Ideal·of·QQ[x·..x·] |
| 9 | ··················0···3 | 9 | ··················0···3 |
| 10 | i2·:·time·fromPluckerToStiefel·dualize·chowForm·C | 10 | i2·:·time·fromPluckerToStiefel·dualize·chowForm·C |
| 11 | ·--·used·0. | 11 | ·--·used·0.124594s·(cpu);·0.0611422s·(thread);·0s·(gc) |
| 12 | ········3···3··········2···2··············2·······2··········2···3···· | 12 | ········3···3··········2···2··············2·······2··········2···3···· |
| 13 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- | 13 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- |
| 14 | ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1·· | 14 | ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1·· |
| 15 | ·····------------------------------------------------------------------------ | 15 | ·····------------------------------------------------------------------------ |
| 16 | ······2·······2···············2···2··································· | 16 | ······2·······2···············2···2··································· |
| 17 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- | 17 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- |
| Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
| 56 | ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x | 56 | ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x |
| 57 | ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3 | 57 | ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3 |
| 58 | o2·:·QQ[x···..x···] | 58 | o2·:·QQ[x···..x···] |
| 59 | ·········0,0···1,3 | 59 | ·········0,0···1,3 |
| 60 | i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) | 60 | i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) |
| 61 | ·--·used·0.03 | 61 | ·--·used·0.0434267s·(cpu);·0.0433729s·(thread);·0s·(gc) |
| 62 | ············3··········2·························2························ | 62 | ············3··········2·························2························ |
| 63 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- | 63 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- |
| 64 | ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3·· | 64 | ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3·· |
| 65 | ·····------------------------------------------------------------------------ | 65 | ·····------------------------------------------------------------------------ |
| 66 | ···········2······3······2 | 66 | ···········2······3······2 |
| 67 | ·····2x···x····+·x····+·x | 67 | ·····2x···x····+·x····+·x |
| Offset 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | o4·:·QQ[a···..a···] | 85 | o4·:·QQ[a···..a···] |
| 86 | ·········0,0···1,1 | 86 | ·········0,0···1,1 |
| 87 | i5·:·w·=·chowForm·C; | 87 | i5·:·w·=·chowForm·C; |
| 88 | i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s)) | 88 | i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s)) |
| 89 | ·--·used·0.0 | 89 | ·--·used·0.067332s·(cpu);·0.0391563s·(thread);·0s·(gc) |
| 90 | ···················3··········2··········3·······················2········ | 90 | ···················3··········2··········3·······················2········ |
| 91 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ | 91 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ |
| 92 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3·· | 92 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3·· |
| 93 | ·····------------------------------------------------------------------------ | 93 | ·····------------------------------------------------------------------------ |
| 94 | ·························2······2············2···3···············2········ | 94 | ·························2······2············2···3···············2········ |
| 95 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ | 95 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ |
| Offset 130, 14 lines modified | Offset 130, 14 lines modified | ||
| 130 | ···········2······3······2 | 130 | ···········2······3······2 |
| 131 | ·····2x···x····-·x····+·x···)} | 131 | ·····2x···x····-·x····+·x···)} |
| 132 | ·······0,0·1,1····1,1····1,0 | 132 | ·······0,0·1,1····1,1····1,0 |
| 133 | o6·:·List | 133 | o6·:·List |
| 134 | i7·:·time·apply(U,u->dim·singularLocus·u) | 134 | i7·:·time·apply(U,u->dim·singularLocus·u) |
| 135 | ·--·used·0.01 | 135 | ·--·used·0.0195029s·(cpu);·0.0192914s·(thread);·0s·(gc) |
| 136 | o7·=·{2,·2,·2,·2,·2,·2} | 136 | o7·=·{2,·2,·2,·2,·2,·2} |
| 137 | o7·:·List | 137 | o7·:·List |
| 138 | i8·:· | 138 | i8·:· |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | ·····--p··+·p·p··+·-p·p··+·-p·p··+·-p·p··+·7p·) | 10 | ·····--p··+·p·p··+·-p·p··+·-p·p··+·-p·p··+·7p·) |
| 11 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 | 11 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 |
| 12 | o1·:·Ideal·of·QQ[p·..p·] | 12 | o1·:·Ideal·of·QQ[p·..p·] |
| 13 | ··················0···4 | 13 | ··················0···4 |
| 14 | i2·:·time·hurwitzForm·Q | 14 | i2·:·time·hurwitzForm·Q |
| 15 | ·--·used·0.0 | 15 | ·--·used·0.0867582s·(cpu);·0.0437026s·(thread);·0s·(gc) |
| 16 | ············2····························2·································· | 16 | ············2····························2·································· |
| 17 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p··· | 17 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p··· |
| 18 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 | 18 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 |
| 19 | ·····------------------------------------------------------------------------ | 19 | ·····------------------------------------------------------------------------ |
| 20 | ···········2··············································2················· | 20 | ···········2··············································2················· |
| 21 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p··· | 21 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p··· |
| Offset 22, 15 lines modified | Offset 22, 15 lines modified | ||
| 22 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] | 22 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] |
| 23 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 23 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 24 | o1·:·-------------------------------------- | 24 | o1·:·-------------------------------------- |
| 25 | ·········p···p····-·p···p····+·p···p | 25 | ·········p···p····-·p···p····+·p···p |
| 26 | ··········1,2·0,3····0,2·1,3····0,1·2,3 | 26 | ··········1,2·0,3····0,2·1,3····0,1·2,3 |
| 27 | i2·:·time·isCoisotropic·w | 27 | i2·:·time·isCoisotropic·w |
| 28 | ·--·used·0.0 | 28 | ·--·used·0.0120116s·(cpu);·0.0127226s·(thread);·0s·(gc) |
| 29 | o2·=·true | 29 | o2·=·true |
| 30 | i3·:·--·random·quadric·in·G(1,3) | 30 | i3·:·--·random·quadric·in·G(1,3) |
| 31 | ·····w'·=·random(2,Grass(1,3)) | 31 | ·····w'·=·random(2,Grass(1,3)) |
| 32 | ·····7·2··················2·····3·························2·····5·········· | 32 | ·····7·2··················2·····3·························2·····5·········· |
| Offset 52, 12 lines modified | Offset 52, 12 lines modified | ||
| 52 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] | 52 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] |
| 53 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 53 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 54 | o3·:·-------------------------------------- | 54 | o3·:·-------------------------------------- |
| 55 | ·········p···p····-·p···p····+·p···p | 55 | ·········p···p····-·p···p····+·p···p |
| 56 | ··········1,2·0,3····0,2·1,3····0,1·2,3 | 56 | ··········1,2·0,3····0,2·1,3····0,1·2,3 |
| 57 | i4·:·time·isCoisotropic·w' | 57 | i4·:·time·isCoisotropic·w' |
| 58 | ·--·used·0.00 | 58 | ·--·used·0.00798541s·(cpu);·0.00934893s·(thread);·0s·(gc) |
| 59 | o4·=·false | 59 | o4·=·false |
| 60 | i5·:· | 60 | i5·:· |
| Offset 31, 12 lines modified | Offset 31, 12 lines modified | ||
| 31 | ··········4········5 | 31 | ··········4········5 |
| 32 | ················ZZ | 32 | ················ZZ |
| 33 | o3·:·Ideal·of·-----[x·..x·] | 33 | o3·:·Ideal·of·-----[x·..x·] |
| 34 | ··············33331··0···5 | 34 | ··············33331··0···5 |
| 35 | i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) | 35 | i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) |
| 36 | ·--·used·0.0 | 36 | ·--·used·0.0275782s·(cpu);·0.0271153s·(thread);·0s·(gc) |
| 37 | o4·=·true | 37 | o4·=·true |
| 38 | i5·:· | 38 | i5·:· |
| Offset 13, 15 lines modified | Offset 13, 15 lines modified | ||
| 13 | ···················2··········2········2······3 | 13 | ···················2··········2········2······3 |
| 14 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} | 14 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 15 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 | 15 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 |
| 16 | o1·:·List | 16 | o1·:·List |
| 17 | i2·:·time·(D,D')·=·macaulayFormula·F | 17 | i2·:·time·(D,D')·=·macaulayFormula·F |
| 18 | ·--·used·0.00 | 18 | ·--·used·0.00385897s·(cpu);·0.0054614s·(thread);·0s·(gc) |
| 19 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0·· | 19 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0·· |
| 20 | ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0·· | 20 | ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0·· |
| 21 | ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0·· | 21 | ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0·· |
| 22 | ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0·· | 22 | ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0·· |
| 23 | ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0·· | 23 | ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0·· |
| 24 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0·· | 24 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0·· |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | ·····6···2·······2·····3 | 78 | ·····6···2·······2·····3 |
| 79 | ·····-p·p··+·2p·p··+·6p·} | 79 | ·····-p·p··+·2p·p··+·6p·} |
| 80 | ·····7·0·2·····1·2·····2 | 80 | ·····7·0·2·····1·2·····2 |
| 81 | o3·:·List | 81 | o3·:·List |
| 82 | i4·:·time·(D,D')·=·macaulayFormula·F | 82 | i4·:·time·(D,D')·=·macaulayFormula·F |
| 83 | ·--·used·0.00 | 83 | ·--·used·0.0042333s·(cpu);·0.00274287s·(thread);·0s·(gc) |
| 84 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0·· | 84 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0·· |
| 85 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0·· | 85 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0·· |
| 86 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0·· | 86 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0·· |
| 87 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0·· | 87 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0·· |
| 88 | ······|·0···0····0····0···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0·· | 88 | ······|·0···0····0····0···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0·· |
| 89 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 | 89 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 |
| Offset 9, 29 lines modified | Offset 9, 29 lines modified | ||
| 9 | ·····------------------------------------------------------------------------ | 9 | ·····------------------------------------------------------------------------ |
| 10 | ·····664x·) | 10 | ·····664x·) |
| 11 | ·········4 | 11 | ·········4 |
| 12 | o3·:·Ideal·of·P4 | 12 | o3·:·Ideal·of·P4 |
| 13 | i4·:·time·p·=·plucker·L | 13 | i4·:·time·p·=·plucker·L |
| 14 | ·--·used·0.00 | 14 | ·--·used·0.00401575s·(cpu);·0.00485961s·(thread);·0s·(gc) |
| 15 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ | 15 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ |
| 16 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3·· | 16 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3·· |
| 17 | ·····------------------------------------------------------------------------ | 17 | ·····------------------------------------------------------------------------ |
| 18 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ | 18 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ |
| 19 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2·· | 19 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2·· |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ·····11804x···,·x····+·14854x···) | 21 | ·····11804x···,·x····+·14854x···) |
| 22 | ···········3,4···0,1·········3,4 | 22 | ···········3,4···0,1·········3,4 |
| 23 | o4·:·Ideal·of·G'1'4 | 23 | o4·:·Ideal·of·G'1'4 |
| 24 | i5·:·time·L'·=·plucker·p | 24 | i5·:·time·L'·=·plucker·p |
| 25 | ·--·used·0.06 | 25 | ·--·used·0.0672588s·(cpu);·0.0396083s·(thread);·0s·(gc) |
| 26 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- | 26 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- |
| 27 | ·············2········3·········4···1········3·········4···0·········3·· | 27 | ·············2········3·········4···1········3·········4···0·········3·· |
| 28 | ·····------------------------------------------------------------------------ | 28 | ·····------------------------------------------------------------------------ |
| 29 | ·····664x·) | 29 | ·····664x·) |
| 30 | ·········4 | 30 | ·········4 |
| Offset 40, 25 lines modified | Offset 40, 25 lines modified | ||
| 40 | i6·:·assert(L'·==·L) | 40 | i6·:·assert(L'·==·L) |
| 41 | i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve | 41 | i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve |
| 42 | o7·:·Ideal·of·G'1'4 | 42 | o7·:·Ideal·of·G'1'4 |
| 43 | i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y | 43 | i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y |
| 44 | ·--·used·0.02 | 44 | ·--·used·0.0294409s·(cpu);·0.03111s·(thread);·0s·(gc) |
| 45 | o8·:·Ideal·of·P4 | 45 | o8·:·Ideal·of·P4 |
| 46 | i9·:·(codim·W,degree·W) | 46 | i9·:·(codim·W,degree·W) |
| 47 | o9·=·(2,·5) | 47 | o9·=·(2,·5) |
| 48 | o9·:·Sequence | 48 | o9·:·Sequence |
| 49 | i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W | 49 | i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W |
| 50 | ·--·used·0.1 | 50 | ·--·used·0.187303s·(cpu);·0.187749s·(thread);·0s·(gc) |
| 51 | o10·:·Ideal·of·G'1'4 | 51 | o10·:·Ideal·of·G'1'4 |
| 52 | i11·:·assert(Y'·==·Y) | 52 | i11·:·assert(Y'·==·Y) |
| 53 | i12·:· | 53 | i12·:· |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | ·····3·····2····9····7·····2····9········3·······1····8····4 | 35 | ·····3·····2····9····7·····2····9········3·······1····8····4 |
| 36 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} | 36 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} |
| 37 | ·····4··········8····8··········7················4····3····5 | 37 | ·····4··········8····8··········7················4····3····5 |
| 38 | o2·:·List | 38 | o2·:·List |
| 39 | i3·:·time·resultant(F,Algorithm=>"Poisson2") | 39 | i3·:·time·resultant(F,Algorithm=>"Poisson2") |
| 40 | ·--·used·0. | 40 | ·--·used·0.22611s·(cpu);·0.140924s·(thread);·0s·(gc) |
| 41 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 41 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 42 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- | 42 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 43 | ···········2222549728809984000000············12700284164628480000000········· | 43 | ···········2222549728809984000000············12700284164628480000000········· |
| 44 | ·····------------------------------------------------------------------------ | 44 | ·····------------------------------------------------------------------------ |
| 45 | ·····348237304382147063838108483692249·3·2·· | 45 | ·····348237304382147063838108483692249·3·2·· |
| 46 | ·····---------------------------------a·b··- | 46 | ·····---------------------------------a·b··- |
| Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
| 56 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 | 56 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 |
| 57 | ·····-------------------------------a*b··-·---------------------------b | 57 | ·····-------------------------------a*b··-·---------------------------b |
| 58 | ··········1119954511872000000000················895963609497600000 | 58 | ··········1119954511872000000000················895963609497600000 |
| 59 | o3·:·QQ[a..b] | 59 | o3·:·QQ[a..b] |
| 60 | i4·:·time·resultant(F,Algorithm=>"Macaulay2") | 60 | i4·:·time·resultant(F,Algorithm=>"Macaulay2") |
| 61 | ·--·used·0. | 61 | ·--·used·0.110768s·(cpu);·0.0687476s·(thread);·0s·(gc) |
| 62 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 62 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 63 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- | 63 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 64 | ···········2222549728809984000000············12700284164628480000000········· | 64 | ···········2222549728809984000000············12700284164628480000000········· |
| 65 | ·····------------------------------------------------------------------------ | 65 | ·····------------------------------------------------------------------------ |
| 66 | ·····348237304382147063838108483692249·3·2·· | 66 | ·····348237304382147063838108483692249·3·2·· |
| 67 | ·····---------------------------------a·b··- | 67 | ·····---------------------------------a·b··- |
| Offset 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 | 77 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 |
| 78 | ·····-------------------------------a*b··-·---------------------------b | 78 | ·····-------------------------------a*b··-·---------------------------b |
| 79 | ··········1119954511872000000000················895963609497600000 | 79 | ··········1119954511872000000000················895963609497600000 |
| 80 | o4·:·QQ[a..b] | 80 | o4·:·QQ[a..b] |
| 81 | i5·:·time·resultant(F,Algorithm=>"Poisson") | 81 | i5·:·time·resultant(F,Algorithm=>"Poisson") |
| 82 | ·--·used·0.2 | 82 | ·--·used·0.255174s·(cpu);·0.255104s·(thread);·0s·(gc) |
| 83 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 83 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 84 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- | 84 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 85 | ···········2222549728809984000000············12700284164628480000000········· | 85 | ···········2222549728809984000000············12700284164628480000000········· |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| 87 | ·····348237304382147063838108483692249·3·2·· | 87 | ·····348237304382147063838108483692249·3·2·· |
| 88 | ·····---------------------------------a·b··- | 88 | ·····---------------------------------a·b··- |
| Offset 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 | 98 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 |
| 99 | ·····-------------------------------a*b··-·---------------------------b | 99 | ·····-------------------------------a*b··-·---------------------------b |
| 100 | ··········1119954511872000000000················895963609497600000 | 100 | ··········1119954511872000000000················895963609497600000 |
| 101 | o5·:·QQ[a..b] | 101 | o5·:·QQ[a..b] |
| 102 | i6·:·time·resultant(F,Algorithm=>"Macaulay") | 102 | i6·:·time·resultant(F,Algorithm=>"Macaulay") |
| 103 | ·--·used·0. | 103 | ·--·used·0.56673s·(cpu);·0.532349s·(thread);·0s·(gc) |
| 104 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 104 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 105 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- | 105 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 106 | ···········2222549728809984000000············12700284164628480000000········· | 106 | ···········2222549728809984000000············12700284164628480000000········· |
| 107 | ·····------------------------------------------------------------------------ | 107 | ·····------------------------------------------------------------------------ |
| 108 | ·····348237304382147063838108483692249·3·2·· | 108 | ·····348237304382147063838108483692249·3·2·· |
| 109 | ·····---------------------------------a·b··- | 109 | ·····---------------------------------a·b··- |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | ·······2···············2····························3······2·········4 | 10 | ·······2···············2····························3······2·········4 |
| 11 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} | 11 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} |
| 12 | o2·:·List | 12 | o2·:·List |
| 13 | i3·:·time·resultant·F | 13 | i3·:·time·resultant·F |
| 14 | ·--·used·0.0 | 14 | ·--·used·0.0239607s·(cpu);·0.024181s·(thread);·0s·(gc) |
| 15 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 | 15 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 |
| 16 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u· | 16 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u· |
| 17 | ·····------------------------------------------------------------------------ | 17 | ·····------------------------------------------------------------------------ |
| 18 | ··············6·7··········5·8·······11··········10·2·········9·3·· | 18 | ··············6·7··········5·8·······11··········10·2·········9·3·· |
| 19 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ | 19 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| Offset 64, 15 lines modified | Offset 64, 15 lines modified | ||
| 64 | ··········3 | 64 | ··········3 |
| 65 | ·····+·c·x·} | 65 | ·····+·c·x·} |
| 66 | ········9·2 | 66 | ········9·2 |
| 67 | o4·:·List | 67 | o4·:·List |
| 68 | i5·:·time·resultant·F | 68 | i5·:·time·resultant·F |
| 69 | ·--·used· | 69 | ·--·used·2.15564s·(cpu);·1.77722s·(thread);·0s·(gc) |
| 70 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2·· | 70 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2·· |
| 71 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- | 71 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- |
| 72 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0·· | 72 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0·· |
| 73 | ·····------------------------------------------------------------------------ | 73 | ·····------------------------------------------------------------------------ |
| 74 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2·· | 74 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2·· |
| 75 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- | 75 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- |
| Offset 1690, 12 lines modified | Offset 1690, 12 lines modified | ||
| 1690 | ··························2·····2···············2························2 | 1690 | ··························2·····2···············2························2 |
| 1691 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} | 1691 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 1692 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 1692 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 1693 | o6·:·List | 1693 | o6·:·List |
| 1694 | i7·:·time·#·terms·resultant·F | 1694 | i7·:·time·#·terms·resultant·F |
| 1695 | ·--·used·0. | 1695 | ·--·used·0.4605s·(cpu);·0.381155s·(thread);·0s·(gc) |
| 1696 | o7·=·21894 | 1696 | o7·=·21894 |
| 1697 | i8·:· | 1697 | i8·:· |
| Offset 8, 15 lines modified | Offset 8, 15 lines modified | ||
| 8 | ···············1·2····0·3·····1·3····0·4·····3····2·4 | 8 | ···············1·2····0·3·····1·3····0·4·····3····2·4 |
| 9 | o2·:·Ideal·of·QQ[p·..p·] | 9 | o2·:·Ideal·of·QQ[p·..p·] |
| 10 | ··················0···4 | 10 | ··················0···4 |
| 11 | i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) | 11 | i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) |
| 12 | ·····time·tangentialChowForm(S,0) | 12 | ·····time·tangentialChowForm(S,0) |
| 13 | ·--·used·0.0 | 13 | ·--·used·0.0944402s·(cpu);·0.0401727s·(thread);·0s·(gc) |
| 14 | ······2·······················································2········ | 14 | ······2·······················································2········ |
| 15 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ | 15 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ |
| 16 | ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4·· | 16 | ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4·· |
| 17 | ·····------------------------------------------------------------------------ | 17 | ·····------------------------------------------------------------------------ |
| 18 | ······2 | 18 | ······2 |
| 19 | ·····p···p····-·2p···p···p····-·p···p···p | 19 | ·····p···p····-·2p···p···p····-·p···p···p |
| Offset 26, 15 lines modified | Offset 26, 15 lines modified | ||
| 26 | ··························································0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 | 26 | ··························································0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4 |
| 27 | o3·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------- | 27 | o3·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 28 | ·····(p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···) | 28 | ·····(p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···) |
| 29 | ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3 | 29 | ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3 |
| 30 | i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) | 30 | i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) |
| 31 | ·····time·tangentialChowForm(S,1) | 31 | ·····time·tangentialChowForm(S,1) |
| 32 | ·--·used·0.0 | 32 | ·--·used·0.0646915s·(cpu);·0.0644347s·(thread);·0s·(gc) |
| 33 | ······2·····2········2·····2···············3········2·····2······ | 33 | ······2·····2········2·····2···············3········2·····2······ |
| 34 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- | 34 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- |
| 35 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4·· | 35 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4·· |
| 36 | ·····------------------------------------------------------------------------ | 36 | ·····------------------------------------------------------------------------ |
| 37 | ·············3·········3···············3············ | 37 | ·············3·········3···············3············ |
| 38 | ·····4p·····p······-·4p·····p······-·2p·····p······+ | 38 | ·····4p·····p······-·4p·····p······-·2p·····p······+ |
| Offset 68, 32 lines modified | Offset 68, 32 lines modified | ||
| 68 | ··············································································0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4 | 68 | ··············································································0,1,2···0,1,3···0,2,3···1,2,3···0,1,4···0,2,4···1,2,4···0,3,4···1,3,4···2,3,4 |
| 69 | o4·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 69 | o4·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 70 | ·····(p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····) | 70 | ·····(p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····) |
| 71 | ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 | 71 | ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 |
| 72 | i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S) | 72 | i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S) |
| 73 | ·····time·tangentialChowForm(S,2) | 73 | ·····time·tangentialChowForm(S,2) |
| 74 | ·--·used·0.0 | 74 | ·--·used·0.0425136s·(cpu);·0.0423079s·(thread);·0s·(gc) |
| 75 | ··············2·············································2 | 75 | ··············2·············································2 |
| 76 | o5·=·p·······p········-·p·······p·······p········+·p·······p | 76 | o5·=·p·······p········-·p·······p·······p········+·p·······p |
| 77 | ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4 | 77 | ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4 |
| 78 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] | 78 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] |
| 79 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4 | 79 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4 |
| 80 | i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing | 80 | i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing |
| 81 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) | 81 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) |
| 82 | ·--·used·0. | 82 | ·--·used·0.103601s·(cpu);·0.0593876s·(thread);·0s·(gc) |
| 83 | ············2···············2 | 83 | ············2···············2 |
| 84 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) | 84 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) |
| 85 | ············1·2····0·1·3····0·4 | 85 | ············1·2····0·1·3····0·4 |
| 86 | o6·:·Ideal·of·QQ[p·..p·] | 86 | o6·:·Ideal·of·QQ[p·..p·] |
| 87 | ··················0···4 | 87 | ··················0···4 |
| 88 | i7·:·--·we·then·can·recover·S | 88 | i7·:·--·we·then·can·recover·S |
| 89 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) | 89 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) |
| 90 | ·--·used·0.102 | 90 | ·--·used·0.150275s·(cpu);·0.110184s·(thread);·0s·(gc) |
| 91 | i8·:· | 91 | i8·:· |
| Offset 87, 22 lines modified | Offset 87, 22 lines modified | ||
| 87 | ············0·1····2·3 | 87 | ············0·1····2·3 |
| 88 | o2·:·Ideal·of·QQ[x·..x·] | 88 | o2·:·Ideal·of·QQ[x·..x·] |
| 89 | ··················0···3</code></pre> | 89 | ··················0···3</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); |
| 93 | ·--·used·0.0 | 93 | ·--·used·0.0990359s·(cpu);·0.063335s·(thread);·0s·(gc)</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ········</table> | 95 | ········</table> |
| 96 | ········<p>In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its·dual·variety.</p> | 96 | ········<p>In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb{P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its·dual·variety.</p> |
| 97 | ········<table·class="examples"> | 97 | ········<table·class="examples"> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) | 99 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) |
| 100 | ·--·used·0.04 | 100 | ·--·used·0.0492793s·(cpu);·0.0525106s·(thread);·0s·(gc) |
| 101 | ··········································································· | 101 | ··········································································· |
| 102 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 102 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 103 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3· | 103 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3· |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ············································································ | 105 | ············································································ |
| 106 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· | 106 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· |
| Offset 127, 22 lines modified | Offset 127, 22 lines modified | ||
| 127 | o4·:·Sequence</code></pre> | 127 | o4·:·Sequence</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ········</table> | 129 | ········</table> |
| 130 | ········<p>If·the·option·<span·class="tt">Duality</span>·is·set·to·<span·class="tt">true</span>,·then·the·method·applies·the·so-called·"dual·Cayley·trick".</p> | 130 | ········<p>If·the·option·<span·class="tt">Duality</span>·is·set·to·<span·class="tt">true</span>,·then·the·method·applies·the·so-called·"dual·Cayley·trick".</p> |
| 131 | ········<table·class="examples"> | 131 | ········<table·class="examples"> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); | 133 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); |
| 134 | ·--·used·0.10 | 134 | ·--·used·0.101765s·(cpu);·0.0724443s·(thread);·0s·(gc)</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))</code></pre> | 137 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); | 140 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); |
| 141 | ·--·used·0.1 | 141 | ·--·used·0.119894s·(cpu);·0.0829232s·(thread);·0s·(gc)</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))</code></pre> | 144 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ········</table> | 146 | ········</table> |
| 147 | ······</div> | 147 | ······</div> |
| 148 | ······<div> | 148 | ······<div> |
| Offset 39, 20 lines modified | Offset 39, 20 lines modified | ||
| 39 | o2·=·ideal(x·x··-·x·x·) | 39 | o2·=·ideal(x·x··-·x·x·) |
| 40 | ············0·1····2·3 | 40 | ············0·1····2·3 |
| 41 | o2·:·Ideal·of·QQ[x·..x·] | 41 | o2·:·Ideal·of·QQ[x·..x·] |
| 42 | ··················0···3 | 42 | ··················0···3 |
| 43 | i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); | 43 | i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); |
| 44 | ·--·used·0.0 | 44 | ·--·used·0.0990359s·(cpu);·0.063335s·(thread);·0s·(gc) |
| 45 | In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb | 45 | In·the·next·example,·we·calculate·the·defining·ideal·of·$\mathbb |
| 46 | {P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its | 46 | {P}^1\times\mathbb{P}^1\times\mathbb{P}^1\subset\mathbb{P}^7$·and·that·of·its |
| 47 | dual·variety. | 47 | dual·variety. |
| 48 | i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) | 48 | i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) |
| 49 | ·--·used·0.04 | 49 | ·--·used·0.0492793s·(cpu);·0.0525106s·(thread);·0s·(gc) |
| 50 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 50 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 51 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3 | 51 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3 |
| 52 | ·····------------------------------------------------------------------------ | 52 | ·····------------------------------------------------------------------------ |
| 53 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x | 53 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x |
| Offset 74, 18 lines modified | Offset 74, 18 lines modified | ||
| 74 | ·····4x···x···x···x····-·2x···x···x···x····+·x···x···)) | 74 | ·····4x···x···x···x····-·2x···x···x···x····+·x···x···)) |
| 75 | ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,3 | 75 | ·······0,0·0,1·1,2·1,3·····0,2·0,3·1,2·1,3····0,2·1,3 |
| 76 | o4·:·Sequence | 76 | o4·:·Sequence |
| 77 | If·the·option·Duality·is·set·to·true,·then·the·method·applies·the·so-called | 77 | If·the·option·Duality·is·set·to·true,·then·the·method·applies·the·so-called |
| 78 | "dual·Cayley·trick". | 78 | "dual·Cayley·trick". |
| 79 | i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); | 79 | i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); |
| 80 | ·--·used·0.10 | 80 | ·--·used·0.101765s·(cpu);·0.0724443s·(thread);·0s·(gc) |
| 81 | i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1')) | 81 | i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1')) |
| 82 | i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); | 82 | i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); |
| 83 | ·--·used·0.1 | 83 | ·--·used·0.119894s·(cpu);·0.0829232s·(thread);·0s·(gc) |
| 84 | i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2')) | 84 | i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2')) |
| 85 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 85 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 86 | ····*·_\x8d_\x8u_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·projective·dual·variety | 86 | ····*·_\x8d_\x8u_\x8a_\x8l_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y·--·projective·dual·variety |
| 87 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ca\x8ay\x8yl\x8le\x8ey\x8yT\x8Tr\x8ri\x8ic\x8ck\x8k:\x8:·*\x8**\x8**\x8**\x8**\x8* | 87 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ca\x8ay\x8yl\x8le\x8ey\x8yT\x8Tr\x8ri\x8ic\x8ck\x8k:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 88 | ····*·cayleyTrick(Ideal,ZZ) | 88 | ····*·cayleyTrick(Ideal,ZZ) |
| 89 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 89 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 90 | The·object·_\x8c_\x8a_\x8y_\x8l_\x8e_\x8y_\x8T_\x8r_\x8i_\x8c_\x8k·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 90 | The·object·_\x8c_\x8a_\x8y_\x8l_\x8e_\x8y_\x8T_\x8r_\x8i_\x8c_\x8k·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 87, 15 lines modified | Offset 87, 15 lines modified | ||
| 87 | ·············0····1····2····3···0·1····1·2····2·3 | 87 | ·············0····1····2····3···0·1····1·2····2·3 |
| 88 | o2·:·Ideal·of·P3</code></pre> | 88 | o2·:·Ideal·of·P3</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·Chow·equations·of·C | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·Chow·equations·of·C |
| 92 | ·····time·eqsC·=·chowEquations·chowForm·C | 92 | ·····time·eqsC·=·chowEquations·chowForm·C |
| 93 | ·--·used·0. | 93 | ·--·used·0.102316s·(cpu);·0.0627419s·(thread);·0s·(gc) |
| 94 | ·············2·2····2·2····2·2····4················2······2·2···2······ | 94 | ·············2·2····2·2····2·2····4················2······2·2···2······ |
| 95 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ | 95 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ |
| 96 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3·· | 96 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3·· |
| 97 | ·····------------------------------------------------------------------------ | 97 | ·····------------------------------------------------------------------------ |
| 98 | ······2········3···········2·········2······3···3·········2··········2····2·2 | 98 | ······2········3···········2·········2······3···3·········2··········2····2·2 |
| 99 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x· | 99 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x· |
| Offset 153, 15 lines modified | Offset 153, 15 lines modified | ||
| 153 | ·············1····0·2···2····0·1·3···1·2····0·3 | 153 | ·············1····0·2···2····0·1·3···1·2····0·3 |
| 154 | o5·:·Ideal·of·P3</code></pre> | 154 | o5·:·Ideal·of·P3</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·Chow·equations·of·D | 157 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·Chow·equations·of·D |
| 158 | ·····time·eqsD·=·chowEquations·chowForm·D | 158 | ·····time·eqsD·=·chowEquations·chowForm·D |
| 159 | ·--·used·0.0 | 159 | ·--·used·0.0448864s·(cpu);·0.0442736s·(thread);·0s·(gc) |
| 160 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2· | 160 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2· |
| 161 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, | 161 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, |
| 162 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3· | 162 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3· |
| 163 | ·····------------------------------------------------------------------------ | 163 | ·····------------------------------------------------------------------------ |
| 164 | ··········2······3·2···3········3·2···4·········2·········2·2·······3···· | 164 | ··········2······3·2···3········3·2···4·········2·········2·2·······3···· |
| 165 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- | 165 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- |
| Offset 205, 28 lines modified | Offset 205, 28 lines modified | ||
| 205 | ············0·1····2·3 | 205 | ············0·1····2·3 |
| 206 | o9·:·Ideal·of·P3</code></pre> | 206 | o9·:·Ideal·of·P3</code></pre> |
| 207 | </td>··········</tr> | 207 | </td>··········</tr> |
| 208 | ··········<tr> | 208 | ··········<tr> |
| 209 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·tangential·Chow·forms·of·Q | 209 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·tangential·Chow·forms·of·Q |
| 210 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2)) | 210 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2)) |
| 211 | ·--·used·0. | 211 | ·--·used·0.1563s·(cpu);·0.114285s·(thread);·0s·(gc) |
| 212 | ·····················2······························2 | 212 | ·····················2······························2 |
| 213 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ | 213 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ |
| 214 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3·· | 214 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3·· |
| 215 | ······----------------------------------------------------------------------- | 215 | ······----------------------------------------------------------------------- |
| 216 | ······x·····x·····) | 216 | ······x·····x·····) |
| 217 | ·······0,2,3·1,2,3 | 217 | ·······0,2,3·1,2,3 |
| 218 | o10·:·Sequence</code></pre> | 218 | o10·:·Sequence</code></pre> |
| 219 | </td>··········</tr> | 219 | </td>··········</tr> |
| 220 | ··········<tr> | 220 | ··········<tr> |
| 221 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2)) | 221 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2)) |
| 222 | ·--·used·0. | 222 | ·--·used·0.113608s·(cpu);·0.0785367s·(thread);·0s·(gc) |
| 223 | o11·=·true</code></pre> | 223 | o11·=·true</code></pre> |
| 224 | </td>··········</tr> | 224 | </td>··········</tr> |
| 225 | ········</table> | 225 | ········</table> |
| 226 | ········<p>Note·that·<span·class="tt">chowEquations(W,0)</span>·is·not·the·same·as·<span·class="tt">chowEquations·W</span>.</p> | 226 | ········<p>Note·that·<span·class="tt">chowEquations(W,0)</span>·is·not·the·same·as·<span·class="tt">chowEquations·W</span>.</p> |
| 227 | ······</div> | 227 | ······</div> |
| 228 | ······<div·class="waystouse"> | 228 | ······<div·class="waystouse"> |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | ·············2····2····2····2 | 29 | ·············2····2····2····2 |
| 30 | o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·) | 30 | o2·=·ideal·(x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x·) |
| 31 | ·············0····1····2····3···0·1····1·2····2·3 | 31 | ·············0····1····2····3···0·1····1·2····2·3 |
| 32 | o2·:·Ideal·of·P3 | 32 | o2·:·Ideal·of·P3 |
| 33 | i3·:·--·Chow·equations·of·C | 33 | i3·:·--·Chow·equations·of·C |
| 34 | ·····time·eqsC·=·chowEquations·chowForm·C | 34 | ·····time·eqsC·=·chowEquations·chowForm·C |
| 35 | ·--·used·0. | 35 | ·--·used·0.102316s·(cpu);·0.0627419s·(thread);·0s·(gc) |
| 36 | ·············2·2····2·2····2·2····4················2······2·2···2 | 36 | ·············2·2····2·2····2·2····4················2······2·2···2 |
| 37 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ | 37 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ |
| 38 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3 | 38 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3 |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ······2········3···········2·········2······3···3·········2··········2····2·2 | 40 | ······2········3···········2·········2······3···3·········2··········2····2·2 |
| 41 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x | 41 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | ·············2··········3··············2····2 | 89 | ·············2··········3··············2····2 |
| 90 | o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·) | 90 | o5·=·ideal·(x··-·x·x·,·x··-·x·x·x·,·x·x··-·x·x·) |
| 91 | ·············1····0·2···2····0·1·3···1·2····0·3 | 91 | ·············1····0·2···2····0·1·3···1·2····0·3 |
| 92 | o5·:·Ideal·of·P3 | 92 | o5·:·Ideal·of·P3 |
| 93 | i6·:·--·Chow·equations·of·D | 93 | i6·:·--·Chow·equations·of·D |
| 94 | ·····time·eqsD·=·chowEquations·chowForm·D | 94 | ·····time·eqsD·=·chowEquations·chowForm·D |
| 95 | ·--·used·0.0 | 95 | ·--·used·0.0448864s·(cpu);·0.0442736s·(thread);·0s·(gc) |
| 96 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2 | 96 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2 |
| 97 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, | 97 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, |
| 98 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3 | 98 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3 |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ··········2······3·2···3········3·2···4·········2·········2·2·······3 | 100 | ··········2······3·2···3········3·2···4·········2·········2·2·······3 |
| 101 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- | 101 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- |
| Offset 136, 27 lines modified | Offset 136, 27 lines modified | ||
| 136 | o9·=·ideal(x·x··+·x·x·) | 136 | o9·=·ideal(x·x··+·x·x·) |
| 137 | ············0·1····2·3 | 137 | ············0·1····2·3 |
| 138 | o9·:·Ideal·of·P3 | 138 | o9·:·Ideal·of·P3 |
| 139 | i10·:·--·tangential·Chow·forms·of·Q | 139 | i10·:·--·tangential·Chow·forms·of·Q |
| 140 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm | 140 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm |
| 141 | (Q,1),tangentialChowForm(Q,2)) | 141 | (Q,1),tangentialChowForm(Q,2)) |
| 142 | ·--·used·0. | 142 | ·--·used·0.1563s·(cpu);·0.114285s·(thread);·0s·(gc) |
| 143 | ·····················2······························2 | 143 | ·····················2······························2 |
| 144 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ | 144 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ |
| 145 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3 | 145 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3 |
| 146 | ······----------------------------------------------------------------------- | 146 | ······----------------------------------------------------------------------- |
| 147 | ······x·····x·····) | 147 | ······x·····x·····) |
| 148 | ·······0,2,3·1,2,3 | 148 | ·······0,2,3·1,2,3 |
| 149 | o10·:·Sequence | 149 | o10·:·Sequence |
| 150 | i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations | 150 | i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations |
| 151 | (W2,2)) | 151 | (W2,2)) |
| 152 | ·--·used·0. | 152 | ·--·used·0.113608s·(cpu);·0.0785367s·(thread);·0s·(gc) |
| 153 | o11·=·true | 153 | o11·=·true |
| 154 | Note·that·chowEquations(W,0)·is·not·the·same·as·chowEquations·W. | 154 | Note·that·chowEquations(W,0)·is·not·the·same·as·chowEquations·W. |
| 155 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wE\x8Eq\x8qu\x8ua\x8at\x8ti\x8io\x8on\x8ns\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* | 155 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wE\x8Eq\x8qu\x8ua\x8at\x8ti\x8io\x8on\x8ns\x8s:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 156 | ····*·chowEquations(RingElement) | 156 | ····*·chowEquations(RingElement) |
| 157 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 157 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 158 | The·object·_\x8c_\x8h_\x8o_\x8w_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 158 | The·object·_\x8c_\x8h_\x8o_\x8w_\x8E_\x8q_\x8u_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | ···············ZZ | 99 | ···············ZZ |
| 100 | o2·:·Ideal·of·----[x·..x·] | 100 | o2·:·Ideal·of·----[x·..x·] |
| 101 | ··············3331··0···5</code></pre> | 101 | ··············3331··0···5</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian) | 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an·affine·chart·of·the·Grassmannian) |
| 105 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) | 105 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) |
| 106 | ·--·used·4. | 106 | ·--·used·4.8072s·(cpu);·4.60683s·(thread);·0s·(gc) |
| 107 | ······4···············2··············2·····2···············2············ | 107 | ······4···············2··············2·····2···············2············ |
| 108 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ | 108 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ |
| 109 | ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5·· | 109 | ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5·· |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ······2·····2··············2······································· | 111 | ······2·····2··············2······································· |
| 112 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ | 112 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ |
| Offset 227, 20 lines modified | Offset 227, 20 lines modified | ||
| 227 | o3·:·------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 227 | o3·:·------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 228 | ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····) | 228 | ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····) |
| 229 | ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre> | 229 | ·······2,3,5·1,4,5····1,3,5·2,4,5····1,2,5·3,4,5···2,3,4·1,4,5····1,3,4·2,4,5····1,2,4·3,4,5···2,3,5·0,4,5····0,3,5·2,4,5····0,2,5·3,4,5···1,3,5·0,4,5····0,3,5·1,4,5····0,1,5·3,4,5···1,2,5·0,4,5····0,2,5·1,4,5····0,1,5·2,4,5···2,3,4·0,4,5····0,3,4·2,4,5····0,2,4·3,4,5···1,3,4·0,4,5····0,3,4·1,4,5····0,1,4·3,4,5···1,2,4·0,4,5····0,2,4·1,4,5····0,1,4·2,4,5···1,2,3·0,4,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·1,3,5····1,3,4·2,3,5····1,2,3·3,4,5···1,2,5·0,3,5····0,2,5·1,3,5····0,1,5·2,3,5···2,3,4·0,3,5····0,3,4·2,3,5····0,2,3·3,4,5···1,3,4·0,3,5····0,3,4·1,3,5····0,1,3·3,4,5···1,2,4·0,3,5····0,2,4·1,3,5····0,1,4·2,3,5····0,1,2·3,4,5···1,2,3·0,3,5····0,2,3·1,3,5····0,1,3·2,3,5···2,3,4·1,2,5····1,2,4·2,3,5····1,2,3·2,4,5···1,3,4·1,2,5····1,2,4·1,3,5····1,2,3·1,4,5···0,3,4·1,2,5····0,2,4·1,3,5····0,1,4·2,3,5····0,2,3·1,4,5····0,1,3·2,4,5····0,1,2·3,4,5···2,3,4·0,2,5····0,2,4·2,3,5····0,2,3·2,4,5···1,3,4·0,2,5····0,2,4·1,3,5····0,2,3·1,4,5····0,1,2·3,4,5···0,3,4·0,2,5····0,2,4·0,3,5····0,2,3·0,4,5···1,2,4·0,2,5····0,2,4·1,2,5····0,1,2·2,4,5···1,2,3·0,2,5····0,2,3·1,2,5····0,1,2·2,3,5···2,3,4·0,1,5····0,1,4·2,3,5····0,1,3·2,4,5····0,1,2·3,4,5···1,3,4·0,1,5····0,1,4·1,3,5····0,1,3·1,4,5···0,3,4·0,1,5····0,1,4·0,3,5····0,1,3·0,4,5···1,2,4·0,1,5····0,1,4·1,2,5····0,1,2·1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5····0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre> |
| 230 | </td>··········</tr> | 230 | </td>··········</tr> |
| 231 | ··········<tr> | 231 | ··········<tr> |
| 232 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·equivalently·(but·faster)... | 232 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·equivalently·(but·faster)... |
| 233 | ·····time·assert(ChowV·===·chowForm·f) | 233 | ·····time·assert(ChowV·===·chowForm·f) |
| 234 | ·--·used· | 234 | ·--·used·1.07888s·(cpu);·0.994322s·(thread);·0s·(gc)</code></pre> |
| 235 | </td>··········</tr> | 235 | </td>··········</tr> |
| 236 | ··········<tr> | 236 | ··········<tr> |
| 237 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·X-resultant·of·V | 237 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·X-resultant·of·V |
| 238 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; | 238 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; |
| 239 | ·--·used·0.1 | 239 | ·--·used·0.184919s·(cpu);·0.150657s·(thread);·0s·(gc)</code></pre> |
| 240 | </td>··········</tr> | 240 | </td>··········</tr> |
| 241 | ··········<tr> | 241 | ··········<tr> |
| 242 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·three·generic·ternary·quadrics | 242 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·three·generic·ternary·quadrics |
| 243 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) | 243 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) |
| 244 | ·········2···············2························2·····2···············2·· | 244 | ·········2···············2························2·····2···············2·· |
| 245 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ | 245 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ |
| Offset 251, 15 lines modified | Offset 251, 15 lines modified | ||
| 251 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 251 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 252 | o6·:·List</code></pre> | 252 | o6·:·List</code></pre> |
| 253 | </td>··········</tr> | 253 | </td>··········</tr> |
| 254 | ··········<tr> | 254 | ··········<tr> |
| 255 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·resultant·of·the·three·forms | 255 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·resultant·of·the·three·forms |
| 256 | ·····time·resF·=·resultant·F; | 256 | ·····time·resF·=·resultant·F; |
| 257 | ·--·used·0.1 | 257 | ·--·used·0.167678s·(cpu);·0.132508s·(thread);·0s·(gc)</code></pre> |
| 258 | </td>··········</tr> | 258 | </td>··········</tr> |
| 259 | ··········<tr> | 259 | ··········<tr> |
| 260 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))</code></pre> | 260 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))</code></pre> |
| 261 | </td>··········</tr> | 261 | </td>··········</tr> |
| 262 | ········</table> | 262 | ········</table> |
| 263 | ······</div> | 263 | ······</div> |
| 264 | ······<div> | 264 | ······<div> |
| Offset 42, 15 lines modified | Offset 42, 15 lines modified | ||
| 42 | ···············ZZ | 42 | ···············ZZ |
| 43 | o2·:·Ideal·of·----[x·..x·] | 43 | o2·:·Ideal·of·----[x·..x·] |
| 44 | ··············3331··0···5 | 44 | ··············3331··0···5 |
| 45 | i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an | 45 | i3·:·--·Chow·form·of·V·in·Grass(2,5)·(performing·internal·computations·on·an |
| 46 | affine·chart·of·the·Grassmannian) | 46 | affine·chart·of·the·Grassmannian) |
| 47 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) | 47 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) |
| 48 | ·--·used·4. | 48 | ·--·used·4.8072s·(cpu);·4.60683s·(thread);·0s·(gc) |
| 49 | ······4···············2··············2·····2···············2 | 49 | ······4···············2··············2·····2···············2 |
| 50 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ | 50 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ |
| 51 | ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5 | 51 | ······1,2,4·····0,2,4·1,2,4·2,3,4····0,2,4·2,3,4·····1,2,3·1,2,4·1,2,5 |
| 52 | ·····------------------------------------------------------------------------ | 52 | ·····------------------------------------------------------------------------ |
| 53 | ······2·····2··············2 | 53 | ······2·····2··············2 |
| 54 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ | 54 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ |
| Offset 235, 33 lines modified | Offset 235, 33 lines modified | ||
| 235 | 1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5 | 235 | 1,4,5···0,2,4·0,1,5····0,1,4·0,2,5····0,1,2·0,4,5···1,2,3·0,1,5····0,1,3·1,2,5 |
| 236 | 0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4 | 236 | 0,1,2·1,3,5···0,2,3·0,1,5····0,1,3·0,2,5····0,1,2·0,3,5···1,2,4·0,3,4····0,2,4 |
| 237 | 1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4 | 237 | 1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4 |
| 238 | 0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3 | 238 | 0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3 |
| 239 | 0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 | 239 | 0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 |
| 240 | i4·:·--·equivalently·(but·faster)... | 240 | i4·:·--·equivalently·(but·faster)... |
| 241 | ·····time·assert(ChowV·===·chowForm·f) | 241 | ·····time·assert(ChowV·===·chowForm·f) |
| 242 | ·--·used· | 242 | ·--·used·1.07888s·(cpu);·0.994322s·(thread);·0s·(gc) |
| 243 | i5·:·--·X-resultant·of·V | 243 | i5·:·--·X-resultant·of·V |
| 244 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; | 244 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; |
| 245 | ·--·used·0.1 | 245 | ·--·used·0.184919s·(cpu);·0.150657s·(thread);·0s·(gc) |
| 246 | i6·:·--·three·generic·ternary·quadrics | 246 | i6·:·--·three·generic·ternary·quadrics |
| 247 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) | 247 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) |
| 248 | ·········2···············2························2·····2···············2 | 248 | ·········2···············2························2·····2···············2 |
| 249 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ | 249 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ |
| 250 | ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1 | 250 | ·······0·0····1·0·1····3·1····2·0·2····4·1·2····5·2···0·0····1·0·1····3·1 |
| 251 | ·····------------------------------------------------------------------------ | 251 | ·····------------------------------------------------------------------------ |
| 252 | ··························2·····2···············2························2 | 252 | ··························2·····2···············2························2 |
| 253 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} | 253 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 254 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 254 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 255 | o6·:·List | 255 | o6·:·List |
| 256 | i7·:·--·resultant·of·the·three·forms | 256 | i7·:·--·resultant·of·the·three·forms |
| 257 | ·····time·resF·=·resultant·F; | 257 | ·····time·resF·=·resultant·F; |
| 258 | ·--·used·0.1 | 258 | ·--·used·0.167678s·(cpu);·0.132508s·(thread);·0s·(gc) |
| 259 | i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring | 259 | i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring |
| 260 | Xres)) | 260 | Xres)) |
| 261 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 261 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 262 | ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety | 262 | ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety |
| 263 | ····*·_\x8h_\x8u_\x8r_\x8w_\x8i_\x8t_\x8z_\x8F_\x8o_\x8r_\x8m·--·Hurwitz·form·of·a·projective·variety | 263 | ····*·_\x8h_\x8u_\x8r_\x8w_\x8i_\x8t_\x8z_\x8F_\x8o_\x8r_\x8m·--·Hurwitz·form·of·a·projective·variety |
| 264 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8* | 264 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·c\x8ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 265 | ····*·chowForm(Ideal) | 265 | ····*·chowForm(Ideal) |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | ········2··············2 | 83 | ········2··············2 |
| 84 | o2·=·a*x··+·b*x*y·+·c*y | 84 | o2·=·a*x··+·b*x*y·+·c*y |
| 85 | o2·:·ZZ[a..c][x..y]</code></pre> | 85 | o2·:·ZZ[a..c][x..y]</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·discriminant·F | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·discriminant·F |
| 89 | ·--·used·0.00 | 89 | ·--·used·0.0100446s·(cpu);·0.00907116s·(thread);·0s·(gc) |
| 90 | ········2 | 90 | ········2 |
| 91 | o3·=·-·b··+·4a*c | 91 | o3·=·-·b··+·4a*c |
| 92 | o3·:·ZZ[a..c]</code></pre> | 92 | o3·:·ZZ[a..c]</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ········3······2·········2······3 | 100 | ········3······2·········2······3 |
| 101 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y | 101 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y |
| 102 | o5·:·ZZ[a..d][x..y]</code></pre> | 102 | o5·:·ZZ[a..d][x..y]</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·discriminant·F | 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·discriminant·F |
| 106 | ·--·used·0.0 | 106 | ·--·used·0.0558115s·(cpu);·0.0267675s·(thread);·0s·(gc) |
| 107 | ········2·2·······3·····3···················2·2 | 107 | ········2·2·······3·····3···················2·2 |
| 108 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d | 108 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d |
| 109 | o6·:·ZZ[a..d]</code></pre> | 109 | o6·:·ZZ[a..d]</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| Offset 149, 15 lines modified | Offset 149, 15 lines modified | ||
| 149 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x | 149 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x |
| 150 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 | 150 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 |
| 151 | o12·:·R'</code></pre> | 151 | o12·:·R'</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·D=discriminant·pencil | 154 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·D=discriminant·pencil |
| 155 | ·--·used·0. | 155 | ·--·used·0.389589s·(cpu);·0.390219s·(thread);·0s·(gc) |
| 156 | ···········108······106·2·······102·6······100·8·······98·10·······96·12·· | 156 | ···········108······106·2·······102·6······100·8·······98·10·······96·12·· |
| 157 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ | 157 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ |
| 158 | ···········0········0···1·······0···1······0···1·······0··1········0··1··· | 158 | ···········0········0···1·······0···1······0···1·······0··1········0··1··· |
| 159 | ······----------------------------------------------------------------------- | 159 | ······----------------------------------------------------------------------- |
| 160 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24·· | 160 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24·· |
| 161 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ | 161 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ |
| Offset 24, 28 lines modified | Offset 24, 28 lines modified | ||
| 24 | i1·:·ZZ[a,b,c][x,y];·F·=·a*x^2+b*x*y+c*y^2 | 24 | i1·:·ZZ[a,b,c][x,y];·F·=·a*x^2+b*x*y+c*y^2 |
| 25 | ········2··············2 | 25 | ········2··············2 |
| 26 | o2·=·a*x··+·b*x*y·+·c*y | 26 | o2·=·a*x··+·b*x*y·+·c*y |
| 27 | o2·:·ZZ[a..c][x..y] | 27 | o2·:·ZZ[a..c][x..y] |
| 28 | i3·:·time·discriminant·F | 28 | i3·:·time·discriminant·F |
| 29 | ·--·used·0.00 | 29 | ·--·used·0.0100446s·(cpu);·0.00907116s·(thread);·0s·(gc) |
| 30 | ········2 | 30 | ········2 |
| 31 | o3·=·-·b··+·4a*c | 31 | o3·=·-·b··+·4a*c |
| 32 | o3·:·ZZ[a..c] | 32 | o3·:·ZZ[a..c] |
| 33 | i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^3 | 33 | i4·:·ZZ[a,b,c,d][x,y];·F·=·a*x^3+b*x^2*y+c*x*y^2+d*y^3 |
| 34 | ········3······2·········2······3 | 34 | ········3······2·········2······3 |
| 35 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y | 35 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y |
| 36 | o5·:·ZZ[a..d][x..y] | 36 | o5·:·ZZ[a..d][x..y] |
| 37 | i6·:·time·discriminant·F | 37 | i6·:·time·discriminant·F |
| 38 | ·--·used·0.0 | 38 | ·--·used·0.0558115s·(cpu);·0.0267675s·(thread);·0s·(gc) |
| 39 | ········2·2·······3·····3···················2·2 | 39 | ········2·2·······3·····3···················2·2 |
| 40 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d | 40 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d |
| 41 | o6·:·ZZ[a..d] | 41 | o6·:·ZZ[a..d] |
| 42 | The·next·example·illustrates·how·computing·the·intersection·of·a·pencil | 42 | The·next·example·illustrates·how·computing·the·intersection·of·a·pencil |
| 43 | generated·by·two·degree·$d$·forms·$F(x_0,\ldots,x_n),·G(x_0,\ldots,x_n)$·with | 43 | generated·by·two·degree·$d$·forms·$F(x_0,\ldots,x_n),·G(x_0,\ldots,x_n)$·with |
| Offset 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | ················4········3······4·············4········3······4 | 75 | ················4········3······4·············4········3······4 |
| 76 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x | 76 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x |
| 77 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 | 77 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 |
| 78 | o12·:·R' | 78 | o12·:·R' |
| 79 | i13·:·time·D=discriminant·pencil | 79 | i13·:·time·D=discriminant·pencil |
| 80 | ·--·used·0. | 80 | ·--·used·0.389589s·(cpu);·0.390219s·(thread);·0s·(gc) |
| 81 | ···········108······106·2·······102·6······100·8·······98·10·······96·12 | 81 | ···········108······106·2·······102·6······100·8·······98·10·······96·12 |
| 82 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ | 82 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ |
| 83 | ···········0········0···1·······0···1······0···1·······0··1········0··1 | 83 | ···········0········0···1·······0···1······0···1·······0··1········0··1 |
| 84 | ······----------------------------------------------------------------------- | 84 | ······----------------------------------------------------------------------- |
| 85 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24 | 85 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24 |
| 86 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ | 86 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ |
| Offset 91, 26 lines modified | Offset 91, 26 lines modified | ||
| 91 | ······0·3 | 91 | ······0·3 |
| 92 | o1·:·Ideal·of·QQ[x·..x·] | 92 | o1·:·Ideal·of·QQ[x·..x·] |
| 93 | ··················0···5</code></pre> | 93 | ··················0···5</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·V'·=·dualVariety·V | 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·V'·=·dualVariety·V |
| 97 | ·--·used·0.1 | 97 | ·--·used·0.183516s·(cpu);·0.144563s·(thread);·0s·(gc) |
| 98 | ············2·················2····2 | 98 | ············2·················2····2 |
| 99 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) | 99 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) |
| 100 | ············2·3····1·2·4····0·4····1·5·····0·3·5 | 100 | ············2·3····1·2·4····0·4····1·5·····0·3·5 |
| 101 | o2·:·Ideal·of·QQ[x·..x·] | 101 | o2·:·Ideal·of·QQ[x·..x·] |
| 102 | ··················0···5</code></pre> | 102 | ··················0···5</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·V·==·dualVariety·V' | 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·V·==·dualVariety·V' |
| 106 | ·--·used·0.1 | 106 | ·--·used·0.158401s·(cpu);·0.135101s·(thread);·0s·(gc) |
| 107 | o3·=·true</code></pre> | 107 | o3·=·true</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ········<p>In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic·form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the·plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$</p> | 110 | ········<p>In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic·form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the·plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$</p> |
| 111 | ········<table·class="examples"> | 111 | ········<table·class="examples"> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| Offset 126, 23 lines modified | Offset 126, 23 lines modified | ||
| 126 | ······ZZ | 126 | ······ZZ |
| 127 | o4·:·----[a·..a·][x·..x·] | 127 | o4·:·----[a·..a·][x·..x·] |
| 128 | ·····3331··0···9···0···2</code></pre> | 128 | ·····3331··0···9···0···2</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·discF·=·ideal·discriminant·F; | 131 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·discF·=·ideal·discriminant·F; |
| 132 | ·--·used·0.0 | 132 | ·--·used·0.0559319s·(cpu);·0.055454s·(thread);·0s·(gc) |
| 133 | ···············ZZ | 133 | ···············ZZ |
| 134 | o5·:·Ideal·of·----[a·..a·] | 134 | o5·:·Ideal·of·----[a·..a·] |
| 135 | ··············3331··0···9</code></pre> | 135 | ··············3331··0···9</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); | 138 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); |
| 139 | ·--·used·0. | 139 | ·--·used·0.713257s·(cpu);·0.674457s·(thread);·0s·(gc) |
| 140 | ···············ZZ | 140 | ···············ZZ |
| 141 | o6·:·Ideal·of·----[x·..x·] | 141 | o6·:·Ideal·of·----[x·..x·] |
| 142 | ··············3331··0···9</code></pre> | 142 | ··············3331··0···9</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) | 145 | <td>··············<pre><code·class="language-macaulay2">i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) |
| Offset 32, 24 lines modified | Offset 32, 24 lines modified | ||
| 32 | ·····------------------------------------------------------------------------ | 32 | ·····------------------------------------------------------------------------ |
| 33 | ·····x·x·) | 33 | ·····x·x·) |
| 34 | ······0·3 | 34 | ······0·3 |
| 35 | o1·:·Ideal·of·QQ[x·..x·] | 35 | o1·:·Ideal·of·QQ[x·..x·] |
| 36 | ··················0···5 | 36 | ··················0···5 |
| 37 | i2·:·time·V'·=·dualVariety·V | 37 | i2·:·time·V'·=·dualVariety·V |
| 38 | ·--·used·0.1 | 38 | ·--·used·0.183516s·(cpu);·0.144563s·(thread);·0s·(gc) |
| 39 | ············2·················2····2 | 39 | ············2·················2····2 |
| 40 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) | 40 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) |
| 41 | ············2·3····1·2·4····0·4····1·5·····0·3·5 | 41 | ············2·3····1·2·4····0·4····1·5·····0·3·5 |
| 42 | o2·:·Ideal·of·QQ[x·..x·] | 42 | o2·:·Ideal·of·QQ[x·..x·] |
| 43 | ··················0···5 | 43 | ··················0···5 |
| 44 | i3·:·time·V·==·dualVariety·V' | 44 | i3·:·time·V·==·dualVariety·V' |
| 45 | ·--·used·0.1 | 45 | ·--·used·0.158401s·(cpu);·0.135101s·(thread);·0s·(gc) |
| 46 | o3·=·true | 46 | o3·=·true |
| 47 | In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic | 47 | In·the·next·example,·we·verify·that·the·discriminant·of·a·generic·ternary·cubic |
| 48 | form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the | 48 | form·coincides·with·the·dual·variety·of·the·3-th·Veronese·embedding·of·the |
| 49 | plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$ | 49 | plane,·which·is·a·hypersurface·of·degree·12·in·$\mathbb{P}^9$ |
| 50 | i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331) | 50 | i4·:·F·=·first·genericPolynomials({3,-1,-1},ZZ/3331) |
| Offset 61, 21 lines modified | Offset 61, 21 lines modified | ||
| 61 | ·····a·x·x··+·a·x | 61 | ·····a·x·x··+·a·x |
| 62 | ······8·1·2····9·2 | 62 | ······8·1·2····9·2 |
| 63 | ······ZZ | 63 | ······ZZ |
| 64 | o4·:·----[a·..a·][x·..x·] | 64 | o4·:·----[a·..a·][x·..x·] |
| 65 | ·····3331··0···9···0···2 | 65 | ·····3331··0···9···0···2 |
| 66 | i5·:·time·discF·=·ideal·discriminant·F; | 66 | i5·:·time·discF·=·ideal·discriminant·F; |
| 67 | ·--·used·0.0 | 67 | ·--·used·0.0559319s·(cpu);·0.055454s·(thread);·0s·(gc) |
| 68 | ···············ZZ | 68 | ···············ZZ |
| 69 | o5·:·Ideal·of·----[a·..a·] | 69 | o5·:·Ideal·of·----[a·..a·] |
| 70 | ··············3331··0···9 | 70 | ··············3331··0···9 |
| 71 | i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); | 71 | i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); |
| 72 | ·--·used·0. | 72 | ·--·used·0.713257s·(cpu);·0.674457s·(thread);·0s·(gc) |
| 73 | ···············ZZ | 73 | ···············ZZ |
| 74 | o6·:·Ideal·of·----[x·..x·] | 74 | o6·:·Ideal·of·----[x·..x·] |
| 75 | ··············3331··0···9 | 75 | ··············3331··0···9 |
| 76 | i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) | 76 | i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) |
| 77 | o7·=·true | 77 | o7·=·true |
| Offset 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ·············2····1·3···1·2····0·3···1····0·2 | 85 | ·············2····1·3···1·2····0·3···1····0·2 |
| 86 | o1·:·Ideal·of·QQ[x·..x·] | 86 | o1·:·Ideal·of·QQ[x·..x·] |
| 87 | ··················0···3</code></pre> | 87 | ··················0···3</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fromPluckerToStiefel·dualize·chowForm·C | 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fromPluckerToStiefel·dualize·chowForm·C |
| 91 | ·--·used·0. | 91 | ·--·used·0.124594s·(cpu);·0.0611422s·(thread);·0s·(gc) |
| 92 | ········3···3··········2···2··············2·······2··········2···3···· | 92 | ········3···3··········2···2··············2·······2··········2···3···· |
| 93 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- | 93 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- |
| 94 | ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1·· | 94 | ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1·· |
| 95 | ·····------------------------------------------------------------------------ | 95 | ·····------------------------------------------------------------------------ |
| 96 | ······2·······2···············2···2··································· | 96 | ······2·······2···············2···2··································· |
| 97 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- | 97 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- |
| Offset 136, 15 lines modified | Offset 136, 15 lines modified | ||
| 136 | ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3 | 136 | ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3 |
| 137 | o2·:·QQ[x···..x···] | 137 | o2·:·QQ[x···..x···] |
| 138 | ·········0,0···1,3</code></pre> | 138 | ·········0,0···1,3</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) | 141 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) |
| 142 | ·--·used·0.03 | 142 | ·--·used·0.0434267s·(cpu);·0.0433729s·(thread);·0s·(gc) |
| 143 | ············3··········2·························2························ | 143 | ············3··········2·························2························ |
| 144 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- | 144 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- |
| 145 | ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3·· | 145 | ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3·· |
| 146 | ·····------------------------------------------------------------------------ | 146 | ·····------------------------------------------------------------------------ |
| 147 | ···········2······3······2 | 147 | ···········2······3······2 |
| 148 | ·····2x···x····+·x····+·x | 148 | ·····2x···x····+·x····+·x |
| Offset 171, 15 lines modified | Offset 171, 15 lines modified | ||
| 171 | ········<p>As·another·application,·we·check·that·the·singular·locus·of·the·Chow·form·of·the·twisted·cubic·has·dimension·2·(on·each·standard·chart).</p> | 171 | ········<p>As·another·application,·we·check·that·the·singular·locus·of·the·Chow·form·of·the·twisted·cubic·has·dimension·2·(on·each·standard·chart).</p> |
| 172 | ········<table·class="examples"> | 172 | ········<table·class="examples"> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i5·:·w·=·chowForm·C;</code></pre> | 174 | <td>··············<pre><code·class="language-macaulay2">i5·:·w·=·chowForm·C;</code></pre> |
| 175 | </td>··········</tr> | 175 | </td>··········</tr> |
| 176 | ··········<tr> | 176 | ··········<tr> |
| 177 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s)) | 177 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s)) |
| 178 | ·--·used·0.0 | 178 | ·--·used·0.067332s·(cpu);·0.0391563s·(thread);·0s·(gc) |
| 179 | ···················3··········2··········3·······················2········ | 179 | ···················3··········2··········3·······················2········ |
| 180 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ | 180 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ |
| 181 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3·· | 181 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3·· |
| 182 | ·····------------------------------------------------------------------------ | 182 | ·····------------------------------------------------------------------------ |
| 183 | ·························2······2············2···3···············2········ | 183 | ·························2······2············2···3···············2········ |
| 184 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ | 184 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ |
| Offset 217, 15 lines modified | Offset 217, 15 lines modified | ||
| 217 | ·····2x···x····-·x····+·x···)} | 217 | ·····2x···x····-·x····+·x···)} |
| 218 | ·······0,0·1,1····1,1····1,0 | 218 | ·······0,0·1,1····1,1····1,0 |
| 219 | o6·:·List</code></pre> | 219 | o6·:·List</code></pre> |
| 220 | </td>··········</tr> | 220 | </td>··········</tr> |
| 221 | ··········<tr> | 221 | ··········<tr> |
| 222 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·apply(U,u->dim·singularLocus·u) | 222 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·apply(U,u->dim·singularLocus·u) |
| 223 | ·--·used·0.01 | 223 | ·--·used·0.0195029s·(cpu);·0.0192914s·(thread);·0s·(gc) |
| 224 | o7·=·{2,·2,·2,·2,·2,·2} | 224 | o7·=·{2,·2,·2,·2,·2,·2} |
| 225 | o7·:·List</code></pre> | 225 | o7·:·List</code></pre> |
| 226 | </td>··········</tr> | 226 | </td>··········</tr> |
| 227 | ········</table> | 227 | ········</table> |
| 228 | ······</div> | 228 | ······</div> |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | ·············2·······················2 | 27 | ·············2·······················2 |
| 28 | o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·) | 28 | o1·=·ideal·(x··-·x·x·,·x·x··-·x·x·,·x··-·x·x·) |
| 29 | ·············2····1·3···1·2····0·3···1····0·2 | 29 | ·············2····1·3···1·2····0·3···1····0·2 |
| 30 | o1·:·Ideal·of·QQ[x·..x·] | 30 | o1·:·Ideal·of·QQ[x·..x·] |
| 31 | ··················0···3 | 31 | ··················0···3 |
| 32 | i2·:·time·fromPluckerToStiefel·dualize·chowForm·C | 32 | i2·:·time·fromPluckerToStiefel·dualize·chowForm·C |
| 33 | ·--·used·0. | 33 | ·--·used·0.124594s·(cpu);·0.0611422s·(thread);·0s·(gc) |
| 34 | ········3···3··········2···2··············2·······2··········2···3 | 34 | ········3···3··········2···2··············2·······2··········2···3 |
| 35 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- | 35 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- |
| 36 | ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1 | 36 | ········0,3·1,0····0,2·0,3·1,0·1,1····0,1·0,3·1,0·1,1····0,0·0,3·1,1 |
| 37 | ·····------------------------------------------------------------------------ | 37 | ·····------------------------------------------------------------------------ |
| 38 | ······2·······2···············2···2 | 38 | ······2·······2···············2···2 |
| 39 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- | 39 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | ··········2·······2·······2···········2······2···········2······3···3 | 76 | ··········2·······2·······2···········2······2···········2······3···3 |
| 77 | ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x | 77 | ·····x···x···x···x····-·2x···x···x···x····-·x···x···x···x····+·x···x |
| 78 | ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3 | 78 | ······0,0·0,1·1,1·1,3·····0,0·0,2·1,1·1,3····0,0·0,1·1,2·1,3····0,0·1,3 |
| 79 | o2·:·QQ[x···..x···] | 79 | o2·:·QQ[x···..x···] |
| 80 | ·········0,0···1,3 | 80 | ·········0,0···1,3 |
| 81 | i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) | 81 | i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) |
| 82 | ·--·used·0.03 | 82 | ·--·used·0.0434267s·(cpu);·0.0433729s·(thread);·0s·(gc) |
| 83 | ············3··········2·························2 | 83 | ············3··········2·························2 |
| 84 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- | 84 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- |
| 85 | ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3 | 85 | ········0,3·1,2····0,2·1,2·1,3····0,2·0,3·1,2····0,2·1,3·····0,3·1,2·1,3 |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| 87 | ···········2······3······2 | 87 | ···········2······3······2 |
| 88 | ·····2x···x····+·x····+·x | 88 | ·····2x···x····+·x····+·x |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | o4·:·QQ[a···..a···] | 106 | o4·:·QQ[a···..a···] |
| 107 | ·········0,0···1,1 | 107 | ·········0,0···1,1 |
| 108 | As·another·application,·we·check·that·the·singular·locus·of·the·Chow·form·of | 108 | As·another·application,·we·check·that·the·singular·locus·of·the·Chow·form·of |
| 109 | the·twisted·cubic·has·dimension·2·(on·each·standard·chart). | 109 | the·twisted·cubic·has·dimension·2·(on·each·standard·chart). |
| 110 | i5·:·w·=·chowForm·C; | 110 | i5·:·w·=·chowForm·C; |
| 111 | i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel | 111 | i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel |
| 112 | (w,AffineChartGrass=>s)) | 112 | (w,AffineChartGrass=>s)) |
| 113 | ·--·used·0.0 | 113 | ·--·used·0.067332s·(cpu);·0.0391563s·(thread);·0s·(gc) |
| 114 | ···················3··········2··········3·······················2 | 114 | ···················3··········2··········3·······················2 |
| 115 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ | 115 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ |
| 116 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3 | 116 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3 |
| 117 | ·····------------------------------------------------------------------------ | 117 | ·····------------------------------------------------------------------------ |
| 118 | ·························2······2············2···3···············2 | 118 | ·························2······2············2···3···············2 |
| 119 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ | 119 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ |
| Offset 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | ·····------------------------------------------------------------------------ | 150 | ·····------------------------------------------------------------------------ |
| 151 | ···········2······3······2 | 151 | ···········2······3······2 |
| 152 | ·····2x···x····-·x····+·x···)} | 152 | ·····2x···x····-·x····+·x···)} |
| 153 | ·······0,0·1,1····1,1····1,0 | 153 | ·······0,0·1,1····1,1····1,0 |
| 154 | o6·:·List | 154 | o6·:·List |
| 155 | i7·:·time·apply(U,u->dim·singularLocus·u) | 155 | i7·:·time·apply(U,u->dim·singularLocus·u) |
| 156 | ·--·used·0.01 | 156 | ·--·used·0.0195029s·(cpu);·0.0192914s·(thread);·0s·(gc) |
| 157 | o7·=·{2,·2,·2,·2,·2,·2} | 157 | o7·=·{2,·2,·2,·2,·2,·2} |
| 158 | o7·:·List | 158 | o7·:·List |
| 159 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fr\x8ro\x8om\x8mP\x8Pl\x8lu\x8uc\x8ck\x8ke\x8er\x8rT\x8To\x8oS\x8St\x8ti\x8ie\x8ef\x8fe\x8el\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* | 159 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·f\x8fr\x8ro\x8om\x8mP\x8Pl\x8lu\x8uc\x8ck\x8ke\x8er\x8rT\x8To\x8oS\x8St\x8ti\x8ie\x8ef\x8fe\x8el\x8l:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 160 | ····*·fromPluckerToStiefel(Ideal) | 160 | ····*·fromPluckerToStiefel(Ideal) |
| 161 | ····*·fromPluckerToStiefel(Matrix) | 161 | ····*·fromPluckerToStiefel(Matrix) |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 | 95 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 |
| 96 | o1·:·Ideal·of·QQ[p·..p·] | 96 | o1·:·Ideal·of·QQ[p·..p·] |
| 97 | ··················0···4</code></pre> | 97 | ··················0···4</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·hurwitzForm·Q | 100 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·hurwitzForm·Q |
| 101 | ·--·used·0.0 | 101 | ·--·used·0.0867582s·(cpu);·0.0437026s·(thread);·0s·(gc) |
| 102 | ············2····························2·································· | 102 | ············2····························2·································· |
| 103 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p··· | 103 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p··· |
| 104 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 | 104 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 |
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ···········2··············································2················· | 106 | ···········2··············································2················· |
| 107 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p··· | 107 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p··· |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | ······7·2··········7·······1·······7·········2 | 35 | ······7·2··········7·······1·······7·········2 |
| 36 | ·····--p··+·p·p··+·-p·p··+·-p·p··+·-p·p··+·7p·) | 36 | ·····--p··+·p·p··+·-p·p··+·-p·p··+·-p·p··+·7p·) |
| 37 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 | 37 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 |
| 38 | o1·:·Ideal·of·QQ[p·..p·] | 38 | o1·:·Ideal·of·QQ[p·..p·] |
| 39 | ··················0···4 | 39 | ··················0···4 |
| 40 | i2·:·time·hurwitzForm·Q | 40 | i2·:·time·hurwitzForm·Q |
| 41 | ·--·used·0.0 | 41 | ·--·used·0.0867582s·(cpu);·0.0437026s·(thread);·0s·(gc) |
| 42 | ············2····························2 | 42 | ············2····························2 |
| 43 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p | 43 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p |
| 44 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 | 44 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ···········2··············································2 | 46 | ···········2··············································2 |
| 47 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p | 47 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p |
| Offset 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 99 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 100 | o1·:·-------------------------------------- | 100 | o1·:·-------------------------------------- |
| 101 | ·········p···p····-·p···p····+·p···p | 101 | ·········p···p····-·p···p····+·p···p |
| 102 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> | 102 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·isCoisotropic·w | 105 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·isCoisotropic·w |
| 106 | ·--·used·0.0 | 106 | ·--·used·0.0120116s·(cpu);·0.0127226s·(thread);·0s·(gc) |
| 107 | o2·=·true</code></pre> | 107 | o2·=·true</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·random·quadric·in·G(1,3) | 110 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·random·quadric·in·G(1,3) |
| 111 | ·····w'·=·random(2,Grass(1,3)) | 111 | ·····w'·=·random(2,Grass(1,3)) |
| Offset 131, 15 lines modified | Offset 131, 15 lines modified | ||
| 131 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 131 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 132 | o3·:·-------------------------------------- | 132 | o3·:·-------------------------------------- |
| 133 | ·········p···p····-·p···p····+·p···p | 133 | ·········p···p····-·p···p····+·p···p |
| 134 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> | 134 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isCoisotropic·w' | 137 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isCoisotropic·w' |
| 138 | ·--·used·0.00 | 138 | ·--·used·0.00798541s·(cpu);·0.00934893s·(thread);·0s·(gc) |
| 139 | o4·=·false</code></pre> | 139 | o4·=·false</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ········</table> | 141 | ········</table> |
| 142 | ······</div> | 142 | ······</div> |
| 143 | ······<div·class="waystouse"> | 143 | ······<div·class="waystouse"> |
| 144 | ········<h2>Ways·to·use·<span·class="tt">isCoisotropic</span>:</h2> | 144 | ········<h2>Ways·to·use·<span·class="tt">isCoisotropic</span>:</h2> |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] | 41 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] |
| 42 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 42 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 43 | o1·:·-------------------------------------- | 43 | o1·:·-------------------------------------- |
| 44 | ·········p···p····-·p···p····+·p···p | 44 | ·········p···p····-·p···p····+·p···p |
| 45 | ··········1,2·0,3····0,2·1,3····0,1·2,3 | 45 | ··········1,2·0,3····0,2·1,3····0,1·2,3 |
| 46 | i2·:·time·isCoisotropic·w | 46 | i2·:·time·isCoisotropic·w |
| 47 | ·--·used·0.0 | 47 | ·--·used·0.0120116s·(cpu);·0.0127226s·(thread);·0s·(gc) |
| 48 | o2·=·true | 48 | o2·=·true |
| 49 | i3·:·--·random·quadric·in·G(1,3) | 49 | i3·:·--·random·quadric·in·G(1,3) |
| 50 | ·····w'·=·random(2,Grass(1,3)) | 50 | ·····w'·=·random(2,Grass(1,3)) |
| 51 | ·····7·2··················2·····3·························2·····5 | 51 | ·····7·2··················2·····3·························2·····5 |
| 52 | o3·=·-p····+·7p···p····+·p····+·-p···p····+·2p···p····+·5p····+·-p···p····+ | 52 | o3·=·-p····+·7p···p····+·p····+·-p···p····+·2p···p····+·5p····+·-p···p····+ |
| Offset 69, 14 lines modified | Offset 69, 14 lines modified | ||
| 69 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] | 69 | ·····QQ[p···..p···,·p···,·p···,·p···,·p···] |
| 70 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 70 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 71 | o3·:·-------------------------------------- | 71 | o3·:·-------------------------------------- |
| 72 | ·········p···p····-·p···p····+·p···p | 72 | ·········p···p····-·p···p····+·p···p |
| 73 | ··········1,2·0,3····0,2·1,3····0,1·2,3 | 73 | ··········1,2·0,3····0,2·1,3····0,1·2,3 |
| 74 | i4·:·time·isCoisotropic·w' | 74 | i4·:·time·isCoisotropic·w' |
| 75 | ·--·used·0.00 | 75 | ·--·used·0.00798541s·(cpu);·0.00934893s·(thread);·0s·(gc) |
| 76 | o4·=·false | 76 | o4·=·false |
| 77 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8* | 77 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 78 | ····*·isCoisotropic(RingElement) | 78 | ····*·isCoisotropic(RingElement) |
| 79 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 79 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 80 | The·object·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 80 | The·object·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | ················ZZ | 114 | ················ZZ |
| 115 | o3·:·Ideal·of·-----[x·..x·] | 115 | o3·:·Ideal·of·-----[x·..x·] |
| 116 | ··············33331··0···5</code></pre> | 116 | ··············33331··0···5</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) | 119 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) |
| 120 | ·--·used·0.0 | 120 | ·--·used·0.0275782s·(cpu);·0.0271153s·(thread);·0s·(gc) |
| 121 | o4·=·true</code></pre> | 121 | o4·=·true</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ········</table> | 123 | ········</table> |
| 124 | ······</div> | 124 | ······</div> |
| 125 | ······<div> | 125 | ······<div> |
| 126 | ········<h2>See·also</h2> | 126 | ········<h2>See·also</h2> |
| Offset 55, 15 lines modified | Offset 55, 15 lines modified | ||
| 55 | ·····2380x··+·9482x·) | 55 | ·····2380x··+·9482x·) |
| 56 | ··········4········5 | 56 | ··········4········5 |
| 57 | ················ZZ | 57 | ················ZZ |
| 58 | o3·:·Ideal·of·-----[x·..x·] | 58 | o3·:·Ideal·of·-----[x·..x·] |
| 59 | ··············33331··0···5 | 59 | ··············33331··0···5 |
| 60 | i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) | 60 | i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) |
| 61 | ·--·used·0.0 | 61 | ·--·used·0.0275782s·(cpu);·0.0271153s·(thread);·0s·(gc) |
| 62 | o4·=·true | 62 | o4·=·true |
| 63 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 63 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 64 | ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety | 64 | ····*·_\x8t_\x8a_\x8n_\x8g_\x8e_\x8n_\x8t_\x8i_\x8a_\x8l_\x8C_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·higher·Chow·forms·of·a·projective·variety |
| 65 | ····*·_\x8p_\x8l_\x8u_\x8c_\x8k_\x8e_\x8r·--·get·the·Plücker·coordinates·of·a·linear·subspace | 65 | ····*·_\x8p_\x8l_\x8u_\x8c_\x8k_\x8e_\x8r·--·get·the·Plücker·coordinates·of·a·linear·subspace |
| 66 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sI\x8In\x8nC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8* | 66 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sI\x8In\x8nC\x8Co\x8oi\x8is\x8so\x8ot\x8tr\x8ro\x8op\x8pi\x8ic\x8c:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 67 | ····*·isInCoisotropic(Ideal,Ideal) | 67 | ····*·isInCoisotropic(Ideal,Ideal) |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} | 84 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 85 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 | 85 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 |
| 86 | o1·:·List</code></pre> | 86 | o1·:·List</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(D,D')·=·macaulayFormula·F | 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(D,D')·=·macaulayFormula·F |
| 90 | ·--·used·0.00 | 90 | ·--·used·0.00385897s·(cpu);·0.0054614s·(thread);·0s·(gc) |
| 91 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0·· | 91 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0·· |
| 92 | ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0·· | 92 | ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0·· |
| 93 | ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0·· | 93 | ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0·· |
| 94 | ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0·· | 94 | ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0·· |
| 95 | ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0·· | 95 | ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0·· |
| 96 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0·· | 96 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0·· |
| Offset 151, 15 lines modified | Offset 151, 15 lines modified | ||
| 151 | ·····-p·p··+·2p·p··+·6p·} | 151 | ·····-p·p··+·2p·p··+·6p·} |
| 152 | ·····7·0·2·····1·2·····2 | 152 | ·····7·0·2·····1·2·····2 |
| 153 | o3·:·List</code></pre> | 153 | o3·:·List</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(D,D')·=·macaulayFormula·F | 156 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(D,D')·=·macaulayFormula·F |
| 157 | ·--·used·0.00 | 157 | ·--·used·0.0042333s·(cpu);·0.00274287s·(thread);·0s·(gc) |
| 158 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0·· | 158 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0·· |
| 159 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0·· | 159 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0·· |
| 160 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0·· | 160 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0·· |
| 161 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0·· | 161 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0·· |
| 162 | ······|·0···0····0····0···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0·· | 162 | ······|·0···0····0····0···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0·· |
| 163 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 | 163 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ···················2··········2········2······3 | 30 | ···················2··········2········2······3 |
| 31 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} | 31 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 32 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 | 32 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 |
| 33 | o1·:·List | 33 | o1·:·List |
| 34 | i2·:·time·(D,D')·=·macaulayFormula·F | 34 | i2·:·time·(D,D')·=·macaulayFormula·F |
| 35 | ·--·used·0.00 | 35 | ·--·used·0.00385897s·(cpu);·0.0054614s·(thread);·0s·(gc) |
| 36 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0 | 36 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0 |
| 37 | ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0 | 37 | ······|·0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0 |
| 38 | ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0 | 38 | ······|·0···0···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0 |
| 39 | ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0 | 39 | ······|·0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0 |
| 40 | ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0 | 40 | ······|·0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0 |
| 41 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0 | 41 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0 |
| Offset 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | ·····------------------------------------------------------------------------ | 92 | ·····------------------------------------------------------------------------ |
| 93 | ·····6···2·······2·····3 | 93 | ·····6···2·······2·····3 |
| 94 | ·····-p·p··+·2p·p··+·6p·} | 94 | ·····-p·p··+·2p·p··+·6p·} |
| 95 | ·····7·0·2·····1·2·····2 | 95 | ·····7·0·2·····1·2·····2 |
| 96 | o3·:·List | 96 | o3·:·List |
| 97 | i4·:·time·(D,D')·=·macaulayFormula·F | 97 | i4·:·time·(D,D')·=·macaulayFormula·F |
| 98 | ·--·used·0.00 | 98 | ·--·used·0.0042333s·(cpu);·0.00274287s·(thread);·0s·(gc) |
| 99 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0 | 99 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0 |
| 100 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0 | 100 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0 |
| 101 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0 | 101 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0 |
| 102 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0 | 102 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0 |
| 103 | ······|·0···0····0····0···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0 | 103 | ······|·0···0····0····0···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0 |
| 104 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 | 104 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 |
| Offset 91, 30 lines modified | Offset 91, 30 lines modified | ||
| 91 | ·····664x·) | 91 | ·····664x·) |
| 92 | ·········4 | 92 | ·········4 |
| 93 | o3·:·Ideal·of·P4</code></pre> | 93 | o3·:·Ideal·of·P4</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·p·=·plucker·L | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·p·=·plucker·L |
| 97 | ·--·used·0.00 | 97 | ·--·used·0.00401575s·(cpu);·0.00485961s·(thread);·0s·(gc) |
| 98 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ | 98 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ |
| 99 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3·· | 99 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3·· |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ | 101 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ |
| 102 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2·· | 102 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2·· |
| 103 | ·····------------------------------------------------------------------------ | 103 | ·····------------------------------------------------------------------------ |
| 104 | ·····11804x···,·x····+·14854x···) | 104 | ·····11804x···,·x····+·14854x···) |
| 105 | ···········3,4···0,1·········3,4 | 105 | ···········3,4···0,1·········3,4 |
| 106 | o4·:·Ideal·of·G'1'4</code></pre> | 106 | o4·:·Ideal·of·G'1'4</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·L'·=·plucker·p | 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·L'·=·plucker·p |
| 110 | ·--·used·0.06 | 110 | ·--·used·0.0672588s·(cpu);·0.0396083s·(thread);·0s·(gc) |
| 111 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- | 111 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- |
| 112 | ·············2········3·········4···1········3·········4···0·········3·· | 112 | ·············2········3·········4···1········3·········4···0·········3·· |
| 113 | ·····------------------------------------------------------------------------ | 113 | ·····------------------------------------------------------------------------ |
| 114 | ·····664x·) | 114 | ·····664x·) |
| 115 | ·········4 | 115 | ·········4 |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve | 130 | <td>··············<pre><code·class="language-macaulay2">i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve |
| 131 | o7·:·Ideal·of·G'1'4</code></pre> | 131 | o7·:·Ideal·of·G'1'4</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y | 134 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y |
| 135 | ·--·used·0.02 | 135 | ·--·used·0.0294409s·(cpu);·0.03111s·(thread);·0s·(gc) |
| 136 | o8·:·Ideal·of·P4</code></pre> | 136 | o8·:·Ideal·of·P4</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i9·:·(codim·W,degree·W) | 139 | <td>··············<pre><code·class="language-macaulay2">i9·:·(codim·W,degree·W) |
| 140 | o9·=·(2,·5) | 140 | o9·=·(2,·5) |
| Offset 145, 15 lines modified | Offset 145, 15 lines modified | ||
| 145 | o9·:·Sequence</code></pre> | 145 | o9·:·Sequence</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ········</table> | 147 | ········</table> |
| 148 | ········<p>In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb{P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$.</p> | 148 | ········<p>In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb{P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$.</p> |
| 149 | ········<table·class="examples"> | 149 | ········<table·class="examples"> |
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W | 151 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W |
| 152 | ·--·used·0.1 | 152 | ·--·used·0.187303s·(cpu);·0.187749s·(thread);·0s·(gc) |
| 153 | o10·:·Ideal·of·G'1'4</code></pre> | 153 | o10·:·Ideal·of·G'1'4</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i11·:·assert(Y'·==·Y)</code></pre> | 156 | <td>··············<pre><code·class="language-macaulay2">i11·:·assert(Y'·==·Y)</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ········</table> | 158 | ········</table> |
| Offset 29, 28 lines modified | Offset 29, 28 lines modified | ||
| 29 | ·············2········3·········4···1········3·········4···0·········3 | 29 | ·············2········3·········4···1········3·········4···0·········3 |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ·····664x·) | 31 | ·····664x·) |
| 32 | ·········4 | 32 | ·········4 |
| 33 | o3·:·Ideal·of·P4 | 33 | o3·:·Ideal·of·P4 |
| 34 | i4·:·time·p·=·plucker·L | 34 | i4·:·time·p·=·plucker·L |
| 35 | ·--·used·0.00 | 35 | ·--·used·0.00401575s·(cpu);·0.00485961s·(thread);·0s·(gc) |
| 36 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ | 36 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ |
| 37 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3 | 37 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3 |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ | 39 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ |
| 40 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2 | 40 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2 |
| 41 | ·····------------------------------------------------------------------------ | 41 | ·····------------------------------------------------------------------------ |
| 42 | ·····11804x···,·x····+·14854x···) | 42 | ·····11804x···,·x····+·14854x···) |
| 43 | ···········3,4···0,1·········3,4 | 43 | ···········3,4···0,1·········3,4 |
| 44 | o4·:·Ideal·of·G'1'4 | 44 | o4·:·Ideal·of·G'1'4 |
| 45 | i5·:·time·L'·=·plucker·p | 45 | i5·:·time·L'·=·plucker·p |
| 46 | ·--·used·0.06 | 46 | ·--·used·0.0672588s·(cpu);·0.0396083s·(thread);·0s·(gc) |
| 47 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- | 47 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- |
| 48 | ·············2········3·········4···1········3·········4···0·········3 | 48 | ·············2········3·········4···1········3·········4···0·········3 |
| 49 | ·····------------------------------------------------------------------------ | 49 | ·····------------------------------------------------------------------------ |
| 50 | ·····664x·) | 50 | ·····664x·) |
| 51 | ·········4 | 51 | ·········4 |
| Offset 61, 26 lines modified | Offset 61, 26 lines modified | ||
| 61 | $W\subset\mathbb{P}^n$·swept·out·by·the·linear·spaces·corresponding·to·points | 61 | $W\subset\mathbb{P}^n$·swept·out·by·the·linear·spaces·corresponding·to·points |
| 62 | of·$Y$.·As·an·example,·we·now·compute·a·surface·scroll·$W\subset\mathbb{P}^4$ | 62 | of·$Y$.·As·an·example,·we·now·compute·a·surface·scroll·$W\subset\mathbb{P}^4$ |
| 63 | over·an·elliptic·curve·$Y\subset\mathbb{G}(1,\mathbb{P}^4)$. | 63 | over·an·elliptic·curve·$Y\subset\mathbb{G}(1,\mathbb{P}^4)$. |
| 64 | i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve | 64 | i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve |
| 65 | o7·:·Ideal·of·G'1'4 | 65 | o7·:·Ideal·of·G'1'4 |
| 66 | i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y | 66 | i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y |
| 67 | ·--·used·0.02 | 67 | ·--·used·0.0294409s·(cpu);·0.03111s·(thread);·0s·(gc) |
| 68 | o8·:·Ideal·of·P4 | 68 | o8·:·Ideal·of·P4 |
| 69 | i9·:·(codim·W,degree·W) | 69 | i9·:·(codim·W,degree·W) |
| 70 | o9·=·(2,·5) | 70 | o9·=·(2,·5) |
| 71 | o9·:·Sequence | 71 | o9·:·Sequence |
| 72 | In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb | 72 | In·this·example,·we·can·recover·the·subvariety·$Y\subset\mathbb{G}(k,\mathbb |
| 73 | {P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$. | 73 | {P}^n)$·by·computing·the·Fano·variety·of·$k$-planes·contained·in·$W$. |
| 74 | i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W | 74 | i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W |
| 75 | ·--·used·0.1 | 75 | ·--·used·0.187303s·(cpu);·0.187749s·(thread);·0s·(gc) |
| 76 | o10·:·Ideal·of·G'1'4 | 76 | o10·:·Ideal·of·G'1'4 |
| 77 | i11·:·assert(Y'·==·Y) | 77 | i11·:·assert(Y'·==·Y) |
| 78 | W\x8Wa\x8ar\x8rn\x8ni\x8in\x8ng\x8g:·Notice·that,·by·default,·the·computation·is·done·on·a·randomly·chosen | 78 | W\x8Wa\x8ar\x8rn\x8ni\x8in\x8ng\x8g:·Notice·that,·by·default,·the·computation·is·done·on·a·randomly·chosen |
| 79 | affine·chart·on·the·Grassmannian.·To·change·this·behavior,·you·can·use·the | 79 | affine·chart·on·the·Grassmannian.·To·change·this·behavior,·you·can·use·the |
| 80 | _\x8A_\x8f_\x8f_\x8i_\x8n_\x8e_\x8C_\x8h_\x8a_\x8r_\x8t_\x8G_\x8r_\x8a_\x8s_\x8s·option. | 80 | _\x8A_\x8f_\x8f_\x8i_\x8n_\x8e_\x8C_\x8h_\x8a_\x8r_\x8t_\x8G_\x8r_\x8a_\x8s_\x8s·option. |
| 81 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pl\x8lu\x8uc\x8ck\x8ke\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 81 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8pl\x8lu\x8uc\x8ck\x8ke\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} | 99 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} |
| 100 | ·····4··········8····8··········7················4····3····5 | 100 | ·····4··········8····8··········7················4····3····5 |
| 101 | o2·:·List</code></pre> | 101 | o2·:·List</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant(F,Algorithm=>"Poisson2") | 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant(F,Algorithm=>"Poisson2") |
| 105 | ·--·used·0. | 105 | ·--·used·0.22611s·(cpu);·0.140924s·(thread);·0s·(gc) |
| 106 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 106 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 107 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- | 107 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 108 | ···········2222549728809984000000············12700284164628480000000········· | 108 | ···········2222549728809984000000············12700284164628480000000········· |
| 109 | ·····------------------------------------------------------------------------ | 109 | ·····------------------------------------------------------------------------ |
| 110 | ·····348237304382147063838108483692249·3·2·· | 110 | ·····348237304382147063838108483692249·3·2·· |
| 111 | ·····---------------------------------a·b··- | 111 | ·····---------------------------------a·b··- |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | ·····-------------------------------a*b··-·---------------------------b | 121 | ·····-------------------------------a*b··-·---------------------------b |
| 122 | ··········1119954511872000000000················895963609497600000 | 122 | ··········1119954511872000000000················895963609497600000 |
| 123 | o3·:·QQ[a..b]</code></pre> | 123 | o3·:·QQ[a..b]</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·resultant(F,Algorithm=>"Macaulay2") | 126 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·resultant(F,Algorithm=>"Macaulay2") |
| 127 | ·--·used·0. | 127 | ·--·used·0.110768s·(cpu);·0.0687476s·(thread);·0s·(gc) |
| 128 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 128 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 129 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- | 129 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 130 | ···········2222549728809984000000············12700284164628480000000········· | 130 | ···········2222549728809984000000············12700284164628480000000········· |
| 131 | ·····------------------------------------------------------------------------ | 131 | ·····------------------------------------------------------------------------ |
| 132 | ·····348237304382147063838108483692249·3·2·· | 132 | ·····348237304382147063838108483692249·3·2·· |
| 133 | ·····---------------------------------a·b··- | 133 | ·····---------------------------------a·b··- |
| Offset 143, 15 lines modified | Offset 143, 15 lines modified | ||
| 143 | ·····-------------------------------a*b··-·---------------------------b | 143 | ·····-------------------------------a*b··-·---------------------------b |
| 144 | ··········1119954511872000000000················895963609497600000 | 144 | ··········1119954511872000000000················895963609497600000 |
| 145 | o4·:·QQ[a..b]</code></pre> | 145 | o4·:·QQ[a..b]</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant(F,Algorithm=>"Poisson") | 148 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant(F,Algorithm=>"Poisson") |
| 149 | ·--·used·0.2 | 149 | ·--·used·0.255174s·(cpu);·0.255104s·(thread);·0s·(gc) |
| 150 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 150 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 151 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- | 151 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 152 | ···········2222549728809984000000············12700284164628480000000········· | 152 | ···········2222549728809984000000············12700284164628480000000········· |
| 153 | ·····------------------------------------------------------------------------ | 153 | ·····------------------------------------------------------------------------ |
| 154 | ·····348237304382147063838108483692249·3·2·· | 154 | ·····348237304382147063838108483692249·3·2·· |
| 155 | ·····---------------------------------a·b··- | 155 | ·····---------------------------------a·b··- |
| Offset 165, 15 lines modified | Offset 165, 15 lines modified | ||
| 165 | ·····-------------------------------a*b··-·---------------------------b | 165 | ·····-------------------------------a*b··-·---------------------------b |
| 166 | ··········1119954511872000000000················895963609497600000 | 166 | ··········1119954511872000000000················895963609497600000 |
| 167 | o5·:·QQ[a..b]</code></pre> | 167 | o5·:·QQ[a..b]</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·resultant(F,Algorithm=>"Macaulay") | 170 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·resultant(F,Algorithm=>"Macaulay") |
| 171 | ·--·used·0. | 171 | ·--·used·0.56673s·(cpu);·0.532349s·(thread);·0s·(gc) |
| 172 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 172 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 173 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- | 173 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 174 | ···········2222549728809984000000············12700284164628480000000········· | 174 | ···········2222549728809984000000············12700284164628480000000········· |
| 175 | ·····------------------------------------------------------------------------ | 175 | ·····------------------------------------------------------------------------ |
| 176 | ·····348237304382147063838108483692249·3·2·· | 176 | ·····348237304382147063838108483692249·3·2·· |
| 177 | ·····---------------------------------a·b··- | 177 | ·····---------------------------------a·b··- |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 59 | ·····------------------------------------------------------------------------ | 59 | ·····------------------------------------------------------------------------ |
| 60 | ·····3·····2····9····7·····2····9········3·······1····8····4 | 60 | ·····3·····2····9····7·····2····9········3·······1····8····4 |
| 61 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} | 61 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} |
| 62 | ·····4··········8····8··········7················4····3····5 | 62 | ·····4··········8····8··········7················4····3····5 |
| 63 | o2·:·List | 63 | o2·:·List |
| 64 | i3·:·time·resultant(F,Algorithm=>"Poisson2") | 64 | i3·:·time·resultant(F,Algorithm=>"Poisson2") |
| 65 | ·--·used·0. | 65 | ·--·used·0.22611s·(cpu);·0.140924s·(thread);·0s·(gc) |
| 66 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 | 66 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 |
| 67 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- | 67 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 68 | ···········2222549728809984000000············12700284164628480000000 | 68 | ···········2222549728809984000000············12700284164628480000000 |
| 69 | ·····------------------------------------------------------------------------ | 69 | ·····------------------------------------------------------------------------ |
| 70 | ·····348237304382147063838108483692249·3·2 | 70 | ·····348237304382147063838108483692249·3·2 |
| 71 | ·····---------------------------------a·b··- | 71 | ·····---------------------------------a·b··- |
| Offset 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | ·····------------------------------------------------------------------------ | 79 | ·····------------------------------------------------------------------------ |
| 80 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 | 80 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 |
| 81 | ·····-------------------------------a*b··-·---------------------------b | 81 | ·····-------------------------------a*b··-·---------------------------b |
| 82 | ··········1119954511872000000000················895963609497600000 | 82 | ··········1119954511872000000000················895963609497600000 |
| 83 | o3·:·QQ[a..b] | 83 | o3·:·QQ[a..b] |
| 84 | i4·:·time·resultant(F,Algorithm=>"Macaulay2") | 84 | i4·:·time·resultant(F,Algorithm=>"Macaulay2") |
| 85 | ·--·used·0. | 85 | ·--·used·0.110768s·(cpu);·0.0687476s·(thread);·0s·(gc) |
| 86 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 | 86 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 |
| 87 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- | 87 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 88 | ···········2222549728809984000000············12700284164628480000000 | 88 | ···········2222549728809984000000············12700284164628480000000 |
| 89 | ·····------------------------------------------------------------------------ | 89 | ·····------------------------------------------------------------------------ |
| 90 | ·····348237304382147063838108483692249·3·2 | 90 | ·····348237304382147063838108483692249·3·2 |
| 91 | ·····---------------------------------a·b··- | 91 | ·····---------------------------------a·b··- |
| Offset 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 | 100 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 |
| 101 | ·····-------------------------------a*b··-·---------------------------b | 101 | ·····-------------------------------a*b··-·---------------------------b |
| 102 | ··········1119954511872000000000················895963609497600000 | 102 | ··········1119954511872000000000················895963609497600000 |
| 103 | o4·:·QQ[a..b] | 103 | o4·:·QQ[a..b] |
| 104 | i5·:·time·resultant(F,Algorithm=>"Poisson") | 104 | i5·:·time·resultant(F,Algorithm=>"Poisson") |
| 105 | ·--·used·0.2 | 105 | ·--·used·0.255174s·(cpu);·0.255104s·(thread);·0s·(gc) |
| 106 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 | 106 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 |
| 107 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- | 107 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 108 | ···········2222549728809984000000············12700284164628480000000 | 108 | ···········2222549728809984000000············12700284164628480000000 |
| 109 | ·····------------------------------------------------------------------------ | 109 | ·····------------------------------------------------------------------------ |
| 110 | ·····348237304382147063838108483692249·3·2 | 110 | ·····348237304382147063838108483692249·3·2 |
| 111 | ·····---------------------------------a·b··- | 111 | ·····---------------------------------a·b··- |
| Offset 119, 15 lines modified | Offset 119, 15 lines modified | ||
| 119 | ·····------------------------------------------------------------------------ | 119 | ·····------------------------------------------------------------------------ |
| 120 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 | 120 | ·····1146977327343523453866040839029···4···194441910898734675845094443·5 |
| 121 | ·····-------------------------------a*b··-·---------------------------b | 121 | ·····-------------------------------a*b··-·---------------------------b |
| 122 | ··········1119954511872000000000················895963609497600000 | 122 | ··········1119954511872000000000················895963609497600000 |
| 123 | o5·:·QQ[a..b] | 123 | o5·:·QQ[a..b] |
| 124 | i6·:·time·resultant(F,Algorithm=>"Macaulay") | 124 | i6·:·time·resultant(F,Algorithm=>"Macaulay") |
| 125 | ·--·used·0. | 125 | ·--·used·0.56673s·(cpu);·0.532349s·(thread);·0s·(gc) |
| 126 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 | 126 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4 |
| 127 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- | 127 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 128 | ···········2222549728809984000000············12700284164628480000000 | 128 | ···········2222549728809984000000············12700284164628480000000 |
| 129 | ·····------------------------------------------------------------------------ | 129 | ·····------------------------------------------------------------------------ |
| 130 | ·····348237304382147063838108483692249·3·2 | 130 | ·····348237304382147063838108483692249·3·2 |
| 131 | ·····---------------------------------a·b··- | 131 | ·····---------------------------------a·b··- |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ·······2···············2····························3······2·········4 | 90 | ·······2···············2····························3······2·········4 |
| 91 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} | 91 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} |
| 92 | o2·:·List</code></pre> | 92 | o2·:·List</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant·F | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant·F |
| 96 | ·--·used·0.0 | 96 | ·--·used·0.0239607s·(cpu);·0.024181s·(thread);·0s·(gc) |
| 97 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 | 97 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 |
| 98 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u· | 98 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u· |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ··············6·7··········5·8·······11··········10·2·········9·3·· | 100 | ··············6·7··········5·8·······11··········10·2·········9·3·· |
| 101 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ | 101 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ |
| 102 | ·····------------------------------------------------------------------------ | 102 | ·····------------------------------------------------------------------------ |
| Offset 149, 15 lines modified | Offset 149, 15 lines modified | ||
| 149 | ·····+·c·x·} | 149 | ·····+·c·x·} |
| 150 | ········9·2 | 150 | ········9·2 |
| 151 | o4·:·List</code></pre> | 151 | o4·:·List</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant·F | 154 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant·F |
| 155 | ·--·used· | 155 | ·--·used·2.15564s·(cpu);·1.77722s·(thread);·0s·(gc) |
| 156 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2·· | 156 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2·· |
| 157 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- | 157 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- |
| 158 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0·· | 158 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0·· |
| 159 | ·····------------------------------------------------------------------------ | 159 | ·····------------------------------------------------------------------------ |
| 160 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2·· | 160 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2·· |
| 161 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- | 161 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- |
| Offset 1780, 15 lines modified | Offset 1780, 15 lines modified | ||
| 1780 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} | 1780 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 1781 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 1781 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 1782 | o6·:·List</code></pre> | 1782 | o6·:·List</code></pre> |
| 1783 | </td>··········</tr> | 1783 | </td>··········</tr> |
| 1784 | ··········<tr> | 1784 | ··········<tr> |
| 1785 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·#·terms·resultant·F | 1785 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·#·terms·resultant·F |
| 1786 | ·--·used·0. | 1786 | ·--·used·0.4605s·(cpu);·0.381155s·(thread);·0s·(gc) |
| 1787 | o7·=·21894</code></pre> | 1787 | o7·=·21894</code></pre> |
| 1788 | </td>··········</tr> | 1788 | </td>··········</tr> |
| 1789 | ········</table> | 1789 | ········</table> |
| 1790 | ······</div> | 1790 | ······</div> |
| 1791 | ······<div> | 1791 | ······<div> |
| 1792 | ········<h2>See·also</h2> | 1792 | ········<h2>See·also</h2> |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | i2·:·F·=·{x^2+3*t*y*z-u*z^2,(t+3*u-1)*x-y,-t*x*y^3+t*x^2*y*z+u*z^4} | 33 | i2·:·F·=·{x^2+3*t*y*z-u*z^2,(t+3*u-1)*x-y,-t*x*y^3+t*x^2*y*z+u*z^4} |
| 34 | ·······2···············2····························3······2·········4 | 34 | ·······2···············2····························3······2·········4 |
| 35 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} | 35 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} |
| 36 | o2·:·List | 36 | o2·:·List |
| 37 | i3·:·time·resultant·F | 37 | i3·:·time·resultant·F |
| 38 | ·--·used·0.0 | 38 | ·--·used·0.0239607s·(cpu);·0.024181s·(thread);·0s·(gc) |
| 39 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 | 39 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 |
| 40 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u | 40 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u |
| 41 | ·····------------------------------------------------------------------------ | 41 | ·····------------------------------------------------------------------------ |
| 42 | ··············6·7··········5·8·······11··········10·2·········9·3 | 42 | ··············6·7··········5·8·······11··········10·2·········9·3 |
| 43 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ | 43 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ |
| 44 | ·····------------------------------------------------------------------------ | 44 | ·····------------------------------------------------------------------------ |
| Offset 87, 15 lines modified | Offset 87, 15 lines modified | ||
| 87 | ·····------------------------------------------------------------------------ | 87 | ·····------------------------------------------------------------------------ |
| 88 | ··········3 | 88 | ··········3 |
| 89 | ·····+·c·x·} | 89 | ·····+·c·x·} |
| 90 | ········9·2 | 90 | ········9·2 |
| 91 | o4·:·List | 91 | o4·:·List |
| 92 | i5·:·time·resultant·F | 92 | i5·:·time·resultant·F |
| 93 | ·--·used· | 93 | ·--·used·2.15564s·(cpu);·1.77722s·(thread);·0s·(gc) |
| 94 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2 | 94 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2 |
| 95 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- | 95 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- |
| 96 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0 | 96 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0 |
| 97 | ·····------------------------------------------------------------------------ | 97 | ·····------------------------------------------------------------------------ |
| 98 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2 | 98 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2 |
| 99 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- | 99 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- |
| Offset 1713, 15 lines modified | Offset 1713, 15 lines modified | ||
| 1713 | ·····------------------------------------------------------------------------ | 1713 | ·····------------------------------------------------------------------------ |
| 1714 | ··························2·····2···············2························2 | 1714 | ··························2·····2···············2························2 |
| 1715 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} | 1715 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 1716 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 1716 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 1717 | o6·:·List | 1717 | o6·:·List |
| 1718 | i7·:·time·#·terms·resultant·F | 1718 | i7·:·time·#·terms·resultant·F |
| 1719 | ·--·used·0. | 1719 | ·--·used·0.4605s·(cpu);·0.381155s·(thread);·0s·(gc) |
| 1720 | o7·=·21894 | 1720 | o7·=·21894 |
| 1721 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 1721 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 1722 | ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety | 1722 | ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety |
| 1723 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8R_\x8i_\x8n_\x8g_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8) | 1723 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8R_\x8i_\x8n_\x8g_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8) |
| 1724 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 1724 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 1725 | ····*·resultant(List) | 1725 | ····*·resultant(List) |
| Offset 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | o2·:·Ideal·of·QQ[p·..p·] | 102 | o2·:·Ideal·of·QQ[p·..p·] |
| 103 | ··················0···4</code></pre> | 103 | ··················0···4</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) | 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) |
| 107 | ·····time·tangentialChowForm(S,0) | 107 | ·····time·tangentialChowForm(S,0) |
| 108 | ·--·used·0.0 | 108 | ·--·used·0.0944402s·(cpu);·0.0401727s·(thread);·0s·(gc) |
| 109 | ······2·······················································2········ | 109 | ······2·······················································2········ |
| 110 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ | 110 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ |
| 111 | ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4·· | 111 | ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4·· |
| 112 | ·····------------------------------------------------------------------------ | 112 | ·····------------------------------------------------------------------------ |
| 113 | ······2 | 113 | ······2 |
| 114 | ·····p···p····-·2p···p···p····-·p···p···p | 114 | ·····p···p····-·2p···p···p····-·p···p···p |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | o3·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------- | 121 | o3·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 122 | ·····(p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···) | 122 | ·····(p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p···p···) |
| 123 | ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3</code></pre> | 123 | ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4····0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1·2,3</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) | 126 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) |
| 127 | ·····time·tangentialChowForm(S,1) | 127 | ·····time·tangentialChowForm(S,1) |
| 128 | ·--·used·0.0 | 128 | ·--·used·0.0646915s·(cpu);·0.0644347s·(thread);·0s·(gc) |
| 129 | ······2·····2········2·····2···············3········2·····2······ | 129 | ······2·····2········2·····2···············3········2·····2······ |
| 130 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- | 130 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- |
| 131 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4·· | 131 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4·· |
| 132 | ·····------------------------------------------------------------------------ | 132 | ·····------------------------------------------------------------------------ |
| 133 | ·············3·········3···············3············ | 133 | ·············3·········3···············3············ |
| 134 | ·····4p·····p······-·4p·····p······-·2p·····p······+ | 134 | ·····4p·····p······-·4p·····p······-·2p·····p······+ |
| Offset 164, 39 lines modified | Offset 164, 39 lines modified | ||
| 164 | o4·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 164 | o4·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 165 | ·····(p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····) | 165 | ·····(p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····) |
| 166 | ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre> | 166 | ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4····0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3·1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S) | 169 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S) |
| 170 | ·····time·tangentialChowForm(S,2) | 170 | ·····time·tangentialChowForm(S,2) |
| 171 | ·--·used·0.0 | 171 | ·--·used·0.0425136s·(cpu);·0.0423079s·(thread);·0s·(gc) |
| 172 | ··············2·············································2 | 172 | ··············2·············································2 |
| 173 | o5·=·p·······p········-·p·······p·······p········+·p·······p | 173 | o5·=·p·······p········-·p·······p·······p········+·p·······p |
| 174 | ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4 | 174 | ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4 |
| 175 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] | 175 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] |
| 176 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4</code></pre> | 176 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ··········<tr> | 178 | ··········<tr> |
| 179 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing | 179 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing |
| 180 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) | 180 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) |
| 181 | ·--·used·0. | 181 | ·--·used·0.103601s·(cpu);·0.0593876s·(thread);·0s·(gc) |
| 182 | ············2···············2 | 182 | ············2···············2 |
| 183 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) | 183 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) |
| 184 | ············1·2····0·1·3····0·4 | 184 | ············1·2····0·1·3····0·4 |
| 185 | o6·:·Ideal·of·QQ[p·..p·] | 185 | o6·:·Ideal·of·QQ[p·..p·] |
| 186 | ··················0···4</code></pre> | 186 | ··················0···4</code></pre> |
| 187 | </td>··········</tr> | 187 | </td>··········</tr> |
| 188 | ··········<tr> | 188 | ··········<tr> |
| 189 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·we·then·can·recover·S | 189 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·we·then·can·recover·S |
| 190 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) | 190 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) |
| 191 | ·--·used·0.102 | 191 | ·--·used·0.150275s·(cpu);·0.110184s·(thread);·0s·(gc)</code></pre> |
| 192 | </td>··········</tr> | 192 | </td>··········</tr> |
| 193 | ········</table> | 193 | ········</table> |
| 194 | ······</div> | 194 | ······</div> |
| 195 | ······<div> | 195 | ······<div> |
| 196 | ········<h2>See·also</h2> | 196 | ········<h2>See·also</h2> |
| 197 | ········<ul> | 197 | ········<ul> |
| 198 | ··········<li> | 198 | ··········<li> |
| Offset 64, 15 lines modified | Offset 64, 15 lines modified | ||
| 64 | o2·=·ideal·(-·p·p··+·p·p·,·-·p·p··+·p·p·,·-·p··+·p·p·) | 64 | o2·=·ideal·(-·p·p··+·p·p·,·-·p·p··+·p·p·,·-·p··+·p·p·) |
| 65 | ···············1·2····0·3·····1·3····0·4·····3····2·4 | 65 | ···············1·2····0·3·····1·3····0·4·····3····2·4 |
| 66 | o2·:·Ideal·of·QQ[p·..p·] | 66 | o2·:·Ideal·of·QQ[p·..p·] |
| 67 | ··················0···4 | 67 | ··················0···4 |
| 68 | i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) | 68 | i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) |
| 69 | ·····time·tangentialChowForm(S,0) | 69 | ·····time·tangentialChowForm(S,0) |
| 70 | ·--·used·0.0 | 70 | ·--·used·0.0944402s·(cpu);·0.0401727s·(thread);·0s·(gc) |
| 71 | ······2·······················································2 | 71 | ······2·······················································2 |
| 72 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ | 72 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ |
| 73 | ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4 | 73 | ······1,3·2,3····1,2·1,3·2,4····0,3·1,3·2,4····0,2·1,4·2,4····1,2·3,4 |
| 74 | ·····------------------------------------------------------------------------ | 74 | ·····------------------------------------------------------------------------ |
| 75 | ······2 | 75 | ······2 |
| 76 | ·····p···p····-·2p···p···p····-·p···p···p | 76 | ·····p···p····-·2p···p···p····-·p···p···p |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | -·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p | 89 | -·p···p····+·p···p···,·p···p····-·p···p····+·p···p···,·p···p····-·p···p····+·p |
| 90 | p···) | 90 | p···) |
| 91 | ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4 | 91 | ·······2,3·1,4····1,3·2,4····1,2·3,4···2,3·0,4····0,3·2,4····0,2·3,4···1,3·0,4 |
| 92 | 0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1 | 92 | 0,3·1,4····0,1·3,4···1,2·0,4····0,2·1,4····0,1·2,4···1,2·0,3····0,2·1,3····0,1 |
| 93 | 2,3 | 93 | 2,3 |
| 94 | i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) | 94 | i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) |
| 95 | ·····time·tangentialChowForm(S,1) | 95 | ·····time·tangentialChowForm(S,1) |
| 96 | ·--·used·0.0 | 96 | ·--·used·0.0646915s·(cpu);·0.0644347s·(thread);·0s·(gc) |
| 97 | ······2·····2········2·····2···············3········2·····2 | 97 | ······2·····2········2·····2···············3········2·····2 |
| 98 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- | 98 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- |
| 99 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4 | 99 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4 |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ·············3·········3···············3 | 101 | ·············3·········3···············3 |
| 102 | ·····4p·····p······-·4p·····p······-·2p·····p······+ | 102 | ·····4p·····p······-·4p·····p······-·2p·····p······+ |
| Offset 139, 35 lines modified | Offset 139, 35 lines modified | ||
| 139 | p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····) | 139 | p······+·p·····p·····,·p·····p······-·p·····p······+·p·····p·····) |
| 140 | ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4 | 140 | ·······1,2,4·0,3,4····0,2,4·1,3,4····0,1,4·2,3,4···1,2,3·0,3,4····0,2,3·1,3,4 |
| 141 | 0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3 | 141 | 0,1,3·2,3,4···1,2,3·0,2,4····0,2,3·1,2,4····0,1,2·2,3,4···1,2,3·0,1,4····0,1,3 |
| 142 | 1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 | 142 | 1,2,4····0,1,2·1,3,4···0,2,3·0,1,4····0,1,3·0,2,4····0,1,2·0,3,4 |
| 143 | i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent | 143 | i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent |
| 144 | hyperplanes·to·S) | 144 | hyperplanes·to·S) |
| 145 | ·····time·tangentialChowForm(S,2) | 145 | ·····time·tangentialChowForm(S,2) |
| 146 | ·--·used·0.0 | 146 | ·--·used·0.0425136s·(cpu);·0.0423079s·(thread);·0s·(gc) |
| 147 | ··············2·············································2 | 147 | ··············2·············································2 |
| 148 | o5·=·p·······p········-·p·······p·······p········+·p·······p | 148 | o5·=·p·······p········-·p·······p·······p········+·p·······p |
| 149 | ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4 | 149 | ······0,1,3,4·0,2,3,4····0,1,2,4·0,2,3,4·1,2,3,4····0,1,2,3·1,2,3,4 |
| 150 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] | 150 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] |
| 151 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4 | 151 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4 |
| 152 | i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing | 152 | i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing |
| 153 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) | 153 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) |
| 154 | ·--·used·0. | 154 | ·--·used·0.103601s·(cpu);·0.0593876s·(thread);·0s·(gc) |
| 155 | ············2···············2 | 155 | ············2···············2 |
| 156 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) | 156 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) |
| 157 | ············1·2····0·1·3····0·4 | 157 | ············1·2····0·1·3····0·4 |
| 158 | o6·:·Ideal·of·QQ[p·..p·] | 158 | o6·:·Ideal·of·QQ[p·..p·] |
| 159 | ··················0···4 | 159 | ··················0···4 |
| 160 | i7·:·--·we·then·can·recover·S | 160 | i7·:·--·we·then·can·recover·S |
| 161 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) | 161 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) |
| 162 | ·--·used·0.102 | 162 | ·--·used·0.150275s·(cpu);·0.110184s·(thread);·0s·(gc) |
| 163 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 163 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 164 | ····*·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·--·whether·a·hypersurface·of·a·Grassmannian·is·a·tangential | 164 | ····*·_\x8i_\x8s_\x8C_\x8o_\x8i_\x8s_\x8o_\x8t_\x8r_\x8o_\x8p_\x8i_\x8c·--·whether·a·hypersurface·of·a·Grassmannian·is·a·tangential |
| 165 | ······Chow·form | 165 | ······Chow·form |
| 166 | ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety | 166 | ····*·_\x8c_\x8h_\x8o_\x8w_\x8F_\x8o_\x8r_\x8m·--·Chow·form·of·a·projective·variety |
| 167 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8ta\x8an\x8ng\x8ge\x8en\x8nt\x8ti\x8ia\x8al\x8lC\x8Ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8* | 167 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8ta\x8an\x8ng\x8ge\x8en\x8nt\x8ti\x8ia\x8al\x8lC\x8Ch\x8ho\x8ow\x8wF\x8Fo\x8or\x8rm\x8m:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 168 | ····*·tangentialChowForm(Ideal,ZZ) | 168 | ····*·tangentialChowForm(Ideal,ZZ) |
| 169 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 169 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | aXNFeHRlcm5hbE0yUGFyZW50 | 8 | aXNFeHRlcm5hbE0yUGFyZW50 |
| 9 | #:len=1043 | 9 | #:len=1043 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiaW5kaWNhdGUgaWYgdGhpcyBwcm9jZXNz | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiaW5kaWNhdGUgaWYgdGhpcyBwcm9jZXNz |
| 11 | IGlzIGEgcGFyZW50IHByb2Nlc3Mgb3Igbm90IiwgImxpbmVudW0iID0+IDg5NCwgImZpbGVuYW1l | 11 | IGlzIGEgcGFyZW50IHByb2Nlc3Mgb3Igbm90IiwgImxpbmVudW0iID0+IDg5NCwgImZpbGVuYW1l |
| Offset 1, 19 lines modified | Offset 1, 24 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1332396467656 | 1 | --·-*-·M2-comint·-*-·hash:·1332396467656 |
| 2 | i1·:·run("ulimit·-a") | 2 | i1·:·run("ulimit·-a") |
| 3 | time(seconds)········700 | ||
| 4 | file(blocks)·········unlimited | ||
| 5 | data(kbytes)·········unlimited | ||
| 6 | stack(kbytes)········8192 | ||
| 7 | coredump(blocks)·····0 | ||
| 8 | memory(kbytes)·······850000 | ||
| 9 | locked·memory(kbytes)·3077552 | ||
| 10 | process··············96081 | ||
| 11 | nofiles··············512 | ||
| 12 | 3 | real-time·non-blocking·time··(microseconds,·-R)·unlimited | |
| 4 | core·file·size··············(blocks,·-c)·0 | ||
| 5 | data·seg·size···············(kbytes,·-d)·unlimited | ||
| 6 | scheduling·priority·················(-e)·0 | ||
| 7 | file·size···················(blocks,·-f)·unlimited | ||
| 8 | pending·signals·····················(-i)·95991 | ||
| 9 | max·locked·memory···········(kbytes,·-l)·3076856 | ||
| 10 | max·memory·size·············(kbytes,·-m)·850000 | ||
| 11 | open·files··························(-n)·512 | ||
| 12 | pipe·size················(512·bytes,·-p)·8 | ||
| 13 | POSIX·message·queues·········(bytes,·-q)·819200 | ||
| 14 | real-time·priority··················(-r)·0 | ||
| 15 | stack·size··················(kbytes,·-s)·8192 | ||
| 16 | cpu·time···················(seconds,·-t)·700 | ||
| 17 | max·user·processes··················(-u)·95991 | ||
| 18 | virtual·memory··············(kbytes,·-v)·unlimited | ||
| 13 | locks················unlimited | 19 | file·locks··························(-x)·unlimited |
| 14 | rtprio···············0 | ||
| 15 | o1·=·0 | 20 | o1·=·0 |
| 16 | i2·:· | 21 | i2·:· |
| Offset 1, 23 lines modified | Offset 1, 23 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·2927978066455787395 | 1 | --·-*-·M2-comint·-*-·hash:·2927978066455787395 |
| 2 | i1·:·fn=temporaryFileName()|".m2" | 2 | i1·:·fn=temporaryFileName()|".m2" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-3676504-0/0.m2 |
| 4 | i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl; | 4 | i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl; |
| 5 | i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl; | 5 | i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl; |
| 6 | i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime();·while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl; | 6 | i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime();·while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl; |
| 7 | i5·:·fn<<flush; | 7 | i5·:·fn<<flush; |
| 8 | i6·:·h=runExternalM2(fn,"square",(4)); | 8 | i6·:·h=runExternalM2(fn,"square",(4)); |
| 9 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 9 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/1.m2"·>"/tmp/M2-3676504-0/1.out"·2>&1·)) |
| 10 | Finished·running. | 10 | Finished·running. |
| 11 | i7·:·h | 11 | i7·:·h |
| 12 | o7·=·HashTable{"answer·file"·=>·null} | 12 | o7·=·HashTable{"answer·file"·=>·null} |
| 13 | ···············"exit·code"·=>·0 | 13 | ···············"exit·code"·=>·0 |
| 14 | ···············"output·file"·=>·null | 14 | ···············"output·file"·=>·null |
| Offset 33, 23 lines modified | Offset 33, 23 lines modified | ||
| 33 | o8·=·true | 33 | o8·=·true |
| 34 | i9·:·h#"exit·code"===0 | 34 | i9·:·h#"exit·code"===0 |
| 35 | o9·=·true | 35 | o9·=·true |
| 36 | i10·:·h=runExternalM2(fn,"justexit",()); | 36 | i10·:·h=runExternalM2(fn,"justexit",()); |
| 37 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 37 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/2.m2"·>"/tmp/M2-3676504-0/2.out"·2>&1·)) |
| 38 | Finished·running. | 38 | Finished·running. |
| 39 | RunExternalM2:·expected·answer·file·does·not·exist | 39 | RunExternalM2:·expected·answer·file·does·not·exist |
| 40 | i11·:·h | 40 | i11·:·h |
| 41 | o11·=·HashTable{"answer·file"·=>·/tmp/M2- | 41 | o11·=·HashTable{"answer·file"·=>·/tmp/M2-3676504-0/2.ans} |
| 42 | ················"exit·code"·=>·27 | 42 | ················"exit·code"·=>·27 |
| 43 | ················"output·file"·=>·/tmp/M2- | 43 | ················"output·file"·=>·/tmp/M2-3676504-0/2.out |
| 44 | ················"return·code"·=>·6912 | 44 | ················"return·code"·=>·6912 |
| 45 | ················"statistics"·=>·null | 45 | ················"statistics"·=>·null |
| 46 | ················"time·used"·=>·1 | 46 | ················"time·used"·=>·1 |
| 47 | ················value·=>·null | 47 | ················value·=>·null |
| 48 | o11·:·HashTable | 48 | o11·:·HashTable |
| Offset 58, 80 lines modified | Offset 58, 79 lines modified | ||
| 58 | o12·=·true | 58 | o12·=·true |
| 59 | i13·:·fileExists(h#"answer·file") | 59 | i13·:·fileExists(h#"answer·file") |
| 60 | o13·=·false | 60 | o13·=·false |
| 61 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); | 61 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); |
| 62 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 62 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/3.m2"·>"/tmp/M2-3676504-0/3.out"·2>&1·)) |
| 63 | Killed | ||
| 64 | Finished·running. | 63 | Finished·running. |
| 65 | RunExternalM2:·expected·answer·file·does·not·exist | 64 | RunExternalM2:·expected·answer·file·does·not·exist |
| 66 | i15·:·h | 65 | i15·:·h |
| 67 | o15·=·HashTable{"answer·file"·=>·/tmp/M2- | 66 | o15·=·HashTable{"answer·file"·=>·/tmp/M2-3676504-0/3.ans} |
| 68 | ················"exit·code"·=>·0 | 67 | ················"exit·code"·=>·0 |
| 69 | ················"output·file"·=>·/tmp/M2- | 68 | ················"output·file"·=>·/tmp/M2-3676504-0/3.out |
| 70 | ················"return·code"·=>·9 | 69 | ················"return·code"·=>·9 |
| 71 | ················"statistics"·=>·null | 70 | ················"statistics"·=>·null |
| 72 | ················"time·used"·=>· | 71 | ················"time·used"·=>·2 |
| 73 | ················value·=>·null | 72 | ················value·=>·null |
| 74 | o15·:·HashTable | 73 | o15·:·HashTable |
| 75 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") | 74 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") |
| 76 | o16·=· | 75 | o16·=· |
| 77 | ······i1·:·--·Script·/tmp/M2- | 76 | ······i1·:·--·Script·/tmp/M2-3676504-0/3.m2·automatically·generated·by·RunExternalM2 |
| 78 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); | 77 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); |
| 79 | ······i2·:·load·"/tmp/M2- | 78 | ······i2·:·load·"/tmp/M2-3676504-0/0.m2"; |
| 80 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2- | 79 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-3676504-0/3.ans",spin·(10)); |
| 81 | ······Spinning!! | 80 | ······Spinning!! |
| 82 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file") | 81 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file") |
| 83 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); | 82 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); |
| 84 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 83 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/4.m2"·>"/tmp/M2-3676504-0/4.out"·2>&1')·>"/tmp/M2-3676504-0/4.stat"·2>&1·)) |
| 85 | Finished·running. | 84 | Finished·running. |
| 86 | i19·:·h#"statistics" | 85 | i19·:·h#"statistics" |
| 87 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 86 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/4.m2"·>"/tmp/M2-3676504-0/4.out"·2>&1" |
| 88 | ··············User·time·(seconds):·4. | 87 | ··············User·time·(seconds):·4.76 |
| 89 | ··············System·time·(seconds):·0. | 88 | ··············System·time·(seconds):·0.20 |
| 90 | ··············Percent·of·CPU·this·job·got:· | 89 | ··············Percent·of·CPU·this·job·got:·76% |
| 91 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:0 | 90 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:06.45 |
| 92 | ··············Average·shared·text·size·(kbytes):·0 | 91 | ··············Average·shared·text·size·(kbytes):·0 |
| 93 | ··············Average·unshared·data·size·(kbytes):·0 | 92 | ··············Average·unshared·data·size·(kbytes):·0 |
| 94 | ··············Average·stack·size·(kbytes):·0 | 93 | ··············Average·stack·size·(kbytes):·0 |
| 95 | ··············Average·total·size·(kbytes):·0 | 94 | ··············Average·total·size·(kbytes):·0 |
| 96 | ··············Maximum·resident·set·size·(kbytes):· | 95 | ··············Maximum·resident·set·size·(kbytes):·298472 |
| 97 | ··············Average·resident·set·size·(kbytes):·0 | 96 | ··············Average·resident·set·size·(kbytes):·0 |
| 98 | ··············Major·(requiring·I/O)·page·faults:·0 | 97 | ··············Major·(requiring·I/O)·page·faults:·0 |
| 99 | ··············Minor·(reclaiming·a·frame)·page·faults:· | 98 | ··············Minor·(reclaiming·a·frame)·page·faults:·31495 |
| 100 | ··············Voluntary·context·switches:· | 99 | ··············Voluntary·context·switches:·8898 |
| 101 | ··············Involuntary·context·switches:· | 100 | ··············Involuntary·context·switches:·3052 |
| 102 | ··············Swaps:·0 | 101 | ··············Swaps:·0 |
| 103 | ··············File·system·inputs:·0 | 102 | ··············File·system·inputs:·0 |
| 104 | ··············File·system·outputs:· | 103 | ··············File·system·outputs:·24 |
| 105 | ··············Socket·messages·sent:·0 | 104 | ··············Socket·messages·sent:·0 |
| 106 | ··············Socket·messages·received:·0 | 105 | ··············Socket·messages·received:·0 |
| 107 | ··············Signals·delivered:·0 | 106 | ··············Signals·delivered:·0 |
| 108 | ··············Page·size·(bytes):·4096 | 107 | ··············Page·size·(bytes):·4096 |
| 109 | ··············Exit·status:·0 | 108 | ··············Exit·status:·0 |
| 110 | i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///; | 109 | i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///; |
| 111 | i21·:·(runExternalM2(fn,identity,v))#value===v | 110 | i21·:·(runExternalM2(fn,identity,v))#value===v |
| 112 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 111 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/6.m2"·>"/tmp/M2-3676504-0/6.out"·2>&1·)) |
| 113 | Finished·running. | 112 | Finished·running. |
| 114 | o21·=·true | 113 | o21·=·true |
| 115 | i22·:·R=QQ[x,y]; | 114 | i22·:·R=QQ[x,y]; |
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| Offset 60, 26 lines modified | Offset 60, 31 lines modified | ||
| 60 | ········<div> | 60 | ········<div> |
| 61 | ··········<p>which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits·unchanged.</p> | 61 | ··········<p>which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits·unchanged.</p> |
| 62 | ··········<p><b>From·within·Macaulay2</b>,·you·can·<b>view</b>·the·ulimits·currently·available·to·the·Macaulay2·process·by·using·the·<a·title="run·an·external·command"·href="../../Macaulay2Doc/html/_run.html">run</a>·command:</p> | 62 | ··········<p><b>From·within·Macaulay2</b>,·you·can·<b>view</b>·the·ulimits·currently·available·to·the·Macaulay2·process·by·using·the·<a·title="run·an·external·command"·href="../../Macaulay2Doc/html/_run.html">run</a>·command:</p> |
| 63 | ········</div> | 63 | ········</div> |
| 64 | ········<table·class="examples"> | 64 | ········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·run("ulimit·-a") | 66 | <td>··············<pre><code·class="language-macaulay2">i1·:·run("ulimit·-a") |
| 67 | time(seconds)········700 | ||
| 68 | file(blocks)·········unlimited | ||
| 69 | data(kbytes)·········unlimited | ||
| 70 | stack(kbytes)········8192 | ||
| 71 | coredump(blocks)·····0 | ||
| 72 | memory(kbytes)·······850000 | ||
| 73 | locked·memory(kbytes)·3077552 | ||
| 74 | process··············96081 | ||
| 75 | nofiles··············512 | ||
| 76 | 67 | real-time·non-blocking·time··(microseconds,·-R)·unlimited | |
| 68 | core·file·size··············(blocks,·-c)·0 | ||
| 69 | data·seg·size···············(kbytes,·-d)·unlimited | ||
| 70 | scheduling·priority·················(-e)·0 | ||
| 71 | file·size···················(blocks,·-f)·unlimited | ||
| 72 | pending·signals·····················(-i)·95991 | ||
| 73 | max·locked·memory···········(kbytes,·-l)·3076856 | ||
| 74 | max·memory·size·············(kbytes,·-m)·850000 | ||
| 75 | open·files··························(-n)·512 | ||
| 76 | pipe·size················(512·bytes,·-p)·8 | ||
| 77 | POSIX·message·queues·········(bytes,·-q)·819200 | ||
| 78 | real-time·priority··················(-r)·0 | ||
| 79 | stack·size··················(kbytes,·-s)·8192 | ||
| 80 | cpu·time···················(seconds,·-t)·700 | ||
| 81 | max·user·processes··················(-u)·95991 | ||
| 82 | virtual·memory··············(kbytes,·-v)·unlimited | ||
| 77 | locks················unlimited | 83 | file·locks··························(-x)·unlimited |
| 78 | rtprio···············0 | ||
| 79 | o1·=·0</code></pre> | 84 | o1·=·0</code></pre> |
| 80 | </td>··········</tr> | 85 | </td>··········</tr> |
| 81 | ········</table> | 86 | ········</table> |
| 82 | ········<div> | 87 | ········<div> |
| 83 | ··········<p>This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case·provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this·should·be·the·same·as·the·ulimits·of·Macaulay2·itself.</p> | 88 | ··········<p>This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case·provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this·should·be·the·same·as·the·ulimits·of·Macaulay2·itself.</p> |
| 84 | ··········<p><b>From·within·Macaulay2</b>,·it·is·not·possible·to·set·ulimits·on·the·current·Macaulay2·process·because·Macaulay2·does·not·provide·access·to·the·<span·class="tt">setrlimit</span>·system·call·(other·than·the·<a·href="../../Macaulay2Doc/html/_limit__Files.html">limitFiles</a>·and·<a·href="../../Macaulay2Doc/html/_limit__Processes.html">limitProcesses</a>·commands).·However,·it·is·possible·to·<b>set</b>·ulimits·on·child·Macaulay2·processes·that·are·started·by·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">runExternalM2</a>,·by·using·the·<a·title="a·way·to·impose·resource·limits"·href="___Pre__Run__Script.html">PreRunScript</a>·option·of·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">runExternalM2</a>.</p> | 89 | ··········<p><b>From·within·Macaulay2</b>,·it·is·not·possible·to·set·ulimits·on·the·current·Macaulay2·process·because·Macaulay2·does·not·provide·access·to·the·<span·class="tt">setrlimit</span>·system·call·(other·than·the·<a·href="../../Macaulay2Doc/html/_limit__Files.html">limitFiles</a>·and·<a·href="../../Macaulay2Doc/html/_limit__Processes.html">limitProcesses</a>·commands).·However,·it·is·possible·to·<b>set</b>·ulimits·on·child·Macaulay2·processes·that·are·started·by·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">runExternalM2</a>,·by·using·the·<a·title="a·way·to·impose·resource·limits"·href="___Pre__Run__Script.html">PreRunScript</a>·option·of·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">runExternalM2</a>.</p> |
| Offset 28, 26 lines modified | Offset 28, 31 lines modified | ||
| 28 | b\x8be\x8es\x8st\x8t·w\x8wa\x8ay\x8y·t\x8to\x8o·s\x8se\x8et\x8t·the·limits·on·a·specific·process·is·to·run·something·like | 28 | b\x8be\x8es\x8st\x8t·w\x8wa\x8ay\x8y·t\x8to\x8o·s\x8se\x8et\x8t·the·limits·on·a·specific·process·is·to·run·something·like |
| 29 | (ulimit·-S·-m·123456·-S·-t·5;·M2) | 29 | (ulimit·-S·-m·123456·-S·-t·5;·M2) |
| 30 | which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits | 30 | which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits |
| 31 | unchanged. | 31 | unchanged. |
| 32 | F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·you·can·v\x8vi\x8ie\x8ew\x8w·the·ulimits·currently·available·to·the | 32 | F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·you·can·v\x8vi\x8ie\x8ew\x8w·the·ulimits·currently·available·to·the |
| 33 | Macaulay2·process·by·using·the·_\x8r_\x8u_\x8n·command: | 33 | Macaulay2·process·by·using·the·_\x8r_\x8u_\x8n·command: |
| 34 | i1·:·run("ulimit·-a") | 34 | i1·:·run("ulimit·-a") |
| 35 | time(seconds)········700 | ||
| 36 | file(blocks)·········unlimited | ||
| 37 | data(kbytes)·········unlimited | ||
| 38 | stack(kbytes)········8192 | ||
| 39 | coredump(blocks)·····0 | ||
| 40 | memory(kbytes)·······850000 | ||
| 41 | locked·memory(kbytes)·3077552 | ||
| 42 | process··············96081 | ||
| 43 | nofiles··············512 | ||
| 44 | 35 | real-time·non-blocking·time··(microseconds,·-R)·unlimited | |
| 36 | core·file·size··············(blocks,·-c)·0 | ||
| 37 | data·seg·size···············(kbytes,·-d)·unlimited | ||
| 38 | scheduling·priority·················(-e)·0 | ||
| 39 | file·size···················(blocks,·-f)·unlimited | ||
| 40 | pending·signals·····················(-i)·95991 | ||
| 41 | max·locked·memory···········(kbytes,·-l)·3076856 | ||
| 42 | max·memory·size·············(kbytes,·-m)·850000 | ||
| 43 | open·files··························(-n)·512 | ||
| 44 | pipe·size················(512·bytes,·-p)·8 | ||
| 45 | POSIX·message·queues·········(bytes,·-q)·819200 | ||
| 46 | real-time·priority··················(-r)·0 | ||
| 47 | stack·size··················(kbytes,·-s)·8192 | ||
| 48 | cpu·time···················(seconds,·-t)·700 | ||
| 49 | max·user·processes··················(-u)·95991 | ||
| 50 | virtual·memory··············(kbytes,·-v)·unlimited | ||
| 45 | locks················unlimited | 51 | file·locks··························(-x)·unlimited |
| 46 | rtprio···············0 | ||
| 47 | o1·=·0 | 52 | o1·=·0 |
| 48 | This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case | 53 | This·starts·a·new·shell·and·executes·the·command·given,·which·in·this·case |
| 49 | provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this | 54 | provides·the·list·of·ulimits·of·the·shell.·Since·ulimits·are·inherited,·this |
| 50 | should·be·the·same·as·the·ulimits·of·Macaulay2·itself. | 55 | should·be·the·same·as·the·ulimits·of·Macaulay2·itself. |
| 51 | F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·it·is·not·possible·to·set·ulimits·on·the·current | 56 | F\x8Fr\x8ro\x8om\x8m·w\x8wi\x8it\x8th\x8hi\x8in\x8n·M\x8Ma\x8ac\x8ca\x8au\x8ul\x8la\x8ay\x8y2\x82,·it·is·not·possible·to·set·ulimits·on·the·current |
| 52 | Macaulay2·process·because·Macaulay2·does·not·provide·access·to·the·setrlimit | 57 | Macaulay2·process·because·Macaulay2·does·not·provide·access·to·the·setrlimit |
| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ··········<p>The·hash·table·<span·class="tt">h</span>·stores·the·<span·class="tt">exit·code</span>·of·the·created·Macaulay2·process,·the·<span·class="tt">return·code</span>·of·the·created·Macaulay2·process·(see·<a·title="run·an·external·command"·href="../../Macaulay2Doc/html/_run.html">run</a>·for·details;·this·is·usually·256·times·the·exit·code,·plus·information·about·any·signals·received·by·the·child),·the·wall-clock·<span·class="tt">time·used</span>·(as·opposed·to·the·CPU·time),·the·name·of·the·<span·class="tt">output·file</span>·(unless·it·was·deleted),·the·name·of·the·<span·class="tt">answer·file</span>·(unless·it·was·deleted),·any·<span·class="tt">statistics</span>·recorded·about·the·resource·usage,·and·the·<span·class="tt">value</span>·returned·by·the·function·<span·class="tt">func</span>.·If·the·child·process·terminates·abnormally,·then·usually·the·<span·class="tt">exit·code</span>·is·nonzero·and·the·<span·class="tt">value</span>·returned·is·<a·title="the·unique·member·of·the·empty·class"·href="../../Macaulay2Doc/html/_null.html">null</a>.</p> | 91 | ··········<p>The·hash·table·<span·class="tt">h</span>·stores·the·<span·class="tt">exit·code</span>·of·the·created·Macaulay2·process,·the·<span·class="tt">return·code</span>·of·the·created·Macaulay2·process·(see·<a·title="run·an·external·command"·href="../../Macaulay2Doc/html/_run.html">run</a>·for·details;·this·is·usually·256·times·the·exit·code,·plus·information·about·any·signals·received·by·the·child),·the·wall-clock·<span·class="tt">time·used</span>·(as·opposed·to·the·CPU·time),·the·name·of·the·<span·class="tt">output·file</span>·(unless·it·was·deleted),·the·name·of·the·<span·class="tt">answer·file</span>·(unless·it·was·deleted),·any·<span·class="tt">statistics</span>·recorded·about·the·resource·usage,·and·the·<span·class="tt">value</span>·returned·by·the·function·<span·class="tt">func</span>.·If·the·child·process·terminates·abnormally,·then·usually·the·<span·class="tt">exit·code</span>·is·nonzero·and·the·<span·class="tt">value</span>·returned·is·<a·title="the·unique·member·of·the·empty·class"·href="../../Macaulay2Doc/html/_null.html">null</a>.</p> |
| 92 | ··········<p>For·example,·we·can·write·a·few·functions·to·a·temporary·file:</p> | 92 | ··········<p>For·example,·we·can·write·a·few·functions·to·a·temporary·file:</p> |
| 93 | ········</div> | 93 | ········</div> |
| 94 | ········<table·class="examples"> | 94 | ········<table·class="examples"> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn=temporaryFileName()|".m2" | 96 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn=temporaryFileName()|".m2" |
| 97 | o1·=·/tmp/M2- | 97 | o1·=·/tmp/M2-3676504-0/0.m2</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl;</code></pre> | 100 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl;</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;</code></pre> | 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| Offset 112, 15 lines modified | Offset 112, 15 lines modified | ||
| 112 | ········</table> | 112 | ········</table> |
| 113 | ········<div> | 113 | ········<div> |
| 114 | ··········<p>and·then·call·them:</p> | 114 | ··········<p>and·then·call·them:</p> |
| 115 | ········</div> | 115 | ········</div> |
| 116 | ········<table·class="examples"> | 116 | ········<table·class="examples"> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·h=runExternalM2(fn,"square",(4)); | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·h=runExternalM2(fn,"square",(4)); |
| 119 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 119 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/1.m2"·>"/tmp/M2-3676504-0/1.out"·2>&1·)) |
| 120 | Finished·running.</code></pre> | 120 | Finished·running.</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·h | 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·h |
| 124 | o7·=·HashTable{"answer·file"·=>·null} | 124 | o7·=·HashTable{"answer·file"·=>·null} |
| 125 | ···············"exit·code"·=>·0 | 125 | ···············"exit·code"·=>·0 |
| Offset 146, 24 lines modified | Offset 146, 24 lines modified | ||
| 146 | ········<div> | 146 | ········<div> |
| 147 | ··········<p></p> | 147 | ··········<p></p> |
| 148 | ··········<p>An·abnormal·program·exit·will·have·a·nonzero·<span·class="tt">exit·code</span>;·also,·the·<span·class="tt">value</span>·will·be·null,·the·<span·class="tt">output·file</span>·should·exist,·but·the·<span·class="tt">answer·file</span>·may·not·exist·unless·the·routine·finished·successfully.</p> | 148 | ··········<p>An·abnormal·program·exit·will·have·a·nonzero·<span·class="tt">exit·code</span>;·also,·the·<span·class="tt">value</span>·will·be·null,·the·<span·class="tt">output·file</span>·should·exist,·but·the·<span·class="tt">answer·file</span>·may·not·exist·unless·the·routine·finished·successfully.</p> |
| 149 | ········</div> | 149 | ········</div> |
| 150 | ········<table·class="examples"> | 150 | ········<table·class="examples"> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i10·:·h=runExternalM2(fn,"justexit",()); | 152 | <td>··············<pre><code·class="language-macaulay2">i10·:·h=runExternalM2(fn,"justexit",()); |
| 153 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 153 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/2.m2"·>"/tmp/M2-3676504-0/2.out"·2>&1·)) |
| 154 | Finished·running. | 154 | Finished·running. |
| 155 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> | 155 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i11·:·h | 158 | <td>··············<pre><code·class="language-macaulay2">i11·:·h |
| 159 | o11·=·HashTable{"answer·file"·=>·/tmp/M2- | 159 | o11·=·HashTable{"answer·file"·=>·/tmp/M2-3676504-0/2.ans} |
| 160 | ················"exit·code"·=>·27 | 160 | ················"exit·code"·=>·27 |
| 161 | ················"output·file"·=>·/tmp/M2- | 161 | ················"output·file"·=>·/tmp/M2-3676504-0/2.out |
| 162 | ················"return·code"·=>·6912 | 162 | ················"return·code"·=>·6912 |
| 163 | ················"statistics"·=>·null | 163 | ················"statistics"·=>·null |
| 164 | ················"time·used"·=>·1 | 164 | ················"time·used"·=>·1 |
| 165 | ················value·=>·null | 165 | ················value·=>·null |
| 166 | o11·:·HashTable</code></pre> | 166 | o11·:·HashTable</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| Offset 180, 79 lines modified | Offset 180, 78 lines modified | ||
| 180 | ········</table> | 180 | ········</table> |
| 181 | ········<div> | 181 | ········<div> |
| 182 | ··········<p>Here,·we·use·<a·title="how·to·use·resource·limits·with·Macaulay2"·href="_resource_splimits.html">resource·limits</a>·to·limit·the·routine·to·2·seconds·of·computational·time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time:</p> | 182 | ··········<p>Here,·we·use·<a·title="how·to·use·resource·limits·with·Macaulay2"·href="_resource_splimits.html">resource·limits</a>·to·limit·the·routine·to·2·seconds·of·computational·time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time:</p> |
| 183 | ········</div> | 183 | ········</div> |
| 184 | ········<table·class="examples"> | 184 | ········<table·class="examples"> |
| 185 | ··········<tr> | 185 | ··········<tr> |
| 186 | <td>··············<pre><code·class="language-macaulay2">i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); | 186 | <td>··············<pre><code·class="language-macaulay2">i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); |
| 187 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 187 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/3.m2"·>"/tmp/M2-3676504-0/3.out"·2>&1·)) |
| 188 | Killed | ||
| 189 | Finished·running. | 188 | Finished·running. |
| 190 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> | 189 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> |
| 191 | </td>··········</tr> | 190 | </td>··········</tr> |
| 192 | ··········<tr> | 191 | ··········<tr> |
| 193 | <td>··············<pre><code·class="language-macaulay2">i15·:·h | 192 | <td>··············<pre><code·class="language-macaulay2">i15·:·h |
| 194 | o15·=·HashTable{"answer·file"·=>·/tmp/M2- | 193 | o15·=·HashTable{"answer·file"·=>·/tmp/M2-3676504-0/3.ans} |
| 195 | ················"exit·code"·=>·0 | 194 | ················"exit·code"·=>·0 |
| 196 | ················"output·file"·=>·/tmp/M2- | 195 | ················"output·file"·=>·/tmp/M2-3676504-0/3.out |
| 197 | ················"return·code"·=>·9 | 196 | ················"return·code"·=>·9 |
| 198 | ················"statistics"·=>·null | 197 | ················"statistics"·=>·null |
| 199 | ················"time·used"·=>· | 198 | ················"time·used"·=>·2 |
| 200 | ················value·=>·null | 199 | ················value·=>·null |
| 201 | o15·:·HashTable</code></pre> | 200 | o15·:·HashTable</code></pre> |
| 202 | </td>··········</tr> | 201 | </td>··········</tr> |
| 203 | ··········<tr> | 202 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") | 203 | <td>··············<pre><code·class="language-macaulay2">i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") |
| 205 | o16·=· | 204 | o16·=· |
| 206 | ······i1·:·--·Script·/tmp/M2- | 205 | ······i1·:·--·Script·/tmp/M2-3676504-0/3.m2·automatically·generated·by·RunExternalM2 |
| 207 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); | 206 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); |
| 208 | ······i2·:·load·"/tmp/M2- | 207 | ······i2·:·load·"/tmp/M2-3676504-0/0.m2"; |
| 209 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2- | 208 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-3676504-0/3.ans",spin·(10)); |
| 210 | ······Spinning!!</code></pre> | 209 | ······Spinning!!</code></pre> |
| 211 | </td>··········</tr> | 210 | </td>··········</tr> |
| 212 | ··········<tr> | 211 | ··········<tr> |
| 213 | <td>··············<pre><code·class="language-macaulay2">i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file")</code></pre> | 212 | <td>··············<pre><code·class="language-macaulay2">i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file")</code></pre> |
| 214 | </td>··········</tr> | 213 | </td>··········</tr> |
| 215 | ········</table> | 214 | ········</table> |
| 216 | ········<div> | 215 | ········<div> |
| 217 | ··········<p></p> | 216 | ··········<p></p> |
| 218 | ··········<p>We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">KeepStatistics</a>·command:</p> | 217 | ··········<p>We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·<a·title="run·a·Macaulay2·function·in·a·new·Macaulay2·process"·href="_run__External__M2.html">KeepStatistics</a>·command:</p> |
| 219 | ········</div> | 218 | ········</div> |
| 220 | ········<table·class="examples"> | 219 | ········<table·class="examples"> |
| 221 | ··········<tr> | 220 | ··········<tr> |
| 222 | <td>··············<pre><code·class="language-macaulay2">i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); | 221 | <td>··············<pre><code·class="language-macaulay2">i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); |
| 223 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 222 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/4.m2"·>"/tmp/M2-3676504-0/4.out"·2>&1')·>"/tmp/M2-3676504-0/4.stat"·2>&1·)) |
| 224 | Finished·running.</code></pre> | 223 | Finished·running.</code></pre> |
| 225 | </td>··········</tr> | 224 | </td>··········</tr> |
| 226 | ··········<tr> | 225 | ··········<tr> |
| 227 | <td>··············<pre><code·class="language-macaulay2">i19·:·h#"statistics" | 226 | <td>··············<pre><code·class="language-macaulay2">i19·:·h#"statistics" |
| 228 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 227 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-3676504-0/4.m2"·>"/tmp/M2-3676504-0/4.out"·2>&1" |
| 229 | ··············User·time·(seconds):·4. | 228 | ··············User·time·(seconds):·4.76 |
| 230 | ··············System·time·(seconds):·0. | 229 | ··············System·time·(seconds):·0.20 |
| 231 | ··············Percent·of·CPU·this·job·got:· | 230 | ··············Percent·of·CPU·this·job·got:·76% |
| 232 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:0 | 231 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:06.45 |
| 233 | ··············Average·shared·text·size·(kbytes):·0 | 232 | ··············Average·shared·text·size·(kbytes):·0 |
| 234 | ··············Average·unshared·data·size·(kbytes):·0 | 233 | ··············Average·unshared·data·size·(kbytes):·0 |
| 235 | ··············Average·stack·size·(kbytes):·0 | 234 | ··············Average·stack·size·(kbytes):·0 |
| 236 | ··············Average·total·size·(kbytes):·0 | 235 | ··············Average·total·size·(kbytes):·0 |
| 237 | ··············Maximum·resident·set·size·(kbytes):· | 236 | ··············Maximum·resident·set·size·(kbytes):·298472 |
| 238 | ··············Average·resident·set·size·(kbytes):·0 | 237 | ··············Average·resident·set·size·(kbytes):·0 |
| 239 | ··············Major·(requiring·I/O)·page·faults:·0 | 238 | ··············Major·(requiring·I/O)·page·faults:·0 |
| 240 | ··············Minor·(reclaiming·a·frame)·page·faults:· | 239 | ··············Minor·(reclaiming·a·frame)·page·faults:·31495 |
| 241 | ··············Voluntary·context·switches:· | 240 | ··············Voluntary·context·switches:·8898 |
| 242 | ··············Involuntary·context·switches:· | 241 | ··············Involuntary·context·switches:·3052 |
| 243 | ··············Swaps:·0 | 242 | ··············Swaps:·0 |
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| Offset 46, 25 lines modified | Offset 46, 25 lines modified | ||
| 46 | the·output·file·(unless·it·was·deleted),·the·name·of·the·answer·file·(unless·it | 46 | the·output·file·(unless·it·was·deleted),·the·name·of·the·answer·file·(unless·it |
| 47 | was·deleted),·any·statistics·recorded·about·the·resource·usage,·and·the·value | 47 | was·deleted),·any·statistics·recorded·about·the·resource·usage,·and·the·value |
| 48 | returned·by·the·function·func.·If·the·child·process·terminates·abnormally,·then | 48 | returned·by·the·function·func.·If·the·child·process·terminates·abnormally,·then |
| 49 | usually·the·exit·code·is·nonzero·and·the·value·returned·is·_\x8n_\x8u_\x8l_\x8l. | 49 | usually·the·exit·code·is·nonzero·and·the·value·returned·is·_\x8n_\x8u_\x8l_\x8l. |
| 50 | For·example,·we·can·write·a·few·functions·to·a·temporary·file: | 50 | For·example,·we·can·write·a·few·functions·to·a·temporary·file: |
| 51 | i1·:·fn=temporaryFileName()|".m2" | 51 | i1·:·fn=temporaryFileName()|".m2" |
| 52 | o1·=·/tmp/M2- | 52 | o1·=·/tmp/M2-3676504-0/0.m2 |
| 53 | i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·/// | 53 | i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·/// |
| 54 | <<endl; | 54 | <<endl; |
| 55 | i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl; | 55 | i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl; |
| 56 | i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime(); | 56 | i4·:·fn<<///·spin·=·(x)·->·(stderr<<"Spinning!!"<<endl;·startTime:=cpuTime(); |
| 57 | while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl; | 57 | while(cpuTime()-startTime<x)·do·for·i·to·10000000·do·i;·return(x););·///<<endl; |
| 58 | i5·:·fn<<flush; | 58 | i5·:·fn<<flush; |
| 59 | and·then·call·them: | 59 | and·then·call·them: |
| 60 | i6·:·h=runExternalM2(fn,"square",(4)); | 60 | i6·:·h=runExternalM2(fn,"square",(4)); |
| 61 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ | 61 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ |
| 62 | M2- | 62 | M2-3676504-0/1.m2"·>"/tmp/M2-3676504-0/1.out"·2>&1·)) |
| 63 | Finished·running. | 63 | Finished·running. |
| 64 | i7·:·h | 64 | i7·:·h |
| 65 | o7·=·HashTable{"answer·file"·=>·null} | 65 | o7·=·HashTable{"answer·file"·=>·null} |
| 66 | ···············"exit·code"·=>·0 | 66 | ···············"exit·code"·=>·0 |
| 67 | ···············"output·file"·=>·null | 67 | ···············"output·file"·=>·null |
| 68 | ···············"return·code"·=>·0 | 68 | ···············"return·code"·=>·0 |
| Offset 80, 22 lines modified | Offset 80, 22 lines modified | ||
| 80 | o9·=·true | 80 | o9·=·true |
| 81 | An·abnormal·program·exit·will·have·a·nonzero·exit·code;·also,·the·value·will·be | 81 | An·abnormal·program·exit·will·have·a·nonzero·exit·code;·also,·the·value·will·be |
| 82 | null,·the·output·file·should·exist,·but·the·answer·file·may·not·exist·unless | 82 | null,·the·output·file·should·exist,·but·the·answer·file·may·not·exist·unless |
| 83 | the·routine·finished·successfully. | 83 | the·routine·finished·successfully. |
| 84 | i10·:·h=runExternalM2(fn,"justexit",()); | 84 | i10·:·h=runExternalM2(fn,"justexit",()); |
| 85 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ | 85 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ |
| 86 | M2- | 86 | M2-3676504-0/2.m2"·>"/tmp/M2-3676504-0/2.out"·2>&1·)) |
| 87 | Finished·running. | 87 | Finished·running. |
| 88 | RunExternalM2:·expected·answer·file·does·not·exist | 88 | RunExternalM2:·expected·answer·file·does·not·exist |
| 89 | i11·:·h | 89 | i11·:·h |
| 90 | o11·=·HashTable{"answer·file"·=>·/tmp/M2- | 90 | o11·=·HashTable{"answer·file"·=>·/tmp/M2-3676504-0/2.ans} |
| 91 | ················"exit·code"·=>·27 | 91 | ················"exit·code"·=>·27 |
| 92 | ················"output·file"·=>·/tmp/M2- | 92 | ················"output·file"·=>·/tmp/M2-3676504-0/2.out |
| 93 | ················"return·code"·=>·6912 | 93 | ················"return·code"·=>·6912 |
| 94 | ················"statistics"·=>·null | 94 | ················"statistics"·=>·null |
| 95 | ················"time·used"·=>·1 | 95 | ················"time·used"·=>·1 |
| 96 | ················value·=>·null | 96 | ················value·=>·null |
| 97 | o11·:·HashTable | 97 | o11·:·HashTable |
| 98 | i12·:·fileExists(h#"output·file") | 98 | i12·:·fileExists(h#"output·file") |
| Offset 104, 143 lines modified | Offset 104, 142 lines modified | ||
| 104 | i13·:·fileExists(h#"answer·file") | 104 | i13·:·fileExists(h#"answer·file") |
| 105 | o13·=·false | 105 | o13·=·false |
| 106 | Here,·we·use·_\x8r_\x8e_\x8s_\x8o_\x8u_\x8r_\x8c_\x8e_\x8·_\x8l_\x8i_\x8m_\x8i_\x8t_\x8s·to·limit·the·routine·to·2·seconds·of·computational | 106 | Here,·we·use·_\x8r_\x8e_\x8s_\x8o_\x8u_\x8r_\x8c_\x8e_\x8·_\x8l_\x8i_\x8m_\x8i_\x8t_\x8s·to·limit·the·routine·to·2·seconds·of·computational |
| 107 | time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time: | 107 | time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time: |
| 108 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); | 108 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); |
| 109 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··- | 109 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··- |
| 110 | q··<"/tmp/M2- | 110 | q··<"/tmp/M2-3676504-0/3.m2"·>"/tmp/M2-3676504-0/3.out"·2>&1·)) |
| 111 | Killed | ||
| 112 | Finished·running. | 111 | Finished·running. |
| 113 | RunExternalM2:·expected·answer·file·does·not·exist | 112 | RunExternalM2:·expected·answer·file·does·not·exist |
| 114 | i15·:·h | 113 | i15·:·h |
| 115 | o15·=·HashTable{"answer·file"·=>·/tmp/M2- | 114 | o15·=·HashTable{"answer·file"·=>·/tmp/M2-3676504-0/3.ans} |
| 116 | ················"exit·code"·=>·0 | 115 | ················"exit·code"·=>·0 |
| 117 | ················"output·file"·=>·/tmp/M2- | 116 | ················"output·file"·=>·/tmp/M2-3676504-0/3.out |
| 118 | ················"return·code"·=>·9 | 117 | ················"return·code"·=>·9 |
| 119 | ················"statistics"·=>·null | 118 | ················"statistics"·=>·null |
| 120 | ················"time·used"·=>· | 119 | ················"time·used"·=>·2 |
| 121 | ················value·=>·null | 120 | ················value·=>·null |
| 122 | o15·:·HashTable | 121 | o15·:·HashTable |
| 123 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get | 122 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get |
| 124 | (h#"output·file") | 123 | (h#"output·file") |
| 125 | o16·= | 124 | o16·= |
| 126 | ······i1·:·--·Script·/tmp/M2- | 125 | ······i1·:·--·Script·/tmp/M2-3676504-0/3.m2·automatically·generated·by |
| 127 | RunExternalM2 | 126 | RunExternalM2 |
| 128 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); | 127 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); |
| 129 | ······i2·:·load·"/tmp/M2- | 128 | ······i2·:·load·"/tmp/M2-3676504-0/0.m2"; |
| 130 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2- | 129 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-3676504-0/3.ans",spin·(10)); |
| 131 | ······Spinning!! | 130 | ······Spinning!! |
| 132 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get | 131 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get |
| 133 | (h#"answer·file") | 132 | (h#"answer·file") |
| 134 | We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·_\x8K_\x8e_\x8e_\x8p_\x8S_\x8t_\x8a_\x8t_\x8i_\x8s_\x8t_\x8i_\x8c_\x8s | 133 | We·can·get·quite·a·lot·of·detail·on·the·resources·used·with·the·_\x8K_\x8e_\x8e_\x8p_\x8S_\x8t_\x8a_\x8t_\x8i_\x8s_\x8t_\x8i_\x8c_\x8s |
| 135 | command: | 134 | command: |
| 136 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); | 135 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); |
| 137 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·- | 136 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·- |
| 138 | -no-debug·--silent··-q··<"/tmp/M2- | 137 | -no-debug·--silent··-q··<"/tmp/M2-3676504-0/4.m2"·>"/tmp/M2-3676504-0/4.out" |
| 139 | 2>&1')·>"/tmp/M2- | 138 | 2>&1')·>"/tmp/M2-3676504-0/4.stat"·2>&1·)) |
| 140 | Finished·running. | 139 | Finished·running. |
| 141 | i19·:·h#"statistics" | 140 | i19·:·h#"statistics" |
| 142 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug | 141 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug |
| 143 | --silent··-q··<"/tmp/M2- | 142 | --silent··-q··<"/tmp/M2-3676504-0/4.m2"·>"/tmp/M2-3676504-0/4.out"·2>&1" |
| 144 | ··············User·time·(seconds):·4. | 143 | ··············User·time·(seconds):·4.76 |
| 145 | ··············System·time·(seconds):·0. | 144 | ··············System·time·(seconds):·0.20 |
| 146 | ··············Percent·of·CPU·this·job·got:· | 145 | ··············Percent·of·CPU·this·job·got:·76% |
| 147 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:0 | 146 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:06.45 |
| 148 | ··············Average·shared·text·size·(kbytes):·0 | 147 | ··············Average·shared·text·size·(kbytes):·0 |
| 149 | ··············Average·unshared·data·size·(kbytes):·0 | 148 | ··············Average·unshared·data·size·(kbytes):·0 |
| 150 | ··············Average·stack·size·(kbytes):·0 | 149 | ··············Average·stack·size·(kbytes):·0 |
| 151 | ··············Average·total·size·(kbytes):·0 | 150 | ··············Average·total·size·(kbytes):·0 |
| 152 | ··············Maximum·resident·set·size·(kbytes):· | 151 | ··············Maximum·resident·set·size·(kbytes):·298472 |
| 153 | ··············Average·resident·set·size·(kbytes):·0 | 152 | ··············Average·resident·set·size·(kbytes):·0 |
| 154 | ··············Major·(requiring·I/O)·page·faults:·0 | 153 | ··············Major·(requiring·I/O)·page·faults:·0 |
| 155 | ··············Minor·(reclaiming·a·frame)·page·faults:· | 154 | ··············Minor·(reclaiming·a·frame)·page·faults:·31495 |
| 156 | ··············Voluntary·context·switches:· | 155 | ··············Voluntary·context·switches:·8898 |
| 157 | ··············Involuntary·context·switches:· | 156 | ··············Involuntary·context·switches:·3052 |
| 158 | ··············Swaps:·0 | 157 | ··············Swaps:·0 |
| 159 | ··············File·system·inputs:·0 | 158 | ··············File·system·inputs:·0 |
| 160 | ··············File·system·outputs:· | 159 | ··············File·system·outputs:·24 |
| 161 | ··············Socket·messages·sent:·0 | 160 | ··············Socket·messages·sent:·0 |
| 162 | ··············Socket·messages·received:·0 | 161 | ··············Socket·messages·received:·0 |
| 163 | ··············Signals·delivered:·0 | 162 | ··············Signals·delivered:·0 |
| 164 | ··············Page·size·(bytes):·4096 | 163 | ··············Page·size·(bytes):·4096 |
| 165 | ··············Exit·status:·0 | 164 | ··············Exit·status:·0 |
| 166 | We·can·handle·most·kinds·of·objects·as·return·values,·although·_\x8M_\x8u_\x8t_\x8a_\x8b_\x8l_\x8e_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x | 165 | We·can·handle·most·kinds·of·objects·as·return·values,·although·_\x8M_\x8u_\x8t_\x8a_\x8b_\x8l_\x8e_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x |
| 167 | does·not·work.·Here,·we·use·the·built-in·_\x8i_\x8d_\x8e_\x8n_\x8t_\x8i_\x8t_\x8y·function: | 166 | does·not·work.·Here,·we·use·the·built-in·_\x8i_\x8d_\x8e_\x8n_\x8t_\x8i_\x8t_\x8y·function: |
| 168 | i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///; | 167 | i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///; |
| 169 | i21·:·(runExternalM2(fn,identity,v))#value===v | 168 | i21·:·(runExternalM2(fn,identity,v))#value===v |
| 170 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ | 169 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ |
| 171 | M2- | 170 | M2-3676504-0/6.m2"·>"/tmp/M2-3676504-0/6.out"·2>&1·)) |
| 172 | Finished·running. | 171 | Finished·running. |
| 173 | o21·=·true | 172 | o21·=·true |
| Max diff block lines reached; 2819/9628 bytes (29.28%) of diff not shown. | |||
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | Y2Fub25pY2FsTW9kdWxlKElkZWFsKQ== | 8 | Y2Fub25pY2FsTW9kdWxlKElkZWFsKQ== |
| 9 | #:len=266 | 9 | #:len=266 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzE1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzE1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjYW5vbmljYWxNb2R1bGUsSWRlYWwpLCJjYW5vbmlj | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjYW5vbmljYWxNb2R1bGUsSWRlYWwpLCJjYW5vbmlj |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=29 | 7 | #:len=29 |
| 8 | UmVtb3RlT2JqZWN0IGFuZCBSZW1vdGVPYmplY3Q= | 8 | UmVtb3RlT2JqZWN0IGFuZCBSZW1vdGVPYmplY3Q= |
| 9 | #:len=217 | 9 | #:len=217 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMwLCAidW5kb2N1bWVudGVkIiA9PiB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMwLCAidW5kb2N1bWVudGVkIiA9PiB0 |
| 11 | cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzeW1ib2wg | 11 | cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhzeW1ib2wg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=21 | 7 | #:len=21 |
| 8 | dHJhbnNwb3NlKEdhdGVNYXRyaXgp | 8 | dHJhbnNwb3NlKEdhdGVNYXRyaXgp |
| 9 | #:len=299 | 9 | #:len=299 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTQ5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTQ5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0cmFuc3Bvc2UsR2F0ZU1hdHJpeCksInRyYW5zcG9z | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0cmFuc3Bvc2UsR2F0ZU1hdHJpeCksInRyYW5zcG9z |
| Offset 30, 23 lines modified | Offset 30, 23 lines modified | ||
| 30 | ············································) | 30 | ············································) |
| 31 | ··························"variable·positions"·=>·{-1} | 31 | ··························"variable·positions"·=>·{-1} |
| 32 | o5·:·InterpretedSLProgram | 32 | o5·:·InterpretedSLProgram |
| 33 | i6·:·time·A·=·evaluate(slp,matrix{{1}}); | 33 | i6·:·time·A·=·evaluate(slp,matrix{{1}}); |
| 34 | ·--·used·0.002 | 34 | ·--·used·0.00289312s·(cpu);·0.000237595s·(thread);·0s·(gc) |
| 35 | ··············1·······1 | 35 | ··············1·······1 |
| 36 | o6·:·Matrix·ZZ··<--·ZZ | 36 | o6·:·Matrix·ZZ··<--·ZZ |
| 37 | i7·:·ZZ[y]; | 37 | i7·:·ZZ[y]; |
| 38 | i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) | 38 | i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) |
| 39 | ·--·used· | 39 | ·--·used·3.33396s·(cpu);·2.56456s·(thread);·0s·(gc) |
| 40 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 | 40 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 |
| 41 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 | 41 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 |
| 42 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 | 42 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 |
| 43 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 | 43 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 |
| 44 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 | 44 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 |
| 45 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 | 45 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 |
| Offset 86, 25 lines modified | Offset 86, 25 lines modified | ||
| 86 | ··························"variable·positions"·=>·{-1} | 86 | ··························"variable·positions"·=>·{-1} |
| 87 | o5·:·InterpretedSLProgram</code></pre> | 87 | o5·:·InterpretedSLProgram</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·A·=·evaluate(slp,matrix{{1}}); | 90 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·A·=·evaluate(slp,matrix{{1}}); |
| 91 | ·--·used·0.002 | 91 | ·--·used·0.00289312s·(cpu);·0.000237595s·(thread);·0s·(gc) |
| 92 | ··············1·······1 | 92 | ··············1·······1 |
| 93 | o6·:·Matrix·ZZ··<--·ZZ</code></pre> | 93 | o6·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·ZZ[y];</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·ZZ[y];</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) | 99 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) |
| 100 | ·--·used· | 100 | ·--·used·3.33396s·(cpu);·2.56456s·(thread);·0s·(gc) |
| 101 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 | 101 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 |
| 102 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 | 102 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 |
| 103 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 | 103 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 |
| 104 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 | 104 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 |
| 105 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 | 105 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 |
| 106 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 | 106 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 |
| Offset 38, 21 lines modified | Offset 38, 21 lines modified | ||
| 38 | ············································output·nodes:·1 | 38 | ············································output·nodes:·1 |
| 39 | ············································) | 39 | ············································) |
| 40 | ··························"variable·positions"·=>·{-1} | 40 | ··························"variable·positions"·=>·{-1} |
| 41 | o5·:·InterpretedSLProgram | 41 | o5·:·InterpretedSLProgram |
| 42 | i6·:·time·A·=·evaluate(slp,matrix{{1}}); | 42 | i6·:·time·A·=·evaluate(slp,matrix{{1}}); |
| 43 | ·--·used·0.002 | 43 | ·--·used·0.00289312s·(cpu);·0.000237595s·(thread);·0s·(gc) |
| 44 | ··············1·······1 | 44 | ··············1·······1 |
| 45 | o6·:·Matrix·ZZ··<--·ZZ | 45 | o6·:·Matrix·ZZ··<--·ZZ |
| 46 | i7·:·ZZ[y]; | 46 | i7·:·ZZ[y]; |
| 47 | i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) | 47 | i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) |
| 48 | ·--·used· | 48 | ·--·used·3.33396s·(cpu);·2.56456s·(thread);·0s·(gc) |
| 49 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 | 49 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 |
| 50 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 | 50 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 |
| 51 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 | 51 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 |
| 52 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 | 52 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 |
| 53 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 | 53 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 |
| 54 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 | 54 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | c2xFcXVpdmFyaWFudFZlY3RvckJ1bmRsZQ== | 8 | c2xFcXVpdmFyaWFudFZlY3RvckJ1bmRsZQ== |
| 9 | #:len=4962 | 9 | #:len=4962 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYSBTTC1lcXVpdmFyaWFu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYSBTTC1lcXVpdmFyaWFu |
| 11 | dCB2ZWN0b3IgYnVuZGxlIG92ZXIgc29tZSBwcm9qZWN0aXZlIHNwYWNlIiwgImxpbmVudW0iID0+ | 11 | dCB2ZWN0b3IgYnVuZGxlIG92ZXIgc29tZSBwcm9qZWN0aXZlIHNwYWNlIiwgImxpbmVudW0iID0+ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | RXhhbXBsZSBmaXJzdCBvcmRlciBkZWZvcm1hdGlvbg== | 8 | RXhhbXBsZSBmaXJzdCBvcmRlciBkZWZvcm1hdGlvbg== |
| 9 | #:len=3174 | 9 | #:len=3174 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRXhhbXBsZSBhY2Nlc3NpbmcgdGhlIGRh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRXhhbXBsZSBhY2Nlc3NpbmcgdGhlIGRh |
| 11 | dGEgc3RvcmVkIGluIGEgZmlyc3Qgb3JkZXIgZGVmb3JtYXRpb24uIiwgImxpbmVudW0iID0+IDQy | 11 | dGEgc3RvcmVkIGluIGEgZmlyc3Qgb3JkZXIgZGVmb3JtYXRpb24uIiwgImxpbmVudW0iID0+IDQy |
| Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
| 56 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 56 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 57 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 | 57 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 |
| 58 | i8·:·complement·C | 58 | i8·:·complement·C |
| 59 | o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x·· | 59 | o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x·· |
| 60 | ········· | 60 | ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2 |
| 61 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 61 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 62 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 | 62 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 |
| 63 | i9·:·R=QQ[x_0..x_5] | 63 | i9·:·R=QQ[x_0..x_5] |
| 64 | o9·=·R | 64 | o9·=·R |
| Offset 146, 15 lines modified | Offset 146, 15 lines modified | ||
| 146 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 146 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 147 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> | 147 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i8·:·complement·C | 150 | <td>··············<pre><code·class="language-macaulay2">i8·:·complement·C |
| 151 | o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x·· | 151 | o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x·· |
| 152 | ········· | 152 | ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2 |
| 153 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 153 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 154 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> | 154 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ········</table> | 156 | ········</table> |
| 157 | ········<div> | 157 | ········<div> |
| 158 | ··········<p></p> | 158 | ··········<p></p> |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | ·········0·1·2··0·1·4··0·3·4··1·2·3··1·2·5··1·4·5··2·3·4··3·4·5 | 95 | ·········0·1·2··0·1·4··0·3·4··1·2·3··1·2·5··1·4·5··2·3·4··3·4·5 |
| 96 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 96 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 97 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 | 97 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 |
| 98 | i8·:·complement·C | 98 | i8·:·complement·C |
| 99 | o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x | 99 | o8·=·2:·x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x··x·x·x |
| 100 | ········· | 100 | ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2 |
| 101 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 101 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 102 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 | 102 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 |
| 103 | i9·:·R=QQ[x_0..x_5] | 103 | i9·:·R=QQ[x_0..x_5] |
| 104 | o9·=·R | 104 | o9·=·R |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=10 | 7 | #:len=10 |
| 8 | U1ZEQ29tcGxleA== | 8 | U1ZEQ29tcGxleA== |
| 9 | #:len=3135 | 9 | #:len=3135 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZSB0aGUgU1ZEIGRlY29tcG9z | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZSB0aGUgU1ZEIGRlY29tcG9z |
| 11 | aXRpb24gb2YgYSBjaGFpbkNvbXBsZXggb3ZlciBSUiIsICJsaW5lbnVtIiA9PiAxMTAyLCBJbnB1 | 11 | aXRpb24gb2YgYSBjaGFpbkNvbXBsZXggb3ZlciBSUiIsICJsaW5lbnVtIiA9PiAxMTAyLCBJbnB1 |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | i3·:·r={5,11,3,2} | 15 | i3·:·r={5,11,3,2} |
| 16 | o3·=·{5,·11,·3,·2} | 16 | o3·=·{5,·11,·3,·2} |
| 17 | o3·:·List | 17 | o3·:·List |
| 18 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) | 18 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) |
| 19 | ·--·.01 | 19 | ·--·.0157644s·elapsed |
| 20 | ·······6·······19·······19·······7·······3 | 20 | ·······6·······19·······19·······7·······3 |
| 21 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ | 21 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ |
| 22 | ········································ | 22 | ········································ |
| 23 | ·····0·······1········2········3·······4 | 23 | ·····0·······1········2········3·······4 |
| 24 | o4·:·ChainComplex | 24 | o4·:·ChainComplex |
| Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
| 51 | ·······53········53·········53·········53········53 | 51 | ·······53········53·········53·········53········53 |
| 52 | ················································ | 52 | ················································ |
| 53 | ·····-1········0··········1··········2·········3 | 53 | ·····-1········0··········1··········2·········3 |
| 54 | o6·:·ChainComplex | 54 | o6·:·ChainComplex |
| 55 | i7·:·elapsedTime·(h,U)=SVDComplex·CR; | 55 | i7·:·elapsedTime·(h,U)=SVDComplex·CR; |
| 56 | ·--·.00 | 56 | ·--·.00672861s·elapsed |
| 57 | i8·:·h | 57 | i8·:·h |
| 58 | o8·=·HashTable{-1·=>·1} | 58 | o8·=·HashTable{-1·=>·1} |
| 59 | ···············0·=>·3 | 59 | ···············0·=>·3 |
| 60 | ···············1·=>·5 | 60 | ···············1·=>·5 |
| 61 | ···············2·=>·2 | 61 | ···············2·=>·2 |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | i12·:·maximalEntry·chainComplex·errors | 95 | i12·:·maximalEntry·chainComplex·errors |
| 96 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} | 96 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} |
| 97 | o12·:·List | 97 | o12·:·List |
| 98 | i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); | 98 | i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); |
| 99 | ·--·.01 | 99 | ·--·.0119765s·elapsed |
| 100 | i14·:·hL·===·h | 100 | i14·:·hL·===·h |
| 101 | o14·=·true | 101 | o14·=·true |
| 102 | i15·:·SigmaL·=source·U; | 102 | i15·:·SigmaL·=source·U; |
| Offset 15, 15 lines modified | Offset 15, 15 lines modified | ||
| 15 | i3·:·r={4,3,3} | 15 | i3·:·r={4,3,3} |
| 16 | o3·=·{4,·3,·3} | 16 | o3·=·{4,·3,·3} |
| 17 | o3·:·List | 17 | o3·:·List |
| 18 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 18 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 19 | ·--·.00 | 19 | ·--·.00231119s·elapsed |
| 20 | ·······5·······10·······11·······5 | 20 | ·······5·······10·······11·······5 |
| 21 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 21 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 22 | ································ | 22 | ································ |
| 23 | ·····0·······1········2········3 | 23 | ·····0·······1········2········3 |
| 24 | o4·:·ChainComplex | 24 | o4·:·ChainComplex |
| Offset 47, 25 lines modified | Offset 47, 25 lines modified | ||
| 47 | ·······53········53·········53·········53 | 47 | ·······53········53·········53·········53 |
| 48 | ······································ | 48 | ······································ |
| 49 | ·····0·········1··········2··········3 | 49 | ·····0·········1··········2··········3 |
| 50 | o6·:·ChainComplex | 50 | o6·:·ChainComplex |
| 51 | i7·:·elapsedTime·(h,h1)=SVDHomology·CR | 51 | i7·:·elapsedTime·(h,h1)=SVDHomology·CR |
| 52 | ·--·.000 | 52 | ·--·.000668804s·elapsed |
| 53 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) | 53 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) |
| 54 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) | 54 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) |
| 55 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) | 55 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) |
| 56 | ················3·=>·2 | 56 | ················3·=>·2 |
| 57 | o7·:·Sequence | 57 | o7·:·Sequence |
| 58 | i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) | 58 | i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) |
| 59 | ·--·.001 | 59 | ·--·.00109977s·elapsed |
| 60 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) | 60 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) |
| 61 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) | 61 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) |
| 62 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) | 62 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) |
| 63 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) | 63 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) |
| 64 | o8·:·Sequence | 64 | o8·:·Sequence |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i4·:·r={4,3,5} | 17 | i4·:·r={4,3,5} |
| 18 | o4·=·{4,·3,·5} | 18 | o4·=·{4,·3,·5} |
| 19 | o4·:·List | 19 | o4·:·List |
| 20 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) | 20 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) |
| 21 | ·--·.00 | 21 | ·--·.00809145s·elapsed |
| 22 | ·······6·······10·······13·······8 | 22 | ·······6·······10·······13·······8 |
| 23 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 23 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 24 | ································ | 24 | ································ |
| 25 | ·····0·······1········2········3 | 25 | ·····0·······1········2········3 |
| 26 | o5·:·ChainComplex | 26 | o5·:·ChainComplex |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i4·:·r={4,3,3} | 17 | i4·:·r={4,3,3} |
| 18 | o4·=·{4,·3,·3} | 18 | o4·=·{4,·3,·3} |
| 19 | o4·:·List | 19 | o4·:·List |
| 20 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 20 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 21 | ·--·.002 | 21 | ·--·.00260108s·elapsed |
| 22 | ·······6·······10·······11·······5 | 22 | ·······6·······10·······11·······5 |
| 23 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 23 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 24 | ································ | 24 | ································ |
| 25 | ·····0·······1········2········3 | 25 | ·····0·······1········2········3 |
| 26 | o5·:·ChainComplex | 26 | o5·:·ChainComplex |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i4·:·r={4,3,3} | 17 | i4·:·r={4,3,3} |
| 18 | o4·=·{4,·3,·3} | 18 | o4·=·{4,·3,·3} |
| 19 | o4·:·List | 19 | o4·:·List |
| 20 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 20 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 21 | ·--·.002 | 21 | ·--·.00299809s·elapsed |
| 22 | ·······6·······10·······11·······5 | 22 | ·······6·······10·······11·······5 |
| 23 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 23 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 24 | ································ | 24 | ································ |
| 25 | ·····0·······1········2········3 | 25 | ·····0·······1········2········3 |
| 26 | o5·:·ChainComplex | 26 | o5·:·ChainComplex |
| Offset 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | o3·=·{5,·11,·3,·2} | 103 | o3·=·{5,·11,·3,·2} |
| 104 | o3·:·List</code></pre> | 104 | o3·:·List</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) | 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) |
| 108 | ·--·.01 | 108 | ·--·.0157644s·elapsed |
| 109 | ·······6·······19·······19·······7·······3 | 109 | ·······6·······19·······19·······7·······3 |
| 110 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ | 110 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ |
| 111 | ········································ | 111 | ········································ |
| 112 | ·····0·······1········2········3·······4 | 112 | ·····0·······1········2········3·······4 |
| 113 | o4·:·ChainComplex</code></pre> | 113 | o4·:·ChainComplex</code></pre> |
| Offset 142, 15 lines modified | Offset 142, 15 lines modified | ||
| 142 | ················································ | 142 | ················································ |
| 143 | ·····-1········0··········1··········2·········3 | 143 | ·····-1········0··········1··········2·········3 |
| 144 | o6·:·ChainComplex</code></pre> | 144 | o6·:·ChainComplex</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,U)=SVDComplex·CR; | 147 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,U)=SVDComplex·CR; |
| 148 | ·--·.00 | 148 | ·--·.00672861s·elapsed</code></pre> |
| 149 | </td>··········</tr> | 149 | </td>··········</tr> |
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i8·:·h | 151 | <td>··············<pre><code·class="language-macaulay2">i8·:·h |
| 152 | o8·=·HashTable{-1·=>·1} | 152 | o8·=·HashTable{-1·=>·1} |
| 153 | ···············0·=>·3 | 153 | ···············0·=>·3 |
| 154 | ···············1·=>·5 | 154 | ···············1·=>·5 |
| Offset 192, 15 lines modified | Offset 192, 15 lines modified | ||
| 192 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} | 192 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} |
| 193 | o12·:·List</code></pre> | 193 | o12·:·List</code></pre> |
| 194 | </td>··········</tr> | 194 | </td>··········</tr> |
| 195 | ··········<tr> | 195 | ··········<tr> |
| 196 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); | 196 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); |
| 197 | ·--·.01 | 197 | ·--·.0119765s·elapsed</code></pre> |
| 198 | </td>··········</tr> | 198 | </td>··········</tr> |
| 199 | ··········<tr> | 199 | ··········<tr> |
| 200 | <td>··············<pre><code·class="language-macaulay2">i14·:·hL·===·h | 200 | <td>··············<pre><code·class="language-macaulay2">i14·:·hL·===·h |
| 201 | o14·=·true</code></pre> | 201 | o14·=·true</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| Offset 38, 15 lines modified | Offset 38, 15 lines modified | ||
| 38 | o2·:·List | 38 | o2·:·List |
| 39 | i3·:·r={5,11,3,2} | 39 | i3·:·r={5,11,3,2} |
| 40 | o3·=·{5,·11,·3,·2} | 40 | o3·=·{5,·11,·3,·2} |
| 41 | o3·:·List | 41 | o3·:·List |
| 42 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) | 42 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) |
| 43 | ·--·.01 | 43 | ·--·.0157644s·elapsed |
| 44 | ·······6·······19·······19·······7·······3 | 44 | ·······6·······19·······19·······7·······3 |
| 45 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ | 45 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ |
| 46 | ·····0·······1········2········3·······4 | 46 | ·····0·······1········2········3·······4 |
| 47 | o4·:·ChainComplex | 47 | o4·:·ChainComplex |
| Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
| 71 | o6·=·RR····<--·RR·····<--·RR·····<--·RR····<--·RR | 71 | o6·=·RR····<--·RR·····<--·RR·····<--·RR····<--·RR |
| 72 | ·······53········53·········53·········53········53 | 72 | ·······53········53·········53·········53········53 |
| 73 | ·····-1········0··········1··········2·········3 | 73 | ·····-1········0··········1··········2·········3 |
| 74 | o6·:·ChainComplex | 74 | o6·:·ChainComplex |
| 75 | i7·:·elapsedTime·(h,U)=SVDComplex·CR; | 75 | i7·:·elapsedTime·(h,U)=SVDComplex·CR; |
| 76 | ·--·.00 | 76 | ·--·.00672861s·elapsed |
| 77 | i8·:·h | 77 | i8·:·h |
| 78 | o8·=·HashTable{-1·=>·1} | 78 | o8·=·HashTable{-1·=>·1} |
| 79 | ···············0·=>·3 | 79 | ···············0·=>·3 |
| 80 | ···············1·=>·5 | 80 | ···············1·=>·5 |
| 81 | ···············2·=>·2 | 81 | ···············2·=>·2 |
| 82 | ···············3·=>·1 | 82 | ···············3·=>·1 |
| Offset 110, 15 lines modified | Offset 110, 15 lines modified | ||
| 110 | 1)*Sigma.dd_ell*transpose·U_ell); | 110 | 1)*Sigma.dd_ell*transpose·U_ell); |
| 111 | i12·:·maximalEntry·chainComplex·errors | 111 | i12·:·maximalEntry·chainComplex·errors |
| 112 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} | 112 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} |
| 113 | o12·:·List | 113 | o12·:·List |
| 114 | i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); | 114 | i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); |
| 115 | ·--·.01 | 115 | ·--·.0119765s·elapsed |
| 116 | i14·:·hL·===·h | 116 | i14·:·hL·===·h |
| 117 | o14·=·true | 117 | o14·=·true |
| 118 | i15·:·SigmaL·=source·U; | 118 | i15·:·SigmaL·=source·U; |
| 119 | i16·:·for·i·from·min·CR+1·to·max·CR·list·maximalEntry(SigmaL.dd_i·-Sigma.dd_i) | 119 | i16·:·for·i·from·min·CR+1·to·max·CR·list·maximalEntry(SigmaL.dd_i·-Sigma.dd_i) |
| 120 | o16·=·{1.06581e-14,·1.13687e-13,·2.84217e-14,·3.55271e-15} | 120 | o16·=·{1.06581e-14,·1.13687e-13,·2.84217e-14,·3.55271e-15} |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | o3·=·{4,·3,·3} | 105 | o3·=·{4,·3,·3} |
| 106 | o3·:·List</code></pre> | 106 | o3·:·List</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 109 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 110 | ·--·.00 | 110 | ·--·.00231119s·elapsed |
| 111 | ·······5·······10·······11·······5 | 111 | ·······5·······10·······11·······5 |
| 112 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 112 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 113 | ································ | 113 | ································ |
| 114 | ·····0·······1········2········3 | 114 | ·····0·······1········2········3 |
| 115 | o4·:·ChainComplex</code></pre> | 115 | o4·:·ChainComplex</code></pre> |
| Offset 140, 26 lines modified | Offset 140, 26 lines modified | ||
| 140 | ······································ | 140 | ······································ |
| 141 | ·····0·········1··········2··········3 | 141 | ·····0·········1··········2··········3 |
| 142 | o6·:·ChainComplex</code></pre> | 142 | o6·:·ChainComplex</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,h1)=SVDHomology·CR | 145 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,h1)=SVDHomology·CR |
| 146 | ·--·.000 | 146 | ·--·.000668804s·elapsed |
| 147 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) | 147 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) |
| 148 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) | 148 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) |
| 149 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) | 149 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) |
| 150 | ················3·=>·2 | 150 | ················3·=>·2 |
| 151 | o7·:·Sequence</code></pre> | 151 | o7·:·Sequence</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) | 154 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) |
| 155 | ·--·.001 | 155 | ·--·.00109977s·elapsed |
| 156 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) | 156 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) |
| 157 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) | 157 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) |
| 158 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) | 158 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) |
| 159 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) | 159 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) |
| 160 | o8·:·Sequence</code></pre> | 160 | o8·:·Sequence</code></pre> |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | o2·:·List | 41 | o2·:·List |
| 42 | i3·:·r={4,3,3} | 42 | i3·:·r={4,3,3} |
| 43 | o3·=·{4,·3,·3} | 43 | o3·=·{4,·3,·3} |
| 44 | o3·:·List | 44 | o3·:·List |
| 45 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 45 | i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 46 | ·--·.00 | 46 | ·--·.00231119s·elapsed |
| 47 | ·······5·······10·······11·······5 | 47 | ·······5·······10·······11·······5 |
| 48 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 48 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 49 | ·····0·······1········2········3 | 49 | ·····0·······1········2········3 |
| 50 | o4·:·ChainComplex | 50 | o4·:·ChainComplex |
| Offset 70, 24 lines modified | Offset 70, 24 lines modified | ||
| 70 | o6·=·RR····<--·RR·····<--·RR·····<--·RR | 70 | o6·=·RR····<--·RR·····<--·RR·····<--·RR |
| 71 | ·······53········53·········53·········53 | 71 | ·······53········53·········53·········53 |
| 72 | ·····0·········1··········2··········3 | 72 | ·····0·········1··········2··········3 |
| 73 | o6·:·ChainComplex | 73 | o6·:·ChainComplex |
| 74 | i7·:·elapsedTime·(h,h1)=SVDHomology·CR | 74 | i7·:·elapsedTime·(h,h1)=SVDHomology·CR |
| 75 | ·--·.000 | 75 | ·--·.000668804s·elapsed |
| 76 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) | 76 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) |
| 77 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) | 77 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) |
| 78 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) | 78 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) |
| 79 | ················3·=>·2 | 79 | ················3·=>·2 |
| 80 | o7·:·Sequence | 80 | o7·:·Sequence |
| 81 | i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) | 81 | i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) |
| 82 | ·--·.001 | 82 | ·--·.00109977s·elapsed |
| 83 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) | 83 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) |
| 84 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) | 84 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) |
| 85 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) | 85 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) |
| 86 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) | 86 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) |
| 87 | o8·:·Sequence | 87 | o8·:·Sequence |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | o4·=·{4,·3,·5} | 104 | o4·=·{4,·3,·5} |
| 105 | o4·:·List</code></pre> | 105 | o4·:·List</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) |
| 109 | ·--·.00 | 109 | ·--·.00809145s·elapsed |
| 110 | ·······6·······10·······13·······8 | 110 | ·······6·······10·······13·······8 |
| 111 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 111 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 112 | ································ | 112 | ································ |
| 113 | ·····0·······1········2········3 | 113 | ·····0·······1········2········3 |
| 114 | o5·:·ChainComplex</code></pre> | 114 | o5·:·ChainComplex</code></pre> |
| Offset 34, 15 lines modified | Offset 34, 15 lines modified | ||
| 34 | o3·:·List | 34 | o3·:·List |
| 35 | i4·:·r={4,3,5} | 35 | i4·:·r={4,3,5} |
| 36 | o4·=·{4,·3,·5} | 36 | o4·=·{4,·3,·5} |
| 37 | o4·:·List | 37 | o4·:·List |
| 38 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) | 38 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) |
| 39 | ·--·.00 | 39 | ·--·.00809145s·elapsed |
| 40 | ·······6·······10·······13·······8 | 40 | ·······6·······10·······13·······8 |
| 41 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 41 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 42 | ·····0·······1········2········3 | 42 | ·····0·······1········2········3 |
| 43 | o5·:·ChainComplex | 43 | o5·:·ChainComplex |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | o4·=·{4,·3,·3} | 95 | o4·=·{4,·3,·3} |
| 96 | o4·:·List</code></pre> | 96 | o4·:·List</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 100 | ·--·.002 | 100 | ·--·.00260108s·elapsed |
| 101 | ·······6·······10·······11·······5 | 101 | ·······6·······10·······11·······5 |
| 102 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 102 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 103 | ································ | 103 | ································ |
| 104 | ·····0·······1········2········3 | 104 | ·····0·······1········2········3 |
| 105 | o5·:·ChainComplex</code></pre> | 105 | o5·:·ChainComplex</code></pre> |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | o3·:·List | 29 | o3·:·List |
| 30 | i4·:·r={4,3,3} | 30 | i4·:·r={4,3,3} |
| 31 | o4·=·{4,·3,·3} | 31 | o4·=·{4,·3,·3} |
| 32 | o4·:·List | 32 | o4·:·List |
| 33 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 33 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 34 | ·--·.002 | 34 | ·--·.00260108s·elapsed |
| 35 | ·······6·······10·······11·······5 | 35 | ·······6·······10·······11·······5 |
| 36 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 36 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 37 | ·····0·······1········2········3 | 37 | ·····0·······1········2········3 |
| 38 | o5·:·ChainComplex | 38 | o5·:·ChainComplex |
| Offset 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | o4·=·{4,·3,·3} | 95 | o4·=·{4,·3,·3} |
| 96 | o4·:·List</code></pre> | 96 | o4·:·List</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 100 | ·--·.002 | 100 | ·--·.00299809s·elapsed |
| 101 | ·······6·······10·······11·······5 | 101 | ·······6·······10·······11·······5 |
| 102 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 102 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 103 | ································ | 103 | ································ |
| 104 | ·····0·······1········2········3 | 104 | ·····0·······1········2········3 |
| 105 | o5·:·ChainComplex</code></pre> | 105 | o5·:·ChainComplex</code></pre> |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | o3·:·List | 29 | o3·:·List |
| 30 | i4·:·r={4,3,3} | 30 | i4·:·r={4,3,3} |
| 31 | o4·=·{4,·3,·3} | 31 | o4·=·{4,·3,·3} |
| 32 | o4·:·List | 32 | o4·:·List |
| 33 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 33 | i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 34 | ·--·.002 | 34 | ·--·.00299809s·elapsed |
| 35 | ·······6·······10·······11·······5 | 35 | ·······6·······10·······11·······5 |
| 36 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 36 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 37 | ·····0·······1········2········3 | 37 | ·····0·······1········2········3 |
| 38 | o5·:·ChainComplex | 38 | o5·:·ChainComplex |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=27 | 7 | #:len=27 |
| 8 | d2VpZ2h0VmVjdG9yc1JlYWxpemluZ1NBR0JJ | 8 | d2VpZ2h0VmVjdG9yc1JlYWxpemluZ1NBR0JJ |
| 9 | #:len=1819 | 9 | #:len=1819 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVGhlIG1haW4gZnVuY3Rpb24gZm9yIGRl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiVGhlIG1haW4gZnVuY3Rpb24gZm9yIGRl |
| 11 | dGVjdGluZyBTQUdCSSBiYXNlcyIsICJsaW5lbnVtIiA9PiAyMTUsIElucHV0cyA9PiB7U1BBTntU | 11 | dGVjdGluZyBTQUdCSSBiYXNlcyIsICJsaW5lbnVtIiA9PiAyMTUsIElucHV0cyA9PiB7U1BBTntU |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | c2F0dXJhdGUoSWRlYWwsTGlzdCk= | 8 | c2F0dXJhdGUoSWRlYWwsTGlzdCk= |
| 9 | #:len=207 | 9 | #:len=207 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOSwgInVuZG9jdW1lbnRlZCIgPT4gdHJ1 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOSwgInVuZG9jdW1lbnRlZCIgPT4gdHJ1 |
| 11 | ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2F0dXJhdGUs | 11 | ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2F0dXJhdGUs |
| Offset 38, 33 lines modified | Offset 38, 33 lines modified | ||
| 38 | o5·:·Ideal·of·S | 38 | o5·:·Ideal·of·S |
| 39 | i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); | 39 | i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); |
| 40 | o6·:·Ideal·of·S | 40 | o6·:·Ideal·of·S |
| 41 | i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); | 41 | i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); |
| 42 | ·--·used·0. | 42 | ·--·used·0.372192s·(cpu);·0.373971s·(thread);·0s·(gc) |
| 43 | o7·:·Ideal·of·S | 43 | o7·:·Ideal·of·S |
| 44 | i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); | 44 | i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); |
| 45 | ·--·used·0. | 45 | ·--·used·0.628958s·(cpu);·0.575339s·(thread);·0s·(gc) |
| 46 | o8·:·Ideal·of·S | 46 | o8·:·Ideal·of·S |
| 47 | i9·:·S·=·ZZ/101[vars(0..4)]; | 47 | i9·:·S·=·ZZ/101[vars(0..4)]; |
| 48 | i10·:·I·=·ideal·vars·S; | 48 | i10·:·I·=·ideal·vars·S; |
| 49 | o10·:·Ideal·of·S | 49 | o10·:·Ideal·of·S |
| 50 | i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); | 50 | i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); |
| 51 | ·--·used·0.01 | 51 | ·--·used·0.019339s·(cpu);·0.0214316s·(thread);·0s·(gc) |
| 52 | o11·:·Ideal·of·S | 52 | o11·:·Ideal·of·S |
| 53 | i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); | 53 | i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); |
| 54 | ·--·used·0.00 | 54 | ·--·used·0.00569003s·(cpu);·0.00687711s·(thread);·0s·(gc) |
| 55 | o12·:·Ideal·of·S | 55 | o12·:·Ideal·of·S |
| 56 | i13·:· | 56 | i13·:· |
| Offset 106, 21 lines modified | Offset 106, 21 lines modified | ||
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); | 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); |
| 108 | o6·:·Ideal·of·S</code></pre> | 108 | o6·:·Ideal·of·S</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); | 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); |
| 112 | ·--·used·0. | 112 | ·--·used·0.372192s·(cpu);·0.373971s·(thread);·0s·(gc) |
| 113 | o7·:·Ideal·of·S</code></pre> | 113 | o7·:·Ideal·of·S</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); | 116 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); |
| 117 | ·--·used·0. | 117 | ·--·used·0.628958s·(cpu);·0.575339s·(thread);·0s·(gc) |
| 118 | o8·:·Ideal·of·S</code></pre> | 118 | o8·:·Ideal·of·S</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ········</table> | 120 | ········</table> |
| 121 | ········<div> | 121 | ········<div> |
| 122 | ··········<p><span·class="tt">Strategy·=>·Quotient</span>·is·faster·in·other·cases:</p> | 122 | ··········<p><span·class="tt">Strategy·=>·Quotient</span>·is·faster·in·other·cases:</p> |
| 123 | ········</div> | 123 | ········</div> |
| Offset 131, 21 lines modified | Offset 131, 21 lines modified | ||
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i10·:·I·=·ideal·vars·S; | 132 | <td>··············<pre><code·class="language-macaulay2">i10·:·I·=·ideal·vars·S; |
| 133 | o10·:·Ideal·of·S</code></pre> | 133 | o10·:·Ideal·of·S</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); | 136 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); |
| 137 | ·--·used·0.01 | 137 | ·--·used·0.019339s·(cpu);·0.0214316s·(thread);·0s·(gc) |
| 138 | o11·:·Ideal·of·S</code></pre> | 138 | o11·:·Ideal·of·S</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); | 141 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); |
| 142 | ·--·used·0.00 | 142 | ·--·used·0.00569003s·(cpu);·0.00687711s·(thread);·0s·(gc) |
| 143 | o12·:·Ideal·of·S</code></pre> | 143 | o12·:·Ideal·of·S</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ········</table> | 145 | ········</table> |
| 146 | ······</div> | 146 | ······</div> |
| 147 | ······<div> | 147 | ······<div> |
| 148 | ········<h2>Further·information</h2> | 148 | ········<h2>Further·information</h2> |
| Offset 57, 32 lines modified | Offset 57, 32 lines modified | ||
| 57 | i5·:·I·=·monomialCurveIdeal(S,·1..n-1); | 57 | i5·:·I·=·monomialCurveIdeal(S,·1..n-1); |
| 58 | o5·:·Ideal·of·S | 58 | o5·:·Ideal·of·S |
| 59 | i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); | 59 | i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); |
| 60 | o6·:·Ideal·of·S | 60 | o6·:·Ideal·of·S |
| 61 | i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); | 61 | i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); |
| 62 | ·--·used·0. | 62 | ·--·used·0.372192s·(cpu);·0.373971s·(thread);·0s·(gc) |
| 63 | o7·:·Ideal·of·S | 63 | o7·:·Ideal·of·S |
| 64 | i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); | 64 | i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); |
| 65 | ·--·used·0. | 65 | ·--·used·0.628958s·(cpu);·0.575339s·(thread);·0s·(gc) |
| 66 | o8·:·Ideal·of·S | 66 | o8·:·Ideal·of·S |
| 67 | Strategy·=>·Quotient·is·faster·in·other·cases: | 67 | Strategy·=>·Quotient·is·faster·in·other·cases: |
| 68 | i9·:·S·=·ZZ/101[vars(0..4)]; | 68 | i9·:·S·=·ZZ/101[vars(0..4)]; |
| 69 | i10·:·I·=·ideal·vars·S; | 69 | i10·:·I·=·ideal·vars·S; |
| 70 | o10·:·Ideal·of·S | 70 | o10·:·Ideal·of·S |
| 71 | i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); | 71 | i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); |
| 72 | ·--·used·0.01 | 72 | ·--·used·0.019339s·(cpu);·0.0214316s·(thread);·0s·(gc) |
| 73 | o11·:·Ideal·of·S | 73 | o11·:·Ideal·of·S |
| 74 | i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); | 74 | i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); |
| 75 | ·--·used·0.00 | 75 | ·--·used·0.00569003s·(cpu);·0.00687711s·(thread);·0s·(gc) |
| 76 | o12·:·Ideal·of·S | 76 | o12·:·Ideal·of·S |
| 77 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 77 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fu\x8ur\x8rt\x8th\x8he\x8er\x8r·i\x8in\x8nf\x8fo\x8or\x8rm\x8ma\x8at\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 78 | ····*·Default·value:·null | 78 | ····*·Default·value:·null |
| 79 | ····*·Function:·_\x8q_\x8u_\x8o_\x8t_\x8i_\x8e_\x8n_\x8t·--·quotient·or·division | 79 | ····*·Function:·_\x8q_\x8u_\x8o_\x8t_\x8i_\x8e_\x8n_\x8t·--·quotient·or·division |
| 80 | ····*·Option·key:·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument | 80 | ····*·Option·key:·_\x8S_\x8t_\x8r_\x8a_\x8t_\x8e_\x8g_\x8y·--·an·optional·argument |
| 81 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* | 81 | *\x8**\x8**\x8**\x8**\x8*·R\x8Re\x8ef\x8fe\x8er\x8re\x8en\x8nc\x8ce\x8es\x8s·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=32 | 7 | #:len=32 |
| 8 | aW5jbHVzaW9uKC4uLixTdWJEaW1lbnNpb249Pi4uLik= | 8 | aW5jbHVzaW9uKC4uLixTdWJEaW1lbnNpb249Pi4uLik= |
| 9 | #:len=260 | 9 | #:len=260 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg1NSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg1NSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaW5jbHVzaW9uLFN1YkRpbWVuc2lvbl0sImluY2x1 | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaW5jbHVzaW9uLFN1YkRpbWVuc2lvbl0sImluY2x1 |
| Offset 40, 23 lines modified | Offset 40, 23 lines modified | ||
| 40 | ··········) | 40 | ··········) |
| 41 | o6·=·f | 41 | o6·=·f |
| 42 | o6·:·FunctionClosure | 42 | o6·:·FunctionClosure |
| 43 | i7·:·for·n·from·2·to·10·list·time·f·n | 43 | i7·:·for·n·from·2·to·10·list·time·f·n |
| 44 | ·--·used·0.00 | 44 | ·--·used·0.00797082s·(cpu);·0.00492844s·(thread);·0s·(gc) |
| 45 | ·--·used·0.00184898s·(cpu);·0.00433621s·(thread);·0s·(gc) | ||
| 46 | ·--·used·0.00 | 45 | ·--·used·0.00342932s·(cpu);·0.00636006s·(thread);·0s·(gc) |
| 46 | ·--·used·0.00903995s·(cpu);·0.0104792s·(thread);·0s·(gc) | ||
| 47 | ·--·used·0.01 | 47 | ·--·used·0.0155025s·(cpu);·0.0185103s·(thread);·0s·(gc) |
| 48 | ·--·used·0.0 | 48 | ·--·used·0.031955s·(cpu);·0.0326615s·(thread);·0s·(gc) |
| 49 | ·--·used·0.0421941s·(cpu);·0.0433922s·(thread);·0s·(gc) | ||
| 50 | ·--·used·0.06 | 49 | ·--·used·0.0682703s·(cpu);·0.0686997s·(thread);·0s·(gc) |
| 51 | ·--·used·0.11 | 50 | ·--·used·0.113303s·(cpu);·0.117s·(thread);·0s·(gc) |
| 52 | ·--·used·0.2 | 51 | ·--·used·0.201554s·(cpu);·0.20397s·(thread);·0s·(gc) |
| 52 | ·--·used·0.315199s·(cpu);·0.275147s·(thread);·0s·(gc) | ||
| 53 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 53 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 54 | ·····------------------------------------------------------------------------ | 54 | ·····------------------------------------------------------------------------ |
| 55 | ·····289139638632755625,·520764738758073845321} | 55 | ·····289139638632755625,·520764738758073845321} |
| 56 | o7·:·List | 56 | o7·:·List |
| Offset 106, 23 lines modified | Offset 106, 23 lines modified | ||
| 106 | o6·=·f | 106 | o6·=·f |
| 107 | o6·:·FunctionClosure</code></pre> | 107 | o6·:·FunctionClosure</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·n·from·2·to·10·list·time·f·n | 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·n·from·2·to·10·list·time·f·n |
| 111 | ·--·used·0.00 | 111 | ·--·used·0.00797082s·(cpu);·0.00492844s·(thread);·0s·(gc) |
| 112 | ·--·used·0.00184898s·(cpu);·0.00433621s·(thread);·0s·(gc) | ||
| 113 | ·--·used·0.00 | 112 | ·--·used·0.00342932s·(cpu);·0.00636006s·(thread);·0s·(gc) |
| 113 | ·--·used·0.00903995s·(cpu);·0.0104792s·(thread);·0s·(gc) | ||
| 114 | ·--·used·0.01 | 114 | ·--·used·0.0155025s·(cpu);·0.0185103s·(thread);·0s·(gc) |
| 115 | ·--·used·0.0 | 115 | ·--·used·0.031955s·(cpu);·0.0326615s·(thread);·0s·(gc) |
| 116 | ·--·used·0.0421941s·(cpu);·0.0433922s·(thread);·0s·(gc) | ||
| 117 | ·--·used·0.06 | 116 | ·--·used·0.0682703s·(cpu);·0.0686997s·(thread);·0s·(gc) |
| 118 | ·--·used·0.11 | 117 | ·--·used·0.113303s·(cpu);·0.117s·(thread);·0s·(gc) |
| 119 | ·--·used·0.2 | 118 | ·--·used·0.201554s·(cpu);·0.20397s·(thread);·0s·(gc) |
| 119 | ·--·used·0.315199s·(cpu);·0.275147s·(thread);·0s·(gc) | ||
| 120 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 120 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 121 | ·····------------------------------------------------------------------------ | 121 | ·····------------------------------------------------------------------------ |
| 122 | ·····289139638632755625,·520764738758073845321} | 122 | ·····289139638632755625,·520764738758073845321} |
| 123 | o7·:·List</code></pre> | 123 | o7·:·List</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| Offset 56, 23 lines modified | Offset 56, 23 lines modified | ||
| 56 | ··········integral·chern·symmetricPower_(2*n-3)·last·bundles·G | 56 | ··········integral·chern·symmetricPower_(2*n-3)·last·bundles·G |
| 57 | ··········) | 57 | ··········) |
| 58 | o6·=·f | 58 | o6·=·f |
| 59 | o6·:·FunctionClosure | 59 | o6·:·FunctionClosure |
| 60 | i7·:·for·n·from·2·to·10·list·time·f·n | 60 | i7·:·for·n·from·2·to·10·list·time·f·n |
| 61 | ·--·used·0.00 | 61 | ·--·used·0.00797082s·(cpu);·0.00492844s·(thread);·0s·(gc) |
| 62 | ·--·used·0.00184898s·(cpu);·0.00433621s·(thread);·0s·(gc) | ||
| 63 | ·--·used·0.00 | 62 | ·--·used·0.00342932s·(cpu);·0.00636006s·(thread);·0s·(gc) |
| 63 | ·--·used·0.00903995s·(cpu);·0.0104792s·(thread);·0s·(gc) | ||
| 64 | ·--·used·0.01 | 64 | ·--·used·0.0155025s·(cpu);·0.0185103s·(thread);·0s·(gc) |
| 65 | ·--·used·0.0 | 65 | ·--·used·0.031955s·(cpu);·0.0326615s·(thread);·0s·(gc) |
| 66 | ·--·used·0.0421941s·(cpu);·0.0433922s·(thread);·0s·(gc) | ||
| 67 | ·--·used·0.06 | 66 | ·--·used·0.0682703s·(cpu);·0.0686997s·(thread);·0s·(gc) |
| 68 | ·--·used·0.11 | 67 | ·--·used·0.113303s·(cpu);·0.117s·(thread);·0s·(gc) |
| 69 | ·--·used·0.2 | 68 | ·--·used·0.201554s·(cpu);·0.20397s·(thread);·0s·(gc) |
| 69 | ·--·used·0.315199s·(cpu);·0.275147s·(thread);·0s·(gc) | ||
| 70 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 70 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 71 | ·····------------------------------------------------------------------------ | 71 | ·····------------------------------------------------------------------------ |
| 72 | ·····289139638632755625,·520764738758073845321} | 72 | ·····289139638632755625,·520764738758073845321} |
| 73 | o7·:·List | 73 | o7·:·List |
| 74 | Note:·in·characteristic·zero,·using·Bertini's·theorem,·the·numbers·computed·can | 74 | Note:·in·characteristic·zero,·using·Bertini's·theorem,·the·numbers·computed·can |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | c2NodXJDb21wbGV4 | 8 | c2NodXJDb21wbGV4 |
| 9 | #:len=3101 | 9 | #:len=3101 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU2NodXIgZnVuY3RvcnMgb2YgY2hhaW4g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiU2NodXIgZnVuY3RvcnMgb2YgY2hhaW4g |
| 11 | Y29tcGxleGVzIiwgImxpbmVudW0iID0+IDU1MiwgSW5wdXRzID0+IHtTUEFOe1RUeyJsYW1iZGEi | 11 | Y29tcGxleGVzIiwgImxpbmVudW0iID0+IDU1MiwgSW5wdXRzID0+IHtTUEFOe1RUeyJsYW1iZGEi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | c3BsaXRDaGFyYWN0ZXI= | 8 | c3BsaXRDaGFyYWN0ZXI= |
| 9 | #:len=913 | 9 | #:len=913 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRGVjb21wb3NlcyBhIHN5bW1ldHJpYyBw | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRGVjb21wb3NlcyBhIHN5bW1ldHJpYyBw |
| 11 | b2x5bm9taWFsIGFzIGEgc3VtIG9mIFNjaHVyIGZ1bmN0aW9ucyIsICJsaW5lbnVtIiA9PiA0MDEs | 11 | b2x5bm9taWFsIGFzIGEgc3VtIG9mIFNjaHVyIGZ1bmN0aW9ucyIsICJsaW5lbnVtIiA9PiA0MDEs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=33 | 7 | #:len=33 |
| 8 | c2NodXJSZXNvbHV0aW9uKFJpbmdFbGVtZW50LExpc3Qp | 8 | c2NodXJSZXNvbHV0aW9uKFJpbmdFbGVtZW50LExpc3Qp |
| 9 | #:len=286 | 9 | #:len=286 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjQ0OSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjQ0OSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2NodXJSZXNvbHV0aW9uLFJpbmdFbGVtZW50LExp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc2NodXJSZXNvbHV0aW9uLFJpbmdFbGVtZW50LExp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | bWFrZUJldHRpVGFsbHk= | 8 | bWFrZUJldHRpVGFsbHk= |
| 9 | #:len=1334 | 9 | #:len=1334 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29udmVydHMgYSBoYXNoIHRhYmxlIHJl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29udmVydHMgYSBoYXNoIHRhYmxlIHJl |
| 11 | cHJlc2VudGluZyBhIEJldHRpIHRhYmxlIHRvIGEgQmV0dGkgdGFsbHkiLCAibGluZW51bSIgPT4g | 11 | cHJlc2VudGluZyBhIEJldHRpIHRhYmxlIHRvIGEgQmV0dGkgdGFsbHkiLCAibGluZW51bSIgPT4g |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | bVJlZ3VsYXI= | 8 | bVJlZ3VsYXI= |
| 9 | #:len=1136 | 9 | #:len=1136 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibVJlZ3VsYXIoRixHKSBjb21wdXRlcyB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibVJlZ3VsYXIoRixHKSBjb21wdXRlcyB0 |
| 11 | aGUgcmVndWxhcml0eSBvZiBGIHdpdGggcmVzcGVjdCB0byBHIChnbG9iYWxseSBnZW5lcmF0ZWQp | 11 | aGUgcmVndWxhcml0eSBvZiBGIHdpdGggcmVzcGVjdCB0byBHIChnbG9iYWxseSBnZW5lcmF0ZWQp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=26 | 7 | #:len=26 |
| 8 | bWFrZVByb2R1Y3RSaW5nKFJpbmcsTGlzdCk= | 8 | bWFrZVByb2R1Y3RSaW5nKFJpbmcsTGlzdCk= |
| 9 | #:len=277 | 9 | #:len=277 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTQxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gOTQxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtYWtlUHJvZHVjdFJpbmcsUmluZyxMaXN0KSwibWFr | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhtYWtlUHJvZHVjdFJpbmcsUmluZyxMaXN0KSwibWFr |
| Offset 53, 15 lines modified | Offset 53, 15 lines modified | ||
| 53 | o9·:·Ideal·of·R | 53 | o9·:·Ideal·of·R |
| 54 | i10·:·X=((W)*ideal(y)+ideal(f)); | 54 | i10·:·X=((W)*ideal(y)+ideal(f)); |
| 55 | o10·:·Ideal·of·R | 55 | o10·:·Ideal·of·R |
| 56 | i11·:·time·isComponentContained(X,Y) | 56 | i11·:·time·isComponentContained(X,Y) |
| 57 | ·--·used·3 | 57 | ·--·used·30.6565s·(cpu);·5.754s·(thread);·0s·(gc) |
| 58 | o11·=·true | 58 | o11·=·true |
| 59 | i12·:·print·"we·could·confirm·this·with·the·computation:" | 59 | i12·:·print·"we·could·confirm·this·with·the·computation:" |
| 60 | we·could·confirm·this·with·the·computation: | 60 | we·could·confirm·this·with·the·computation: |
| 61 | i13·:·B=ideal(x)*ideal(y)*ideal(z) | 61 | i13·:·B=ideal(x)*ideal(y)*ideal(z) |
| Offset 71, 12 lines modified | Offset 71, 12 lines modified | ||
| 71 | ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g, | 71 | ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g, |
| 72 | ······----------------------------------------------------------------------- | 72 | ······----------------------------------------------------------------------- |
| 73 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) | 73 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) |
| 74 | o13·:·Ideal·of·R | 74 | o13·:·Ideal·of·R |
| 75 | i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) | 75 | i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) |
| 76 | ·--·used· | 76 | ·--·used·80.4937s·(cpu);·55.7243s·(thread);·0s·(gc) |
| 77 | o14·=·true | 77 | o14·=·true |
| 78 | i15·:· | 78 | i15·:· |
| Offset 23, 24 lines modified | Offset 23, 24 lines modified | ||
| 23 | i5·:·A·=·makeChowRing(R) | 23 | i5·:·A·=·makeChowRing(R) |
| 24 | o5·=·A | 24 | o5·=·A |
| 25 | o5·:·QuotientRing | 25 | o5·:·QuotientRing |
| 26 | i6·:·time·s·=·segreDimX(X,Y,A) | 26 | i6·:·time·s·=·segreDimX(X,Y,A) |
| 27 | ·--·used·5. | 27 | ·--·used·5.31504s·(cpu);·0.726945s·(thread);·0s·(gc) |
| 28 | ·······2·············2 | 28 | ·······2·············2 |
| 29 | o6·=·2H··+·4H·H··+·2H | 29 | o6·=·2H··+·4H·H··+·2H |
| 30 | ·······1·····1·2·····2 | 30 | ·······1·····1·2·····2 |
| 31 | o6·:·A | 31 | o6·:·A |
| 32 | i7·:·time·segre(X,Y,A) | 32 | i7·:·time·segre(X,Y,A) |
| 33 | ·--·used·0. | 33 | ·--·used·0.246335s·(cpu);·0.0982144s·(thread);·0s·(gc) |
| 34 | ········2·2·····2·········2·····2·············2 | 34 | ········2·2·····2·········2·····2·············2 |
| 35 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H | 35 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H |
| 36 | ········1·2·····1·2·····1·2·····1·····1·2·····2 | 36 | ········1·2·····1·2·····1·2·····1·····1·2·····2 |
| 37 | o7·:·A | 37 | o7·:·A |
| Offset 144, 15 lines modified | Offset 144, 15 lines modified | ||
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i10·:·X=((W)*ideal(y)+ideal(f)); | 145 | <td>··············<pre><code·class="language-macaulay2">i10·:·X=((W)*ideal(y)+ideal(f)); |
| 146 | o10·:·Ideal·of·R</code></pre> | 146 | o10·:·Ideal·of·R</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·isComponentContained(X,Y) | 149 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·isComponentContained(X,Y) |
| 150 | ·--·used·3 | 150 | ·--·used·30.6565s·(cpu);·5.754s·(thread);·0s·(gc) |
| 151 | o11·=·true</code></pre> | 151 | o11·=·true</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i12·:·print·"we·could·confirm·this·with·the·computation:" | 154 | <td>··············<pre><code·class="language-macaulay2">i12·:·print·"we·could·confirm·this·with·the·computation:" |
| 155 | we·could·confirm·this·with·the·computation:</code></pre> | 155 | we·could·confirm·this·with·the·computation:</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| Offset 165, 15 lines modified | Offset 165, 15 lines modified | ||
| 165 | ······----------------------------------------------------------------------- | 165 | ······----------------------------------------------------------------------- |
| 166 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) | 166 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) |
| 167 | o13·:·Ideal·of·R</code></pre> | 167 | o13·:·Ideal·of·R</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) | 170 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) |
| 171 | ·--·used· | 171 | ·--·used·80.4937s·(cpu);·55.7243s·(thread);·0s·(gc) |
| 172 | o14·=·true</code></pre> | 172 | o14·=·true</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ········</table> | 174 | ········</table> |
| 175 | ······</div> | 175 | ······</div> |
| 176 | ······<div·class="waystouse"> | 176 | ······<div·class="waystouse"> |
| 177 | ········<h2>Ways·to·use·<span·class="tt">isComponentContained</span>:</h2> | 177 | ········<h2>Ways·to·use·<span·class="tt">isComponentContained</span>:</h2> |
| Offset 69, 29 lines modified | Offset 69, 29 lines modified | ||
| 69 | i9·:·Y=ideal·(z_0*W_0-z_1*W_1)+ideal(f); | 69 | i9·:·Y=ideal·(z_0*W_0-z_1*W_1)+ideal(f); |
| 70 | o9·:·Ideal·of·R | 70 | o9·:·Ideal·of·R |
| 71 | i10·:·X=((W)*ideal(y)+ideal(f)); | 71 | i10·:·X=((W)*ideal(y)+ideal(f)); |
| 72 | o10·:·Ideal·of·R | 72 | o10·:·Ideal·of·R |
| 73 | i11·:·time·isComponentContained(X,Y) | 73 | i11·:·time·isComponentContained(X,Y) |
| 74 | ·--·used·3 | 74 | ·--·used·30.6565s·(cpu);·5.754s·(thread);·0s·(gc) |
| 75 | o11·=·true | 75 | o11·=·true |
| 76 | i12·:·print·"we·could·confirm·this·with·the·computation:" | 76 | i12·:·print·"we·could·confirm·this·with·the·computation:" |
| 77 | we·could·confirm·this·with·the·computation: | 77 | we·could·confirm·this·with·the·computation: |
| 78 | i13·:·B=ideal(x)*ideal(y)*ideal(z) | 78 | i13·:·B=ideal(x)*ideal(y)*ideal(z) |
| 79 | o13·=·ideal·(a*d*g,·a*d*h,·a*d*i,·a*e*g,·a*e*h,·a*e*i,·a*f*g,·a*f*h,·a*f*i, | 79 | o13·=·ideal·(a*d*g,·a*d*h,·a*d*i,·a*e*g,·a*e*h,·a*e*i,·a*f*g,·a*f*h,·a*f*i, |
| 80 | ······----------------------------------------------------------------------- | 80 | ······----------------------------------------------------------------------- |
| 81 | ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g, | 81 | ······b*d*g,·b*d*h,·b*d*i,·b*e*g,·b*e*h,·b*e*i,·b*f*g,·b*f*h,·b*f*i,·c*d*g, |
| 82 | ······----------------------------------------------------------------------- | 82 | ······----------------------------------------------------------------------- |
| 83 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) | 83 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) |
| 84 | o13·:·Ideal·of·R | 84 | o13·:·Ideal·of·R |
| 85 | i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) | 85 | i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) |
| 86 | ·--·used· | 86 | ·--·used·80.4937s·(cpu);·55.7243s·(thread);·0s·(gc) |
| 87 | o14·=·true | 87 | o14·=·true |
| 88 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8tC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8ne\x8ed\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 88 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sC\x8Co\x8om\x8mp\x8po\x8on\x8ne\x8en\x8nt\x8tC\x8Co\x8on\x8nt\x8ta\x8ai\x8in\x8ne\x8ed\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 89 | ····*·isComponentContained(Ideal,Ideal) | 89 | ····*·isComponentContained(Ideal,Ideal) |
| 90 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 90 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 91 | The·object·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8C_\x8o_\x8n_\x8t_\x8a_\x8i_\x8n_\x8e_\x8d·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. | 91 | The·object·_\x8i_\x8s_\x8C_\x8o_\x8m_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8C_\x8o_\x8n_\x8t_\x8a_\x8i_\x8n_\x8e_\x8d·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n_\x8·_\x8w_\x8i_\x8t_\x8h_\x8·_\x8o_\x8p_\x8t_\x8i_\x8o_\x8n_\x8s. |
| Offset 111, 25 lines modified | Offset 111, 25 lines modified | ||
| 111 | o5·=·A | 111 | o5·=·A |
| 112 | o5·:·QuotientRing</code></pre> | 112 | o5·:·QuotientRing</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·s·=·segreDimX(X,Y,A) | 115 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·s·=·segreDimX(X,Y,A) |
| 116 | ·--·used·5. | 116 | ·--·used·5.31504s·(cpu);·0.726945s·(thread);·0s·(gc) |
| 117 | ·······2·············2 | 117 | ·······2·············2 |
| 118 | o6·=·2H··+·4H·H··+·2H | 118 | o6·=·2H··+·4H·H··+·2H |
| 119 | ·······1·····1·2·····2 | 119 | ·······1·····1·2·····2 |
| 120 | o6·:·A</code></pre> | 120 | o6·:·A</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·segre(X,Y,A) | 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·segre(X,Y,A) |
| 124 | ·--·used·0. | 124 | ·--·used·0.246335s·(cpu);·0.0982144s·(thread);·0s·(gc) |
| 125 | ········2·2·····2·········2·····2·············2 | 125 | ········2·2·····2·········2·····2·············2 |
| 126 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H | 126 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H |
| 127 | ········1·2·····1·2·····1·2·····1·····1·2·····2 | 127 | ········1·2·····1·2·····1·2·····1·····1·2·····2 |
| 128 | o7·:·A</code></pre> | 128 | o7·:·A</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| Offset 49, 23 lines modified | Offset 49, 23 lines modified | ||
| 49 | o4·:·Ideal·of·R | 49 | o4·:·Ideal·of·R |
| 50 | i5·:·A·=·makeChowRing(R) | 50 | i5·:·A·=·makeChowRing(R) |
| 51 | o5·=·A | 51 | o5·=·A |
| 52 | o5·:·QuotientRing | 52 | o5·:·QuotientRing |
| 53 | i6·:·time·s·=·segreDimX(X,Y,A) | 53 | i6·:·time·s·=·segreDimX(X,Y,A) |
| 54 | ·--·used·5. | 54 | ·--·used·5.31504s·(cpu);·0.726945s·(thread);·0s·(gc) |
| 55 | ·······2·············2 | 55 | ·······2·············2 |
| 56 | o6·=·2H··+·4H·H··+·2H | 56 | o6·=·2H··+·4H·H··+·2H |
| 57 | ·······1·····1·2·····2 | 57 | ·······1·····1·2·····2 |
| 58 | o6·:·A | 58 | o6·:·A |
| 59 | i7·:·time·segre(X,Y,A) | 59 | i7·:·time·segre(X,Y,A) |
| 60 | ·--·used·0. | 60 | ·--·used·0.246335s·(cpu);·0.0982144s·(thread);·0s·(gc) |
| 61 | ········2·2·····2·········2·····2·············2 | 61 | ········2·2·····2·········2·····2·············2 |
| 62 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H | 62 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H |
| 63 | ········1·2·····1·2·····1·2·····1·····1·2·····2 | 63 | ········1·2·····1·2·····1·2·····1·····1·2·····2 |
| 64 | o7·:·A | 64 | o7·:·A |
| 65 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8se\x8eg\x8gr\x8re\x8eD\x8Di\x8im\x8mX\x8X:\x8:·*\x8**\x8**\x8**\x8**\x8* | 65 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8se\x8eg\x8gr\x8re\x8eD\x8Di\x8im\x8mX\x8X:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=28 | 7 | #:len=28 |
| 8 | b3B0aW1pemUoLi4uLFZlcmJvc2l0eT0+Li4uKQ== | 8 | b3B0aW1pemUoLi4uLFZlcmJvc2l0eT0+Li4uKQ== |
| 9 | #:len=300 | 9 | #:len=300 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzkyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzkyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=22 | 7 | #:len=22 |
| 8 | YmV0dGVyTm9ybWFsaXphdGlvbk1hcA== | 8 | YmV0dGVyTm9ybWFsaXphdGlvbk1hcA== |
| 9 | #:len=1762 | 9 | #:len=1762 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibm9ybWFsaXplcyBub24gZG9tYWlucyIs | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibm9ybWFsaXplcyBub24gZG9tYWlucyIs |
| 11 | ICJsaW5lbnVtIiA9PiA4ODIsIElucHV0cyA9PiB7U1BBTntUVHsiUyJ9LCIsICIsU1BBTnsiYSAi | 11 | ICJsaW5lbnVtIiA9PiA4ODIsIElucHV0cyA9PiB7U1BBTntUVHsiUyJ9LCIsICIsU1BBTnsiYSAi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=13 | 7 | #:len=13 |
| 8 | U2VyaWFsaXphdGlvbg== | 8 | U2VyaWFsaXphdGlvbg== |
| 9 | #:len=554 | 9 | #:len=554 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV2ZXJzaWJsZSBjb252ZXJzaW9uIG9m | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV2ZXJzaWJsZSBjb252ZXJzaW9uIG9m |
| 11 | IGFsbCBNYWNhdWxheTIgb2JqZWN0cyB0byBzdHJpbmdzIiwgRGVzY3JpcHRpb24gPT4gMTooRElW | 11 | IGFsbCBNYWNhdWxheTIgb2JqZWN0cyB0byBzdHJpbmdzIiwgRGVzY3JpcHRpb24gPT4gMTooRElW |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | YXJYaXYoU3RyaW5nLFN0cmluZyk= | 8 | YXJYaXYoU3RyaW5nLFN0cmluZyk= |
| 9 | #:len=236 | 9 | #:len=236 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhclhpdixTdHJpbmcsU3RyaW5nKSwiYXJYaXYoU3Ry | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhclhpdixTdHJpbmcsU3RyaW5nKSwiYXJYaXYoU3Ry |
| Offset 1, 6 lines modified | Offset 1, 6 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1331702921222 | 1 | --·-*-·M2-comint·-*-·hash:·1331702921222 |
| 2 | i1·:·check·SimpleDoc | 2 | i1·:·check·SimpleDoc |
| 3 | ·--·capturing·check(0,·"SimpleDoc")···········--·.0 | 3 | ·--·capturing·check(0,·"SimpleDoc")···········--·.0746118s·elapsed |
| 4 | i2·:· | 4 | i2·:· |
| Offset 69, 15 lines modified | Offset 69, 15 lines modified | ||
| 69 | ········</table> | 69 | ········</table> |
| 70 | ········<div> | 70 | ········<div> |
| 71 | ··········<p>The·<a·title="perform·tests·of·a·package"·href="../../Macaulay2Doc/html/_check.html">check</a>·method·executes·all·package·tests·defined·this·way.</p> | 71 | ··········<p>The·<a·title="perform·tests·of·a·package"·href="../../Macaulay2Doc/html/_check.html">check</a>·method·executes·all·package·tests·defined·this·way.</p> |
| 72 | ········</div> | 72 | ········</div> |
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·check·SimpleDoc | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·check·SimpleDoc |
| 76 | ·--·capturing·check(0,·"SimpleDoc")···········--·.0 | 76 | ·--·capturing·check(0,·"SimpleDoc")···········--·.0746118s·elapsed</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ········</table> | 78 | ········</table> |
| 79 | ······</div> | 79 | ······</div> |
| 80 | ······<div> | 80 | ······<div> |
| 81 | ········<h2>See·also</h2> | 81 | ········<h2>See·also</h2> |
| 82 | ········<ul> | 82 | ········<ul> |
| 83 | ··········<li> | 83 | ··········<li> |
| Offset 12, 15 lines modified | Offset 12, 15 lines modified | ||
| 12 | (String)·(missing·documentation)·to·write·a·test·case. | 12 | (String)·(missing·documentation)·to·write·a·test·case. |
| 13 | TEST·///·-*·test·for·simpleDocFrob·*- | 13 | TEST·///·-*·test·for·simpleDocFrob·*- |
| 14 | ··assert(simpleDocFrob(2,matrix{{1,2}})·==·matrix{{1,2,0,0},{0,0,1,2}}) | 14 | ··assert(simpleDocFrob(2,matrix{{1,2}})·==·matrix{{1,2,0,0},{0,0,1,2}}) |
| 15 | /// | 15 | /// |
| 16 | The·_\x8c_\x8h_\x8e_\x8c_\x8k·method·executes·all·package·tests·defined·this·way. | 16 | The·_\x8c_\x8h_\x8e_\x8c_\x8k·method·executes·all·package·tests·defined·this·way. |
| 17 | i1·:·check·SimpleDoc | 17 | i1·:·check·SimpleDoc |
| 18 | ·--·capturing·check(0,·"SimpleDoc")···········--·.0 | 18 | ·--·capturing·check(0,·"SimpleDoc")···········--·.0746118s·elapsed |
| 19 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 19 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 20 | ····*·_\x8T_\x8E_\x8S_\x8T·--·add·a·test·for·a·package | 20 | ····*·_\x8T_\x8E_\x8S_\x8T·--·add·a·test·for·a·package |
| 21 | ····*·_\x8c_\x8h_\x8e_\x8c_\x8k·--·perform·tests·of·a·package | 21 | ····*·_\x8c_\x8h_\x8e_\x8c_\x8k·--·perform·tests·of·a·package |
| 22 | ····*·_\x8p_\x8a_\x8c_\x8k_\x8a_\x8g_\x8e_\x8T_\x8e_\x8m_\x8p_\x8l_\x8a_\x8t_\x8e·--·a·template·for·a·package | 22 | ····*·_\x8p_\x8a_\x8c_\x8k_\x8a_\x8g_\x8e_\x8T_\x8e_\x8m_\x8p_\x8l_\x8a_\x8t_\x8e·--·a·template·for·a·package |
| 23 | ····*·_\x8d_\x8o_\x8c_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e·--·an·example·of·a·documentation·string | 23 | ····*·_\x8d_\x8o_\x8c_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e·--·an·example·of·a·documentation·string |
| 24 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 24 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| 25 | The·object·_\x8t_\x8e_\x8s_\x8t_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g. | 25 | The·object·_\x8t_\x8e_\x8s_\x8t_\x8E_\x8x_\x8a_\x8m_\x8p_\x8l_\x8e·is·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | ZWxlbWVudGFyeUNvbGxhcHNl | 8 | ZWxlbWVudGFyeUNvbGxhcHNl |
| 9 | #:len=365 | 9 | #:len=365 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU1Mywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU1Mywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsiZWxlbWVudGFyeUNvbGxhcHNlIiwiZWxlbWVudGFy | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsiZWxlbWVudGFyeUNvbGxhcHNlIiwiZWxlbWVudGFy |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=30 | 7 | #:len=30 |
| 8 | c2hlbGxpbmdPcmRlciguLi4sUmFuZG9tPT4uLi4p | 8 | c2hlbGxpbmdPcmRlciguLi4sUmFuZG9tPT4uLi4p |
| 9 | #:len=311 | 9 | #:len=311 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODk0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODk0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tzaGVsbGluZ09yZGVyLFJhbmRvbV0sInNoZWxsaW5n | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tzaGVsbGluZ09yZGVyLFJhbmRvbV0sInNoZWxsaW5n |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=9 | 7 | #:len=9 |
| 8 | aXNCb29sZWFu | 8 | aXNCb29sZWFu |
| 9 | #:len=1246 | 9 | #:len=1246 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRGV0ZXJtaW5lIGlmIGEgcG9zZXQgaXMg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiRGV0ZXJtaW5lIGlmIGEgcG9zZXQgaXMg |
| 11 | YSBib29sZWFuIGFsZ2VicmEuIiwgImxpbmVudW0iID0+IDMyNywgSW5wdXRzID0+IHtTUEFOe1RU | 11 | YSBib29sZWFuIGFsZ2VicmEuIiwgImxpbmVudW0iID0+IDMyNywgSW5wdXRzID0+IHtTUEFOe1RU |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | dW5pdmVyc2FsSWRlYWw= | 8 | dW5pdmVyc2FsSWRlYWw= |
| 9 | #:len=2182 | 9 | #:len=2182 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgdGhlIHVuaXZlcnNhbCBy | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgdGhlIHVuaXZlcnNhbCBy |
| 11 | ZWFsaXphdGlvbiBpZGVhbCBvZiBhIG1hdHJvaWQiLCAibGluZW51bSIgPT4gMjE0MiwgSW5wdXRz | 11 | ZWFsaXphdGlvbiBpZGVhbCBvZiBhIG1hdHJvaWQiLCAibGluZW51bSIgPT4gMjE0MiwgSW5wdXRz |
| Offset 9, 14 lines modified | Offset 9, 14 lines modified | ||
| 9 | i3·:·(Y,·T)·=·setOnesForest·X; | 9 | i3·:·(Y,·T)·=·setOnesForest·X; |
| 10 | i4·:·remVars·:=·flatten·entries·Y·-·set{0_(ring·Y),·1_(ring·Y)}; | 10 | i4·:·remVars·:=·flatten·entries·Y·-·set{0_(ring·Y),·1_(ring·Y)}; |
| 11 | i5·:·h·=·rehomogenizePolynomial(X,·Y,·T,·remVars_0^2+remVars_0*remVars_1-1) | 11 | i5·:·h·=·rehomogenizePolynomial(X,·Y,·T,·remVars_0^2+remVars_0*remVars_1-1) |
| 12 | ······2·2·····2··2·················2··2·····2·2·····2·2 | ||
| 13 | 12 | ······2·2·2·2··········2·2·2·2··················2·2 | |
| 13 | o5·=·x·x·x·x·x··x···-·x·x·x·x·x··x···+·x·x·x·x·x·x·x·x | ||
| 14 | ······1·4·6·7·10·11···· | 14 | ······1·4·6·7·10·11····2·3·5·8·10·11····1·2·3·4·6·7·9·12 |
| 15 | o5·:·R | 15 | o5·:·R |
| 16 | i6·:· | 16 | i6·:· |
| Offset 14, 20 lines modified | Offset 14, 20 lines modified | ||
| 14 | ························4·················4 | 14 | ························4·················4 |
| 15 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) | 15 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) |
| 16 | ·················0···7·············0···7 | 16 | ·················0···7·············0···7 |
| 17 | i3·:·(Y,·F)·=·setOnesForest·X | 17 | i3·:·(Y,·F)·=·setOnesForest·X |
| 18 | o3·=·(|·0·1· | 18 | o3·=·(|·0·1·0···1·|,·Graph{"edges"·=>·{{y·,·y·},·{y·,·y·},·{y·,·y·},·{y·, |
| 19 | ······|·1·0· | 19 | ······|·1·0·0···1·|······················1···4·····3···4·····0···5·····2· |
| 20 | ······|·0· | 20 | ······|·0·1·1···0·|········"ring"·=>·QQ[y·..y·] |
| 21 | ······|·1·0· | 21 | ······|·1·0·x_7·0·|······················0···7 |
| 22 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} | 22 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} |
| 23 | ···········································0···1···2···3···4···5···6···7 | 23 | ···········································0···1···2···3···4···5···6···7 |
| 24 | ·····------------------------------------------------------------------------ | 24 | ·····------------------------------------------------------------------------ |
| 25 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) | 25 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) |
| 26 | ······ | 26 | ······5·····2···6·····0···7·····1···7 |
| 27 | o3·:·Sequence | 27 | o3·:·Sequence |
| 28 | i4·:· | 28 | i4·:· |
| Offset 93, 17 lines modified | Offset 93, 17 lines modified | ||
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·remVars·:=·flatten·entries·Y·-·set{0_(ring·Y),·1_(ring·Y)};</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·remVars·:=·flatten·entries·Y·-·set{0_(ring·Y),·1_(ring·Y)};</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·h·=·rehomogenizePolynomial(X,·Y,·T,·remVars_0^2+remVars_0*remVars_1-1) | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·h·=·rehomogenizePolynomial(X,·Y,·T,·remVars_0^2+remVars_0*remVars_1-1) |
| 99 | ······2·2·····2··2·················2··2·····2·2·····2·2 | ||
| 100 | 99 | ······2·2·2·2··········2·2·2·2··················2·2 | |
| 100 | o5·=·x·x·x·x·x··x···-·x·x·x·x·x··x···+·x·x·x·x·x·x·x·x | ||
| 101 | ······1·4·6·7·10·11···· | 101 | ······1·4·6·7·10·11····2·3·5·8·10·11····1·2·3·4·6·7·9·12 |
| 102 | o5·:·R</code></pre> | 102 | o5·:·R</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ········</table> | 104 | ········</table> |
| 105 | ······</div> | 105 | ······</div> |
| 106 | ······<div> | 106 | ······<div> |
| 107 | ········<h2>See·also</h2> | 107 | ········<h2>See·also</h2> |
| Offset 32, 17 lines modified | Offset 32, 17 lines modified | ||
| 32 | ·············6······5 | 32 | ·············6······5 |
| 33 | o2·:·Matrix·R··<--·R | 33 | o2·:·Matrix·R··<--·R |
| 34 | i3·:·(Y,·T)·=·setOnesForest·X; | 34 | i3·:·(Y,·T)·=·setOnesForest·X; |
| 35 | i4·:·remVars·:=·flatten·entries·Y·-·set{0_(ring·Y),·1_(ring·Y)}; | 35 | i4·:·remVars·:=·flatten·entries·Y·-·set{0_(ring·Y),·1_(ring·Y)}; |
| 36 | i5·:·h·=·rehomogenizePolynomial(X,·Y,·T,·remVars_0^2+remVars_0*remVars_1-1) | 36 | i5·:·h·=·rehomogenizePolynomial(X,·Y,·T,·remVars_0^2+remVars_0*remVars_1-1) |
| 37 | ······2·2·····2··2·················2··2·····2·2·····2·2 | ||
| 38 | 37 | ······2·2·2·2··········2·2·2·2··················2·2 | |
| 38 | o5·=·x·x·x·x·x··x···-·x·x·x·x·x··x···+·x·x·x·x·x·x·x·x | ||
| 39 | ······1·4·6·7·10·11···· | 39 | ······1·4·6·7·10·11····2·3·5·8·10·11····1·2·3·4·6·7·9·12 |
| 40 | o5·:·R | 40 | o5·:·R |
| 41 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 41 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 42 | ····*·_\x8s_\x8e_\x8t_\x8O_\x8n_\x8e_\x8s_\x8F_\x8o_\x8r_\x8e_\x8s_\x8t·--·sets·to·1·variables·in·a·symbolic·slack·matrix·which | 42 | ····*·_\x8s_\x8e_\x8t_\x8O_\x8n_\x8e_\x8s_\x8F_\x8o_\x8r_\x8e_\x8s_\x8t·--·sets·to·1·variables·in·a·symbolic·slack·matrix·which |
| 43 | ······corresponding·to·edges·of·a·spanning·forest | 43 | ······corresponding·to·edges·of·a·spanning·forest |
| 44 | ····*·_\x8s_\x8l_\x8a_\x8c_\x8k_\x8I_\x8d_\x8e_\x8a_\x8l·--·computes·the·slack·ideal | 44 | ····*·_\x8s_\x8l_\x8a_\x8c_\x8k_\x8I_\x8d_\x8e_\x8a_\x8l·--·computes·the·slack·ideal |
| 45 | ····*·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l_\x8i_\x8c_\x8S_\x8l_\x8a_\x8c_\x8k_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·computes·the·symbolic·slack·matrix | 45 | ····*·_\x8s_\x8y_\x8m_\x8b_\x8o_\x8l_\x8i_\x8c_\x8S_\x8l_\x8a_\x8c_\x8k_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·computes·the·symbolic·slack·matrix |
| Offset 91, 23 lines modified | Offset 91, 23 lines modified | ||
| 91 | ························4·················4 | 91 | ························4·················4 |
| 92 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) | 92 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) |
| 93 | ·················0···7·············0···7</code></pre> | 93 | ·················0···7·············0···7</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·(Y,·F)·=·setOnesForest·X | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·(Y,·F)·=·setOnesForest·X |
| 97 | o3·=·(|·0·1· | 97 | o3·=·(|·0·1·0···1·|,·Graph{"edges"·=>·{{y·,·y·},·{y·,·y·},·{y·,·y·},·{y·, |
| 98 | ······|·1·0· | 98 | ······|·1·0·0···1·|······················1···4·····3···4·····0···5·····2· |
| 99 | ······|·0· | 99 | ······|·0·1·1···0·|········"ring"·=>·QQ[y·..y·] |
| 100 | ······|·1·0· | 100 | ······|·1·0·x_7·0·|······················0···7 |
| 101 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} | 101 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} |
| 102 | ···········································0···1···2···3···4···5···6···7 | 102 | ···········································0···1···2···3···4···5···6···7 |
| 103 | ·····------------------------------------------------------------------------ | 103 | ·····------------------------------------------------------------------------ |
| 104 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) | 104 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) |
| 105 | ······ | 105 | ······5·····2···6·····0···7·····1···7 |
| 106 | o3·:·Sequence</code></pre> | 106 | o3·:·Sequence</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ········</table> | 108 | ········</table> |
| 109 | ······</div> | 109 | ······</div> |
| 110 | ······<div> | 110 | ······<div> |
| 111 | ········<h2>See·also</h2> | 111 | ········<h2>See·also</h2> |
| Offset 37, 23 lines modified | Offset 37, 23 lines modified | ||
| 37 | ·····|·x_6·0···x_7·0···| | 37 | ·····|·x_6·0···x_7·0···| |
| 38 | ························4·················4 | 38 | ························4·················4 |
| 39 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) | 39 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) |
| 40 | ·················0···7·············0···7 | 40 | ·················0···7·············0···7 |
| 41 | i3·:·(Y,·F)·=·setOnesForest·X | 41 | i3·:·(Y,·F)·=·setOnesForest·X |
| 42 | o3·=·(|·0·1· | 42 | o3·=·(|·0·1·0···1·|,·Graph{"edges"·=>·{{y·,·y·},·{y·,·y·},·{y·,·y·},·{y·, |
| 43 | ······|·1·0· | 43 | ······|·1·0·0···1·|······················1···4·····3···4·····0···5·····2 |
| 44 | ······|·0· | 44 | ······|·0·1·1···0·|········"ring"·=>·QQ[y·..y·] |
| 45 | ······|·1·0· | 45 | ······|·1·0·x_7·0·|······················0···7 |
| 46 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} | 46 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} |
| 47 | ···········································0···1···2···3···4···5···6···7 | 47 | ···········································0···1···2···3···4···5···6···7 |
| 48 | ·····------------------------------------------------------------------------ | 48 | ·····------------------------------------------------------------------------ |
| 49 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) | 49 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) |
| 50 | ······ | 50 | ······5·····2···6·····0···7·····1···7 |
| 51 | o3·:·Sequence | 51 | o3·:·Sequence |
| 52 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 52 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 53 | ····*·_\x8g_\x8r_\x8a_\x8p_\x8h_\x8F_\x8r_\x8o_\x8m_\x8S_\x8l_\x8a_\x8c_\x8k_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·creates·the·vertex-edge·incidence·matrix·for·the | 53 | ····*·_\x8g_\x8r_\x8a_\x8p_\x8h_\x8F_\x8r_\x8o_\x8m_\x8S_\x8l_\x8a_\x8c_\x8k_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·creates·the·vertex-edge·incidence·matrix·for·the |
| 54 | ······bipartite·non-incidence·graph·with·adjacency·matrix·the·given·slack | 54 | ······bipartite·non-incidence·graph·with·adjacency·matrix·the·given·slack |
| 55 | ······matrix | 55 | ······matrix |
| 56 | ····*·_\x8s_\x8l_\x8a_\x8c_\x8k_\x8I_\x8d_\x8e_\x8a_\x8l·--·computes·the·slack·ideal | 56 | ····*·_\x8s_\x8l_\x8a_\x8c_\x8k_\x8I_\x8d_\x8e_\x8a_\x8l·--·computes·the·slack·ideal |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=16 | 7 | #:len=16 |
| 8 | aXNTbW9vdGhBQ01CZXR0aQ== | 8 | aXNTbW9vdGhBQ01CZXR0aQ== |
| 9 | #:len=902 | 9 | #:len=902 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hlY2tzIHdoZXRoZXIgYSBCZXR0aSB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hlY2tzIHdoZXRoZXIgYSBCZXR0aSB0 |
| 11 | YWJsZSBpcyB0aGF0IG9mIGEgc21vb3RoIEFDTSBjdXJ2ZSIsICJsaW5lbnVtIiA9PiAxMjY5LCBJ | 11 | YWJsZSBpcyB0aGF0IG9mIGEgc21vb3RoIEFDTSBjdXJ2ZSIsICJsaW5lbnVtIiA9PiAxMjY5LCBJ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=47 | 7 | #:len=47 |
| 8 | TXVsdGlkaW1lbnNpb25hbE1hdHJpeCAqIE11bHRpZGltZW5zaW9uYWxNYXRyaXg= | 8 | TXVsdGlkaW1lbnNpb25hbE1hdHJpeCAqIE11bHRpZGltZW5zaW9uYWxNYXRyaXg= |
| 9 | #:len=1779 | 9 | #:len=1779 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJvZHVjdCBvZiBtdWx0aWRpbWVuc2lv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJvZHVjdCBvZiBtdWx0aWRpbWVuc2lv |
| 11 | bmFsIG1hdHJpY2VzIiwgImxpbmVudW0iID0+IDE0MjYsIElucHV0cyA9PiB7U1BBTntUVHsiTSJ9 | 11 | bmFsIG1hdHJpY2VzIiwgImxpbmVudW0iID0+IDE0MjYsIElucHV0cyA9PiB7U1BBTntUVHsiTSJ9 |
| Offset 3, 24 lines modified | Offset 3, 24 lines modified | ||
| 3 | i1·:·n·=·{2,3,2} | 3 | i1·:·n·=·{2,3,2} |
| 4 | o1·=·{2,·3,·2} | 4 | o1·=·{2,·3,·2} |
| 5 | o1·:·List | 5 | o1·:·List |
| 6 | i2·:·time·degreeDeterminant·n | 6 | i2·:·time·degreeDeterminant·n |
| 7 | ·--·used·0.00 | 7 | ·--·used·0.000819276s·(cpu);·5.7347e-05s·(thread);·0s·(gc) |
| 8 | o2·=·6 | 8 | o2·=·6 |
| 9 | i3·:·M·=·genericMultidimensionalMatrix·n; | 9 | i3·:·M·=·genericMultidimensionalMatrix·n; |
| 10 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] | 10 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] |
| 11 | ······················································0,0,0···1,2,1 | 11 | ······················································0,0,0···1,2,1 |
| 12 | i4·:·time·degree·determinant·M | 12 | i4·:·time·degree·determinant·M |
| 13 | ·--·used·0.4 | 13 | ·--·used·0.471634s·(cpu);·0.126881s·(thread);·0s·(gc) |
| 14 | o4·=·{6} | 14 | o4·=·{6} |
| 15 | o4·:·List | 15 | o4·:·List |
| 16 | i5·:· | 16 | i5·:· |
| Offset 1, 13 lines modified | Offset 1, 13 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·17130321902108223178 | 1 | --·-*-·M2-comint·-*-·hash:·17130321902108223178 |
| 2 | i1·:·(d,n)·:=·(2,3); | 2 | i1·:·(d,n)·:=·(2,3); |
| 3 | i2·:·time·Disc·=·denseDiscriminant(d,n) | 3 | i2·:·time·Disc·=·denseDiscriminant(d,n) |
| 4 | ·--·used·0.2 | 4 | ·--·used·0.292381s·(cpu);·0.211044s·(thread);·0s·(gc) |
| 5 | o2·=·Disc | 5 | o2·=·Disc |
| 6 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|) | 6 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|) |
| 7 | ···························································|·0·0·0·1·1·2·0·0·1·0·| | 7 | ···························································|·0·0·0·1·1·2·0·0·1·0·| |
| 8 | ···························································|·0·1·2·0·1·0·0·1·0·0·| | 8 | ···························································|·0·1·2·0·1·0·0·1·0·0·| |
| Offset 9, 18 lines modified | Offset 9, 18 lines modified | ||
| 9 | ·················2 | 9 | ·················2 |
| 10 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 10 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 11 | ······4·1·2····2·2····3·1····1·2····0 | 11 | ······4·1·2····2·2····3·1····1·2····0 |
| 12 | o1·:·Sequence | 12 | o1·:·Sequence |
| 13 | i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula | 13 | i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula |
| 14 | ·--·used·0.0 | 14 | ·--·used·0.083125s·(cpu);·0.0824314s·(thread);·0s·(gc) |
| 15 | i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula | 15 | i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula |
| 16 | ·--·used·0. | 16 | ·--·used·0.309592s·(cpu);·0.273035s·(thread);·0s·(gc) |
| 17 | i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant | 17 | i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant |
| 18 | ·--·used·0.5 | 18 | ·--·used·0.53325s·(cpu);·0.321035s·(thread);·0s·(gc) |
| 19 | i5·:·assert(o2·==·o3·and·o3·==·o4) | 19 | i5·:·assert(o2·==·o3·and·o3·==·o4) |
| 20 | i6·:· | 20 | i6·:· |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2, | 5 | o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2, |
| 6 | ·····------------------------------------------------------------------------ | 6 | ·····------------------------------------------------------------------------ |
| 7 | ·····3}}}} | 7 | ·····3}}}} |
| 8 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ | 8 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ |
| 9 | i2·:·time·det·M | 9 | i2·:·time·det·M |
| 10 | ·--·used·0. | 10 | ·--·used·0.829927s·(cpu);·0.14424s·(thread);·0s·(gc) |
| 11 | o2·=·9698337990421512192 | 11 | o2·=·9698337990421512192 |
| 12 | i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) | 12 | i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) |
| 13 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, | 13 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, |
| 14 | ·····------------------------------------------------------------------------ | 14 | ·····------------------------------------------------------------------------ |
| Offset 24, 13 lines modified | Offset 24, 13 lines modified | ||
| 24 | ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6, | 24 | ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6, |
| 25 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 26 | ·····4,·8,·4,·2}}}}} | 26 | ·····4,·8,·4,·2}}}}} |
| 27 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ | 27 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ |
| 28 | i4·:·time·det·M | 28 | i4·:·time·det·M |
| 29 | ·--·used·0. | 29 | ·--·used·0.47748s·(cpu);·0.434654s·(thread);·0s·(gc) |
| 30 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 | 30 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 |
| 31 | ·····9257139493926586400187927813888 | 31 | ·····9257139493926586400187927813888 |
| 32 | i5·:· | 32 | i5·:· |
| Offset 16, 41 lines modified | Offset 16, 41 lines modified | ||
| 16 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] | 16 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] |
| 17 | ······················································0···3 | 17 | ······················································0···3 |
| 18 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) | 18 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) |
| 19 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 19 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 20 | ······························ | 20 | ······························3····2········3·······0········2···0··········· |
| 21 | ·····------------------------------------------------------------------------ | 21 | ·····------------------------------------------------------------------------ |
| 22 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 22 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 23 | ········· | 23 | ·········3···2····················3··········1······2······1··············3· |
| 24 | ·····------------------------------------------------------------------------ | 24 | ·····------------------------------------------------------------------------ |
| 25 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 25 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 26 | ········· | 26 | ·········0·····3·········1····················0····1·················2····0· |
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| 28 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 28 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 29 | ··········· | 29 | ···········2·······1········0···1 |
| 30 | ···················································ZZ | 30 | ···················································ZZ |
| 31 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] | 31 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] |
| 32 | ··················································101··0···3 | 32 | ··················································101··0···3 |
| 33 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") | 33 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") |
| 34 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, | 34 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, |
| 35 | ······························ | 35 | ······························3····2········3·······0········2···0··········· |
| 36 | ·····------------------------------------------------------------------------ | 36 | ·····------------------------------------------------------------------------ |
| 37 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, | 37 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, |
| 38 | ········· | 38 | ·········3···2····················3··········1······2······1··············3· |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, | 40 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, |
| 41 | ········· | 41 | ·········0·····3·········1····················0····1·················2····0· |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} | 43 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} |
| 44 | ··········· | 44 | ···········2·······1········0···1 |
| 45 | ···················································ZZ | 45 | ···················································ZZ |
| 46 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] | 46 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] |
| 47 | ··················································101··0···3 | 47 | ··················································101··0···3 |
| 48 | i4·:· | 48 | i4·:· |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z | 11 | ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z |
| 12 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 | 12 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 |
| 13 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] | 13 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] |
| 14 | ·········0,0,0···1,2,1···0···1···0···2···0···1 | 14 | ·········0,0,0···1,2,1···0···1···0···2···0···1 |
| 15 | i2·:·time·sparseDiscriminant·f | 15 | i2·:·time·sparseDiscriminant·f |
| 16 | ·--·used· | 16 | ·--·used·2.4708s·(cpu);·2.25023s·(thread);·0s·(gc) |
| 17 | ···················································2························ | 17 | ···················································2························ |
| 18 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- | 18 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- |
| 19 | ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0·· | 19 | ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0·· |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ············2·····2································2············ | 21 | ············2·····2································2············ |
| 22 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- | 22 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·16228363821945730064 | 1 | --·-*-·M2-comint·-*-·hash:·16228363821945730064 |
| 2 | i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}}) | 2 | i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}}) |
| 3 | ·--·used·0. | 3 | ·--·used·0.719682s·(cpu);·0.525034s·(thread);·0s·(gc) |
| 4 | o1·=·Res | 4 | o1·=·Res |
| 5 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|}) | 5 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|}) |
| 6 | ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·| | 6 | ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·| |
| 7 | i2·:·QQ[c_(1,1)..c_(3,4)][x,y]; | 7 | i2·:·QQ[c_(1,1)..c_(3,4)][x,y]; |
| Offset 18, 15 lines modified | Offset 18, 15 lines modified | ||
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ·····c···x*y·+·c···x·+·c···y·+·c···) | 19 | ·····c···x*y·+·c···x·+·c···y·+·c···) |
| 20 | ······3,3·······3,4·····3,2·····3,1 | 20 | ······3,3·······3,4·····3,2·····3,1 |
| 21 | o3·:·Sequence | 21 | o3·:·Sequence |
| 22 | i4·:·time·Res(f,g,h) | 22 | i4·:·time·Res(f,g,h) |
| 23 | ·--·used·0.01 | 23 | ·--·used·0.0116366s·(cpu);·0.00843484s·(thread);·0s·(gc) |
| 24 | ········2·······················4······2···2···············4···· | 24 | ········2·······················4······2···2···············4···· |
| 25 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ | 25 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ |
| 26 | ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1·· | 26 | ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1·· |
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| 28 | ······3·······2·······3···············2···················3········ | 28 | ······3·······2·······3···············2···················3········ |
| 29 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ | 29 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ |
| Offset 730, 30 lines modified | Offset 730, 30 lines modified | ||
| 730 | o4·:·QQ[c···..c···] | 730 | o4·:·QQ[c···..c···] |
| 731 | ·········1,1···3,4 | 731 | ·········1,1···3,4 |
| 732 | i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h)) | 732 | i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h)) |
| 733 | i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331); | 733 | i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331); |
| 734 | ·--·used·0. | 734 | ·--·used·0.58309s·(cpu);·0.0794051s·(thread);·0s·(gc) |
| 735 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331) | 735 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331) |
| 736 | ·····························································|·0·1·0·1·| | 736 | ·····························································|·0·1·0·1·| |
| 737 | i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y]; | 737 | i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y]; |
| 738 | i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y,·c_0·+·c_1*x·+·c_2*y·+·c_3*x*y) | 738 | i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y,·c_0·+·c_1*x·+·c_2*y·+·c_3*x*y) |
| 739 | o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·) | 739 | o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·) |
| 740 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 | 740 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 |
| 741 | o8·:·Sequence | 741 | o8·:·Sequence |
| 742 | i9·:·time·Res(f,g,h) | 742 | i9·:·time·Res(f,g,h) |
| 743 | ·--·used·0.0012 | 743 | ·--·used·0.00120943s·(cpu);·0.00274605s·(thread);·0s·(gc) |
| 744 | ······2·····2············2············2········2·2····2·········· | 744 | ······2·····2············2············2········2·2····2·········· |
| 745 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- | 745 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- |
| 746 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1·· | 746 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1·· |
| 747 | ·····------------------------------------------------------------------------ | 747 | ·····------------------------------------------------------------------------ |
| 748 | ·························2·······················2························· | 748 | ·························2·······················2························· |
| 749 | ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+ | 749 | ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+ |
| Offset 822, 15 lines modified | Offset 822, 15 lines modified | ||
| 822 | ··················2 | 822 | ··················2 |
| 823 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 823 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 824 | ·······4·1·2····2·2····3·1····1·2····0 | 824 | ·······4·1·2····2·2····3·1····1·2····0 |
| 825 | o11·:·Sequence | 825 | o11·:·Sequence |
| 826 | i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true)); | 826 | i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true)); |
| 827 | ·--·used·1. | 827 | ·--·used·1.25678s·(cpu);·0.480174s·(thread);·0s·(gc) |
| 828 | i13·:·quotientRemainder(UnmixedRes,MixedRes) | 828 | i13·:·quotientRemainder(UnmixedRes,MixedRes) |
| 829 | ········2·2···················2····2·······························2·2 | 829 | ········2·2···················2····2·······························2·2 |
| 830 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) | 830 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) |
| 831 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 | 831 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 |
| Offset 73, 27 lines modified | Offset 73, 27 lines modified | ||
| 73 | o1·=·{2,·3,·2} | 73 | o1·=·{2,·3,·2} |
| 74 | o1·:·List</code></pre> | 74 | o1·:·List</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·degreeDeterminant·n | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·degreeDeterminant·n |
| 78 | ·--·used·0.00 | 78 | ·--·used·0.000819276s·(cpu);·5.7347e-05s·(thread);·0s·(gc) |
| 79 | o2·=·6</code></pre> | 79 | o2·=·6</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·genericMultidimensionalMatrix·n; | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·genericMultidimensionalMatrix·n; |
| 83 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] | 83 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] |
| 84 | ······················································0,0,0···1,2,1</code></pre> | 84 | ······················································0,0,0···1,2,1</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree·determinant·M | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree·determinant·M |
| 88 | ·--·used·0.4 | 88 | ·--·used·0.471634s·(cpu);·0.126881s·(thread);·0s·(gc) |
| 89 | o4·=·{6} | 89 | o4·=·{6} |
| 90 | o4·:·List</code></pre> | 90 | o4·:·List</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ········</table> | 92 | ········</table> |
| 93 | ······</div> | 93 | ······</div> |
| Offset 16, 23 lines modified | Offset 16, 23 lines modified | ||
| 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 16 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 17 | i1·:·n·=·{2,3,2} | 17 | i1·:·n·=·{2,3,2} |
| 18 | o1·=·{2,·3,·2} | 18 | o1·=·{2,·3,·2} |
| 19 | o1·:·List | 19 | o1·:·List |
| 20 | i2·:·time·degreeDeterminant·n | 20 | i2·:·time·degreeDeterminant·n |
| 21 | ·--·used·0.00 | 21 | ·--·used·0.000819276s·(cpu);·5.7347e-05s·(thread);·0s·(gc) |
| 22 | o2·=·6 | 22 | o2·=·6 |
| 23 | i3·:·M·=·genericMultidimensionalMatrix·n; | 23 | i3·:·M·=·genericMultidimensionalMatrix·n; |
| 24 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] | 24 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] |
| 25 | ······················································0,0,0···1,2,1 | 25 | ······················································0,0,0···1,2,1 |
| 26 | i4·:·time·degree·determinant·M | 26 | i4·:·time·degree·determinant·M |
| 27 | ·--·used·0.4 | 27 | ·--·used·0.471634s·(cpu);·0.126881s·(thread);·0s·(gc) |
| 28 | o4·=·{6} | 28 | o4·=·{6} |
| 29 | o4·:·List | 29 | o4·:·List |
| 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 30 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 31 | ····*·_\x8d_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·hyperdeterminant·of·a | 31 | ····*·_\x8d_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x_\x8)·--·hyperdeterminant·of·a |
| 32 | ······multidimensional·matrix | 32 | ······multidimensional·matrix |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | ········<h2>Description</h2> | 82 | ········<h2>Description</h2> |
| 83 | ········<table·class="examples"> | 83 | ········<table·class="examples"> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·(d,n)·:=·(2,3);</code></pre> | 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·(d,n)·:=·(2,3);</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·Disc·=·denseDiscriminant(d,n) | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·Disc·=·denseDiscriminant(d,n) |
| 89 | ·--·used·0.2 | 89 | ·--·used·0.292381s·(cpu);·0.211044s·(thread);·0s·(gc) |
| 90 | o2·=·Disc | 90 | o2·=·Disc |
| 91 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|) | 91 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|) |
| 92 | ···························································|·0·0·0·1·1·2·0·0·1·0·| | 92 | ···························································|·0·0·0·1·1·2·0·0·1·0·| |
| 93 | ···························································|·0·1·2·0·1·0·0·1·0·0·|</code></pre> | 93 | ···························································|·0·1·2·0·1·0·0·1·0·0·|</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | ····*·Outputs: | 19 | ····*·Outputs: |
| 20 | ··········o·for·(d,n),·this·is·the·same·as·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x | 20 | ··········o·for·(d,n),·this·is·the·same·as·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x |
| 21 | ············"\x8"g\x8ge\x8en\x8ne\x8er\x8ri\x8ic\x8c·p\x8po\x8ol\x8ly\x8yn\x8no\x8om\x8mi\x8ia\x8al\x8l·o\x8of\x8f·d\x8de\x8eg\x8gr\x8re\x8ee\x8e·d\x8d·i\x8in\x8n·n\x8n·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s"\x8";\x8; | 21 | ············"\x8"g\x8ge\x8en\x8ne\x8er\x8ri\x8ic\x8c·p\x8po\x8ol\x8ly\x8yn\x8no\x8om\x8mi\x8ia\x8al\x8l·o\x8of\x8f·d\x8de\x8eg\x8gr\x8re\x8ee\x8e·d\x8d·i\x8in\x8n·n\x8n·v\x8va\x8ar\x8ri\x8ia\x8ab\x8bl\x8le\x8es\x8s"\x8";\x8; |
| 22 | ··········o·for·f,·this·is·the·same·as·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t(f). | 22 | ··········o·for·f,·this·is·the·same·as·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t(f). |
| 23 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 23 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 24 | i1·:·(d,n)·:=·(2,3); | 24 | i1·:·(d,n)·:=·(2,3); |
| 25 | i2·:·time·Disc·=·denseDiscriminant(d,n) | 25 | i2·:·time·Disc·=·denseDiscriminant(d,n) |
| 26 | ·--·used·0.2 | 26 | ·--·used·0.292381s·(cpu);·0.211044s·(thread);·0s·(gc) |
| 27 | o2·=·Disc | 27 | o2·=·Disc |
| 28 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1 | 28 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1 |
| 29 | 2·|) | 29 | 2·|) |
| 30 | ···························································|·0·0·0·1·1·2·0·0·1 | 30 | ···························································|·0·0·0·1·1·2·0·0·1 |
| 31 | 0·| | 31 | 0·| |
| Offset 92, 23 lines modified | Offset 92, 23 lines modified | ||
| 92 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 92 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 93 | ······4·1·2····2·2····3·1····1·2····0 | 93 | ······4·1·2····2·2····3·1····1·2····0 |
| 94 | o1·:·Sequence</code></pre> | 94 | o1·:·Sequence</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula | 97 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula |
| 98 | ·--·used·0.0 | 98 | ·--·used·0.083125s·(cpu);·0.0824314s·(thread);·0s·(gc)</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula | 101 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula |
| 102 | ·--·used·0. | 102 | ·--·used·0.309592s·(cpu);·0.273035s·(thread);·0s·(gc)</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant |
| 106 | ·--·used·0.5 | 106 | ·--·used·0.53325s·(cpu);·0.321035s·(thread);·0s·(gc)</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(o2·==·o3·and·o3·==·o4)</code></pre> | 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(o2·==·o3·and·o3·==·o4)</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| 112 | ······</div> | 112 | ······</div> |
| 113 | ······<div> | 113 | ······<div> |
| Offset 29, 20 lines modified | Offset 29, 20 lines modified | ||
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ·················2 | 30 | ·················2 |
| 31 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 31 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 32 | ······4·1·2····2·2····3·1····1·2····0 | 32 | ······4·1·2····2·2····3·1····1·2····0 |
| 33 | o1·:·Sequence | 33 | o1·:·Sequence |
| 34 | i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula | 34 | i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula |
| 35 | ·--·used·0.0 | 35 | ·--·used·0.083125s·(cpu);·0.0824314s·(thread);·0s·(gc) |
| 36 | i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay | 36 | i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay |
| 37 | formula | 37 | formula |
| 38 | ·--·used·0. | 38 | ·--·used·0.309592s·(cpu);·0.273035s·(thread);·0s·(gc) |
| 39 | i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant | 39 | i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant |
| 40 | ·--·used·0.5 | 40 | ·--·used·0.53325s·(cpu);·0.321035s·(thread);·0s·(gc) |
| 41 | i5·:·assert(o2·==·o3·and·o3·==·o4) | 41 | i5·:·assert(o2·==·o3·and·o3·==·o4) |
| 42 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 42 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 43 | ····*·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·sparse·resultant·(A-resultant) | 43 | ····*·_\x8s_\x8p_\x8a_\x8r_\x8s_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·sparse·resultant·(A-resultant) |
| 44 | ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·affine·resultant | 44 | ····*·_\x8a_\x8f_\x8f_\x8i_\x8n_\x8e_\x8R_\x8e_\x8s_\x8u_\x8l_\x8t_\x8a_\x8n_\x8t·--·affine·resultant |
| 45 | ····*·_\x8d_\x8e_\x8n_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·dense·discriminant·(classical·discriminant) | 45 | ····*·_\x8d_\x8e_\x8n_\x8s_\x8e_\x8D_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·dense·discriminant·(classical·discriminant) |
| 46 | ····*·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·exponents·in·one·or·more·polynomials | 46 | ····*·_\x8e_\x8x_\x8p_\x8o_\x8n_\x8e_\x8n_\x8t_\x8s_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·exponents·in·one·or·more·polynomials |
| 47 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8L_\x8a_\x8u_\x8r_\x8e_\x8n_\x8t_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·generic·(Laurent)·polynomials | 47 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8L_\x8a_\x8u_\x8r_\x8e_\x8n_\x8t_\x8P_\x8o_\x8l_\x8y_\x8n_\x8o_\x8m_\x8i_\x8a_\x8l_\x8s·--·generic·(Laurent)·polynomials |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ·····------------------------------------------------------------------------ | 84 | ·····------------------------------------------------------------------------ |
| 85 | ·····3}}}} | 85 | ·····3}}}} |
| 86 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ</code></pre> | 86 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·det·M | 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·det·M |
| 90 | ·--·used·0. | 90 | ·--·used·0.829927s·(cpu);·0.14424s·(thread);·0s·(gc) |
| 91 | o2·=·9698337990421512192</code></pre> | 91 | o2·=·9698337990421512192</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) | 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) |
| 95 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, | 95 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ·····4,·8,·4,·2}}}}} | 106 | ·····4,·8,·4,·2}}}}} |
| 107 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ</code></pre> | 107 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·det·M | 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·det·M |
| 111 | ·--·used·0. | 111 | ·--·used·0.47748s·(cpu);·0.434654s·(thread);·0s·(gc) |
| 112 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 | 112 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 |
| 113 | ·····9257139493926586400187927813888</code></pre> | 113 | ·····9257139493926586400187927813888</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ········</table> | 115 | ········</table> |
| 116 | ······</div> | 116 | ······</div> |
| 117 | ······<div> | 117 | ······<div> |
| Offset 26, 15 lines modified | Offset 26, 15 lines modified | ||
| 26 | o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2, | 26 | o1·=·{{{{8,·1},·{3,·7}},·{{8,·3},·{3,·7}}},·{{{8,·8},·{5,·7}},·{{8,·5},·{2, |
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| 28 | ·····3}}}} | 28 | ·····3}}}} |
| 29 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ | 29 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ |
| 30 | i2·:·time·det·M | 30 | i2·:·time·det·M |
| 31 | ·--·used·0. | 31 | ·--·used·0.829927s·(cpu);·0.14424s·(thread);·0s·(gc) |
| 32 | o2·=·9698337990421512192 | 32 | o2·=·9698337990421512192 |
| 33 | i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) | 33 | i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) |
| 34 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, | 34 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, |
| 35 | ·····------------------------------------------------------------------------ | 35 | ·····------------------------------------------------------------------------ |
| 36 | ·····6}}},·{{{3,·5,·7,·7,·9},·{4,·5,·0,·4,·3}},·{{1,·8,·9,·1,·2},·{9,·6,·6, | 36 | ·····6}}},·{{{3,·5,·7,·7,·9},·{4,·5,·0,·4,·3}},·{{1,·8,·9,·1,·2},·{9,·6,·6, |
| Offset 43, 15 lines modified | Offset 43, 15 lines modified | ||
| 43 | ·····------------------------------------------------------------------------ | 43 | ·····------------------------------------------------------------------------ |
| 44 | ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6, | 44 | ·····7,·4,·5}}},·{{{4,·0,·1,·4,·4},·{2,·6,·1,·1,·4}},·{{5,·4,·9,·7,·4},·{6, |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ·····4,·8,·4,·2}}}}} | 46 | ·····4,·8,·4,·2}}}}} |
| 47 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ | 47 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ |
| 48 | i4·:·time·det·M | 48 | i4·:·time·det·M |
| 49 | ·--·used·0. | 49 | ·--·used·0.47748s·(cpu);·0.434654s·(thread);·0s·(gc) |
| 50 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 | 50 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 |
| 51 | ·····9257139493926586400187927813888 | 51 | ·····9257139493926586400187927813888 |
| 52 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 52 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 53 | ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·the·class·of·all·multidimensional·matrices | 53 | ····*·_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·the·class·of·all·multidimensional·matrices |
| 54 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8D_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·degree·of·the·hyperdeterminant·of·a·generic | 54 | ····*·_\x8d_\x8e_\x8g_\x8r_\x8e_\x8e_\x8D_\x8e_\x8t_\x8e_\x8r_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t·--·degree·of·the·hyperdeterminant·of·a·generic |
| 55 | ······multidimensional·matrix | 55 | ······multidimensional·matrix |
| Offset 95, 43 lines modified | Offset 95, 43 lines modified | ||
| 95 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] | 95 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] |
| 96 | ······················································0···3</code></pre> | 96 | ······················································0···3</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) | 99 | <td>··············<pre><code·class="language-macaulay2">i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) |
| 100 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 100 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 101 | ······························ | 101 | ······························3····2········3·······0········2···0··········· |
| 102 | ·····------------------------------------------------------------------------ | 102 | ·····------------------------------------------------------------------------ |
| 103 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 103 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 104 | ········· | 104 | ·········3···2····················3··········1······2······1··············3· |
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 106 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 107 | ········· | 107 | ·········0·····3·········1····················0····1·················2····0· |
| 108 | ·····------------------------------------------------------------------------ | 108 | ·····------------------------------------------------------------------------ |
| 109 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 109 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 110 | ··········· | 110 | ···········2·······1········0···1 |
| 111 | ···················································ZZ | 111 | ···················································ZZ |
| 112 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] | 112 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] |
| 113 | ··················································101··0···3</code></pre> | 113 | ··················································101··0···3</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") | 116 | <td>··············<pre><code·class="language-macaulay2">i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") |
| 117 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, | 117 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, |
| 118 | ······························ | 118 | ······························3····2········3·······0········2···0··········· |
| 119 | ·····------------------------------------------------------------------------ | 119 | ·····------------------------------------------------------------------------ |
| 120 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, | 120 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, |
| 121 | ········· | 121 | ·········3···2····················3··········1······2······1··············3· |
| 122 | ·····------------------------------------------------------------------------ | 122 | ·····------------------------------------------------------------------------ |
| 123 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, | 123 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, |
| 124 | ········· | 124 | ·········0·····3·········1····················0····1·················2····0· |
| 125 | ·····------------------------------------------------------------------------ | 125 | ·····------------------------------------------------------------------------ |
| 126 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} | 126 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} |
| 127 | ··········· | 127 | ···········2·······1········0···1 |
| 128 | ···················································ZZ | 128 | ···················································ZZ |
| 129 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] | 129 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] |
| 130 | ··················································101··0···3</code></pre> | 130 | ··················································101··0···3</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ········</table> | 132 | ········</table> |
| 133 | ······</div> | 133 | ······</div> |
| Offset 34, 42 lines modified | Offset 34, 42 lines modified | ||
| 34 | ···········2·······1········0···1 | 34 | ···········2·······1········0···1 |
| 35 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] | 35 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] |
| 36 | ······················································0···3 | 36 | ······················································0···3 |
| 37 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) | 37 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) |
| 38 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 38 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 39 | ······························ | 39 | ······························3····2········3·······0········2···0 |
| 40 | ·····------------------------------------------------------------------------ | 40 | ·····------------------------------------------------------------------------ |
| 41 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 41 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 42 | ········· | 42 | ·········3···2····················3··········1······2······1··············3 |
| 43 | ·····------------------------------------------------------------------------ | 43 | ·····------------------------------------------------------------------------ |
| 44 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 44 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 45 | ········· | 45 | ·········0·····3·········1····················0····1·················2····0 |
| 46 | ·····------------------------------------------------------------------------ | 46 | ·····------------------------------------------------------------------------ |
| 47 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 47 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 48 | ··········· | 48 | ···········2·······1········0···1 |
| 49 | ···················································ZZ | 49 | ···················································ZZ |
| 50 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] | 50 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] |
| 51 | ··················································101··0···3 | 51 | ··················································101··0···3 |
| 52 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/ | 52 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/ |
| 53 | 101,Variable=>"b") | 53 | 101,Variable=>"b") |
| 54 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, | 54 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, |
| 55 | ······························ | 55 | ······························3····2········3·······0········2···0 |
| 56 | ·····------------------------------------------------------------------------ | 56 | ·····------------------------------------------------------------------------ |
| 57 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, | 57 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, |
| 58 | ········· | 58 | ·········3···2····················3··········1······2······1··············3 |
| 59 | ·····------------------------------------------------------------------------ | 59 | ·····------------------------------------------------------------------------ |
| 60 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, | 60 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, |
| 61 | ········· | 61 | ·········0·····3·········1····················0····1·················2····0 |
| 62 | ·····------------------------------------------------------------------------ | 62 | ·····------------------------------------------------------------------------ |
| 63 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} | 63 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} |
| 64 | ··········· | 64 | ···········2·······1········0···1 |
| 65 | ···················································ZZ | 65 | ···················································ZZ |
| 66 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] | 66 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] |
| 67 | ··················································101··0···3 | 67 | ··················································101··0···3 |
| 68 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 68 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 69 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·make·a·generic·multidimensional·matrix | 69 | ····*·_\x8g_\x8e_\x8n_\x8e_\x8r_\x8i_\x8c_\x8M_\x8u_\x8l_\x8t_\x8i_\x8d_\x8i_\x8m_\x8e_\x8n_\x8s_\x8i_\x8o_\x8n_\x8a_\x8l_\x8M_\x8a_\x8t_\x8r_\x8i_\x8x·--·make·a·generic·multidimensional·matrix |
| 70 | ······of·variables | 70 | ······of·variables |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 | 89 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 |
| 90 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] | 90 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] |
| 91 | ·········0,0,0···1,2,1···0···1···0···2···0···1</code></pre> | 91 | ·········0,0,0···1,2,1···0···1···0···2···0···1</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·sparseDiscriminant·f | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·sparseDiscriminant·f |
| 95 | ·--·used· | 95 | ·--·used·2.4708s·(cpu);·2.25023s·(thread);·0s·(gc) |
| 96 | ···················································2························ | 96 | ···················································2························ |
| 97 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- | 97 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- |
| 98 | ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0·· | 98 | ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0·· |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ············2·····2································2············ | 100 | ············2·····2································2············ |
| 101 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- | 101 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- |
| Offset 38, 15 lines modified | Offset 38, 15 lines modified | ||
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z | 39 | ·····a·····x·y·z··+·a·····x·y·z··+·a·····x·y·z |
| 40 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 | 40 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 |
| 41 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] | 41 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] |
| 42 | ·········0,0,0···1,2,1···0···1···0···2···0···1 | 42 | ·········0,0,0···1,2,1···0···1···0···2···0···1 |
| 43 | i2·:·time·sparseDiscriminant·f | 43 | i2·:·time·sparseDiscriminant·f |
| 44 | ·--·used· | 44 | ·--·used·2.4708s·(cpu);·2.25023s·(thread);·0s·(gc) |
| 45 | ···················································2 | 45 | ···················································2 |
| 46 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- | 46 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- |
| 47 | ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0 | 47 | ······0,1,1·0,2,0·0,2,1·1,0,0·1,0,1·1,1,0····0,1,0·0,2,1·1,0,0·1,0,1·1,1,0 |
| 48 | ·····------------------------------------------------------------------------ | 48 | ·····------------------------------------------------------------------------ |
| 49 | ············2·····2································2 | 49 | ············2·····2································2 |
| 50 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- | 50 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | ······<div> | 76 | ······<div> |
| 77 | ········<h2>Description</h2> | 77 | ········<h2>Description</h2> |
| 78 | ········<p>Alternatively,·one·can·apply·the·method·directly·to·the·list·of·Laurent·polynomials·$f_0,\ldots,f_n$.·In·this·case,·the·matrices·$A_0,\ldots,A_n$·are·automatically·determined·by·<a·title="exponents·in·one·or·more·polynomials"·href="_exponents__Matrix.html">exponentsMatrix</a>.·If·you·want·require·that·$A_0=\cdots=A_n$,·then·use·the·option·<span·class="tt">Unmixed=>true</span>·(this·could·be·faster).·Below·we·consider·some·examples.</p> | 78 | ········<p>Alternatively,·one·can·apply·the·method·directly·to·the·list·of·Laurent·polynomials·$f_0,\ldots,f_n$.·In·this·case,·the·matrices·$A_0,\ldots,A_n$·are·automatically·determined·by·<a·title="exponents·in·one·or·more·polynomials"·href="_exponents__Matrix.html">exponentsMatrix</a>.·If·you·want·require·that·$A_0=\cdots=A_n$,·then·use·the·option·<span·class="tt">Unmixed=>true</span>·(this·could·be·faster).·Below·we·consider·some·examples.</p> |
| 79 | ········<p>In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to·the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{(1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{(2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$.</p> | 79 | ········<p>In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to·the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{(1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{(2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$.</p> |
| 80 | ········<table·class="examples"> | 80 | ········<table·class="examples"> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}}) | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2},{1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}}) |
| 83 | ·--·used·0. | 83 | ·--·used·0.719682s·(cpu);·0.525034s·(thread);·0s·(gc) |
| 84 | o1·=·Res | 84 | o1·=·Res |
| 85 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|}) | 85 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|}) |
| 86 | ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|</code></pre> | 86 | ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ·····c···x*y·+·c···x·+·c···y·+·c···) | 100 | ·····c···x*y·+·c···x·+·c···y·+·c···) |
| 101 | ······3,3·······3,4·····3,2·····3,1 | 101 | ······3,3·······3,4·····3,2·····3,1 |
| 102 | o3·:·Sequence</code></pre> | 102 | o3·:·Sequence</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Res(f,g,h) | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Res(f,g,h) |
| 106 | ·--·used·0.01 | 106 | ·--·used·0.0116366s·(cpu);·0.00843484s·(thread);·0s·(gc) |
| 107 | ········2·······················4······2···2···············4···· | 107 | ········2·······················4······2···2···············4···· |
| 108 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ | 108 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ |
| 109 | ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1·· | 109 | ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1·· |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ······3·······2·······3···············2···················3········ | 111 | ······3·······2·······3···············2···················3········ |
| 112 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ | 112 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ |
| Offset 817, 15 lines modified | Offset 817, 15 lines modified | ||
| 817 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h))</code></pre> | 817 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h))</code></pre> |
| 818 | </td>··········</tr> | 818 | </td>··········</tr> |
| 819 | ········</table> | 819 | ········</table> |
| 820 | ········<p>In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to·the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0·+·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over·$\mathbb{Z}/3331$.</p> | 820 | ········<p>In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to·the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials·$f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0·+·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over·$\mathbb{Z}/3331$.</p> |
| 821 | ········<table·class="examples"> | 821 | ········<table·class="examples"> |
| 822 | ··········<tr> | 822 | ··········<tr> |
| 823 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331); | 823 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331); |
| 824 | ·--·used·0. | 824 | ·--·used·0.58309s·(cpu);·0.0794051s·(thread);·0s·(gc) |
| 825 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331) | 825 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331) |
| 826 | ·····························································|·0·1·0·1·|</code></pre> | 826 | ·····························································|·0·1·0·1·|</code></pre> |
| 827 | </td>··········</tr> | 827 | </td>··········</tr> |
| 828 | ··········<tr> | 828 | ··········<tr> |
| 829 | <td>··············<pre><code·class="language-macaulay2">i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];</code></pre> | 829 | <td>··············<pre><code·class="language-macaulay2">i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];</code></pre> |
| 830 | </td>··········</tr> | 830 | </td>··········</tr> |
| Offset 835, 15 lines modified | Offset 835, 15 lines modified | ||
| 835 | o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·) | 835 | o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·) |
| 836 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 | 836 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 |
| 837 | o8·:·Sequence</code></pre> | 837 | o8·:·Sequence</code></pre> |
| 838 | </td>··········</tr> | 838 | </td>··········</tr> |
| 839 | ··········<tr> | 839 | ··········<tr> |
| 840 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·Res(f,g,h) | 840 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·Res(f,g,h) |
| 841 | ·--·used·0.0012 | 841 | ·--·used·0.00120943s·(cpu);·0.00274605s·(thread);·0s·(gc) |
| 842 | ······2·····2············2············2········2·2····2·········· | 842 | ······2·····2············2············2········2·2····2·········· |
| 843 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- | 843 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- |
| 844 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1·· | 844 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1·· |
| 845 | ·····------------------------------------------------------------------------ | 845 | ·····------------------------------------------------------------------------ |
| 846 | ·························2·······················2························· | 846 | ·························2·······················2························· |
| 847 | ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+ | 847 | ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+ |
| Offset 918, 15 lines modified | Offset 918, 15 lines modified | ||
| 918 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 918 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 919 | ·······4·1·2····2·2····3·1····1·2····0 | 919 | ·······4·1·2····2·2····3·1····1·2····0 |
| 920 | o11·:·Sequence</code></pre> | 920 | o11·:·Sequence</code></pre> |
| 921 | </td>··········</tr> | 921 | </td>··········</tr> |
| 922 | ··········<tr> | 922 | ··········<tr> |
| 923 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true)); | 923 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true)); |
| 924 | ·--·used·1. | 924 | ·--·used·1.25678s·(cpu);·0.480174s·(thread);·0s·(gc)</code></pre> |
| 925 | </td>··········</tr> | 925 | </td>··········</tr> |
| 926 | ··········<tr> | 926 | ··········<tr> |
| 927 | <td>··············<pre><code·class="language-macaulay2">i13·:·quotientRemainder(UnmixedRes,MixedRes) | 927 | <td>··············<pre><code·class="language-macaulay2">i13·:·quotientRemainder(UnmixedRes,MixedRes) |
| 928 | ········2·2···················2····2·······························2·2 | 928 | ········2·2···················2····2·······························2·2 |
| 929 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) | 929 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) |
| 930 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 | 930 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 |
| Offset 35, 15 lines modified | Offset 35, 15 lines modified | ||
| 35 | In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to | 35 | In·the·first·example,·we·calculate·the·sparse·(mixed)·resultant·associated·to |
| 36 | the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$. | 36 | the·three·sets·of·monomials·$(1,x·y,x^2·y,x),(y,x^2·y^2,x^2·y,x),(1,y,x·y,x)$. |
| 37 | Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{ | 37 | Then·we·evaluate·it·at·the·three·polynomials·$f·=·c_{(1,1)}+c_{(1,2)}·x·y+c_{ |
| 38 | (1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{ | 38 | (1,3)}·x^2·y+c_{(1,4)}·x,·g·=·c_{(2,1)}·y+c_{(2,2)}·x^2·y^2+c_{(2,3)}·x^2·y+c_{ |
| 39 | (2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$. | 39 | (2,4)}·x,·h·=·c_{(3,1)}+c_{(3,2)}·y+c_{(3,3)}·x·y+c_{(3,4)}·x$. |
| 40 | i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2}, | 40 | i1·:·time·Res·=·sparseResultant(matrix{{0,1,1,2},{0,0,1,1}},matrix{{0,1,2,2}, |
| 41 | {1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}}) | 41 | {1,0,1,2}},matrix{{0,0,1,1},{0,1,0,1}}) |
| 42 | ·--·used·0. | 42 | ·--·used·0.719682s·(cpu);·0.525034s·(thread);·0s·(gc) |
| 43 | o1·=·Res | 43 | o1·=·Res |
| 44 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1 | 44 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1 |
| 45 | 2·2·|,·|·0·0·1·1·|}) | 45 | 2·2·|,·|·0·0·1·1·|}) |
| 46 | ····························································|·0·0·1·1·|··|·1·0 | 46 | ····························································|·0·0·1·1·|··|·1·0 |
| 47 | 1·2·|··|·0·1·0·1·| | 47 | 1·2·|··|·0·1·0·1·| |
| Offset 56, 15 lines modified | Offset 56, 15 lines modified | ||
| 56 | ·······1,3·······1,2·······1,4·····1,1···2,2········2,3·······2,4·····2,1 | 56 | ·······1,3·······1,2·······1,4·····1,1···2,2········2,3·······2,4·····2,1 |
| 57 | ·····------------------------------------------------------------------------ | 57 | ·····------------------------------------------------------------------------ |
| 58 | ·····c···x*y·+·c···x·+·c···y·+·c···) | 58 | ·····c···x*y·+·c···x·+·c···y·+·c···) |
| 59 | ······3,3·······3,4·····3,2·····3,1 | 59 | ······3,3·······3,4·····3,2·····3,1 |
| 60 | o3·:·Sequence | 60 | o3·:·Sequence |
| 61 | i4·:·time·Res(f,g,h) | 61 | i4·:·time·Res(f,g,h) |
| 62 | ·--·used·0.01 | 62 | ·--·used·0.0116366s·(cpu);·0.00843484s·(thread);·0s·(gc) |
| 63 | ········2·······················4······2···2···············4 | 63 | ········2·······················4······2···2···············4 |
| 64 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ | 64 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ |
| 65 | ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1 | 65 | ········1,2·1,3·1,4·2,1·2,2·2,3·3,1····1,2·1,3·2,1·2,2·2,4·3,1 |
| 66 | ·····------------------------------------------------------------------------ | 66 | ·····------------------------------------------------------------------------ |
| 67 | ······3·······2·······3···············2···················3 | 67 | ······3·······2·······3···············2···················3 |
| 68 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ | 68 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ |
| Offset 772, 29 lines modified | Offset 772, 29 lines modified | ||
| 772 | In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to | 772 | In·the·second·example,·we·calculate·the·sparse·unmixed·resultant·associated·to |
| 773 | the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials | 773 | the·set·of·monomials·$(1,x,y,xy)$.·Then·we·evaluate·it·at·the·three·polynomials |
| 774 | $f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0 | 774 | $f·=·a_0·+·a_1·x·+·a_2·y·+·a_3·x·y,·g·=·b_0·+·b_1·x·+·b_2·y·+·b_3·x·y,·h·=·c_0 |
| 775 | +·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over | 775 | +·c_1·x·+·c_2·y·+·c_3·x·y$.·Moreover,·we·perform·all·the·computation·over |
| 776 | $\mathbb{Z}/3331$. | 776 | $\mathbb{Z}/3331$. |
| 777 | i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1}, | 777 | i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1}, |
| 778 | {0,1,0,1}},CoefficientRing=>ZZ/3331); | 778 | {0,1,0,1}},CoefficientRing=>ZZ/3331); |
| 779 | ·--·used·0. | 779 | ·--·used·0.58309s·(cpu);·0.0794051s·(thread);·0s·(gc) |
| 780 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over | 780 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over |
| 781 | ZZ/3331) | 781 | ZZ/3331) |
| 782 | ·····························································|·0·1·0·1·| | 782 | ·····························································|·0·1·0·1·| |
| 783 | i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y]; | 783 | i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y]; |
| 784 | i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y, | 784 | i8·:·(f,g,h)·=·(a_0·+·a_1*x·+·a_2*y·+·a_3*x*y,·b_0·+·b_1*x·+·b_2*y·+·b_3*x*y, |
| 785 | c_0·+·c_1*x·+·c_2*y·+·c_3*x*y) | 785 | c_0·+·c_1*x·+·c_2*y·+·c_3*x*y) |
| 786 | o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·) | 786 | o8·=·(a·x*y·+·a·x·+·a·y·+·a·,·b·x*y·+·b·x·+·b·y·+·b·,·c·x*y·+·c·x·+·c·y·+·c·) |
| 787 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 | 787 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 |
| 788 | o8·:·Sequence | 788 | o8·:·Sequence |
| 789 | i9·:·time·Res(f,g,h) | 789 | i9·:·time·Res(f,g,h) |
| 790 | ·--·used·0.0012 | 790 | ·--·used·0.00120943s·(cpu);·0.00274605s·(thread);·0s·(gc) |
| 791 | ······2·····2············2············2········2·2····2 | 791 | ······2·····2············2············2········2·2····2 |
| 792 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- | 792 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- |
| 793 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1 | 793 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1 |
| 794 | ·····------------------------------------------------------------------------ | 794 | ·····------------------------------------------------------------------------ |
| 795 | ·························2·······················2 | 795 | ·························2·······················2 |
| 796 | ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+ | 796 | ·····a·a·b·b·c·c··+·a·a·b·c·c··+·a·a·b·b·c·c··+·a·b·b·c·c··-·a·a·b·b·c·c··+ |
| Offset 864, 15 lines modified | Offset 864, 15 lines modified | ||
| 864 | ··················2 | 864 | ··················2 |
| 865 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 865 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 866 | ·······4·1·2····2·2····3·1····1·2····0 | 866 | ·······4·1·2····2·2····3·1····1·2····0 |
| 867 | o11·:·Sequence | 867 | o11·:·Sequence |
| 868 | i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant | 868 | i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant |
| 869 | (f,g,h,Unmixed=>true)); | 869 | (f,g,h,Unmixed=>true)); |
| 870 | ·--·used·1. | 870 | ·--·used·1.25678s·(cpu);·0.480174s·(thread);·0s·(gc) |
| 871 | i13·:·quotientRemainder(UnmixedRes,MixedRes) | 871 | i13·:·quotientRemainder(UnmixedRes,MixedRes) |
| 872 | ········2·2···················2····2·······························2·2 | 872 | ········2·2···················2····2·······························2·2 |
| 873 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) | 873 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) |
| 874 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 | 874 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 |
| 875 | o13·:·Sequence | 875 | o13·:·Sequence |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=38 | 7 | #:len=38 |
| 8 | c2NodXJQb2x5bm9taWFsKC4uLixBc0V4cHJlc3Npb249Pi4uLik= | 8 | c2NodXJQb2x5bm9taWFsKC4uLixBc0V4cHJlc3Npb249Pi4uLik= |
| 9 | #:len=287 | 9 | #:len=287 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzMwNSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzMwNSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc2NodXJQb2x5bm9taWFsLEFzRXhwcmVzc2lvbl0s | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc2NodXJQb2x5bm9taWFsLEFzRXhwcmVzc2lvbl0s |
| Offset 25, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | o4·=·|·0·1·| | 25 | o4·=·|·0·1·| |
| 26 | ·····|·2·3·| | 26 | ·····|·2·3·| |
| 27 | ·····|·4·| | 27 | ·····|·4·| |
| 28 | o4·:·YoungTableau | 28 | o4·:·YoungTableau |
| 29 | i5·:·time·higherSpechtPolynomial(S,T,R) | 29 | i5·:·time·higherSpechtPolynomial(S,T,R) |
| 30 | ·--·used·0.000 | 30 | ·--·used·0.000300263s·(cpu);·0.00126291s·(thread);·0s·(gc) |
| 31 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· | 31 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· |
| 32 | o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 32 | o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| 33 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· | 33 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· |
| 34 | ·····------------------------------------------------------------------------ | 34 | ·····------------------------------------------------------------------------ |
| 35 | ······3·2········3·2········2·3········2·3········3···2········3·2···· | 35 | ······3·2········3·2········2·3········2·3········3···2········3·2···· |
| 36 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 36 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
| 46 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 | 46 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 |
| 47 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x | 47 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 48 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 | 48 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 49 | o5·:·R | 49 | o5·:·R |
| 50 | i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) | 50 | i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) |
| 51 | ·--·used·0.0002 | 51 | ·--·used·0.000222056s·(cpu);·0.00121759s·(thread);·0s·(gc) |
| 52 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· | 52 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· |
| 53 | o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 53 | o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| 54 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· | 54 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· |
| 55 | ·····------------------------------------------------------------------------ | 55 | ·····------------------------------------------------------------------------ |
| 56 | ······3·2········3·2········2·3········2·3········3···2········3·2···· | 56 | ······3·2········3·2········2·3········2·3········3···2········3·2···· |
| 57 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 57 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 | 67 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 |
| 68 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x | 68 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 69 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 | 69 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 70 | o6·:·R | 70 | o6·:·R |
| 71 | i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) | 71 | i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) |
| 72 | ·--·used·0.00 | 72 | ·--·used·0.00255557s·(cpu);·0.00204318s·(thread);·0s·(gc) |
| 73 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·)) | 73 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·)) |
| 74 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0 | 74 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0 |
| 75 | o7·:·Expression·of·class·Product | 75 | o7·:·Expression·of·class·Product |
| 76 | i8·:· | 76 | i8·:· |
| Offset 25, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | o2·:·List | 25 | o2·:·List |
| 26 | i3·:·tal·:=·tally·apply·(H,h->conjugacyClass·h); | 26 | i3·:·tal·:=·tally·apply·(H,h->conjugacyClass·h); |
| 27 | i4·:·partis·=·partitions·6; | 27 | i4·:·partis·=·partitions·6; |
| 28 | i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p)) | 28 | i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p)) |
| 29 | ·--·used·0.19 | 29 | ·--·used·0.21911s·(cpu);·0.17827s·(thread);·0s·(gc) |
| 30 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} | 30 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} |
| 31 | ···············Partition{2,·1,·1,·1,·1}·=>·0 | 31 | ···············Partition{2,·1,·1,·1,·1}·=>·0 |
| 32 | ···············Partition{2,·2,·1,·1}·=>·1 | 32 | ···············Partition{2,·2,·1,·1}·=>·1 |
| 33 | ···············Partition{2,·2,·2}·=>·1 | 33 | ···············Partition{2,·2,·2}·=>·1 |
| 34 | ···············Partition{3,·1,·1,·1}·=>·0 | 34 | ···············Partition{3,·1,·1,·1}·=>·0 |
| 35 | ···············Partition{3,·2,·1}·=>·0 | 35 | ···············Partition{3,·2,·1}·=>·0 |
| Offset 9, 15 lines modified | Offset 9, 15 lines modified | ||
| 9 | i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}} | 9 | i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}} |
| 10 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} | 10 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} |
| 11 | o2·:·List | 11 | o2·:·List |
| 12 | i3·:·time·seco·=·secondaryInvariants(genList,R); | 12 | i3·:·time·seco·=·secondaryInvariants(genList,R); |
| 13 | ·--·used·0. | 13 | ·--·used·0.527265s·(cpu);·0.435396s·(thread);·0s·(gc) |
| 14 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) | 14 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) |
| 15 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) | 15 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) |
| 16 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) | 16 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) |
| 17 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 17 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| 18 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) | 18 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) |
| 19 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) | 19 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) |
| 20 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 20 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| Offset 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ·····|·2·3·| | 122 | ·····|·2·3·| |
| 123 | ·····|·4·| | 123 | ·····|·4·| |
| 124 | o4·:·YoungTableau</code></pre> | 124 | o4·:·YoungTableau</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·higherSpechtPolynomial(S,T,R) | 127 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·higherSpechtPolynomial(S,T,R) |
| 128 | ·--·used·0.000 | 128 | ·--·used·0.000300263s·(cpu);·0.00126291s·(thread);·0s·(gc) |
| 129 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· | 129 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· |
| 130 | o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 130 | o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| 131 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· | 131 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· |
| 132 | ·····------------------------------------------------------------------------ | 132 | ·····------------------------------------------------------------------------ |
| 133 | ······3·2········3·2········2·3········2·3········3···2········3·2···· | 133 | ······3·2········3·2········2·3········2·3········3···2········3·2···· |
| 134 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 134 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| Offset 144, 15 lines modified | Offset 144, 15 lines modified | ||
| 144 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x | 144 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 145 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 | 145 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 146 | o5·:·R</code></pre> | 146 | o5·:·R</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) | 149 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) |
| 150 | ·--·used·0.0002 | 150 | ·--·used·0.000222056s·(cpu);·0.00121759s·(thread);·0s·(gc) |
| 151 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· | 151 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· |
| 152 | o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 152 | o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| 153 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· | 153 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· |
| 154 | ·····------------------------------------------------------------------------ | 154 | ·····------------------------------------------------------------------------ |
| 155 | ······3·2········3·2········2·3········2·3········3···2········3·2···· | 155 | ······3·2········3·2········2·3········2·3········3···2········3·2···· |
| 156 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 156 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| Offset 166, 15 lines modified | Offset 166, 15 lines modified | ||
| 166 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x | 166 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 167 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 | 167 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 168 | o6·:·R</code></pre> | 168 | o6·:·R</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) | 171 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) |
| 172 | ·--·used·0.00 | 172 | ·--·used·0.00255557s·(cpu);·0.00204318s·(thread);·0s·(gc) |
| 173 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·)) | 173 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·)) |
| 174 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0 | 174 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0 |
| 175 | o7·:·Expression·of·class·Product</code></pre> | 175 | o7·:·Expression·of·class·Product</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ········</table> | 177 | ········</table> |
| Offset 69, 15 lines modified | Offset 69, 15 lines modified | ||
| 69 | o4·=·|·0·1·| | 69 | o4·=·|·0·1·| |
| 70 | ·····|·2·3·| | 70 | ·····|·2·3·| |
| 71 | ·····|·4·| | 71 | ·····|·4·| |
| 72 | o4·:·YoungTableau | 72 | o4·:·YoungTableau |
| 73 | i5·:·time·higherSpechtPolynomial(S,T,R) | 73 | i5·:·time·higherSpechtPolynomial(S,T,R) |
| 74 | ·--·used·0.000 | 74 | ·--·used·0.000300263s·(cpu);·0.00126291s·(thread);·0s·(gc) |
| 75 | ······3·2··········2·3······3·····2········3·2····3···2······2···3 | 75 | ······3·2··········2·3······3·····2········3·2····3···2······2···3 |
| 76 | o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 76 | o5·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| 77 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4 | 77 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4 |
| 78 | ·····------------------------------------------------------------------------ | 78 | ·····------------------------------------------------------------------------ |
| 79 | ······3·2········3·2········2·3········2·3········3···2········3·2 | 79 | ······3·2········3·2········2·3········2·3········3···2········3·2 |
| 80 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 80 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | ·····------------------------------------------------------------------------ | 89 | ·····------------------------------------------------------------------------ |
| 90 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 | 90 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 |
| 91 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x | 91 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 92 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 | 92 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 93 | o5·:·R | 93 | o5·:·R |
| 94 | i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) | 94 | i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) |
| 95 | ·--·used·0.0002 | 95 | ·--·used·0.000222056s·(cpu);·0.00121759s·(thread);·0s·(gc) |
| 96 | ······3·2··········2·3······3·····2········3·2····3···2······2···3 | 96 | ······3·2··········2·3······3·····2········3·2····3···2······2···3 |
| 97 | o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 97 | o6·=·x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| 98 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4 | 98 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4 |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ······3·2········3·2········2·3········2·3········3···2········3·2 | 100 | ······3·2········3·2········2·3········2·3········3···2········3·2 |
| 101 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 101 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- |
| Offset 109, 15 lines modified | Offset 109, 15 lines modified | ||
| 109 | ·····------------------------------------------------------------------------ | 109 | ·····------------------------------------------------------------------------ |
| 110 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 | 110 | ········2···3····2·····3····2·····3······2···3········2·3········2·3 |
| 111 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x | 111 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 112 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 | 112 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 113 | o6·:·R | 113 | o6·:·R |
| 114 | i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) | 114 | i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) |
| 115 | ·--·used·0.00 | 115 | ·--·used·0.00255557s·(cpu);·0.00204318s·(thread);·0s·(gc) |
| 116 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·) | 116 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·) |
| 117 | (x·)(x·)) | 117 | (x·)(x·)) |
| 118 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4 | 118 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4 |
| 119 | 2···0 | 119 | 2···0 |
| 120 | o7·:·Expression·of·class·Product | 120 | o7·:·Expression·of·class·Product |
| Offset 119, 15 lines modified | Offset 119, 15 lines modified | ||
| 119 | ········</div> | 119 | ········</div> |
| 120 | ········<table·class="examples"> | 120 | ········<table·class="examples"> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·partis·=·partitions·6;</code></pre> | 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·partis·=·partitions·6;</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p)) | 125 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p)) |
| 126 | ·--·used·0.19 | 126 | ·--·used·0.21911s·(cpu);·0.17827s·(thread);·0s·(gc) |
| 127 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} | 127 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} |
| 128 | ···············Partition{2,·1,·1,·1,·1}·=>·0 | 128 | ···············Partition{2,·1,·1,·1,·1}·=>·0 |
| 129 | ···············Partition{2,·2,·1,·1}·=>·1 | 129 | ···············Partition{2,·2,·1,·1}·=>·1 |
| 130 | ···············Partition{2,·2,·2}·=>·1 | 130 | ···············Partition{2,·2,·2}·=>·1 |
| 131 | ···············Partition{3,·1,·1,·1}·=>·0 | 131 | ···············Partition{3,·1,·1,·1}·=>·0 |
| 132 | ···············Partition{3,·2,·1}·=>·0 | 132 | ···············Partition{3,·2,·1}·=>·0 |
| Offset 64, 15 lines modified | Offset 64, 15 lines modified | ||
| 64 | representations·of·$H$·in·each·irreducible·representation·of·$S_6$.·We·take | 64 | representations·of·$H$·in·each·irreducible·representation·of·$S_6$.·We·take |
| 65 | into·account·that·there·are·multiple·copies·of·each·representation·by | 65 | into·account·that·there·are·multiple·copies·of·each·representation·by |
| 66 | multiplying·the·values·with·the·number·of·copies·which·is·given·by·the | 66 | multiplying·the·values·with·the·number·of·copies·which·is·given·by·the |
| 67 | hookLengthFormula. | 67 | hookLengthFormula. |
| 68 | i4·:·partis·=·partitions·6; | 68 | i4·:·partis·=·partitions·6; |
| 69 | i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity | 69 | i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity |
| 70 | (tal,p)) | 70 | (tal,p)) |
| 71 | ·--·used·0.19 | 71 | ·--·used·0.21911s·(cpu);·0.17827s·(thread);·0s·(gc) |
| 72 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} | 72 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} |
| 73 | ···············Partition{2,·1,·1,·1,·1}·=>·0 | 73 | ···············Partition{2,·1,·1,·1,·1}·=>·0 |
| 74 | ···············Partition{2,·2,·1,·1}·=>·1 | 74 | ···············Partition{2,·2,·1,·1}·=>·1 |
| 75 | ···············Partition{2,·2,·2}·=>·1 | 75 | ···············Partition{2,·2,·2}·=>·1 |
| 76 | ···············Partition{3,·1,·1,·1}·=>·0 | 76 | ···············Partition{3,·1,·1,·1}·=>·0 |
| 77 | ···············Partition{3,·2,·1}·=>·0 | 77 | ···············Partition{3,·2,·1}·=>·0 |
| Offset 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} | 98 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} |
| 99 | o2·:·List</code></pre> | 99 | o2·:·List</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·seco·=·secondaryInvariants(genList,R); | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·seco·=·secondaryInvariants(genList,R); |
| 103 | ·--·used·0. | 103 | ·--·used·0.527265s·(cpu);·0.435396s·(thread);·0s·(gc) |
| 104 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) | 104 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) |
| 105 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) | 105 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) |
| 106 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) | 106 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) |
| 107 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 107 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| 108 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) | 108 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) |
| 109 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) | 109 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) |
| 110 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 110 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
| 46 | o1·:·PolynomialRing | 46 | o1·:·PolynomialRing |
| 47 | i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}} | 47 | i2·:·genList·=·{{1,2,3,0,5,4},{0,4,2,5,1,3}} |
| 48 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} | 48 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} |
| 49 | o2·:·List | 49 | o2·:·List |
| 50 | i3·:·time·seco·=·secondaryInvariants(genList,R); | 50 | i3·:·time·seco·=·secondaryInvariants(genList,R); |
| 51 | ·--·used·0. | 51 | ·--·used·0.527265s·(cpu);·0.435396s·(thread);·0s·(gc) |
| 52 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) | 52 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) |
| 53 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) | 53 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) |
| 54 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) | 54 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) |
| 55 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 55 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| 56 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) | 56 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) |
| 57 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) | 57 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) |
| 58 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 58 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | SW50ZXJzZWN0aW9uT2ZUaHJlZVF1YWRyaWNzSW5QNw== | 8 | SW50ZXJzZWN0aW9uT2ZUaHJlZVF1YWRyaWNzSW5QNw== |
| 9 | #:len=625 | 9 | #:len=625 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGNsYXNzIG9mIGFsbCBzcGVjaWFs | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGNsYXNzIG9mIGFsbCBzcGVjaWFs |
| 11 | IGludGVyc2VjdGlvbiBvZiB0aHJlZSBxdWFkcmljcyBpbiBQXjciLCAibGluZW51bSIgPT4gMzY1 | 11 | IGludGVyc2VjdGlvbiBvZiB0aHJlZSBxdWFkcmljcyBpbiBQXjciLCAibGluZW51bSIgPT4gMzY1 |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | ·····of·discriminant·31·=·det|·8·1·| | 10 | ·····of·discriminant·31·=·det|·8·1·| |
| 11 | ·····························|·1·4·| | 11 | ·····························|·1·4·| |
| 12 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 | 12 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 |
| 13 | ·····cut·out·by·5·hypersurfaces·of·degree·1 | 13 | ·····cut·out·by·5·hypersurfaces·of·degree·1 |
| 14 | ·····(This·is·a·classical·example·of·rational·fourfold) | 14 | ·····(This·is·a·classical·example·of·rational·fourfold) |
| 15 | i3·:·time·U'·=·associatedCastelnuovoSurface·X; | 15 | i3·:·time·U'·=·associatedCastelnuovoSurface·X; |
| 16 | ·--·used·3. | 16 | ·--·used·3.63712s·(cpu);·1.06309s·(thread);·0s·(gc) |
| 17 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X | 17 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X |
| 18 | i4·:·(mu,U,C,f)·=·building·U'; | 18 | i4·:·(mu,U,C,f)·=·building·U'; |
| 19 | i5·:·?·mu | 19 | i5·:·?·mu |
| Offset 7, 15 lines modified | Offset 7, 15 lines modified | ||
| 7 | i2·:·describe·X | 7 | i2·:·describe·X |
| 8 | o2·=·Special·cubic·fourfold·of·discriminant·14 | 8 | o2·=·Special·cubic·fourfold·of·discriminant·14 |
| 9 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 | 9 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 |
| 10 | ·····cut·out·by·6·hypersurfaces·of·degree·2 | 10 | ·····cut·out·by·6·hypersurfaces·of·degree·2 |
| 11 | i3·:·time·U'·=·associatedK3surface·X; | 11 | i3·:·time·U'·=·associatedK3surface·X; |
| 12 | ·--·used·3. | 12 | ·--·used·3.51081s·(cpu);·1.11905s·(thread);·0s·(gc) |
| 13 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X | 13 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X |
| 14 | i4·:·(mu,U,C,f)·=·building·U'; | 14 | i4·:·(mu,U,C,f)·=·building·U'; |
| 15 | i5·:·?·mu | 15 | i5·:·?·mu |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 | 10 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 |
| 11 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 11 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 12 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 12 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 13 | ·····Type:·ordinary | 13 | ·····Type:·ordinary |
| 14 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) | 14 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) |
| 15 | i3·:·time·U'·=·associatedK3surface·X; | 15 | i3·:·time·U'·=·associatedK3surface·X; |
| 16 | ·--·used· | 16 | ·--·used·8.77535s·(cpu);·3.87788s·(thread);·0s·(gc) |
| 17 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X | 17 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X |
| 18 | i4·:·(mu,U,C,f)·=·building·U'; | 18 | i4·:·(mu,U,C,f)·=·building·U'; |
| 19 | i5·:·?·mu | 19 | i5·:·?·mu |
| Offset 8, 28 lines modified | Offset 8, 28 lines modified | ||
| 8 | i2·:·describe·X | 8 | i2·:·describe·X |
| 9 | o2·=·Special·cubic·fourfold·of·discriminant·26 | 9 | o2·=·Special·cubic·fourfold·of·discriminant·26 |
| 10 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 10 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 11 | ·····cut·out·by·13·hypersurfaces·of·degree·3 | 11 | ·····cut·out·by·13·hypersurfaces·of·degree·3 |
| 12 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 12 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 13 | ·--·used· | 13 | ·--·used·3.68941s·(cpu);·1.72777s·(thread);·0s·(gc) |
| 14 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8 | 14 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8 |
| 15 | number·2-secant·lines·=·7 | 15 | number·2-secant·lines·=·7 |
| 16 | number·5-secant·conics·=·1 | 16 | number·5-secant·conics·=·1 |
| 17 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5 | 17 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5 |
| 18 | i4·:·p·:=·point·ambient·X·--·random·point·on·P^5 | 18 | i4·:·p·:=·point·ambient·X·--·random·point·on·P^5 |
| 19 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] | 19 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] |
| 20 | o4·:·ProjectiveVariety,·a·point·in·PP^5 | 20 | o4·:·ProjectiveVariety,·a·point·in·PP^5 |
| 21 | i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface | 21 | i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface |
| 22 | ·--·used·0. | 22 | ·--·used·0.462009s·(cpu);·0.272577s·(thread);·0s·(gc) |
| 23 | o5·:·ProjectiveVariety,·curve·in·PP^5 | 23 | o5·:·ProjectiveVariety,·curve·in·PP^5 |
| 24 | i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C)) | 24 | i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C)) |
| 25 | i7·:· | 25 | i7·:· |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·2 | 11 | ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·2 |
| 12 | ·····cut·out·by·19·hypersurfaces·of·degree·2 | 12 | ·····cut·out·by·19·hypersurfaces·of·degree·2 |
| 13 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) | 13 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) |
| 14 | ·····Type:·ordinary | 14 | ·····Type:·ordinary |
| 15 | ·····(case·17·of·Table·1·in·arXiv:2002.07026) | 15 | ·····(case·17·of·Table·1·in·arXiv:2002.07026) |
| 16 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 16 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 17 | ·--·used· | 17 | ·--·used·15.1792s·(cpu);·5.95335s·(thread);·0s·(gc) |
| 18 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7 | 18 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7 |
| 19 | number·1-secant·lines·=·6 | 19 | number·1-secant·lines·=·6 |
| 20 | number·3-secant·conics·=·1 | 20 | number·3-secant·conics·=·1 |
| 21 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8 | 21 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8 |
| 22 | i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X | 22 | i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X |
| Offset 29, 15 lines modified | Offset 29, 15 lines modified | ||
| 29 | i5·:·p·:=·point·Y·--·random·point·on·Y | 29 | i5·:·p·:=·point·Y·--·random·point·on·Y |
| 30 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1] | 30 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1] |
| 31 | o5·:·ProjectiveVariety,·a·point·in·PP^8 | 31 | o5·:·ProjectiveVariety,·a·point·in·PP^8 |
| 32 | i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface | 32 | i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface |
| 33 | ·--·used·0.2 | 33 | ·--·used·0.236722s·(cpu);·0.226179s·(thread);·0s·(gc) |
| 34 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y) | 34 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y) |
| 35 | i7·:·S·=·surface·X; | 35 | i7·:·S·=·surface·X; |
| 36 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y) | 36 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y) |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1729890813579561111 | 1 | --·-*-·M2-comint·-*-·hash:·1729890813579561111 |
| 2 | i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; | 2 | i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; |
| 3 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1 | 3 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1 |
| 4 | i2·:·time·discriminant·X | 4 | i2·:·time·discriminant·X |
| 5 | ·--·used·0. | 5 | ·--·used·0.320878s·(cpu);·0.111983s·(thread);·0s·(gc) |
| 6 | o2·=·14 | 6 | o2·=·14 |
| 7 | i3·:· | 7 | i3·:· |
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| 1 | --·-*-·M2-comint·-*-·hash:·1730220932418738713 | 1 | --·-*-·M2-comint·-*-·hash:·1730220932418738713 |
| 2 | i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; | 2 | i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; |
| 3 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0 | 3 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0 |
| 4 | i2·:·time·discriminant·X | 4 | i2·:·time·discriminant·X |
| 5 | ·--·used· | 5 | ·--·used·1.2555s·(cpu);·0.416401s·(thread);·0s·(gc) |
| 6 | o2·=·10 | 6 | o2·=·10 |
| 7 | i3·:· | 7 | i3·:· |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | o2·:·ProjectiveVariety,·curve·in·PP^5 | 5 | o2·:·ProjectiveVariety,·curve·in·PP^5 |
| 6 | i3·:·X·=·random({{2},{2},{2}},S); | 6 | i3·:·X·=·random({{2},{2},{2}},S); |
| 7 | o3·:·ProjectiveVariety,·surface·in·PP^5 | 7 | o3·:·ProjectiveVariety,·surface·in·PP^5 |
| 8 | i4·:·time·parameterCount(S,X,Verbose=>true) | 8 | i4·:·time·parameterCount(S,X,Verbose=>true) |
| 9 | ·--·used·0.2 | 9 | ·--·used·0.231675s·(cpu);·0.168377s·(thread);·0s·(gc) |
| 10 | S:·rational·normal·curve·of·degree·5·in·PP^5 | 10 | S:·rational·normal·curve·of·degree·5·in·PP^5 |
| 11 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2 | 11 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2 |
| 12 | (assumption:·h^1(N_{S,P^5})·=·0) | 12 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 13 | h^0(N_{S,P^5})·=·32 | 13 | h^0(N_{S,P^5})·=·32 |
| 14 | h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2)); | 14 | h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2)); |
| 15 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal | 15 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal |
| 16 | dim·GG(2,9)·=·21 | 16 | dim·GG(2,9)·=·21 |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | o2·:·ProjectiveVariety,·surface·in·PP^5 | 5 | o2·:·ProjectiveVariety,·surface·in·PP^5 |
| 6 | i3·:·X·=·specialCubicFourfold·V; | 6 | i3·:·X·=·specialCubicFourfold·V; |
| 7 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0 | 7 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0 |
| 8 | i4·:·time·parameterCount(X,Verbose=>true) | 8 | i4·:·time·parameterCount(X,Verbose=>true) |
| 9 | ·--·used·0.3 | 9 | ·--·used·0.437433s·(cpu);·0.308585s·(thread);·0s·(gc) |
| 10 | S:·Veronese·surface·in·PP^5 | 10 | S:·Veronese·surface·in·PP^5 |
| 11 | X:·smooth·cubic·hypersurface·in·PP^5 | 11 | X:·smooth·cubic·hypersurface·in·PP^5 |
| 12 | (assumption:·h^1(N_{S,P^5})·=·0) | 12 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 13 | h^0(N_{S,P^5})·=·27 | 13 | h^0(N_{S,P^5})·=·27 |
| 14 | h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3)); | 14 | h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3)); |
| 15 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal | 15 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal |
| 16 | h^0(N_{S,P^5})·+·27·=·54 | 16 | h^0(N_{S,P^5})·+·27·=·54 |
| Offset 11, 15 lines modified | Offset 11, 15 lines modified | ||
| 11 | o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G) | 11 | o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G) |
| 12 | i3·:·X·=·specialGushelMukaiFourfold·S; | 12 | i3·:·X·=·specialGushelMukaiFourfold·S; |
| 13 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0 | 13 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0 |
| 14 | i4·:·time·parameterCount(X,Verbose=>true) | 14 | i4·:·time·parameterCount(X,Verbose=>true) |
| 15 | ·--·used·2. | 15 | ·--·used·2.97136s·(cpu);·2.04224s·(thread);·0s·(gc) |
| 16 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) | 16 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) |
| 17 | X:·GM·fourfold·containing·S | 17 | X:·GM·fourfold·containing·S |
| 18 | Y:·del·Pezzo·fivefold·containing·X | 18 | Y:·del·Pezzo·fivefold·containing·X |
| 19 | h^1(N_{S,Y})·=·0 | 19 | h^1(N_{S,Y})·=·0 |
| 20 | h^0(N_{S,Y})·=·11 | 20 | h^0(N_{S,Y})·=·11 |
| 21 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); | 21 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); |
| 22 | in·particular,·h^0(I_{S,Y}(2))·is·minimal | 22 | in·particular,·h^0(I_{S,Y}(2))·is·minimal |
| Offset 6, 15 lines modified | Offset 6, 15 lines modified | ||
| 6 | i3·:·?·X | 6 | i3·:·?·X |
| 7 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees | 7 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees |
| 8 | ·····1^2·2^5 | 8 | ·····1^2·2^5 |
| 9 | i4·:·time·parametrizeFanoFourfold·X | 9 | i4·:·time·parametrizeFanoFourfold·X |
| 10 | ·--·used·2. | 10 | ·--·used·2.13666s·(cpu);·0.714743s·(thread);·0s·(gc) |
| 11 | o4·=·multi-rational·map·consisting·of·one·single·rational·map | 11 | o4·=·multi-rational·map·consisting·of·one·single·rational·map |
| 12 | ·····source·variety:·PP^4 | 12 | ·····source·variety:·PP^4 |
| 13 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5· | 13 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5· |
| 14 | ·····dominance:·true | 14 | ·····dominance:·true |
| 15 | ·····degree:·1 | 15 | ·····degree:·1 |
| Offset 7, 22 lines modified | Offset 7, 22 lines modified | ||
| 7 | o3·:·ProjectiveVariety,·surface·in·PP^5 | 7 | o3·:·ProjectiveVariety,·surface·in·PP^5 |
| 8 | i4·:·X·=·projectiveVariety·ideal(x_1^2*x_3+x_0*x_2*x_3-6*x_1*x_2*x_3-x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+2*x_0^2*x_4-10*x_0*x_1*x_4+13*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2); | 8 | i4·:·X·=·projectiveVariety·ideal(x_1^2*x_3+x_0*x_2*x_3-6*x_1*x_2*x_3-x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+2*x_0^2*x_4-10*x_0*x_1*x_4+13*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2); |
| 9 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5 | 9 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5 |
| 10 | i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); | 10 | i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); |
| 11 | ·--·used·0.00 | 11 | ·--·used·0.00789046s·(cpu);·0.00717831s·(thread);·0s·(gc) |
| 12 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0 | 12 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0 |
| 13 | i6·:·time·describe·F | 13 | i6·:·time·describe·F |
| 14 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 14 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 15 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 15 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 16 | ·--·used·0. | 16 | ·--·used·0.623971s·(cpu);·0.199632s·(thread);·0s·(gc) |
| 17 | o6·=·Special·cubic·fourfold·of·discriminant·26 | 17 | o6·=·Special·cubic·fourfold·of·discriminant·26 |
| 18 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 18 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 19 | ·····cut·out·by·13·hypersurfaces·of·degree·3 | 19 | ·····cut·out·by·13·hypersurfaces·of·degree·3 |
| 20 | i7·:·assert(F·==·X) | 20 | i7·:·assert(F·==·X) |
| Offset 7, 22 lines modified | Offset 7, 22 lines modified | ||
| 7 | o3·:·ProjectiveVariety,·surface·in·PP^8 | 7 | o3·:·ProjectiveVariety,·surface·in·PP^8 |
| 8 | i4·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); | 8 | i4·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); |
| 9 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8 | 9 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8 |
| 10 | i5·:·time·F·=·specialGushelMukaiFourfold(S,X); | 10 | i5·:·time·F·=·specialGushelMukaiFourfold(S,X); |
| 11 | ·--·used·1. | 11 | ·--·used·1.59885s·(cpu);·1.31817s·(thread);·0s·(gc) |
| 12 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0 | 12 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0 |
| 13 | i6·:·time·describe·F | 13 | i6·:·time·describe·F |
| 14 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 14 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 15 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 15 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 16 | ·--·used· | 16 | ·--·used·7.68056s·(cpu);·2.91449s·(thread);·0s·(gc) |
| 17 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') | 17 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') |
| 18 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 | 18 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 |
| 19 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 19 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 20 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 20 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 21 | ·····Type:·ordinary | 21 | ·····Type:·ordinary |
| 22 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) | 22 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·X·=·specialGushelMukaiFourfold(ideal(x_6-x_7,·x_5,·x_3-x_4,·x_1,·x_0-x_4,·x_2*x_7-x_4*x_8),·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8)); | 5 | i2·:·X·=·specialGushelMukaiFourfold(ideal(x_6-x_7,·x_5,·x_3-x_4,·x_1,·x_0-x_4,·x_2*x_7-x_4*x_8),·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8)); |
| 6 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0 | 6 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0 |
| 7 | i3·:·time·toGrass·X | 7 | i3·:·time·toGrass·X |
| 8 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 8 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 9 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 9 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 10 | ·--·used· | 10 | ·--·used·6.8058s·(cpu);·2.8028s·(thread);·0s·(gc) |
| 11 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 11 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 12 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2 | 12 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2 |
| 13 | ·····target·variety:·GG(1,4)·⊂·PP^9 | 13 | ·····target·variety:·GG(1,4)·⊂·PP^9 |
| 14 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) | 14 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | i2·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8); | 5 | i2·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8); |
| 6 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8 | 6 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8 |
| 7 | i3·:·time·toGrass·X | 7 | i3·:·time·toGrass·X |
| 8 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 8 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 9 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 9 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 10 | ·--·used·6. | 10 | ·--·used·6.96933s·(cpu);·2.84332s·(thread);·0s·(gc) |
| 11 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 11 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 12 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2 | 12 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2 |
| 13 | ·····target·variety:·GG(1,4)·⊂·PP^9 | 13 | ·····target·variety:·GG(1,4)·⊂·PP^9 |
| 14 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) | 14 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) |
| Offset 5, 15 lines modified | Offset 5, 15 lines modified | ||
| 5 | o2·:·ProjectiveVariety,·surface·in·PP^5 | 5 | o2·:·ProjectiveVariety,·surface·in·PP^5 |
| 6 | i3·:·X·=·specialCubicFourfold·S; | 6 | i3·:·X·=·specialCubicFourfold·S; |
| 7 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0 | 7 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0 |
| 8 | i4·:·time·f·=·unirationalParametrization·X; | 8 | i4·:·time·f·=·unirationalParametrization·X; |
| 9 | ·--·used· | 9 | ·--·used·1.03184s·(cpu);·0.425636s·(thread);·0s·(gc) |
| 10 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X) | 10 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X) |
| 11 | i5·:·degreeSequence·f | 11 | i5·:·degreeSequence·f |
| 12 | o5·=·{[10]} | 12 | o5·=·{[10]} |
| Offset 110, 15 lines modified | Offset 110, 15 lines modified | ||
| 110 | ·····························|·1·4·| | 110 | ·····························|·1·4·| |
| 111 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 | 111 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 |
| 112 | ·····cut·out·by·5·hypersurfaces·of·degree·1 | 112 | ·····cut·out·by·5·hypersurfaces·of·degree·1 |
| 113 | ·····(This·is·a·classical·example·of·rational·fourfold)</code></pre> | 113 | ·····(This·is·a·classical·example·of·rational·fourfold)</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedCastelnuovoSurface·X; | 116 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedCastelnuovoSurface·X; |
| 117 | ·--·used·3. | 117 | ·--·used·3.63712s·(cpu);·1.06309s·(thread);·0s·(gc) |
| 118 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X</code></pre> | 118 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> | 121 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| Offset 42, 15 lines modified | Offset 42, 15 lines modified | ||
| 42 | o2·=·Complete·intersection·of·3·quadrics·in·PP^7 | 42 | o2·=·Complete·intersection·of·3·quadrics·in·PP^7 |
| 43 | ·····of·discriminant·31·=·det|·8·1·| | 43 | ·····of·discriminant·31·=·det|·8·1·| |
| 44 | ·····························|·1·4·| | 44 | ·····························|·1·4·| |
| 45 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 | 45 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 |
| 46 | ·····cut·out·by·5·hypersurfaces·of·degree·1 | 46 | ·····cut·out·by·5·hypersurfaces·of·degree·1 |
| 47 | ·····(This·is·a·classical·example·of·rational·fourfold) | 47 | ·····(This·is·a·classical·example·of·rational·fourfold) |
| 48 | i3·:·time·U'·=·associatedCastelnuovoSurface·X; | 48 | i3·:·time·U'·=·associatedCastelnuovoSurface·X; |
| 49 | ·--·used·3. | 49 | ·--·used·3.63712s·(cpu);·1.06309s·(thread);·0s·(gc) |
| 50 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X | 50 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X |
| 51 | i4·:·(mu,U,C,f)·=·building·U'; | 51 | i4·:·(mu,U,C,f)·=·building·U'; |
| 52 | i5·:·?·mu | 52 | i5·:·?·mu |
| 53 | o5·=·multi-rational·map·consisting·of·one·single·rational·map | 53 | o5·=·multi-rational·map·consisting·of·one·single·rational·map |
| 54 | ·····source·variety:·5-dimensional·subvariety·of·PP^7·cut·out·by·2 | 54 | ·····source·variety:·5-dimensional·subvariety·of·PP^7·cut·out·by·2 |
| Offset 109, 15 lines modified | Offset 109, 15 lines modified | ||
| 109 | o2·=·Special·cubic·fourfold·of·discriminant·14 | 109 | o2·=·Special·cubic·fourfold·of·discriminant·14 |
| 110 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 | 110 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 |
| 111 | ·····cut·out·by·6·hypersurfaces·of·degree·2</code></pre> | 111 | ·····cut·out·by·6·hypersurfaces·of·degree·2</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; | 114 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; |
| 115 | ·--·used·3. | 115 | ·--·used·3.51081s·(cpu);·1.11905s·(thread);·0s·(gc) |
| 116 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> | 116 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> | 119 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| Offset 42, 15 lines modified | Offset 42, 15 lines modified | ||
| 42 | sectional·genus·0 | 42 | sectional·genus·0 |
| 43 | i2·:·describe·X | 43 | i2·:·describe·X |
| 44 | o2·=·Special·cubic·fourfold·of·discriminant·14 | 44 | o2·=·Special·cubic·fourfold·of·discriminant·14 |
| 45 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 | 45 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 |
| 46 | ·····cut·out·by·6·hypersurfaces·of·degree·2 | 46 | ·····cut·out·by·6·hypersurfaces·of·degree·2 |
| 47 | i3·:·time·U'·=·associatedK3surface·X; | 47 | i3·:·time·U'·=·associatedK3surface·X; |
| 48 | ·--·used·3. | 48 | ·--·used·3.51081s·(cpu);·1.11905s·(thread);·0s·(gc) |
| 49 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X | 49 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X |
| 50 | i4·:·(mu,U,C,f)·=·building·U'; | 50 | i4·:·(mu,U,C,f)·=·building·U'; |
| 51 | i5·:·?·mu | 51 | i5·:·?·mu |
| 52 | o5·=·multi-rational·map·consisting·of·one·single·rational·map | 52 | o5·=·multi-rational·map·consisting·of·one·single·rational·map |
| 53 | ·····source·variety:·PP^5 | 53 | ·····source·variety:·PP^5 |
| Offset 112, 15 lines modified | Offset 112, 15 lines modified | ||
| 112 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 112 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 113 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 113 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 114 | ·····Type:·ordinary | 114 | ·····Type:·ordinary |
| 115 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> | 115 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; | 118 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; |
| 119 | ·--·used· | 119 | ·--·used·8.77535s·(cpu);·3.87788s·(thread);·0s·(gc) |
| 120 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> | 120 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> | 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| Offset 44, 15 lines modified | Offset 44, 15 lines modified | ||
| 44 | o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') | 44 | o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') |
| 45 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 | 45 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 |
| 46 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 46 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 47 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 47 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 48 | ·····Type:·ordinary | 48 | ·····Type:·ordinary |
| 49 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) | 49 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) |
| 50 | i3·:·time·U'·=·associatedK3surface·X; | 50 | i3·:·time·U'·=·associatedK3surface·X; |
| 51 | ·--·used· | 51 | ·--·used·8.77535s·(cpu);·3.87788s·(thread);·0s·(gc) |
| 52 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X | 52 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X |
| 53 | i4·:·(mu,U,C,f)·=·building·U'; | 53 | i4·:·(mu,U,C,f)·=·building·U'; |
| 54 | i5·:·?·mu | 54 | i5·:·?·mu |
| 55 | o5·=·multi-rational·map·consisting·of·one·single·rational·map | 55 | o5·=·multi-rational·map·consisting·of·one·single·rational·map |
| 56 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5 | 56 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5 |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | o2·=·Special·cubic·fourfold·of·discriminant·26 | 90 | o2·=·Special·cubic·fourfold·of·discriminant·26 |
| 91 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 91 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 92 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> | 92 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 96 | ·--·used· | 96 | ·--·used·3.68941s·(cpu);·1.72777s·(thread);·0s·(gc) |
| 97 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8 | 97 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8 |
| 98 | number·2-secant·lines·=·7 | 98 | number·2-secant·lines·=·7 |
| 99 | number·5-secant·conics·=·1 | 99 | number·5-secant·conics·=·1 |
| 100 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5</code></pre> | 100 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] | 106 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] |
| 107 | o4·:·ProjectiveVariety,·a·point·in·PP^5</code></pre> | 107 | o4·:·ProjectiveVariety,·a·point·in·PP^5</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface |
| 111 | ·--·used·0. | 111 | ·--·used·0.462009s·(cpu);·0.272577s·(thread);·0s·(gc) |
| 112 | o5·:·ProjectiveVariety,·curve·in·PP^5</code></pre> | 112 | o5·:·ProjectiveVariety,·curve·in·PP^5</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C))</code></pre> | 115 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree(C·*·surface·X)·==·5·and·isSubset(p,·C))</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ········</table> | 117 | ········</table> |
| Offset 31, 28 lines modified | Offset 31, 28 lines modified | ||
| 31 | sectional·genus·0 | 31 | sectional·genus·0 |
| 32 | i2·:·describe·X | 32 | i2·:·describe·X |
| 33 | o2·=·Special·cubic·fourfold·of·discriminant·26 | 33 | o2·=·Special·cubic·fourfold·of·discriminant·26 |
| 34 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 34 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 35 | ·····cut·out·by·13·hypersurfaces·of·degree·3 | 35 | ·····cut·out·by·13·hypersurfaces·of·degree·3 |
| 36 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 36 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 37 | ·--·used· | 37 | ·--·used·3.68941s·(cpu);·1.72777s·(thread);·0s·(gc) |
| 38 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a | 38 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a |
| 39 | general·point:·8 | 39 | general·point:·8 |
| 40 | number·2-secant·lines·=·7 | 40 | number·2-secant·lines·=·7 |
| 41 | number·5-secant·conics·=·1 | 41 | number·5-secant·conics·=·1 |
| 42 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5 | 42 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5 |
| 43 | i4·:·p·:=·point·ambient·X·--·random·point·on·P^5 | 43 | i4·:·p·:=·point·ambient·X·--·random·point·on·P^5 |
| 44 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] | 44 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] |
| 45 | o4·:·ProjectiveVariety,·a·point·in·PP^5 | 45 | o4·:·ProjectiveVariety,·a·point·in·PP^5 |
| 46 | i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface | 46 | i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface |
| 47 | ·--·used·0. | 47 | ·--·used·0.462009s·(cpu);·0.272577s·(thread);·0s·(gc) |
| 48 | o5·:·ProjectiveVariety,·curve·in·PP^5 | 48 | o5·:·ProjectiveVariety,·curve·in·PP^5 |
| 49 | i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree | 49 | i6·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C·*·surface·X)·==·0·and·degree |
| 50 | (C·*·surface·X)·==·5·and·isSubset(p,·C)) | 50 | (C·*·surface·X)·==·5·and·isSubset(p,·C)) |
| 51 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 51 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 52 | ····*·_\x8d_\x8e_\x8t_\x8e_\x8c_\x8t_\x8C_\x8o_\x8n_\x8g_\x8r_\x8u_\x8e_\x8n_\x8c_\x8e_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8,_\x8Z_\x8Z_\x8)·--·detect·and·return·a | 52 | ····*·_\x8d_\x8e_\x8t_\x8e_\x8c_\x8t_\x8C_\x8o_\x8n_\x8g_\x8r_\x8u_\x8e_\x8n_\x8c_\x8e_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8,_\x8Z_\x8Z_\x8)·--·detect·and·return·a |
| 53 | ······congruence·of·(2e-1)-secant·curves·of·degree·e·inside·a·del·Pezzo | 53 | ······congruence·of·(2e-1)-secant·curves·of·degree·e·inside·a·del·Pezzo |
| Offset 93, 15 lines modified | Offset 93, 15 lines modified | ||
| 93 | ·····cut·out·by·19·hypersurfaces·of·degree·2 | 93 | ·····cut·out·by·19·hypersurfaces·of·degree·2 |
| 94 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) | 94 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) |
| 95 | ·····Type:·ordinary | 95 | ·····Type:·ordinary |
| 96 | ·····(case·17·of·Table·1·in·arXiv:2002.07026)</code></pre> | 96 | ·····(case·17·of·Table·1·in·arXiv:2002.07026)</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 100 | ·--·used· | 100 | ·--·used·15.1792s·(cpu);·5.95335s·(thread);·0s·(gc) |
| 101 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7 | 101 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7 |
| 102 | number·1-secant·lines·=·6 | 102 | number·1-secant·lines·=·6 |
| 103 | number·3-secant·conics·=·1 | 103 | number·3-secant·conics·=·1 |
| 104 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8</code></pre> | 104 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| Offset 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1] | 114 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1] |
| 115 | o5·:·ProjectiveVariety,·a·point·in·PP^8</code></pre> | 115 | o5·:·ProjectiveVariety,·a·point·in·PP^8</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface |
| 119 | ·--·used·0.2 | 119 | ·--·used·0.236722s·(cpu);·0.226179s·(thread);·0s·(gc) |
| 120 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)</code></pre> | 120 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·S·=·surface·X; | 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·S·=·surface·X; |
| 124 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)</code></pre> | 124 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)</code></pre> |
| Offset 37, 15 lines modified | Offset 37, 15 lines modified | ||
| 37 | o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·20 | 37 | o2·=·Special·Gushel-Mukai·fourfold·of·discriminant·20 |
| 38 | ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·2 | 38 | ·····containing·a·surface·in·PP^8·of·degree·9·and·sectional·genus·2 |
| 39 | ·····cut·out·by·19·hypersurfaces·of·degree·2 | 39 | ·····cut·out·by·19·hypersurfaces·of·degree·2 |
| 40 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) | 40 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) |
| 41 | ·····Type:·ordinary | 41 | ·····Type:·ordinary |
| 42 | ·····(case·17·of·Table·1·in·arXiv:2002.07026) | 42 | ·····(case·17·of·Table·1·in·arXiv:2002.07026) |
| 43 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 43 | i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 44 | ·--·used· | 44 | ·--·used·15.1792s·(cpu);·5.95335s·(thread);·0s·(gc) |
| 45 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a | 45 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a |
| 46 | general·point:·7 | 46 | general·point:·7 |
| 47 | number·1-secant·lines·=·6 | 47 | number·1-secant·lines·=·6 |
| 48 | number·3-secant·conics·=·1 | 48 | number·3-secant·conics·=·1 |
| 49 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8 | 49 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8 |
| 50 | i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X | 50 | i4·:·Y·=·ambientFivefold·X;·--·del·Pezzo·fivefold·containing·X |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | i5·:·p·:=·point·Y·--·random·point·on·Y | 54 | i5·:·p·:=·point·Y·--·random·point·on·Y |
| 55 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937, | 55 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937, |
| 56 | 13402,·1] | 56 | 13402,·1] |
| 57 | o5·:·ProjectiveVariety,·a·point·in·PP^8 | 57 | o5·:·ProjectiveVariety,·a·point·in·PP^8 |
| 58 | i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface | 58 | i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface |
| 59 | ·--·used·0.2 | 59 | ·--·used·0.236722s·(cpu);·0.226179s·(thread);·0s·(gc) |
| 60 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y) | 60 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y) |
| 61 | i7·:·S·=·surface·X; | 61 | i7·:·S·=·surface·X; |
| 62 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y) | 62 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y) |
| 63 | i8·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C*S)·==·0·and·degree(C*S)·==·3 | 63 | i8·:·assert(dim·C·==·1·and·degree·C·==·2·and·dim(C*S)·==·0·and·degree(C*S)·==·3 |
| 64 | and·isSubset(p,C)·and·isSubset(C,Y)) | 64 | and·isSubset(p,C)·and·isSubset(C,Y)) |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; | 81 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; |
| 82 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1</code></pre> | 82 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X |
| 86 | ·--·used·0. | 86 | ·--·used·0.320878s·(cpu);·0.111983s·(thread);·0s·(gc) |
| 87 | o2·=·14</code></pre> | 87 | o2·=·14</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| 90 | ······</div> | 90 | ······</div> |
| 91 | ······<div> | 91 | ······<div> |
| 92 | ········<h2>See·also</h2> | 92 | ········<h2>See·also</h2> |
| Offset 21, 15 lines modified | Offset 21, 15 lines modified | ||
| 21 | thanks·to·the·functions·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm | 21 | thanks·to·the·functions·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm |
| 22 | allows·you·to·select·the·method). | 22 | allows·you·to·select·the·method). |
| 23 | i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; | 23 | i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; |
| 24 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and | 24 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and |
| 25 | sectional·genus·1 | 25 | sectional·genus·1 |
| 26 | i2·:·time·discriminant·X | 26 | i2·:·time·discriminant·X |
| 27 | ·--·used·0. | 27 | ·--·used·0.320878s·(cpu);·0.111983s·(thread);·0s·(gc) |
| 28 | o2·=·14 | 28 | o2·=·14 |
| 29 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 30 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special | 30 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special |
| 31 | ······Gushel-Mukai·fourfold | 31 | ······Gushel-Mukai·fourfold |
| 32 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 32 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 33 | ····*·discriminant(HodgeSpecialFourfold) | 33 | ····*·discriminant(HodgeSpecialFourfold) |
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| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; | 81 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; |
| 82 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> | 82 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X |
| 86 | ·--·used· | 86 | ·--·used·1.2555s·(cpu);·0.416401s·(thread);·0s·(gc) |
| 87 | o2·=·10</code></pre> | 87 | o2·=·10</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| 90 | ······</div> | 90 | ······</div> |
| 91 | ······<div> | 91 | ······<div> |
| 92 | ········<h2>See·also</h2> | 92 | ········<h2>See·also</h2> |
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| 21 | the·functions·_\x8c_\x8y_\x8c_\x8l_\x8e_\x8C_\x8l_\x8a_\x8s_\x8s,·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm | 21 | the·functions·_\x8c_\x8y_\x8c_\x8l_\x8e_\x8C_\x8l_\x8a_\x8s_\x8s,·_\x8E_\x8u_\x8l_\x8e_\x8r_\x8C_\x8h_\x8a_\x8r_\x8a_\x8c_\x8t_\x8e_\x8r_\x8i_\x8s_\x8t_\x8i_\x8c·and·_\x8E_\x8u_\x8l_\x8e_\x8r·(the·option·Algorithm |
| 22 | allows·you·to·select·the·method). | 22 | allows·you·to·select·the·method). |
| 23 | i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; | 23 | i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; |
| 24 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and | 24 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and |
| 25 | sectional·genus·0 | 25 | sectional·genus·0 |
| 26 | i2·:·time·discriminant·X | 26 | i2·:·time·discriminant·X |
| 27 | ·--·used· | 27 | ·--·used·1.2555s·(cpu);·0.416401s·(thread);·0s·(gc) |
| 28 | o2·=·10 | 28 | o2·=·10 |
| 29 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 29 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 30 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special·cubic | 30 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special·cubic |
| 31 | ······fourfold | 31 | ······fourfold |
| 32 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 32 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 33 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special | 33 | ····*·_\x8d_\x8i_\x8s_\x8c_\x8r_\x8i_\x8m_\x8i_\x8n_\x8a_\x8n_\x8t_\x8(_\x8S_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8G_\x8u_\x8s_\x8h_\x8e_\x8l_\x8M_\x8u_\x8k_\x8a_\x8i_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8)·--·discriminant·of·a·special |
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| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·random({{2},{2},{2}},S); | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·random({{2},{2},{2}},S); |
| 88 | o3·:·ProjectiveVariety,·surface·in·PP^5</code></pre> | 88 | o3·:·ProjectiveVariety,·surface·in·PP^5</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(S,X,Verbose=>true) | 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(S,X,Verbose=>true) |
| 92 | ·--·used·0.2 | 92 | ·--·used·0.231675s·(cpu);·0.168377s·(thread);·0s·(gc) |
| 93 | S:·rational·normal·curve·of·degree·5·in·PP^5 | 93 | S:·rational·normal·curve·of·degree·5·in·PP^5 |
| 94 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2 | 94 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2 |
| 95 | (assumption:·h^1(N_{S,P^5})·=·0) | 95 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 96 | h^0(N_{S,P^5})·=·32 | 96 | h^0(N_{S,P^5})·=·32 |
| 97 | h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2)); | 97 | h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2)); |
| 98 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal | 98 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal |
| 99 | dim·GG(2,9)·=·21 | 99 | dim·GG(2,9)·=·21 |
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| 24 | i1·:·K·=·ZZ/33331;·S·=·PP_K^(1,5); | 24 | i1·:·K·=·ZZ/33331;·S·=·PP_K^(1,5); |
| 25 | o2·:·ProjectiveVariety,·curve·in·PP^5 | 25 | o2·:·ProjectiveVariety,·curve·in·PP^5 |
| 26 | i3·:·X·=·random({{2},{2},{2}},S); | 26 | i3·:·X·=·random({{2},{2},{2}},S); |
| 27 | o3·:·ProjectiveVariety,·surface·in·PP^5 | 27 | o3·:·ProjectiveVariety,·surface·in·PP^5 |
| 28 | i4·:·time·parameterCount(S,X,Verbose=>true) | 28 | i4·:·time·parameterCount(S,X,Verbose=>true) |
| 29 | ·--·used·0.2 | 29 | ·--·used·0.231675s·(cpu);·0.168377s·(thread);·0s·(gc) |
| 30 | S:·rational·normal·curve·of·degree·5·in·PP^5 | 30 | S:·rational·normal·curve·of·degree·5·in·PP^5 |
| 31 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3 | 31 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3 |
| 32 | hypersurfaces·of·degree·2 | 32 | hypersurfaces·of·degree·2 |
| 33 | (assumption:·h^1(N_{S,P^5})·=·0) | 33 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 34 | h^0(N_{S,P^5})·=·32 | 34 | h^0(N_{S,P^5})·=·32 |
| 35 | h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2)); | 35 | h^1(O_S(2))·=·0,·and·h^0(I_{S,P^5}(2))·=·10·=·h^0(O_(P^5)(2))·-·\chi(O_S(2)); |
| 36 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal | 36 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal |
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| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·V; | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·V; |
| 90 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> | 90 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) |
| 94 | ·--·used·0.3 | 94 | ·--·used·0.437433s·(cpu);·0.308585s·(thread);·0s·(gc) |
| 95 | S:·Veronese·surface·in·PP^5 | 95 | S:·Veronese·surface·in·PP^5 |
| 96 | X:·smooth·cubic·hypersurface·in·PP^5 | 96 | X:·smooth·cubic·hypersurface·in·PP^5 |
| 97 | (assumption:·h^1(N_{S,P^5})·=·0) | 97 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 98 | h^0(N_{S,P^5})·=·27 | 98 | h^0(N_{S,P^5})·=·27 |
| 99 | h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3)); | 99 | h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3)); |
| 100 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal | 100 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal |
| 101 | h^0(N_{S,P^5})·+·27·=·54 | 101 | h^0(N_{S,P^5})·+·27·=·54 |
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| 34 | o2·:·ProjectiveVariety,·surface·in·PP^5 | 34 | o2·:·ProjectiveVariety,·surface·in·PP^5 |
| 35 | i3·:·X·=·specialCubicFourfold·V; | 35 | i3·:·X·=·specialCubicFourfold·V; |
| 36 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and | 36 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and |
| 37 | sectional·genus·0 | 37 | sectional·genus·0 |
| 38 | i4·:·time·parameterCount(X,Verbose=>true) | 38 | i4·:·time·parameterCount(X,Verbose=>true) |
| 39 | ·--·used·0.3 | 39 | ·--·used·0.437433s·(cpu);·0.308585s·(thread);·0s·(gc) |
| 40 | S:·Veronese·surface·in·PP^5 | 40 | S:·Veronese·surface·in·PP^5 |
| 41 | X:·smooth·cubic·hypersurface·in·PP^5 | 41 | X:·smooth·cubic·hypersurface·in·PP^5 |
| 42 | (assumption:·h^1(N_{S,P^5})·=·0) | 42 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 43 | h^0(N_{S,P^5})·=·27 | 43 | h^0(N_{S,P^5})·=·27 |
| 44 | h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3)); | 44 | h^1(O_S(3))·=·0,·and·h^0(I_{S,P^5}(3))·=·28·=·h^0(O_(P^5)(3))·-·\chi(O_S(3)); |
| 45 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal | 45 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal |
| 46 | h^0(N_{S,P^5})·+·27·=·54 | 46 | h^0(N_{S,P^5})·+·27·=·54 |
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| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialGushelMukaiFourfold·S; | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialGushelMukaiFourfold·S; |
| 97 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0</code></pre> | 97 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) |
| 101 | ·--·used·2. | 101 | ·--·used·2.97136s·(cpu);·2.04224s·(thread);·0s·(gc) |
| 102 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) | 102 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) |
| 103 | X:·GM·fourfold·containing·S | 103 | X:·GM·fourfold·containing·S |
| 104 | Y:·del·Pezzo·fivefold·containing·X | 104 | Y:·del·Pezzo·fivefold·containing·X |
| 105 | h^1(N_{S,Y})·=·0 | 105 | h^1(N_{S,Y})·=·0 |
| 106 | h^0(N_{S,Y})·=·11 | 106 | h^0(N_{S,Y})·=·11 |
| 107 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); | 107 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); |
| 108 | in·particular,·h^0(I_{S,Y}(2))·is·minimal | 108 | in·particular,·h^0(I_{S,Y}(2))·is·minimal |
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| 36 | o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G) | 36 | o2·:·ProjectiveVariety,·surface·in·PP^9·(subvariety·of·codimension·4·in·G) |
| 37 | i3·:·X·=·specialGushelMukaiFourfold·S; | 37 | i3·:·X·=·specialGushelMukaiFourfold·S; |
| 38 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and | 38 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and |
| 39 | sectional·genus·0 | 39 | sectional·genus·0 |
| 40 | i4·:·time·parameterCount(X,Verbose=>true) | 40 | i4·:·time·parameterCount(X,Verbose=>true) |
| 41 | ·--·used·2. | 41 | ·--·used·2.97136s·(cpu);·2.04224s·(thread);·0s·(gc) |
| 42 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) | 42 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) |
| 43 | X:·GM·fourfold·containing·S | 43 | X:·GM·fourfold·containing·S |
| 44 | Y:·del·Pezzo·fivefold·containing·X | 44 | Y:·del·Pezzo·fivefold·containing·X |
| 45 | h^1(N_{S,Y})·=·0 | 45 | h^1(N_{S,Y})·=·0 |
| 46 | h^0(N_{S,Y})·=·11 | 46 | h^0(N_{S,Y})·=·11 |
| 47 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); | 47 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); |
| 48 | in·particular,·h^0(I_{S,Y}(2))·is·minimal | 48 | in·particular,·h^0(I_{S,Y}(2))·is·minimal |
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| 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·?·X | 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·?·X |
| 86 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees | 86 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees |
| 87 | ·····1^2·2^5</code></pre> | 87 | ·····1^2·2^5</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parametrizeFanoFourfold·X | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parametrizeFanoFourfold·X |
| 91 | ·--·used·2. | 91 | ·--·used·2.13666s·(cpu);·0.714743s·(thread);·0s·(gc) |
| 92 | o4·=·multi-rational·map·consisting·of·one·single·rational·map | 92 | o4·=·multi-rational·map·consisting·of·one·single·rational·map |
| 93 | ·····source·variety:·PP^4 | 93 | ·····source·variety:·PP^4 |
| 94 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5· | 94 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5· |
| 95 | ·····dominance:·true | 95 | ·····dominance:·true |
| 96 | ·····degree:·1 | 96 | ·····degree:·1 |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^9 | 30 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^9 |
| 31 | i3·:·?·X | 31 | i3·:·?·X |
| 32 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees | 32 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees |
| 33 | ·····1^2·2^5 | 33 | ·····1^2·2^5 |
| 34 | i4·:·time·parametrizeFanoFourfold·X | 34 | i4·:·time·parametrizeFanoFourfold·X |
| 35 | ·--·used·2. | 35 | ·--·used·2.13666s·(cpu);·0.714743s·(thread);·0s·(gc) |
| 36 | o4·=·multi-rational·map·consisting·of·one·single·rational·map | 36 | o4·=·multi-rational·map·consisting·of·one·single·rational·map |
| 37 | ·····source·variety:·PP^4 | 37 | ·····source·variety:·PP^4 |
| 38 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7 | 38 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7 |
| 39 | hypersurfaces·of·degrees·1^2·2^5 | 39 | hypersurfaces·of·degrees·1^2·2^5 |
| 40 | ·····dominance:·true | 40 | ·····dominance:·true |
| 41 | ·····degree:·1 | 41 | ·····degree:·1 |
| Offset 93, 23 lines modified | Offset 93, 23 lines modified | ||
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·X·=·projectiveVariety·ideal(x_1^2*x_3+x_0*x_2*x_3-6*x_1*x_2*x_3-x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+2*x_0^2*x_4-10*x_0*x_1*x_4+13*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2); | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·X·=·projectiveVariety·ideal(x_1^2*x_3+x_0*x_2*x_3-6*x_1*x_2*x_3-x_0*x_3^2-4*x_1*x_3^2-3*x_2*x_3^2+2*x_0^2*x_4-10*x_0*x_1*x_4+13*x_1^2*x_4-x_0*x_2*x_4-3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2-7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3-x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5-x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2); |
| 95 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5</code></pre> | 95 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); |
| 99 | ·--·used·0.00 | 99 | ·--·used·0.00789046s·(cpu);·0.00717831s·(thread);·0s·(gc) |
| 100 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0</code></pre> | 100 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F | 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F |
| 104 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 104 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 105 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 105 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 106 | ·--·used·0. | 106 | ·--·used·0.623971s·(cpu);·0.199632s·(thread);·0s·(gc) |
| 107 | o6·=·Special·cubic·fourfold·of·discriminant·26 | 107 | o6·=·Special·cubic·fourfold·of·discriminant·26 |
| 108 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 108 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 109 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> | 109 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(F·==·X)</code></pre> | 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(F·==·X)</code></pre> |
| Offset 116, 24 lines modified | Offset 116, 24 lines modified | ||
| 116 | 3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2- | 116 | 3*x_1*x_2*x_4+3*x_2^2*x_4+14*x_0*x_3*x_4-8*x_1*x_3*x_4-4*x_3^2*x_4+x_0*x_4^2- |
| 117 | 7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3- | 117 | 7*x_1*x_4^2+4*x_2*x_4^2-2*x_3*x_4^2-2*x_4^3- |
| 118 | x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5- | 118 | x_0*x_1*x_5+x_1^2*x_5+2*x_1*x_2*x_5+3*x_0*x_3*x_5+3*x_1*x_3*x_5-x_3^2*x_5- |
| 119 | x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2); | 119 | x_0*x_4*x_5-4*x_1*x_4*x_5+3*x_2*x_4*x_5+2*x_3*x_4*x_5-x_1*x_5^2); |
| 120 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5 | 120 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5 |
| 121 | i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); | 121 | i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); |
| 122 | ·--·used·0.00 | 122 | ·--·used·0.00789046s·(cpu);·0.00717831s·(thread);·0s·(gc) |
| 123 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and | 123 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and |
| 124 | sectional·genus·0 | 124 | sectional·genus·0 |
| 125 | i6·:·time·describe·F | 125 | i6·:·time·describe·F |
| 126 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables | 126 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables |
| 127 | based·on·it | 127 | based·on·it |
| 128 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- | 128 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- |
| 129 | debug·9868 | 129 | debug·9868 |
| 130 | ·--·used·0. | 130 | ·--·used·0.623971s·(cpu);·0.199632s·(thread);·0s·(gc) |
| 131 | o6·=·Special·cubic·fourfold·of·discriminant·26 | 131 | o6·=·Special·cubic·fourfold·of·discriminant·26 |
| 132 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 132 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 133 | ·····cut·out·by·13·hypersurfaces·of·degree·3 | 133 | ·····cut·out·by·13·hypersurfaces·of·degree·3 |
| 134 | i7·:·assert(F·==·X) | 134 | i7·:·assert(F·==·X) |
| 135 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 135 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 136 | ····*·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8(_\x8E_\x8m_\x8b_\x8e_\x8d_\x8d_\x8e_\x8d_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·random·special·cubic | 136 | ····*·_\x8s_\x8p_\x8e_\x8c_\x8i_\x8a_\x8l_\x8C_\x8u_\x8b_\x8i_\x8c_\x8F_\x8o_\x8u_\x8r_\x8f_\x8o_\x8l_\x8d_\x8(_\x8E_\x8m_\x8b_\x8e_\x8d_\x8d_\x8e_\x8d_\x8P_\x8r_\x8o_\x8j_\x8e_\x8c_\x8t_\x8i_\x8v_\x8e_\x8V_\x8a_\x8r_\x8i_\x8e_\x8t_\x8y_\x8)·--·random·special·cubic |
| Offset 90, 23 lines modified | Offset 90, 23 lines modified | ||
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); | 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·X·=·projectiveVariety·ideal(x_4*x_6-x_3*x_7+x_1*x_8,·x_4*x_5-x_2*x_7+x_0*x_8,·x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8,·x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7,·x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2-x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4-2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2-3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); |
| 92 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8</code></pre> | 92 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialGushelMukaiFourfold(S,X); | 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialGushelMukaiFourfold(S,X); |
| 96 | ·--·used·1. | 96 | ·--·used·1.59885s·(cpu);·1.31817s·(thread);·0s·(gc) |
| 97 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> | 97 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F | 100 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F |
| 101 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 101 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 102 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 102 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 103 | ·--·used· | 103 | ·--·used·7.68056s·(cpu);·2.91449s·(thread);·0s·(gc) |
| 104 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') | 104 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') |
| 105 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 | 105 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 |
| 106 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 106 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 107 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 107 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 108 | ·····Type:·ordinary | 108 | ·····Type:·ordinary |
| 109 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> | 109 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> |
| Offset 34, 24 lines modified | Offset 34, 24 lines modified | ||
| 34 | x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2- | 34 | x_2*x_7+x_0*x_8,·x_0^2+x_0*x_1+x_1^2+x_0*x_2+2*x_0*x_3+x_1*x_3+x_2*x_3+x_3^2- |
| 35 | x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4- | 35 | x_0*x_4-x_1*x_4-2*x_2*x_4-x_3*x_4- |
| 36 | 2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2- | 36 | 2*x_4^2+x_0*x_5+x_2*x_5+x_5^2+2*x_0*x_6+x_1*x_6+2*x_2*x_6+x_3*x_6+x_5*x_6+x_6^2- |
| 37 | 3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); | 37 | 3*x_4*x_7+2*x_5*x_7-x_7^2+x_1*x_8+x_3*x_8-3*x_4*x_8+2*x_5*x_8+x_6*x_8-x_7*x_8); |
| 38 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8 | 38 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8 |
| 39 | i5·:·time·F·=·specialGushelMukaiFourfold(S,X); | 39 | i5·:·time·F·=·specialGushelMukaiFourfold(S,X); |
| 40 | ·--·used·1. | 40 | ·--·used·1.59885s·(cpu);·1.31817s·(thread);·0s·(gc) |
| 41 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and | 41 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and |
| 42 | sectional·genus·0 | 42 | sectional·genus·0 |
| 43 | i6·:·time·describe·F | 43 | i6·:·time·describe·F |
| 44 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables | 44 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables |
| 45 | based·on·it | 45 | based·on·it |
| 46 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- | 46 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- |
| 47 | debug·9868 | 47 | debug·9868 |
| 48 | ·--·used· | 48 | ·--·used·7.68056s·(cpu);·2.91449s·(thread);·0s·(gc) |
| 49 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') | 49 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') |
| 50 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 | 50 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 |
| 51 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 51 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 52 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 52 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 53 | ·····Type:·ordinary | 53 | ·····Type:·ordinary |
| 54 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) | 54 | ·····(case·1·of·Table·1·in·arXiv:2002.07026) |
| Offset 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> | 76 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X | 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X |
| 80 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 80 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 81 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 81 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 82 | ·--·used· | 82 | ·--·used·6.8058s·(cpu);·2.8028s·(thread);·0s·(gc) |
| 83 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 83 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 84 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2 | 84 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2 |
| 85 | ·····target·variety:·GG(1,4)·⊂·PP^9 | 85 | ·····target·variety:·GG(1,4)·⊂·PP^9 |
| 86 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> | 86 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| Offset 27, 15 lines modified | Offset 27, 15 lines modified | ||
| 27 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and | 27 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and |
| 28 | sectional·genus·0 | 28 | sectional·genus·0 |
| 29 | i3·:·time·toGrass·X | 29 | i3·:·time·toGrass·X |
| 30 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables | 30 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables |
| 31 | based·on·it | 31 | based·on·it |
| 32 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- | 32 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- |
| 33 | debug·9868 | 33 | debug·9868 |
| 34 | ·--·used· | 34 | ·--·used·6.8058s·(cpu);·2.8028s·(thread);·0s·(gc) |
| 35 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 35 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 36 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces | 36 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces |
| 37 | of·degree·2 | 37 | of·degree·2 |
| 38 | ·····target·variety:·GG(1,4)·â·PP^9 | 38 | ·····target·variety:·GG(1,4)·â·PP^9 |
| 39 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) | 39 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8</code></pre> | 78 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X |
| 82 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 82 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 83 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 83 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 84 | ·--·used·6. | 84 | ·--·used·6.96933s·(cpu);·2.84332s·(thread);·0s·(gc) |
| 85 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 85 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 86 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2 | 86 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2 |
| 87 | ·····target·variety:·GG(1,4)·⊂·PP^9 | 87 | ·····target·variety:·GG(1,4)·⊂·PP^9 |
| 88 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> | 88 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| Offset 26, 15 lines modified | Offset 26, 15 lines modified | ||
| 26 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8 | 26 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8 |
| 27 | i3·:·time·toGrass·X | 27 | i3·:·time·toGrass·X |
| 28 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables | 28 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables |
| 29 | based·on·it | 29 | based·on·it |
| 30 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- | 30 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···-- |
| 31 | debug·9868 | 31 | debug·9868 |
| 32 | ·--·used·6. | 32 | ·--·used·6.96933s·(cpu);·2.84332s·(thread);·0s·(gc) |
| 33 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 33 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 34 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5 | 34 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5 |
| 35 | hypersurfaces·of·degree·2 | 35 | hypersurfaces·of·degree·2 |
| 36 | ·····target·variety:·GG(1,4)·â·PP^9 | 36 | ·····target·variety:·GG(1,4)·â·PP^9 |
| 37 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) | 37 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4)) |
| Offset 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·S; | 78 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·S; |
| 79 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> | 79 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·f·=·unirationalParametrization·X; | 82 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·f·=·unirationalParametrization·X; |
| 83 | ·--·used· | 83 | ·--·used·1.03184s·(cpu);·0.425636s·(thread);·0s·(gc) |
| 84 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)</code></pre> | 84 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·degreeSequence·f | 87 | <td>··············<pre><code·class="language-macaulay2">i5·:·degreeSequence·f |
| 88 | o5·=·{[10]} | 88 | o5·=·{[10]} |
| Offset 19, 15 lines modified | Offset 19, 15 lines modified | ||
| 19 | o2·:·ProjectiveVariety,·surface·in·PP^5 | 19 | o2·:·ProjectiveVariety,·surface·in·PP^5 |
| 20 | i3·:·X·=·specialCubicFourfold·S; | 20 | i3·:·X·=·specialCubicFourfold·S; |
| 21 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and | 21 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and |
| 22 | sectional·genus·0 | 22 | sectional·genus·0 |
| 23 | i4·:·time·f·=·unirationalParametrization·X; | 23 | i4·:·time·f·=·unirationalParametrization·X; |
| 24 | ·--·used· | 24 | ·--·used·1.03184s·(cpu);·0.425636s·(thread);·0s·(gc) |
| 25 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X) | 25 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X) |
| 26 | i5·:·degreeSequence·f | 26 | i5·:·degreeSequence·f |
| 27 | o5·=·{[10]} | 27 | o5·=·{[10]} |
| 28 | o5·:·List | 28 | o5·:·List |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=33 | 7 | #:len=33 |
| 8 | U3BlY3RyYWxTZXF1ZW5jZSBeIEluZmluaXRlTnVtYmVy | 8 | U3BlY3RyYWxTZXF1ZW5jZSBeIEluZmluaXRlTnVtYmVy |
| 9 | #:len=967 | 9 | #:len=967 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGluZmluaXR5IHBhZ2Ugb2YgYSBz | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGluZmluaXR5IHBhZ2Ugb2YgYSBz |
| 11 | cGVjdHJhbCBzZXF1ZW5jZSIsICJsaW5lbnVtIiA9PiAzNDk4LCBJbnB1dHMgPT4ge1NQQU57VFR7 | 11 | cGVjdHJhbCBzZXF1ZW5jZSIsICJsaW5lbnVtIiA9PiAzNDk4LCBJbnB1dHMgPT4ge1NQQU57VFR7 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=19 | 7 | #:len=19 |
| 8 | aXNMb29wbGVzcyhEaWdyYXBoKQ== | 8 | aXNMb29wbGVzcyhEaWdyYXBoKQ== |
| 9 | #:len=247 | 9 | #:len=247 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODU0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODU0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpc0xvb3BsZXNzLERpZ3JhcGgpLCJpc0xvb3BsZXNz | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpc0xvb3BsZXNzLERpZ3JhcGgpLCJpc0xvb3BsZXNz |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | ······························b·=>·{a,·c} | 30 | ······························b·=>·{a,·c} |
| 31 | ······························c·=>·{b} | 31 | ······························c·=>·{b} |
| 32 | o2·:·HashTable | 32 | o2·:·HashTable |
| 33 | i3·:·keys·(graph·G) | 33 | i3·:·keys·(graph·G) |
| 34 | o3·=·{ | 34 | o3·=·{Digraph,·Bigraph,·Graph} |
| 35 | o3·:·List | 35 | o3·:·List |
| 36 | i4·:·(graph·G)#Bigraph·===·bigraph·G | 36 | i4·:·(graph·G)#Bigraph·===·bigraph·G |
| 37 | o4·=·true | 37 | o4·=·true |
| Offset 11, 12 lines modified | Offset 11, 12 lines modified | ||
| 11 | ················Graph·=>·Graph{1·=>·{3}} | 11 | ················Graph·=>·Graph{1·=>·{3}} |
| 12 | ·······························3·=>·{1} | 12 | ·······························3·=>·{1} |
| 13 | o1·:·MixedGraph | 13 | o1·:·MixedGraph |
| 14 | i2·:·toString·G | 14 | i2·:·toString·G |
| 15 | o2·=·new·HashTable·from·{ | 15 | o2·=·new·HashTable·from·{Bigraph·=>·bigraph·({3,·4,·2},·{{4,·3},·{4,·2}}), |
| 16 | ····· | 16 | ·····Graph·=>·graph·({3,·1},·{{1,·3}}),·Digraph·=>·digraph·({1,·2,·3},·{{1, |
| 17 | ····· | 17 | ·····2},·{2,·3}})} |
| 18 | i3·:· | 18 | i3·:· |
| Offset 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | ······························c·=>·{b} | 115 | ······························c·=>·{b} |
| 116 | o2·:·HashTable</code></pre> | 116 | o2·:·HashTable</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·(graph·G) | 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·(graph·G) |
| 120 | o3·=·{ | 120 | o3·=·{Digraph,·Bigraph,·Graph} |
| 121 | o3·:·List</code></pre> | 121 | o3·:·List</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i4·:·(graph·G)#Bigraph·===·bigraph·G | 124 | <td>··············<pre><code·class="language-macaulay2">i4·:·(graph·G)#Bigraph·===·bigraph·G |
| 125 | o4·=·true</code></pre> | 125 | o4·=·true</code></pre> |
| Offset 47, 15 lines modified | Offset 47, 15 lines modified | ||
| 47 | ···············Graph·=>·Graph{a·=>·{b}···} | 47 | ···············Graph·=>·Graph{a·=>·{b}···} |
| 48 | ······························b·=>·{a,·c} | 48 | ······························b·=>·{a,·c} |
| 49 | ······························c·=>·{b} | 49 | ······························c·=>·{b} |
| 50 | o2·:·HashTable | 50 | o2·:·HashTable |
| 51 | i3·:·keys·(graph·G) | 51 | i3·:·keys·(graph·G) |
| 52 | o3·=·{ | 52 | o3·=·{Digraph,·Bigraph,·Graph} |
| 53 | o3·:·List | 53 | o3·:·List |
| 54 | i4·:·(graph·G)#Bigraph·===·bigraph·G | 54 | i4·:·(graph·G)#Bigraph·===·bigraph·G |
| 55 | o4·=·true | 55 | o4·=·true |
| 56 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 56 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 57 | ····*·_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h·--·a·graph·that·has·undirected,·directed·and·bidirected·edges | 57 | ····*·_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h·--·a·graph·that·has·undirected,·directed·and·bidirected·edges |
| Offset 86, 17 lines modified | Offset 86, 17 lines modified | ||
| 86 | ·······························3·=>·{1} | 86 | ·······························3·=>·{1} |
| 87 | o1·:·MixedGraph</code></pre> | 87 | o1·:·MixedGraph</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·toString·G | 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·toString·G |
| 91 | o2·=·new·HashTable·from·{ | 91 | o2·=·new·HashTable·from·{Bigraph·=>·bigraph·({3,·4,·2},·{{4,·3},·{4,·2}}), |
| 92 | ····· | 92 | ·····Graph·=>·graph·({3,·1},·{{1,·3}}),·Digraph·=>·digraph·({1,·2,·3},·{{1, |
| 93 | ····· | 93 | ·····2},·{2,·3}})}</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ········</table> | 95 | ········</table> |
| 96 | ······</div> | 96 | ······</div> |
| 97 | ······<div> | 97 | ······<div> |
| 98 | ········<h2>See·also</h2> | 98 | ········<h2>See·also</h2> |
| 99 | ········<ul> | 99 | ········<ul> |
| 100 | ··········<li> | 100 | ··········<li> |
| Offset 24, 16 lines modified | Offset 24, 16 lines modified | ||
| 24 | ···································3·=>·{} | 24 | ···································3·=>·{} |
| 25 | ················Graph·=>·Graph{1·=>·{3}} | 25 | ················Graph·=>·Graph{1·=>·{3}} |
| 26 | ·······························3·=>·{1} | 26 | ·······························3·=>·{1} |
| 27 | o1·:·MixedGraph | 27 | o1·:·MixedGraph |
| 28 | i2·:·toString·G | 28 | i2·:·toString·G |
| 29 | o2·=·new·HashTable·from·{ | 29 | o2·=·new·HashTable·from·{Bigraph·=>·bigraph·({3,·4,·2},·{{4,·3},·{4,·2}}), |
| 30 | ····· | 30 | ·····Graph·=>·graph·({3,·1},·{{1,·3}}),·Digraph·=>·digraph·({1,·2,·3},·{{1, |
| 31 | ····· | 31 | ·····2},·{2,·3}})} |
| 32 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 32 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 33 | ····*·_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h·--·a·graph·that·has·undirected,·directed·and·bidirected·edges | 33 | ····*·_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h·--·a·graph·that·has·undirected,·directed·and·bidirected·edges |
| 34 | ····*·_\x8n_\x8e_\x8t_\x8(_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8)·--·print·a·mixed·graph·as·a·net | 34 | ····*·_\x8n_\x8e_\x8t_\x8(_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8)·--·print·a·mixed·graph·as·a·net |
| 35 | ····*·_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g·--·the·class·of·all·strings | 35 | ····*·_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g·--·the·class·of·all·strings |
| 36 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·_\x8t_\x8o_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8(_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8)·--·print·a·mixed·graph·as·a·string | 37 | ····*·_\x8t_\x8o_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8(_\x8M_\x8i_\x8x_\x8e_\x8d_\x8G_\x8r_\x8a_\x8p_\x8h_\x8)·--·print·a·mixed·graph·as·a·string |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 8 | bWFjYXVsYXlEZWNvbXBvc2l0aW9uKFJpbmdFbGVtZW50KQ== | 8 | bWFjYXVsYXlEZWNvbXBvc2l0aW9uKFJpbmdFbGVtZW50KQ== |
| 9 | #:len=329 | 9 | #:len=329 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzkzLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
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| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=5 | 7 | #:len=5 |
| 8 | U3R5bGU= | 8 | U3R5bGU= |
| 9 | #:len=344 | 9 | #:len=344 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAic3R5bGUgc2hlZXRzIGFuZCBpbWFnZXMg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAic3R5bGUgc2hlZXRzIGFuZCBpbWFnZXMg |
| 11 | Zm9yIHRoZSBkb2N1bWVudGF0aW9uIiwgRGVzY3JpcHRpb24gPT4gMTooIlRoaXMgcGFja2FnZSBp | 11 | Zm9yIHRoZSBkb2N1bWVudGF0aW9uIiwgRGVzY3JpcHRpb24gPT4gMTooIlRoaXMgcGFja2FnZSBp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=24 | 7 | #:len=24 |
| 8 | c2FnYmkoLi4uLFN0cmF0ZWd5PT4uLi4p | 8 | c2FnYmkoLi4uLFN0cmF0ZWd5PT4uLi4p |
| 9 | #:len=300 | 9 | #:len=300 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU3OSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjU3OSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc2FnYmksU3RyYXRlZ3ldLCJzYWdiaSguLi4sU3Ry | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbc2FnYmksU3RyYXRlZ3ldLCJzYWdiaSguLi4sU3Ry |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=30 | 7 | #:len=30 |
| 8 | bG93ZXJCb3VuZCguLi4sVmVyYm9zaXR5PT4uLi4p | 8 | bG93ZXJCb3VuZCguLi4sVmVyYm9zaXR5PT4uLi4p |
| 9 | #:len=302 | 9 | #:len=302 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODg4LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODg4LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tsb3dlckJvdW5kLFZlcmJvc2l0eV0sImxvd2VyQm91 | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tsb3dlckJvdW5kLFZlcmJvc2l0eV0sImxvd2VyQm91 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=6 | 7 | #:len=6 |
| 8 | cGFyaXR5 | 8 | cGFyaXR5 |
| 9 | #:len=1717 | 9 | #:len=1717 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicGFyaXR5IG9mIGFuIGVsZW1lbnQgb2Yg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicGFyaXR5IG9mIGFuIGVsZW1lbnQgb2Yg |
| 11 | YSBzdXBlciByaW5nLiIsICJsaW5lbnVtIiA9PiA2MTAsIElucHV0cyA9PiB7U1BBTntUVHsiZiJ9 | 11 | YSBzdXBlciByaW5nLiIsICJsaW5lbnVtIiA9PiA2MTAsIElucHV0cyA9PiB7U1BBTntUVHsiZiJ9 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=33 | 7 | #:len=33 |
| 8 | ZmllbGRCYXNlQ2hhbmdlKFJpbmcsR2Fsb2lzRmllbGQp | 8 | ZmllbGRCYXNlQ2hhbmdlKFJpbmcsR2Fsb2lzRmllbGQp |
| 9 | #:len=300 | 9 | #:len=300 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk4LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk4LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmaWVsZEJhc2VDaGFuZ2UsUmluZyxHYWxvaXNGaWVs | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhmaWVsZEJhc2VDaGFuZ2UsUmluZyxHYWxvaXNGaWVs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=15 | 7 | #:len=15 |
| 8 | bm9QYWNrZWRBbGxTdWJz | 8 | bm9QYWNrZWRBbGxTdWJz |
| 9 | #:len=1151 | 9 | #:len=1151 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZHMgYWxsIHN1YnN0aXR1dGlvbnMg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZHMgYWxsIHN1YnN0aXR1dGlvbnMg |
| 11 | b2YgdmFyaWFibGVzIGJ5IDEgYW5kL29yIDAgZm9yIHdoaWNoIGlkZWFsIGlzIG5vdCBLb25pZy4i | 11 | b2YgdmFyaWFibGVzIGJ5IDEgYW5kL29yIDAgZm9yIHdoaWNoIGlkZWFsIGlzIG5vdCBLb25pZy4i |
| Offset 31, 15 lines modified | Offset 31, 15 lines modified | ||
| 31 | o5·:·Ideal·of·QQ[x..z] | 31 | o5·:·Ideal·of·QQ[x..z] |
| 32 | i6·:·isHomogeneous·P | 32 | i6·:·isHomogeneous·P |
| 33 | o6·=·false | 33 | o6·=·false |
| 34 | i7·:·time·symbolicPower(P,4); | 34 | i7·:·time·symbolicPower(P,4); |
| 35 | ·--·used·0.1 | 35 | ·--·used·0.171931s·(cpu);·0.1371s·(thread);·0s·(gc) |
| 36 | o7·:·Ideal·of·QQ[x..z] | 36 | o7·:·Ideal·of·QQ[x..z] |
| 37 | i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5}) | 37 | i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5}) |
| 38 | ·············2·········3·········2·····2 | 38 | ·············2·········3·········2·····2 |
| 39 | o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·) | 39 | o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·) |
| Offset 47, 12 lines modified | Offset 47, 12 lines modified | ||
| 47 | o8·:·Ideal·of·QQ[x..z] | 47 | o8·:·Ideal·of·QQ[x..z] |
| 48 | i9·:·isHomogeneous·Q | 48 | i9·:·isHomogeneous·Q |
| 49 | o9·=·true | 49 | o9·=·true |
| 50 | i10·:·time·symbolicPower(Q,4); | 50 | i10·:·time·symbolicPower(Q,4); |
| 51 | ·--·used·0.0 | 51 | ·--·used·0.0813728s·(cpu);·0.0393011s·(thread);·0s·(gc) |
| 52 | o10·:·Ideal·of·QQ[x..z] | 52 | o10·:·Ideal·of·QQ[x..z] |
| 53 | i11·:· | 53 | i11·:· |
| Offset 132, 15 lines modified | Offset 132, 15 lines modified | ||
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i6·:·isHomogeneous·P | 133 | <td>··············<pre><code·class="language-macaulay2">i6·:·isHomogeneous·P |
| 134 | o6·=·false</code></pre> | 134 | o6·=·false</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·symbolicPower(P,4); | 137 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·symbolicPower(P,4); |
| 138 | ·--·used·0.1 | 138 | ·--·used·0.171931s·(cpu);·0.1371s·(thread);·0s·(gc) |
| 139 | o7·:·Ideal·of·QQ[x..z]</code></pre> | 139 | o7·:·Ideal·of·QQ[x..z]</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5}) | 142 | <td>··············<pre><code·class="language-macaulay2">i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5}) |
| 143 | ·············2·········3·········2·····2 | 143 | ·············2·········3·········2·····2 |
| Offset 151, 15 lines modified | Offset 151, 15 lines modified | ||
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i9·:·isHomogeneous·Q | 152 | <td>··············<pre><code·class="language-macaulay2">i9·:·isHomogeneous·Q |
| 153 | o9·=·true</code></pre> | 153 | o9·=·true</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·symbolicPower(Q,4); | 156 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·symbolicPower(Q,4); |
| 157 | ·--·used·0.0 | 157 | ·--·used·0.0813728s·(cpu);·0.0393011s·(thread);·0s·(gc) |
| 158 | o10·:·Ideal·of·QQ[x..z]</code></pre> | 158 | o10·:·Ideal·of·QQ[x..z]</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ········</table> | 160 | ········</table> |
| 161 | ······</div> | 161 | ······</div> |
| 162 | ······<div> | 162 | ······<div> |
| 163 | ········<h2>See·also</h2> | 163 | ········<h2>See·also</h2> |
| Offset 60, 28 lines modified | Offset 60, 28 lines modified | ||
| 60 | o5·=·ideal·(y··-·x*z,·x·y·-·z·,·x··-·y*z) | 60 | o5·=·ideal·(y··-·x*z,·x·y·-·z·,·x··-·y*z) |
| 61 | o5·:·Ideal·of·QQ[x..z] | 61 | o5·:·Ideal·of·QQ[x..z] |
| 62 | i6·:·isHomogeneous·P | 62 | i6·:·isHomogeneous·P |
| 63 | o6·=·false | 63 | o6·=·false |
| 64 | i7·:·time·symbolicPower(P,4); | 64 | i7·:·time·symbolicPower(P,4); |
| 65 | ·--·used·0.1 | 65 | ·--·used·0.171931s·(cpu);·0.1371s·(thread);·0s·(gc) |
| 66 | o7·:·Ideal·of·QQ[x..z] | 66 | o7·:·Ideal·of·QQ[x..z] |
| 67 | i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5}) | 67 | i8·:·Q·=·ker·map(QQ[t],QQ[x,y,z,·Degrees·=>·{3,4,5}],{t^3,t^4,t^5}) |
| 68 | ·············2·········3·········2·····2 | 68 | ·············2·········3·········2·····2 |
| 69 | o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·) | 69 | o8·=·ideal·(y··-·x*z,·x··-·y*z,·x·y·-·z·) |
| 70 | o8·:·Ideal·of·QQ[x..z] | 70 | o8·:·Ideal·of·QQ[x..z] |
| 71 | i9·:·isHomogeneous·Q | 71 | i9·:·isHomogeneous·Q |
| 72 | o9·=·true | 72 | o9·=·true |
| 73 | i10·:·time·symbolicPower(Q,4); | 73 | i10·:·time·symbolicPower(Q,4); |
| 74 | ·--·used·0.0 | 74 | ·--·used·0.0813728s·(cpu);·0.0393011s·(thread);·0s·(gc) |
| 75 | o10·:·Ideal·of·QQ[x..z] | 75 | o10·:·Ideal·of·QQ[x..z] |
| 76 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 76 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 77 | ····*·_\x8s_\x8y_\x8m_\x8b_\x8P_\x8o_\x8w_\x8e_\x8r_\x8P_\x8r_\x8i_\x8m_\x8e_\x8P_\x8o_\x8s_\x8C_\x8h_\x8a_\x8r | 77 | ····*·_\x8s_\x8y_\x8m_\x8b_\x8P_\x8o_\x8w_\x8e_\x8r_\x8P_\x8r_\x8i_\x8m_\x8e_\x8P_\x8o_\x8s_\x8C_\x8h_\x8a_\x8r |
| 78 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8ym\x8mb\x8bo\x8ol\x8li\x8ic\x8cP\x8Po\x8ow\x8we\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 78 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8ym\x8mb\x8bo\x8ol\x8li\x8ic\x8cP\x8Po\x8ow\x8we\x8er\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 79 | ····*·symbolicPower(Ideal,ZZ) | 79 | ····*·symbolicPower(Ideal,ZZ) |
| 80 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* | 80 | *\x8**\x8**\x8**\x8**\x8*·F\x8Fo\x8or\x8r·t\x8th\x8he\x8e·p\x8pr\x8ro\x8og\x8gr\x8ra\x8am\x8mm\x8me\x8er\x8r·*\x8**\x8**\x8**\x8**\x8* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=32 | 7 | #:len=32 |
| 8 | YnVpbGRTeW1tZXRyaWNHQihQb2x5bm9taWFsUmluZyk= | 8 | YnVpbGRTeW1tZXRyaWNHQihQb2x5bm9taWFsUmluZyk= |
| 9 | #:len=936 | 9 | #:len=936 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiR3JvZWJuZXIgYmFzaXMgb2YgZWxlbWVu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiR3JvZWJuZXIgYmFzaXMgb2YgZWxlbWVu |
| 11 | dGFyeSBzeW1tZXRyaWMgcG9seW5vbWlhbHMgYWxnZWJyYSIsICJsaW5lbnVtIiA9PiAxNzAsIElu | 11 | dGFyeSBzeW1tZXRyaWMgcG9seW5vbWlhbHMgYWxnZWJyYSIsICJsaW5lbnVtIiA9PiAxNzAsIElu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | Y291bnRUTGV4TW9uKC4uLixGaXhlZE1heD0+Li4uKQ== | 8 | Y291bnRUTGV4TW9uKC4uLixGaXhlZE1heD0+Li4uKQ== |
| 9 | #:len=268 | 9 | #:len=268 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTM4Miwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTM4Miwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbY291bnRUTGV4TW9uLEZpeGVkTWF4XSwiY291bnRU | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbY291bnRUTGV4TW9uLEZpeGVkTWF4XSwiY291bnRU |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=11 | 7 | #:len=11 |
| 8 | VGFuZ2VudENvbmU= | 8 | VGFuZ2VudENvbmU= |
| 9 | #:len=312 | 9 | #:len=312 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGFuZ2VudCBjb25lcyIsIERlc2NyaXB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGFuZ2VudCBjb25lcyIsIERlc2NyaXB0 |
| 11 | aW9uID0+IDE6KCJUaGlzIHBhY2thZ2UgcHJvdmlkZXMgYSBzaW5nbGUgZnVuY3Rpb24gdGhhdCBj | 11 | aW9uID0+IDE6KCJUaGlzIHBhY2thZ2UgcHJvdmlkZXMgYSBzaW5nbGUgZnVuY3Rpb24gdGhhdCBj |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=39 | 7 | #:len=39 |
| 8 | YWN0aW9uT25EaXJlY3RJbWFnZShJZGVhbCxDaGFpbkNvbXBsZXgp | 8 | YWN0aW9uT25EaXJlY3RJbWFnZShJZGVhbCxDaGFpbkNvbXBsZXgp |
| 9 | #:len=318 | 9 | #:len=318 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjA2Mywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjA2Mywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYWN0aW9uT25EaXJlY3RJbWFnZSxJZGVhbCxDaGFp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoYWN0aW9uT25EaXJlY3RJbWFnZSxJZGVhbCxDaGFp |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | o3·=·0··<--·E··<--·0 | 10 | o3·=·0··<--·E··<--·0 |
| 11 | ···················· | 11 | ···················· |
| 12 | ·····-1·····0······1 | 12 | ·····-1·····0······1 |
| 13 | o3·:·ChainComplex | 13 | o3·:·ChainComplex |
| 14 | i4·:·time·T=tateExtension·W; | 14 | i4·:·time·T=tateExtension·W; |
| 15 | ·--·used·0.3 | 15 | ·--·used·0.364998s·(cpu);·0.168595s·(thread);·0s·(gc) |
| 16 | i5·:·cohomologyMatrix(T,-{3,3},{3,3}) | 16 | i5·:·cohomologyMatrix(T,-{3,3},{3,3}) |
| 17 | o5·=·|·8h··4h··0·4··8··12·16·| | 17 | o5·=·|·8h··4h··0·4··8··12·16·| |
| 18 | ·····|·6h··3h··0·3··6··9··12·| | 18 | ·····|·6h··3h··0·3··6··9··12·| |
| 19 | ·····|·4h··2h··0·2··4··6··8··| | 19 | ·····|·4h··2h··0·2··4··6··8··| |
| 20 | ·····|·2h··h···0·1··2··3··4··| | 20 | ·····|·2h··h···0·1··2··3··4··| |
| Offset 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ···················· | 85 | ···················· |
| 86 | ·····-1·····0······1 | 86 | ·····-1·····0······1 |
| 87 | o3·:·ChainComplex</code></pre> | 87 | o3·:·ChainComplex</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·T=tateExtension·W; | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·T=tateExtension·W; |
| 91 | ·--·used·0.3 | 91 | ·--·used·0.364998s·(cpu);·0.168595s·(thread);·0s·(gc)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·cohomologyMatrix(T,-{3,3},{3,3}) | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·cohomologyMatrix(T,-{3,3},{3,3}) |
| 95 | o5·=·|·8h··4h··0·4··8··12·16·| | 95 | o5·=·|·8h··4h··0·4··8··12·16·| |
| 96 | ·····|·6h··3h··0·3··6··9··12·| | 96 | ·····|·6h··3h··0·3··6··9··12·| |
| 97 | ·····|·4h··2h··0·2··4··6··8··| | 97 | ·····|·4h··2h··0·2··4··6··8··| |
| Offset 24, 15 lines modified | Offset 24, 15 lines modified | ||
| 24 | ·············1 | 24 | ·············1 |
| 25 | o3·=·0··<--·E··<--·0 | 25 | o3·=·0··<--·E··<--·0 |
| 26 | ·····-1·····0······1 | 26 | ·····-1·····0······1 |
| 27 | o3·:·ChainComplex | 27 | o3·:·ChainComplex |
| 28 | i4·:·time·T=tateExtension·W; | 28 | i4·:·time·T=tateExtension·W; |
| 29 | ·--·used·0.3 | 29 | ·--·used·0.364998s·(cpu);·0.168595s·(thread);·0s·(gc) |
| 30 | i5·:·cohomologyMatrix(T,-{3,3},{3,3}) | 30 | i5·:·cohomologyMatrix(T,-{3,3},{3,3}) |
| 31 | o5·=·|·8h··4h··0·4··8··12·16·| | 31 | o5·=·|·8h··4h··0·4··8··12·16·| |
| 32 | ·····|·6h··3h··0·3··6··9··12·| | 32 | ·····|·6h··3h··0·3··6··9··12·| |
| 33 | ·····|·4h··2h··0·2··4··6··8··| | 33 | ·····|·4h··2h··0·2··4··6··8··| |
| 34 | ·····|·2h··h···0·1··2··3··4··| | 34 | ·····|·2h··h···0·1··2··3··4··| |
| 35 | ·····|·0···0···0·0··0··0··0··| | 35 | ·····|·0···0···0·0··0··0··0··| |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=31 | 7 | #:len=31 |
| 8 | bWlub3JzTWFwKE1hdHJpeCxMYWJlbGVkTW9kdWxlKQ== | 8 | bWlub3JzTWFwKE1hdHJpeCxMYWJlbGVkTW9kdWxlKQ== |
| 9 | #:len=285 | 9 | #:len=285 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTkzNywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTkzNywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobWlub3JzTWFwLE1hdHJpeCxMYWJlbGVkTW9kdWxl | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobWlub3JzTWFwLE1hdHJpeCxMYWJlbGVkTW9kdWxl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=26 | 7 | #:len=26 |
| 8 | dGVycmFjaW5pTG9jdXMoWlosUmluZ01hcCk= | 8 | dGVycmFjaW5pTG9jdXMoWlosUmluZ01hcCk= |
| 9 | #:len=278 | 9 | #:len=278 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTkyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTkyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0ZXJyYWNpbmlMb2N1cyxaWixSaW5nTWFwKSwidGVy | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0ZXJyYWNpbmlMb2N1cyxaWixSaW5nTWFwKSwidGVy |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=17 | 7 | #:len=17 |
| 8 | ZnJvYmVuaXVzUHJlaW1hZ2U= | 8 | ZnJvYmVuaXVzUHJlaW1hZ2U= |
| 9 | #:len=934 | 9 | #:len=934 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZHMgdGhlIGlkZWFsIG9mIGVsZW1l | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZHMgdGhlIGlkZWFsIG9mIGVsZW1l |
| 11 | bnRzIG1hcHBlZCBpbnRvIGEgZ2l2ZW4gaWRlYWwsIHVuZGVyIGFsbCAkcF57LWV9JC1saW5lYXIg | 11 | bnRzIG1hcHBlZCBpbnRvIGEgZ2l2ZW4gaWRlYWwsIHVuZGVyIGFsbCAkcF57LWV9JC1saW5lYXIg |
| Offset 63, 20 lines modified | Offset 63, 20 lines modified | ||
| 63 | o15·:·Ideal·of·R | 63 | o15·:·Ideal·of·R |
| 64 | i16·:·I3·=·ideal(x^50*y^50*z^50); | 64 | i16·:·I3·=·ideal(x^50*y^50*z^50); |
| 65 | o16·:·Ideal·of·R | 65 | o16·:·Ideal·of·R |
| 66 | i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); | 66 | i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); |
| 67 | ·--·used·0. | 67 | ·--·used·0.633937s·(cpu);·0.539461s·(thread);·0s·(gc) |
| 68 | o17·:·Ideal·of·R | 68 | o17·:·Ideal·of·R |
| 69 | i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); | 69 | i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); |
| 70 | ·--·used· | 70 | ·--·used·2.00842s·(cpu);·1.78333s·(thread);·0s·(gc) |
| 71 | o18·:·Ideal·of·R | 71 | o18·:·Ideal·of·R |
| 72 | i19·:·J1·==·J2 | 72 | i19·:·J1·==·J2 |
| 73 | o19·=·true | 73 | o19·=·true |
| Offset 7, 20 lines modified | Offset 7, 20 lines modified | ||
| 7 | i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3}); | 7 | i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3}); |
| 8 | o3·:·RingMap·T·<--·S | 8 | o3·:·RingMap·T·<--·S |
| 9 | i4·:·R·=·S/(ker·g); | 9 | i4·:·R·=·S/(ker·g); |
| 10 | i5·:·time·isCohenMacaulay(R) | 10 | i5·:·time·isCohenMacaulay(R) |
| 11 | ·--·used·0.00 | 11 | ·--·used·0.00226418s·(cpu);·0.0015745s·(thread);·0s·(gc) |
| 12 | o5·=·true | 12 | o5·=·true |
| 13 | i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) | 13 | i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) |
| 14 | ·--·used·0.00 | 14 | ·--·used·0.00157514s·(cpu);·0.00389984s·(thread);·0s·(gc) |
| 15 | o6·=·true | 15 | o6·=·true |
| 16 | i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v); | 16 | i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v); |
| 17 | i8·:·isCohenMacaulay(R) | 17 | i8·:·isCohenMacaulay(R) |
| Offset 60, 49 lines modified | Offset 60, 49 lines modified | ||
| 60 | i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3) | 60 | i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3) |
| 61 | o19·=·R | 61 | o19·=·R |
| 62 | o19·:·QuotientRing | 62 | o19·:·QuotientRing |
| 63 | i20·:·time·isFInjective(R) | 63 | i20·:·time·isFInjective(R) |
| 64 | ·--·used·0.0 | 64 | ·--·used·0.0312927s·(cpu);·0.0328877s·(thread);·0s·(gc) |
| 65 | o20·=·true | 65 | o20·=·true |
| 66 | i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) | 66 | i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) |
| 67 | ·--·used·1. | 67 | ·--·used·1.80349s·(cpu);·1.12131s·(thread);·0s·(gc) |
| 68 | o21·=·true | 68 | o21·=·true |
| 69 | i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5); | 69 | i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5); |
| 70 | i23·:·time·isFInjective(R) | 70 | i23·:·time·isFInjective(R) |
| 71 | ·--·used·0.1 | 71 | ·--·used·0.115144s·(cpu);·0.0736929s·(thread);·0s·(gc) |
| 72 | o23·=·false | 72 | o23·=·false |
| 73 | i24·:·time·isFInjective(R,·AtOrigin·=>·true) | 73 | i24·:·time·isFInjective(R,·AtOrigin·=>·true) |
| 74 | ·--·used·0.0 | 74 | ·--·used·0.062424s·(cpu);·0.064012s·(thread);·0s·(gc) |
| 75 | o24·=·true | 75 | o24·=·true |
| 76 | i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt]; | 76 | i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt]; |
| 77 | i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2); | 77 | i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2); |
| 78 | i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t}); | 78 | i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t}); |
| 79 | o27·:·RingMap·EP1·<--·S | 79 | o27·:·RingMap·EP1·<--·S |
| 80 | i28·:·R·=·S/(ker·f); | 80 | i28·:·R·=·S/(ker·f); |
| 81 | i29·:·time·isFInjective(R) | 81 | i29·:·time·isFInjective(R) |
| 82 | ·--·used·0. | 82 | ·--·used·0.742423s·(cpu);·0.618456s·(thread);·0s·(gc) |
| 83 | o29·=·false | 83 | o29·=·false |
| 84 | i30·:·time·isFInjective(R,·AssumeCM·=>·true) | 84 | i30·:·time·isFInjective(R,·AssumeCM·=>·true) |
| 85 | ·--·used·0.2 | 85 | ·--·used·0.272417s·(cpu);·0.196127s·(thread);·0s·(gc) |
| 86 | o30·=·true | 86 | o30·=·true |
| 87 | i31·:· | 87 | i31·:· |
| Offset 79, 20 lines modified | Offset 79, 20 lines modified | ||
| 79 | i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}}); | 79 | i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}}); |
| 80 | o25·:·Ideal·of·S | 80 | o25·:·Ideal·of·S |
| 81 | i26·:·debugLevel·=·1; | 81 | i26·:·debugLevel·=·1; |
| 82 | i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) | 82 | i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) |
| 83 | ·--·used·0.0 | 83 | ·--·used·0.0915203s·(cpu);·0.0530946s·(thread);·0s·(gc) |
| 84 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply. | 84 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply. |
| 85 | o27·=·false | 85 | o27·=·false |
| 86 | i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) | 86 | i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) |
| 87 | ·--·used·0.1 | 87 | ·--·used·0.133497s·(cpu);·0.134546s·(thread);·0s·(gc) |
| 88 | o28·=·true | 88 | o28·=·true |
| 89 | i29·:·debugLevel·=·0; | 89 | i29·:·debugLevel·=·0; |
| 90 | i30·:· | 90 | i30·:· |
| Offset 81, 21 lines modified | Offset 81, 21 lines modified | ||
| 81 | i22·:·testIdeal({3/4,·2/3,·3/5},·L) | 81 | i22·:·testIdeal({3/4,·2/3,·3/5},·L) |
| 82 | o22·=·ideal·(y,·x) | 82 | o22·=·ideal·(y,·x) |
| 83 | o22·:·Ideal·of·R | 83 | o22·:·Ideal·of·R |
| 84 | i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) | 84 | i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) |
| 85 | ·--·used·0. | 85 | ·--·used·0.227326s·(cpu);·0.152245s·(thread);·0s·(gc) |
| 86 | o23·=·ideal·(y,·x) | 86 | o23·=·ideal·(y,·x) |
| 87 | o23·:·Ideal·of·R | 87 | o23·:·Ideal·of·R |
| 88 | i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) | 88 | i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) |
| 89 | ·--·used·0. | 89 | ·--·used·0.36108s·(cpu);·0.248258s·(thread);·0s·(gc) |
| 90 | o24·=·ideal·(y,·x) | 90 | o24·=·ideal·(y,·x) |
| 91 | o24·:·Ideal·of·R | 91 | o24·:·Ideal·of·R |
| 92 | i25·:· | 92 | i25·:· |
| Offset 205, 21 lines modified | Offset 205, 21 lines modified | ||
| 205 | ··········<tr> | 205 | ··········<tr> |
| 206 | <td>··············<pre><code·class="language-macaulay2">i16·:·I3·=·ideal(x^50*y^50*z^50); | 206 | <td>··············<pre><code·class="language-macaulay2">i16·:·I3·=·ideal(x^50*y^50*z^50); |
| 207 | o16·:·Ideal·of·R</code></pre> | 207 | o16·:·Ideal·of·R</code></pre> |
| 208 | </td>··········</tr> | 208 | </td>··········</tr> |
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); | 210 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); |
| 211 | ·--·used·0. | 211 | ·--·used·0.633937s·(cpu);·0.539461s·(thread);·0s·(gc) |
| 212 | o17·:·Ideal·of·R</code></pre> | 212 | o17·:·Ideal·of·R</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ··········<tr> | 214 | ··········<tr> |
| 215 | <td>··············<pre><code·class="language-macaulay2">i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); | 215 | <td>··············<pre><code·class="language-macaulay2">i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); |
| 216 | ·--·used· | 216 | ·--·used·2.00842s·(cpu);·1.78333s·(thread);·0s·(gc) |
| 217 | o18·:·Ideal·of·R</code></pre> | 217 | o18·:·Ideal·of·R</code></pre> |
| 218 | </td>··········</tr> | 218 | </td>··········</tr> |
| 219 | ··········<tr> | 219 | ··········<tr> |
| 220 | <td>··············<pre><code·class="language-macaulay2">i19·:·J1·==·J2 | 220 | <td>··············<pre><code·class="language-macaulay2">i19·:·J1·==·J2 |
| 221 | o19·=·true</code></pre> | 221 | o19·=·true</code></pre> |
| Offset 107, 19 lines modified | Offset 107, 19 lines modified | ||
| 107 | i15·:·I2·=·ideal(x^20*y^100,·x·+·z^100); | 107 | i15·:·I2·=·ideal(x^20*y^100,·x·+·z^100); |
| 108 | o15·:·Ideal·of·R | 108 | o15·:·Ideal·of·R |
| 109 | i16·:·I3·=·ideal(x^50*y^50*z^50); | 109 | i16·:·I3·=·ideal(x^50*y^50*z^50); |
| 110 | o16·:·Ideal·of·R | 110 | o16·:·Ideal·of·R |
| 111 | i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); | 111 | i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); |
| 112 | ·--·used·0. | 112 | ·--·used·0.633937s·(cpu);·0.539461s·(thread);·0s·(gc) |
| 113 | o17·:·Ideal·of·R | 113 | o17·:·Ideal·of·R |
| 114 | i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); | 114 | i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); |
| 115 | ·--·used· | 115 | ·--·used·2.00842s·(cpu);·1.78333s·(thread);·0s·(gc) |
| 116 | o18·:·Ideal·of·R | 116 | o18·:·Ideal·of·R |
| 117 | i19·:·J1·==·J2 | 117 | i19·:·J1·==·J2 |
| 118 | o19·=·true | 118 | o19·=·true |
| 119 | For·legacy·reasons,·the·last·ideal·in·the·list·can·be·specified·separately, | 119 | For·legacy·reasons,·the·last·ideal·in·the·list·can·be·specified·separately, |
| 120 | using·frobeniusRoot(e,·\{a_1,\ldots,a_n\},·\{I_1,\ldots,I_n\},·I).·The·last | 120 | using·frobeniusRoot(e,·\{a_1,\ldots,a_n\},·\{I_1,\ldots,I_n\},·I).·The·last |
| Offset 89, 21 lines modified | Offset 89, 21 lines modified | ||
| 89 | o3·:·RingMap·T·<--·S</code></pre> | 89 | o3·:·RingMap·T·<--·S</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·R·=·S/(ker·g);</code></pre> | 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·R·=·S/(ker·g);</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isCohenMacaulay(R) | 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isCohenMacaulay(R) |
| 96 | ·--·used·0.00 | 96 | ·--·used·0.00226418s·(cpu);·0.0015745s·(thread);·0s·(gc) |
| 97 | o5·=·true</code></pre> | 97 | o5·=·true</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) | 100 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) |
| 101 | ·--·used·0.00 | 101 | ·--·used·0.00157514s·(cpu);·0.00389984s·(thread);·0s·(gc) |
| 102 | o6·=·true</code></pre> | 102 | o6·=·true</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ········</table> | 104 | ········</table> |
| 105 | ········<table·class="examples"> | 105 | ········<table·class="examples"> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);</code></pre> |
| Offset 24, 19 lines modified | Offset 24, 19 lines modified | ||
| 24 | i1·:·T·=·ZZ/5[x,y]; | 24 | i1·:·T·=·ZZ/5[x,y]; |
| 25 | i2·:·S·=·ZZ/5[a,b,c,d]; | 25 | i2·:·S·=·ZZ/5[a,b,c,d]; |
| 26 | i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3}); | 26 | i3·:·g·=·map(T,·S,·{x^3,·x^2*y,·x*y^2,·y^3}); |
| 27 | o3·:·RingMap·T·<--·S | 27 | o3·:·RingMap·T·<--·S |
| 28 | i4·:·R·=·S/(ker·g); | 28 | i4·:·R·=·S/(ker·g); |
| 29 | i5·:·time·isCohenMacaulay(R) | 29 | i5·:·time·isCohenMacaulay(R) |
| 30 | ·--·used·0.00 | 30 | ·--·used·0.00226418s·(cpu);·0.0015745s·(thread);·0s·(gc) |
| 31 | o5·=·true | 31 | o5·=·true |
| 32 | i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) | 32 | i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) |
| 33 | ·--·used·0.00 | 33 | ·--·used·0.00157514s·(cpu);·0.00389984s·(thread);·0s·(gc) |
| 34 | o6·=·true | 34 | o6·=·true |
| 35 | i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v); | 35 | i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v); |
| 36 | i8·:·isCohenMacaulay(R) | 36 | i8·:·isCohenMacaulay(R) |
| 37 | o8·=·false | 37 | o8·=·false |
| 38 | The·function·isCohenMacaulay·considers·$R$·as·a·quotient·of·a·polynomial·ring, | 38 | The·function·isCohenMacaulay·considers·$R$·as·a·quotient·of·a·polynomial·ring, |
| Offset 182, 41 lines modified | Offset 182, 41 lines modified | ||
| 182 | o19·=·R | 182 | o19·=·R |
| 183 | o19·:·QuotientRing</code></pre> | 183 | o19·:·QuotientRing</code></pre> |
| 184 | </td>··········</tr> | 184 | </td>··········</tr> |
| 185 | ··········<tr> | 185 | ··········<tr> |
| 186 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·isFInjective(R) | 186 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·isFInjective(R) |
| 187 | ·--·used·0.0 | 187 | ·--·used·0.0312927s·(cpu);·0.0328877s·(thread);·0s·(gc) |
| 188 | o20·=·true</code></pre> | 188 | o20·=·true</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) | 191 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) |
| 192 | ·--·used·1. | 192 | ·--·used·1.80349s·(cpu);·1.12131s·(thread);·0s·(gc) |
| 193 | o21·=·true</code></pre> | 193 | o21·=·true</code></pre> |
| 194 | </td>··········</tr> | 194 | </td>··········</tr> |
| 195 | ········</table> | 195 | ········</table> |
| 196 | ········<div> | 196 | ········<div> |
| 197 | ··········<p>If·the·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·<span·class="tt">isFInjective</span>·will·only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$-injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be·slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$-injective·ring.</p> | 197 | ··········<p>If·the·option·<span·class="tt">AtOrigin</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·<span·class="tt">isFInjective</span>·will·only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$-injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be·slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$-injective·ring.</p> |
| 198 | ········</div> | 198 | ········</div> |
| 199 | ········<table·class="examples"> | 199 | ········<table·class="examples"> |
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);</code></pre> | 201 | <td>··············<pre><code·class="language-macaulay2">i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·isFInjective(R) | 204 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·isFInjective(R) |
| 205 | ·--·used·0.1 | 205 | ·--·used·0.115144s·(cpu);·0.0736929s·(thread);·0s·(gc) |
| 206 | o23·=·false</code></pre> | 206 | o23·=·false</code></pre> |
| 207 | </td>··········</tr> | 207 | </td>··········</tr> |
| 208 | ··········<tr> | 208 | ··········<tr> |
| 209 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·isFInjective(R,·AtOrigin·=>·true) | 209 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·isFInjective(R,·AtOrigin·=>·true) |
| 210 | ·--·used·0.0 | 210 | ·--·used·0.062424s·(cpu);·0.064012s·(thread);·0s·(gc) |
| 211 | o24·=·true</code></pre> | 211 | o24·=·true</code></pre> |
| 212 | </td>··········</tr> | 212 | </td>··········</tr> |
| 213 | ········</table> | 213 | ········</table> |
| 214 | ········<div> | 214 | ········<div> |
| 215 | ··········<p>If·the·option·<span·class="tt">AssumeCM</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·then·<span·class="tt">isFInjective</span>·only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much·faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective·Frobenius·occurs·in·a·lower·degree.··Consider·the·example·of·the·cone·over·a·supersingular·elliptic·curve·times·$\mathbb{P}^1$.</p> | 215 | ··········<p>If·the·option·<span·class="tt">AssumeCM</span>·(default·value·<span·class="tt">false</span>)·is·set·to·<span·class="tt">true</span>,·then·<span·class="tt">isFInjective</span>·only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much·faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective·Frobenius·occurs·in·a·lower·degree.··Consider·the·example·of·the·cone·over·a·supersingular·elliptic·curve·times·$\mathbb{P}^1$.</p> |
| 216 | ········</div> | 216 | ········</div> |
| Offset 233, 21 lines modified | Offset 233, 21 lines modified | ||
| 233 | o27·:·RingMap·EP1·<--·S</code></pre> | 233 | o27·:·RingMap·EP1·<--·S</code></pre> |
| 234 | </td>··········</tr> | 234 | </td>··········</tr> |
| 235 | ··········<tr> | 235 | ··········<tr> |
| 236 | <td>··············<pre><code·class="language-macaulay2">i28·:·R·=·S/(ker·f);</code></pre> | 236 | <td>··············<pre><code·class="language-macaulay2">i28·:·R·=·S/(ker·f);</code></pre> |
| 237 | </td>··········</tr> | 237 | </td>··········</tr> |
| 238 | ··········<tr> | 238 | ··········<tr> |
| 239 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·isFInjective(R) | 239 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·isFInjective(R) |
| 240 | ·--·used·0. | 240 | ·--·used·0.742423s·(cpu);·0.618456s·(thread);·0s·(gc) |
| 241 | o29·=·false</code></pre> | 241 | o29·=·false</code></pre> |
| 242 | </td>··········</tr> | 242 | </td>··········</tr> |
| 243 | ··········<tr> | 243 | ··········<tr> |
| 244 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·isFInjective(R,·AssumeCM·=>·true) | 244 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·isFInjective(R,·AssumeCM·=>·true) |
| 245 | ·--·used·0.2 | 245 | ·--·used·0.272417s·(cpu);·0.196127s·(thread);·0s·(gc) |
| 246 | o30·=·true</code></pre> | 246 | o30·=·true</code></pre> |
| 247 | </td>··········</tr> | 247 | </td>··········</tr> |
| 248 | ········</table> | 248 | ········</table> |
| 249 | ········<div> | 249 | ········<div> |
| 250 | ··········<p>If·the·option·<span·class="tt">AssumedReduced</span>·is·set·to·<span·class="tt">true</span>·(its·default·behavior),·then·the·bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top·potentially·nonzero·Ext·is·not·computed).</p> | 250 | ··········<p>If·the·option·<span·class="tt">AssumedReduced</span>·is·set·to·<span·class="tt">true</span>·(its·default·behavior),·then·the·bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top·potentially·nonzero·Ext·is·not·computed).</p> |
| 251 | ········</div> | 251 | ········</div> |
| Offset 82, 52 lines modified | Offset 82, 52 lines modified | ||
| 82 | much·faster. | 82 | much·faster. |
| 83 | i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3) | 83 | i19·:·R·=·ZZ/5[x,y,z]/(y^2*z·+·x*y*z-x^3) |
| 84 | o19·=·R | 84 | o19·=·R |
| 85 | o19·:·QuotientRing | 85 | o19·:·QuotientRing |
| 86 | i20·:·time·isFInjective(R) | 86 | i20·:·time·isFInjective(R) |
| 87 | ·--·used·0.0 | 87 | ·--·used·0.0312927s·(cpu);·0.0328877s·(thread);·0s·(gc) |
| 88 | o20·=·true | 88 | o20·=·true |
| 89 | i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) | 89 | i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) |
| 90 | ·--·used·1. | 90 | ·--·used·1.80349s·(cpu);·1.12131s·(thread);·0s·(gc) |
| 91 | o21·=·true | 91 | o21·=·true |
| 92 | If·the·option·AtOrigin·(default·value·false)·is·set·to·true,·isFInjective·will | 92 | If·the·option·AtOrigin·(default·value·false)·is·set·to·true,·isFInjective·will |
| 93 | only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$- | 93 | only·check·$F$-injectivity·at·the·origin.·Otherwise,·it·will·check·$F$- |
| 94 | injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be | 94 | injectivity·globally.·Note·that·checking·$F$-injectivity·at·the·origin·can·be |
| 95 | slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$- | 95 | slower·than·checking·it·globally.·Consider·the·following·example·of·a·non-$F$- |
| 96 | injective·ring. | 96 | injective·ring. |
| 97 | i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5); | 97 | i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5); |
| 98 | i23·:·time·isFInjective(R) | 98 | i23·:·time·isFInjective(R) |
| 99 | ·--·used·0.1 | 99 | ·--·used·0.115144s·(cpu);·0.0736929s·(thread);·0s·(gc) |
| 100 | o23·=·false | 100 | o23·=·false |
| 101 | i24·:·time·isFInjective(R,·AtOrigin·=>·true) | 101 | i24·:·time·isFInjective(R,·AtOrigin·=>·true) |
| 102 | ·--·used·0.0 | 102 | ·--·used·0.062424s·(cpu);·0.064012s·(thread);·0s·(gc) |
| 103 | o24·=·true | 103 | o24·=·true |
| 104 | If·the·option·AssumeCM·(default·value·false)·is·set·to·true,·then·isFInjective | 104 | If·the·option·AssumeCM·(default·value·false)·is·set·to·true,·then·isFInjective |
| 105 | only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much | 105 | only·checks·the·Frobenius·action·on·top·cohomology·(which·is·typically·much |
| 106 | faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective | 106 | faster).·Note·that·it·can·give·an·incorrect·answer·if·the·non-injective |
| 107 | Frobenius·occurs·in·a·lower·degree.·Consider·the·example·of·the·cone·over·a | 107 | Frobenius·occurs·in·a·lower·degree.·Consider·the·example·of·the·cone·over·a |
| 108 | supersingular·elliptic·curve·times·$\mathbb{P}^1$. | 108 | supersingular·elliptic·curve·times·$\mathbb{P}^1$. |
| 109 | i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt]; | 109 | i25·:·S·=·ZZ/3[xs,·ys,·zs,·xt,·yt,·zt]; |
| 110 | i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2); | 110 | i26·:·EP1·=·ZZ/3[x,y,z,s,t]/(x^3·+·y^2*z·-·x*z^2); |
| 111 | i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t}); | 111 | i27·:·f·=·map(EP1,·S,·{x*s,·y*s,·z*s,·x*t,·y*t,·z*t}); |
| 112 | o27·:·RingMap·EP1·<--·S | 112 | o27·:·RingMap·EP1·<--·S |
| 113 | i28·:·R·=·S/(ker·f); | 113 | i28·:·R·=·S/(ker·f); |
| 114 | i29·:·time·isFInjective(R) | 114 | i29·:·time·isFInjective(R) |
| 115 | ·--·used·0. | 115 | ·--·used·0.742423s·(cpu);·0.618456s·(thread);·0s·(gc) |
| 116 | o29·=·false | 116 | o29·=·false |
| 117 | i30·:·time·isFInjective(R,·AssumeCM·=>·true) | 117 | i30·:·time·isFInjective(R,·AssumeCM·=>·true) |
| 118 | ·--·used·0.2 | 118 | ·--·used·0.272417s·(cpu);·0.196127s·(thread);·0s·(gc) |
| 119 | o30·=·true | 119 | o30·=·true |
| 120 | If·the·option·AssumedReduced·is·set·to·true·(its·default·behavior),·then·the | 120 | If·the·option·AssumedReduced·is·set·to·true·(its·default·behavior),·then·the |
| 121 | bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top | 121 | bottom·local·cohomology·is·avoided·(this·means·the·Frobenius·action·on·the·top |
| 122 | potentially·nonzero·Ext·is·not·computed). | 122 | potentially·nonzero·Ext·is·not·computed). |
| 123 | If·the·option·AssumeNormal·(default·value·false)·is·set·to·true,·then·the | 123 | If·the·option·AssumeNormal·(default·value·false)·is·set·to·true,·then·the |
| 124 | bottom·two·local·cohomology·modules·(or,·rather,·their·duals)·need·not·be | 124 | bottom·two·local·cohomology·modules·(or,·rather,·their·duals)·need·not·be |
| Offset 230, 22 lines modified | Offset 230, 22 lines modified | ||
| 230 | o25·:·Ideal·of·S</code></pre> | 230 | o25·:·Ideal·of·S</code></pre> |
| 231 | </td>··········</tr> | 231 | </td>··········</tr> |
| 232 | ··········<tr> | 232 | ··········<tr> |
| 233 | <td>··············<pre><code·class="language-macaulay2">i26·:·debugLevel·=·1;</code></pre> | 233 | <td>··············<pre><code·class="language-macaulay2">i26·:·debugLevel·=·1;</code></pre> |
| 234 | </td>··········</tr> | 234 | </td>··········</tr> |
| 235 | ··········<tr> | 235 | ··········<tr> |
| 236 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) | 236 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) |
| 237 | ·--·used·0.0 | 237 | ·--·used·0.0915203s·(cpu);·0.0530946s·(thread);·0s·(gc) |
| 238 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply. | 238 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply. |
| 239 | o27·=·false</code></pre> | 239 | o27·=·false</code></pre> |
| 240 | </td>··········</tr> | 240 | </td>··········</tr> |
| 241 | ··········<tr> | 241 | ··········<tr> |
| 242 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) | 242 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) |
| 243 | ·--·used·0.1 | 243 | ·--·used·0.133497s·(cpu);·0.134546s·(thread);·0s·(gc) |
| 244 | o28·=·true</code></pre> | 244 | o28·=·true</code></pre> |
| 245 | </td>··········</tr> | 245 | </td>··········</tr> |
| 246 | ··········<tr> | 246 | ··········<tr> |
| 247 | <td>··············<pre><code·class="language-macaulay2">i29·:·debugLevel·=·0;</code></pre> | 247 | <td>··············<pre><code·class="language-macaulay2">i29·:·debugLevel·=·0;</code></pre> |
| 248 | </td>··········</tr> | 248 | </td>··········</tr> |
| 249 | ········</table> | 249 | ········</table> |
| Offset 113, 21 lines modified | Offset 113, 21 lines modified | ||
| 113 | also·use·the·option·DepthOfSearch·to·increase·the·depth·of·search. | 113 | also·use·the·option·DepthOfSearch·to·increase·the·depth·of·search. |
| 114 | i24·:·S·=·ZZ/7[x,y,z,u,v,w]; | 114 | i24·:·S·=·ZZ/7[x,y,z,u,v,w]; |
| 115 | i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}}); | 115 | i25·:·I·=·minors(2,·matrix·{{x,·y,·z},·{u,·v,·w}}); |
| 116 | o25·:·Ideal·of·S | 116 | o25·:·Ideal·of·S |
| 117 | i26·:·debugLevel·=·1; | 117 | i26·:·debugLevel·=·1; |
| 118 | i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) | 118 | i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) |
| 119 | ·--·used·0.0 | 119 | ·--·used·0.0915203s·(cpu);·0.0530946s·(thread);·0s·(gc) |
| 120 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing | 120 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing |
| 121 | DepthOfSearch·will·let·the·function·search·more·deeply. | 121 | DepthOfSearch·will·let·the·function·search·more·deeply. |
| 122 | o27·=·false | 122 | o27·=·false |
| 123 | i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) | 123 | i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) |
| 124 | ·--·used·0.1 | 124 | ·--·used·0.133497s·(cpu);·0.134546s·(thread);·0s·(gc) |
| 125 | o28·=·true | 125 | o28·=·true |
| 126 | i29·:·debugLevel·=·0; | 126 | i29·:·debugLevel·=·0; |
| 127 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 127 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 128 | ····*·_\x8t_\x8e_\x8s_\x8t_\x8I_\x8d_\x8e_\x8a_\x8l·--·compute·a·test·ideal·in·a·Q-Gorenstein·ring | 128 | ····*·_\x8t_\x8e_\x8s_\x8t_\x8I_\x8d_\x8e_\x8a_\x8l·--·compute·a·test·ideal·in·a·Q-Gorenstein·ring |
| 129 | ····*·_\x8i_\x8s_\x8F_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·ring·is·F-rational | 129 | ····*·_\x8i_\x8s_\x8F_\x8R_\x8a_\x8t_\x8i_\x8o_\x8n_\x8a_\x8l·--·whether·a·ring·is·F-rational |
| 130 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sF\x8FR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* | 130 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·i\x8is\x8sF\x8FR\x8Re\x8eg\x8gu\x8ul\x8la\x8ar\x8r:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| Offset 219, 23 lines modified | Offset 219, 23 lines modified | ||
| 219 | ········</table> | 219 | ········</table> |
| 220 | ········<div> | 220 | ········<div> |
| 221 | ··········<p>It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common·denominator·and·passing·a·single·element,·since·<span·class="tt">testIdeal</span>·can·do·things·in·a·more·intelligent·way·for·such·a·list.</p> | 221 | ··········<p>It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common·denominator·and·passing·a·single·element,·since·<span·class="tt">testIdeal</span>·can·do·things·in·a·more·intelligent·way·for·such·a·list.</p> |
| 222 | ········</div> | 222 | ········</div> |
| 223 | ········<table·class="examples"> | 223 | ········<table·class="examples"> |
| 224 | ··········<tr> | 224 | ··········<tr> |
| 225 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) | 225 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) |
| 226 | ·--·used·0. | 226 | ·--·used·0.227326s·(cpu);·0.152245s·(thread);·0s·(gc) |
| 227 | o23·=·ideal·(y,·x) | 227 | o23·=·ideal·(y,·x) |
| 228 | o23·:·Ideal·of·R</code></pre> | 228 | o23·:·Ideal·of·R</code></pre> |
| 229 | </td>··········</tr> | 229 | </td>··········</tr> |
| 230 | ··········<tr> | 230 | ··········<tr> |
| 231 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) | 231 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) |
| 232 | ·--·used·0. | 232 | ·--·used·0.36108s·(cpu);·0.248258s·(thread);·0s·(gc) |
| 233 | o24·=·ideal·(y,·x) | 233 | o24·=·ideal·(y,·x) |
| 234 | o24·:·Ideal·of·R</code></pre> | 234 | o24·:·Ideal·of·R</code></pre> |
| 235 | </td>··········</tr> | 235 | </td>··········</tr> |
| 236 | ········</table> | 236 | ········</table> |
| 237 | ········<div> | 237 | ········<div> |
| Offset 101, 21 lines modified | Offset 101, 21 lines modified | ||
| 101 | o22·=·ideal·(y,·x) | 101 | o22·=·ideal·(y,·x) |
| 102 | o22·:·Ideal·of·R | 102 | o22·:·Ideal·of·R |
| 103 | It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common | 103 | It·is·often·more·efficient·to·pass·a·list,·as·opposed·to·finding·a·common |
| 104 | denominator·and·passing·a·single·element,·since·testIdeal·can·do·things·in·a | 104 | denominator·and·passing·a·single·element,·since·testIdeal·can·do·things·in·a |
| 105 | more·intelligent·way·for·such·a·list. | 105 | more·intelligent·way·for·such·a·list. |
| 106 | i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) | 106 | i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) |
| 107 | ·--·used·0. | 107 | ·--·used·0.227326s·(cpu);·0.152245s·(thread);·0s·(gc) |
| 108 | o23·=·ideal·(y,·x) | 108 | o23·=·ideal·(y,·x) |
| 109 | o23·:·Ideal·of·R | 109 | o23·:·Ideal·of·R |
| 110 | i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) | 110 | i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) |
| 111 | ·--·used·0. | 111 | ·--·used·0.36108s·(cpu);·0.248258s·(thread);·0s·(gc) |
| 112 | o24·=·ideal·(y,·x) | 112 | o24·=·ideal·(y,·x) |
| 113 | o24·:·Ideal·of·R | 113 | o24·:·Ideal·of·R |
| 114 | The·option·AssumeDomain·(default·value·false)·is·used·when·finding·a·test | 114 | The·option·AssumeDomain·(default·value·false)·is·used·when·finding·a·test |
| 115 | element.·The·option·FrobeniusRootStrategy·(default·value·Substitution)·is | 115 | element.·The·option·FrobeniusRootStrategy·(default·value·Substitution)·is |
| 116 | passed·to·internal·_\x8f_\x8r_\x8o_\x8b_\x8e_\x8n_\x8i_\x8u_\x8s_\x8R_\x8o_\x8o_\x8t·calls. | 116 | passed·to·internal·_\x8f_\x8r_\x8o_\x8b_\x8e_\x8n_\x8i_\x8u_\x8s_\x8R_\x8o_\x8o_\x8t·calls. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | bmV3IFRPSCBmcm9tIFRoaW5n | 8 | bmV3IFRPSCBmcm9tIFRoaW5n |
| 9 | #:len=219 | 9 | #:len=219 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODQxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gODQxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhOZXdGcm9tTWV0aG9kLFRPSCxUaGluZyksIm5ldyBU | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhOZXdGcm9tTWV0aG9kLFRPSCxUaGluZyksIm5ldyBU |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=20 | 7 | #:len=20 |
| 8 | aXNUaWdodChUb3JpY1F1aXZlcik= | 8 | aXNUaWdodChUb3JpY1F1aXZlcik= |
| 9 | #:len=268 | 9 | #:len=268 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzA1OSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzA1OSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNUaWdodCxUb3JpY1F1aXZlciksImlzVGlnaHQo | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoaXNUaWdodCxUb3JpY1F1aXZlciksImlzVGlnaHQo |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=9 | 7 | #:len=9 |
| 8 | dGdiKExpc3Qp | 8 | dGdiKExpc3Qp |
| 9 | #:len=213 | 9 | #:len=213 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY4LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY4LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0Z2IsTGlzdCksInRnYihMaXN0KSIsIlRocmVhZGVk | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0Z2IsTGlzdCksInRnYihMaXN0KSIsIlRocmVhZGVk |
| Offset 17, 18 lines modified | Offset 17, 16 lines modified | ||
| 17 | ························2 | 17 | ························2 |
| 18 | ··················2·=>·b | 18 | ··················2·=>·b |
| 19 | o3·:·LineageTable | 19 | o3·:·LineageTable |
| 20 | i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 20 | i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 21 | ········································3 | ||
| 22 | o4·=·LineageTable{(((0,·1),·0),·0)·=>·-c·} | ||
| 23 | ··································· | 21 | ···································3 |
| 24 | 22 | o4·=·LineageTable{((0,·2),·0)·=>·-c······} | |
| 25 | ···································2 | 23 | ···································2 |
| 26 | ··················((1,·2),·0)·=>·-c | 24 | ··················((1,·2),·0)·=>·-c |
| 27 | ·····························2 | 25 | ·····························2 |
| 28 | ··················(0,·1)·=>·a·c | 26 | ··················(0,·1)·=>·a·c |
| 29 | ·······························2 | 27 | ·······························2 |
| 30 | ··················(0,·2)·=>·b*c | 28 | ··················(0,·2)·=>·b*c |
| 31 | ··················(1,·2)·=>·-a*c | 29 | ··················(1,·2)·=>·-a*c |
| Offset 39, 16 lines modified | Offset 37, 15 lines modified | ||
| 39 | ························2 | 37 | ························2 |
| 40 | ··················2·=>·b | 38 | ··················2·=>·b |
| 41 | o4·:·LineageTable | 39 | o4·:·LineageTable |
| 42 | i5·:·minimize·T | 40 | i5·:·minimize·T |
| 43 | o5·=·LineageTable{(( | 41 | o5·=·LineageTable{((0,·2),·0)·=>·null} |
| 44 | ··················((0,·1),·0)·=>·null | ||
| 45 | ··································2 | 42 | ··································2 |
| 46 | ··················((1,·2),·0)·=>·c | 43 | ··················((1,·2),·0)·=>·c |
| 47 | ··················(0,·1)·=>·null | 44 | ··················(0,·1)·=>·null |
| 48 | ··················(0,·2)·=>·null | 45 | ··················(0,·2)·=>·null |
| 49 | ··················(1,·2)·=>·a*c | 46 | ··················(1,·2)·=>·a*c |
| 50 | ··················0·=>·null | 47 | ··················0·=>·null |
| 51 | ··················1·=>·null | 48 | ··················1·=>·null |
| Offset 22, 32 lines modified | Offset 22, 38 lines modified | ||
| 22 | i3·:·allowableThreads··=··4 | 22 | i3·:·allowableThreads··=··4 |
| 23 | o3·=·4 | 23 | o3·=·4 |
| 24 | i4·:·g·=·tgb(rnc) | 24 | i4·:·g·=·tgb(rnc) |
| 25 | ··································2 | 25 | ············································4········2···3 |
| 26 | o4·=·LineageTable{((2,· | 26 | o4·=·LineageTable{((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x·} |
| 27 | ············································0·5·4····0·3·2 | ||
| 28 | ·······································3·2······4 | ||
| 29 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x | ||
| 30 | ·······································0·4····0·2 | ||
| 31 | ··································2············2 | ||
| 32 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x | ||
| 27 | ··································0·5····0·3·2 | 33 | ··································0·5·2····0·3·2 |
| 34 | ······································2······3 | ||
| 35 | ··················((1,·2),·8)·=>·x·x·x··-·x·x | ||
| 36 | ··································0·5·2····3·2 | ||
| 28 | ········································3 | 37 | ········································3 |
| 29 | ··················(1,·2)·=>·-·x·x·x··+·x | 38 | ··················(1,·2)·=>·-·x·x·x··+·x |
| 30 | ·······························0·4·2····2 | 39 | ·······························0·4·2····2 |
| 31 | ··········································2 | 40 | ··········································2 |
| 32 | ··················(1,·4)·=>·-·x·x·x··+·x·x | 41 | ··················(1,·4)·=>·-·x·x·x··+·x·x |
| 33 | ·······························0·5·2····3·2 | 42 | ·······························0·5·2····3·2 |
| 34 | ·································2······2 | 43 | ·································2······2 |
| 35 | ··················(1,·7)·=>·-·x·x··+·x·x | 44 | ··················(1,·7)·=>·-·x·x··+·x·x |
| 36 | ·······························0·4····4·2 | 45 | ·······························0·4····4·2 |
| 37 | ····································2 | 46 | ····································2 |
| 38 | ··················(2,·3)·=>·x·x··-·x | 47 | ··················(2,·3)·=>·x·x··-·x |
| 39 | ·····························0·4····2 | 48 | ·····························0·4····2 |
| 40 | ··········································2 | ||
| 41 | ··················(3,·7)·=>·-·x·x·x··+·x·x | ||
| 42 | ·······························0·5·4····5·2 | ||
| 43 | ··················(4,·6)·=>·x·x··-·x·x | 49 | ··················(4,·6)·=>·x·x··-·x·x |
| 44 | ·····························0·5····3·2 | 50 | ·····························0·5····3·2 |
| 45 | ·································2····2 | 51 | ·································2····2 |
| 46 | ··················(6,·7)·=>·-·x·x··+·x·x | 52 | ··················(6,·7)·=>·-·x·x··+·x·x |
| 47 | ·······························0·5····4·2 | 53 | ·······························0·5····4·2 |
| 48 | ·······························2······3 | 54 | ·······························2······3 |
| 49 | ··················(8,·9)·=>·-·x·x··+·x | 55 | ··················(8,·9)·=>·-·x·x··+·x |
| Offset 103, 22 lines modified | Offset 109, 24 lines modified | ||
| 103 | ········0·4·2····2 | 109 | ········0·4·2····2 |
| 104 | o7·:·QQ[x·,·x·,·x·,·x·,·x·,·x·] | 110 | o7·:·QQ[x·,·x·,·x·,·x·,·x·,·x·] |
| 105 | ·········1···0···3···5···4···2 | 111 | ·········1···0···3···5···4···2 |
| 106 | i8·:·minimize·g | 112 | i8·:·minimize·g |
| 107 | o8·=·LineageTable{((2,· | 113 | o8·=·LineageTable{((((1,·2),·1),·1),·6)·=>·null} |
| 114 | ··················(((1,·2),·1),·1)·=>·null | ||
| 115 | ··················((1,·2),·1)·=>·null | ||
| 116 | ··················((1,·2),·8)·=>·null | ||
| 108 | ··················(1,·2)·=>·null | 117 | ··················(1,·2)·=>·null |
| 109 | ··················(1,·4)·=>·null | 118 | ··················(1,·4)·=>·null |
| 110 | ··················(1,·7)·=>·null | 119 | ··················(1,·7)·=>·null |
| 111 | ····································2 | 120 | ····································2 |
| 112 | ··················(2,·3)·=>·x·x··-·x | 121 | ··················(2,·3)·=>·x·x··-·x |
| 113 | ·····························0·4····2 | 122 | ·····························0·4····2 |
| 114 | ··················(3,·7)·=>·null | ||
| 115 | ··················(4,·6)·=>·x·x··-·x·x | 123 | ··················(4,·6)·=>·x·x··-·x·x |
| 116 | ·····························0·5····3·2 | 124 | ·····························0·5····3·2 |
| 117 | ··················(6,·7)·=>·null | 125 | ··················(6,·7)·=>·null |
| 118 | ·····························2······3 | 126 | ·····························2······3 |
| 119 | ··················(8,·9)·=>·x·x··-·x | 127 | ··················(8,·9)·=>·x·x··-·x |
| 120 | ·····························5·2····4 | 128 | ·····························5·2····4 |
| 121 | ························2 | 129 | ························2 |
| Offset 143, 22 lines modified | Offset 151, 24 lines modified | ||
| 143 | ··················9·=>·x·x··-·x | 151 | ··················9·=>·x·x··-·x |
| 144 | ························3·5····4 | 152 | ························3·5····4 |
| 145 | o8·:·LineageTable | 153 | o8·:·LineageTable |
| 146 | i9·:·gRed·=·reduce·g | 154 | i9·:·gRed·=·reduce·g |
| 147 | o9·=·LineageTable{((2,· | 155 | o9·=·LineageTable{((((1,·2),·1),·1),·6)·=>·null} |
| 156 | ··················(((1,·2),·1),·1)·=>·null | ||
| 157 | ··················((1,·2),·1)·=>·null | ||
| 158 | ··················((1,·2),·8)·=>·null | ||
| 148 | ··················(1,·2)·=>·null | 159 | ··················(1,·2)·=>·null |
| 149 | ··················(1,·4)·=>·null | 160 | ··················(1,·4)·=>·null |
| 150 | ··················(1,·7)·=>·null | 161 | ··················(1,·7)·=>·null |
| 151 | ····································2 | 162 | ····································2 |
| 152 | ··················(2,·3)·=>·x·x··-·x | 163 | ··················(2,·3)·=>·x·x··-·x |
| 153 | ·····························0·4····2 | 164 | ·····························0·4····2 |
| 154 | ··················(3,·7)·=>·null | ||
| 155 | ··················(4,·6)·=>·x·x··-·x·x | 165 | ··················(4,·6)·=>·x·x··-·x·x |
| 156 | ·····························0·5····3·2 | 166 | ·····························0·5····3·2 |
| 157 | ··················(6,·7)·=>·null | 167 | ··················(6,·7)·=>·null |
| 158 | ·····························2······3 | 168 | ·····························2······3 |
| 159 | ··················(8,·9)·=>·x·x··-·x | 169 | ··················(8,·9)·=>·x·x··-·x |
| 160 | ·····························5·2····4 | 170 | ·····························5·2····4 |
| 161 | ························2 | 171 | ························2 |
| Offset 2, 17 lines modified | Offset 2, 16 lines modified | ||
| 2 | i1·:·R·=·ZZ/101[a,b,c]; | 2 | i1·:·R·=·ZZ/101[a,b,c]; |
| 3 | i2·:·allowableThreads=·2; | 3 | i2·:·allowableThreads=·2; |
| 4 | i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 4 | i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 5 | o3·=·LineageTable{((0,·2),·0)·=>·null} | ||
| 6 | ··································2 | 5 | ··································2 |
| 7 | 6 | o3·=·LineageTable{((1,·2),·0)·=>·c·} | |
| 8 | ··················(0,·1)·=>·null | 7 | ··················(0,·1)·=>·null |
| 9 | ··················(0,·2)·=>·null | 8 | ··················(0,·2)·=>·null |
| 10 | ··················(1,·2)·=>·a*c | 9 | ··················(1,·2)·=>·a*c |
| 11 | ··················0·=>·null | 10 | ··················0·=>·null |
| 12 | ··················1·=>·null | 11 | ··················1·=>·null |
| 13 | ························2 | 12 | ························2 |
| 14 | ··················2·=>·b | 13 | ··················2·=>·b |
| Offset 2, 16 lines modified | Offset 2, 20 lines modified | ||
| 2 | i1·:·R·=·ZZ/101[a,b,c]; | 2 | i1·:·R·=·ZZ/101[a,b,c]; |
| 3 | i2·:·allowableThreads=·2; | 3 | i2·:·allowableThreads=·2; |
| 4 | i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" | 4 | i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" |
| 5 | ········································3 | ||
| 6 | o3·=·LineageTable{(((0,·1),·0),·0)·=>·-c·} | ||
| 7 | ·····································2 | ||
| 8 | ··················((0,·1),·0)·=>·-a*c | ||
| 5 | ·································· | 9 | ··································3 |
| 6 | 10 | ··················((0,·1),·1)·=>·a·c | |
| 7 | ···································2 | 11 | ···································2 |
| 8 | ··················((1,·2),·0)·=>·-c | 12 | ··················((1,·2),·0)·=>·-c |
| 9 | ·····························2 | 13 | ·····························2 |
| 10 | ··················(0,·1)·=>·a·c | 14 | ··················(0,·1)·=>·a·c |
| 11 | ·······························2 | 15 | ·······························2 |
| 12 | ··················(0,·2)·=>·b*c | 16 | ··················(0,·2)·=>·b*c |
| 13 | ··················(1,·2)·=>·-a*c | 17 | ··················(1,·2)·=>·-a*c |
| Offset 22, 15 lines modified | Offset 26, 17 lines modified | ||
| 22 | ························2 | 26 | ························2 |
| 23 | ··················2·=>·b | 27 | ··················2·=>·b |
| 24 | o3·:·LineageTable | 28 | o3·:·LineageTable |
| 25 | i4·:·reduce·T | 29 | i4·:·reduce·T |
| 26 | o4·=·LineageTable{((0,· | 30 | o4·=·LineageTable{(((0,·1),·0),·0)·=>·null} |
| 31 | ··················((0,·1),·0)·=>·null | ||
| 32 | ··················((0,·1),·1)·=>·null | ||
| 27 | ··································2 | 33 | ··································2 |
| 28 | ··················((1,·2),·0)·=>·c | 34 | ··················((1,·2),·0)·=>·c |
| 29 | ··················(0,·1)·=>·null | 35 | ··················(0,·1)·=>·null |
| 30 | ··················(0,·2)·=>·null | 36 | ··················(0,·2)·=>·null |
| 31 | ··················(1,·2)·=>·a*c | 37 | ··················(1,·2)·=>·a*c |
| 32 | ··················0·=>·null | 38 | ··················0·=>·null |
| 33 | ··················1·=>·null | 39 | ··················1·=>·null |
| Offset 6, 32 lines modified | Offset 6, 36 lines modified | ||
| 6 | o2·:·Ideal·of·R | 6 | o2·:·Ideal·of·R |
| 7 | i3·:·allowableThreads··=·4; | 7 | i3·:·allowableThreads··=·4; |
| 8 | i4·:·H·=·tgb·I | 8 | i4·:·H·=·tgb·I |
| 9 | ····································2·6······2· | 9 | ····································2·6······2·4 |
| 10 | o4·=·LineageTable{((0,·1),· | 10 | o4·=·LineageTable{((0,·1),·2)·=>·23y·z··+·19y·z······} |
| 11 | ···································2·5······2·4 | ||
| 12 | ··················((0,·1),·3)·=>·7y·z··+·19y·z | ||
| 13 | ·········································2·5······2·4 | ||
| 14 | ··················((0,·3),·(0,·1))·=>·36y·z··+·40y·z | ||
| 11 | ····································2·5······2·4 | 15 | ····································2·5······2·4 |
| 12 | ··················((0,· | 16 | ··················((0,·3),·1)·=>·29y·z··-·22y·z |
| 13 | ·····································2·4 | 17 | ·····································2·4 |
| 14 | ··················((0,· | 18 | ··················((0,·3),·2)·=>·-14y·z |
| 15 | ·································5·2······3·4 | 19 | ·································5·2······3·4 |
| 16 | ··················(0,·1)·=>·-·25y·z··-·19y·z | 20 | ··················(0,·1)·=>·-·25y·z··-·19y·z |
| 17 | ······························ | 21 | ······························5·3·····2·4 |
| 18 | ··················(0,·2)·=>· | 22 | ··················(0,·2)·=>·5y·z··+·9y·z |
| 19 | ·······························5·······3·4 | 23 | ·······························5·······3·4 |
| 20 | ··················(0,·3)·=>·28y·z·-·24y·z | 24 | ··················(0,·3)·=>·28y·z·-·24y·z |
| 25 | ·································4·5······3·8 | ||
| 26 | ··················(1,·2)·=>·-·45y·z··+·30y·z | ||
| 27 | ·······························3·7······3·6 | ||
| 28 | ··················(1,·3)·=>·30y·z··-·34y·z | ||
| 21 | ······························ | 29 | ······························3·4·····2·4 |
| 22 | ··················(1,·2)·=>·21y·z··-·14y·z | ||
| 23 | ·································2·6······2·5 | ||
| 24 | ··················(1,·3)·=>·-·14y·z··-·38y·z | ||
| 25 | ·································2·7·····2·4 | ||
| 26 | ··················(2,·3)·=>· | 30 | ··················(2,·3)·=>·7y·z··-·9y·z |
| 27 | ·······························2 | 31 | ·······························2 |
| 28 | ··················0·=>·2x·+·10y·z | 32 | ··················0·=>·2x·+·10y·z |
| 29 | ·························2···········3 | 33 | ·························2···········3 |
| 30 | ··················1·=>·8x·y·+·10x*y*z | 34 | ··················1·=>·8x·y·+·10x*y*z |
| 31 | ···························3·2·······3 | 35 | ···························3·2·······3 |
| 32 | ··················2·=>·5x*y·z··+·9x*z | 36 | ··················2·=>·5x*y·z··+·9x*z |
| 33 | ···························3·········3 | 37 | ···························3·········3 |
| Offset 85, 18 lines modified | Offset 85, 16 lines modified | ||
| 85 | ········<div> | 85 | ········<div> |
| 86 | ··········<p>By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the·distributed·computation·is·finished:</p> | 86 | ··········<p>By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the·distributed·computation·is·finished:</p> |
| 87 | ········</div> | 87 | ········</div> |
| 88 | ········<table·class="examples"> | 88 | ········<table·class="examples"> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 91 | ········································3 | ||
| 92 | o4·=·LineageTable{(((0,·1),·0),·0)·=>·-c·} | ||
| 93 | ··································· | 91 | ···································3 |
| 94 | 92 | o4·=·LineageTable{((0,·2),·0)·=>·-c······} | |
| 95 | ···································2 | 93 | ···································2 |
| 96 | ··················((1,·2),·0)·=>·-c | 94 | ··················((1,·2),·0)·=>·-c |
| 97 | ·····························2 | 95 | ·····························2 |
| 98 | ··················(0,·1)·=>·a·c | 96 | ··················(0,·1)·=>·a·c |
| 99 | ·······························2 | 97 | ·······························2 |
| 100 | ··················(0,·2)·=>·b*c | 98 | ··················(0,·2)·=>·b*c |
| 101 | ··················(1,·2)·=>·-a*c | 99 | ··················(1,·2)·=>·-a*c |
| Offset 108, 16 lines modified | Offset 106, 15 lines modified | ||
| 108 | ··················2·=>·b | 106 | ··················2·=>·b |
| 109 | o4·:·LineageTable</code></pre> | 107 | o4·:·LineageTable</code></pre> |
| 110 | </td>··········</tr> | 108 | </td>··········</tr> |
| 111 | ··········<tr> | 109 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·minimize·T | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·minimize·T |
| 113 | o5·=·LineageTable{(( | 111 | o5·=·LineageTable{((0,·2),·0)·=>·null} |
| 114 | ··················((0,·1),·0)·=>·null | ||
| 115 | ··································2 | 112 | ··································2 |
| 116 | ··················((1,·2),·0)·=>·c | 113 | ··················((1,·2),·0)·=>·c |
| 117 | ··················(0,·1)·=>·null | 114 | ··················(0,·1)·=>·null |
| 118 | ··················(0,·2)·=>·null | 115 | ··················(0,·2)·=>·null |
| 119 | ··················(1,·2)·=>·a*c | 116 | ··················(1,·2)·=>·a*c |
| 120 | ··················0·=>·null | 117 | ··················0·=>·null |
| 121 | ··················1·=>·null | 118 | ··················1·=>·null |
| Offset 29, 18 lines modified | Offset 29, 16 lines modified | ||
| 29 | ··················2·=>·b | 29 | ··················2·=>·b |
| 30 | o3·:·LineageTable | 30 | o3·:·LineageTable |
| 31 | By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the | 31 | By·default,·the·option·is·false.·The·basis·can·also·be·minimized·after·the |
| 32 | distributed·computation·is·finished: | 32 | distributed·computation·is·finished: |
| 33 | i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 33 | i4·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 34 | ········································3 | ||
| 35 | o4·=·LineageTable{(((0,·1),·0),·0)·=>·-c·} | ||
| 36 | ··································· | 34 | ···································3 |
| 37 | 35 | o4·=·LineageTable{((0,·2),·0)·=>·-c······} | |
| 38 | ···································2 | 36 | ···································2 |
| 39 | ··················((1,·2),·0)·=>·-c | 37 | ··················((1,·2),·0)·=>·-c |
| 40 | ·····························2 | 38 | ·····························2 |
| 41 | ··················(0,·1)·=>·a·c | 39 | ··················(0,·1)·=>·a·c |
| 42 | ·······························2 | 40 | ·······························2 |
| 43 | ··················(0,·2)·=>·b*c | 41 | ··················(0,·2)·=>·b*c |
| 44 | ··················(1,·2)·=>·-a*c | 42 | ··················(1,·2)·=>·-a*c |
| Offset 50, 16 lines modified | Offset 48, 15 lines modified | ||
| 50 | ··················1·=>·-·b·c·+·a*b··+·a*c | 48 | ··················1·=>·-·b·c·+·a*b··+·a*c |
| 51 | ························2 | 49 | ························2 |
| 52 | ··················2·=>·b | 50 | ··················2·=>·b |
| 53 | o4·:·LineageTable | 51 | o4·:·LineageTable |
| 54 | i5·:·minimize·T | 52 | i5·:·minimize·T |
| 55 | o5·=·LineageTable{(( | 53 | o5·=·LineageTable{((0,·2),·0)·=>·null} |
| 56 | ··················((0,·1),·0)·=>·null | ||
| 57 | ··································2 | 54 | ··································2 |
| 58 | ··················((1,·2),·0)·=>·c | 55 | ··················((1,·2),·0)·=>·c |
| 59 | ··················(0,·1)·=>·null | 56 | ··················(0,·1)·=>·null |
| 60 | ··················(0,·2)·=>·null | 57 | ··················(0,·2)·=>·null |
| 61 | ··················(1,·2)·=>·a*c | 58 | ··················(1,·2)·=>·a*c |
| 62 | ··················0·=>·null | 59 | ··················0·=>·null |
| 63 | ··················1·=>·null | 60 | ··················1·=>·null |
| Offset 84, 17 lines modified | Offset 84, 16 lines modified | ||
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 90 | o3·=·LineageTable{((0,·2),·0)·=>·null} | ||
| 91 | ··································2 | 90 | ··································2 |
| 92 | 91 | o3·=·LineageTable{((1,·2),·0)·=>·c·} | |
| 93 | ··················(0,·1)·=>·null | 92 | ··················(0,·1)·=>·null |
| 94 | ··················(0,·2)·=>·null | 93 | ··················(0,·2)·=>·null |
| 95 | ··················(1,·2)·=>·a*c | 94 | ··················(1,·2)·=>·a*c |
| 96 | ··················0·=>·null | 95 | ··················0·=>·null |
| 97 | ··················1·=>·null | 96 | ··················1·=>·null |
| 98 | ························2 | 97 | ························2 |
| 99 | ··················2·=>·b | 98 | ··················2·=>·b |
| Offset 20, 17 lines modified | Offset 20, 16 lines modified | ||
| 20 | This·simple·function·just·returns·the·Gr\"obner·basis·computed·with·threaded | 20 | This·simple·function·just·returns·the·Gr\"obner·basis·computed·with·threaded |
| 21 | Gr\"obner·basis·function·_\x8t_\x8g_\x8b·in·the·expected·Macaulay2·format,·so·that·further | 21 | Gr\"obner·basis·function·_\x8t_\x8g_\x8b·in·the·expected·Macaulay2·format,·so·that·further |
| 22 | computation·are·one·step·easier·to·set·up. | 22 | computation·are·one·step·easier·to·set·up. |
| 23 | i1·:·R·=·ZZ/101[a,b,c]; | 23 | i1·:·R·=·ZZ/101[a,b,c]; |
| 24 | i2·:·allowableThreads=·2; | 24 | i2·:·allowableThreads=·2; |
| 25 | i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 25 | i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 26 | o3·=·LineageTable{((0,·2),·0)·=>·null} | ||
| 27 | ··································2 | 26 | ··································2 |
| 28 | 27 | o3·=·LineageTable{((1,·2),·0)·=>·c·} | |
| 29 | ··················(0,·1)·=>·null | 28 | ··················(0,·1)·=>·null |
| 30 | ··················(0,·2)·=>·null | 29 | ··················(0,·2)·=>·null |
| 31 | ··················(1,·2)·=>·a*c | 30 | ··················(1,·2)·=>·a*c |
| 32 | ··················0·=>·null | 31 | ··················0·=>·null |
| 33 | ··················1·=>·null | 32 | ··················1·=>·null |
| 34 | ························2 | 33 | ························2 |
| 35 | ··················2·=>·b | 34 | ··················2·=>·b |
| Offset 77, 16 lines modified | Offset 77, 20 lines modified | ||
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" |
| 83 | ········································3 | ||
| 84 | o3·=·LineageTable{(((0,·1),·0),·0)·=>·-c·} | ||
| 85 | ·····································2 | ||
| 86 | ··················((0,·1),·0)·=>·-a*c | ||
| 83 | ·································· | 87 | ··································3 |
| 84 | 88 | ··················((0,·1),·1)·=>·a·c | |
| 85 | ···································2 | 89 | ···································2 |
| 86 | ··················((1,·2),·0)·=>·-c | 90 | ··················((1,·2),·0)·=>·-c |
| 87 | ·····························2 | 91 | ·····························2 |
| 88 | ··················(0,·1)·=>·a·c | 92 | ··················(0,·1)·=>·a·c |
| 89 | ·······························2 | 93 | ·······························2 |
| 90 | ··················(0,·2)·=>·b*c | 94 | ··················(0,·2)·=>·b*c |
| 91 | ··················(1,·2)·=>·-a*c | 95 | ··················(1,·2)·=>·-a*c |
| Offset 98, 15 lines modified | Offset 102, 17 lines modified | ||
| 98 | ··················2·=>·b | 102 | ··················2·=>·b |
| 99 | o3·:·LineageTable</code></pre> | 103 | o3·:·LineageTable</code></pre> |
| 100 | </td>··········</tr> | 104 | </td>··········</tr> |
| 101 | ··········<tr> | 105 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·reduce·T | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·reduce·T |
| 103 | o4·=·LineageTable{((0,· | 107 | o4·=·LineageTable{(((0,·1),·0),·0)·=>·null} |
| 108 | ··················((0,·1),·0)·=>·null | ||
| 109 | ··················((0,·1),·1)·=>·null | ||
| 104 | ··································2 | 110 | ··································2 |
| 105 | ··················((1,·2),·0)·=>·c | 111 | ··················((1,·2),·0)·=>·c |
| 106 | ··················(0,·1)·=>·null | 112 | ··················(0,·1)·=>·null |
| 107 | ··················(0,·2)·=>·null | 113 | ··················(0,·2)·=>·null |
| 108 | ··················(1,·2)·=>·a*c | 114 | ··················(1,·2)·=>·a*c |
| 109 | ··················0·=>·null | 115 | ··················0·=>·null |
| 110 | ··················1·=>·null | 116 | ··················1·=>·null |
| Offset 21, 16 lines modified | Offset 21, 20 lines modified | ||
| 21 | remainder·on·the·division·by·the·remaining·values·H. | 21 | remainder·on·the·division·by·the·remaining·values·H. |
| 22 | If·values·H·constitute·a·Gr\"obner·basis·of·the·ideal·they·generate,·this | 22 | If·values·H·constitute·a·Gr\"obner·basis·of·the·ideal·they·generate,·this |
| 23 | method·returns·a·reduced·Gr\"obner·basis. | 23 | method·returns·a·reduced·Gr\"obner·basis. |
| 24 | i1·:·R·=·ZZ/101[a,b,c]; | 24 | i1·:·R·=·ZZ/101[a,b,c]; |
| 25 | i2·:·allowableThreads=·2; | 25 | i2·:·allowableThreads=·2; |
| 26 | i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" | 26 | i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" |
| 27 | ········································3 | ||
| 28 | o3·=·LineageTable{(((0,·1),·0),·0)·=>·-c·} | ||
| 29 | ·····································2 | ||
| 30 | ··················((0,·1),·0)·=>·-a*c | ||
| 27 | ·································· | 31 | ··································3 |
| 28 | 32 | ··················((0,·1),·1)·=>·a·c | |
| 29 | ···································2 | 33 | ···································2 |
| 30 | ··················((1,·2),·0)·=>·-c | 34 | ··················((1,·2),·0)·=>·-c |
| 31 | ·····························2 | 35 | ·····························2 |
| 32 | ··················(0,·1)·=>·a·c | 36 | ··················(0,·1)·=>·a·c |
| 33 | ·······························2 | 37 | ·······························2 |
| 34 | ··················(0,·2)·=>·b*c | 38 | ··················(0,·2)·=>·b*c |
| 35 | ··················(1,·2)·=>·-a*c | 39 | ··················(1,·2)·=>·-a*c |
| Offset 40, 15 lines modified | Offset 44, 17 lines modified | ||
| 40 | ··················1·=>·-·b·c·+·a*b··+·a*c | 44 | ··················1·=>·-·b·c·+·a*b··+·a*c |
| 41 | ························2 | 45 | ························2 |
| 42 | ··················2·=>·b | 46 | ··················2·=>·b |
| 43 | o3·:·LineageTable | 47 | o3·:·LineageTable |
| 44 | i4·:·reduce·T | 48 | i4·:·reduce·T |
| 45 | o4·=·LineageTable{((0,· | 49 | o4·=·LineageTable{(((0,·1),·0),·0)·=>·null} |
| 50 | ··················((0,·1),·0)·=>·null | ||
| 51 | ··················((0,·1),·1)·=>·null | ||
| 46 | ··································2 | 52 | ··································2 |
| 47 | ··················((1,·2),·0)·=>·c | 53 | ··················((1,·2),·0)·=>·c |
| 48 | ··················(0,·1)·=>·null | 54 | ··················(0,·1)·=>·null |
| 49 | ··················(0,·2)·=>·null | 55 | ··················(0,·2)·=>·null |
| 50 | ··················(1,·2)·=>·a*c | 56 | ··················(1,·2)·=>·a*c |
| 51 | ··················0·=>·null | 57 | ··················0·=>·null |
| 52 | ··················1·=>·null | 58 | ··················1·=>·null |
| Offset 92, 32 lines modified | Offset 92, 36 lines modified | ||
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=·4;</code></pre> | 94 | <td>··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=·4;</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·H·=·tgb·I | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·H·=·tgb·I |
| 98 | ····································2·6······2· | 98 | ····································2·6······2·4 |
| 99 | o4·=·LineageTable{((0,·1),· | 99 | o4·=·LineageTable{((0,·1),·2)·=>·23y·z··+·19y·z······} |
| 100 | ···································2·5······2·4 | ||
| 101 | ··················((0,·1),·3)·=>·7y·z··+·19y·z | ||
| 102 | ·········································2·5······2·4 | ||
| 103 | ··················((0,·3),·(0,·1))·=>·36y·z··+·40y·z | ||
| 100 | ····································2·5······2·4 | 104 | ····································2·5······2·4 |
| 101 | ··················((0,· | 105 | ··················((0,·3),·1)·=>·29y·z··-·22y·z |
| 102 | ·····································2·4 | 106 | ·····································2·4 |
| 103 | ··················((0,· | 107 | ··················((0,·3),·2)·=>·-14y·z |
| 104 | ·································5·2······3·4 | 108 | ·································5·2······3·4 |
| 105 | ··················(0,·1)·=>·-·25y·z··-·19y·z | 109 | ··················(0,·1)·=>·-·25y·z··-·19y·z |
| 106 | ······························ | 110 | ······························5·3·····2·4 |
| 107 | ··················(0,·2)·=>· | 111 | ··················(0,·2)·=>·5y·z··+·9y·z |
| 108 | ·······························5·······3·4 | 112 | ·······························5·······3·4 |
| 109 | ··················(0,·3)·=>·28y·z·-·24y·z | 113 | ··················(0,·3)·=>·28y·z·-·24y·z |
| 114 | ·································4·5······3·8 | ||
| 115 | ··················(1,·2)·=>·-·45y·z··+·30y·z | ||
| 116 | ·······························3·7······3·6 | ||
| 117 | ··················(1,·3)·=>·30y·z··-·34y·z | ||
| 110 | ······························ | 118 | ······························3·4·····2·4 |
| 111 | ··················(1,·2)·=>·21y·z··-·14y·z | ||
| 112 | ·································2·6······2·5 | ||
| 113 | ··················(1,·3)·=>·-·14y·z··-·38y·z | ||
| 114 | ·································2·7·····2·4 | ||
| 115 | ··················(2,·3)·=>· | 119 | ··················(2,·3)·=>·7y·z··-·9y·z |
| 116 | ·······························2 | 120 | ·······························2 |
| 117 | ··················0·=>·2x·+·10y·z | 121 | ··················0·=>·2x·+·10y·z |
| 118 | ·························2···········3 | 122 | ·························2···········3 |
| 119 | ··················1·=>·8x·y·+·10x*y*z | 123 | ··················1·=>·8x·y·+·10x*y*z |
| 120 | ···························3·2·······3 | 124 | ···························3·2·······3 |
| 121 | ··················2·=>·5x*y·z··+·9x*z | 125 | ··················2·=>·5x*y·z··+·9x*z |
| 122 | ···························3·········3 | 126 | ···························3·········3 |
| Offset 27, 32 lines modified | Offset 27, 36 lines modified | ||
| 27 | i2·:·I·=·ideal·{2*x·+·10*y^2*z,·8*x^2*y·+·10*x*y*z^3,·5*x*y^3*z^2·+·9*x*z^3, | 27 | i2·:·I·=·ideal·{2*x·+·10*y^2*z,·8*x^2*y·+·10*x*y*z^3,·5*x*y^3*z^2·+·9*x*z^3, |
| 28 | 9*x*y^3*z·+·10*x*y^3}; | 28 | 9*x*y^3*z·+·10*x*y^3}; |
| 29 | o2·:·Ideal·of·R | 29 | o2·:·Ideal·of·R |
| 30 | i3·:·allowableThreads··=·4; | 30 | i3·:·allowableThreads··=·4; |
| 31 | i4·:·H·=·tgb·I | 31 | i4·:·H·=·tgb·I |
| 32 | ····································2·6······2· | 32 | ····································2·6······2·4 |
| 33 | o4·=·LineageTable{((0,·1),· | 33 | o4·=·LineageTable{((0,·1),·2)·=>·23y·z··+·19y·z······} |
| 34 | ···································2·5······2·4 | ||
| 35 | ··················((0,·1),·3)·=>·7y·z··+·19y·z | ||
| 36 | ·········································2·5······2·4 | ||
| 37 | ··················((0,·3),·(0,·1))·=>·36y·z··+·40y·z | ||
| 34 | ····································2·5······2·4 | 38 | ····································2·5······2·4 |
| 35 | ··················((0,· | 39 | ··················((0,·3),·1)·=>·29y·z··-·22y·z |
| 36 | ·····································2·4 | 40 | ·····································2·4 |
| 37 | ··················((0,· | 41 | ··················((0,·3),·2)·=>·-14y·z |
| 38 | ·································5·2······3·4 | 42 | ·································5·2······3·4 |
| 39 | ··················(0,·1)·=>·-·25y·z··-·19y·z | 43 | ··················(0,·1)·=>·-·25y·z··-·19y·z |
| 40 | ······························ | 44 | ······························5·3·····2·4 |
| 41 | ··················(0,·2)·=>· | 45 | ··················(0,·2)·=>·5y·z··+·9y·z |
| 42 | ·······························5·······3·4 | 46 | ·······························5·······3·4 |
| 43 | ··················(0,·3)·=>·28y·z·-·24y·z | 47 | ··················(0,·3)·=>·28y·z·-·24y·z |
| 48 | ·································4·5······3·8 | ||
| 49 | ··················(1,·2)·=>·-·45y·z··+·30y·z | ||
| 50 | ·······························3·7······3·6 | ||
| 51 | ··················(1,·3)·=>·30y·z··-·34y·z | ||
| 44 | ······························ | 52 | ······························3·4·····2·4 |
| 45 | ··················(1,·2)·=>·21y·z··-·14y·z | ||
| 46 | ·································2·6······2·5 | ||
| 47 | ··················(1,·3)·=>·-·14y·z··-·38y·z | ||
| 48 | ·································2·7·····2·4 | ||
| 49 | ··················(2,·3)·=>· | 53 | ··················(2,·3)·=>·7y·z··-·9y·z |
| 50 | ·······························2 | 54 | ·······························2 |
| 51 | ··················0·=>·2x·+·10y·z | 55 | ··················0·=>·2x·+·10y·z |
| 52 | ·························2···········3 | 56 | ·························2···········3 |
| 53 | ··················1·=>·8x·y·+·10x*y*z | 57 | ··················1·=>·8x·y·+·10x*y*z |
| 54 | ···························3·2·······3 | 58 | ···························3·2·······3 |
| 55 | ··················2·=>·5x*y·z··+·9x*z | 59 | ··················2·=>·5x*y·z··+·9x*z |
| 56 | ···························3·········3 | 60 | ···························3·········3 |
| Offset 75, 32 lines modified | Offset 75, 38 lines modified | ||
| 75 | <td>··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=··4 | 75 | <td>··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=··4 |
| 76 | o3·=·4</code></pre> | 76 | o3·=·4</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i4·:·g·=·tgb(rnc) | 79 | <td>··············<pre><code·class="language-macaulay2">i4·:·g·=·tgb(rnc) |
| 80 | ··································2 | 80 | ············································4········2···3 |
| 81 | o4·=·LineageTable{((2,· | 81 | o4·=·LineageTable{((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x·} |
| 82 | ············································0·5·4····0·3·2 | ||
| 83 | ·······································3·2······4 | ||
| 84 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x | ||
| 85 | ·······································0·4····0·2 | ||
| 86 | ··································2············2 | ||
| 87 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x | ||
| 82 | ··································0·5····0·3·2 | 88 | ··································0·5·2····0·3·2 |
| 89 | ······································2······3 | ||
| 90 | ··················((1,·2),·8)·=>·x·x·x··-·x·x | ||
| 91 | ··································0·5·2····3·2 | ||
| 83 | ········································3 | 92 | ········································3 |
| 84 | ··················(1,·2)·=>·-·x·x·x··+·x | 93 | ··················(1,·2)·=>·-·x·x·x··+·x |
| 85 | ·······························0·4·2····2 | 94 | ·······························0·4·2····2 |
| 86 | ··········································2 | 95 | ··········································2 |
| 87 | ··················(1,·4)·=>·-·x·x·x··+·x·x | 96 | ··················(1,·4)·=>·-·x·x·x··+·x·x |
| 88 | ·······························0·5·2····3·2 | 97 | ·······························0·5·2····3·2 |
| 89 | ·································2······2 | 98 | ·································2······2 |
| 90 | ··················(1,·7)·=>·-·x·x··+·x·x | 99 | ··················(1,·7)·=>·-·x·x··+·x·x |
| 91 | ·······························0·4····4·2 | 100 | ·······························0·4····4·2 |
| 92 | ····································2 | 101 | ····································2 |
| 93 | ··················(2,·3)·=>·x·x··-·x | 102 | ··················(2,·3)·=>·x·x··-·x |
| 94 | ·····························0·4····2 | 103 | ·····························0·4····2 |
| 95 | ··········································2 | ||
| 96 | ··················(3,·7)·=>·-·x·x·x··+·x·x | ||
| 97 | ·······························0·5·4····5·2 | ||
| 98 | ··················(4,·6)·=>·x·x··-·x·x | 104 | ··················(4,·6)·=>·x·x··-·x·x |
| 99 | ·····························0·5····3·2 | 105 | ·····························0·5····3·2 |
| 100 | ·································2····2 | 106 | ·································2····2 |
| 101 | ··················(6,·7)·=>·-·x·x··+·x·x | 107 | ··················(6,·7)·=>·-·x·x··+·x·x |
| 102 | ·······························0·5····4·2 | 108 | ·······························0·5····4·2 |
| 103 | ·······························2······3 | 109 | ·······························2······3 |
| 104 | ··················(8,·9)·=>·-·x·x··+·x | 110 | ··················(8,·9)·=>·-·x·x··+·x |
| Offset 178, 22 lines modified | Offset 184, 24 lines modified | ||
| 178 | ··········<p>As·the·algorithm·continues,·keys·are·concatenated,·so·that·for·example·the·remainder·of·S(0,S(1,2))·will·have·lineage·(0,(1,2)),·and·so·on.···For·more·complicated·lineage·examples,·see·<a·title="threaded·Gr\\"obner·bases"·href="_tgb.html">tgb</a>.</p> | 184 | ··········<p>As·the·algorithm·continues,·keys·are·concatenated,·so·that·for·example·the·remainder·of·S(0,S(1,2))·will·have·lineage·(0,(1,2)),·and·so·on.···For·more·complicated·lineage·examples,·see·<a·title="threaded·Gr\\"obner·bases"·href="_tgb.html">tgb</a>.</p> |
| 179 | ··········<p>Naturally,·one·can·obtain·a·minimal·basis·or·the·reduced·one·as·follows.·In·the·output·below,·elements·that·are·reduced·are·replaced·by·null,·but·their·lineage·keys·are·retained·for·informative·purposes.</p> | 185 | ··········<p>Naturally,·one·can·obtain·a·minimal·basis·or·the·reduced·one·as·follows.·In·the·output·below,·elements·that·are·reduced·are·replaced·by·null,·but·their·lineage·keys·are·retained·for·informative·purposes.</p> |
| 180 | ········</div> | 186 | ········</div> |
| 181 | ········<table·class="examples"> | 187 | ········<table·class="examples"> |
| 182 | ··········<tr> | 188 | ··········<tr> |
| 183 | <td>··············<pre><code·class="language-macaulay2">i8·:·minimize·g | 189 | <td>··············<pre><code·class="language-macaulay2">i8·:·minimize·g |
| 184 | o8·=·LineageTable{((2,· | 190 | o8·=·LineageTable{((((1,·2),·1),·1),·6)·=>·null} |
| 191 | ··················(((1,·2),·1),·1)·=>·null | ||
| 192 | ··················((1,·2),·1)·=>·null | ||
| 193 | ··················((1,·2),·8)·=>·null | ||
| 185 | ··················(1,·2)·=>·null | 194 | ··················(1,·2)·=>·null |
| 186 | ··················(1,·4)·=>·null | 195 | ··················(1,·4)·=>·null |
| 187 | ··················(1,·7)·=>·null | 196 | ··················(1,·7)·=>·null |
| 188 | ····································2 | 197 | ····································2 |
| 189 | ··················(2,·3)·=>·x·x··-·x | 198 | ··················(2,·3)·=>·x·x··-·x |
| 190 | ·····························0·4····2 | 199 | ·····························0·4····2 |
| 191 | ··················(3,·7)·=>·null | ||
| 192 | ··················(4,·6)·=>·x·x··-·x·x | 200 | ··················(4,·6)·=>·x·x··-·x·x |
| 193 | ·····························0·5····3·2 | 201 | ·····························0·5····3·2 |
| 194 | ··················(6,·7)·=>·null | 202 | ··················(6,·7)·=>·null |
| 195 | ·····························2······3 | 203 | ·····························2······3 |
| 196 | ··················(8,·9)·=>·x·x··-·x | 204 | ··················(8,·9)·=>·x·x··-·x |
| 197 | ·····························5·2····4 | 205 | ·····························5·2····4 |
| 198 | ························2 | 206 | ························2 |
| Offset 219, 22 lines modified | Offset 227, 24 lines modified | ||
| 219 | ························3·5····4 | 227 | ························3·5····4 |
| 220 | o8·:·LineageTable</code></pre> | 228 | o8·:·LineageTable</code></pre> |
| 221 | </td>··········</tr> | 229 | </td>··········</tr> |
| 222 | ··········<tr> | 230 | ··········<tr> |
| 223 | <td>··············<pre><code·class="language-macaulay2">i9·:·gRed·=·reduce·g | 231 | <td>··············<pre><code·class="language-macaulay2">i9·:·gRed·=·reduce·g |
| 224 | o9·=·LineageTable{((2,· | 232 | o9·=·LineageTable{((((1,·2),·1),·1),·6)·=>·null} |
| 233 | ··················(((1,·2),·1),·1)·=>·null | ||
| 234 | ··················((1,·2),·1)·=>·null | ||
| 235 | ··················((1,·2),·8)·=>·null | ||
| 225 | ··················(1,·2)·=>·null | 236 | ··················(1,·2)·=>·null |
| 226 | ··················(1,·4)·=>·null | 237 | ··················(1,·4)·=>·null |
| 227 | ··················(1,·7)·=>·null | 238 | ··················(1,·7)·=>·null |
| 228 | ····································2 | 239 | ····································2 |
| 229 | ··················(2,·3)·=>·x·x··-·x | 240 | ··················(2,·3)·=>·x·x··-·x |
| 230 | ·····························0·4····2 | 241 | ·····························0·4····2 |
| 231 | ··················(3,·7)·=>·null | ||
| 232 | ··················(4,·6)·=>·x·x··-·x·x | 242 | ··················(4,·6)·=>·x·x··-·x·x |
| 233 | ·····························0·5····3·2 | 243 | ·····························0·5····3·2 |
| 234 | ··················(6,·7)·=>·null | 244 | ··················(6,·7)·=>·null |
| 235 | ·····························2······3 | 245 | ·····························2······3 |
| 236 | ··················(8,·9)·=>·x·x··-·x | 246 | ··················(8,·9)·=>·x·x··-·x |
| 237 | ·····························5·2····4 | 247 | ·····························5·2····4 |
| 238 | ························2 | 248 | ························2 |
| Offset 39, 32 lines modified | Offset 39, 38 lines modified | ||
| 39 | o2·:·Ideal·of·QQ[x·,·x·,·x·,·x·,·x·,·x·] | 39 | o2·:·Ideal·of·QQ[x·,·x·,·x·,·x·,·x·,·x·] |
| 40 | ··················1···0···3···5···4···2 | 40 | ··················1···0···3···5···4···2 |
| 41 | i3·:·allowableThreads··=··4 | 41 | i3·:·allowableThreads··=··4 |
| 42 | o3·=·4 | 42 | o3·=·4 |
| 43 | i4·:·g·=·tgb(rnc) | 43 | i4·:·g·=·tgb(rnc) |
| 44 | ··································2 | 44 | ············································4········2···3 |
| 45 | o4·=·LineageTable{((2,· | 45 | o4·=·LineageTable{((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x·} |
| 46 | ············································0·5·4····0·3·2 | ||
| 47 | ·······································3·2······4 | ||
| 48 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x | ||
| 49 | ·······································0·4····0·2 | ||
| 50 | ··································2············2 | ||
| 51 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x | ||
| 46 | ··································0·5····0·3·2 | 52 | ··································0·5·2····0·3·2 |
| 53 | ······································2······3 | ||
| 54 | ··················((1,·2),·8)·=>·x·x·x··-·x·x | ||
| 55 | ··································0·5·2····3·2 | ||
| 47 | ········································3 | 56 | ········································3 |
| 48 | ··················(1,·2)·=>·-·x·x·x··+·x | 57 | ··················(1,·2)·=>·-·x·x·x··+·x |
| 49 | ·······························0·4·2····2 | 58 | ·······························0·4·2····2 |
| 50 | ··········································2 | 59 | ··········································2 |
| 51 | ··················(1,·4)·=>·-·x·x·x··+·x·x | 60 | ··················(1,·4)·=>·-·x·x·x··+·x·x |
| 52 | ·······························0·5·2····3·2 | 61 | ·······························0·5·2····3·2 |
| 53 | ·································2······2 | 62 | ·································2······2 |
| 54 | ··················(1,·7)·=>·-·x·x··+·x·x | 63 | ··················(1,·7)·=>·-·x·x··+·x·x |
| 55 | ·······························0·4····4·2 | 64 | ·······························0·4····4·2 |
| 56 | ····································2 | 65 | ····································2 |
| 57 | ··················(2,·3)·=>·x·x··-·x | 66 | ··················(2,·3)·=>·x·x··-·x |
| 58 | ·····························0·4····2 | 67 | ·····························0·4····2 |
| 59 | ··········································2 | ||
| 60 | ··················(3,·7)·=>·-·x·x·x··+·x·x | ||
| 61 | ·······························0·5·4····5·2 | ||
| 62 | ··················(4,·6)·=>·x·x··-·x·x | 68 | ··················(4,·6)·=>·x·x··-·x·x |
| 63 | ·····························0·5····3·2 | 69 | ·····························0·5····3·2 |
| 64 | ·································2····2 | 70 | ·································2····2 |
| 65 | ··················(6,·7)·=>·-·x·x··+·x·x | 71 | ··················(6,·7)·=>·-·x·x··+·x·x |
| 66 | ·······························0·5····4·2 | 72 | ·······························0·5····4·2 |
| 67 | ·······························2······3 | 73 | ·······························2······3 |
| 68 | ··················(8,·9)·=>·-·x·x··+·x | 74 | ··················(8,·9)·=>·-·x·x··+·x |
| Offset 131, 22 lines modified | Offset 137, 24 lines modified | ||
| 131 | remainder·of·S(0,S(1,2))·will·have·lineage·(0,(1,2)),·and·so·on.·For·more | 137 | remainder·of·S(0,S(1,2))·will·have·lineage·(0,(1,2)),·and·so·on.·For·more |
| 132 | complicated·lineage·examples,·see·_\x8t_\x8g_\x8b. | 138 | complicated·lineage·examples,·see·_\x8t_\x8g_\x8b. |
| 133 | Naturally,·one·can·obtain·a·minimal·basis·or·the·reduced·one·as·follows.·In·the | 139 | Naturally,·one·can·obtain·a·minimal·basis·or·the·reduced·one·as·follows.·In·the |
| 134 | output·below,·elements·that·are·reduced·are·replaced·by·null,·but·their·lineage | 140 | output·below,·elements·that·are·reduced·are·replaced·by·null,·but·their·lineage |
| 135 | keys·are·retained·for·informative·purposes. | 141 | keys·are·retained·for·informative·purposes. |
| 136 | i8·:·minimize·g | 142 | i8·:·minimize·g |
| 137 | o8·=·LineageTable{((2,· | 143 | o8·=·LineageTable{((((1,·2),·1),·1),·6)·=>·null} |
| 144 | ··················(((1,·2),·1),·1)·=>·null | ||
| 145 | ··················((1,·2),·1)·=>·null | ||
| 146 | ··················((1,·2),·8)·=>·null | ||
| 138 | ··················(1,·2)·=>·null | 147 | ··················(1,·2)·=>·null |
| 139 | ··················(1,·4)·=>·null | 148 | ··················(1,·4)·=>·null |
| 140 | ··················(1,·7)·=>·null | 149 | ··················(1,·7)·=>·null |
| 141 | ····································2 | 150 | ····································2 |
| 142 | ··················(2,·3)·=>·x·x··-·x | 151 | ··················(2,·3)·=>·x·x··-·x |
| 143 | ·····························0·4····2 | 152 | ·····························0·4····2 |
| 144 | ··················(3,·7)·=>·null | ||
| 145 | ··················(4,·6)·=>·x·x··-·x·x | 153 | ··················(4,·6)·=>·x·x··-·x·x |
| 146 | ·····························0·5····3·2 | 154 | ·····························0·5····3·2 |
| 147 | ··················(6,·7)·=>·null | 155 | ··················(6,·7)·=>·null |
| 148 | ·····························2······3 | 156 | ·····························2······3 |
| 149 | ··················(8,·9)·=>·x·x··-·x | 157 | ··················(8,·9)·=>·x·x··-·x |
| 150 | ·····························5·2····4 | 158 | ·····························5·2····4 |
| 151 | ························2 | 159 | ························2 |
| Offset 170, 22 lines modified | Offset 178, 24 lines modified | ||
| 170 | ·······························2 | 178 | ·······························2 |
| 171 | ··················9·=>·x·x··-·x | 179 | ··················9·=>·x·x··-·x |
| 172 | ························3·5····4 | 180 | ························3·5····4 |
| 173 | o8·:·LineageTable | 181 | o8·:·LineageTable |
| 174 | i9·:·gRed·=·reduce·g | 182 | i9·:·gRed·=·reduce·g |
| 175 | o9·=·LineageTable{((2,· | 183 | o9·=·LineageTable{((((1,·2),·1),·1),·6)·=>·null} |
| 184 | ··················(((1,·2),·1),·1)·=>·null | ||
| 185 | ··················((1,·2),·1)·=>·null | ||
| 186 | ··················((1,·2),·8)·=>·null | ||
| 176 | ··················(1,·2)·=>·null | 187 | ··················(1,·2)·=>·null |
| 177 | ··················(1,·4)·=>·null | 188 | ··················(1,·4)·=>·null |
| 178 | ··················(1,·7)·=>·null | 189 | ··················(1,·7)·=>·null |
| 179 | ····································2 | 190 | ····································2 |
| 180 | ··················(2,·3)·=>·x·x··-·x | 191 | ··················(2,·3)·=>·x·x··-·x |
| 181 | ·····························0·4····2 | 192 | ·····························0·4····2 |
| 182 | ··················(3,·7)·=>·null | ||
| 183 | ··················(4,·6)·=>·x·x··-·x·x | 193 | ··················(4,·6)·=>·x·x··-·x·x |
| 184 | ·····························0·5····3·2 | 194 | ·····························0·5····3·2 |
| 185 | ··················(6,·7)·=>·null | 195 | ··················(6,·7)·=>·null |
| 186 | ·····························2······3 | 196 | ·····························2······3 |
| 187 | ··················(8,·9)·=>·x·x··-·x | 197 | ··················(8,·9)·=>·x·x··-·x |
| 188 | ·····························5·2····4 | 198 | ·····························5·2····4 |
| 189 | ························2 | 199 | ························2 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=15 | 7 | #:len=15 |
| 8 | Y2hpcm90b3BlU3RyaW5n | 8 | Y2hpcm90b3BlU3RyaW5n |
| 9 | #:len=253 | 9 | #:len=253 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzI2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzI2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJjaGlyb3RvcGVTdHJpbmciLCJjaGlyb3RvcGVTdHJp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJjaGlyb3RvcGVTdHJpbmciLCJjaGlyb3RvcGVTdHJp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=12 | 7 | #:len=12 |
| 8 | aXNHb3JlbnN0ZWlu | 8 | aXNHb3JlbnN0ZWlu |
| 9 | #:len=1402 | 9 | #:len=1402 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAid2hldGhlciB0aGUgcmluZyBpcyBHb3Jl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAid2hldGhlciB0aGUgcmluZyBpcyBHb3Jl |
| 11 | bnN0ZWluIiwgImxpbmVudW0iID0+IDEyNDMsIElucHV0cyA9PiB7U1BBTntUVHsiUiJ9LCIsICIs | 11 | bnN0ZWluIiwgImxpbmVudW0iID0+IDEyNDMsIElucHV0cyA9PiB7U1BBTntUVHsiUiJ9LCIsICIs |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=5 | 7 | #:len=5 |
| 8 | ZWREZWc= | 8 | ZWREZWc= |
| 9 | #:len=2501 | 9 | #:len=2501 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIChnZW5lcmljKSBF | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIChnZW5lcmljKSBF |
| 11 | dWNsaWRlYW4gZGlzdGFuY2UgZGVncmVlIG9mIGEgcHJvamVjdGl2ZSB0b3JpYyB2YXJpZXR5Iiwg | 11 | dWNsaWRlYW4gZGlzdGFuY2UgZGVncmVlIG9mIGEgcHJvamVjdGl2ZSB0b3JpYyB2YXJpZXR5Iiwg |
| Offset 31, 15 lines modified | Offset 31, 15 lines modified | ||
| 31 | ·····|·0·1·2·0·2·0·| | 31 | ·····|·0·1·2·0·2·0·| |
| 32 | ·····|·1·1·1·1·1·1·| | 32 | ·····|·1·1·1·1·1·1·| |
| 33 | ··············4·······6 | 33 | ··············4·······6 |
| 34 | o3·:·Matrix·ZZ··<--·ZZ | 34 | o3·:·Matrix·ZZ··<--·ZZ |
| 35 | i4·:·time·edDeg(A) | 35 | i4·:·time·edDeg(A) |
| 36 | ·--·used·0. | 36 | ·--·used·0.967326s·(cpu);·0.670759s·(thread);·0s·(gc) |
| 37 | The·toric·variety·has·degree·=·28 | 37 | The·toric·variety·has·degree·=·28 |
| 38 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 38 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 39 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 39 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 40 | Polar·Degrees:·{45,·98,·81,·28} | 40 | Polar·Degrees:·{45,·98,·81,·28} |
| 41 | ED·Degree·=·252 | 41 | ED·Degree·=·252 |
| Offset 47, 15 lines modified | Offset 47, 15 lines modified | ||
| 47 | Chern-Mather·Class:·20h··+·23h··+·31h··+·28h | 47 | Chern-Mather·Class:·20h··+·23h··+·31h··+·28h |
| 48 | o4·=·252 | 48 | o4·=·252 |
| 49 | o4·:·QQ | 49 | o4·:·QQ |
| 50 | i5·:·time·edDeg(A,ForceAmat=>true) | 50 | i5·:·time·edDeg(A,ForceAmat=>true) |
| 51 | ·--·used·3. | 51 | ·--·used·3.84836s·(cpu);·2.68517s·(thread);·0s·(gc) |
| 52 | The·toric·variety·has·degree·=·28 | 52 | The·toric·variety·has·degree·=·28 |
| 53 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 53 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 54 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 54 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 55 | Polar·Degrees:·{45,·98,·81,·28} | 55 | Polar·Degrees:·{45,·98,·81,·28} |
| 56 | ED·Degree·=·252 | 56 | ED·Degree·=·252 |
| Offset 119, 15 lines modified | Offset 119, 15 lines modified | ||
| 119 | ·····|·1·1·1·1·1·1·| | 119 | ·····|·1·1·1·1·1·1·| |
| 120 | ··············4·······6 | 120 | ··············4·······6 |
| 121 | o3·:·Matrix·ZZ··<--·ZZ</code></pre> | 121 | o3·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·edDeg(A) | 124 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·edDeg(A) |
| 125 | ·--·used·0. | 125 | ·--·used·0.967326s·(cpu);·0.670759s·(thread);·0s·(gc) |
| 126 | The·toric·variety·has·degree·=·28 | 126 | The·toric·variety·has·degree·=·28 |
| 127 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 127 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 128 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 128 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 129 | Polar·Degrees:·{45,·98,·81,·28} | 129 | Polar·Degrees:·{45,·98,·81,·28} |
| 130 | ED·Degree·=·252 | 130 | ED·Degree·=·252 |
| Offset 136, 15 lines modified | Offset 136, 15 lines modified | ||
| 136 | o4·=·252 | 136 | o4·=·252 |
| 137 | o4·:·QQ</code></pre> | 137 | o4·:·QQ</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·edDeg(A,ForceAmat=>true) | 140 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·edDeg(A,ForceAmat=>true) |
| 141 | ·--·used·3. | 141 | ·--·used·3.84836s·(cpu);·2.68517s·(thread);·0s·(gc) |
| 142 | The·toric·variety·has·degree·=·28 | 142 | The·toric·variety·has·degree·=·28 |
| 143 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 143 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 144 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 144 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 145 | Polar·Degrees:·{45,·98,·81,·28} | 145 | Polar·Degrees:·{45,·98,·81,·28} |
| 146 | ED·Degree·=·252 | 146 | ED·Degree·=·252 |
| Offset 58, 30 lines modified | Offset 58, 30 lines modified | ||
| 58 | ·····|·3·5·0·2·1·3·| | 58 | ·····|·3·5·0·2·1·3·| |
| 59 | ·····|·0·1·2·0·2·0·| | 59 | ·····|·0·1·2·0·2·0·| |
| 60 | ·····|·1·1·1·1·1·1·| | 60 | ·····|·1·1·1·1·1·1·| |
| 61 | ··············4·······6 | 61 | ··············4·······6 |
| 62 | o3·:·Matrix·ZZ··<--·ZZ | 62 | o3·:·Matrix·ZZ··<--·ZZ |
| 63 | i4·:·time·edDeg(A) | 63 | i4·:·time·edDeg(A) |
| 64 | ·--·used·0. | 64 | ·--·used·0.967326s·(cpu);·0.670759s·(thread);·0s·(gc) |
| 65 | The·toric·variety·has·degree·=·28 | 65 | The·toric·variety·has·degree·=·28 |
| 66 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 66 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 67 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 67 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 68 | Polar·Degrees:·{45,·98,·81,·28} | 68 | Polar·Degrees:·{45,·98,·81,·28} |
| 69 | ED·Degree·=·252 | 69 | ED·Degree·=·252 |
| 70 | ·······················5······4······3······2 | 70 | ·······················5······4······3······2 |
| 71 | Chern-Mather·Class:·20h··+·23h··+·31h··+·28h | 71 | Chern-Mather·Class:·20h··+·23h··+·31h··+·28h |
| 72 | o4·=·252 | 72 | o4·=·252 |
| 73 | o4·:·QQ | 73 | o4·:·QQ |
| 74 | i5·:·time·edDeg(A,ForceAmat=>true) | 74 | i5·:·time·edDeg(A,ForceAmat=>true) |
| 75 | ·--·used·3. | 75 | ·--·used·3.84836s·(cpu);·2.68517s·(thread);·0s·(gc) |
| 76 | The·toric·variety·has·degree·=·28 | 76 | The·toric·variety·has·degree·=·28 |
| 77 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 77 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 78 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 78 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 79 | Polar·Degrees:·{45,·98,·81,·28} | 79 | Polar·Degrees:·{45,·98,·81,·28} |
| 80 | ED·Degree·=·252 | 80 | ED·Degree·=·252 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=17 | 7 | #:len=17 |
| 8 | aGVzc2VuYmVyZ1ZhcmlldHk= | 8 | aGVzc2VuYmVyZ1ZhcmlldHk= |
| 9 | #:len=736 | 9 | #:len=736 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiSGVzc2VuYmVyZyB2YXJpZXR5IGFzc2Nv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiSGVzc2VuYmVyZyB2YXJpZXR5IGFzc2Nv |
| 11 | aWF0ZWQgdG8gdGhlIG4tcGVybXV0YWhlZHJvbiIsICJsaW5lbnVtIiA9PiA2MzksIElucHV0cyA9 | 11 | aWF0ZWQgdG8gdGhlIG4tcGVybXV0YWhlZHJvbiIsICJsaW5lbnVtIiA9PiA2MzksIElucHV0cyA9 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=23 | 7 | #:len=23 |
| 8 | ZHVhbChUb3JpY1ZlY3RvckJ1bmRsZSk= | 8 | ZHVhbChUb3JpY1ZlY3RvckJ1bmRsZSk= |
| 9 | #:len=1504 | 9 | #:len=1504 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiIHRoZSBkdWFsIGJ1bmRsZSBvZiBhIHRv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiIHRoZSBkdWFsIGJ1bmRsZSBvZiBhIHRv |
| 11 | cmljIHZlY3RvciBidW5kbGUiLCAibGluZW51bSIgPT4gMjgyMywgSW5wdXRzID0+IHtTUEFOe1RU | 11 | cmljIHZlY3RvciBidW5kbGUiLCAibGluZW51bSIgPT4gMjgyMywgSW5wdXRzID0+IHtTUEFOe1RU |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=14 | 7 | #:len=14 |
| 8 | Y2hlY2tJbnRlcmZhY2U= | 8 | Y2hlY2tJbnRlcmZhY2U= |
| 9 | #:len=792 | 9 | #:len=792 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAid2hldGhlciB0aGUgTWFwbGUgaW50ZXJm | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAid2hldGhlciB0aGUgTWFwbGUgaW50ZXJm |
| 11 | YWNlIGlzIHdvcmtpbmcgKGZvciBkZXZlbG9wZXJzKSIsICJsaW5lbnVtIiA9PiAzMzUsIElucHV0 | 11 | YWNlIGlzIHdvcmtpbmcgKGZvciBkZXZlbG9wZXJzKSIsICJsaW5lbnVtIiA9PiAzMzUsIElucHV0 |
| Offset 4, 16 lines modified | Offset 4, 16 lines modified | ||
| 4 | i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; | 4 | i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; |
| 5 | o2·:·Ideal·of·R | 5 | o2·:·Ideal·of·R |
| 6 | i3·:·triangularize·I | 6 | i3·:·triangularize·I |
| 7 | o3·=·{{ | 7 | o3·=·{{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d,·f,·h}, |
| 8 | ·····------------------------------------------------------------------------ | 8 | ·····------------------------------------------------------------------------ |
| 9 | ·····d,· | 9 | ·····{c,·d,·f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{b,·d,·e,·f},·{c,·d,·e,·f},·{a*d·- |
| 10 | ·····------------------------------------------------------------------------ | 10 | ·····------------------------------------------------------------------------ |
| 11 | ····· | 11 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} |
| 12 | o3·:·List | 12 | o3·:·List |
| 13 | i4·:· | 13 | i4·:· |
| Offset 2, 25 lines modified | Offset 2, 25 lines modified | ||
| 2 | i1·:·R·=·QQ[a..h,·MonomialOrder=>Lex]; | 2 | i1·:·R·=·QQ[a..h,·MonomialOrder=>Lex]; |
| 3 | i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; | 3 | i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; |
| 4 | i3·:·TT·=·triangularize(R,F,{}) | 4 | i3·:·TT·=·triangularize(R,F,{}) |
| 5 | o3·=·{{c,·d,· | 5 | o3·=·{{c,·d,·e,·f},·{a*d·-·b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c, |
| 6 | ·····------------------------------------------------------------------------ | 6 | ·····------------------------------------------------------------------------ |
| 7 | ····· | 7 | ·····d,·g,·h},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d, |
| 8 | ·····------------------------------------------------------------------------ | 8 | ·····------------------------------------------------------------------------ |
| 9 | ·····f,·h},·{ | 9 | ·····f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·f,·h},·{b,·d,·e,·f}} |
| 10 | o3·:·List | 10 | o3·:·List |
| 11 | i4·:·first·TT | 11 | i4·:·first·TT |
| 12 | o4·=·{c,·d,· | 12 | o4·=·{c,·d,·e,·f} |
| 13 | o4·:·TriaSystem | 13 | o4·:·TriaSystem |
| 14 | i5·:·H·=·{b,d}; | 14 | i5·:·H·=·{b,d}; |
| 15 | i6·:·triangularize(R,F,H) | 15 | i6·:·triangularize(R,F,H) |
| Offset 92, 26 lines modified | Offset 92, 26 lines modified | ||
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g};</code></pre> | 94 | <td>··············<pre><code·class="language-macaulay2">i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g};</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·TT·=·triangularize(R,F,{}) | 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·TT·=·triangularize(R,F,{}) |
| 98 | o3·=·{{c,·d,· | 98 | o3·=·{{c,·d,·e,·f},·{a*d·-·b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c, |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ····· | 100 | ·····d,·g,·h},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d, |
| 101 | ·····------------------------------------------------------------------------ | 101 | ·····------------------------------------------------------------------------ |
| 102 | ·····f,·h},·{ | 102 | ·····f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·f,·h},·{b,·d,·e,·f}} |
| 103 | o3·:·List</code></pre> | 103 | o3·:·List</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·first·TT | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·first·TT |
| 107 | o4·=·{c,·d,· | 107 | o4·=·{c,·d,·e,·f} |
| 108 | o4·:·TriaSystem</code></pre> | 108 | o4·:·TriaSystem</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ········</table> | 110 | ········</table> |
| 111 | ········<div> | 111 | ········<div> |
| 112 | ··········<p>We·now·include·some·inequations.</p> | 112 | ··········<p>We·now·include·some·inequations.</p> |
| 113 | ········</div> | 113 | ········</div> |
| Offset 31, 24 lines modified | Offset 31, 24 lines modified | ||
| 31 | U_1)\cup\cdots\cup·Z(T_r/U_r).$$·These·simpler·sets,·called·_\x8t_\x8r_\x8i_\x8a_\x8n_\x8g_\x8u_\x8l_\x8a_\x8r_\x8·_\x8s_\x8y_\x8s_\x8t_\x8e_\x8m_\x8s, | 31 | U_1)\cup\cdots\cup·Z(T_r/U_r).$$·These·simpler·sets,·called·_\x8t_\x8r_\x8i_\x8a_\x8n_\x8g_\x8u_\x8l_\x8a_\x8r_\x8·_\x8s_\x8y_\x8s_\x8t_\x8e_\x8m_\x8s, |
| 32 | have·very·nice·algorithmic·properties. | 32 | have·very·nice·algorithmic·properties. |
| 33 | As·a·first·example·we·consider·a·case·without·inequations·($H=\emptyset$). | 33 | As·a·first·example·we·consider·a·case·without·inequations·($H=\emptyset$). |
| 34 | i1·:·R·=·QQ[a..h,·MonomialOrder=>Lex]; | 34 | i1·:·R·=·QQ[a..h,·MonomialOrder=>Lex]; |
| 35 | i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; | 35 | i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; |
| 36 | i3·:·TT·=·triangularize(R,F,{}) | 36 | i3·:·TT·=·triangularize(R,F,{}) |
| 37 | o3·=·{{c,·d,· | 37 | o3·=·{{c,·d,·e,·f},·{a*d·-·b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c, |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ····· | 39 | ·····d,·g,·h},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d, |
| 40 | ·····------------------------------------------------------------------------ | 40 | ·····------------------------------------------------------------------------ |
| 41 | ·····f,·h},·{ | 41 | ·····f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·f,·h},·{b,·d,·e,·f}} |
| 42 | o3·:·List | 42 | o3·:·List |
| 43 | i4·:·first·TT | 43 | i4·:·first·TT |
| 44 | o4·=·{c,·d,· | 44 | o4·=·{c,·d,·e,·f} |
| 45 | o4·:·TriaSystem | 45 | o4·:·TriaSystem |
| 46 | We·now·include·some·inequations. | 46 | We·now·include·some·inequations. |
| 47 | i5·:·H·=·{b,d}; | 47 | i5·:·H·=·{b,d}; |
| 48 | i6·:·triangularize(R,F,H) | 48 | i6·:·triangularize(R,F,H) |
| 49 | o6·=·{{a*d·-·b*c,·c*f·-·d*e,·g,·h}·/·{b,·d,·f},·{a*d·-·b*c,·c*f·-·d*e,·e*h·- | 49 | o6·=·{{a*d·-·b*c,·c*f·-·d*e,·g,·h}·/·{b,·d,·f},·{a*d·-·b*c,·c*f·-·d*e,·e*h·- |
| Offset 52, 19 lines modified | Offset 52, 19 lines modified | ||
| 52 | <td>··············<pre><code·class="language-macaulay2">i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; | 52 | <td>··············<pre><code·class="language-macaulay2">i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; |
| 53 | o2·:·Ideal·of·R</code></pre> | 53 | o2·:·Ideal·of·R</code></pre> |
| 54 | </td>··········</tr> | 54 | </td>··········</tr> |
| 55 | ··········<tr> | 55 | ··········<tr> |
| 56 | <td>··············<pre><code·class="language-macaulay2">i3·:·triangularize·I | 56 | <td>··············<pre><code·class="language-macaulay2">i3·:·triangularize·I |
| 57 | o3·=·{{ | 57 | o3·=·{{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d,·f,·h}, |
| 58 | ·····------------------------------------------------------------------------ | 58 | ·····------------------------------------------------------------------------ |
| 59 | ·····d,· | 59 | ·····{c,·d,·f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{b,·d,·e,·f},·{c,·d,·e,·f},·{a*d·- |
| 60 | ·····------------------------------------------------------------------------ | 60 | ·····------------------------------------------------------------------------ |
| 61 | ····· | 61 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} |
| 62 | o3·:·List</code></pre> | 62 | o3·:·List</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ········</table> | 64 | ········</table> |
| 65 | <br>The·method·<a·title="triangular·decomposition·of·polynomial·systems"·href="_triangularize.html">triangularize</a>·is·implemented·in·M2·only·for·monomial·and·binomial·ideals.·For·the·general·case·we·interface·to·Maple.<br><br>This·package·also·provides·methods·for·manipulating·triangular·sets:·········<ul> | 65 | <br>The·method·<a·title="triangular·decomposition·of·polynomial·systems"·href="_triangularize.html">triangularize</a>·is·implemented·in·M2·only·for·monomial·and·binomial·ideals.·For·the·general·case·we·interface·to·Maple.<br><br>This·package·also·provides·methods·for·manipulating·triangular·sets:·········<ul> |
| 66 | ··········<li> | 66 | ··········<li> |
| 67 | <span><a·title="dimension·of·a·triangular·set"·href="_dim_lp__Tria__System_rp.html">dim(TriaSystem)</a>·--·dimension·of·a·triangular·set</span>··········</li> | 67 | <span><a·title="dimension·of·a·triangular·set"·href="_dim_lp__Tria__System_rp.html">dim(TriaSystem)</a>·--·dimension·of·a·triangular·set</span>··········</li> |
| Offset 8, 19 lines modified | Offset 8, 19 lines modified | ||
| 8 | This·package·allows·to·decompose·polynomial·ideals·into·_\x8t_\x8r_\x8i_\x8a_\x8n_\x8g_\x8u_\x8l_\x8a_\x8r_\x8·_\x8s_\x8e_\x8t_\x8s | 8 | This·package·allows·to·decompose·polynomial·ideals·into·_\x8t_\x8r_\x8i_\x8a_\x8n_\x8g_\x8u_\x8l_\x8a_\x8r_\x8·_\x8s_\x8e_\x8t_\x8s |
| 9 | i1·:·R·=·QQ[a..h,·MonomialOrder=>Lex]; | 9 | i1·:·R·=·QQ[a..h,·MonomialOrder=>Lex]; |
| 10 | i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; | 10 | i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; |
| 11 | o2·:·Ideal·of·R | 11 | o2·:·Ideal·of·R |
| 12 | i3·:·triangularize·I | 12 | i3·:·triangularize·I |
| 13 | o3·=·{{ | 13 | o3·=·{{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d,·f,·h}, |
| 14 | ·····------------------------------------------------------------------------ | 14 | ·····------------------------------------------------------------------------ |
| 15 | ·····d,· | 15 | ·····{c,·d,·f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{b,·d,·e,·f},·{c,·d,·e,·f},·{a*d·- |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ····· | 17 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} |
| 18 | o3·:·List | 18 | o3·:·List |
| 19 | The·method·_\x8t_\x8r_\x8i_\x8a_\x8n_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8z_\x8e·is·implemented·in·M2·only·for·monomial·and·binomial | 19 | The·method·_\x8t_\x8r_\x8i_\x8a_\x8n_\x8g_\x8u_\x8l_\x8a_\x8r_\x8i_\x8z_\x8e·is·implemented·in·M2·only·for·monomial·and·binomial |
| 20 | ideals.·For·the·general·case·we·interface·to·Maple. | 20 | ideals.·For·the·general·case·we·interface·to·Maple. |
| 21 | This·package·also·provides·methods·for·manipulating·triangular·sets: | 21 | This·package·also·provides·methods·for·manipulating·triangular·sets: |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=17 | 7 | #:len=17 |
| 8 | YWxsVHJpYW5ndWxhdGlvbnM= | 8 | YWxsVHJpYW5ndWxhdGlvbnM= |
| 9 | #:len=285 | 9 | #:len=285 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzcyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzcyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJhbGxUcmlhbmd1bGF0aW9ucyIsImFsbFRyaWFuZ3Vs | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJhbGxUcmlhbmd1bGF0aW9ucyIsImFsbFRyaWFuZ3Vs |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | ·····|·-1·1··2··-1·-1·1·-1·1·0·0·| | 17 | ·····|·-1·1··2··-1·-1·1·-1·1·0·0·| |
| 18 | ·····|·1··0··-1·0··0··0·0··0·0·0·| | 18 | ·····|·1··0··-1·0··0··0·0··0·0·0·| |
| 19 | ··············4·······10 | 19 | ··············4·······10 |
| 20 | o2·:·Matrix·ZZ··<--·ZZ | 20 | o2·:·Matrix·ZZ··<--·ZZ |
| 21 | i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); | 21 | i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); |
| 22 | ·--·.1 | 22 | ·--·.136775s·elapsed |
| 23 | i4·:·select(Ts,·T·->·isStar·T) | 23 | i4·:·select(Ts,·T·->·isStar·T) |
| 24 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, | 24 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, |
| 25 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 26 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, | 26 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, |
| 27 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| Offset 50, 14 lines modified | Offset 50, 14 lines modified | ||
| 50 | i7·:·T·=·regularFineTriangulation·A | 50 | i7·:·T·=·regularFineTriangulation·A |
| 51 | o7·=·triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,·1,·6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},·{0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,·7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,·3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}} | 51 | o7·=·triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,·1,·6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},·{0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,·7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,·3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}} |
| 52 | o7·:·Triangulation | 52 | o7·:·Triangulation |
| 53 | i8·:·elapsedTime·Ts2·=·generateTriangulations·T; | 53 | i8·:·elapsedTime·Ts2·=·generateTriangulations·T; |
| 54 | ·--· | 54 | ·--·1.64645s·elapsed |
| 55 | i9·:·#Ts2·==·#Ts | 55 | i9·:·#Ts2·==·#Ts |
| 56 | o9·=·true | 56 | o9·=·true |
| 57 | i10·:· | 57 | i10·:· |
| Offset 21, 57 lines modified | Offset 21, 15 lines modified | ||
| 21 | o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}} | 21 | o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}} |
| 22 | o3·:·Triangulation | 22 | o3·:·Triangulation |
| 23 | i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. | 23 | i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. |
| 24 | o4·=·{triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | ||
| 25 | ·····------------------------------------------------------------------------ | ||
| 26 | ·····{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | ||
| 27 | ·····------------------------------------------------------------------------ | ||
| 28 | ·····{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},·triangulation | ||
| 29 | ·····------------------------------------------------------------------------ | ||
| 30 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·6}, | ||
| 31 | ·····------------------------------------------------------------------------ | ||
| 32 | ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·6}, | ||
| 33 | ·····------------------------------------------------------------------------ | ||
| 34 | ·····{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation·{{0,·1,·3,·5}, | ||
| 35 | ·····------------------------------------------------------------------------ | ||
| 36 | ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}}, | ||
| 37 | ·····------------------------------------------------------------------------ | ||
| 38 | ·····triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, | ||
| 39 | ·····------------------------------------------------------------------------ | ||
| 40 | ·····{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4}, | ||
| 41 | ·····------------------------------------------------------------------------ | ||
| 42 | ·····{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},·triangulation | ||
| 43 | ·····------------------------------------------------------------------------ | ||
| 44 | ·····{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7}, | ||
| 45 | ·····------------------------------------------------------------------------ | ||
| 46 | ·····{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},·{0,·3,·4,·6}, | ||
| 47 | ·····------------------------------------------------------------------------ | ||
| 48 | ·····{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, | ||
| 49 | ·····------------------------------------------------------------------------ | ||
| 50 | ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}}, | ||
| 51 | ·····------------------------------------------------------------------------ | ||
| 52 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7}, | ||
| 53 | ·····------------------------------------------------------------------------ | ||
| 54 | ·····{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6}, | ||
| 55 | ·····------------------------------------------------------------------------ | ||
| 56 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 57 | ·····------------------------------------------------------------------------ | ||
| 58 | ·····{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·7}, | ||
| 59 | ·····------------------------------------------------------------------------ | ||
| 60 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},·{0,·2,·3,·6}, | ||
| 61 | ·····------------------------------------------------------------------------ | ||
| 62 | ·····{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, | ||
| 63 | ·····------------------------------------------------------------------------ | ||
| 64 | ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}}, | ||
| 65 | ·····------------------------------------------------------------------------ | ||
| 66 | 24 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7}, | |
| 67 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 68 | ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, | 26 | ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, |
| 69 | ·····------------------------------------------------------------------------ | 27 | ·····------------------------------------------------------------------------ |
| 70 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation | 28 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation |
| 71 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 72 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7}, | 30 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7}, |
| 73 | ·····------------------------------------------------------------------------ | 31 | ·····------------------------------------------------------------------------ |
| Offset 227, 57 lines modified | Offset 185, 63 lines modified | ||
| 227 | ·····------------------------------------------------------------------------ | 185 | ·····------------------------------------------------------------------------ |
| 228 | ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5}, | 186 | ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5}, |
| 229 | ·····------------------------------------------------------------------------ | 187 | ·····------------------------------------------------------------------------ |
| 230 | ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation | 188 | ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation |
| 231 | ·····------------------------------------------------------------------------ | 189 | ·····------------------------------------------------------------------------ |
| 232 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7}, | 190 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7}, |
| 233 | ·····------------------------------------------------------------------------ | 191 | ·····------------------------------------------------------------------------ |
| 192 | ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7}, | ||
| 234 | ·····{1,·4,·6,·7}}} | ||
| 235 | o4·:·List | ||
| 236 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 237 | o5·=·{{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, | ||
| 238 | ·····------------------------------------------------------------------------ | 193 | ·····------------------------------------------------------------------------ |
| 239 | ·····{0,· | 194 | ·····{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7}, |
| 240 | ·····------------------------------------------------------------------------ | 195 | ·····------------------------------------------------------------------------ |
| 241 | ·····{0,· | 196 | ·····{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}}, |
| 242 | ·····------------------------------------------------------------------------ | 197 | ·····------------------------------------------------------------------------ |
| 243 | ····· | 198 | ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7}, |
| 244 | ·····------------------------------------------------------------------------ | 199 | ·····------------------------------------------------------------------------ |
| 245 | ·····{0,· | 200 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, |
| 246 | ·····------------------------------------------------------------------------ | 201 | ·····------------------------------------------------------------------------ |
| 247 | ·····{0,·2,·3,·6},·{0,·3,· | 202 | ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation |
| 248 | ·····------------------------------------------------------------------------ | 203 | ·····------------------------------------------------------------------------ |
| 249 | ·····{{0,·1,· | 204 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6}, |
| 250 | ·····------------------------------------------------------------------------ | 205 | ·····------------------------------------------------------------------------ |
| 251 | ·····{ | 206 | ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6}, |
| 252 | ·····------------------------------------------------------------------------ | 207 | ·····------------------------------------------------------------------------ |
| 253 | ·····{ | 208 | ·····{1,·2,·3,·5},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4}, |
| 254 | ·····------------------------------------------------------------------------ | 209 | ·····------------------------------------------------------------------------ |
| 255 | ·····{ | 210 | ·····{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}}, |
| 256 | ·····------------------------------------------------------------------------ | 211 | ·····------------------------------------------------------------------------ |
| 257 | ····· | 212 | ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6}, |
| 258 | ·····------------------------------------------------------------------------ | 213 | ·····------------------------------------------------------------------------ |
| 259 | ·····{ | 214 | ·····{3,·4,·5,·7},·{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6}, |
| 260 | ·····------------------------------------------------------------------------ | 215 | ·····------------------------------------------------------------------------ |
| 261 | ·····{ | 216 | ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation |
| 262 | ·····------------------------------------------------------------------------ | 217 | ·····------------------------------------------------------------------------ |
| 263 | ·····{ | 218 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6}, |
| 264 | ·····------------------------------------------------------------------------ | 219 | ·····------------------------------------------------------------------------ |
| 265 | ·····{ | 220 | ·····{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5}, |
| 266 | ·····------------------------------------------------------------------------ | 221 | ·····------------------------------------------------------------------------ |
| 267 | ·····{ | 222 | ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6}, |
| 268 | ·····------------------------------------------------------------------------ | 223 | ·····------------------------------------------------------------------------ |
| 269 | ·····{0,· | 224 | ·····{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}}, |
| 270 | ·····------------------------------------------------------------------------ | 225 | ·····------------------------------------------------------------------------ |
| 271 | ····· | 226 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7}, |
| 272 | ·····------------------------------------------------------------------------ | 227 | ·····------------------------------------------------------------------------ |
| 228 | ·····{2,·3,·4,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6}, | ||
| 229 | ·····------------------------------------------------------------------------ | ||
| 230 | ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 231 | ·····------------------------------------------------------------------------ | ||
| 232 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6}, | ||
| 233 | ·····------------------------------------------------------------------------ | ||
| 234 | ·····{2,·5,·6,·7}}} | ||
| 235 | o4·:·List | ||
| 236 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 273 | 237 | o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7}, | |
| 274 | ·····------------------------------------------------------------------------ | 238 | ·····------------------------------------------------------------------------ |
| 275 | ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 239 | ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 276 | ·····------------------------------------------------------------------------ | 240 | ·····------------------------------------------------------------------------ |
| 277 | ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 241 | ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 278 | ·····------------------------------------------------------------------------ | 242 | ·····------------------------------------------------------------------------ |
| 279 | ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7}, | 243 | ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7}, |
| Max diff block lines reached; 40070/50448 bytes (79.43%) of diff not shown. | |||
| Offset 116, 57 lines modified | Offset 116, 15 lines modified | ||
| 116 | o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}} | 116 | o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}} |
| 117 | o3·:·Triangulation</code></pre> | 117 | o3·:·Triangulation</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. | 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. |
| 121 | o4·=·{triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | ||
| 122 | ·····------------------------------------------------------------------------ | ||
| 123 | ·····{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | ||
| 124 | ·····------------------------------------------------------------------------ | ||
| 125 | ·····{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},·triangulation | ||
| 126 | ·····------------------------------------------------------------------------ | ||
| 127 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·6}, | ||
| 128 | ·····------------------------------------------------------------------------ | ||
| 129 | ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·6}, | ||
| 130 | ·····------------------------------------------------------------------------ | ||
| 131 | ·····{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation·{{0,·1,·3,·5}, | ||
| 132 | ·····------------------------------------------------------------------------ | ||
| 133 | ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}}, | ||
| 134 | ·····------------------------------------------------------------------------ | ||
| 135 | ·····triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, | ||
| 136 | ·····------------------------------------------------------------------------ | ||
| 137 | ·····{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4}, | ||
| 138 | ·····------------------------------------------------------------------------ | ||
| 139 | ·····{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},·triangulation | ||
| 140 | ·····------------------------------------------------------------------------ | ||
| 141 | ·····{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7}, | ||
| 142 | ·····------------------------------------------------------------------------ | ||
| 143 | ·····{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},·{0,·3,·4,·6}, | ||
| 144 | ·····------------------------------------------------------------------------ | ||
| 145 | ·····{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, | ||
| 146 | ·····------------------------------------------------------------------------ | ||
| 147 | ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}}, | ||
| 148 | ·····------------------------------------------------------------------------ | ||
| 149 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7}, | ||
| 150 | ·····------------------------------------------------------------------------ | ||
| 151 | ·····{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6}, | ||
| 152 | ·····------------------------------------------------------------------------ | ||
| 153 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 154 | ·····------------------------------------------------------------------------ | ||
| 155 | ·····{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·7}, | ||
| 156 | ·····------------------------------------------------------------------------ | ||
| 157 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},·{0,·2,·3,·6}, | ||
| 158 | ·····------------------------------------------------------------------------ | ||
| 159 | ·····{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, | ||
| 160 | ·····------------------------------------------------------------------------ | ||
| 161 | ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}}, | ||
| 162 | ·····------------------------------------------------------------------------ | ||
| 163 | 121 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7}, | |
| 164 | ·····------------------------------------------------------------------------ | 122 | ·····------------------------------------------------------------------------ |
| 165 | ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, | 123 | ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, |
| 166 | ·····------------------------------------------------------------------------ | 124 | ·····------------------------------------------------------------------------ |
| 167 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation | 125 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation |
| 168 | ·····------------------------------------------------------------------------ | 126 | ·····------------------------------------------------------------------------ |
| 169 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7}, | 127 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7}, |
| 170 | ·····------------------------------------------------------------------------ | 128 | ·····------------------------------------------------------------------------ |
| Offset 322, 58 lines modified | Offset 280, 64 lines modified | ||
| 322 | ·····------------------------------------------------------------------------ | 280 | ·····------------------------------------------------------------------------ |
| 323 | ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5}, | 281 | ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5}, |
| 324 | ·····------------------------------------------------------------------------ | 282 | ·····------------------------------------------------------------------------ |
| 325 | ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation | 283 | ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation |
| 326 | ·····------------------------------------------------------------------------ | 284 | ·····------------------------------------------------------------------------ |
| 327 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7}, | 285 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7}, |
| 328 | ·····------------------------------------------------------------------------ | 286 | ·····------------------------------------------------------------------------ |
| 287 | ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7}, | ||
| 288 | ·····------------------------------------------------------------------------ | ||
| 289 | ·····{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7}, | ||
| 290 | ·····------------------------------------------------------------------------ | ||
| 329 | ·····{1,·4,·6,·7}}} | ||
| 330 | o4·:·List</code></pre> | ||
| 331 | </td>··········</tr> | ||
| 332 | ··········<tr> | ||
| 333 | <td>··············<pre><code·class="language-macaulay2">i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 334 | 291 | ·····{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}}, | |
| 335 | ·····------------------------------------------------------------------------ | 292 | ·····------------------------------------------------------------------------ |
| 336 | ····· | 293 | ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7}, |
| 337 | ·····------------------------------------------------------------------------ | 294 | ·····------------------------------------------------------------------------ |
| 338 | ·····{0,·4,·5,· | 295 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, |
| 339 | ·····------------------------------------------------------------------------ | 296 | ·····------------------------------------------------------------------------ |
| 340 | ·····{0,· | 297 | ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation |
| 341 | ·····------------------------------------------------------------------------ | 298 | ·····------------------------------------------------------------------------ |
| 342 | ·····{0,· | 299 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6}, |
| 343 | ·····------------------------------------------------------------------------ | 300 | ·····------------------------------------------------------------------------ |
| 344 | ·····{0,· | 301 | ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6}, |
| 345 | ·····------------------------------------------------------------------------ | 302 | ·····------------------------------------------------------------------------ |
| 346 | ·····{ | 303 | ·····{1,·2,·3,·5},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4}, |
| 347 | ·····------------------------------------------------------------------------ | 304 | ·····------------------------------------------------------------------------ |
| 348 | ·····{ | 305 | ·····{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}}, |
| 349 | ·····------------------------------------------------------------------------ | 306 | ·····------------------------------------------------------------------------ |
| 350 | ····· | 307 | ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6}, |
| 351 | ·····------------------------------------------------------------------------ | 308 | ·····------------------------------------------------------------------------ |
| 352 | ·····{ | 309 | ·····{3,·4,·5,·7},·{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6}, |
| 353 | ·····------------------------------------------------------------------------ | 310 | ·····------------------------------------------------------------------------ |
| 354 | ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},· | 311 | ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation |
| 355 | ·····------------------------------------------------------------------------ | 312 | ·····------------------------------------------------------------------------ |
| 356 | ·····{0,· | 313 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6}, |
| 357 | ·····------------------------------------------------------------------------ | 314 | ·····------------------------------------------------------------------------ |
| 358 | ·····{ | 315 | ·····{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5}, |
| 359 | ·····------------------------------------------------------------------------ | 316 | ·····------------------------------------------------------------------------ |
| 360 | ·····{2,· | 317 | ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6}, |
| 361 | ·····------------------------------------------------------------------------ | 318 | ·····------------------------------------------------------------------------ |
| 362 | ·····{ | 319 | ·····{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}}, |
| 363 | ·····------------------------------------------------------------------------ | 320 | ·····------------------------------------------------------------------------ |
| 364 | ····· | 321 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7}, |
| 365 | ·····------------------------------------------------------------------------ | 322 | ·····------------------------------------------------------------------------ |
| 366 | ·····{ | 323 | ·····{2,·3,·4,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6}, |
| 367 | ·····------------------------------------------------------------------------ | 324 | ·····------------------------------------------------------------------------ |
| 368 | ·····{0,·2,· | 325 | ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation |
| 369 | ·····------------------------------------------------------------------------ | 326 | ·····------------------------------------------------------------------------ |
| 327 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6}, | ||
| 328 | ·····------------------------------------------------------------------------ | ||
| 329 | ·····{2,·5,·6,·7}}} | ||
| 330 | o4·:·List</code></pre> | ||
| 331 | </td>··········</tr> | ||
| 332 | ··········<tr> | ||
| 333 | <td>··············<pre><code·class="language-macaulay2">i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 370 | 334 | o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7}, | |
| 371 | ·····------------------------------------------------------------------------ | 335 | ·····------------------------------------------------------------------------ |
| 372 | ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 336 | ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 373 | ·····------------------------------------------------------------------------ | 337 | ·····------------------------------------------------------------------------ |
| 374 | ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 338 | ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 375 | ·····------------------------------------------------------------------------ | 339 | ·····------------------------------------------------------------------------ |
| Max diff block lines reached; 41195/51809 bytes (79.51%) of diff not shown. | |||
| Offset 58, 57 lines modified | Offset 58, 15 lines modified | ||
| 58 | o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3, | 58 | o3·=·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3, |
| 59 | 4,·5,·6},·{3,·5,·6,·7}} | 59 | 4,·5,·6},·{3,·5,·6,·7}} |
| 60 | o3·:·Triangulation | 60 | o3·:·Triangulation |
| 61 | i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. | 61 | i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. |
| 62 | o4·=·{triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | ||
| 63 | ·····------------------------------------------------------------------------ | ||
| 64 | ·····{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | ||
| 65 | ·····------------------------------------------------------------------------ | ||
| 66 | ·····{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}},·triangulation | ||
| 67 | ·····------------------------------------------------------------------------ | ||
| 68 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·6}, | ||
| 69 | ·····------------------------------------------------------------------------ | ||
| 70 | ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·6}, | ||
| 71 | ·····------------------------------------------------------------------------ | ||
| 72 | ·····{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation·{{0,·1,·3,·5}, | ||
| 73 | ·····------------------------------------------------------------------------ | ||
| 74 | ·····{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}}, | ||
| 75 | ·····------------------------------------------------------------------------ | ||
| 76 | ·····triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, | ||
| 77 | ·····------------------------------------------------------------------------ | ||
| 78 | ·····{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4}, | ||
| 79 | ·····------------------------------------------------------------------------ | ||
| 80 | ·····{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}},·triangulation | ||
| 81 | ·····------------------------------------------------------------------------ | ||
| 82 | ·····{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7}, | ||
| 83 | ·····------------------------------------------------------------------------ | ||
| 84 | ·····{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6},·{0,·3,·4,·6}, | ||
| 85 | ·····------------------------------------------------------------------------ | ||
| 86 | ·····{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, | ||
| 87 | ·····------------------------------------------------------------------------ | ||
| 88 | ·····{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6},·{3,·5,·6,·7}}, | ||
| 89 | ·····------------------------------------------------------------------------ | ||
| 90 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5},·{2,·3,·5,·7}, | ||
| 91 | ·····------------------------------------------------------------------------ | ||
| 92 | ·····{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6}, | ||
| 93 | ·····------------------------------------------------------------------------ | ||
| 94 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 95 | ·····------------------------------------------------------------------------ | ||
| 96 | ·····{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·7}, | ||
| 97 | ·····------------------------------------------------------------------------ | ||
| 98 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6},·{0,·2,·3,·6}, | ||
| 99 | ·····------------------------------------------------------------------------ | ||
| 100 | ·····{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation·{{0,·1,·2,·5}, | ||
| 101 | ·····------------------------------------------------------------------------ | ||
| 102 | ·····{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}}, | ||
| 103 | ·····------------------------------------------------------------------------ | ||
| 104 | 62 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7}, | |
| 105 | ·····------------------------------------------------------------------------ | 63 | ·····------------------------------------------------------------------------ |
| 106 | ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, | 64 | ·····{1,·2,·3,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, |
| 107 | ·····------------------------------------------------------------------------ | 65 | ·····------------------------------------------------------------------------ |
| 108 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation | 66 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation |
| 109 | ·····------------------------------------------------------------------------ | 67 | ·····------------------------------------------------------------------------ |
| 110 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7}, | 68 | ·····{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7},·{0,·4,·5,·7}, |
| 111 | ·····------------------------------------------------------------------------ | 69 | ·····------------------------------------------------------------------------ |
| Offset 264, 56 lines modified | Offset 222, 62 lines modified | ||
| 264 | ·····------------------------------------------------------------------------ | 222 | ·····------------------------------------------------------------------------ |
| 265 | ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5}, | 223 | ·····{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5}, |
| 266 | ·····------------------------------------------------------------------------ | 224 | ·····------------------------------------------------------------------------ |
| 267 | ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation | 225 | ·····{0,·2,·5,·6},·{0,·4,·5,·6},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation |
| 268 | ·····------------------------------------------------------------------------ | 226 | ·····------------------------------------------------------------------------ |
| 269 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7}, | 227 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·7}, |
| 270 | ·····------------------------------------------------------------------------ | 228 | ·····------------------------------------------------------------------------ |
| 229 | ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7}, | ||
| 271 | ·····{1,·4,·6,·7}}} | ||
| 272 | o4·:·List | ||
| 273 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 274 | o5·=·{{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, | ||
| 275 | ·····------------------------------------------------------------------------ | 230 | ·····------------------------------------------------------------------------ |
| 276 | ·····{0,· | 231 | ·····{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·triangulation·{{0,·1,·3,·7}, |
| 277 | ·····------------------------------------------------------------------------ | 232 | ·····------------------------------------------------------------------------ |
| 278 | ·····{0,· | 233 | ·····{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{2,·4,·6,·7}}, |
| 279 | ·····------------------------------------------------------------------------ | 234 | ·····------------------------------------------------------------------------ |
| 280 | ····· | 235 | ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·3,·5,·7}, |
| 281 | ·····------------------------------------------------------------------------ | 236 | ·····------------------------------------------------------------------------ |
| 282 | ·····{0,· | 237 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·4,·7}, |
| 283 | ·····------------------------------------------------------------------------ | 238 | ·····------------------------------------------------------------------------ |
| 284 | ·····{0,·2,·3,·6},·{0,·3,· | 239 | ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·6,·7},·{1,·4,·5,·7}},·triangulation |
| 285 | ·····------------------------------------------------------------------------ | 240 | ·····------------------------------------------------------------------------ |
| 286 | ·····{{0,·1,· | 241 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·7},·{0,·3,·6,·7},·{0,·4,·5,·6}, |
| 287 | ·····------------------------------------------------------------------------ | 242 | ·····------------------------------------------------------------------------ |
| 288 | ·····{ | 243 | ·····{0,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6}, |
| 289 | ·····------------------------------------------------------------------------ | 244 | ·····------------------------------------------------------------------------ |
| 290 | ·····{ | 245 | ·····{1,·2,·3,·5},·{2,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·3,·4}, |
| 291 | ·····------------------------------------------------------------------------ | 246 | ·····------------------------------------------------------------------------ |
| 292 | ·····{ | 247 | ·····{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·7},·{2,·4,·6,·7},·{3,·4,·5,·7}}, |
| 293 | ·····------------------------------------------------------------------------ | 248 | ·····------------------------------------------------------------------------ |
| 249 | ·····triangulation·{{0,·1,·3,·5},·{0,·2,·3,·4},·{0,·3,·4,·5},·{2,·3,·4,·6}, | ||
| 250 | ·····------------------------------------------------------------------------ | ||
| 251 | ·····{3,·4,·5,·7},·{3,·4,·6,·7}},·triangulation·{{0,·1,·3,·4},·{0,·2,·3,·6}, | ||
| 252 | ·····------------------------------------------------------------------------ | ||
| 294 | ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},· | 253 | ·····{0,·3,·4,·6},·{1,·3,·4,·5},·{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation |
| 295 | ·····------------------------------------------------------------------------ | 254 | ·····------------------------------------------------------------------------ |
| 296 | ·····{0,· | 255 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·6},·{2,·4,·5,·6}, |
| 256 | ·····------------------------------------------------------------------------ | ||
| 257 | ·····{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·5},·{1,·2,·4,·5}, | ||
| 297 | ·····------------------------------------------------------------------------ | 258 | ·····------------------------------------------------------------------------ |
| 298 | ·····{ | 259 | ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·2,·6}, |
| 299 | ·····------------------------------------------------------------------------ | 260 | ·····------------------------------------------------------------------------ |
| 300 | ·····{ | 261 | ·····{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}}, |
| 301 | ·····------------------------------------------------------------------------ | 262 | ·····------------------------------------------------------------------------ |
| 302 | ····· | 263 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7},·{1,·4,·5,·7}, |
| 303 | ·····------------------------------------------------------------------------ | 264 | ·····------------------------------------------------------------------------ |
| 304 | ·····{ | 265 | ·····{2,·3,·4,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·3,·6},·{0,·1,·4,·6}, |
| 305 | ·····------------------------------------------------------------------------ | 266 | ·····------------------------------------------------------------------------ |
| 306 | ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},· | 267 | ·····{0,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation |
| 307 | ·····------------------------------------------------------------------------ | 268 | ·····------------------------------------------------------------------------ |
| 308 | ·····{0,· | 269 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·7},·{1,·2,·5,·7},·{2,·4,·5,·6}, |
| 309 | ·····------------------------------------------------------------------------ | 270 | ·····------------------------------------------------------------------------ |
| 271 | ·····{2,·5,·6,·7}}} | ||
| 272 | o4·:·List | ||
| 273 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 310 | 274 | o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·4,·7},·{0,·4,·5,·7},·{1,·2,·3,·7}, | |
| 311 | ·····------------------------------------------------------------------------ | 275 | ·····------------------------------------------------------------------------ |
| 312 | ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 276 | ·····{2,·4,·6,·7}},·{{0,·1,·3,·7},·{0,·1,·4,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 313 | ·····------------------------------------------------------------------------ | 277 | ·····------------------------------------------------------------------------ |
| 314 | ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 278 | ·····{0,·4,·6,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 315 | ·····------------------------------------------------------------------------ | 279 | ·····------------------------------------------------------------------------ |
| 316 | ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7}, | 280 | ·····{0,·3,·5,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7}, |
| 317 | ·····------------------------------------------------------------------------ | 281 | ·····------------------------------------------------------------------------ |
| Offset 445, 62 lines modified | Offset 409, 56 lines modified | ||
| Max diff block lines reached; 39937/50332 bytes (79.35%) of diff not shown. | |||
| Offset 158, 15 lines modified | Offset 158, 15 lines modified | ||
| 158 | ·····|·1··0··-1·0··0··0·0··0·0·0·| | 158 | ·····|·1··0··-1·0··0··0·0··0·0·0·| |
| 159 | ··············4·······10 | 159 | ··············4·······10 |
| 160 | o2·:·Matrix·ZZ··<--·ZZ</code></pre> | 160 | o2·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 161 | </td>··········</tr> | 161 | </td>··········</tr> |
| 162 | ··········<tr> | 162 | ··········<tr> |
| 163 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); | 163 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); |
| 164 | ·--·.1 | 164 | ·--·.136775s·elapsed</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i4·:·select(Ts,·T·->·isStar·T) | 167 | <td>··············<pre><code·class="language-macaulay2">i4·:·select(Ts,·T·->·isStar·T) |
| 168 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, | 168 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, |
| 169 | ·····------------------------------------------------------------------------ | 169 | ·····------------------------------------------------------------------------ |
| 170 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, | 170 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, |
| Offset 196, 15 lines modified | Offset 196, 15 lines modified | ||
| 196 | o7·=·triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,·1,·6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},·{0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,·7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,·3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}} | 196 | o7·=·triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0,·1,·6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8},·{0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6,·7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2,·3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}} |
| 197 | o7·:·Triangulation</code></pre> | 197 | o7·:·Triangulation</code></pre> |
| 198 | </td>··········</tr> | 198 | </td>··········</tr> |
| 199 | ··········<tr> | 199 | ··········<tr> |
| 200 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·Ts2·=·generateTriangulations·T; | 200 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·Ts2·=·generateTriangulations·T; |
| 201 | ·--· | 201 | ·--·1.64645s·elapsed</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i9·:·#Ts2·==·#Ts | 204 | <td>··············<pre><code·class="language-macaulay2">i9·:·#Ts2·==·#Ts |
| 205 | o9·=·true</code></pre> | 205 | o9·=·true</code></pre> |
| 206 | </td>··········</tr> | 206 | </td>··········</tr> |
| 207 | ········</table> | 207 | ········</table> |
| Offset 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | ·····|·0··0··0··1··0··0·-1·0·0·0·| | 54 | ·····|·0··0··0··1··0··0·-1·0·0·0·| |
| 55 | ·····|·-1·1··2··-1·-1·1·-1·1·0·0·| | 55 | ·····|·-1·1··2··-1·-1·1·-1·1·0·0·| |
| 56 | ·····|·1··0··-1·0··0··0·0··0·0·0·| | 56 | ·····|·1··0··-1·0··0··0·0··0·0·0·| |
| 57 | ··············4·······10 | 57 | ··············4·······10 |
| 58 | o2·:·Matrix·ZZ··<--·ZZ | 58 | o2·:·Matrix·ZZ··<--·ZZ |
| 59 | i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); | 59 | i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); |
| 60 | ·--·.1 | 60 | ·--·.136775s·elapsed |
| 61 | i4·:·select(Ts,·T·->·isStar·T) | 61 | i4·:·select(Ts,·T·->·isStar·T) |
| 62 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, | 62 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, |
| 63 | ·····------------------------------------------------------------------------ | 63 | ·····------------------------------------------------------------------------ |
| 64 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, | 64 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, |
| 65 | ·····------------------------------------------------------------------------ | 65 | ·····------------------------------------------------------------------------ |
| 66 | ·····5,·7,·9},·{0,·3,·5,·8,·9},·{0,·4,·6,·8,·9},·{0,·5,·6,·7,·9},·{0,·5,·6, | 66 | ·····5,·7,·9},·{0,·3,·5,·8,·9},·{0,·4,·6,·8,·9},·{0,·5,·6,·7,·9},·{0,·5,·6, |
| Offset 86, 15 lines modified | Offset 86, 15 lines modified | ||
| 86 | 6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8}, | 86 | 6,·7,·9},·{0,·2,·3,·4,·6},·{0,·2,·3,·4,·9},·{0,·2,·4,·6,·9},·{0,·3,·4,·7,·8}, |
| 87 | {0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6, | 87 | {0,·3,·4,·7,·9},·{0,·3,·5,·7,·8},·{0,·4,·6,·7,·8},·{0,·4,·6,·7,·9},·{0,·5,·6, |
| 88 | 7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2, | 88 | 7,·8},·{1,·2,·3,·7,·9},·{1,·2,·6,·7,·9},·{2,·3,·4,·7,·8},·{2,·3,·4,·7,·9},·{2, |
| 89 | 3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}} | 89 | 3,·5,·7,·8},·{2,·4,·6,·7,·8},·{2,·4,·6,·7,·9},·{2,·5,·6,·7,·8}} |
| 90 | o7·:·Triangulation | 90 | o7·:·Triangulation |
| 91 | i8·:·elapsedTime·Ts2·=·generateTriangulations·T; | 91 | i8·:·elapsedTime·Ts2·=·generateTriangulations·T; |
| 92 | ·--· | 92 | ·--·1.64645s·elapsed |
| 93 | i9·:·#Ts2·==·#Ts | 93 | i9·:·#Ts2·==·#Ts |
| 94 | o9·=·true | 94 | o9·=·true |
| 95 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 95 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 96 | ····*·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·--·for·computations·with·convex·polyhedra,·cones,·and·fans | 96 | ····*·_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a·--·for·computations·with·convex·polyhedra,·cones,·and·fans |
| 97 | ····*·_\x8T_\x8o_\x8p_\x8c_\x8o_\x8m·--·interface·to·selected·functions·from·topcom·package | 97 | ····*·_\x8T_\x8o_\x8p_\x8c_\x8o_\x8m·--·interface·to·selected·functions·from·topcom·package |
| 98 | ····*·_\x8R_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8v_\x8e_\x8P_\x8o_\x8l_\x8y_\x8t_\x8o_\x8p_\x8e_\x8s_\x8D_\x8B·--·simple·access·to·Kreuzer-Skarke·database·of | 98 | ····*·_\x8R_\x8e_\x8f_\x8l_\x8e_\x8x_\x8i_\x8v_\x8e_\x8P_\x8o_\x8l_\x8y_\x8t_\x8o_\x8p_\x8e_\x8s_\x8D_\x8B·--·simple·access·to·Kreuzer-Skarke·database·of |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
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| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=10 | 7 | #:len=10 |
| 8 | Y29tbXV0YXRvcg== | 8 | Y29tbXV0YXRvcg== |
| 9 | #:len=3282 | 9 | #:len=3282 |
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| 11 | ZWN0aW9uIG9mIHZlY3RvciBmaWVsZHMiLCAibGluZW51bSIgPT4gMjE1NSwgSW5wdXRzID0+IHtT | 11 | ZWN0aW9uIG9mIHZlY3RvciBmaWVsZHMiLCAibGluZW51bSIgPT4gMjE1NSwgSW5wdXRzID0+IHtT |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
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| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | dGV4KFNWRyk= | 8 | dGV4KFNWRyk= |
| 9 | #:len=181 | 9 | #:len=181 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg4MywgInVuZG9jdW1lbnRlZCIgPT4g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg4MywgInVuZG9jdW1lbnRlZCIgPT4g |
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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
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| 9 | #:len=588 | 9 | #:len=588 |
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| Offset 6, 30 lines modified | Offset 6, 30 lines modified | ||
| 6 | o2·=·|·xz·yz·z2·x3·| | 6 | o2·=·|·xz·yz·z2·x3·| |
| 7 | ·············1······4 | 7 | ·············1······4 |
| 8 | o2·:·Matrix·S··<--·S | 8 | o2·:·Matrix·S··<--·S |
| 9 | i3·:·time·(F,R,G,C)=localHilbertScheme(F0); | 9 | i3·:·time·(F,R,G,C)=localHilbertScheme(F0); |
| 10 | ·--·used·0. | 10 | ·--·used·0.90466s·(cpu);·0.655409s·(thread);·0s·(gc) |
| 11 | i4·:·T=ring·first·G; | 11 | i4·:·T=ring·first·G; |
| 12 | i5·:·sum·G | 12 | i5·:·sum·G |
| 13 | o5·=·|·t_1t_16·············| | 13 | o5·=·|·t_1t_16·············| |
| 14 | ·····|·t_9t_16·············| | 14 | ·····|·t_9t_16·············| |
| 15 | ·····|·-t_4t_16············| | 15 | ·····|·-t_4t_16············| |
| 16 | ·····|·-2t_14t_16+t_15t_16·| | 16 | ·····|·-2t_14t_16+t_15t_16·| |
| 17 | ·············4······1 | 17 | ·············4······1 |
| 18 | o5·:·Matrix·T··<--·T | 18 | o5·:·Matrix·T··<--·T |
| 19 | i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); | 19 | i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); |
| 20 | ·--·used·0. | 20 | ·--·used·0.564302s·(cpu);·0.385399s·(thread);·0s·(gc) |
| 21 | i7·:·sum·G | 21 | i7·:·sum·G |
| 22 | o7·=·|·t_1t_16····························································· | 22 | o7·=·|·t_1t_16····························································· |
| 23 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ | 23 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ |
| 24 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t | 24 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t |
| 25 | ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2- | 25 | ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2- |
| Offset 59, 15 lines modified | Offset 59, 15 lines modified | ||
| 59 | o2·:·Matrix·S··<--·S</code></pre> | 59 | o2·:·Matrix·S··<--·S</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ········</table> | 61 | ········</table> |
| 62 | ········<p>With·the·default·setting·<span·class="tt">SmartLift=>true</span>·we·get·very·nice·equations·for·the·base·space:</p> | 62 | ········<p>With·the·default·setting·<span·class="tt">SmartLift=>true</span>·we·get·very·nice·equations·for·the·base·space:</p> |
| 63 | ········<table·class="examples"> | 63 | ········<table·class="examples"> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(F,R,G,C)=localHilbertScheme(F0); | 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(F,R,G,C)=localHilbertScheme(F0); |
| 66 | ·--·used·0. | 66 | ·--·used·0.90466s·(cpu);·0.655409s·(thread);·0s·(gc)</code></pre> |
| 67 | </td>··········</tr> | 67 | </td>··········</tr> |
| 68 | ··········<tr> | 68 | ··········<tr> |
| 69 | <td>··············<pre><code·class="language-macaulay2">i4·:·T=ring·first·G;</code></pre> | 69 | <td>··············<pre><code·class="language-macaulay2">i4·:·T=ring·first·G;</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i5·:·sum·G | 72 | <td>··············<pre><code·class="language-macaulay2">i5·:·sum·G |
| Offset 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | o5·:·Matrix·T··<--·T</code></pre> | 80 | o5·:·Matrix·T··<--·T</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ········</table> | 82 | ········</table> |
| 83 | ········<p>With·the·setting·<span·class="tt">SmartLift=>false</span>·the·calculation·is·faster,·but·the·equations·are·no·longer·homogeneous:</p> | 83 | ········<p>With·the·setting·<span·class="tt">SmartLift=>false</span>·the·calculation·is·faster,·but·the·equations·are·no·longer·homogeneous:</p> |
| 84 | ········<table·class="examples"> | 84 | ········<table·class="examples"> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); | 86 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); |
| 87 | ·--·used·0. | 87 | ·--·used·0.564302s·(cpu);·0.385399s·(thread);·0s·(gc)</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i7·:·sum·G | 90 | <td>··············<pre><code·class="language-macaulay2">i7·:·sum·G |
| 91 | o7·=·|·t_1t_16····························································· | 91 | o7·=·|·t_1t_16····························································· |
| 92 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ | 92 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ |
| 93 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t | 93 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t |
| Offset 18, 29 lines modified | Offset 18, 29 lines modified | ||
| 18 | o2·=·|·xz·yz·z2·x3·| | 18 | o2·=·|·xz·yz·z2·x3·| |
| 19 | ·············1······4 | 19 | ·············1······4 |
| 20 | o2·:·Matrix·S··<--·S | 20 | o2·:·Matrix·S··<--·S |
| 21 | With·the·default·setting·SmartLift=>true·we·get·very·nice·equations·for·the | 21 | With·the·default·setting·SmartLift=>true·we·get·very·nice·equations·for·the |
| 22 | base·space: | 22 | base·space: |
| 23 | i3·:·time·(F,R,G,C)=localHilbertScheme(F0); | 23 | i3·:·time·(F,R,G,C)=localHilbertScheme(F0); |
| 24 | ·--·used·0. | 24 | ·--·used·0.90466s·(cpu);·0.655409s·(thread);·0s·(gc) |
| 25 | i4·:·T=ring·first·G; | 25 | i4·:·T=ring·first·G; |
| 26 | i5·:·sum·G | 26 | i5·:·sum·G |
| 27 | o5·=·|·t_1t_16·············| | 27 | o5·=·|·t_1t_16·············| |
| 28 | ·····|·t_9t_16·············| | 28 | ·····|·t_9t_16·············| |
| 29 | ·····|·-t_4t_16············| | 29 | ·····|·-t_4t_16············| |
| 30 | ·····|·-2t_14t_16+t_15t_16·| | 30 | ·····|·-2t_14t_16+t_15t_16·| |
| 31 | ·············4······1 | 31 | ·············4······1 |
| 32 | o5·:·Matrix·T··<--·T | 32 | o5·:·Matrix·T··<--·T |
| 33 | With·the·setting·SmartLift=>false·the·calculation·is·faster,·but·the·equations | 33 | With·the·setting·SmartLift=>false·the·calculation·is·faster,·but·the·equations |
| 34 | are·no·longer·homogeneous: | 34 | are·no·longer·homogeneous: |
| 35 | i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); | 35 | i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); |
| 36 | ·--·used·0. | 36 | ·--·used·0.564302s·(cpu);·0.385399s·(thread);·0s·(gc) |
| 37 | i7·:·sum·G | 37 | i7·:·sum·G |
| 38 | o7·=·|·t_1t_16 | 38 | o7·=·|·t_1t_16 |
| 39 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ | 39 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ |
| 40 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t | 40 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t |
| 41 | ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2- | 41 | ·····|·2t_5t_10t_16^2+2t_7t_11t_16^2+4t_10t_12t_16+2t_11t_13t_16-t_8t_16^2- |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=42 | 7 | #:len=42 |
| 8 | bXVsdGlncmFkZWRSZWd1bGFyaXR5KC4uLixMb3dlckxpbWl0PT4uLi4p | 8 | bXVsdGlncmFkZWRSZWd1bGFyaXR5KC4uLixMb3dlckxpbWl0PT4uLi4p |
| 9 | #:len=334 | 9 | #:len=334 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTgyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNTgyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1ttdWx0aWdyYWRlZFJlZ3VsYXJpdHksTG93ZXJMaW1p | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1ttdWx0aWdyYWRlZFJlZ3VsYXJpdHksTG93ZXJMaW1p |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=29 | 7 | #:len=29 |
| 8 | dmlzdWFsaXplKEdyYXBoLFZlcmJvc2U9Pi4uLik= | 8 | dmlzdWFsaXplKEdyYXBoLFZlcmJvc2U9Pi4uLik= |
| 9 | #:len=1329 | 9 | #:len=1329 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gdG8gdmlldyBjb21tdW5pY2F0aW9u | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gdG8gdmlldyBjb21tdW5pY2F0aW9u |
| 11 | IGJldHdlZW4gTWFjYXVsYXkyIHNlcnZlciBhbmQgYnJvd3NlciAiLCAibGluZW51bSIgPT4gMjA3 | 11 | IGJldHdlZW4gTWFjYXVsYXkyIHNlcnZlciBhbmQgYnJvd3NlciAiLCAibGluZW51bSIgPT4gMjA3 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=18 | 7 | #:len=18 |
| 8 | ZXh0cmFjdFZhcnNBbGdlYnJh | 8 | ZXh0cmFjdFZhcnNBbGdlYnJh |
| 9 | #:len=1106 | 9 | #:len=1106 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidW5kZXJseWluZyBwb2x5bm9taWFsIHJp | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidW5kZXJseWluZyBwb2x5bm9taWFsIHJp |
| 11 | bmcgaW4gdGhlIG9yZGluYXJ5IHZhcmlhYmxlcyBvZiBhIFdleWwgYWxnZWJyYSIsICJsaW5lbnVt | 11 | bmcgaW4gdGhlIG9yZGluYXJ5IHZhcmlhYmxlcyBvZiBhIFdleWwgYWxnZWJyYSIsICJsaW5lbnVt |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=23 | 7 | #:len=23 |
| 8 | V2V5bEdyb3VwRWxlbWVudCAqIFJvb3Q= | 8 | V2V5bEdyb3VwRWxlbWVudCAqIFJvb3Q= |
| 9 | #:len=994 | 9 | #:len=994 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYXBwbHkgYW4gZWxlbWVudCBvZiBhIFdl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYXBwbHkgYW4gZWxlbWVudCBvZiBhIFdl |
| 11 | eWwgZ3JvdXAgdG8gYSByb290IiwgImxpbmVudW0iID0+IDI5NjMsIElucHV0cyA9PiB7U1BBTntU | 11 | eWwgZ3JvdXAgdG8gYSByb290IiwgImxpbmVudW0iID0+IDI5NjMsIElucHV0cyA9PiB7U1BBTntU |
| Offset 36, 34 lines modified | Offset 36, 34 lines modified | ||
| 36 | ···········································|··2·| | 36 | ···········································|··2·| |
| 37 | ···········································|·-1·| | 37 | ···········································|·-1·| |
| 38 | o3·:·List | 38 | o3·:·List |
| 39 | i4·:·aboveBruhat(L1) | 39 | i4·:·aboveBruhat(L1) |
| 40 | o4·=·{{WeylGroupElement{RootSystem{...8...},·|·· | 40 | o4·=·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{1,·|·-1·|},·{2,·|·-1 |
| 41 | ·············································|··1·|········|··1·|·······|··2 | ||
| 41 | ·············································|·-2·|········|··1·|·······|·-1 | 42 | ·············································|·-2·|········|··1·|·······|·-1 |
| 42 | ·············································|··3·|········|·-1·|·······|··0 | ||
| 43 | ·····------------------------------------------------------------------------ | 43 | ·····------------------------------------------------------------------------ |
| 44 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·· | 44 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|··3·|},·{{1,·|··0·|},·{2, |
| 45 | ·····|············································|··1·|········|··1·|······ | ||
| 46 | ·····|············································|·-2·|········|· | 45 | ·····|············································|·-2·|········|·-1·|······ |
| 46 | ·····|············································|··1·|········|··2·|······ | ||
| 47 | ·····------------------------------------------------------------------------ | 47 | ·····------------------------------------------------------------------------ |
| 48 | ·····|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|· | 48 | ·····|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|}, |
| 49 | ·····|··2·|············································|·-2·|········|·-1·|·· | ||
| 50 | ·····|· | 49 | ·····|··1·|············································|··1·|········|··2·|·· |
| 50 | ·····|··1·|············································|··2·|········|·-1·|·· | ||
| 51 | ·····------------------------------------------------------------------------ | 51 | ·····------------------------------------------------------------------------ |
| 52 | ·····{ | 52 | ·····{1,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0 |
| 53 | ·········|··1·|············································|··1·|········|··2 | ||
| 54 | ·········|··1·|············································|·· | 53 | ·········|··1·|············································|··3·|········|·-1 |
| 54 | ·········|·-1·|············································|·-1·|········|··2 | ||
| 55 | ·····------------------------------------------------------------------------ | 55 | ·····------------------------------------------------------------------------ |
| 56 | ·····|},·{ | 56 | ·····|},·{2,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0, |
| 57 | ·····|·······|··1·|············································|··3·|······· | ||
| 58 | ·····|·······|·-1·|············································|·- | 57 | ·····|·······|·-1·|············································|·-2·|······· |
| 58 | ·····|·······|··0·|············································|··3·|······· | ||
| 59 | ·····------------------------------------------------------------------------ | 59 | ·····------------------------------------------------------------------------ |
| 60 | ·····|·· | 60 | ·····|··1·|},·{1,·|··2·|}}}} |
| 61 | ·····|· | 61 | ·····|··1·|·······|·-1·| |
| 62 | ·····|· | 62 | ·····|·-1·|·······|··0·| |
| 63 | o4·:·List | 63 | o4·:·List |
| 64 | i5·:· | 64 | i5·:· |
| Offset 4, 25 lines modified | Offset 4, 25 lines modified | ||
| 4 | o1·=·RootSystem{...8...} | 4 | o1·=·RootSystem{...8...} |
| 5 | o1·:·RootSystem | 5 | o1·:·RootSystem |
| 6 | i2·:·L=toList(positiveRoots(R)) | 6 | i2·:·L=toList(positiveRoots(R)) |
| 7 | o2·=·{|·-1·|,·|·1·|,·|··2·|} | ||
| 8 | 7 | o2·=·{|·1·|,·|··2·|,·|·-1·|} | |
| 8 | ······|·1·|··|·-1·|··|··2·| | ||
| 9 | o2·:·List | 9 | o2·:·List |
| 10 | i3·:·eval(R,1,L#0) | 10 | i3·:·eval(R,1,L#0) |
| 11 | o3·=· | 11 | o3·=·1 |
| 12 | i4·:·eval(R,1,L#1) | 12 | i4·:·eval(R,1,L#1) |
| 13 | o4·=·1 | 13 | o4·=·1 |
| 14 | i5·:·eval(R,1,L#2) | 14 | i5·:·eval(R,1,L#2) |
| 15 | o5·=· | 15 | o5·=·0 |
| 16 | i6·:· | 16 | i6·:· |
| Offset 20, 26 lines modified | Offset 20, 26 lines modified | ||
| 20 | ···········································|·-2·| | 20 | ···········································|·-2·| |
| 21 | ···········································|··1·| | 21 | ···········································|··1·| |
| 22 | o3·:·WeylGroupElement | 22 | o3·:·WeylGroupElement |
| 23 | i4·:·myInterval=intervalBruhat(w1,w2) | 23 | i4·:·myInterval=intervalBruhat(w1,w2) |
| 24 | o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}} | ||
| 25 | ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|············································|·-1·|········|·-1·|··············································|·-1·| | ||
| 26 | 24 | o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}},·{{WeylGroupElement{RootSystem[·...·truncated·by·diffoscope;·len:·25,·SHA:·681e071fee4a8cf2af531899a8824f2395fb7ebd9aba6210a84a4873acf6536f·...·] | |
| 25 | ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|·-1·|············································|·-3·|········|··1·|··············································|·-1·| | ||
| 26 | ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··2·|············································|··1·|········|··1·|··············································|··3·| | ||
| 27 | o4·:·HasseDiagram | 27 | o4·:·HasseDiagram |
| 28 | i5·:·myInterval#1 | 28 | i5·:·myInterval#1 |
| 29 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|· | 29 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}, |
| 30 | ·············································|·- | 30 | ·············································|·-1·|········|·-1·|···· |
| 31 | ·············································|·· | 31 | ·············································|··2·|········|··2·|···· |
| 32 | ·····------------------------------------------------------------------------ | 32 | ·····------------------------------------------------------------------------ |
| 33 | ·····{WeylGroupElement{RootSystem{...8...},·|· | 33 | ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}} |
| 34 | ············································|·- | 34 | ············································|·-3·|········|··1·| |
| 35 | ············································|·· | 35 | ············································|··1·|········|··1·| |
| 36 | o5·:·List | 36 | o5·:·List |
| 37 | i6·:· | 37 | i6·:· |
| Offset 1, 13 lines modified | Offset 1, 13 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1330776363660 | 1 | --·-*-·M2-comint·-*-·hash:·1330776363660 |
| 2 | i1·:·listWeylGroupElements(rootSystemG2,4) | 2 | i1·:·listWeylGroupElements(rootSystemG2,4) |
| 3 | o1·=·{WeylGroupElement{RootSystem{...8...},·|· | 3 | o1·=·{WeylGroupElement{RootSystem{...8...},·|··4·|}, |
| 4 | ············································|· | 4 | ············································|·-3·|·· |
| 5 | ·····------------------------------------------------------------------------ | 5 | ·····------------------------------------------------------------------------ |
| 6 | ·····WeylGroupElement{RootSystem{...8...},·|· | 6 | ·····WeylGroupElement{RootSystem{...8...},·|·-5·|}} |
| 7 | ···········································|· | 7 | ···········································|··2·| |
| 8 | o1·:·List | 8 | o1·:·List |
| 9 | i2·:· | 9 | i2·:· |
| Offset 110, 37 lines modified | Offset 110, 37 lines modified | ||
| 110 | ···········································|·-1·| | 110 | ···········································|·-1·| |
| 111 | o3·:·List</code></pre> | 111 | o3·:·List</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i4·:·aboveBruhat(L1) | 114 | <td>··············<pre><code·class="language-macaulay2">i4·:·aboveBruhat(L1) |
| 115 | o4·=·{{WeylGroupElement{RootSystem{...8...},·|·· | 115 | o4·=·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{1,·|·-1·|},·{2,·|·-1 |
| 116 | ·············································|··1·|········|··1·|·······|··2 | ||
| 116 | ·············································|·-2·|········|··1·|·······|·-1 | 117 | ·············································|·-2·|········|··1·|·······|·-1 |
| 117 | ·············································|··3·|········|·-1·|·······|··0 | ||
| 118 | ·····------------------------------------------------------------------------ | 118 | ·····------------------------------------------------------------------------ |
| 119 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·· | 119 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|··3·|},·{{1,·|··0·|},·{2, |
| 120 | ·····|············································|··1·|········|··1·|······ | ||
| 121 | ·····|············································|·-2·|········|· | 120 | ·····|············································|·-2·|········|·-1·|······ |
| 121 | ·····|············································|··1·|········|··2·|······ | ||
| 122 | ·····------------------------------------------------------------------------ | 122 | ·····------------------------------------------------------------------------ |
| 123 | ·····|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|· | 123 | ·····|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|}, |
| 124 | ·····|··2·|············································|·-2·|········|·-1·|·· | ||
| 125 | ·····|· | 124 | ·····|··1·|············································|··1·|········|··2·|·· |
| 125 | ·····|··1·|············································|··2·|········|·-1·|·· | ||
| 126 | ·····------------------------------------------------------------------------ | 126 | ·····------------------------------------------------------------------------ |
| 127 | ·····{ | 127 | ·····{1,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0 |
| 128 | ·········|··1·|············································|··1·|········|··2 | ||
| 129 | ·········|··1·|············································|·· | 128 | ·········|··1·|············································|··3·|········|·-1 |
| 129 | ·········|·-1·|············································|·-1·|········|··2 | ||
| 130 | ·····------------------------------------------------------------------------ | 130 | ·····------------------------------------------------------------------------ |
| 131 | ·····|},·{ | 131 | ·····|},·{2,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0, |
| 132 | ·····|·······|··1·|············································|··3·|······· | ||
| 133 | ·····|·······|·-1·|············································|·- | 132 | ·····|·······|·-1·|············································|·-2·|······· |
| 133 | ·····|·······|··0·|············································|··3·|······· | ||
| 134 | ·····------------------------------------------------------------------------ | 134 | ·····------------------------------------------------------------------------ |
| 135 | ·····|·· | 135 | ·····|··1·|},·{1,·|··2·|}}}} |
| 136 | ·····|· | 136 | ·····|··1·|·······|·-1·| |
| 137 | ·····|· | 137 | ·····|·-1·|·······|··0·| |
| 138 | o4·:·List</code></pre> | 138 | o4·:·List</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ········</table> | 140 | ········</table> |
| 141 | ······</div> | 141 | ······</div> |
| 142 | ······<div·class="waystouse"> | 142 | ······<div·class="waystouse"> |
| 143 | ········<h2>Ways·to·use·this·method:</h2> | 143 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 49, 35 lines modified | Offset 49, 35 lines modified | ||
| 49 | ·····WeylGroupElement{RootSystem{...8...},·|··1·|}} | 49 | ·····WeylGroupElement{RootSystem{...8...},·|··1·|}} |
| 50 | ···········································|··2·| | 50 | ···········································|··2·| |
| 51 | ···········································|·-1·| | 51 | ···········································|·-1·| |
| 52 | o3·:·List | 52 | o3·:·List |
| 53 | i4·:·aboveBruhat(L1) | 53 | i4·:·aboveBruhat(L1) |
| 54 | o4·=·{{WeylGroupElement{RootSystem{...8...},·|·· | 54 | o4·=·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{1,·|·-1·|},·{2,·|·-1 |
| 55 | ·············································|··1·|········|··1·|·······|··2 | ||
| 55 | ·············································|·-2·|········|··1·|·······|·-1 | 56 | ·············································|·-2·|········|··1·|·······|·-1 |
| 56 | ·············································|··3·|········|·-1·|·······|··0 | ||
| 57 | ·····------------------------------------------------------------------------ | 57 | ·····------------------------------------------------------------------------ |
| 58 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·· | 58 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|··3·|},·{{1,·|··0·|},·{2, |
| 59 | ·····|············································|··1·|········|··1·| | ||
| 60 | ·····|············································|·-2·|········|· | 59 | ·····|············································|·-2·|········|·-1·| |
| 60 | ·····|············································|··1·|········|··2·| | ||
| 61 | ·····------------------------------------------------------------------------ | 61 | ·····------------------------------------------------------------------------ |
| 62 | ·····|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|· | 62 | ·····|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·-1·|}, |
| 63 | ·····|··2·|············································|·-2·|········|·-1·| | ||
| 64 | ·····|· | 63 | ·····|··1·|············································|··1·|········|··2·| |
| 64 | ·····|··1·|············································|··2·|········|·-1·| | ||
| 65 | ·····------------------------------------------------------------------------ | 65 | ·····------------------------------------------------------------------------ |
| 66 | ·····{ | 66 | ·····{1,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0 |
| 67 | ·········|··1·|············································|··1·|········|··2 | ||
| 68 | ·········|··1·|············································|·· | 67 | ·········|··1·|············································|··3·|········|·-1 |
| 68 | ·········|·-1·|············································|·-1·|········|··2 | ||
| 69 | ·····------------------------------------------------------------------------ | 69 | ·····------------------------------------------------------------------------ |
| 70 | ·····|},·{ | 70 | ·····|},·{2,·|··2·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0, |
| 71 | ·····|·······|··1·|············································|··3·| | ||
| 72 | ·····|·······|·-1·|············································|·- | 71 | ·····|·······|·-1·|············································|·-2·| |
| 72 | ·····|·······|··0·|············································|··3·| | ||
| 73 | ·····------------------------------------------------------------------------ | 73 | ·····------------------------------------------------------------------------ |
| 74 | ·····|·· | 74 | ·····|··1·|},·{1,·|··2·|}}}} |
| 75 | ·····|· | 75 | ·····|··1·|·······|·-1·| |
| 76 | ·····|· | 76 | ·····|·-1·|·······|··0·| |
| 77 | o4·:·List | 77 | o4·:·List |
| 78 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 78 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 79 | ····*·_\x8a_\x8b_\x8o_\x8v_\x8e_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8B_\x8a_\x8s_\x8i_\x8c_\x8L_\x8i_\x8s_\x8t_\x8)·--·The·Weyl·group·elements·just·under·the·ones·in | 79 | ····*·_\x8a_\x8b_\x8o_\x8v_\x8e_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8B_\x8a_\x8s_\x8i_\x8c_\x8L_\x8i_\x8s_\x8t_\x8)·--·The·Weyl·group·elements·just·under·the·ones·in |
| 80 | ······the·list·for·the·Bruhat·order | 80 | ······the·list·for·the·Bruhat·order |
| Offset 80, 33 lines modified | Offset 80, 33 lines modified | ||
| 80 | o1·=·RootSystem{...8...} | 80 | o1·=·RootSystem{...8...} |
| 81 | o1·:·RootSystem</code></pre> | 81 | o1·:·RootSystem</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·L=toList(positiveRoots(R)) | 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·L=toList(positiveRoots(R)) |
| 85 | o2·=·{|·-1·|,·|·1·|,·|··2·|} | ||
| 86 | 85 | o2·=·{|·1·|,·|··2·|,·|·-1·|} | |
| 86 | ······|·1·|··|·-1·|··|··2·| | ||
| 87 | o2·:·List</code></pre> | 87 | o2·:·List</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·eval(R,1,L#0) | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·eval(R,1,L#0) |
| 91 | o3·=· | 91 | o3·=·1</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·eval(R,1,L#1) | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·eval(R,1,L#1) |
| 95 | o4·=·1</code></pre> | 95 | o4·=·1</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·eval(R,1,L#2) | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·eval(R,1,L#2) |
| 99 | o5·=· | 99 | o5·=·0</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ········</table> | 101 | ········</table> |
| 102 | ······</div> | 102 | ······</div> |
| 103 | ······<div·class="waystouse"> | 103 | ······<div·class="waystouse"> |
| 104 | ········<h2>Ways·to·use·this·method:</h2> | 104 | ········<h2>Ways·to·use·this·method:</h2> |
| 105 | ········<ul> | 105 | ········<ul> |
| 106 | ··········<li> | 106 | ··········<li> |
| Offset 20, 23 lines modified | Offset 20, 23 lines modified | ||
| 20 | i1·:·R=rootSystemA(2) | 20 | i1·:·R=rootSystemA(2) |
| 21 | o1·=·RootSystem{...8...} | 21 | o1·=·RootSystem{...8...} |
| 22 | o1·:·RootSystem | 22 | o1·:·RootSystem |
| 23 | i2·:·L=toList(positiveRoots(R)) | 23 | i2·:·L=toList(positiveRoots(R)) |
| 24 | o2·=·{|·-1·|,·|·1·|,·|··2·|} | ||
| 25 | 24 | o2·=·{|·1·|,·|··2·|,·|·-1·|} | |
| 25 | ······|·1·|··|·-1·|··|··2·| | ||
| 26 | o2·:·List | 26 | o2·:·List |
| 27 | i3·:·eval(R,1,L#0) | 27 | i3·:·eval(R,1,L#0) |
| 28 | o3·=· | 28 | o3·=·1 |
| 29 | i4·:·eval(R,1,L#1) | 29 | i4·:·eval(R,1,L#1) |
| 30 | o4·=·1 | 30 | o4·=·1 |
| 31 | i5·:·eval(R,1,L#2) | 31 | i5·:·eval(R,1,L#2) |
| 32 | o5·=· | 32 | o5·=·0 |
| 33 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 33 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 34 | ····*·_\x8e_\x8v_\x8a_\x8l_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8Z_\x8Z_\x8,_\x8R_\x8o_\x8o_\x8t_\x8)·--·evaluate·the·dual·of·a·root·at·a·fundamental | 34 | ····*·_\x8e_\x8v_\x8a_\x8l_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8Z_\x8Z_\x8,_\x8R_\x8o_\x8o_\x8t_\x8)·--·evaluate·the·dual·of·a·root·at·a·fundamental |
| 35 | ······weight | 35 | ······weight |
| Offset 96, 35 lines modified | Offset 96, 35 lines modified | ||
| 96 | ···········································|··1·| | 96 | ···········································|··1·| |
| 97 | o3·:·WeylGroupElement</code></pre> | 97 | o3·:·WeylGroupElement</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·myInterval=intervalBruhat(w1,w2) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·myInterval=intervalBruhat(w1,w2) |
| 101 | o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··0·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}} | ||
| 102 | ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|············································|·-1·|········|·-1·|··············································|·-1·| | ||
| 103 | 101 | o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}},·{{WeylGroupElement{RootSystem[·...·truncated·by·diffoscope;·len:·25,·SHA:·681e071fee4a8cf2af531899a8824f2395fb7ebd9aba6210a84a4873acf6536f·...·] | |
| 102 | ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|·-1·|············································|·-3·|········|··1·|··············································|·-1·| | ||
| 103 | ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··2·|············································|··1·|········|··1·|··············································|··3·| | ||
| 104 | o4·:·HasseDiagram</code></pre> | 104 | o4·:·HasseDiagram</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | ········<div> | 107 | ········<div> |
| 108 | ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p> | 108 | ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p> |
| 109 | ········</div> | 109 | ········</div> |
| 110 | ········<table·class="examples"> | 110 | ········<table·class="examples"> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·myInterval#1 | 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·myInterval#1 |
| 113 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|· | 113 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}, |
| 114 | ·············································|·- | 114 | ·············································|·-1·|········|·-1·|···· |
| 115 | ·············································|·· | 115 | ·············································|··2·|········|··2·|···· |
| 116 | ·····------------------------------------------------------------------------ | 116 | ·····------------------------------------------------------------------------ |
| 117 | ·····{WeylGroupElement{RootSystem{...8...},·|· | 117 | ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}} |
| 118 | ············································|·- | 118 | ············································|·-3·|········|··1·| |
| 119 | ············································|·· | 119 | ············································|··1·|········|··1·| |
| 120 | o5·:·List</code></pre> | 120 | o5·:·List</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ········</table> | 122 | ········</table> |
| 123 | ······</div> | 123 | ······</div> |
| 124 | ······<div·class="waystouse"> | 124 | ······<div·class="waystouse"> |
| 125 | ········<h2>Ways·to·use·this·method:</h2> | 125 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 37, 35 lines modified | Offset 37, 35 lines modified | ||
| 37 | o3·=·WeylGroupElement{RootSystem{...8...},·|·-1·|} | 37 | o3·=·WeylGroupElement{RootSystem{...8...},·|·-1·|} |
| 38 | ···········································|·-2·| | 38 | ···········································|·-2·| |
| 39 | ···········································|··1·| | 39 | ···········································|··1·| |
| 40 | o3·:·WeylGroupElement | 40 | o3·:·WeylGroupElement |
| 41 | i4·:·myInterval=intervalBruhat(w1,w2) | 41 | i4·:·myInterval=intervalBruhat(w1,w2) |
| 42 | o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|· | 42 | o4·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·- |
| 43 | |},·{1,·|· | 43 | 1·|},·{1,·|··0·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·| |
| 44 | 44 | 0·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}},·{ | |
| 45 | {WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}} | 45 | {WeylGroupElement{RootSystem{...8...},·|·-1·|},·{}}}} |
| 46 | ··························································|·-2·|········|· | 46 | ··························································|·-2·|········|··2·| |
| 47 | |· | 47 | |·-1·|··············································|·-1·|········|·-1·| |
| 48 | |·- | 48 | |·-3·|········|··1·|··············································|·-1·| |
| 49 | ··························································|··1·|········|· | 49 | ··························································|··1·|········|·-1·| |
| 50 | |· | 50 | |··2·|··············································|··2·|········|··2·| |
| 51 | |·· | 51 | |··1·|········|··1·|··············································|··3·| |
| 52 | o4·:·HasseDiagram | 52 | o4·:·HasseDiagram |
| 53 | Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length | 53 | Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length |
| 54 | together·with·their·links·to·the·next·row. | 54 | together·with·their·links·to·the·next·row. |
| 55 | i5·:·myInterval#1 | 55 | i5·:·myInterval#1 |
| 56 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|· | 56 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}, |
| 57 | ·············································|·- | 57 | ·············································|·-1·|········|·-1·| |
| 58 | ·············································|·· | 58 | ·············································|··2·|········|··2·| |
| 59 | ·····------------------------------------------------------------------------ | 59 | ·····------------------------------------------------------------------------ |
| 60 | ·····{WeylGroupElement{RootSystem{...8...},·|· | 60 | ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}} |
| 61 | ············································|·- | 61 | ············································|·-3·|········|··1·| |
| 62 | ············································|·· | 62 | ············································|··1·|········|··1·| |
| 63 | o5·:·List | 63 | o5·:·List |
| 64 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 64 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 65 | ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8)·--·elements·between·two | 65 | ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8)·--·elements·between·two |
| 66 | ······given·ones·for·the·Bruhat·order·on·a·Weyl·group | 66 | ······given·ones·for·the·Bruhat·order·on·a·Weyl·group |
| Offset 71, 19 lines modified | Offset 71, 19 lines modified | ||
| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>Description</h2> | 73 | ········<h2>Description</h2> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·listWeylGroupElements(rootSystemG2,4) | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·listWeylGroupElements(rootSystemG2,4) |
| 77 | o1·=·{WeylGroupElement{RootSystem{...8...},·|· | 77 | o1·=·{WeylGroupElement{RootSystem{...8...},·|··4·|}, |
| 78 | ············································|· | 78 | ············································|·-3·|·· |
| 79 | ·····------------------------------------------------------------------------ | 79 | ·····------------------------------------------------------------------------ |
| 80 | ·····WeylGroupElement{RootSystem{...8...},·|· | 80 | ·····WeylGroupElement{RootSystem{...8...},·|·-5·|}} |
| 81 | ···········································|· | 81 | ···········································|··2·| |
| 82 | o1·:·List</code></pre> | 82 | o1·:·List</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ········</table> | 84 | ········</table> |
| 85 | ······</div> | 85 | ······</div> |
| 86 | ······<div·class="waystouse"> | 86 | ······<div·class="waystouse"> |
| 87 | ········<h2>Ways·to·use·this·method:</h2> | 87 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 13, 17 lines modified | Offset 13, 17 lines modified | ||
| 13 | ··········o·R,·an·instance·of·the·type·_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m, | 13 | ··········o·R,·an·instance·of·the·type·_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m, |
| 14 | ··········o·k,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r, | 14 | ··········o·k,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r, |
| 15 | ····*·Outputs: | 15 | ····*·Outputs: |
| 16 | ··········o·a·_\x8l_\x8i_\x8s_\x8t,·of·all·elements·of·length·k·in·the·Weyl·group·of·R | 16 | ··········o·a·_\x8l_\x8i_\x8s_\x8t,·of·all·elements·of·length·k·in·the·Weyl·group·of·R |
| 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* | 17 | *\x8**\x8**\x8**\x8**\x8*·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·*\x8**\x8**\x8**\x8**\x8* |
| 18 | i1·:·listWeylGroupElements(rootSystemG2,4) | 18 | i1·:·listWeylGroupElements(rootSystemG2,4) |
| 19 | o1·=·{WeylGroupElement{RootSystem{...8...},·|· | 19 | o1·=·{WeylGroupElement{RootSystem{...8...},·|··4·|}, |
| 20 | ············································|· | 20 | ············································|·-3·| |
| 21 | ·····------------------------------------------------------------------------ | 21 | ·····------------------------------------------------------------------------ |
| 22 | ·····WeylGroupElement{RootSystem{...8...},·|· | 22 | ·····WeylGroupElement{RootSystem{...8...},·|·-5·|}} |
| 23 | ···········································|· | 23 | ···········································|··2·| |
| 24 | o1·:·List | 24 | o1·:·List |
| 25 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* | 25 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8th\x8hi\x8is\x8s·m\x8me\x8et\x8th\x8ho\x8od\x8d:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 26 | ····*·_\x8l_\x8i_\x8s_\x8t_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8s_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8Z_\x8Z_\x8)·--·list·all·elements·of·a·given | 26 | ····*·_\x8l_\x8i_\x8s_\x8t_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8E_\x8l_\x8e_\x8m_\x8e_\x8n_\x8t_\x8s_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8Z_\x8Z_\x8)·--·list·all·elements·of·a·given |
| 27 | ······length·in·a·Weyl·group | 27 | ······length·in·a·Weyl·group |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=8 | 7 | #:len=8 |
| 8 | Y29ub3JtYWw= | 8 | Y29ub3JtYWw= |
| 9 | #:len=1037 | 9 | #:len=1037 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIGNvbm9ybWFsIHZh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIGNvbm9ybWFsIHZh |
| 11 | cmlldHkiLCAibGluZW51bSIgPT4gNjc2LCBJbnB1dHMgPT4ge1NQQU57VFR7IkkifSwiLCAiLFNQ | 11 | cmlldHkiLCAibGluZW51bSIgPT4gNjc2LCBJbnB1dHMgPT4ge1NQQU57VFR7IkkifSwiLCAiLFNQ |
| Offset 90, 41 lines modified | Offset 90, 41 lines modified | ||
| 90 | i22·:·peek·last·ms | 90 | i22·:·peek·last·ms |
| 91 | o22·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 91 | o22·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 92 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 92 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 93 | ·······················2·=>·{ideal·0} | 93 | ·······················2·=>·{ideal·0} |
| 94 | i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") | 94 | i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") |
| 95 | ·--·used·1.6 | 95 | ·--·used·1.86284s·(cpu);·1.04569s·(thread);·0s·(gc) |
| 96 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 96 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 97 | o23·:·List | 97 | o23·:·List |
| 98 | i24·:·peek·last·ms | 98 | i24·:·peek·last·ms |
| 99 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 99 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 100 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 100 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 101 | ·······················2·=>·{ideal·0} | 101 | ·······················2·=>·{ideal·0} |
| 102 | i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") | 102 | i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") |
| 103 | ·--·used·17. | 103 | ·--·used·17.071s·(cpu);·4.07349s·(thread);·0s·(gc) |
| 104 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 104 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 105 | o25·:·List | 105 | o25·:·List |
| 106 | i26·:·peek·last·ms | 106 | i26·:·peek·last·ms |
| 107 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 107 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 108 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 108 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 109 | ·······················2·=>·{ideal·0} | 109 | ·······················2·=>·{ideal·0} |
| 110 | i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") | 110 | i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") |
| 111 | ·--·used·1 | 111 | ·--·used·18.8037s·(cpu);·4.40751s·(thread);·0s·(gc) |
| 112 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 112 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 113 | o27·:·List | 113 | o27·:·List |
| 114 | i28·:·peek·last·ms | 114 | i28·:·peek·last·ms |
| Offset 222, 45 lines modified | Offset 222, 45 lines modified | ||
| 222 | ········</table> | 222 | ········</table> |
| 223 | ········<div> | 223 | ········<div> |
| 224 | ··········<p>Finally·we·remark·that·the·option:·StratsToFind,·may·be·used·with·this·function,·but·should·only·be·used·with·care.·The·default·setting·is·StratsToFind=>"all",·and·this·is·the·only·value·of·the·option·which·is·guaranteed·to·compute·the·complete·stratification,·the·other·options·may·fail·to·find·all·strata·but·are·provided·to·allow·the·user·to·obtain·partial·information·on·larger·examples·which·may·take·too·long·to·run·on·the·default·"all"·setting.·The·other·possible·values·are·StratsToFind=>"singularOnly",·and·StratsToFind=>"most".·The·option··StratsToFind=>"singularOnly"·is·the·fastest,·but·also·the·most·likely·to·return·incomplete·answers,·and·hence·the·output·of·this·command·should·be·treated·as·a·partial·answer·only.·The·option·StratsToFind=>"most"·will·most·often·get·the·full·answer,·but·can·miss·strata,·so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below·all·options·return·the·complete·answer,·but·only·the·output·with·StratsToFind=>"all"·should·be·considered·complete;·StratsToFind=>"all"·is·run·when·no·option·is·given.</p> | 224 | ··········<p>Finally·we·remark·that·the·option:·StratsToFind,·may·be·used·with·this·function,·but·should·only·be·used·with·care.·The·default·setting·is·StratsToFind=>"all",·and·this·is·the·only·value·of·the·option·which·is·guaranteed·to·compute·the·complete·stratification,·the·other·options·may·fail·to·find·all·strata·but·are·provided·to·allow·the·user·to·obtain·partial·information·on·larger·examples·which·may·take·too·long·to·run·on·the·default·"all"·setting.·The·other·possible·values·are·StratsToFind=>"singularOnly",·and·StratsToFind=>"most".·The·option··StratsToFind=>"singularOnly"·is·the·fastest,·but·also·the·most·likely·to·return·incomplete·answers,·and·hence·the·output·of·this·command·should·be·treated·as·a·partial·answer·only.·The·option·StratsToFind=>"most"·will·most·often·get·the·full·answer,·but·can·miss·strata,·so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below·all·options·return·the·complete·answer,·but·only·the·output·with·StratsToFind=>"all"·should·be·considered·complete;·StratsToFind=>"all"·is·run·when·no·option·is·given.</p> |
| 225 | ········</div> | 225 | ········</div> |
| 226 | ········<table·class="examples"> | 226 | ········<table·class="examples"> |
| 227 | ··········<tr> | 227 | ··········<tr> |
| 228 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") | 228 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") |
| 229 | ·--·used·1.6 | 229 | ·--·used·1.86284s·(cpu);·1.04569s·(thread);·0s·(gc) |
| 230 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 230 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 231 | o23·:·List</code></pre> | 231 | o23·:·List</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| 233 | ··········<tr> | 233 | ··········<tr> |
| 234 | <td>··············<pre><code·class="language-macaulay2">i24·:·peek·last·ms | 234 | <td>··············<pre><code·class="language-macaulay2">i24·:·peek·last·ms |
| 235 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 235 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 236 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 236 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 237 | ·······················2·=>·{ideal·0}</code></pre> | 237 | ·······················2·=>·{ideal·0}</code></pre> |
| 238 | </td>··········</tr> | 238 | </td>··········</tr> |
| 239 | ··········<tr> | 239 | ··········<tr> |
| 240 | <td>··············<pre><code·class="language-macaulay2">i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") | 240 | <td>··············<pre><code·class="language-macaulay2">i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") |
| 241 | ·--·used·17. | 241 | ·--·used·17.071s·(cpu);·4.07349s·(thread);·0s·(gc) |
| 242 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 242 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 243 | o25·:·List</code></pre> | 243 | o25·:·List</code></pre> |
| 244 | </td>··········</tr> | 244 | </td>··········</tr> |
| 245 | ··········<tr> | 245 | ··········<tr> |
| 246 | <td>··············<pre><code·class="language-macaulay2">i26·:·peek·last·ms | 246 | <td>··············<pre><code·class="language-macaulay2">i26·:·peek·last·ms |
| 247 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 247 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 248 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 248 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 249 | ·······················2·=>·{ideal·0}</code></pre> | 249 | ·······················2·=>·{ideal·0}</code></pre> |
| 250 | </td>··········</tr> | 250 | </td>··········</tr> |
| 251 | ··········<tr> | 251 | ··········<tr> |
| 252 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") | 252 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") |
| 253 | ·--·used·1 | 253 | ·--·used·18.8037s·(cpu);·4.40751s·(thread);·0s·(gc) |
| 254 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 254 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 255 | o27·:·List</code></pre> | 255 | o27·:·List</code></pre> |
| 256 | </td>··········</tr> | 256 | </td>··········</tr> |
| 257 | ··········<tr> | 257 | ··········<tr> |
| 258 | <td>··············<pre><code·class="language-macaulay2">i28·:·peek·last·ms | 258 | <td>··············<pre><code·class="language-macaulay2">i28·:·peek·last·ms |
| Offset 149, 37 lines modified | Offset 149, 37 lines modified | ||
| 149 | this·command·should·be·treated·as·a·partial·answer·only.·The·option | 149 | this·command·should·be·treated·as·a·partial·answer·only.·The·option |
| 150 | StratsToFind=>"most"·will·most·often·get·the·full·answer,·but·can·miss·strata, | 150 | StratsToFind=>"most"·will·most·often·get·the·full·answer,·but·can·miss·strata, |
| 151 | so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below | 151 | so·again·the·output·should·be·treated·as·a·partial·answer.·In·the·example·below |
| 152 | all·options·return·the·complete·answer,·but·only·the·output·with | 152 | all·options·return·the·complete·answer,·but·only·the·output·with |
| 153 | StratsToFind=>"all"·should·be·considered·complete;·StratsToFind=>"all"·is·run | 153 | StratsToFind=>"all"·should·be·considered·complete;·StratsToFind=>"all"·is·run |
| 154 | when·no·option·is·given. | 154 | when·no·option·is·given. |
| 155 | i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") | 155 | i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") |
| 156 | ·--·used·1.6 | 156 | ·--·used·1.86284s·(cpu);·1.04569s·(thread);·0s·(gc) |
| 157 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 157 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 158 | o23·:·List | 158 | o23·:·List |
| 159 | i24·:·peek·last·ms | 159 | i24·:·peek·last·ms |
| 160 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 160 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 161 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 161 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 162 | ·······················2·=>·{ideal·0} | 162 | ·······················2·=>·{ideal·0} |
| 163 | i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") | 163 | i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") |
| 164 | ·--·used·17. | 164 | ·--·used·17.071s·(cpu);·4.07349s·(thread);·0s·(gc) |
| 165 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 165 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 166 | o25·:·List | 166 | o25·:·List |
| 167 | i26·:·peek·last·ms | 167 | i26·:·peek·last·ms |
| 168 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 168 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 169 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 169 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 170 | ·······················2·=>·{ideal·0} | 170 | ·······················2·=>·{ideal·0} |
| 171 | i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") | 171 | i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") |
| 172 | ·--·used·1 | 172 | ·--·used·18.8037s·(cpu);·4.40751s·(thread);·0s·(gc) |
| 173 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 173 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 174 | o27·:·List | 174 | o27·:·List |
| 175 | i28·:·peek·last·ms | 175 | i28·:·peek·last·ms |
| 176 | o28·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 176 | o28·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=25 | 7 | #:len=25 |
| 8 | Z2V0QXR0cmlidXRlcyhMaWJ4bWxOb2RlKQ== | 8 | Z2V0QXR0cmlidXRlcyhMaWJ4bWxOb2RlKQ== |
| 9 | #:len=465 | 9 | #:len=465 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZ2V0IHRoZSBsaXN0IG9mIGF0dHJpYnV0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZ2V0IHRoZSBsaXN0IG9mIGF0dHJpYnV0 |
| 11 | ZXMgb2YgYW4gWE1MIG5vZGUiLCBEZXNjcmlwdGlvbiA9PiAxOihUQUJMRXsiY2xhc3MiID0+ICJl | 11 | ZXMgb2YgYW4gWE1MIG5vZGUiLCBEZXNjcmlwdGlvbiA9PiAxOihUQUJMRXsiY2xhc3MiID0+ICJl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·S | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
| 4 | #:uid= | 4 | #:uid=2222,user=pbuilder2,gid=2222,group=pbuilder2,mode=644 |
| 5 | #:format=standard | 5 | #:format=standard |
| 6 | #·End·of·header | 6 | #·End·of·header |
| 7 | #:len=33 | 7 | #:len=33 |
| 8 | Z2ZhblBvbHlub21pYWxTZXRVbmlvbihMaXN0LExpc3Qp | 8 | Z2ZhblBvbHlub21pYWxTZXRVbmlvbihMaXN0LExpc3Qp |
| 9 | #:len=309 | 9 | #:len=309 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzY0Miwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzY0Miwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2ZhblBvbHlub21pYWxTZXRVbmlvbixMaXN0LExp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoZ2ZhblBvbHlub21pYWxTZXRVbmlvbixMaXN0LExp |
| Offset 17, 15 lines modified | Offset 17, 15 lines modified | ||
| 17 | i4·:·prefixDirectory·|·currentLayout#"programs" | 17 | i4·:·prefixDirectory·|·currentLayout#"programs" |
| 18 | o4·=·/usr/x86_64-Linux- | 18 | o4·=·/usr/x86_64-Linux- |
| 19 | ·····Debian-trixie/libexec/Macaulay2/bin/ | 19 | ·····Debian-trixie/libexec/Macaulay2/bin/ |
| 20 | i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true); | 20 | i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true); |
| 21 | ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2- | 21 | ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-3604690-0/172 |
| 22 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm. | 22 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm. |
| 23 | Options: | 23 | Options: |
| 24 | -g: | 24 | -g: |
| 25 | ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis. | 25 | ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis. |
| 26 | --symmetry: | 26 | --symmetry: |
| 27 | ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup. | 27 | ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup. |
| Offset 36, 16 lines modified | Offset 36, 16 lines modified | ||
| 36 | --disableSymmetryTest: | 36 | --disableSymmetryTest: |
| 37 | ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal. | 37 | ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal. |
| 38 | --parameters·value: | 38 | --parameters·value: |
| 39 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 39 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 40 | --interrupt·value: | 40 | --interrupt·value: |
| 41 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans). | 41 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans). |
| 42 | using·temporary·file·/tmp/M2- | 42 | using·temporary·file·/tmp/M2-3604690-0/172 |
| 43 | ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2- | 43 | ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-3604690-0/174 |
| 44 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]). | 44 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]). |
| 45 | Options: | 45 | Options: |
| 46 | -w: | 46 | -w: |
| 47 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read. | 47 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read. |
| 48 | -r: | 48 | -r: |
| 49 | ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used. | 49 | ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used. |
| Offset 54, 69 lines modified | Offset 54, 69 lines modified | ||
| 54 | ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored. | 54 | ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored. |
| 55 | -g: | 55 | -g: |
| 56 | ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. | 56 | ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. |
| 57 | --parameters·value: | 57 | --parameters·value: |
| 58 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 58 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 59 | using·temporary·file·/tmp/M2- | 59 | using·temporary·file·/tmp/M2-3604690-0/174 |
| 60 | ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2- | 60 | ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-3604690-0/176 |
| 61 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false. | 61 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false. |
| 62 | Options: | 62 | Options: |
| 63 | --remainder: | 63 | --remainder: |
| 64 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. | 64 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. |
| 65 | --multiplier: | 65 | --multiplier: |
| 66 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. | 66 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. |
| 67 | using·temporary·file·/tmp/M2- | 67 | using·temporary·file·/tmp/M2-3604690-0/176 |
| 68 | ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2- | 68 | ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-3604690-0/178 |
| 69 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. | 69 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. |
| 70 | Options: | 70 | Options: |
| 71 | -i1·value: | 71 | -i1·value: |
| 72 | ·Specify·the·name·of·the·first·input·file. | 72 | ·Specify·the·name·of·the·first·input·file. |
| 73 | -i2·value: | 73 | -i2·value: |
| 74 | ·Specify·the·name·of·the·second·input·file. | 74 | ·Specify·the·name·of·the·second·input·file. |
| 75 | --stable: | 75 | --stable: |
| 76 | ·Compute·the·stable·intersection. | 76 | ·Compute·the·stable·intersection. |
| 77 | using·temporary·file·/tmp/M2- | 77 | using·temporary·file·/tmp/M2-3604690-0/178 |
| 78 | ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2- | 78 | ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-3604690-0/180 |
| 79 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector. | 79 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector. |
| 80 | Options: | 80 | Options: |
| 81 | -i·value: | 81 | -i·value: |
| 82 | ·Specify·the·name·of·the·input·file. | 82 | ·Specify·the·name·of·the·input·file. |
| 83 | --symmetry: | 83 | --symmetry: |
| 84 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. | 84 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. |
| 85 | --star: | 85 | --star: |
| 86 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. | 86 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. |
| 87 | using·temporary·file·/tmp/M2- | 87 | using·temporary·file·/tmp/M2-3604690-0/180 |
| 88 | ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2- | 88 | ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-3604690-0/182 |
| 89 | This·program·takes·two·polyhedral·fans·and·computes·their·product. | 89 | This·program·takes·two·polyhedral·fans·and·computes·their·product. |
| 90 | Options: | 90 | Options: |
| 91 | -i1·value: | 91 | -i1·value: |
| 92 | ·Specify·the·name·of·the·first·input·file. | 92 | ·Specify·the·name·of·the·first·input·file. |
| 93 | -i2·value: | 93 | -i2·value: |
| 94 | ·Specify·the·name·of·the·second·input·file. | 94 | ·Specify·the·name·of·the·second·input·file. |
| 95 | using·temporary·file·/tmp/M2- | 95 | using·temporary·file·/tmp/M2-3604690-0/182 |
| 96 | ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2- | 96 | ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-3604690-0/184 |
| 97 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS. | 97 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS. |
| 98 | Options: | 98 | Options: |
| 99 | --restrict: | 99 | --restrict: |
| 100 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. | 100 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. |
| 101 | --pair: | 101 | --pair: |
| 102 | ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual. | 102 | ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual. |
| 103 | --asfan: | 103 | --asfan: |
| 104 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. | 104 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. |
| 105 | --vectorinput: | 105 | --vectorinput: |
| 106 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations. | 106 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations. |
| 107 | using·temporary·file·/tmp/M2- | 107 | using·temporary·file·/tmp/M2-3604690-0/184 |
| 108 | ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2- | 108 | ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-3604690-0/186 |
| 109 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose. | 109 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose. |
| 110 | Options: | 110 | Options: |
| 111 | using·temporary·file·/tmp/M2- | 111 | using·temporary·file·/tmp/M2-3604690-0/186 |
| 112 | ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2- | 112 | ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-3604690-0/188 |
| 113 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree. | 113 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree. |
| 114 | Example: | 114 | Example: |
| 115 | Input: | 115 | Input: |
| 116 | Q[x,y]{y-1} | 116 | Q[x,y]{y-1} |
| 117 | z | 117 | z |
| 118 | Output: | 118 | Output: |
| 119 | Q[x,y,z]{y-z} | 119 | Q[x,y,z]{y-z} |
| Offset 124, 30 lines modified | Offset 124, 30 lines modified | ||
| 124 | -i: | 124 | -i: |
| 125 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it. | 125 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it. |
| 126 | -w: | 126 | -w: |
| 127 | ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials. | 127 | ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials. |
| 128 | -H: | 128 | -H: |
| 129 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. | 129 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. |
| 130 | using·temporary·file·/tmp/M2- | 130 | using·temporary·file·/tmp/M2-3604690-0/188 |
| 131 | ·--·running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2- | 131 | ·--·running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2-3604690-0/190 |
| 132 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. | 132 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. |
| 133 | Options: | 133 | Options: |
| 134 | --ideal: | 134 | --ideal: |
| 135 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program. | 135 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program. |
| 136 | --pair: | 136 | --pair: |
| 137 | ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal. | 137 | ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal. |
| 138 | --mark: | 138 | --mark: |
| 139 | ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector. | 139 | ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector. |
| 140 | --list: | 140 | --list: |
| 141 | ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output. | 141 | ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output. |
| 142 | using·temporary·file·/tmp/M2- | 142 | using·temporary·file·/tmp/M2-3604690-0/190 |
| 143 | ·--·running:·/usr/bin/gfan·_interactive·--help·<·/tmp/M2- | 143 | ·--·running:·/usr/bin/gfan·_interactive·--help·<·/tmp/M2-3604690-0/192 |
| 144 | This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program. | 144 | This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program. |
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| Offset 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ········<div> | 91 | ········<div> |
| 92 | ··········<p>If·you·would·like·to·see·the·input·and·output·files·used·to·communicate·with·<span·class="tt">gfan</span>·you·can·set·the·<span·class="tt">"keepfiles"</span>·configuration·option·to·<span·class="tt">true</span>.·If·<span·class="tt">"verbose"</span>·is·set·to·<span·class="tt">true</span>,·<span·class="tt">gfanInterface</span>·will·output·the·names·of·the·temporary·files·used.</p> | 92 | ··········<p>If·you·would·like·to·see·the·input·and·output·files·used·to·communicate·with·<span·class="tt">gfan</span>·you·can·set·the·<span·class="tt">"keepfiles"</span>·configuration·option·to·<span·class="tt">true</span>.·If·<span·class="tt">"verbose"</span>·is·set·to·<span·class="tt">true</span>,·<span·class="tt">gfanInterface</span>·will·output·the·names·of·the·temporary·files·used.</p> |
| 93 | ··········<p></p> | 93 | ··········<p></p> |
| 94 | ········</div> | 94 | ········</div> |
| 95 | ········<table·class="examples"> | 95 | ········<table·class="examples"> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true); | 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true); |
| 98 | ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2- | 98 | ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-3604690-0/172 |
| 99 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm. | 99 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial·ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By·default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the·ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done·up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting·Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it·will·compute·one·using·Buchberger's·algorithm. |
| 100 | Options: | 100 | Options: |
| 101 | -g: | 101 | -g: |
| 102 | ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis. | 102 | ·Tells·the·program·that·the·input·is·already·a·Groebner·basis·(with·the·initial·term·of·each·polynomial·being·the·first·ones·listed).·Use·this·option·if·it·takes·too·much·time·to·compute·the·starting·(standard·degree·lexicographic)·Groebner·basis·and·the·input·is·already·a·Groebner·basis. |
| 103 | --symmetry: | 103 | --symmetry: |
| 104 | ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup. | 104 | ·Tells·the·program·to·read·in·generators·for·a·group·of·symmetries·(subgroup·of·$S_n$)·after·having·read·in·the·ideal.·The·program·checks·that·the·ideal·stays·fixed·when·permuting·the·variables·with·respect·to·elements·in·the·group.·The·program·uses·breadth·first·search·to·compute·the·set·of·reduced·Groebner·bases·up·to·symmetry·with·respect·to·the·specified·subgroup. |
| Offset 110, 16 lines modified | Offset 110, 16 lines modified | ||
| 110 | --disableSymmetryTest: | 110 | --disableSymmetryTest: |
| 111 | ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal. | 111 | ·When·using·--symmetry·this·option·will·disable·the·check·that·the·group·read·off·from·the·input·actually·is·a·symmetry·group·with·respect·to·the·input·ideal. |
| 112 | --parameters·value: | 112 | --parameters·value: |
| 113 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 113 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 114 | --interrupt·value: | 114 | --interrupt·value: |
| 115 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans). | 115 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been·computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for·non-symmetric·traversals·or·for·traversals·restricted·to·fans). |
| 116 | using·temporary·file·/tmp/M2- | 116 | using·temporary·file·/tmp/M2-3604690-0/172 |
| 117 | ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2- | 117 | ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-3604690-0/174 |
| 118 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]). | 118 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial·ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm.·The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q[a,b,c,...]). |
| 119 | Options: | 119 | Options: |
| 120 | -w: | 120 | -w: |
| 121 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read. | 121 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with·$a>b>c...$·instead.·The·degrees·are·given·by·a·weight·vector·which·is·read·from·the·input·after·the·generating·set·has·been·read. |
| 122 | -r: | 122 | -r: |
| 123 | ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used. | 123 | ·Use·the·reverse·lexicographic·order·(or·the·reverse·lexicographic·order·as·a·tie·breaker·if·-w·is·used).·The·input·must·be·homogeneous·if·the·pure·reverse·lexicographic·order·is·chosen.·Ignored·if·-W·is·used. |
| Offset 128, 69 lines modified | Offset 128, 69 lines modified | ||
| 128 | ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored. | 128 | ·Do·a·Groebner·walk.·The·input·must·be·a·minimal·Groebner·basis.·If·-W·is·used·-w·is·ignored. |
| 129 | -g: | 129 | -g: |
| 130 | ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. | 130 | ·Do·a·generic·Groebner·walk.·The·input·must·be·homogeneous·and·must·be·a·minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order.·The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. |
| 131 | --parameters·value: | 131 | --parameters·value: |
| 132 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 132 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters·instead·of·variables.·This·makes·it·possible·to·do·computations·where·the·coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 133 | using·temporary·file·/tmp/M2- | 133 | using·temporary·file·/tmp/M2-3604690-0/174 |
| 134 | ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2- | 134 | ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-3604690-0/176 |
| 135 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false. | 135 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of·polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by·applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and·0·for·false. |
| 136 | Options: | 136 | Options: |
| 137 | --remainder: | 137 | --remainder: |
| 138 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. | 138 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. |
| 139 | --multiplier: | 139 | --multiplier: |
| 140 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. | 140 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. |
| 141 | using·temporary·file·/tmp/M2- | 141 | using·temporary·file·/tmp/M2-3604690-0/176 |
| 142 | ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2- | 142 | ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-3604690-0/178 |
| 143 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. | 143 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. |
| 144 | Options: | 144 | Options: |
| 145 | -i1·value: | 145 | -i1·value: |
| 146 | ·Specify·the·name·of·the·first·input·file. | 146 | ·Specify·the·name·of·the·first·input·file. |
| 147 | -i2·value: | 147 | -i2·value: |
| 148 | ·Specify·the·name·of·the·second·input·file. | 148 | ·Specify·the·name·of·the·second·input·file. |
| 149 | --stable: | 149 | --stable: |
| 150 | ·Compute·the·stable·intersection. | 150 | ·Compute·the·stable·intersection. |
| 151 | using·temporary·file·/tmp/M2- | 151 | using·temporary·file·/tmp/M2-3604690-0/178 |
| 152 | ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2- | 152 | ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-3604690-0/180 |
| 153 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector. | 153 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the·polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension·equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan·containing·the·vector. |
| 154 | Options: | 154 | Options: |
| 155 | -i·value: | 155 | -i·value: |
| 156 | ·Specify·the·name·of·the·input·file. | 156 | ·Specify·the·name·of·the·input·file. |
| 157 | --symmetry: | 157 | --symmetry: |
| 158 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. | 158 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. |
| 159 | --star: | 159 | --star: |
| 160 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. | 160 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. |
| 161 | using·temporary·file·/tmp/M2- | 161 | using·temporary·file·/tmp/M2-3604690-0/180 |
| 162 | ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2- | 162 | ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-3604690-0/182 |
| 163 | This·program·takes·two·polyhedral·fans·and·computes·their·product. | 163 | This·program·takes·two·polyhedral·fans·and·computes·their·product. |
| 164 | Options: | 164 | Options: |
| 165 | -i1·value: | 165 | -i1·value: |
| 166 | ·Specify·the·name·of·the·first·input·file. | 166 | ·Specify·the·name·of·the·first·input·file. |
| 167 | -i2·value: | 167 | -i2·value: |
| 168 | ·Specify·the·name·of·the·second·input·file. | 168 | ·Specify·the·name·of·the·second·input·file. |
| 169 | using·temporary·file·/tmp/M2- | 169 | using·temporary·file·/tmp/M2-3604690-0/182 |
| 170 | ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2- | 170 | ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-3604690-0/184 |
| 171 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS. | 171 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The·input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is·computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone·computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones·are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case·is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of·Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair.·The·facets·of·the·cone·can·be·read·off·in·section·FACETS·and·the·equations·in·section·IMPLIED_EQUATIONS. |
| 172 | Options: | 172 | Options: |
| 173 | --restrict: | 173 | --restrict: |
| 174 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. | 174 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. |
| 175 | --pair: | 175 | --pair: |
| 176 | ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual. | 176 | ·The·Groebner·cone·is·given·by·a·pair·of·compatible·Groebner·bases.·The·first·basis·is·for·the·initial·ideal·and·the·second·for·the·ideal·itself.·See·the·tropical·section·of·the·manual. |
| 177 | --asfan: | 177 | --asfan: |
| 178 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. | 178 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. |
| 179 | --vectorinput: | 179 | --vectorinput: |
| 180 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations. | 180 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The·input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list·of·inequalities·given·as·vectors·and·a·list·of·equations. |
| 181 | using·temporary·file·/tmp/M2- | 181 | using·temporary·file·/tmp/M2-3604690-0/184 |
| 182 | ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2- | 182 | ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-3604690-0/186 |
| 183 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose. | 183 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a·cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section·LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first·compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A·reduced·Groebner·basis·will·always·suffice·for·this·purpose. |
| 184 | Options: | 184 | Options: |
| 185 | using·temporary·file·/tmp/M2- | 185 | using·temporary·file·/tmp/M2-3604690-0/186 |
| 186 | ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2- | 186 | ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-3604690-0/188 |
| 187 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree. | 187 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra·variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input·after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done·with·respect·to·total·degree. |
| 188 | Example: | 188 | Example: |
| 189 | Input: | 189 | Input: |
| 190 | Q[x,y]{y-1} | 190 | Q[x,y]{y-1} |
| 191 | z | 191 | z |
| 192 | Output: | 192 | Output: |
| 193 | Q[x,y,z]{y-z} | 193 | Q[x,y,z]{y-z} |
| Offset 198, 30 lines modified | Offset 198, 30 lines modified | ||
| 198 | -i: | 198 | -i: |
| 199 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it. | 199 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·homogenisation·of·the·input·ideal.·This·is·done·by·computing·a·degree·Groebner·basis·and·homogenising·it. |
| 200 | -w: | 200 | -w: |
| 201 | ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials. | 201 | ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as·the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after·the·list·of·polynomials. |
| 202 | -H: | 202 | -H: |
| 203 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. | 203 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. |
| 204 | using·temporary·file·/tmp/M2- | 204 | using·temporary·file·/tmp/M2-3604690-0/188 |
| 205 | ·--·running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2- | 205 | ·--·running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2-3604690-0/190 |
| 206 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. | 206 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. |
| 207 | Options: | 207 | Options: |
| 208 | --ideal: | 208 | --ideal: |
| 209 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program. | 209 | ·Treat·input·as·an·ideal.·This·will·make·the·program·compute·the·initial·ideal·of·the·ideal·generated·by·the·input·polynomials.·The·computation·is·done·by·computing·a·Groebner·basis·with·respect·to·the·given·vector.·The·vector·must·be·positive·or·the·input·polynomials·must·be·homogeneous·in·a·positive·grading.·None·of·these·conditions·are·checked·by·the·program. |
| 210 | --pair: | 210 | --pair: |
| 211 | ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal. | 211 | ·Produce·a·pair·of·polynomial·lists.·Used·together·with·--ideal·this·option·will·also·write·a·compatible·reduced·Groebner·basis·for·the·input·ideal·to·the·output.·This·is·useful·for·finding·the·Groebner·cone·of·a·non-monomial·initial·ideal. |
| 212 | --mark: | 212 | --mark: |
| 213 | ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector. | 213 | ·If·the·--pair·option·is·and·the·--ideal·option·is·not·used·this·option·will·still·make·sure·that·the·second·output·basis·is·marked·consistently·with·the·vector. |
| 214 | --list: | 214 | --list: |
| 215 | ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output. | 215 | ·Read·in·a·list·of·vectors·instead·of·a·single·vector·and·produce·a·list·of·polynomial·sets·as·output. |
| 216 | using·temporary·file·/tmp/M2- | 216 | using·temporary·file·/tmp/M2-3604690-0/190 |
| 217 | ·--·running:·/usr/bin/gfan·_interactive·--help·<·/tmp/M2- | 217 | ·--·running:·/usr/bin/gfan·_interactive·--help·<·/tmp/M2-3604690-0/192 |
| 218 | This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program. | 218 | This·is·a·program·for·doing·interactive·walks·in·the·Groebner·fan·of·an·ideal.·The·input·is·a·Groebner·basis·defining·the·starting·Groebner·cone·of·the·walk.·The·program·will·list·all·flippable·facets·of·the·Groebner·cone·and·ask·the·user·to·choose·one.·The·user·types·in·the·index·(number)·of·the·facet·in·the·list.·The·program·will·walk·through·the·selected·facet·and·display·the·new·Groebner·basis·and·a·list·of·new·facet·normals·for·the·user·to·choose·from.·Since·the·program·reads·the·user's·choices·through·the·the·standard·input·it·is·recommended·not·to·redirect·the·standard·input·for·this·program. |
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| 39 | o4·=·/usr/x86_64-Linux- | 39 | o4·=·/usr/x86_64-Linux- |
| 40 | ·····Debian-trixie/libexec/Macaulay2/bin/ | 40 | ·····Debian-trixie/libexec/Macaulay2/bin/ |
| 41 | If·you·would·like·to·see·the·input·and·output·files·used·to·communicate·with | 41 | If·you·would·like·to·see·the·input·and·output·files·used·to·communicate·with |
| 42 | gfan·you·can·set·the·"keepfiles"·configuration·option·to·true.·If·"verbose"·is | 42 | gfan·you·can·set·the·"keepfiles"·configuration·option·to·true.·If·"verbose"·is |
| 43 | set·to·true,·gfanInterface·will·output·the·names·of·the·temporary·files·used. | 43 | set·to·true,·gfanInterface·will·output·the·names·of·the·temporary·files·used. |
| 44 | i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true, | 44 | i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true, |
| 45 | "verbose"·=>·true},·Reload·=>·true); | 45 | "verbose"·=>·true},·Reload·=>·true); |
| 46 | ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2- | 46 | ·--·running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-3604690-0/172 |
| 47 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial | 47 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial |
| 48 | ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By | 48 | ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By |
| 49 | default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the | 49 | default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the |
| 50 | ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done | 50 | ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done |
| 51 | up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting | 51 | up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting |
| 52 | Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it | 52 | Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it |
| 53 | will·compute·one·using·Buchberger's·algorithm. | 53 | will·compute·one·using·Buchberger's·algorithm. |
| Offset 77, 16 lines modified | Offset 77, 16 lines modified | ||
| 77 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters | 77 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters |
| 78 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the | 78 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the |
| 79 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 79 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 80 | --interrupt·value: | 80 | --interrupt·value: |
| 81 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been | 81 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been |
| 82 | computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for | 82 | computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for |
| 83 | non-symmetric·traversals·or·for·traversals·restricted·to·fans). | 83 | non-symmetric·traversals·or·for·traversals·restricted·to·fans). |
| 84 | using·temporary·file·/tmp/M2- | 84 | using·temporary·file·/tmp/M2-3604690-0/172 |
| 85 | ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2- | 85 | ·--·running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-3604690-0/174 |
| 86 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial | 86 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial |
| 87 | ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm. | 87 | ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm. |
| 88 | The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q | 88 | The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q |
| 89 | [a,b,c,...]). | 89 | [a,b,c,...]). |
| 90 | Options: | 90 | Options: |
| 91 | -w: | 91 | -w: |
| 92 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with | 92 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with |
| Offset 107, 63 lines modified | Offset 107, 63 lines modified | ||
| 107 | minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order. | 107 | minimal·Groebner·basis·with·respect·to·the·reverse·lexicographic·term·order. |
| 108 | The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. | 108 | The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. |
| 109 | --parameters·value: | 109 | --parameters·value: |
| 110 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters | 110 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters |
| 111 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the | 111 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the |
| 112 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 112 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 113 | using·temporary·file·/tmp/M2- | 113 | using·temporary·file·/tmp/M2-3604690-0/174 |
| 114 | ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2- | 114 | ·--·running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-3604690-0/176 |
| 115 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of | 115 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of |
| 116 | polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by | 116 | polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by |
| 117 | applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and | 117 | applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and |
| 118 | 0·for·false. | 118 | 0·for·false. |
| 119 | Options: | 119 | Options: |
| 120 | --remainder: | 120 | --remainder: |
| 121 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than | 121 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than |
| 122 | outputting·0·or·1. | 122 | outputting·0·or·1. |
| 123 | --multiplier: | 123 | --multiplier: |
| 124 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided | 124 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided |
| 125 | before·doing·the·division. | 125 | before·doing·the·division. |
| 126 | using·temporary·file·/tmp/M2- | 126 | using·temporary·file·/tmp/M2-3604690-0/176 |
| 127 | ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2- | 127 | ·--·running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-3604690-0/178 |
| 128 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. | 128 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. |
| 129 | Options: | 129 | Options: |
| 130 | -i1·value: | 130 | -i1·value: |
| 131 | ·Specify·the·name·of·the·first·input·file. | 131 | ·Specify·the·name·of·the·first·input·file. |
| 132 | -i2·value: | 132 | -i2·value: |
| 133 | ·Specify·the·name·of·the·second·input·file. | 133 | ·Specify·the·name·of·the·second·input·file. |
| 134 | --stable: | 134 | --stable: |
| 135 | ·Compute·the·stable·intersection. | 135 | ·Compute·the·stable·intersection. |
| 136 | using·temporary·file·/tmp/M2- | 136 | using·temporary·file·/tmp/M2-3604690-0/178 |
| 137 | ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2- | 137 | ·--·running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-3604690-0/180 |
| 138 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the | 138 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the |
| 139 | polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension | 139 | polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension |
| 140 | equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan | 140 | equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan |
| 141 | containing·the·vector. | 141 | containing·the·vector. |
| 142 | Options: | 142 | Options: |
| 143 | -i·value: | 143 | -i·value: |
| 144 | ·Specify·the·name·of·the·input·file. | 144 | ·Specify·the·name·of·the·input·file. |
| 145 | --symmetry: | 145 | --symmetry: |
| 146 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must | 146 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must |
| 147 | be·given·on·the·standard·input. | 147 | be·given·on·the·standard·input. |
| 148 | --star: | 148 | --star: |
| 149 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan | 149 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan |
| 150 | containing·all·cones·of·the·original·fan·containing·the·vector. | 150 | containing·all·cones·of·the·original·fan·containing·the·vector. |
| 151 | using·temporary·file·/tmp/M2- | 151 | using·temporary·file·/tmp/M2-3604690-0/180 |
| 152 | ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2- | 152 | ·--·running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-3604690-0/182 |
| 153 | This·program·takes·two·polyhedral·fans·and·computes·their·product. | 153 | This·program·takes·two·polyhedral·fans·and·computes·their·product. |
| 154 | Options: | 154 | Options: |
| 155 | -i1·value: | 155 | -i1·value: |
| 156 | ·Specify·the·name·of·the·first·input·file. | 156 | ·Specify·the·name·of·the·first·input·file. |
| 157 | -i2·value: | 157 | -i2·value: |
| 158 | ·Specify·the·name·of·the·second·input·file. | 158 | ·Specify·the·name·of·the·second·input·file. |
| 159 | using·temporary·file·/tmp/M2- | 159 | using·temporary·file·/tmp/M2-3604690-0/182 |
| 160 | ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2- | 160 | ·--·running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-3604690-0/184 |
| 161 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The | 161 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The |
| 162 | input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is | 162 | input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is |
| 163 | computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone | 163 | computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone |
| 164 | computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones | 164 | computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones |
| 165 | are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case | 165 | are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case |
| 166 | is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of | 166 | is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of |
| 167 | Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair. | 167 | Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair. |
| Offset 180, 24 lines modified | Offset 180, 24 lines modified | ||
| 180 | --asfan: | 180 | --asfan: |
| 181 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way | 181 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way |
| 182 | the·extreme·rays·of·the·cone·are·also·computed. | 182 | the·extreme·rays·of·the·cone·are·also·computed. |
| 183 | --vectorinput: | 183 | --vectorinput: |
| 184 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The | 184 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The |
| 185 | input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list | 185 | input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list |
| 186 | of·inequalities·given·as·vectors·and·a·list·of·equations. | 186 | of·inequalities·given·as·vectors·and·a·list·of·equations. |
| 187 | using·temporary·file·/tmp/M2- | 187 | using·temporary·file·/tmp/M2-3604690-0/184 |
| 188 | ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2- | 188 | ·--·running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-3604690-0/186 |
| 189 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a | 189 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a |
| 190 | cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section | 190 | cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section |
| 191 | LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first | 191 | LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first |
| 192 | compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A | 192 | compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A |
| 193 | reduced·Groebner·basis·will·always·suffice·for·this·purpose. | 193 | reduced·Groebner·basis·will·always·suffice·for·this·purpose. |
| 194 | Options: | 194 | Options: |
| 195 | using·temporary·file·/tmp/M2- | 195 | using·temporary·file·/tmp/M2-3604690-0/186 |
| 196 | ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2- | 196 | ·--·running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-3604690-0/188 |
| 197 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra | 197 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra |
| 198 | variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input | 198 | variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input |
| 199 | after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done | 199 | after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done |
| 200 | with·respect·to·total·degree. | 200 | with·respect·to·total·degree. |
| 201 | Example: | 201 | Example: |
| 202 | Input: | 202 | Input: |
| 203 | Q[x,y]{y-1} | 203 | Q[x,y]{y-1} |
| Offset 213, 16 lines modified | Offset 213, 16 lines modified | ||
| 213 | ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as | 213 | ·Specify·a·homogenisation·vector.·The·length·of·the·vector·must·be·the·same·as |
| 214 | the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after | 214 | the·number·of·variables·in·the·ring.·The·vector·is·read·from·the·input·after |
| 215 | the·list·of·polynomials. | 215 | the·list·of·polynomials. |
| 216 | -H: | 216 | -H: |
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| Offset 6047, 16 lines modified | Offset 6047, 16 lines modified | ||
| 000179e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000179e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000179f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000179f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00017a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00017a10:·3320·3a20·656c·6170·7365·6454·696d·6520··3·:·elapsedTime· | 00017a10:·3320·3a20·656c·6170·7365·6454·696d·6520··3·:·elapsedTime· | ||
| 00017a20:·6275·726b·6552·6573·6f6c·7574·696f·6e28··burkeResolution( | 00017a20:·6275·726b·6552·6573·6f6c·7574·696f·6e28··burkeResolution( | ||
| 00017a30:·4d2c·2037·2c20·4368·6563·6b20·3d3e·2066··M,·7,·Check·=>·f | 00017a30:·4d2c·2037·2c20·4368·6563·6b20·3d3e·2066··M,·7,·Check·=>·f | ||
| 00017a40:·616c·7365·2920·2020·2020·2020·2020·2020··alse)··········· | 00017a40:·616c·7365·2920·2020·2020·2020·2020·2020··alse)··········· | ||
| 00017a50:·7c0a·7c20·2d2d·2031·2e3 | 00017a50:·7c0a·7c20·2d2d·2031·2e35·3437·3334·7320··|.|·--·1.54734s· | ||
| 00017a60:·6 | 00017a60:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00017a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017a90:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00017a90:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00017aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017ad0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00017ad0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
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| 00017c80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017c80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017ca0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017ca0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017cb0:·2d2d·2d2d·2b0a·7c69·3420·3a20·656c·6170··----+.|i4·:·elap | 00017cb0:·2d2d·2d2d·2b0a·7c69·3420·3a20·656c·6170··----+.|i4·:·elap | ||
| 00017cc0:·7365·6454·696d·6520·6275·726b·6552·6573··sedTime·burkeRes | 00017cc0:·7365·6454·696d·6520·6275·726b·6552·6573··sedTime·burkeRes | ||
| 00017cd0:·6f6c·7574·696f·6e28·4d2c·2037·2c20·4368··olution(M,·7,·Ch | 00017cd0:·6f6c·7574·696f·6e28·4d2c·2037·2c20·4368··olution(M,·7,·Ch | ||
| 00017ce0:·6563·6b20·3d3e·2074·7275·6529·2020·2020··eck·=>·true)···· | 00017ce0:·6563·6b20·3d3e·2074·7275·6529·2020·2020··eck·=>·true)···· | ||
| 00017cf0:·2020·2020·2020·2020·7c0a·7c20·2d2d·203 | 00017cf0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2032··········|.|·--·2 | ||
| 00017d00:·2e3 | 00017d00:·2e32·3739·3732·7320·656c·6170·7365·6420··.27972s·elapsed· | ||
| 00017d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017d30:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00017d30:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00017d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017d70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017d70:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00002ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | 00002ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | ||
| 00002af0:·3020·3a20·656c·6170·7365·6454·696d·6520··0·:·elapsedTime· | 00002af0:·3020·3a20·656c·6170·7365·6454·696d·6520··0·:·elapsedTime· | ||
| 00002b00:·6649·3d72·6573·2049·2020·2020·2020·2020··fI=res·I········ | 00002b00:·6649·3d72·6573·2049·2020·2020·2020·2020··fI=res·I········ | ||
| 00002b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002b30:·7c0a·7c20·2d2d·202e·303 | 00002b30:·7c0a·7c20·2d2d·202e·3032·3037·3337·3973··|.|·--·.0207379s | ||
| 00002b40:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 00002b40:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 00002b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002b60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002b60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002b70:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00002b70:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00002b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00005f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005f70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005f70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005f80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005f80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005f90:·2d2d·2d2d·2d2b·0a7c·6931·3520·3a20·656c··-----+.|i15·:·el | 00005f90:·2d2d·2d2d·2d2b·0a7c·6931·3520·3a20·656c··-----+.|i15·:·el | ||
| 00005fa0:·6170·7365·6454·696d·6520·6265·7474·6928··apsedTime·betti( | 00005fa0:·6170·7365·6454·696d·6520·6265·7474·6928··apsedTime·betti( | ||
| 00005fb0:·4927·3d74·7269·6d20·6b65·7220·7068·6929··I'=trim·ker·phi) | 00005fb0:·4927·3d74·7269·6d20·6b65·7220·7068·6929··I'=trim·ker·phi) | ||
| 00005fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005fd0:·7c0a·7c20·2d2d·202e·3 | 00005fd0:·7c0a·7c20·2d2d·202e·3531·3932·3333·7320··|.|·--·.519233s· | ||
| 00005fe0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 00005fe0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00005ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006000:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00006000:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00006010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006040:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00006040:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
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| 000062d0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 000062d0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 000062e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000062e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000062f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000062f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006300:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3137··----------+.|i17 | 00006300:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3137··----------+.|i17 | ||
| 00006310:·203a·2065·6c61·7073·6564·5469·6d65·2062···:·elapsedTime·b | 00006310:·203a·2065·6c61·7073·6564·5469·6d65·2062···:·elapsedTime·b | ||
| 00006320:·6173·6550·7473·3d70·7269·6d61·7279·4465··asePts=primaryDe | 00006320:·6173·6550·7473·3d70·7269·6d61·7279·4465··asePts=primaryDe | ||
| 00006330:·636f·6d70·6f73·6974·696f·6e20·6964·6561··composition·idea | 00006330:·636f·6d70·6f73·6974·696f·6e20·6964·6561··composition·idea | ||
| 00006340:·6c20·483b·207c·0a7c·202d·2d20·3 | 00006340:·6c20·483b·207c·0a7c·202d·2d20·352e·3437··l·H;·|.|·--·5.47 | ||
| 00006350:·3 | 00006350:·3873·2065·6c61·7073·6564·2020·2020·2020··8s·elapsed······ | ||
| 00006360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006380:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | 00006380:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00006390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000063a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000063a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000063b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | 000063b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | ||
| 000063c0:·3820·3a20·7461·6c6c·7920·6170·706c·7928··8·:·tally·apply( | 000063c0:·3820·3a20·7461·6c6c·7920·6170·706c·7928··8·:·tally·apply( | ||
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| 00009c50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009c50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009c60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009c60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009c70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009c70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009c80:·2d2b·0a7c·6931·3420·3a20·656c·6170·7365··-+.|i14·:·elapse | 00009c80:·2d2b·0a7c·6931·3420·3a20·656c·6170·7365··-+.|i14·:·elapse | ||
| 00009c90:·6454·696d·6520·7375·6228·492c·4829·2020··dTime·sub(I,H)·· | 00009c90:·6454·696d·6520·7375·6228·492c·4829·2020··dTime·sub(I,H)·· | ||
| 00009ca0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ca0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009cb0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00009cb0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00009cc0:·2d2d·202e·303 | 00009cc0:·2d2d·202e·3032·3735·3337·3773·2065·6c61··--·.0275377s·ela | ||
| 00009cd0:· | 00009cd0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 00009ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009cf0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00009cf0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00009d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009d30:·2020·7c0a·7c6f·3134·203d·2069·6465·616c····|.|o14·=·ideal | 00009d30:·2020·7c0a·7c6f·3134·203d·2069·6465·616c····|.|o14·=·ideal | ||
| 00009d40:·2028·302c·2030·2c20·302c·2030·2c20·302c···(0,·0,·0,·0,·0, | 00009d40:·2028·302c·2030·2c20·302c·2030·2c20·302c···(0,·0,·0,·0,·0, | ||
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| 00009ed0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00009ed0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00009ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009f00:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3136··----------+.|i16 | 00009f00:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3136··----------+.|i16 | ||
| 00009f10:·203a·2065·6c61·7073·6564·5469·6d65·2062···:·elapsedTime·b | 00009f10:·203a·2065·6c61·7073·6564·5469·6d65·2062···:·elapsedTime·b | ||
| 00009f20:·6574·7469·2849·273d·7472·696d·206b·6572··etti(I'=trim·ker | 00009f20:·6574·7469·2849·273d·7472·696d·206b·6572··etti(I'=trim·ker | ||
| 00009f30:·2070·6869·2920·2020·2020·2020·2020·2020···phi)··········· | 00009f30:·2070·6869·2920·2020·2020·2020·2020·2020···phi)··········· | ||
| 00009f40:·2020·2020·207c·0a7c·202d·2d20·2e30·3 | 00009f40:·2020·2020·207c·0a7c·202d·2d20·2e30·3730·······|.|·--·.070 | ||
| 00009f50:·353 | 00009f50:·3536·3131·7320·656c·6170·7365·6420·2020··5611s·elapsed··· | ||
| 00009f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f80:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00009f80:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00009f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fb0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00009fb0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00009fc0:·2020·2020·2020·2020·2020·2030·2020·3120·············0··1· | 00009fc0:·2020·2020·2020·2020·2020·2030·2020·3120·············0··1· | ||
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| 0000a210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a240:·2d2d·2d2d·2b0a·7c69·3138·203a·2065·6c61··----+.|i18·:·ela | 0000a240:·2d2d·2d2d·2b0a·7c69·3138·203a·2065·6c61··----+.|i18·:·ela | ||
| 0000a250:·7073·6564·5469·6d65·2062·6173·6550·7473··psedTime·basePts | 0000a250:·7073·6564·5469·6d65·2062·6173·6550·7473··psedTime·basePts | ||
| 0000a260:·3d70·7269·6d61·7279·4465·636f·6d70·6f73··=primaryDecompos | 0000a260:·3d70·7269·6d61·7279·4465·636f·6d70·6f73··=primaryDecompos | ||
| 0000a270:·6974·696f·6e20·6964·6561·6c20·483b·207c··ition·ideal·H;·| | 0000a270:·6974·696f·6e20·6964·6561·6c20·483b·207c··ition·ideal·H;·| | ||
| 0000a280:·0a7c·202d·2d20·312e·3 | 0000a280:·0a7c·202d·2d20·312e·3736·3836·3673·2065··.|·--·1.76866s·e | ||
| 0000a290:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 0000a290:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 0000a2a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a2a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a2b0:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | 0000a2b0:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | ||
| 0000a2c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a2c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a2d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a2d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a2e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a2e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a2f0:·2d2d·2d2d·2d2b·0a7c·6931·3920·3a20·7461··-----+.|i19·:·ta | 0000a2f0:·2d2d·2d2d·2d2b·0a7c·6931·3920·3a20·7461··-----+.|i19·:·ta |
| Offset 4214, 17 lines modified | Offset 4214, 17 lines modified | ||
| 00010750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010760:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010760:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010780:·2d2d·2d2d·2d2b·0a7c·6931·3420·3a20·7469··-----+.|i14·:·ti | 00010780:·2d2d·2d2d·2d2b·0a7c·6931·3420·3a20·7469··-----+.|i14·:·ti | ||
| 00010790:·6d65·2062·6574·7469·2028·4620·3d20·7075··me·betti·(F·=·pu | 00010790:·6d65·2062·6574·7469·2028·4620·3d20·7075··me·betti·(F·=·pu | ||
| 000107a0:·7265·5265·736f·6c75·7469·6f6e·284d·2c7b··reResolution(M,{ | 000107a0:·7265·5265·736f·6c75·7469·6f6e·284d·2c7b··reResolution(M,{ | ||
| 000107b0:·302c·322c·347d·2929·2020·2020·207c·0a7c··0,2,4}))·····|.| | 000107b0:·302c·322c·347d·2929·2020·2020·207c·0a7c··0,2,4}))·····|.| | ||
| 000107c0:·202d·2d20·7573·6564·2030·2e3 | 000107c0:·202d·2d20·7573·6564·2030·2e35·3237·3133···--·used·0.52713 | ||
| 000107d0:·3773·2028·6370·7529·3b20·302e·3 | 000107d0:·3773·2028·6370·7529·3b20·302e·3333·3033··7s·(cpu);·0.3303 | ||
| 000107e0:·3 | 000107e0:·3837·7320·2874·6872·6561·6429·3b20·3073··87s·(thread);·0s | ||
| 000107f0:·2028·6763·297c·0a7c·2020·2020·2020·2020···(gc)|.|········ | 000107f0:·2028·6763·297c·0a7c·2020·2020·2020·2020···(gc)|.|········ | ||
| 00010800:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010800:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010820:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00010820:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00010830:·2020·2020·2020·2020·2020·2020·2030·2031···············0·1 | 00010830:·2020·2020·2020·2020·2020·2020·2030·2031···············0·1 | ||
| 00010840:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | 00010840:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | ||
| 00010850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 4279, 17 lines modified | Offset 4279, 17 lines modified | ||
| 00010b60:·0a0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··..+------------- | 00010b60:·0a0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··..+------------- | ||
| 00010b70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010b70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010b90:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3135·203a··--------+.|i15·: | 00010b90:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3135·203a··--------+.|i15·: | ||
| 00010ba0:·2074·696d·6520·6265·7474·6920·2846·203d···time·betti·(F·= | 00010ba0:·2074·696d·6520·6265·7474·6920·2846·203d···time·betti·(F·= | ||
| 00010bb0:·2070·7572·6552·6573·6f6c·7574·696f·6e28···pureResolution( | 00010bb0:·2070·7572·6552·6573·6f6c·7574·696f·6e28···pureResolution( | ||
| 00010bc0:·3131·2c34·2c7b·302c·322c·347d·2929·2020··11,4,{0,2,4}))·· | 00010bc0:·3131·2c34·2c7b·302c·322c·347d·2929·2020··11,4,{0,2,4}))·· | ||
| 00010bd0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3 | 00010bd0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3538··|.|·--·used·0.58 | ||
| 00010be0:·3 | 00010be0:·3531·3232·7320·2863·7075·293b·2030·2e33··5122s·(cpu);·0.3 | ||
| 00010bf0:·3 | 00010bf0:·3835·3732·3673·2028·7468·7265·6164·293b··85726s·(thread); | ||
| 00010c00:·2030·7320·2867·6329·7c0a·7c20·2020·2020···0s·(gc)|.|····· | 00010c00:·2030·7320·2867·6329·7c0a·7c20·2020·2020···0s·(gc)|.|····· | ||
| 00010c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010c40:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00010c40:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00010c50:·3020·3120·3220·2020·2020·2020·2020·2020··0·1·2··········· | 00010c50:·3020·3120·3220·2020·2020·2020·2020·2020··0·1·2··········· | ||
| 00010c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00000910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00000910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00000920:·7c69·3120·3a20·7275·6e42·656e·6368·6d61··|i1·:·runBenchma | 00000920:·7c69·3120·3a20·7275·6e42·656e·6368·6d61··|i1·:·runBenchma | ||
| 00000930:·726b·7320·2272·6573·3339·2220·2020·2020··rks·"res39"····· | 00000930:·726b·7320·2272·6573·3339·2220·2020·2020··rks·"res39"····· | ||
| 00000940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000960:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00000960:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00000970:·7c2d·2d20·6265·6769·6e6e·696e·6720·636f··|--·beginning·co | 00000970:·7c2d·2d20·6265·6769·6e6e·696e·6720·636f··|--·beginning·co | ||
| 00000980:·6d70·7574·6174·696f·6e20·5 | 00000980:·6d70·7574·6174·696f·6e20·5765·6420·4465··mputation·Wed·De | ||
| 00000990:· | 00000990:·6320·3137·2031·303a·3034·3a33·3120·2b31··c·17·10:04:31·+1 | ||
| 000009a0:·3 | 000009a0:·3420·3230·3235·2020·2020·2020·2020·2020··4·2025·········· | ||
| 000009b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000009b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000009c0:·7c2d·2d20·4c69·6e75·7820·69 | 000009c0:·7c2d·2d20·4c69·6e75·7820·692d·6361·7074··|--·Linux·i-capt | ||
| 000009d0:·312d·616d·6436·3420·362e·312e·302d·3237··1-amd64·6.1.0-27 | |||
| 000009e0:·2d63·6c6f·7564·2d61·6d64·3634·2023·3120··-cloud-amd64·#1· | |||
| 000009f0:·534d·5020·5052·4545·4d50·545f·4459·4e41··SMP·PREEMPT_DYNA | |||
| 00000 | 000009d0:·7572·652d·7468·652d·686f·7374·6e61·6d65··ure-the-hostname | ||
| 000009e0:·2036·2e31·302e·3131·2b62·706f·2d61·6d64···6.10.11+bpo-amd | |||
| 000009f0:·3634·2023·3120·534d·5020·5052·4545·4d50··64·#1·SMP·PREEMP | |||
| 00000a00:·545f·4459·4e41·4d49·4320·2020·2020·7c0a··T_DYNAMIC·····|. | |||
| 00000a10:·7c2d·2d20·414d·4420·4550·5943·2d52·6f6d··|--·AMD·EPYC-Rom | 00000a10:·7c2d·2d20·414d·4420·4550·5943·2d52·6f6d··|--·AMD·EPYC-Rom | ||
| 00000a20:·6520·5072·6f63·6573·736f·7220·2041·7574··e·Processor··Aut | 00000a20:·6520·5072·6f63·6573·736f·7220·2041·7574··e·Processor··Aut | ||
| 00000a30:·6865·6e74·6963·414d·4420·2063·7075·204d··henticAMD··cpu·M | 00000a30:·6865·6e74·6963·414d·4420·2063·7075·204d··henticAMD··cpu·M | ||
| 00000a40:·487a·203 | 00000a40:·487a·2031·3939·362e·3235·3020·2020·2020··Hz·1996.250····· | ||
| 00000a50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00000a50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00000a60:·7c2d·2d20·4d61·6361·756c·6179·3220·312e··|--·Macaulay2·1. | 00000a60:·7c2d·2d20·4d61·6361·756c·6179·3220·312e··|--·Macaulay2·1. | ||
| 00000a70:·3234·2e31·312c·2063·6f6d·7069·6c65·6420··24.11,·compiled· | 00000a70:·3234·2e31·312c·2063·6f6d·7069·6c65·6420··24.11,·compiled· | ||
| 00000a80:·7769·7468·2067·6363·2031·342e·322e·3020··with·gcc·14.2.0· | 00000a80:·7769·7468·2067·6363·2031·342e·322e·3020··with·gcc·14.2.0· | ||
| 00000a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000aa0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00000aa0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00000ab0:·7c2d·2d20·7265·7333·393a·2072·6573·206f··|--·res39:·res·o | 00000ab0:·7c2d·2d20·7265·7333·393a·2072·6573·206f··|--·res39:·res·o | ||
| 00000ac0:·6620·6120·6765·6e65·7269·6320·3320·6279··f·a·generic·3·by | 00000ac0:·6620·6120·6765·6e65·7269·6320·3320·6279··f·a·generic·3·by | ||
| 00000ad0:·2039·206d·6174·7269·7820·6f76·6572·205a···9·matrix·over·Z | 00000ad0:·2039·206d·6174·7269·7820·6f76·6572·205a···9·matrix·over·Z | ||
| 00000ae0:·5a2f·3130·313a·202e·3 | 00000ae0:·5a2f·3130·313a·202e·3138·3234·3438·2073··Z/101:·.182448·s | ||
| 00000af0:· | 00000af0:·6563·6f6e·6473·2020·2020·2020·2020·7c0a··econds········|. | ||
| 00000b00:·7c2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|--------------- | 00000b00:·7c2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|--------------- | ||
| 00000b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|. | 00000b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|. | ||
| 00000b50:·7c36·2e31·2e31·3135·2d31·2028·3230·3234··|6.1.115-1·(2024 | |||
| 00000b | 00000b50:·7c44·6562·6961·6e20·362e·3130·2e31·312d··|Debian·6.10.11- | ||
| 00000b60:·317e·6270·6f31·322b·3120·2832·3032·342d··1~bpo12+1·(2024- | |||
| 00000b70:·3130·2d30·3329·2078·3836·5f36·3420·474e··10-03)·x86_64·GN | |||
| 00000b | 00000b80:·552f·4c69·6e75·7820·2020·2020·2020·2020··U/Linux········· | ||
| 00000b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000b90:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00000b90:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00000ba0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 00000ba0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 00000bb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000bb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000bc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000bc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000bd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000bd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000be0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00000be0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00000bf0:·0a46·6f72·2074·6865·2070·726f·6772·616d··.For·the·program | 00000bf0:·0a46·6f72·2074·6865·2070·726f·6772·616d··.For·the·program |
| Offset 2113, 15 lines modified | Offset 2113, 15 lines modified | ||
| 00008400:·6e75·6d62·6572·0a20·2020·2020·2020·206f··number.········o | 00008400:·6e75·6d62·6572·0a20·2020·2020·2020·206f··number.········o | ||
| 00008410:·7220·7261·6e64·6f6d·2063·6f6d·706c·6578··r·random·complex | 00008410:·7220·7261·6e64·6f6d·2063·6f6d·706c·6578··r·random·complex | ||
| 00008420:·206e·756d·6265·720a·2020·2020·2020·2a20···number.······*· | 00008420:·206e·756d·6265·720a·2020·2020·2020·2a20···number.······*· | ||
| 00008430:·2a6e·6f74·6520·546f·7044·6972·6563·746f··*note·TopDirecto | 00008430:·2a6e·6f74·6520·546f·7044·6972·6563·746f··*note·TopDirecto | ||
| 00008440:·7279·3a20·546f·7044·6972·6563·746f·7279··ry:·TopDirectory | 00008440:·7279·3a20·546f·7044·6972·6563·746f·7279··ry:·TopDirectory | ||
| 00008450:·2c20·3d3e·202e·2e2e·2c20·6465·6661·756c··,·=>·...,·defaul | 00008450:·2c20·3d3e·202e·2e2e·2c20·6465·6661·756c··,·=>·...,·defaul | ||
| 00008460:·7420·7661·6c75·650a·2020·2020·2020·2020··t·value.········ | 00008460:·7420·7661·6c75·650a·2020·2020·2020·2020··t·value.········ | ||
| 00008470:·222f·746d·702f·4d32·2d3 | 00008470:·222f·746d·702f·4d32·2d33·3636·3730·3833··"/tmp/M2-3667083 | ||
| 00008480:·2d30·2f30·222c·204f·7074·696f·6e20·746f··-0/0",·Option·to | 00008480:·2d30·2f30·222c·204f·7074·696f·6e20·746f··-0/0",·Option·to | ||
| 00008490:·2063·6861·6e67·6520·6469·7265·6374·6f72···change·director | 00008490:·2063·6861·6e67·6520·6469·7265·6374·6f72···change·director | ||
| 000084a0:·7920·666f·7220·6669·6c65·2073·746f·7261··y·for·file·stora | 000084a0:·7920·666f·7220·6669·6c65·2073·746f·7261··y·for·file·stora | ||
| 000084b0:·6765·2e0a·2020·2020·2020·2a20·2a6e·6f74··ge..······*·*not | 000084b0:·6765·2e0a·2020·2020·2020·2a20·2a6e·6f74··ge..······*·*not | ||
| 000084c0:·6520·5665·7262·6f73·653a·2062·6572·7469··e·Verbose:·berti | 000084c0:·6520·5665·7262·6f73·653a·2062·6572·7469··e·Verbose:·berti | ||
| 000084d0:·6e69·5472·6163·6b48·6f6d·6f74·6f70·795f··niTrackHomotopy_ | 000084d0:·6e69·5472·6163·6b48·6f6d·6f74·6f70·795f··niTrackHomotopy_ | ||
| 000084e0:·6c70·5f70·645f·7064·5f70·645f·636d·5665··lp_pd_pd_pd_cmVe | 000084e0:·6c70·5f70·645f·7064·5f70·645f·636d·5665··lp_pd_pd_pd_cmVe | ||
| Offset 4780, 16 lines modified | Offset 4780, 16 lines modified | ||
| 00012ab0:·696e·6720·646f·6375·6d65·6e74·6174·696f··ing·documentatio | 00012ab0:·696e·6720·646f·6375·6d65·6e74·6174·696f··ing·documentatio | ||
| 00012ac0:·6e29·203d·3e20·2e2e·2e2c·2064·6566·6175··n)·=>·...,·defau | 00012ac0:·6e29·203d·3e20·2e2e·2e2c·2064·6566·6175··n)·=>·...,·defau | ||
| 00012ad0:·6c74·2076·616c·7565·207b·7d2c·200a·2020··lt·value·{},·.·· | 00012ad0:·6c74·2076·616c·7565·207b·7d2c·200a·2020··lt·value·{},·.·· | ||
| 00012ae0:·2020·2020·2a20·2a6e·6f74·6520·546f·7044······*·*note·TopD | 00012ae0:·2020·2020·2a20·2a6e·6f74·6520·546f·7044······*·*note·TopD | ||
| 00012af0:·6972·6563·746f·7279·3a20·546f·7044·6972··irectory:·TopDir | 00012af0:·6972·6563·746f·7279·3a20·546f·7044·6972··irectory:·TopDir | ||
| 00012b00:·6563·746f·7279·2c20·3d3e·202e·2e2e·2c20··ectory,·=>·...,· | 00012b00:·6563·746f·7279·2c20·3d3e·202e·2e2e·2c20··ectory,·=>·...,· | ||
| 00012b10:·6465·6661·756c·7420·7661·6c75·650a·2020··default·value.·· | 00012b10:·6465·6661·756c·7420·7661·6c75·650a·2020··default·value.·· | ||
| 00012b20:·2020·2020·2020·222f·746d·702f·4d32·2d3 | 00012b20:·2020·2020·2020·222f·746d·702f·4d32·2d33········"/tmp/M2-3 | ||
| 00012b30:·3 | 00012b30:·3636·3730·3833·2d30·2f30·222c·204f·7074··667083-0/0",·Opt | ||
| 00012b40:·696f·6e20·746f·2063·6861·6e67·6520·6469··ion·to·change·di | 00012b40:·696f·6e20·746f·2063·6861·6e67·6520·6469··ion·to·change·di | ||
| 00012b50:·7265·6374·6f72·7920·666f·7220·6669·6c65··rectory·for·file | 00012b50:·7265·6374·6f72·7920·666f·7220·6669·6c65··rectory·for·file | ||
| 00012b60:·2073·746f·7261·6765·2e0a·2020·2020·2020···storage..······ | 00012b60:·2073·746f·7261·6765·2e0a·2020·2020·2020···storage..······ | ||
| 00012b70:·2a20·2a6e·6f74·6520·5665·7262·6f73·653a··*·*note·Verbose: | 00012b70:·2a20·2a6e·6f74·6520·5665·7262·6f73·653a··*·*note·Verbose: | ||
| 00012b80:·2062·6572·7469·6e69·5472·6163·6b48·6f6d···bertiniTrackHom | 00012b80:·2062·6572·7469·6e69·5472·6163·6b48·6f6d···bertiniTrackHom | ||
| 00012b90:·6f74·6f70·795f·6c70·5f70·645f·7064·5f70··otopy_lp_pd_pd_p | 00012b90:·6f74·6f70·795f·6c70·5f70·645f·7064·5f70··otopy_lp_pd_pd_p | ||
| 00012ba0:·645f·636d·5665·7262·6f73·653d·3e5f·7064··d_cmVerbose=>_pd | 00012ba0:·645f·636d·5665·7262·6f73·653d·3e5f·7064··d_cmVerbose=>_pd | ||
| Offset 5271, 15 lines modified | Offset 5271, 15 lines modified | ||
| 00014960:·2020·2020·2020·6f72·2072·616e·646f·6d20········or·random· | 00014960:·2020·2020·2020·6f72·2072·616e·646f·6d20········or·random· | ||
| 00014970:·636f·6d70·6c65·7820·6e75·6d62·6572·0a20··complex·number.· | 00014970:·636f·6d70·6c65·7820·6e75·6d62·6572·0a20··complex·number.· | ||
| 00014980:·2020·2020·202a·202a·6e6f·7465·2054·6f70·······*·*note·Top | 00014980:·2020·2020·202a·202a·6e6f·7465·2054·6f70·······*·*note·Top | ||
| 00014990:·4469·7265·6374·6f72·793a·2054·6f70·4469··Directory:·TopDi | 00014990:·4469·7265·6374·6f72·793a·2054·6f70·4469··Directory:·TopDi | ||
| 000149a0:·7265·6374·6f72·792c·203d·3e20·2e2e·2e2c··rectory,·=>·..., | 000149a0:·7265·6374·6f72·792c·203d·3e20·2e2e·2e2c··rectory,·=>·..., | ||
| 000149b0:·2064·6566·6175·6c74·2076·616c·7565·0a20···default·value.· | 000149b0:·2064·6566·6175·6c74·2076·616c·7565·0a20···default·value.· | ||
| 000149c0:·2020·2020·2020·2022·2f74·6d70·2f4d·322d·········"/tmp/M2- | 000149c0:·2020·2020·2020·2022·2f74·6d70·2f4d·322d·········"/tmp/M2- | ||
| 000149d0:·3 | 000149d0:·3336·3637·3038·332d·302f·3022·2c20·4f70··3667083-0/0",·Op | ||
| 000149e0:·7469·6f6e·2074·6f20·6368·616e·6765·2064··tion·to·change·d | 000149e0:·7469·6f6e·2074·6f20·6368·616e·6765·2064··tion·to·change·d | ||
| 000149f0:·6972·6563·746f·7279·2066·6f72·2066·696c··irectory·for·fil | 000149f0:·6972·6563·746f·7279·2066·6f72·2066·696c··irectory·for·fil | ||
| 00014a00:·6520·7374·6f72·6167·652e·0a20·2020·2020··e·storage..····· | 00014a00:·6520·7374·6f72·6167·652e·0a20·2020·2020··e·storage..····· | ||
| 00014a10:·202a·2055·7365·5265·6765·6e65·7261·7469···*·UseRegenerati | 00014a10:·202a·2055·7365·5265·6765·6e65·7261·7469···*·UseRegenerati | ||
| 00014a20:·6f6e·2028·6d69·7373·696e·6720·646f·6375··on·(missing·docu | 00014a20:·6f6e·2028·6d69·7373·696e·6720·646f·6375··on·(missing·docu | ||
| 00014a30:·6d65·6e74·6174·696f·6e29·203d·3e20·2e2e··mentation)·=>·.. | 00014a30:·6d65·6e74·6174·696f·6e29·203d·3e20·2e2e··mentation)·=>·.. | ||
| 00014a40:·2e2c·2064·6566·6175·6c74·2076·616c·7565··.,·default·value | 00014a40:·2e2c·2064·6566·6175·6c74·2076·616c·7565··.,·default·value |
| Offset 12411, 15 lines modified | Offset 12411, 15 lines modified | ||
| 000307a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000307a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000307b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 000307b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 000307c0:·6939·203a·2065·6c61·7073·6564·5469·6d65··i9·:·elapsedTime | 000307c0:·6939·203a·2065·6c61·7073·6564·5469·6d65··i9·:·elapsedTime | ||
| 000307d0:·2063·203d·2063·6861·7261·6374·6572·2041···c·=·character·A | 000307d0:·2063·203d·2063·6861·7261·6374·6572·2041···c·=·character·A | ||
| 000307e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000307e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000307f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000307f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030800:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00030800:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00030810:·202d·2d20·2e3 | 00030810:·202d·2d20·2e36·3332·3330·3373·2065·6c61···--·.632303s·ela | ||
| 00030820:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 00030820:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 00030830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030850:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00030850:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00030860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 13607, 16 lines modified | Offset 13607, 16 lines modified | ||
| 00035260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00035260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00035270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00035270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00035280:·2d2b·0a7c·6937·203a·2065·6c61·7073·6564··-+.|i7·:·elapsed | 00035280:·2d2b·0a7c·6937·203a·2065·6c61·7073·6564··-+.|i7·:·elapsed | ||
| 00035290:·5469·6d65·2063·3d63·6861·7261·6374·6572··Time·c=character | 00035290:·5469·6d65·2063·3d63·6861·7261·6374·6572··Time·c=character | ||
| 000352a0:·2041·2020·2020·2020·2020·2020·2020·2020···A·············· | 000352a0:·2041·2020·2020·2020·2020·2020·2020·2020···A·············· | ||
| 000352b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000352b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000352c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000352c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000352d0:·207c·0a7c·202d·2d20·2e34·3 | 000352d0:·207c·0a7c·202d·2d20·2e34·3533·3333·3773···|.|·--·.453337s | ||
| 000352e0:·6c61·7073·6564·2020·2020·2020·2020· | 000352e0:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 000352f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000352f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035320:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00035320:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00035330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 15025, 16 lines modified | Offset 15025, 16 lines modified | ||
| 0003ab00:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | 0003ab00:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 0003ab10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ab10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ab20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ab20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ab30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 0003ab30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 0003ab40:·7c69·3230·203a·2065·6c61·7073·6564·5469··|i20·:·elapsedTi | 0003ab40:·7c69·3230·203a·2065·6c61·7073·6564·5469··|i20·:·elapsedTi | ||
| 0003ab50:·6d65·2061·3120·3d20·6368·6172·6163·7465··me·a1·=·characte | 0003ab50:·6d65·2061·3120·3d20·6368·6172·6163·7465··me·a1·=·characte | ||
| 0003ab60:·7220·4131·2020·2020·2020·2020·2020·2020··r·A1············ | 0003ab60:·7220·4131·2020·2020·2020·2020·2020·2020··r·A1············ | ||
| 0003ab70:·2020·207c·0a7c·202d·2d20· | 0003ab70:·2020·207c·0a7c·202d·2d20·2e39·3339·3634·····|.|·--·.93964 | ||
| 0003ab80:·3 | 0003ab80:·3773·2065·6c61·7073·6564·2020·2020·2020··7s·elapsed······ | ||
| 0003ab90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ab90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003aba0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 0003aba0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 0003abb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003abb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003abc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003abc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003abd0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0003abd0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0003abe0:·6f32·3020·3d20·4368·6172·6163·7465·7220··o20·=·Character· | 0003abe0:·6f32·3020·3d20·4368·6172·6163·7465·7220··o20·=·Character· | ||
| 0003abf0:·6f76·6572·2052·2020·2020·2020·2020·2020··over·R·········· | 0003abf0:·6f76·6572·2052·2020·2020·2020·2020·2020··over·R·········· | ||
| Offset 15065, 15 lines modified | Offset 15065, 15 lines modified | ||
| 0003ad80:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | 0003ad80:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
| 0003ad90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ad90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ada0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ada0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003adb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3231··----------+.|i21 | 0003adb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3231··----------+.|i21 | ||
| 0003adc0:·203a·2065·6c61·7073·6564·5469·6d65·2061···:·elapsedTime·a | 0003adc0:·203a·2065·6c61·7073·6564·5469·6d65·2061···:·elapsedTime·a | ||
| 0003add0:·3220·3d20·6368·6172·6163·7465·7220·4132··2·=·character·A2 | 0003add0:·3220·3d20·6368·6172·6163·7465·7220·4132··2·=·character·A2 | ||
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| 0001e890:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 0001e890:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
| 0001e8a0:·3420·3d20·7b6 | 0001e8a0:·3420·3d20·7b62·2063·202c·2061·2a62·2a63··4·=·{b·c·,·a*b*c | ||
| 0001e8b0:·2c20 | 0001e8b0:·202c·2061·2a62·2063·2c20·6120·622a·6320···,·a*b·c,·a·b*c· | ||
| 0001e8c0:· | 0001e8c0:·2c20·6120·6220·7d20·2020·2020·2020·2020··,·a·b·}········· | ||
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| 0001e930:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 0001e930:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
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| 000204c0:· | 000204c0:·2020·3220·2020·2034·2035·2020·2032·2020····2····4·5···2·· | ||
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| 00020500:·207c·0a7c·6f35·203d·207b·782 | 00020500:·207c·0a7c·6f35·203d·207b·782a·7920·7a2c···|.|o5·=·{x*y·z, | ||
| 00020510:·2078·2079·202c·2078·2079·2 | 00020510:·2078·2079·202c·2078·2079·2a7a·2c20·7820···x·y·,·x·y*z,·x· | ||
| 00020520:· | 00020520:·7920·7d20·2020·2020·2020·2020·2020·2020··y·}············· | ||
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| 00011a30:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00011a30:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00011a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011a60:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3320·3a20··-------+.|i13·:· | 00011a60:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3320·3a20··-------+.|i13·:· | ||
| 00011a70:·7469·6d65·206d·203d·206d·696e·696d·697a··time·m·=·minimiz | 00011a70:·7469·6d65·206d·203d·206d·696e·696d·697a··time·m·=·minimiz | ||
| 00011a80:·6520·2845·5b31·5d29·3b20·2020·2020·2020··e·(E[1]);······· | 00011a80:·6520·2845·5b31·5d29·3b20·2020·2020·2020··e·(E[1]);······· | ||
| 00011a90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00011a90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00011aa0:·0a7c·202d·2d20·7573·6564·2030·2e32·3 | 00011aa0:·0a7c·202d·2d20·7573·6564·2030·2e32·3630··.|·--·used·0.260 | ||
| 00011ab0:·3 | 00011ab0:·3433·3173·2028·6370·7529·3b20·302e·3230··431s·(cpu);·0.20 | ||
| 00011ac0:·3 | 00011ac0:·3139·3733·7320·2874·6872·6561·6429·3b20··1973s·(thread);· | ||
| 00011ad0:·3073·2028·6763·297c·0a2b·2d2d·2d2d·2d2d··0s·(gc)|.+------ | 00011ad0:·3073·2028·6763·297c·0a2b·2d2d·2d2d·2d2d··0s·(gc)|.+------ | ||
| 00011ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00011b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00011b10:·0a7c·6931·3420·3a20·6973·5175·6173·6949··.|i14·:·isQuasiI | 00011b10:·0a7c·6931·3420·3a20·6973·5175·6173·6949··.|i14·:·isQuasiI | ||
| 00011b20:·736f·6d6f·7270·6869·736d·206d·2020·2020··somorphism·m···· | 00011b20:·736f·6d6f·7270·6869·736d·206d·2020·2020··somorphism·m···· | ||
| 00011b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00018340:·2d2d·2d2d·2d2d·2b0a·7c69·3820·3a20·7469··------+.|i8·:·ti | 00018340:·2d2d·2d2d·2d2d·2b0a·7c69·3820·3a20·7469··------+.|i8·:·ti | ||
| 00018350:·6d65·206d·203d·2072·6573·6f6c·7574·696f··me·m·=·resolutio | 00018350:·6d65·206d·203d·2072·6573·6f6c·7574·696f··me·m·=·resolutio | ||
| 00018360:·6e4f·6643·6861·696e·436f·6d70·6c65·7820··nOfChainComplex· | 00018360:·6e4f·6643·6861·696e·436f·6d70·6c65·7820··nOfChainComplex· | ||
| 00018370:·433b·2020·2020·2020·2020·2020·2020·2020··C;·············· | 00018370:·433b·2020·2020·2020·2020·2020·2020·2020··C;·············· | ||
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| 00018390:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00018390:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 000183a0:·6420·302e·313 | 000183a0:·6420·302e·3134·3835·3732·7320·2863·7075··d·0.148572s·(cpu | ||
| 000183b0:·293b·2030·2e30·3930·3331·3333·7320·2874··);·0.0903133s·(t | |||
| 000183 | 000183b0:·293b·2030·2e31·3034·3739·3673·2028·7468··);·0.104796s·(th | ||
| 000183c0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | |||
| 000183d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000183d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000183e0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | 000183e0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 000183f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000183f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018430:·2d2d·2d2d·2d2d·2b0a·7c69·3920·3a20·7469··------+.|i9·:·ti | 00018430:·2d2d·2d2d·2d2d·2b0a·7c69·3920·3a20·7469··------+.|i9·:·ti | ||
| 00018440:·6d65·206e·203d·2063·6172·7461·6e45·696c··me·n·=·cartanEil | 00018440:·6d65·206e·203d·2063·6172·7461·6e45·696c··me·n·=·cartanEil | ||
| 00018450:·656e·6265·7267·5265·736f·6c75·7469·6f6e··enbergResolution | 00018450:·656e·6265·7267·5265·736f·6c75·7469·6f6e··enbergResolution | ||
| 00018460:·2043·3b20·2020·2020·2020·2020·2020·2020···C;············· | 00018460:·2043·3b20·2020·2020·2020·2020·2020·2020···C;············· | ||
| 00018470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018480:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00018480:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00018490:·6420·302e·313 | 00018490:·6420·302e·3132·3631·3734·7320·2863·7075··d·0.126174s·(cpu | ||
| 000184a0:·293b·2030·2e31·3 | 000184a0:·293b·2030·2e31·3236·3739·3673·2028·7468··);·0.126796s·(th | ||
| 000184b0:·6561 | 000184b0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 000184c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000184c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000184d0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | 000184d0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 000184e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000184e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000184f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000184f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018510:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018510:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018520:·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a·2062··------+.|i10·:·b | 00018520:·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a·2062··------+.|i10·:·b |
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| 00013c90:·2020·2020·2020·2020·2035·203d·3e20·7b69···········5·=>·{i | 00013c90:·2020·2020·2020·2020·2035·203d·3e20·7b69···········5·=>·{i | ||
| 00013ca0:·6465·616c·2028·7820·2c20·7820·2c20·7820··deal·(x·,·x·,·x· | 00013ca0:·6465·616c·2028·7820·2c20·7820·2c20·7820··deal·(x·,·x·,·x· | ||
| 00013cb0:·2c20·7820·2c20·7820·292c·2069·6465·616c··,·x·,·x·),·ideal | 00013cb0:·2c20·7820·2c20·7820·292c·2069·6465·616c··,·x·,·x·),·ideal | ||
| 00013cc0:·2028·7820·2c20·7820·2c20·7820·2c20·7820···(x·,·x·,·x·,·x· | 00013cc0:·2028·7820·2c20·7820·2c20·7820·2c20·7820···(x·,·x·,·x·,·x· | ||
| 00013cd0:·2c20·7820·292c·207c·0a7c·2020·2020·2020··,·x·),·|.|······ | 00013cd0:·2c20·7820·292c·207c·0a7c·2020·2020·2020··,·x·),·|.|······ | ||
| 00013ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013cf0:·2020·2020·2020·2031·2020·203 | 00013cf0:·2020·2020·2020·2031·2020·2032·2020·2034·········1···2···4 | ||
| 00013d00:·2020·203 | 00013d00:·2020·2035·2020·2037·2020·2020·2020·2020·····5···7········ | ||
| 00013d10:·2020·2031·2020·203 | 00013d10:·2020·2031·2020·2033·2020·2034·2020·2036·····1···3···4···6 | ||
| 00013d20:·2020·2037·2020·207c·0a7c·2020·2020·2020·····7···|.|······ | 00013d20:·2020·2037·2020·207c·0a7c·2020·2020·2020·····7···|.|······ | ||
| 00013d30:·2020·2020·2020·2020·2036·203d·3e20·7b7d···········6·=>·{} | 00013d30:·2020·2020·2020·2020·2036·203d·3e20·7b7d···········6·=>·{} | ||
| 00013d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013d70:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00013d70:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00013d80:·2020·2020·2020·2020·2037·203d·3e20·7b7d···········7·=>·{} | 00013d80:·2020·2020·2020·2020·2037·203d·3e20·7b7d···········7·=>·{} | ||
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| 00013f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013f50:·2020·2020·2020·207c·0a7c·6964·6561·6c20·········|.|ideal· | 00013f50:·2020·2020·2020·207c·0a7c·6964·6561·6c20·········|.|ideal· | ||
| 00013f60:·2878·202c·2078·202c·2078·202c·2078·202c··(x·,·x·,·x·,·x·, | 00013f60:·2878·202c·2078·202c·2078·202c·2078·202c··(x·,·x·,·x·,·x·, | ||
| 00013f70:·2078·2029·2c20·6964·6561·6c20·2878·202c···x·),·ideal·(x·, | 00013f70:·2078·2029·2c20·6964·6561·6c20·2878·202c···x·),·ideal·(x·, | ||
| 00013f80:·2078·202c·2078·202c·2078·202c·2078·2029···x·,·x·,·x·,·x·) | 00013f80:·2078·202c·2078·202c·2078·202c·2078·2029···x·,·x·,·x·,·x·) | ||
| 00013f90:·2c20·6964·6561·6c20·2878·202c·2078·202c··,·ideal·(x·,·x·, | 00013f90:·2c20·6964·6561·6c20·2878·202c·2078·202c··,·ideal·(x·,·x·, | ||
| 00013fa0:·2078·202c·2020·207c·0a7c·2020·2020·2020···x·,···|.|······ | 00013fa0:·2078·202c·2020·207c·0a7c·2020·2020·2020···x·,···|.|······ | ||
| 00013fb0:·2020·3120·2020·3220·2020·3420·2020·3 | 00013fb0:·2020·3120·2020·3220·2020·3420·2020·3620····1···2···4···6· | ||
| 00013fc0:·2020·3720·2020·2020·2020·2020·2020·3220····7···········2· | 00013fc0:·2020·3720·2020·2020·2020·2020·2020·3220····7···········2· | ||
| 00013fd0:·2020·3320·2020·3520·2020·3 | 00013fd0:·2020·3320·2020·3520·2020·3720·2020·3820····3···5···7···8· | ||
| 00013fe0:·2020·2020·2020·2020·2020·3 | 00013fe0:·2020·2020·2020·2020·2020·3220·2020·3420············2···4· | ||
| 00013ff0:·2020·3520·2020·207c·0a7c·2d2d·2d2d·2d2d····5····|.|------ | 00013ff0:·2020·3520·2020·207c·0a7c·2d2d·2d2d·2d2d····5····|.|------ | ||
| 00014000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014040:·2d2d·2d2d·2d2d·2d7c·0a7c·2020·2020·2020··-------|.|······ | 00014040:·2d2d·2d2d·2d2d·2d7c·0a7c·2020·2020·2020··-------|.|······ | ||
| 00014050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000140c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000140c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000140d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000140d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000140e0:·2020·2020·2020·207c·0a7c·7820·2c20·7820·········|.|x·,·x· | 000140e0:·2020·2020·2020·207c·0a7c·7820·2c20·7820·········|.|x·,·x· | ||
| 000140f0:·292c·2069·6465·616c·2028·7820·2c20·7820··),·ideal·(x·,·x· | 000140f0:·292c·2069·6465·616c·2028·7820·2c20·7820··),·ideal·(x·,·x· | ||
| 00014100:·2c20·7820·2c20·7820·2c20·7820·292c·2069··,·x·,·x·,·x·),·i | 00014100:·2c20·7820·2c20·7820·2c20·7820·292c·2069··,·x·,·x·,·x·),·i | ||
| 00014110:·6465·616c·2028·7820·2c20·7820·2c20·7820··deal·(x·,·x·,·x· | 00014110:·6465·616c·2028·7820·2c20·7820·2c20·7820··deal·(x·,·x·,·x· | ||
| 00014120:·2c20·7820·2c20·7820·292c·2069·6465·616c··,·x·,·x·),·ideal | 00014120:·2c20·7820·2c20·7820·292c·2069·6465·616c··,·x·,·x·),·ideal | ||
| 00014130:·2028·7820·2c20·207c·0a7c·203 | 00014130:·2028·7820·2c20·207c·0a7c·2037·2020·2038···(x·,··|.|·7···8 | ||
| 00014140:·2020·2020·2020·2020·2020·203 | 00014140:·2020·2020·2020·2020·2020·2032·2020·2033·············2···3 | ||
| 00014150:·2020·203 | 00014150:·2020·2035·2020·2036·2020·2038·2020·2020·····5···6···8···· | ||
| 00014160:·2020·2020·2020·203 | 00014160:·2020·2020·2020·2031·2020·2033·2020·2035·········1···3···5 | ||
| 00014170:·2020·203 | 00014170:·2020·2036·2020·2038·2020·2020·2020·2020·····6···8········ | ||
| 00014180:·2020·203 | 00014180:·2020·2031·2020·207c·0a7c·2d2d·2d2d·2d2d·····1···|.|------ | ||
| 00014190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000141a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000141a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000141b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000141b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000141c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000141c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000141d0:·2d2d·2d2d·2d2d·2d7c·0a7c·2020·2020·2020··-------|.|······ | 000141d0:·2d2d·2d2d·2d2d·2d7c·0a7c·2020·2020·2020··-------|.|······ | ||
| 000141e0:·2020·2020·2020·2020·2020·7d20·2020·2020············}····· | 000141e0:·2020·2020·2020·2020·2020·7d20·2020·2020············}····· | ||
| 000141f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000141f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00014250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014270:·2020·2020·2020·207c·0a7c·7820·2c20·7820·········|.|x·,·x· | 00014270:·2020·2020·2020·207c·0a7c·7820·2c20·7820·········|.|x·,·x· | ||
| 00014280:·2c20·7820·2c20·7820·297d·2020·2020·2020··,·x·,·x·)}······ | 00014280:·2c20·7820·2c20·7820·297d·2020·2020·2020··,·x·,·x·)}······ | ||
| 00014290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000142a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000142a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000142b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000142b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000142c0:·2020·2020·2020·207c·0a7c·2033·2020·203 | 000142c0:·2020·2020·2020·207c·0a7c·2033·2020·2034·········|.|·3···4 | ||
| 000142d0:·2020·203 | 000142d0:·2020·2036·2020·2038·2020·2020·2020·2020·····6···8········ | ||
| 000142e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000142e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000142f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000142f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014310:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 00014310:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00014320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014330:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014330:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014340:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014340:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00031910:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00031910:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00031920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00031920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00031930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00031930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00031940:·2020·2020·7c0a·7c6f·3220·3d20·696d·6167······|.|o2·=·imag | 00031940:·2020·2020·7c0a·7c6f·3220·3d20·696d·6167······|.|o2·=·imag | ||
| 00031950:·6520·7c20·3120·3020·3120·3120·7c20·2020··e·|·1·0·1·1·|··· | 00031950:·6520·7c20·3120·3020·3120·3120·7c20·2020··e·|·1·0·1·1·|··· | ||
| 00031960:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00031960:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00031970:·2020·2020·2020·2020·2020·207c·2031·2031·············|·1·1 | 00031970:·2020·2020·2020·2020·2020·207c·2031·2031·············|·1·1 | ||
| 00031980:·203 | 00031980:·2031·2030·207c·2020·2020·2020·2020·2020···1·0·|·········· | ||
| 00031990:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00031990:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 000319a0:·2020·2020·7c20·3120·3120·3 | 000319a0:·2020·2020·7c20·3120·3120·3020·3120·7c20······|·1·1·0·1·|· | ||
| 000319b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000319b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000319c0:·0a7c·2020·2020·2020·2020·2020·207c·2031··.|···········|·1 | 000319c0:·0a7c·2020·2020·2020·2020·2020·207c·2031··.|···········|·1 | ||
| 000319d0:·2030·2030·2030·207c·2020·2020·2020·2020···0·0·0·|········ | 000319d0:·2030·2030·2030·207c·2020·2020·2020·2020···0·0·0·|········ | ||
| 000319e0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 000319e0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 000319f0:·2020·2020·2020·7c20·3020·3120·3020·3020········|·0·1·0·0· | 000319f0:·2020·2020·2020·7c20·3020·3120·3020·3020········|·0·1·0·0· | ||
| 00031a00:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00031a00:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00031a10:·207c·0a7c·2020·2020·2020·2020·2020·207c···|.|···········| | 00031a10:·207c·0a7c·2020·2020·2020·2020·2020·207c···|.|···········| | ||
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| 0005dec0:·462c·7b7b·312c·312c·317d·7d29·3b7c·0a2b··F,{{1,1,1}});|.+ | 0005dec0:·462c·7b7b·312c·312c·317d·7d29·3b7c·0a2b··F,{{1,1,1}});|.+ | ||
| 0005ded0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0005ded0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0005dee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0005dee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0005def0:·0a7c·6933·203a·206d·6573·7361·6765·7320··.|i3·:·messages· | 0005def0:·0a7c·6933·203a·206d·6573·7361·6765·7320··.|i3·:·messages· | ||
| 0005df00:·5220·2020·2020·2020·2020·2020·2020·2020··R··············· | 0005df00:·5220·2020·2020·2020·2020·2020·2020·2020··R··············· | ||
| 0005df10:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0005df10:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0005df20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0005df20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0005df30:·2020·207c·0a7c·6f33·203d·207b·7b3 | 0005df30:·2020·207c·0a7c·6f33·203d·207b·7b30·7d2c·····|.|o3·=·{{0}, | ||
| 0005df40:·207b· | 0005df40:·207b·317d·2c20·7b61·7d2c·207b·6120·2b20···{1},·{a},·{a·+· | ||
| 0005df50:·3 | 0005df50:·317d·7d20·207c·0a7c·2020·2020·2020·2020··1}}··|.|········ | ||
| 0005df60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0005df60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0005df70:·2020·2020·2020·207c·0a7c·6f33·203a·204c·········|.|o3·:·L | 0005df70:·2020·2020·2020·207c·0a7c·6f33·203a·204c·········|.|o3·:·L | ||
| 0005df80:·6973·7420·2020·2020·2020·2020·2020·2020··ist············· | 0005df80:·6973·7420·2020·2020·2020·2020·2020·2020··ist············· | ||
| 0005df90:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | 0005df90:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 0005dfa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0005dfa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0005dfb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a2b·2d2d··-----------+.+-- | 0005dfb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a2b·2d2d··-----------+.+-- | ||
| 0005dfc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0005dfc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000068f0:·6d65·2063·6f68·6f6d·7665·6331·203d·2063··me·cohomvec1·=·c | 000068f0:·6d65·2063·6f68·6f6d·7665·6331·203d·2063··me·cohomvec1·=·c | ||
| 00006900:·6f68·6f6d·4361·6c67·2858·5f33·202b·2058··ohomCalg(X_3·+·X | 00006900:·6f68·6f6d·4361·6c67·2858·5f33·202b·2058··ohomCalg(X_3·+·X | ||
| 00006910:·5f37·202b·2058·5f38·2920·2020·2020·2020··_7·+·X_8)······· | 00006910:·5f37·202b·2058·5f38·2920·2020·2020·2020··_7·+·X_8)······· | ||
| 00006920:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00006920:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00006930:·7c20·2d2d·202e·3 | 00006930:·7c20·2d2d·202e·3538·3834·3831·7320·656c··|·--·.588481s·el | ||
| 00006940:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 00006940:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 00006950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006970:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00006970:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00006980:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00006980:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00006990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000069a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000069a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00006af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00006b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00006b10:·7c69·3234·203a·2065·6c61·7073·6564·5469··|i24·:·elapsedTi | 00006b10:·7c69·3234·203a·2065·6c61·7073·6564·5469··|i24·:·elapsedTi | ||
| 00006b20:·6d65·2063·6f68·6f6d·7665·6332·203d·2066··me·cohomvec2·=·f | 00006b20:·6d65·2063·6f68·6f6d·7665·6332·203d·2066··me·cohomvec2·=·f | ||
| 00006b30:·6f72·206a·2066·726f·6d20·3020·746f·2064··or·j·from·0·to·d | 00006b30:·6f72·206a·2066·726f·6d20·3020·746f·2064··or·j·from·0·to·d | ||
| 00006b40:·696d·2058·206c·6973·7420·7261·6e6b·2048··im·X·list·rank·H | 00006b40:·696d·2058·206c·6973·7420·7261·6e6b·2048··im·X·list·rank·H | ||
| 00006b50:·485e·6a28·582c·2020·2020·2020·2020·7c0a··H^j(X,········|. | 00006b50:·485e·6a28·582c·2020·2020·2020·2020·7c0a··H^j(X,········|. | ||
| 00006b60:·7c20·2d2d·203 | 00006b60:·7c20·2d2d·2031·3235·2e32·3836·7320·656c··|·--·125.286s·el | ||
| 00006b70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 00006b70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 00006b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ba0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00006ba0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00006bb0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00006bb0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00006bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00007040:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007040:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007050:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00007050:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00007060:·7c69·3237·203a·2065·6c61·7073·6564·5469··|i27·:·elapsedTi | 00007060:·7c69·3237·203a·2065·6c61·7073·6564·5469··|i27·:·elapsedTi | ||
| 00007070:·6d65·2063·6f68·6f6d·7665·6331·203d·2063··me·cohomvec1·=·c | 00007070:·6d65·2063·6f68·6f6d·7665·6331·203d·2063··me·cohomvec1·=·c | ||
| 00007080:·6f68·6f6d·4361·6c67·2858·5f33·202b·2058··ohomCalg(X_3·+·X | 00007080:·6f68·6f6d·4361·6c67·2858·5f33·202b·2058··ohomCalg(X_3·+·X | ||
| 00007090:·5f37·202d·2058·5f38·2920·2020·2020·2020··_7·-·X_8)······· | 00007090:·5f37·202d·2058·5f38·2920·2020·2020·2020··_7·-·X_8)······· | ||
| 000070a0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000070a0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000070b0:·7c20·2d2d·202e·3 | 000070b0:·7c20·2d2d·202e·3533·3236·3236·7320·656c··|·--·.532626s·el | ||
| 000070c0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 000070c0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 000070d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000070d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000070e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000070e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000070f0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000070f0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00007100:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00007100:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00007110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00007270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00007280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00007290:·7c69·3238·203a·2065·6c61·7073·6564·5469··|i28·:·elapsedTi | 00007290:·7c69·3238·203a·2065·6c61·7073·6564·5469··|i28·:·elapsedTi | ||
| 000072a0:·6d65·2063·6f68·6f6d·7665·6332·203d·2065··me·cohomvec2·=·e | 000072a0:·6d65·2063·6f68·6f6d·7665·6332·203d·2065··me·cohomvec2·=·e | ||
| 000072b0:·6c61·7073·6564·5469·6d65·2066·6f72·206a··lapsedTime·for·j | 000072b0:·6c61·7073·6564·5469·6d65·2066·6f72·206a··lapsedTime·for·j | ||
| 000072c0:·2066·726f·6d20·3020·746f·2064·696d·2058···from·0·to·dim·X | 000072c0:·2066·726f·6d20·3020·746f·2064·696d·2058···from·0·to·dim·X | ||
| 000072d0:·206c·6973·7420·7261·6e6b·2020·2020·7c0a···list·rank····|. | 000072d0:·206c·6973·7420·7261·6e6b·2020·2020·7c0a···list·rank····|. | ||
| 000072e0:·7c20·2d2d·202e·333 | 000072e0:·7c20·2d2d·202e·3335·3932·3773·2065·6c61··|·--·.35927s·ela | ||
| 000072f0:· | 000072f0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 00007300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007320:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00007320:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00007330:·7c20·2d2d·202e·333 | 00007330:·7c20·2d2d·202e·3335·3933·3133·7320·656c··|·--·.359313s·el | ||
| 00007340:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 00007340:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 00007350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007370:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00007370:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00007380:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00007380:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00007390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000073a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000073a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00010050:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010050:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010060:·2d2d·2d2d·2d2b·0a7c·6937·203a·2074·696d··-----+.|i7·:·tim | 00010060:·2d2d·2d2d·2d2b·0a7c·6937·203a·2074·696d··-----+.|i7·:·tim | ||
| 00010070:·6520·4720·3d20·4569·7365·6e62·7564·5368··e·G·=·EisenbudSh | 00010070:·6520·4720·3d20·4569·7365·6e62·7564·5368··e·G·=·EisenbudSh | ||
| 00010080:·616d·6173·6828·6666·2c46·2c6c·656e·2920··amash(ff,F,len)· | 00010080:·616d·6173·6828·6666·2c46·2c6c·656e·2920··amash(ff,F,len)· | ||
| 00010090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000100a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000100a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000100b0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 000100b0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 000100c0:·203 | 000100c0:·2038·2e37·3136·3038·7320·2863·7075·293b···8.71608s·(cpu); | ||
| 000100d0:·203 | 000100d0:·2035·2e34·3835·3232·7320·2874·6872·6561···5.48522s·(threa | ||
| 000100e0:·293b | 000100e0:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 000100f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000100f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010100:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00010100:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00010110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010150:·2020·2020·207c·0a7c·2020·2020·202f·2020·······|.|·····/·· | 00010150:·2020·2020·207c·0a7c·2020·2020·202f·2020·······|.|·····/·· | ||
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| 00012210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012230:·2d2d·2d2b·0a7c·6932·3020·3a20·4646·203d··---+.|i20·:·FF·= | 00012230:·2d2d·2d2b·0a7c·6932·3020·3a20·4646·203d··---+.|i20·:·FF·= | ||
| 00012240:·2074·696d·6520·5368·616d·6173·6828·5231···time·Shamash(R1 | 00012240:·2074·696d·6520·5368·616d·6173·6828·5231···time·Shamash(R1 | ||
| 00012250:·2c46·2c34·2920·2020·2020·2020·2020·2020··,F,4)··········· | 00012250:·2c46·2c34·2920·2020·2020·2020·2020·2020··,F,4)··········· | ||
| 00012260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012270:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 00012270:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 00012280:·2030·2e31·3 | 00012280:·2030·2e31·3336·3035·3473·2028·6370·7529···0.136054s·(cpu) | ||
| 00012290:·3b20·302e·3038·3 | 00012290:·3b20·302e·3038·3432·3037·3773·2028·7468··;·0.0842077s·(th | ||
| 000122a0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 000122a0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 000122b0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000122b0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 000122c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000122c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000122d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000122d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000122e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000122e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000122f0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000122f0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00012300:·2020·2020·3120·2020·2020·2020·3620·2020······1·······6··· | 00012300:·2020·2020·3120·2020·2020·2020·3620·2020······1·······6··· | ||
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| 000124a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000124a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000124b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000124b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000124c0:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3120·3a20··-------+.|i21·:· | 000124c0:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3120·3a20··-------+.|i21·:· | ||
| 000124d0:·4747·203d·2074·696d·6520·4569·7365·6e62··GG·=·time·Eisenb | 000124d0:·4747·203d·2074·696d·6520·4569·7365·6e62··GG·=·time·Eisenb | ||
| 000124e0:·7564·5368·616d·6173·6828·6666·2c46·2c34··udShamash(ff,F,4 | 000124e0:·7564·5368·616d·6173·6828·6666·2c46·2c34··udShamash(ff,F,4 | ||
| 000124f0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 000124f0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00012500:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00012500:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00012510:·7573·6564·2031·2e3 | 00012510:·7573·6564·2031·2e32·3839·3831·7320·2863··used·1.28981s·(c | ||
| 00012520:·7075·293b·2030·2e36·3733·3733·3173·2028··pu);·0.673731s·( | |||
| 000125 | 00012520:·7075·293b·2030·2e38·3535·3931·7320·2874··pu);·0.85591s·(t | ||
| 00012530:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | |||
| 00012540:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00012540:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00012550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012580:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00012580:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00012590:·2020·2020·2020·2f20·525c·3120·2020·2020········/·R\1····· | 00012590:·2020·2020·2020·2f20·525c·3120·2020·2020········/·R\1····· | ||
| 000125a0:·2f20·525c·3620·2020·2020·2f20·525c·3138··/·R\6·····/·R\18 | 000125a0:·2f20·525c·3620·2020·2020·2f20·525c·3138··/·R\6·····/·R\18 | ||
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| 00012830:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012830:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012860:·2d2b·0a7c·6932·3220·3a20·4747·203d·2074··-+.|i22·:·GG·=·t | 00012860:·2d2b·0a7c·6932·3220·3a20·4747·203d·2074··-+.|i22·:·GG·=·t | ||
| 00012870:·696d·6520·4569·7365·6e62·7564·5368·616d··ime·EisenbudSham | 00012870:·696d·6520·4569·7365·6e62·7564·5368·616d··ime·EisenbudSham | ||
| 00012880:·6173·6828·5231·2c46·5b32·5d2c·3429·2020··ash(R1,F[2],4)·· | 00012880:·6173·6828·5231·2c46·5b32·5d2c·3429·2020··ash(R1,F[2],4)·· | ||
| 00012890:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | 00012890:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | ||
| 000128a0:·7365·6420·312e·3 | 000128a0:·7365·6420·312e·3333·3939·3973·2028·6370··sed·1.33999s·(cp | ||
| 000128b0:·7529·3b20·302e·3 | 000128b0:·7529·3b20·302e·3831·3630·3131·7320·2874··u);·0.816011s·(t | ||
| 000128c0:·6872·6561·6429·3b20·3073·2028·6763·297c··hread);·0s·(gc)| | 000128c0:·6872·6561·6429·3b20·3073·2028·6763·297c··hread);·0s·(gc)| | ||
| 000128d0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 000128d0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 000128e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000128e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000128f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000128f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012900:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00012900:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00012910:·2031·2020·2020·2020·2036·2020·2020·2020···1·······6······ | 00012910:·2031·2020·2020·2020·2036·2020·2020·2020···1·······6······ | ||
| 00012920:·2031·3820·2020·2020·2020·3338·2020·2020···18·······38···· | 00012920:·2031·3820·2020·2020·2020·3338·2020·2020···18·······38···· | ||
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| 0006bf40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006bf40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006bf50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006bf50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006bf60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0006bf60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0006bf70:·3220·3a20·7375·6d54·776f·4d6f·6e6f·6d69··2·:·sumTwoMonomi | 0006bf70:·3220·3a20·7375·6d54·776f·4d6f·6e6f·6d69··2·:·sumTwoMonomi | ||
| 0006bf80:·616c·7328·322c·3329·2020·2020·2020·2020··als(2,3)········ | 0006bf80:·616c·7328·322c·3329·2020·2020·2020·2020··als(2,3)········ | ||
| 0006bf90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006bf90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006bfa0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | 0006bfa0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | ||
| 0006bfb0:·7365·6420·312e·323 | 0006bfb0:·7365·6420·312e·3234·3036·3373·2028·6370··sed·1.24063s·(cp | ||
| 0006bfc0:·7529·3b20·302e·3 | 0006bfc0:·7529·3b20·302e·3431·3538·3432·7320·2874··u);·0.415842s·(t | ||
| 0006bfd0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 0006bfd0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 0006bfe0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 0006bfe0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
| 0006bff0:·302e·343 | 0006bff0:·302e·3435·3236·3533·7320·2863·7075·293b··0.452653s·(cpu); | ||
| 0006c000:·2030·2e31·3 | 0006c000:·2030·2e31·3534·3335·3673·2028·7468·7265···0.154356s·(thre | ||
| 0006c010:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | 0006c010:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 0006c020:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | 0006c020:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 0006c030:·3031·3 | 0006c030:·3031·3137·3830·3173·2028·6370·7529·3b20··0117801s·(cpu);· | ||
| 0006c040:·3 | 0006c040:·322e·3033·3465·2d30·3673·2028·7468·7265··2.034e-06s·(thre | ||
| 0006c050:·6164·293b·2030·7320·2867·6329·7c0a·7c32··ad);·0s·(gc)|.|2 | 0006c050:·6164·293b·2030·7320·2867·6329·7c0a·7c32··ad);·0s·(gc)|.|2 | ||
| 0006c060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006c060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006c070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006c070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006c080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006c080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006c090:·2020·2020·2020·2020·7c0a·7c54·616c·6c79··········|.|Tally | 0006c090:·2020·2020·2020·2020·7c0a·7c54·616c·6c79··········|.|Tally | ||
| 0006c0a0:·7b7b·7b32·2c20·327d·2c20·7b31·2c20·327d··{{{2,·2},·{1,·2} | 0006c0a0:·7b7b·7b32·2c20·327d·2c20·7b31·2c20·327d··{{{2,·2},·{1,·2} | ||
| 0006c0b0:·7d20·3d3e·2033·7d20·2020·2020·2020·2020··}·=>·3}········· | 0006c0b0:·7d20·3d3e·2033·7d20·2020·2020·2020·2020··}·=>·3}········· | ||
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| 0006df30:·3d20·522f·286d·312c·206d·3229·2077·6865··=·R/(m1,·m2)·whe | 0006df30:·3d20·522f·286d·312c·206d·3229·2077·6865··=·R/(m1,·m2)·whe | ||
| 0006df40:·7265·206d·3120·616e·6420·6d32·2061·7265··re·m1·and·m2·are | 0006df40:·7265·206d·3120·616e·6420·6d32·2061·7265··re·m1·and·m2·are | ||
| 0006df50:·0a6d·6f6e·6f6d·6961·6c73·206f·6620·7468··.monomials·of·th | 0006df50:·0a6d·6f6e·6f6d·6961·6c73·206f·6620·7468··.monomials·of·th | ||
| 0006df60:·6520·7361·6d65·2064·6567·7265·652e·0a0a··e·same·degree... | 0006df60:·6520·7361·6d65·2064·6567·7265·652e·0a0a··e·same·degree... | ||
| 0006df70:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 0006df70:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 0006df80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006df80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006df90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006df90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006dfa0:·2d2d·2d2d·2d2 | 0006dfa0:·2d2d·2d2d·2d2d·2b0a·7c69·3120·3a20·7365··------+.|i1·:·se | ||
| 0006dfb0:·5261 | 0006dfb0:·7452·616e·646f·6d53·6565·6420·3020·2020··tRandomSeed·0··· | ||
| 0006dfc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006dfc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006dfd0:·2020·2020·2020·2020·2020·2020· | 0006dfd0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0006dfe0:· | 0006dfe0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 0006dff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006dff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006e000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006e000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006e010:·2020·20 | 0006e010:·2020·2020·2020·7c0a·7c6f·3120·3d20·3020········|.|o1·=·0· | ||
| 0006e020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006e020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006e030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006e030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006e040:·2020·2020·2020·2020·2020· | 0006e040:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0006e050:·2 | 0006e050:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 0006e060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006e060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006e070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006e070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006e080:·2d2b·0a7c·6932·203a·2074·776f·4d6f·6e6f··-+.|i2·:·twoMono | |||
| 0006e0 | 0006e080:·2d2d·2d2d·2d2d·2b0a·7c69·3220·3a20·7477··------+.|i2·:·tw | ||
| 0006e090:·6f4d·6f6e·6f6d·6961·6c73·2832·2c33·2920··oMonomials(2,3)· | |||
| 0006e0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006e0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006e0b0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | |||
| 0006e0c0:·7365·6420·322e·3239·3939·3173·2028·6370··sed·2.29991s·(cp | |||
| 0006e0d0:·7529·3b20·302e·3639·3834·3136·7320·2874··u);·0.698416s·(t | |||
| 0006e0e0:·6872·6561·6429·3b20·3073·2028·6763·297c··hread);·0s·(gc)| | |||
| 0006e0 | 0006e0b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0006e0c0:·7c20·2d2d·2075·7365·6420·322e·3239·3335··|·--·used·2.2935 | |||
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| 00004900:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004900:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00004910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00004920:·0a7c·6935·203a·2048·4220·3d20·4848·2042··.|i5·:·HB·=·HH·B | 00004920:·0a7c·6935·203a·2048·4220·3d20·4848·2042··.|i5·:·HB·=·HH·B | ||
| 00004930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004960:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00004960:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00004970:·0a7c·202d·2d20·7573·6564·2030·2e36·3 | 00004970:·0a7c·202d·2d20·7573·6564·2030·2e36·3032··.|·--·used·0.602 | ||
| 00004980:·39 | 00004980:·3973·2028·6370·7529·3b20·302e·3037·3138··9s·(cpu);·0.0718 | ||
| 00004990:·3 | 00004990:·3535·3573·2028·7468·7265·6164·293b·2030··555s·(thread);·0 | ||
| 000049a0:· | 000049a0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 000049b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000049b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000049c0:·0a7c·4669·6e64·696e·6720·6561·7379·2072··.|Finding·easy·r | 000049c0:·0a7c·4669·6e64·696e·6720·6561·7379·2072··.|Finding·easy·r | ||
| 000049d0:·656c·6174·696f·6e73·2020·2020·2020·2020··elations········ | 000049d0:·656c·6174·696f·6e73·2020·2020·2020·2020··elations········ | ||
| 000049e0:·2020·203a·2020·2020·2020·2020·2020·2020·····:············ | 000049e0:·2020·203a·2020·2020·2020·2020·2020·2020·····:············ | ||
| 000049f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000049f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004a00:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00004a00:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00004a10:·0a7c·6f35·203d·2048·4220·2020·2020·2020··.|o5·=·HB······· | 00004a10:·0a7c·6f35·203d·2048·4220·2020·2020·2020··.|o5·=·HB······· | ||
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| 00005770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000057a0:·2d2d·2b0a·7c69·3130·203a·2068·6f6d·6f6c··--+.|i10·:·homol | 000057a0:·2d2d·2b0a·7c69·3130·203a·2068·6f6d·6f6c··--+.|i10·:·homol | ||
| 000057b0:·6f67·7941·6c67·6562·7261·2843·2c47·656e··ogyAlgebra(C,Gen | 000057b0:·6f67·7941·6c67·6562·7261·2843·2c47·656e··ogyAlgebra(C,Gen | ||
| 000057c0:·4465·6772·6565·4c69·6d69·743d·3e34·2c52··DegreeLimit=>4,R | 000057c0:·4465·6772·6565·4c69·6d69·743d·3e34·2c52··DegreeLimit=>4,R | ||
| 000057d0:·656c·4465·6772·6565·4c69·6d69·743d·3e34··elDegreeLimit=>4 | 000057d0:·656c·4465·6772·6565·4c69·6d69·743d·3e34··elDegreeLimit=>4 | ||
| 000057e0:·297c·0a7c·202d·2d20·7573·6564·203 | 000057e0:·297c·0a7c·202d·2d20·7573·6564·2030·2e39··)|.|·--·used·0.9 | ||
| 000057f0:·3 | 000057f0:·3533·3438·3773·2028·6370·7529·3b20·302e··53487s·(cpu);·0. | ||
| 00005800:·3 | 00005800:·3137·3238·3773·2028·7468·7265·6164·293b··17287s·(thread); | ||
| 00005810:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 00005810:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 00005820:·7c0a·7c46·696e·6469·6e67·2065·6173·7920··|.|Finding·easy· | 00005820:·7c0a·7c46·696e·6469·6e67·2065·6173·7920··|.|Finding·easy· | ||
| 00005830:·7265·6c61·7469·6f6e·7320·2020·2020·2020··relations······· | 00005830:·7265·6c61·7469·6f6e·7320·2020·2020·2020··relations······· | ||
| 00005840:·2020·2020·3a20·2020·2020·2020·2020·2020······:··········· | 00005840:·2020·2020·3a20·2020·2020·2020·2020·2020······:··········· | ||
| 00005850:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00005850:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00005860:·0a7c·2020·2020·2020·205a·5a20·2020·2020··.|·······ZZ····· | 00005860:·0a7c·2020·2020·2020·205a·5a20·2020·2020··.|·······ZZ····· | ||
| 00005870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2539, 17 lines modified | Offset 2539, 17 lines modified | ||
| 00009ea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009eb0:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·484b··------+.|i7·:·HK | 00009eb0:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·484b··------+.|i7·:·HK | ||
| 00009ec0:·5220·3d20·4848·204b·5220·2020·2020·2020··R·=·HH·KR······· | 00009ec0:·5220·3d20·4848·204b·5220·2020·2020·2020··R·=·HH·KR······· | ||
| 00009ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f00:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00009f00:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00009f10:·6420·302e·3 | 00009f10:·6420·302e·3538·3435·3738·7320·2863·7075··d·0.584578s·(cpu | ||
| 00009f20:·293b·2030·2e31·3035·3039·3773·2028·7468··);·0.105097s·(th | |||
| 00009f | 00009f20:·293b·2030·2e30·3933·3231·3439·7320·2874··);·0.0932149s·(t | ||
| 00009f30:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | |||
| 00009f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f50:·2020·2020·2020·7c0a·7c46·696e·6469·6e67········|.|Finding | 00009f50:·2020·2020·2020·7c0a·7c46·696e·6469·6e67········|.|Finding | ||
| 00009f60:·2065·6173·7920·7265·6c61·7469·6f6e·7320···easy·relations· | 00009f60:·2065·6173·7920·7265·6c61·7469·6f6e·7320···easy·relations· | ||
| 00009f70:·2020·2020·2020·2020·2020·3a20·2020·2020············:····· | 00009f70:·2020·2020·2020·2020·2020·3a20·2020·2020············:····· | ||
| 00009f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fa0:·2020·2020·2020·7c0a·7c6f·3720·3d20·484b········|.|o7·=·HK | 00009fa0:·2020·2020·2020·7c0a·7c6f·3720·3d20·484b········|.|o7·=·HK | ||
| Offset 2644, 16 lines modified | Offset 2644, 16 lines modified | ||
| 0000a530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a540:·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a·2048··------+.|i10·:·H | 0000a540:·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a·2048··------+.|i10·:·H | ||
| 0000a550:·4b52·2720·3d20·4848·206b·6f73·7a75·6c43··KR'·=·HH·koszulC | 0000a550:·4b52·2720·3d20·4848·206b·6f73·7a75·6c43··KR'·=·HH·koszulC | ||
| 0000a560:·6f6d·706c·6578·4447·4120·5227·2020·2020··omplexDGA·R'···· | 0000a560:·6f6d·706c·6578·4447·4120·5227·2020·2020··omplexDGA·R'···· | ||
| 0000a570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a580:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a580:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a590:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 0000a590:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 0000a5a0:·6420·322e·3 | 0000a5a0:·6420·322e·3433·3934·3873·2028·6370·7529··d·2.43948s·(cpu) | ||
| 0000a5b0:·3b20·302e·3 | 0000a5b0:·3b20·302e·3734·3037·3134·7320·2874·6872··;·0.740714s·(thr | ||
| 0000a5c0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | 0000a5c0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 0000a5d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a5d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a5e0:·2020·2020·2020·7c0a·7c46·696e·6469·6e67········|.|Finding | 0000a5e0:·2020·2020·2020·7c0a·7c46·696e·6469·6e67········|.|Finding | ||
| 0000a5f0:·2065·6173·7920·7265·6c61·7469·6f6e·7320···easy·relations· | 0000a5f0:·2065·6173·7920·7265·6c61·7469·6f6e·7320···easy·relations· | ||
| 0000a600:·2020·2020·2020·2020·2020·3a20·2020·2020············:····· | 0000a600:·2020·2020·2020·2020·2020·3a20·2020·2020············:····· | ||
| 0000a610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 4348, 17 lines modified | Offset 4348, 17 lines modified | ||
| 00010fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010fd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010fd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010fe0:·2d2d·2d2d·2d2d·2b0a·7c69·3137·203a·2048··------+.|i17·:·H | 00010fe0:·2d2d·2d2d·2d2d·2b0a·7c69·3137·203a·2048··------+.|i17·:·H | ||
| 00010ff0:·4867·203d·2048·4820·6720·2020·2020·2020··Hg·=·HH·g······· | 00010ff0:·4867·203d·2048·4820·6720·2020·2020·2020··Hg·=·HH·g······· | ||
| 00011000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011010:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00011010:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00011020:·0a7c·202d·2d20·7573·6564·2030·2e35·3 | 00011020:·0a7c·202d·2d20·7573·6564·2030·2e35·3432··.|·--·used·0.542 | ||
| 00011030:·3 | 00011030:·3133·7320·2863·7075·293b·2030·2e30·3730··13s·(cpu);·0.070 | ||
| 00011040:·3 | 00011040:·3433·3537·7320·2874·6872·6561·6429·3b20··4357s·(thread);· | ||
| 00011050:·3073·2028·6763·2920·7c0a·7c46·696e·6469··0s·(gc)·|.|Findi | 00011050:·3073·2028·6763·2920·7c0a·7c46·696e·6469··0s·(gc)·|.|Findi | ||
| 00011060:·6e67·2065·6173·7920·7265·6c61·7469·6f6e··ng·easy·relation | 00011060:·6e67·2065·6173·7920·7265·6c61·7469·6f6e··ng·easy·relation | ||
| 00011070:·7320·2020·2020·2020·2020·2020·3a20·2020··s···········:··· | 00011070:·7320·2020·2020·2020·2020·2020·3a20·2020··s···········:··· | ||
| 00011080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011090:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00011090:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 000110a0:·2020·2020·2020·2020·2020·2020·2020·5a5a················ZZ | 000110a0:·2020·2020·2020·2020·2020·2020·2020·5a5a················ZZ | ||
| 000110b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000110b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00017190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000171a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000171a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000171b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000171b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000171c0:·2d2d·2b0a·7c69·3420·3a20·4841·203d·2068··--+.|i4·:·HA·=·h | 000171c0:·2d2d·2b0a·7c69·3420·3a20·4841·203d·2068··--+.|i4·:·HA·=·h | ||
| 000171d0:·6f6d·6f6c·6f67·7941·6c67·6562·7261·2841··omologyAlgebra(A | 000171d0:·6f6d·6f6c·6f67·7941·6c67·6562·7261·2841··omologyAlgebra(A | ||
| 000171e0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 000171e0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 000171f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000171f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017200:·2020·7c0a·7c20·2d2d·2075·7365·6420·3 | 00017200:·2020·7c0a·7c20·2d2d·2075·7365·6420·312e····|.|·--·used·1. | ||
| 00017210:·3734·3436·3634·7320·2863·7075·293b·2030··744664s·(cpu);·0 | |||
| 000172 | 00017210:·3736·3332·3573·2028·6370·7529·3b20·302e··76325s·(cpu);·0. | ||
| 00017220:·3235·3538·3834·7320·2874·6872·6561·6429··255884s·(thread) | |||
| 00017230:· | 00017230:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 00017240:·2020·7c0a·7c46·696e·6469·6e67·2065·6173····|.|Finding·eas | 00017240:·2020·7c0a·7c46·696e·6469·6e67·2065·6173····|.|Finding·eas | ||
| 00017250:·7920·7265·6c61·7469·6f6e·7320·2020·2020··y·relations····· | 00017250:·7920·7265·6c61·7469·6f6e·7320·2020·2020··y·relations····· | ||
| 00017260:·2020·2020·2020·3a20·2020·2020·2020·2020········:········· | 00017260:·2020·2020·2020·3a20·2020·2020·2020·2020········:········· | ||
| 00017270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017280:·2020·7c0a·7c6f·3420·3d20·4841·2020·2020····|.|o4·=·HA···· | 00017280:·2020·7c0a·7c6f·3420·3d20·4841·2020·2020····|.|o4·=·HA···· | ||
| 00017290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000172a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000172a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0003a460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003a460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003a470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003a470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003a480:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20··--------+.|i7·:· | 0003a480:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20··--------+.|i7·:· | ||
| 0003a490:·4848·6720·3d20·4848·2067·2020·2020·2020··HHg·=·HH·g······ | 0003a490:·4848·6720·3d20·4848·2067·2020·2020·2020··HHg·=·HH·g······ | ||
| 0003a4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003a4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003a4b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003a4b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003a4c0:·207c·0a7c·202d·2d20·7573·6564·2030·2e35···|.|·--·used·0.5 | 0003a4c0:·207c·0a7c·202d·2d20·7573·6564·2030·2e35···|.|·--·used·0.5 | ||
| 0003a4d0:·3 | 0003a4d0:·3431·3535·3673·2028·6370·7529·3b20·302e··41556s·(cpu);·0. | ||
| 0003a4e0:·303 | 0003a4e0:·3038·3131·3836·7320·2874·6872·6561·6429··081186s·(thread) | ||
| 0003a4f0:· | 0003a4f0:·3b20·3073·2028·6763·2920·7c0a·7c46·696e··;·0s·(gc)·|.|Fin | ||
| 0003a500:·6469·6e67·2065·6173·7920·7265·6c61·7469··ding·easy·relati | 0003a500:·6469·6e67·2065·6173·7920·7265·6c61·7469··ding·easy·relati | ||
| 0003a510:·6f6e·7320·2020·2020·2020·2020·2020·3a20··ons···········:· | 0003a510:·6f6e·7320·2020·2020·2020·2020·2020·3a20··ons···········:· | ||
| 0003a520:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003a520:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003a530:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0003a530:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0003a540:·2020·2020·2020·2020·2020·2020·2020·205a·················Z | 0003a540:·2020·2020·2020·2020·2020·2020·2020·205a·················Z | ||
| 0003a550:·5a20·2020·2020·2020·2020·2020·2020·2020··Z··············· | 0003a550:·5a20·2020·2020·2020·2020·2020·2020·2020··Z··············· | ||
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| 00009c20:·292c·2069·6465·616c·2879·2c7a·292c·2069··),·ideal(y,z),·i | 00009c20:·292c·2069·6465·616c·2879·2c7a·292c·2069··),·ideal(y,z),·i | ||
| 00009c30:·6465·616c·2878·2d79·2c20·782d·7a29·7d29··deal(x-y,·x-z)}) | 00009c30:·6465·616c·2878·2d79·2c20·782d·7a29·7d29··deal(x-y,·x-z)}) | ||
| 00009c40:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00009c40:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00009c50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c80:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 00009c80:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
| 00009c90:·3420·3d20·3 | 00009c90:·3420·3d20·332a·4469·7628·782c·207a·2920··4·=·3*Div(x,·z)· | ||
| 00009ca0:·2b20·302a·4469·7628·792c·207a·2920·2b20··+·0*Div(y,·z)·+· | |||
| 00009c | 00009cb0:·2d44·6976·2878·2d79·2c20·782d·7a29·2020··-Div(x-y,·x-z)·· | ||
| 00009cb0:·202b·2033·2a44·6976·2878·2c20·7a29·2020···+·3*Div(x,·z)·· | |||
| 00009cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009cd0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00009cd0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00009ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009cf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009cf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009d20:·207c·0a7c·6f31·3420·3a20·5765·696c·4469···|.|o14·:·WeilDi | 00009d20:·207c·0a7c·6f31·3420·3a20·5765·696c·4469···|.|o14·:·WeilDi | ||
| Offset 2527, 16 lines modified | Offset 2527, 16 lines modified | ||
| 00009de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009e00:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00009e00:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00009e10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009e10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009e20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009e20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009e30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009e30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009e40:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00009e40:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00009e50:·6f31·3520·3d20·4469 | 00009e50:·6f31·3520·3d20·2d33·2a44·6976·2878·2c20··o15·=·-3*Div(x,· | ||
| 00009e60:· | 00009e60:·7a29·202b·2044·6976·2878·2d79·2c20·782d··z)·+·Div(x-y,·x- | ||
| 00009e70:·7a29·2020·2020·2020·2020·2020·2020·2020··z)·············· | 00009e70:·7a29·2020·2020·2020·2020·2020·2020·2020··z)·············· | ||
| 00009e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009e90:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00009e90:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00009ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2555, 17 lines modified | Offset 2555, 17 lines modified | ||
| 00009fa0:·6c28·782c·207a·292c·2069·6465·616c·2879··l(x,·z),·ideal(y | 00009fa0:·6c28·782c·207a·292c·2069·6465·616c·2879··l(x,·z),·ideal(y | ||
| 00009fb0:·2c20·7a29·7d29·2020·2020·2020·2020·2020··,·z)})·········· | 00009fb0:·2c20·7a29·7d29·2020·2020·2020·2020·2020··,·z)})·········· | ||
| 00009fc0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00009fc0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00009fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a000:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000a000:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000a010:·0a7c·6f31·3620·3d20· | 0000a010:·0a7c·6f31·3620·3d20·332f·322a·4469·7628··.|o16·=·3/2*Div( | ||
| 0000a020:· | 0000a020:·782c·207a·2920·2b20·2d32·2f33·2a44·6976··x,·z)·+·-2/3*Div | ||
| 0000a030:·287 | 0000a030:·2879·2c20·7a29·2020·2020·2020·2020·2020··(y,·z)·········· | ||
| 0000a040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a050:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0000a050:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0000a060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a0a0:·2020·2020·207c·0a7c·6f31·3620·3a20·5765·······|.|o16·:·We | 0000a0a0:·2020·2020·207c·0a7c·6f31·3620·3a20·5765·······|.|o16·:·We | ||
| Offset 2583, 17 lines modified | Offset 2583, 17 lines modified | ||
| 0000a160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a180:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 0000a180:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 0000a190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a1b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a1c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1d0:·207c·0a7c·6f31·3720·3d20·3 | 0000a1d0:·207c·0a7c·6f31·3720·3d20·2d33·2f32·2a44···|.|o17·=·-3/2*D | ||
| 0000a1e0:·7628 | 0000a1e0:·6976·2878·2c20·7a29·202b·2032·2f33·2a44··iv(x,·z)·+·2/3*D | ||
| 0000a1f0:·6976·287 | 0000a1f0:·6976·2879·2c20·7a29·2020·2020·2020·2020··iv(y,·z)········ | ||
| 0000a200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a210:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000a210:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0000a220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a260:·2020·2020·2020·207c·0a7c·6f31·3720·3a20·········|.|o17·:· | 0000a260:·2020·2020·2020·207c·0a7c·6f31·3720·3a20·········|.|o17·:· | ||
| Offset 3130, 16 lines modified | Offset 3130, 16 lines modified | ||
| 0000c390:·7669·736f·7228·7b31·2c30·2c2d·327d·2c20··visor({1,0,-2},· | 0000c390:·7669·736f·7228·7b31·2c30·2c2d·327d·2c20··visor({1,0,-2},· | ||
| 0000c3a0:·7b69·6465·616c·2878·292c·2069·6465·616c··{ideal(x),·ideal | 0000c3a0:·7b69·6465·616c·2878·292c·2069·6465·616c··{ideal(x),·ideal | ||
| 0000c3b0:·2879·292c·2069·6465·616c·287a·297d·297c··(y),·ideal(z)})| | 0000c3b0:·2879·292c·2069·6465·616c·287a·297d·297c··(y),·ideal(z)})| | ||
| 0000c3c0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 0000c3c0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 0000c3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c3e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c3e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c3f0:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | 0000c3f0:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 0000c400:·3220·3d20·4469·7628·7 | 0000c400:·3220·3d20·302a·4469·7628·7929·202b·202d··2·=·0*Div(y)·+·- | ||
| 0000c410:· | 0000c410:·322a·4469·7628·7a29·202b·2044·6976·2878··2*Div(z)·+·Div(x | ||
| 0000c420:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 0000c420:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 0000c430:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 0000c430:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 0000c440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c470:·2020·2020·2020·7c0a·7c6f·3220·3a20·5765········|.|o2·:·We | 0000c470:·2020·2020·2020·7c0a·7c6f·3220·3a20·5765········|.|o2·:·We | ||
| 0000c480:·696c·4469·7669·736f·7220·6f6e·2052·2020··ilDivisor·on·R·· | 0000c480:·696c·4469·7669·736f·7220·6f6e·2052·2020··ilDivisor·on·R·· | ||
| Offset 3153, 16 lines modified | Offset 3153, 16 lines modified | ||
| 0000c500:·706f·7274·2844·2920·2020·2020·2020·2020··port(D)········· | 0000c500:·706f·7274·2844·2920·2020·2020·2020·2020··port(D)········· | ||
| 0000c510:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c510:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c520:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000c520:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000c530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c560:·2020·2020·2020·2020·2020·7c0a·7c6f·3320············|.|o3· | 0000c560:·2020·2020·2020·2020·2020·7c0a·7c6f·3320············|.|o3· | ||
| 0000c570:·3d20· | 0000c570:·3d20·2d32·2a44·6976·287a·2920·2b20·4469··=·-2*Div(z)·+·Di | ||
| 0000c580:·7628·7 | 0000c580:·7628·7829·2020·2020·2020·2020·2020·2020··v(x)············ | ||
| 0000c590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c5a0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 0000c5a0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 0000c5b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c5b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c5c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c5c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c5d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c5d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c5e0:·2020·2020·7c0a·7c6f·3320·3a20·5765·696c······|.|o3·:·Weil | 0000c5e0:·2020·2020·7c0a·7c6f·3320·3a20·5765·696c······|.|o3·:·Weil | ||
| 0000c5f0:·4469·7669·736f·7220·6f6e·2052·2020·2020··Divisor·on·R···· | 0000c5f0:·4469·7669·736f·7220·6f6e·2052·2020·2020··Divisor·on·R···· | ||
| Offset 4501, 19 lines modified | Offset 4501, 19 lines modified | ||
| 00011940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011950:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00011950:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00011960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000119a0:·2020·2020·2020·2020·2020·7c0a·7c6f·3135············|.|o15 | 000119a0:·2020·2020·2020·2020·2020·7c0a·7c6f·3135············|.|o15 | ||
| 000119b0:·203d·2044·6976·287 | 000119b0:·203d·2032·2a44·6976·2879·7a32·2c20·7932···=·2*Div(yz2,·y2 | ||
| 000119c0:·7 | 000119c0:·7a2c·2079·332c·2078·797a·2c20·7879·322c··z,·y3,·xyz,·xy2, | ||
| 000119d0:· | 000119d0:·2078·3279·2920·2b20·4469·7628·7a33·2c20···x2y)·+·Div(z3,· | ||
| 000119e0:· | 000119e0:·797a·322c·2079·327a·2c20·787a·322c·2078··yz2,·y2z,·xz2,·x | ||
| 000119f0:·79 | 000119f0:·797a·2c20·7832·7a29·2020·7c0a·7c20·2020··yz,·x2z)··|.|··· | ||
| 00011a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a40:·2020·2020·2020·2020·2020·7c0a·7c6f·3135············|.|o15 | 00011a40:·2020·2020·2020·2020·2020·7c0a·7c6f·3135············|.|o15 | ||
| 00011a50:·203a·2057·6569·6c44·6976·6973·6f72·206f···:·WeilDivisor·o | 00011a50:·203a·2057·6569·6c44·6976·6973·6f72·206f···:·WeilDivisor·o | ||
| 00011a60:·6e20·4120·2020·2020·2020·2020·2020·2020··n·A············· | 00011a60:·6e20·4120·2020·2020·2020·2020·2020·2020··n·A············· | ||
| Offset 4552, 17 lines modified | Offset 4552, 17 lines modified | ||
| 00011c70:·6465·616c·2878·297d·2c20·2020·2020·2020··deal(x)},······· | 00011c70:·6465·616c·2878·297d·2c20·2020·2020·2020··deal(x)},······· | ||
| Max diff block lines reached; 46079/55931 bytes (82.39%) of diff not shown. | |||
| Offset 3635, 17 lines modified | Offset 3635, 17 lines modified | ||
| 0000e320:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000e320:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000e330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e370:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000e370:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000e380:·6f33·203d·2047·7261·7068·7b22·6564·6765··o3·=·Graph{"edge | 0000e380:·6f33·203d·2047·7261·7068·7b22·6564·6765··o3·=·Graph{"edge | ||
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| 0000e3a0:·622c·2065·7d2c·207b·622c·2064·7d2c·207b··b,·e},·{b,·d},·{ | |||
| 0000e3 | 0000e3a0:·612c·2063·7d2c·207b·622c·2065·7d2c·207b··a,·c},·{b,·e},·{ | ||
| 0000e3b0:·622c·2064·7d2c·207b·632c·2065·7d7d·7d20··b,·d},·{c,·e}}}· | |||
| 0000e3c0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000e3c0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000e3d0:·2020·2020·2020·2020·2020·2022·7269·6e67·············"ring | 0000e3d0:·2020·2020·2020·2020·2020·2022·7269·6e67·············"ring | ||
| 0000e3e0:·2220·3d3e·2052·2020·2020·2020·2020·2020··"·=>·R·········· | 0000e3e0:·2220·3d3e·2052·2020·2020·2020·2020·2020··"·=>·R·········· | ||
| 0000e3f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e3f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e410:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000e410:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000e420:·2020·2020·2020·2020·2020·2022·7665·7274·············"vert | 0000e420:·2020·2020·2020·2020·2020·2022·7665·7274·············"vert | ||
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| 0001d5f0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0001d5f0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 0001d600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001d600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001d610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001d610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001d620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001d620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001d630:·2020·7c0a·7c6f·3420·3d20·4879·7065·7247····|.|o4·=·HyperG | 0001d630:·2020·7c0a·7c6f·3420·3d20·4879·7065·7247····|.|o4·=·HyperG | ||
| 0001d640:·7261·7068·7b22·6564·6765·7322·203d·3e20··raph{"edges"·=>· | 0001d640:·7261·7068·7b22·6564·6765·7322·203d·3e20··raph{"edges"·=>· | ||
| 0001d650:·7b7b·6 | 0001d650:·7b7b·632c·2064·7d2c·207b·622c·2063·7d2c··{{c,·d},·{b,·c}, | ||
| 0001d660:·207b·6 | 0001d660:·207b·612c·2065·7d7d·7d20·2020·2020·2020···{a,·e}}}······· | ||
| 0001d670:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 0001d670:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 0001d680:·2020·2020·2020·2022·7269·6e67·2220·3d3e·········"ring"·=> | 0001d680:·2020·2020·2020·2022·7269·6e67·2220·3d3e·········"ring"·=> | ||
| 0001d690:·2053·2020·2020·2020·2020·2020·2020·2020···S·············· | 0001d690:·2053·2020·2020·2020·2020·2020·2020·2020···S·············· | ||
| 0001d6a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001d6a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001d6b0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 0001d6b0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 0001d6c0:·2020·2020·2020·2020·2022·7665·7274·6963···········"vertic | 0001d6c0:·2020·2020·2020·2020·2022·7665·7274·6963···········"vertic | ||
| 0001d6d0:·6573·2220·3d3e·207b·612c·2062·2c20·632c··es"·=>·{a,·b,·c, | 0001d6d0:·6573·2220·3d3e·207b·612c·2062·2c20·632c··es"·=>·{a,·b,·c, | ||
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| 00050360:·207c·0a7c·6f33·203d·2048·7970·6572·4772···|.|o3·=·HyperGr | 00050360:·207c·0a7c·6f33·203d·2048·7970·6572·4772···|.|o3·=·HyperGr | ||
| 00050370:·6170·687b·2265·6467·6573·2220·3d3e·207b··aph{"edges"·=>·{ | 00050370:·6170·687b·2265·6467·6573·2220·3d3e·207b··aph{"edges"·=>·{ | ||
| 00050380:·7b78·202c·2078·202c·2078·207d·2c20·7b78··{x·,·x·,·x·},·{x | 00050380:·7b78·202c·2078·202c·2078·207d·2c20·7b78··{x·,·x·,·x·},·{x | ||
| 00050390:·202c·2078·207d·2c20·7b78·202c·2078·202c···,·x·},·{x·,·x·, | 00050390:·202c·2078·207d·2c20·7b78·202c·2078·202c···,·x·},·{x·,·x·, | ||
| 000503a0:·2078·202c·2078·207d·7d7d·2020·2020·2020···x·,·x·}}}······ | 000503a0:·2078·202c·2078·207d·7d7d·2020·2020·2020···x·,·x·}}}······ | ||
| 000503b0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 000503b0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 000503c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000503c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000503d0:·2020·3 | 000503d0:·2020·3120·2020·3320·2020·3520·2020·2020····1···3···5····· | ||
| 000503e0:·3 | 000503e0:·3420·2020·3520·2020·2020·3120·2020·3220··4···5·····1···2· | ||
| 000503f0:·2020·3 | 000503f0:·2020·3320·2020·3420·2020·2020·2020·2020····3···4········· | ||
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| 00050410:·2020·2020·2272·696e·6722·203d·3e20·5220······"ring"·=>·R· | 00050410:·2020·2020·2272·696e·6722·203d·3e20·5220······"ring"·=>·R· | ||
| 00050420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00050420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00050460:·2020·2020·2276·6572·7469·6365·7322·203d······"vertices"·= | 00050460:·2020·2020·2276·6572·7469·6365·7322·203d······"vertices"·= | ||
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| 00050680:·207c·0a7c·6f34·203d·2048·7970·6572·4772···|.|o4·=·HyperGr | |||
| 00050690:·6170·687b·2265·6467·6573·2220·3d3e·207b··aph{"edges"·=>·{ | |||
| 000506a0:·7b78·202c·2078·202c·2078·207d·2c20·7b78··{x·,·x·,·x·},·{x | |||
| 000506b0:·202c·2078·207d·2c20·7b78·202c·2078·202c···,·x·},·{x·,·x·, | |||
| 000506c0:·2078·202c·2078·207d·7d7d·2020·2020·2020···x·,·x·}}}······ | |||
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| 00050 | 00050630:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
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| 00050680:·2d2b·0a7c·6935·203a·2072·616e·646f·6d48··-+.|i5·:·randomH | |||
| 00050690:·7970·6572·4772·6170·6828·522c·7b34·2c34··yperGraph(R,{4,4 | |||
| 000506a0:·2c32·2c32·7d29·202d·2d20·696d·706f·7373··,2,2})·--·imposs | |||
| 000506b0:·6962·6c65·2c20·7265·7475·726e·7320·6e75··ible,·returns·nu | |||
| 000506c0:·6c6c·2077·6865·6e20·2020·2020·2020·2020··ll·when········· | |||
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| 00050720:·2d7c·0a7c·7469·6d65·2f62·7261·6e63·6820··-|.|time/branch· | |||
| 00050730:·6c69·6d69·7420·7265·6163·6865·6420·2020··limit·reached··· | |||
| 00050740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00050740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00050750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00050750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | Diff chunk too large, falling back to line-by-line diff (420 lines added, 420 lines removed) | |
| 00050760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00050760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00050790:· | 00050790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00000b10:·7c0a·7c20·2d2d·202e·3 | 00000b10:·7c0a·7c20·2d2d·202e·3433·3830·3531·7320··|.|·--·.438051s· | ||
| 00000b20:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 00000b20:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00000b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000b60:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | 00000b60:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00000b70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000b70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00001110:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001110:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001120:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001120:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001130:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:· | 00001130:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:· | ||
| 00001140:·7469·6d65·2065·6c69·6d69·6e61·7465·2878··time·eliminate(x | 00001140:·7469·6d65·2065·6c69·6d69·6e61·7465·2878··time·eliminate(x | ||
| 00001150:·2c69·6465·616c·2866·2c67·2929·2020·2020··,ideal(f,g))···· | 00001150:·2c69·6465·616c·2866·2c67·2929·2020·2020··,ideal(f,g))···· | ||
| 00001160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001170:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 00001170:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
| 00001180:·302e·3030·3 | 00001180:·302e·3030·3239·3630·3033·7320·2863·7075··0.00296003s·(cpu | ||
| 00001190:·293b·2030·2e30·3032·3 | 00001190:·293b·2030·2e30·3032·3937·3636·3373·2028··);·0.00297663s·( | ||
| 000011a0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | 000011a0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 000011b0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 000011b0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 000011c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000011c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000011d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000011d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000011e0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000011e0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000011f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000011f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001200:·2020·2020·2032·2020·2020·3220·2020·2020·······2····2····· | 00001200:·2020·2020·2032·2020·2020·3220·2020·2020·······2····2····· | ||
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| 000012f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000012f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001310:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20··--------+.|i5·:· | 00001310:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20··--------+.|i5·:· | ||
| 00001320:·7469·6d65·2069·6465·616c·2072·6573·756c··time·ideal·resul | 00001320:·7469·6d65·2069·6465·616c·2072·6573·756c··time·ideal·resul | ||
| 00001330:·7461·6e74·2866·2c67·2c78·2920·2020·2020··tant(f,g,x)····· | 00001330:·7461·6e74·2866·2c67·2c78·2920·2020·2020··tant(f,g,x)····· | ||
| 00001340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001350:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 00001350:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
| 00001360:·302e·3030·3133·3131·3032·7320·2863·7075··0.00131102s·(cpu | |||
| 000013 | 00001370:·293b·2030·2e30·3031·3538·3334·3773·2028··);·0.00158347s·( | ||
| 00001370:·7529·3b20·302e·3030·3132·3337·3273·2028··u);·0.0012372s·( | |||
| 00001380:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | 00001380:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 00001390:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00001390:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 000013a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000013a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000013b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000013b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000013c0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000013c0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000013d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000013d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000013e0:·2020·2020·2020·2032·2020·2020·3220·2020·········2····2··· | 000013e0:·2020·2020·2020·2032·2020·2020·3220·2020·········2····2··· | ||
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| 00002230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002250:·2d2d·2d2d·2d2b·0a7c·6934·203a·2074·696d··-----+.|i4·:·tim | 00002250:·2d2d·2d2d·2d2b·0a7c·6934·203a·2074·696d··-----+.|i4·:·tim | ||
| 00002260:·6520·656c·696d·696e·6174·6528·782c·6964··e·eliminate(x,id | 00002260:·6520·656c·696d·696e·6174·6528·782c·6964··e·eliminate(x,id | ||
| 00002270:·6561·6c28·662c·6729·2920·2020·2020·2020··eal(f,g))······· | 00002270:·6561·6c28·662c·6729·2920·2020·2020·2020··eal(f,g))······· | ||
| 00002280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002290:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | 00002290:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | ||
| 000022a0:·3030·3430·303 | 000022a0:·3030·3430·3037·3134·7320·2863·7075·293b··00400714s·(cpu); | ||
| 000022b0:·2030·2e30·303 | 000022b0:·2030·2e30·3032·3432·3236·3973·2028·7468···0.00242269s·(th | ||
| 000022c0:·7265·6164·293b·2030·7320·2867·6329·207c··read);·0s·(gc)·| | 000022c0:·7265·6164·293b·2030·7320·2867·6329·207c··read);·0s·(gc)·| | ||
| 000022d0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 000022d0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 000022e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000022e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000022f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000022f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002300:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00002300:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00002310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002320:·2020·2020·2032·2020·2020·3220·2020·2020·······2····2····· | 00002320:·2020·2020·2032·2020·2020·3220·2020·2020·······2····2····· | ||
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| 00002410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002430:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00002430:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00002440:·6935·203a·2074·696d·6520·6964·6561·6c20··i5·:·time·ideal· | 00002440:·6935·203a·2074·696d·6520·6964·6561·6c20··i5·:·time·ideal· | ||
| 00002450:·7265·7375·6c74·616e·7428·662c·672c·7829··resultant(f,g,x) | 00002450:·7265·7375·6c74·616e·7428·662c·672c·7829··resultant(f,g,x) | ||
| 00002460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002470:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00002470:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00002480:·2075·7365·6420·302e·3030·3032·3 | 00002480:·2075·7365·6420·302e·3030·3032·3834·3139···used·0.00028419 | ||
| 00002490:·3 | 00002490:·3373·2028·6370·7529·3b20·302e·3030·3132··3s·(cpu);·0.0012 | ||
| 000024a0:·3 | 000024a0:·3832·3031·7320·2874·6872·6561·6429·3b20··8201s·(thread);· | ||
| 000024b0:·3073·2028·6763·297c·0a7c·2020·2020·2020··0s·(gc)|.|······ | 000024b0:·3073·2028·6763·297c·0a7c·2020·2020·2020··0s·(gc)|.|······ | ||
| 000024c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000024d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000024e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000024f0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 000024f0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00002500:·2020·2020·2020·2020·2020·2020·2020·2032·················2 | 00002500:·2020·2020·2020·2020·2020·2020·2020·2032·················2 | ||
| 00002510:·2020·2020·3220·2020·2020·2020·2020·2020······2··········· | 00002510:·2020·2020·3220·2020·2020·2020·2020·2020······2··········· | ||
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| 00003850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003860:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00003860:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00003870:·7c69·3420·3a20·7469·6d65·2065·6c69·6d69··|i4·:·time·elimi | 00003870:·7c69·3420·3a20·7469·6d65·2065·6c69·6d69··|i4·:·time·elimi | ||
| 00003880:·6e61·7465·2869·6465·616c·2866·2c67·292c··nate(ideal(f,g), | 00003880:·6e61·7465·2869·6465·616c·2866·2c67·292c··nate(ideal(f,g), | ||
| 00003890:·7829·2020·2020·2020·2020·2020·2020·2020··x)·············· | 00003890:·7829·2020·2020·2020·2020·2020·2020·2020··x)·············· | ||
| 000038a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000038a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000038b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000038b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000038c0:·7c20·2d2d·2075·7365·6420·312e·3 | 000038c0:·7c20·2d2d·2075·7365·6420·312e·3431·3336··|·--·used·1.4136 | ||
| 000038d0:·2028·6370·7529·3b20·312e·3 | 000038d0:·3173·2028·6370·7529·3b20·312e·3236·3937··1s·(cpu);·1.2697 | ||
| 000038e0:·2874 | 000038e0:·3573·2028·7468·7265·6164·293b·2030·7320··5s·(thread);·0s· | ||
| 000038f0:·2 | 000038f0:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 00003900:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00003900:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00003910:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00003910:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00003920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003950:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00003950:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00003960:·7c20·2020·2020·2020·2020·2020·2037·2020··|············7·· | 00003960:·7c20·2020·2020·2020·2020·2020·2037·2020··|············7·· | ||
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| 000049d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000049d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000049e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 000049e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 000049f0:·7c69·3520·3a20·7469·6d65·2069·6465·616c··|i5·:·time·ideal | 000049f0:·7c69·3520·3a20·7469·6d65·2069·6465·616c··|i5·:·time·ideal | ||
| 00004a00:·2072·6573·756c·7461·6e74·2866·2c67·2c78···resultant(f,g,x | 00004a00:·2072·6573·756c·7461·6e74·2866·2c67·2c78···resultant(f,g,x | ||
| 00004a10:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 00004a10:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00004a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004a30:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00004a30:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00004a40:·7c20·2d2d·2075·7365·6420·302e·3031·3 | 00004a40:·7c20·2d2d·2075·7365·6420·302e·3031·3934··|·--·used·0.0194 | ||
| 00004a50:·3639·7320·2863·7075·293b·2030·2e30·3132··69s·(cpu);·0.012 | |||
| 00004a | 00004a50:·3733·3173·2028·6370·7529·3b20·302e·3031··731s·(cpu);·0.01 | ||
| 00004a60:·3631·3235·3773·2028·7468·7265·6164·293b··61257s·(thread); | |||
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| 00004a80:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00004a80:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 00007660:·7c0a·7c20·2020·2020·2d2d·2075·7365·6420··|.|·····--·used· | 00007660:·7c0a·7c20·2020·2020·2d2d·2075·7365·6420··|.|·····--·used· | ||
| 00007670:·2e30·3 | 00007670:·2e30·3334·3532·3634·2073·6563·6f6e·6473··.0345264·seconds | ||
| 00007680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000076a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076b0:·7c0a·7c20·2020·2020·2d2d·2075·7365·6420··|.|·····--·used· | 000076b0:·7c0a·7c20·2020·2020·2d2d·2075·7365·6420··|.|·····--·used· | ||
| 000076c0:·2e3 | 000076c0:·2e37·3038·3732·2073·6563·6f6e·6473·2020··.70872·seconds·· | ||
| 000076d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007700:·7c0a·7c28·3439·2c20·3231·3729·2020·2020··|.|(49,·217)···· | 00007700:·7c0a·7c28·3439·2c20·3231·3729·2020·2020··|.|(49,·217)···· | ||
| 00007710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00003930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003940:·2d2d·2d2d·2d2d·2b0a·7c69·3135·203a·2074··------+.|i15·:·t | 00003940:·2d2d·2d2d·2d2d·2b0a·7c69·3135·203a·2074··------+.|i15·:·t | ||
| 00003950:·696d·6520·493d·636f·3146·6974·7469·6e67··ime·I=co1Fitting | 00003950:·696d·6520·493d·636f·3146·6974·7469·6e67··ime·I=co1Fitting | ||
| 00003960:·284b·3329·2020·2020·2020·2020·2020·2020··(K3)············ | 00003960:·284b·3329·2020·2020·2020·2020·2020·2020··(K3)············ | ||
| 00003970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003990:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 00003990:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 000039a0:·3034·3032·3439·3673·2028·6370·7529·3b20··0402496s·(cpu);· | |||
| 000039 | 000039a0:·3030·3835·3937·3332·7320·2863·7075·293b··00859732s·(cpu); | ||
| 000039b0:·2030·2e30·3032·3035·3433·3373·2028·7468···0.00205433s·(th | |||
| 000039c0:·6561 | 000039c0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 000039d0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000039d0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000039e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000039e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000039f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000039f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003a20:·2020·2020·2020·207c·0a7c·6f31·3520·3d20·········|.|o15·=· | 00003a20:·2020·2020·2020·207c·0a7c·6f31·3520·3d20·········|.|o15·=· | ||
| 00003a30:·6964·6561·6c20·2861·2061·2020·202b·2061··ideal·(a·a···+·a | 00003a30:·6964·6561·6c20·2861·2061·2020·202b·2061··ideal·(a·a···+·a | ||
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| 00003b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003b80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00003b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00003ba0:·7c69·3136·203a·2074·696d·6520·4a3d·6669··|i16·:·time·J=fi | 00003ba0:·7c69·3136·203a·2074·696d·6520·4a3d·6669··|i16·:·time·J=fi | ||
| 00003bb0:·7474·696e·6749·6465·616c·2832·2d31·2c63··ttingIdeal(2-1,c | 00003bb0:·7474·696e·6749·6465·616c·2832·2d31·2c63··ttingIdeal(2-1,c | ||
| 00003bc0:·6f6b·6572·204b·3329·3b20·2020·2020·2020··oker·K3);······· | 00003bc0:·6f6b·6572·204b·3329·3b20·2020·2020·2020··oker·K3);······· | ||
| 00003bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003be0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00003be0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00003bf0:·7573·6564·2030·2e30·303 | 00003bf0:·7573·6564·2030·2e30·3035·3038·3633·3373··used·0.00508633s | ||
| 00003c00:·2028·6370·7529·3b20·302e·3030·343 | 00003c00:·2028·6370·7529·3b20·302e·3030·3439·3630···(cpu);·0.004960 | ||
| 00003c10:·3 | 00003c10:·3435·7320·2874·6872·6561·6429·3b20·3073··45s·(thread);·0s | ||
| 00003c20:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 00003c20:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00003c30:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00003c30:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00003c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003c50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003c50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003c70:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00003c70:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00003c80:·0a7c·6f31·3620·3a20·4964·6561·6c20·6f66··.|o16·:·Ideal·of | 00003c80:·0a7c·6f31·3620·3a20·4964·6561·6c20·6f66··.|o16·:·Ideal·of |
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| 0000d060:·203d·206d·616c·6c6f·6320·3820·2020·2020···=·malloc·8····· | 0000d060:·203d·206d·616c·6c6f·6320·3820·2020·2020···=·malloc·8····· | ||
| 0000d070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000d090:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 0000d090:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 0000d0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d0c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d0d0:·7c6f·3137·203d·2030·7837·66 | 0000d0d0:·7c6f·3137·203d·2030·7837·6631·3032·3430··|o17·=·0x7f10240 | ||
| 0000d0e0:·3633·3964·3020·2020·2020·2020·2020·2020··639d0··········· | 0000d0e0:·3633·3964·3020·2020·2020·2020·2020·2020··639d0··········· | ||
| 0000d0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d100:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0000d100:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0000d110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000d130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d140:·2020·2020·2020·7c0a·7c6f·3137·203a·2046········|.|o17·:·F | 0000d140:·2020·2020·2020·7c0a·7c6f·3137·203a·2046········|.|o17·:·F | ||
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| 0000d7f0:·2d2b·0a7c·6932·203a·2070·6565·6b20·6d70··-+.|i2·:·peek·mp | 0000d7f0:·2d2b·0a7c·6932·203a·2070·6565·6b20·6d70··-+.|i2·:·peek·mp | ||
| 0000d800:·6672·2020·2020·2020·2020·2020·2020·2020··fr·············· | 0000d800:·6672·2020·2020·2020·2020·2020·2020·2020··fr·············· | ||
| 0000d810:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000d810:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0000d820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d840:·2020·2020·2020·207c·0a7c·6f32·203d·2053·········|.|o2·=·S | 0000d840:·2020·2020·2020·207c·0a7c·6f32·203d·2053·········|.|o2·=·S | ||
| 0000d850:·6861·7265·644c·6962·7261·7279·7b30·7837··haredLibrary{0x7 | 0000d850:·6861·7265·644c·6962·7261·7279·7b30·7837··haredLibrary{0x7 | ||
| 0000d860:·66 | 0000d860:·6665·6666·6432·6235·3535·302c·206d·7066··feffd2b5550,·mpf | ||
| 0000d870:·727d·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d··r}|.+----------- | 0000d870:·727d·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d··r}|.+----------- | ||
| 0000d880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d890:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a0a··-------------+.. | 0000d890:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a0a··-------------+.. | ||
| 0000d8a0:·4675·6e63·7469·6f6e·7320·616e·6420·6d65··Functions·and·me | 0000d8a0:·4675·6e63·7469·6f6e·7320·616e·6420·6d65··Functions·and·me | ||
| 0000d8b0:·7468·6f64·7320·7265·7475·726e·696e·6720··thods·returning· | 0000d8b0:·7468·6f64·7320·7265·7475·726e·696e·6720··thods·returning· | ||
| 0000d8c0:·6120·7368·6172·6564·206c·6962·7261·7279··a·shared·library | 0000d8c0:·6120·7368·6172·6564·206c·6962·7261·7279··a·shared·library | ||
| 0000d8d0:·3a0a·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··:.============== | 0000d8d0:·3a0a·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··:.============== | ||
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| 00013cf0:·6520·706f·696e·7465·722e·0a0a·2b2d·2d2d··e·pointer...+--- | 00013cf0:·6520·706f·696e·7465·722e·0a0a·2b2d·2d2d··e·pointer...+--- | ||
| 00013d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00013d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00013d10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00013d10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00013d20:·6931·203a·2070·7472·203d·2061·6464·7265··i1·:·ptr·=·addre | 00013d20:·6931·203a·2070·7472·203d·2061·6464·7265··i1·:·ptr·=·addre | ||
| 00013d30:·7373·2069·6e74·2030·2020·2020·2020·2020··ss·int·0········ | 00013d30:·7373·2069·6e74·2030·2020·2020·2020·2020··ss·int·0········ | ||
| 00013d40:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00013d40:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00013d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013d60:·2020·207c·0a7c·6f31·203d·2030·7837·66 | 00013d60:·2020·207c·0a7c·6f31·203d·2030·7837·6633·····|.|o1·=·0x7f3 | ||
| 00013d70:· | 00013d70:·6465·6561·6433·3139·3020·2020·2020·2020··deead3190······· | ||
| 00013d80:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00013d80:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00013d90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013d90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013da0:·2020·2020·2020·2020·207c·0a7c·6f31·203a···········|.|o1·: | 00013da0:·2020·2020·2020·2020·207c·0a7c·6f31·203a···········|.|o1·: | ||
| 00013db0:·2050·6f69·6e74·6572·2020·2020·2020·2020···Pointer········ | 00013db0:·2050·6f69·6e74·6572·2020·2020·2020·2020···Pointer········ | ||
| 00013dc0:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | 00013dc0:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | ||
| 00013dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00013dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00013de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00013de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00013df0:·0a7c·6932·203a·2076·6f69·6473·7461·7220··.|i2·:·voidstar· | 00013df0:·0a7c·6932·203a·2076·6f69·6473·7461·7220··.|i2·:·voidstar· | ||
| 00013e00:·7074·7220·2020·2020·2020·2020·2020·2020··ptr············· | 00013e00:·7074·7220·2020·2020·2020·2020·2020·2020··ptr············· | ||
| 00013e10:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00013e10:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00013e20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013e20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013e30:·2020·2020·207c·0a7c·6f32·203d·2030·7837·······|.|o2·=·0x7 | 00013e30:·2020·2020·207c·0a7c·6f32·203d·2030·7837·······|.|o2·=·0x7 | ||
| 00013e40:·66 | 00013e40:·6633·6465·6561·6433·3139·3020·2020·2020··f3deead3190····· | ||
| 00013e50:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00013e50:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00013e60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00013e60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00013e70:·2020·2020·2020·2020·2020·207c·0a7c·6f32·············|.|o2 | 00013e70:·2020·2020·2020·2020·2020·207c·0a7c·6f32·············|.|o2 | ||
| 00013e80:·203a·2046·6f72·6569·676e·4f62·6a65·6374···:·ForeignObject | 00013e80:·203a·2046·6f72·6569·676e·4f62·6a65·6374···:·ForeignObject | ||
| 00013e90:·206f·6620·7479·7065·2076·6f69·642a·7c0a···of·type·void*|. | 00013e90:·206f·6620·7479·7065·2076·6f69·642a·7c0a···of·type·void*|. | ||
| 00013ea0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 00013ea0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 00013eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00013eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000142a0:·7065·2069·6e74·3332·7c0a·2b2d·2d2d·2d2d··pe·int32|.+----- | 000142a0:·7065·2069·6e74·3332·7c0a·2b2d·2d2d·2d2d··pe·int32|.+----- | ||
| 000142b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000142b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000142c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932··-----------+.|i2 | 000142c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932··-----------+.|i2 | ||
| 000142d0:·203a·2070·7472·203d·2061·6464·7265·7373···:·ptr·=·address | 000142d0:·203a·2070·7472·203d·2061·6464·7265·7373···:·ptr·=·address | ||
| 000142e0:·2078·2020·2020·2020·2020·2020·2020·7c0a···x············|. | 000142e0:·2078·2020·2020·2020·2020·2020·2020·7c0a···x············|. | ||
| 000142f0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 000142f0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00014300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014310:·207c·0a7c·6f32·203d·2030·7837·66 | 00014310:·207c·0a7c·6f32·203d·2030·7837·6665·3262···|.|o2·=·0x7fe2b | ||
| 00014320:·3 | 00014320:·3263·6632·3634·3020·2020·2020·2020·2020··2cf2640········· | ||
| 00014330:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00014330:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00014340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014350:·2020·2020·2020·207c·0a7c·6f32·203a·2050·········|.|o2·:·P | 00014350:·2020·2020·2020·207c·0a7c·6f32·203a·2050·········|.|o2·:·P | ||
| 00014360:·6f69·6e74·6572·2020·2020·2020·2020·2020··ointer·········· | 00014360:·6f69·6e74·6572·2020·2020·2020·2020·2020··ointer·········· | ||
| 00014370:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | 00014370:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | ||
| 00014380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00014390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
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| 00014b40:·7465·7273·2e0a·0a2b·2d2d·2d2d·2d2d·2d2d··ters...+-------- | 00014b40:·7465·7273·2e0a·0a2b·2d2d·2d2d·2d2d·2d2d··ters...+-------- | ||
| 00014b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014b60:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·203a··---------+.|i1·: | 00014b60:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·203a··---------+.|i1·: | ||
| 00014b70:·2070·7472·203d·2076·6f69·6473·7461·7220···ptr·=·voidstar· | 00014b70:·2070·7472·203d·2076·6f69·6473·7461·7220···ptr·=·voidstar· | ||
| 00014b80:·6164·6472·6573·7320·696e·7420·357c·0a7c··address·int·5|.| | 00014b80:·6164·6472·6573·7320·696e·7420·357c·0a7c··address·int·5|.| | ||
| 00014b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014bb0:·207c·0a7c·6f31·203d·2030·7837·66 | 00014bb0:·207c·0a7c·6f31·203d·2030·7837·6631·6132···|.|o1·=·0x7f1a2 | ||
| 00014bc0:·3 | 00014bc0:·3831·3934·3235·3020·2020·2020·2020·2020··8194250········· | ||
| 00014bd0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00014bd0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00014be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014bf0:·2020·2020·2020·2020·207c·0a7c·6f31·203a···········|.|o1·: | 00014bf0:·2020·2020·2020·2020·207c·0a7c·6f31·203a···········|.|o1·: | ||
| 00014c00:·2046·6f72·6569·676e·4f62·6a65·6374·206f···ForeignObject·o | 00014c00:·2046·6f72·6569·676e·4f62·6a65·6374·206f···ForeignObject·o | ||
| 00014c10:·6620·7479·7065·2076·6f69·642a·207c·0a2b··f·type·void*·|.+ | 00014c10:·6620·7479·7065·2076·6f69·642a·207c·0a2b··f·type·void*·|.+ | ||
| 00014c20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014c20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000150a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 000150a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 000150b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000150b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000150c0:·2d2b·0a7c·6931·203a·2070·7472·203d·2067··-+.|i1·:·ptr·=·g | 000150c0:·2d2b·0a7c·6931·203a·2070·7472·203d·2067··-+.|i1·:·ptr·=·g | ||
| 000150d0:·6574·4d65·6d6f·7279·2038·2020·2020·2020··etMemory·8······ | 000150d0:·6574·4d65·6d6f·7279·2038·2020·2020·2020··etMemory·8······ | ||
| 000150e0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 000150e0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 000150f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000150f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00015100:·2020·2020·2020·207c·0a7c·6f31·203d·2030·········|.|o1·=·0 | 00015100:·2020·2020·2020·207c·0a7c·6f31·203d·2030·········|.|o1·=·0 | ||
| 00015110:·7837·66 | 00015110:·7837·6635·3532·3962·6163·3961·3020·2020··x7f5529bac9a0··· | ||
| 00015120:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00015120:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00015130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00015140:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00015140:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00015150:·6f31·203a·2046·6f72·6569·676e·4f62·6a65··o1·:·ForeignObje | 00015150:·6f31·203a·2046·6f72·6569·676e·4f62·6a65··o1·:·ForeignObje | ||
| 00015160:·6374·206f·6620·7479·7065·2076·6f69·642a··ct·of·type·void* | 00015160:·6374·206f·6620·7479·7065·2076·6f69·642a··ct·of·type·void* | ||
| 00015170:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | 00015170:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00015180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00015180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00015210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00015210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00015220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932··-----------+.|i2 | 00015220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932··-----------+.|i2 | ||
| 00015230:·203a·2070·7472·203d·2067·6574·4d65·6d6f···:·ptr·=·getMemo | 00015230:·203a·2070·7472·203d·2067·6574·4d65·6d6f···:·ptr·=·getMemo | ||
| 00015240:·7279·2838·2c20·4174·6f6d·6963·203d·3e20··ry(8,·Atomic·=>· | 00015240:·7279·2838·2c20·4174·6f6d·6963·203d·3e20··ry(8,·Atomic·=>· | ||
| 00015250:·7472·7565·297c·0a7c·2020·2020·2020·2020··true)|.|········ | 00015250:·7472·7565·297c·0a7c·2020·2020·2020·2020··true)|.|········ | ||
| 00015260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00015270:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00015270:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00015280:·0a7c·6f32·203d·2030·7837·66 | 00015280:·0a7c·6f32·203d·2030·7837·6635·3533·3530··.|o2·=·0x7f55350 | ||
| 00015290:·6 | 00015290:·6632·3435·3020·2020·2020·2020·2020·2020··f2450··········· | ||
| 000152a0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000152a0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000152b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000152b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000152c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000152c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000152d0:·2020·207c·0a7c·6f32·203a·2046·6f72·6569·····|.|o2·:·Forei | 000152d0:·2020·207c·0a7c·6f32·203a·2046·6f72·6569·····|.|o2·:·Forei | ||
| 000152e0:·676e·4f62·6a65·6374·206f·6620·7479·7065··gnObject·of·type | 000152e0:·676e·4f62·6a65·6374·206f·6620·7479·7065··gnObject·of·type | ||
| 000152f0:·2076·6f69·642a·2020·2020·2020·207c·0a2b···void*·······|.+ | 000152f0:·2076·6f69·642a·2020·2020·2020·207c·0a2b···void*·······|.+ | ||
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| 00002ea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002ea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3220··----------+.|i2· | 00002eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3220··----------+.|i2· | ||
| 00002ec0:·3a20·7320·3d20·7465·6d70·6f72·6172·7946··:·s·=·temporaryF | 00002ec0:·3a20·7320·3d20·7465·6d70·6f72·6172·7946··:·s·=·temporaryF | ||
| 00002ed0:·696c·654e·616d·6528·2920·2020·2020·207c··ileName()······| | 00002ed0:·696c·654e·616d·6528·2920·2020·2020·207c··ileName()······| | ||
| 00002ee0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00002ee0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00002ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f00:·2020·2020·7c0a·7c6f·3220·3d20·2f74·6d70······|.|o2·=·/tmp | 00002f00:·2020·2020·7c0a·7c6f·3220·3d20·2f74·6d70······|.|o2·=·/tmp | ||
| 00002f10:·2f4d·322d·3 | 00002f10:·2f4d·322d·3335·3739·3637·362d·302f·3020··/M2-3579676-0/0· | ||
| 00002f20:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | 00002f20:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 00002f30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002f30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002f40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00002f40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00002f50:·7c69·3320·3a20·4620·3d20·6f70·656e·4f75··|i3·:·F·=·openOu | 00002f50:·7c69·3320·3a20·4620·3d20·6f70·656e·4f75··|i3·:·F·=·openOu | ||
| 00002f60:·7428·7329·2020·2020·2020·2020·2020·2020··t(s)············ | 00002f60:·7428·7329·2020·2020·2020·2020·2020·2020··t(s)············ | ||
| 00002f70:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00002f70:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 00002f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f90:·2020·2020·2020·2020·7c0a·7c6f·3320·3d20··········|.|o3·=· | 00002f90:·2020·2020·2020·2020·7c0a·7c6f·3320·3d20··········|.|o3·=· | ||
| 00002fa0:·2f74·6d70·2f4d·322d·3 | 00002fa0:·2f74·6d70·2f4d·322d·3335·3739·3637·362d··/tmp/M2-3579676- | ||
| 00002fb0:·302f·3020·2020·2020·2020·2020·207c·0a7c··0/0··········|.| | 00002fb0:·302f·3020·2020·2020·2020·2020·207c·0a7c··0/0··········|.| | ||
| 00002fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002fe0:·2020·7c0a·7c6f·3320·3a20·4669·6c65·2020····|.|o3·:·File·· | 00002fe0:·2020·7c0a·7c6f·3320·3a20·4669·6c65·2020····|.|o3·:·File·· | ||
| 00002ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003000:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 00003000:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00003010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00003060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003070:·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20·636c··------+.|i5·:·cl | 00003070:·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20·636c··------+.|i5·:·cl | ||
| 00003080:·6f73·6528·4629·2020·2020·2020·2020·2020··ose(F)·········· | 00003080:·6f73·6528·4629·2020·2020·2020·2020·2020··ose(F)·········· | ||
| 00003090:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00003090:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 000030a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000030b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000030c0:·7c0a·7c6f·3520·3d20·2f74·6d70·2f4d·322d··|.|o5·=·/tmp/M2- | 000030c0:·7c0a·7c6f·3520·3d20·2f74·6d70·2f4d·322d··|.|o5·=·/tmp/M2- | ||
| 000030d0:·3 | 000030d0:·3335·3739·3637·362d·302f·3020·2020·2020··3579676-0/0····· | ||
| 000030e0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 000030e0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 000030f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003100:·2020·2020·2020·2020·2020·7c0a·7c6f·3520············|.|o5· | 00003100:·2020·2020·2020·2020·2020·7c0a·7c6f·3520············|.|o5· | ||
| 00003110:·3a20·4669·6c65·2020·2020·2020·2020·2020··:·File·········· | 00003110:·3a20·4669·6c65·2020·2020·2020·2020·2020··:·File·········· | ||
| 00003120:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00003120:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00003130:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00003130:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00003140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00009d10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009d10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009d20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00009d20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00009d30:·6932·3720·3a20·7469·6d65·206e·756d·6572··i27·:·time·numer | 00009d30:·6932·3720·3a20·7469·6d65·206e·756d·6572··i27·:·time·numer | ||
| 00009d40:·6963·2066·7074·2866·2c20·4465·7074·684f··ic·fpt(f,·DepthO | 00009d40:·6963·2066·7074·2866·2c20·4465·7074·684f··ic·fpt(f,·DepthO | ||
| 00009d50:·6653·6561·7263·6820·3d3e·2033·2c20·4669··fSearch·=>·3,·Fi | 00009d50:·6653·6561·7263·6820·3d3e·2033·2c20·4669··fSearch·=>·3,·Fi | ||
| 00009d60:·6e61·6c41·7474·656d·7074·203d·3e20·7472··nalAttempt·=>·tr | 00009d60:·6e61·6c41·7474·656d·7074·203d·3e20·7472··nalAttempt·=>·tr | ||
| 00009d70:·7565·297c·0a7c·202d·2d20·7573·6564·2031··ue)|.|·--·used·1 | 00009d70:·7565·297c·0a7c·202d·2d20·7573·6564·2031··ue)|.|·--·used·1 | ||
| 00009d80:·2e3 | 00009d80:·2e37·3735·3632·7320·2863·7075·293b·2031··.77562s·(cpu);·1 | ||
| 00009d90:·2e3 | 00009d90:·2e31·3134·3736·7320·2874·6872·6561·6429··.11476s·(thread) | ||
| 00009da0:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | 00009da0:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 00009db0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00009db0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00009dc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009dc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009dd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009dd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009df0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00009df0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00009e00:·0a7c·6f32·3720·3d20·7b2e·3134·3230·3637··.|o27·=·{.142067 | 00009e00:·0a7c·6f32·3720·3d20·7b2e·3134·3230·3637··.|o27·=·{.142067 | ||
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| 00009ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009f00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009f00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009f10:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3820·3a20··-------+.|i28·:· | 00009f10:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3820·3a20··-------+.|i28·:· | ||
| 00009f20:·7469·6d65·2066·7074·2866·2c20·4465·7074··time·fpt(f,·Dept | 00009f20:·7469·6d65·2066·7074·2866·2c20·4465·7074··time·fpt(f,·Dept | ||
| 00009f30:·684f·6653·6561·7263·6820·3d3e·2033·2c20··hOfSearch·=>·3,· | 00009f30:·684f·6653·6561·7263·6820·3d3e·2033·2c20··hOfSearch·=>·3,· | ||
| 00009f40:·4174·7465·6d70·7473·203d·3e20·3729·2020··Attempts·=>·7)·· | 00009f40:·4174·7465·6d70·7473·203d·3e20·3729·2020··Attempts·=>·7)·· | ||
| 00009f50:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00009f50:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00009f60:·202d·2d20·7573·6564·203 | 00009f60:·202d·2d20·7573·6564·2031·2e30·3935·3439···--·used·1.09549 | ||
| 00009f70:·3373·2028·6370·7529·3b20·302e·3635·3531··3s·(cpu);·0.6551 | |||
| 00009f | 00009f70:·7320·2863·7075·293b·2030·2e37·3036·3736··s·(cpu);·0.70676 | ||
| 00009f80:·3673·2028·7468·7265·6164·293b·2030·7320··6s·(thread);·0s· | |||
| 00009f90:·2 | 00009f90:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 00009fa0:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00009fa0:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 00009fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fe0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00009fe0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00009ff0:·2020·3120·2020·2020·2020·2020·2020·2020····1············· | 00009ff0:·2020·3120·2020·2020·2020·2020·2020·2020····1············· | ||
| 0000a000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000a170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 0000a180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 0000a190:·6932·3920·3a20·7469·6d65·2066·7074·2866··i29·:·time·fpt(f | 0000a190:·6932·3920·3a20·7469·6d65·2066·7074·2866··i29·:·time·fpt(f | ||
| 0000a1a0:·2c20·4465·7074·684f·6653·6561·7263·6820··,·DepthOfSearch· | 0000a1a0:·2c20·4465·7074·684f·6653·6561·7263·6820··,·DepthOfSearch· | ||
| 0000a1b0:·3d3e·2034·2920·2020·2020·2020·2020·2020··=>·4)··········· | 0000a1b0:·3d3e·2034·2920·2020·2020·2020·2020·2020··=>·4)··········· | ||
| 0000a1c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a1c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1d0:·2020·207c·0a7c·202d·2d20·7573·6564·2030·····|.|·--·used·0 | 0000a1d0:·2020·207c·0a7c·202d·2d20·7573·6564·2030·····|.|·--·used·0 | ||
| 0000a1e0:·2e37·3 | 0000a1e0:·2e37·3938·3633·3373·2028·6370·7529·3b20··.798633s·(cpu);· | ||
| 0000a1f0:·302e·3 | 0000a1f0:·302e·3532·3031·3038·7320·2874·6872·6561··0.520108s·(threa | ||
| 0000a200:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | 0000a200:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 0000a210:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 0000a210:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 0000a220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a250:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000a250:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000a260:·0a7c·2020·2020·2020·3120·2020·2020·2020··.|······1······· | 0000a260:·0a7c·2020·2020·2020·3120·2020·2020·2020··.|······1······· | ||
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| 0000d960:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d960:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d970:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d970:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d980:·2d2d·2d2b·0a7c·6931·3520·3a20·7469·6d65··---+.|i15·:·time | 0000d980:·2d2d·2d2b·0a7c·6931·3520·3a20·7469·6d65··---+.|i15·:·time | ||
| 0000d990:·2066·726f·6265·6e69·7573·4e75·2833·2c20···frobeniusNu(3,· | 0000d990:·2066·726f·6265·6e69·7573·4e75·2833·2c20···frobeniusNu(3,· | ||
| 0000d9a0:·6629·2020·2020·2020·2020·2020·2020·2020··f)·············· | 0000d9a0:·6629·2020·2020·2020·2020·2020·2020·2020··f)·············· | ||
| 0000d9b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d9b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d9c0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 0000d9c0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 0000d9d0:·303 | 0000d9d0:·3034·3030·3039·3273·2028·6370·7529·3b20··0400092s·(cpu);· | ||
| 0000d9e0:·302e·3030·333 | 0000d9e0:·302e·3030·3336·3438·3436·7320·2874·6872··0.00364846s·(thr | ||
| 0000d9f0:·6561·6429·3b20·3073·2028·6763·2920·207c··ead);·0s·(gc)··| | 0000d9f0:·6561·6429·3b20·3073·2028·6763·2920·207c··ead);·0s·(gc)··| | ||
| 0000da00:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 0000da00:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 0000da10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000da10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000da20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000da20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000da30:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000da30:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000da40:·6f31·3520·3d20·3337·3536·2020·2020·2020··o15·=·3756······ | 0000da40:·6f31·3520·3d20·3337·3536·2020·2020·2020··o15·=·3756······ | ||
| 0000da50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000da50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000da90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000da90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000daa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000daa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000dab0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3620··---------+.|i16· | 0000dab0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3620··---------+.|i16· | ||
| 0000dac0:·3a20·7469·6d65·2066·726f·6265·6e69·7573··:·time·frobenius | 0000dac0:·3a20·7469·6d65·2066·726f·6265·6e69·7573··:·time·frobenius | ||
| 0000dad0:·4e75·2833·2c20·662c·2055·7365·5370·6563··Nu(3,·f,·UseSpec | 0000dad0:·4e75·2833·2c20·662c·2055·7365·5370·6563··Nu(3,·f,·UseSpec | ||
| 0000dae0:·6961·6c41·6c67·6f72·6974·686d·7320·3d3e··ialAlgorithms·=> | 0000dae0:·6961·6c41·6c67·6f72·6974·686d·7320·3d3e··ialAlgorithms·=> | ||
| 0000daf0:·2066·616c·7365·297c·0a7c·202d·2d20·7573···false)|.|·--·us | 0000daf0:·2066·616c·7365·297c·0a7c·202d·2d20·7573···false)|.|·--·us | ||
| 0000db00:·6564·2030·2e32·3 | 0000db00:·6564·2030·2e32·3838·3631·3773·2028·6370··ed·0.288617s·(cp | ||
| 0000db10:·7529·3b20·302e·323 | 0000db10:·7529·3b20·302e·3231·3433·3737·7320·2874··u);·0.214377s·(t | ||
| 0000db20:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 0000db20:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 0000db30:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 0000db30:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 0000db40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000db50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000db60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000db70:·2020·207c·0a7c·6f31·3620·3d20·3337·3536·····|.|o16·=·3756 | 0000db70:·2020·207c·0a7c·6f31·3620·3d20·3337·3536·····|.|o16·=·3756 | ||
| 0000db80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e1d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e1d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e1e0:·2d2d·2d2b·0a7c·6931·3920·3a20·7469·6d65··---+.|i19·:·time | 0000e1e0:·2d2d·2d2b·0a7c·6931·3920·3a20·7469·6d65··---+.|i19·:·time | ||
| 0000e1f0:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | 0000e1f0:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | ||
| 0000e200:·6629·202d·2d20·436f·6e74·6169·6e6d·656e··f)·--·Containmen | 0000e200:·6629·202d·2d20·436f·6e74·6169·6e6d·656e··f)·--·Containmen | ||
| 0000e210:·7454·6573·7420·6973·2073·6574·2074·6f20··tTest·is·set·to· | 0000e210:·7454·6573·7420·6973·2073·6574·2074·6f20··tTest·is·set·to· | ||
| 0000e220:·4672·6f62·656e·6975·7352·6f6f·742c·2062··FrobeniusRoot,·b | 0000e220:·4672·6f62·656e·6975·7352·6f6f·742c·2062··FrobeniusRoot,·b | ||
| 0000e230:·7920·207c·0a7c·202d·2d20·7573·6564·2030··y··|.|·--·used·0 | 0000e230:·7920·207c·0a7c·202d·2d20·7573·6564·2030··y··|.|·--·used·0 | ||
| 0000e240:·2e32·3 | 0000e240:·2e32·3937·3036·3373·2028·6370·7529·3b20··.297063s·(cpu);· | ||
| 0000e250:·302e·313 | 0000e250:·302e·3138·3335·3631·7320·2874·6872·6561··0.183561s·(threa | ||
| 0000e260:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | 0000e260:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 0000e270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e280:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0000e280:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0000e290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e2a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e2a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e2b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e2b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e2c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e2c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e3f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e3f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e410:·2d2d·2d2b·0a7c·6932·3020·3a20·7469·6d65··---+.|i20·:·time | 0000e410:·2d2d·2d2b·0a7c·6932·3020·3a20·7469·6d65··---+.|i20·:·time | ||
| 0000e420:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | 0000e420:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | ||
| 0000e430:·662c·2043·6f6e·7461·696e·6d65·6e74·5465··f,·ContainmentTe | 0000e430:·662c·2043·6f6e·7461·696e·6d65·6e74·5465··f,·ContainmentTe | ||
| 0000e440:·7374·203d·3e20·5374·616e·6461·7264·506f··st·=>·StandardPo | 0000e440:·7374·203d·3e20·5374·616e·6461·7264·506f··st·=>·StandardPo | ||
| 0000e450:·7765·7229·2020·2020·2020·2020·2020·2020··wer)············ | 0000e450:·7765·7229·2020·2020·2020·2020·2020·2020··wer)············ | ||
| 0000e460:·2020·207c·0a7c·202d·2d20·7573·6564·203 | 0000e460:·2020·207c·0a7c·202d·2d20·7573·6564·2031·····|.|·--·used·1 | ||
| 0000e470:·2e39·3437·3538·3673·2028·6370·7529·3b20··.947586s·(cpu);· | |||
| 0000e480:·302e·3832·3933·3632·7320·2874·6872·6561··0.829362s·(threa | |||
| 0000e4 | 0000e470:·2e31·3438·3235·7320·2863·7075·293b·2030··.14825s·(cpu);·0 | ||
| 0000e480:·2e39·3731·3732·3573·2028·7468·7265·6164··.971725s·(thread | |||
| 0000e490:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | |||
| 0000e4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e4b0:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0000e4b0:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0000e4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e4d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e4e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e4f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e500:·2020·207c·0a7c·6f32·3020·3d20·3439·3920·····|.|o20·=·499· | 0000e500:·2020·207c·0a7c·6f32·3020·3d20·3439·3920·····|.|o20·=·499· | ||
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| 0000eef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000eef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000421e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000421e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000421f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000421f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00042200:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3720··---------+.|i27· | 00042200:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3720··---------+.|i27· | ||
| 00042210:·3a20·7469·6d65·2043·203d·206f·7262·6974··:·time·C·=·orbit | 00042210:·3a20·7469·6d65·2043·203d·206f·7262·6974··:·time·C·=·orbit | ||
| 00042220:·436c·6f73·7572·6528·582c·4d61·7429·2020··Closure(X,Mat)·· | 00042220:·436c·6f73·7572·6528·582c·4d61·7429·2020··Closure(X,Mat)·· | ||
| 00042230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00042230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00042240:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00042240:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00042250:·7573·6564·2032·3 | 00042250:·7573·6564·2032·362e·3432·3439·7320·2863··used·26.4249s·(c | ||
| 00042260:·7075·293b·2033·2e3 | 00042260:·7075·293b·2033·2e32·3537·3234·7320·2874··pu);·3.25724s·(t | ||
| 00042270:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00042270:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00042280:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00042280:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
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| 000422a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000422a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000422c0:·2020·2020·2020·2020·207c·0a7c·6f32·3720···········|.|o27· | 000422c0:·2020·2020·2020·2020·207c·0a7c·6f32·3720···········|.|o27· | ||
| 000422d0:·3d20·616e·2022·6571·7569·7661·7269·616e··=·an·"equivarian | 000422d0:·3d20·616e·2022·6571·7569·7661·7269·616e··=·an·"equivarian | ||
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| 000423b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000423b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000423c0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3820··---------+.|i28· | 000423c0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3820··---------+.|i28· | ||
| 000423d0:·3a20·7469·6d65·2043·203d·206f·7262·6974··:·time·C·=·orbit | 000423d0:·3a20·7469·6d65·2043·203d·206f·7262·6974··:·time·C·=·orbit | ||
| 000423e0:·436c·6f73·7572·6528·582c·4d61·742c·2052··Closure(X,Mat,·R | 000423e0:·436c·6f73·7572·6528·582c·4d61·742c·2052··Closure(X,Mat,·R | ||
| 000423f0:·5245·464d·6574·686f·6420·3d3e·2074·7275··REFMethod·=>·tru | 000423f0:·5245·464d·6574·686f·6420·3d3e·2074·7275··REFMethod·=>·tru | ||
| 00042400:·6529·2020·2020·2020·207c·0a7c·202d·2d20··e)·······|.|·--· | 00042400:·6529·2020·2020·2020·207c·0a7c·202d·2d20··e)·······|.|·--· | ||
| 00042410:·7573·6564·203 | 00042410:·7573·6564·2032·362e·3935·3337·7320·2863··used·26.9537s·(c | ||
| 00042420:·7075·293b·203 | 00042420:·7075·293b·2033·2e38·3539·3934·7320·2874··pu);·3.85994s·(t | ||
| 00042430:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00042430:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00042440:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00042440:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
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| 00042480:·2020·2020·2020·2020·207c·0a7c·6f32·3820···········|.|o28· | 00042480:·2020·2020·2020·2020·207c·0a7c·6f32·3820···········|.|o28· | ||
| 00042490:·3d20·616e·2022·6571·7569·7661·7269·616e··=·an·"equivarian | 00042490:·3d20·616e·2022·6571·7569·7661·7269·616e··=·an·"equivarian |
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| 000416a0:·2020·2020·7c0a·7c6f·3320·3d20·7b6 | 000416a0:·2020·2020·7c0a·7c6f·3320·3d20·7b6d·6170······|.|o3·=·{map | ||
| 000416b0:· | 000416b0:·2c20·6e65·7744·6967·7261·7068·2c20·6469··,·newDigraph,·di | ||
| 000416c0:·6772·6170·687d·2020·2020·2020·2020·2020··graph}·········· | 000416c0:·6772·6170·687d·2020·2020·2020·2020·2020··graph}·········· | ||
| 000416d0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000416d0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 00000cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00000d10:·7c69·3520·3a20·656c·6170·7365·6454·696d··|i5·:·elapsedTim | 00000d10:·7c69·3520·3a20·656c·6170·7365·6454·696d··|i5·:·elapsedTim | ||
| 00000d20:·6520·6762·2049·3220·2020·2020·2020·2020··e·gb·I2········· | 00000d20:·6520·6762·2049·3220·2020·2020·2020·2020··e·gb·I2········· | ||
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| 00000fb0:·6c61·7073·6564·5469·6d65·2067·726f·6562··lapsedTime·groeb | 00000fb0:·6c61·7073·6564·5469·6d65·2067·726f·6562··lapsedTime·groeb | ||
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| 00000fe0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00000fe0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 00001040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f080:·6265·7461·2c20·7729·2020·2020·2020·2020··beta,·w)········ | 0000f080:·6265·7461·2c20·7729·2020·2020·2020·2020··beta,·w)········ | ||
| 0000f090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f0b0:·2020·207c·0a7c·202d·2d20·2e30·3030·3030·····|.|·--·.00000 | 0000f0b0:·2020·207c·0a7c·202d·2d20·2e30·3030·3030·····|.|·--·.00000 | ||
| 0000f0c0:·3 | 0000f0c0:·3437·3939·7320·656c·6170·7365·6420·2020··4799s·elapsed··· | ||
| 0000f0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f0e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f0e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f100:·2020·207c·0a7c·202d·2d20·2e30·3030·3030·····|.|·--·.00000 | 0000f100:·2020·207c·0a7c·202d·2d20·2e30·3030·3030·····|.|·--·.00000 | ||
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| 0000f120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f1e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f1e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00014e80:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320··----------+.|i3· | 00014e80:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320··----------+.|i3· | ||
| 00014e90:·3a20·736f·6c76·6546·726f·6265·6e69·7573··:·solveFrobenius | 00014e90:·3a20·736f·6c76·6546·726f·6265·6e69·7573··:·solveFrobenius | ||
| 00014ea0:·4964·6561·6c20·4920·2020·2020·2020·2020··Ideal·I········· | 00014ea0:·4964·6561·6c20·4920·2020·2020·2020·2020··Ideal·I········· | ||
| 00014eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ed0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00014ed0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00014ee0:·202e·3030·3030·303 | 00014ee0:·202e·3030·3030·3035·3130·3973·2065·6c61···.000005109s·ela | ||
| 00014ef0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 00014ef0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 00014f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f20:·2020·2020·2020·2020·2020·7c0a·7c57·6172············|.|War | 00014f20:·2020·2020·2020·2020·2020·7c0a·7c57·6172············|.|War | ||
| 00014f30:·6e69·6e67·3a20·2046·3420·416c·676f·7269··ning:··F4·Algori | 00014f30:·6e69·6e67·3a20·2046·3420·416c·676f·7269··ning:··F4·Algori | ||
| 00014f40:·7468·6d20·6e6f·7420·6176·6169·6c61·626c··thm·not·availabl | 00014f40:·7468·6d20·6e6f·7420·6176·6169·6c61·626c··thm·not·availabl | ||
| 00014f50:·6520·6f76·6572·2063·7572·7265·6e74·2063··e·over·current·c | 00014f50:·6520·6f76·6572·2063·7572·7265·6e74·2063··e·over·current·c | ||
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| 00015610:·3a20·736f·6c76·6546·726f·6265·6e69·7573··:·solveFrobenius | 00015610:·3a20·736f·6c76·6546·726f·6265·6e69·7573··:·solveFrobenius | ||
| 00015620:·4964·6561·6c28·492c·2057·2920·2020·2020··Ideal(I,·W)····· | 00015620:·4964·6561·6c28·492c·2057·2920·2020·2020··Ideal(I,·W)····· | ||
| 00015630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00015640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00015650:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00015650:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00015660:·202e·3030·3030·303 | 00015660:·202e·3030·3030·3035·3734·3173·2065·6c61···.000005741s·ela | ||
| 00015670:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 00015670:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 00015680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00015690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000156a0:·2020·2020·2020·2020·2020·7c0a·7c57·6172············|.|War | 000156a0:·2020·2020·2020·2020·2020·7c0a·7c57·6172············|.|War | ||
| 000156b0:·6e69·6e67·3a20·2046·3420·416c·676f·7269··ning:··F4·Algori | 000156b0:·6e69·6e67·3a20·2046·3420·416c·676f·7269··ning:··F4·Algori | ||
| 000156c0:·7468·6d20·6e6f·7420·6176·6169·6c61·626c··thm·not·availabl | 000156c0:·7468·6d20·6e6f·7420·6176·6169·6c61·626c··thm·not·availabl | ||
| 000156d0:·6520·6f76·6572·2063·7572·7265·6e74·2063··e·over·current·c | 000156d0:·6520·6f76·6572·2063·7572·7265·6e74·2063··e·over·current·c |
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| 000070b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000070b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000070c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000070c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000070d0:·2d2b·0a7c·6934·203a·204c·203d·2061·6e61··-+.|i4·:·L·=·ana | 000070d0:·2d2b·0a7c·6934·203a·204c·203d·2061·6e61··-+.|i4·:·L·=·ana | ||
| 000070e0:·6c79·7a65·5374·7261·6e64·2846·2c61·293b··lyzeStrand(F,a); | 000070e0:·6c79·7a65·5374·7261·6e64·2846·2c61·293b··lyzeStrand(F,a); | ||
| 000070f0:·2023·4c20·2020·2020·2020·2020·2020·2020···#L············· | 000070f0:·2023·4c20·2020·2020·2020·2020·2020·2020···#L············· | ||
| 00007100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007120:·207c·0a7c·202d·2d20·2e30·3 | 00007120:·207c·0a7c·202d·2d20·2e30·3331·3733·3931···|.|·--·.0317391 | ||
| 00007130:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00007130:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00007140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007170:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00007170:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00007180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 1939, 36 lines modified | Offset 1939, 36 lines modified | ||
| 00007920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007940:·2d2b·0a7c·6931·3020·3a20·6361·7270·6574··-+.|i10·:·carpet | 00007940:·2d2b·0a7c·6931·3020·3a20·6361·7270·6574··-+.|i10·:·carpet | ||
| 00007950:·4265·7474·6954·6162·6c65·2861·2c62·2c33··BettiTable(a,b,3 | 00007950:·4265·7474·6954·6162·6c65·2861·2c62·2c33··BettiTable(a,b,3 | ||
| 00007960:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 00007960:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00007970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007990:·207c·0a7c·202d·2d20·2e30·303 | 00007990:·207c·0a7c·202d·2d20·2e30·3032·3034·3634···|.|·--·.0020464 | ||
| 000079a0:·3 | 000079a0:·3173·2065·6c61·7073·6564·2020·2020·2020··1s·elapsed······ | ||
| 000079b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000079b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000079c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000079c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000079d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000079d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000079e0:·207c·0a7c·202d·2d20·2e30·303 | 000079e0:·207c·0a7c·202d·2d20·2e30·3036·3932·3838···|.|·--·.0069288 | ||
| 000079f0:·3 | 000079f0:·3873·2065·6c61·7073·6564·2020·2020·2020··8s·elapsed······ | ||
| 00007a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007a30:·207c·0a7c·202d·2d20·2e30·323 | 00007a30:·207c·0a7c·202d·2d20·2e30·3236·3330·3935···|.|·--·.0263095 | ||
| 00007a40:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00007a40:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00007a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007a80:·207c·0a7c·202d·2d20·2e30·3 | 00007a80:·207c·0a7c·202d·2d20·2e30·3130·3839·3639···|.|·--·.0108969 | ||
| 00007a90:· | 00007a90:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00007aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007ad0:·207c·0a7c·202d·2d20·2e30·3033·3 | 00007ad0:·207c·0a7c·202d·2d20·2e30·3033·3637·3431···|.|·--·.0036741 | ||
| 00007ae0:·7320 | 00007ae0:·3173·2065·6c61·7073·6564·2020·2020·2020··1s·elapsed······ | ||
| 00007af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007b00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007b00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007b20:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00007b20:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00007b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3576, 34 lines modified | Offset 3576, 34 lines modified | ||
| 0000df70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000df70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000df80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000df80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000df90:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3220·3a20··--------+.|i2·:· | 0000df90:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3220·3a20··--------+.|i2·:· | ||
| 0000dfa0:·656c·6170·7365·6454·696d·6520·543d·6361··elapsedTime·T=ca | 0000dfa0:·656c·6170·7365·6454·696d·6520·543d·6361··elapsedTime·T=ca | ||
| 0000dfb0:·7270·6574·4265·7474·6954·6162·6c65·2861··rpetBettiTable(a | 0000dfb0:·7270·6574·4265·7474·6954·6162·6c65·2861··rpetBettiTable(a | ||
| 0000dfc0:·2c62·2c33·2920·2020·2020·2020·2020·2020··,b,3)··········· | 0000dfc0:·2c62·2c33·2920·2020·2020·2020·2020·2020··,b,3)··········· | ||
| 0000dfd0:·2020·2020·207c·0a7c·202d·2d20·2e30·3031·······|.|·--·.001 | 0000dfd0:·2020·2020·207c·0a7c·202d·2d20·2e30·3031·······|.|·--·.001 | ||
| 0000dfe0:·3 | 0000dfe0:·3930·3539·3273·2065·6c61·7073·6564·2020··90592s·elapsed·· | ||
| 0000dff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e010:·2020·7c0a·7c20·2d2d·202e·3030·3 | 0000e010:·2020·7c0a·7c20·2d2d·202e·3030·3532·3738····|.|·--·.005278 | ||
| 0000e020:·3 | 0000e020:·3032·7320·656c·6170·7365·6420·2020·2020··02s·elapsed····· | ||
| 0000e030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e040:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000e040:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000e050:·0a7c·202d·2d20·2e30·3 | 0000e050:·0a7c·202d·2d20·2e30·3430·3935·3131·7320··.|·--·.0409511s· | ||
| 0000e060:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 0000e060:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 0000e070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e080:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000e080:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0000e090:·2d2d·202e·303 | 0000e090:·2d2d·202e·3031·3234·3534·7320·656c·6170··--·.012454s·elap | ||
| 0000e0a0:· | 0000e0a0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 0000e0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e0c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 0000e0c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 0000e0d0:·2e30·303 | 0000e0d0:·2e30·3033·3333·3839·3773·2065·6c61·7073··.00333897s·elaps | ||
| 0000e0e0:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | 0000e0e0:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | ||
| 0000e0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e100:·2020·2020·2020·7c0a·7c20·2d2d·202e·3 | 0000e100:·2020·2020·2020·7c0a·7c20·2d2d·202e·3333········|.|·--·.33 | ||
| 0000e110:·3 | 0000e110:·3937·3373·2065·6c61·7073·6564·2020·2020··973s·elapsed···· | ||
| 0000e120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e140:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0000e140:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0000e150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e180:·7c0a·7c20·2020·2020·2020·2020·2020·2030··|.|············0 | 0000e180:·7c0a·7c20·2020·2020·2020·2020·2020·2030··|.|············0 | ||
| Offset 3663, 16 lines modified | Offset 3663, 16 lines modified | ||
| 0000e4e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e4e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e4f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e4f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e510:·2d2d·2d2b·0a7c·6934·203a·2065·6c61·7073··---+.|i4·:·elaps | 0000e510:·2d2d·2d2b·0a7c·6934·203a·2065·6c61·7073··---+.|i4·:·elaps | ||
| 0000e520:·6564·5469·6d65·2054·273d·6d69·6e69·6d61··edTime·T'=minima | 0000e520:·6564·5469·6d65·2054·273d·6d69·6e69·6d61··edTime·T'=minima | ||
| 0000e530:·6c42·6574·7469·204a·2020·2020·2020·2020··lBetti·J········ | 0000e530:·6c42·6574·7469·204a·2020·2020·2020·2020··lBetti·J········ | ||
| 0000e540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e550:·7c0a·7c20·2d2d·202e·3 | 0000e550:·7c0a·7c20·2d2d·202e·3238·3935·3573·2065··|.|·--·.28955s·e | ||
| 0000e560:·6 | 0000e560:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 0000e570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e580:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000e580:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000e590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e5a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e5a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e5b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e5b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e5c0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0000e5c0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0000e5d0:·2020·2020·2020·2020·2030·2020·3120·2020···········0··1··· | 0000e5d0:·2020·2020·2020·2020·2030·2020·3120·2020···········0··1··· | ||
| Offset 3747, 42 lines modified | Offset 3747, 42 lines modified | ||
| 0000ea20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ea20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ea30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ea30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ea40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ea40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ea50:·2d2b·0a7c·6936·203a·2065·6c61·7073·6564··-+.|i6·:·elapsed | 0000ea50:·2d2b·0a7c·6936·203a·2065·6c61·7073·6564··-+.|i6·:·elapsed | ||
| 0000ea60:·5469·6d65·2068·3d63·6172·7065·7442·6574··Time·h=carpetBet | 0000ea60:·5469·6d65·2068·3d63·6172·7065·7442·6574··Time·h=carpetBet | ||
| 0000ea70:·7469·5461·626c·6573·2836·2c36·293b·2020··tiTables(6,6);·· | 0000ea70:·7469·5461·626c·6573·2836·2c36·293b·2020··tiTables(6,6);·· | ||
| 0000ea80:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000ea80:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000ea90:·7c20·2d2d·202e·3030·333 | 0000ea90:·7c20·2d2d·202e·3030·3338·3936·3634·7320··|·--·.00389664s· | ||
| 0000eaa0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 0000eaa0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
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| 000092d0:·2020·2020·2020·2020·2035·3020·2020·2020···········50····· | 000092d0:·2020·2020·2020·2020·2035·3020·2020·2020···········50····· | ||
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| 000093a0:·6934·203a·2074·696d·6520·4c4c·4c28·6d2c··i4·:·time·LLL(m, | 000093a0:·6934·203a·2074·696d·6520·4c4c·4c28·6d2c··i4·:·time·LLL(m, | ||
| 000093b0:·2053·7472·6174·6567·793d·3e43·6f68·656e···Strategy=>Cohen | 000093b0:·2053·7472·6174·6567·793d·3e43·6f68·656e···Strategy=>Cohen | ||
| 000093c0:·456e·6769·6e65·293b·2020·2020·2020·2020··Engine);········ | 000093c0:·456e·6769·6e65·293b·2020·2020·2020·2020··Engine);········ | ||
| 000093d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000093d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000093e0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 000093e0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
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| 00009420:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00009420:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
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| 00009530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009540:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2074··-------+.|i5·:·t | 00009540:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2074··-------+.|i5·:·t | ||
| 00009550:·696d·6520·4c4c·4c28·6d2c·2053·7472·6174··ime·LLL(m,·Strat | 00009550:·696d·6520·4c4c·4c28·6d2c·2053·7472·6174··ime·LLL(m,·Strat | ||
| 00009560:·6567·793d·3e43·6f68·656e·546f·704c·6576··egy=>CohenTopLev | 00009560:·6567·793d·3e43·6f68·656e·546f·704c·6576··egy=>CohenTopLev | ||
| 00009570:·656c·293b·2020·2020·2020·2020·2020·2020··el);············ | 00009570:·656c·293b·2020·2020·2020·2020·2020·2020··el);············ | ||
| 00009580:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00009580:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00009590:·7c20·2d2d·2075·7365·6420·302e·3 | 00009590:·7c20·2d2d·2075·7365·6420·302e·3130·3336··|·--·used·0.1036 | ||
| 000095a0:·3 | 000095a0:·3535·7320·2863·7075·293b·2030·2e31·3033··55s·(cpu);·0.103 | ||
| 000095b0:·3 | 000095b0:·3535·3273·2028·7468·7265·6164·293b·2030··552s·(thread);·0 | ||
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| 000095d0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 000095d0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 000095e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000095e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000095f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000095f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00009620:·2020·2020·2020·2020·2020·2020·2035·3020···············50· | 00009620:·2020·2020·2020·2020·2020·2020·2035·3020···············50· | ||
| 00009630:·2020·2020·2020·3437·2020·2020·2020·2020········47········ | 00009630:·2020·2020·2020·3437·2020·2020·2020·2020········47········ | ||
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| 000096e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000096e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000096f0:·2d2b·0a7c·6936·203a·2074·696d·6520·4c4c··-+.|i6·:·time·LL | 000096f0:·2d2b·0a7c·6936·203a·2074·696d·6520·4c4c··-+.|i6·:·time·LL | ||
| 00009700:·4c28·6d2c·2053·7472·6174·6567·793d·3e7b··L(m,·Strategy=>{ | 00009700:·4c28·6d2c·2053·7472·6174·6567·793d·3e7b··L(m,·Strategy=>{ | ||
| 00009710:·4769·7665·6e73·2c52·6561·6c46·507d·293b··Givens,RealFP}); | 00009710:·4769·7665·6e73·2c52·6561·6c46·507d·293b··Givens,RealFP}); | ||
| 00009720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009730:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | 00009730:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | ||
| 00009740:·7365·6420·302e·303 | 00009740:·7365·6420·302e·3031·3031·3432·3873·2028··sed·0.0101428s·( | ||
| 00009750:· | 00009750:·6370·7529·3b20·302e·3031·3130·3436·3273··cpu);·0.0110462s | ||
| 00009760:· | 00009760:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | ||
| 00009770:· | 00009770:·6329·2020·2020·2020·2020·2020·2020·207c··c)·············| | ||
| 00009780:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00009780:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00009790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000097a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000097a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000097b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000097b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000097c0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 000097c0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 000097d0:·2020·2020·2020·2035·3020·2020·2020·2020·········50······· | 000097d0:·2020·2020·2020·2035·3020·2020·2020·2020·········50······· | ||
| 000097e0:·3437·2020·2020·2020·2020·2020·2020·2020··47·············· | 000097e0:·3437·2020·2020·2020·2020·2020·2020·2020··47·············· | ||
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| 00009880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009890:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937··-----------+.|i7 | 00009890:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937··-----------+.|i7 | ||
| 000098a0:·203a·2074·696d·6520·4c4c·4c28·6d2c·2053···:·time·LLL(m,·S | 000098a0:·203a·2074·696d·6520·4c4c·4c28·6d2c·2053···:·time·LLL(m,·S | ||
| 000098b0:·7472·6174·6567·793d·3e7b·4769·7665·6e73··trategy=>{Givens | 000098b0:·7472·6174·6567·793d·3e7b·4769·7665·6e73··trategy=>{Givens | ||
| 000098c0:·2c52·6561·6c51·507d·293b·2020·2020·2020··,RealQP});······ | 000098c0:·2c52·6561·6c51·507d·293b·2020·2020·2020··,RealQP});······ | ||
| 000098d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000098d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000098e0:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | 000098e0:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | ||
| 000098f0:·3034·3833·3330·3273·2028·6370·7529·3b20··0483302s·(cpu);· | |||
| 00009900:·302e·3035·3037·3873·2028·7468·7265·6164··0.05078s·(thread | |||
| 00009 | 000098f0:·3035·3035·3739·7320·2863·7075·293b·2030··050579s·(cpu);·0 | ||
| 00009900:·2e30·3531·3137·3434·7320·2874·6872·6561··.0511744s·(threa | |||
| 00009910:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | |||
| 00009920:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00009920:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00009930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00009980:·2035·3020·2020·2020·2020·3437·2020·2020···50·······47···· | 00009980:·2035·3020·2020·2020·2020·3437·2020·2020···50·······47···· | ||
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| 00009a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009a30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009a30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009a40:·2d2d·2d2d·2d2b·0a7c·6938·203a·2074·696d··-----+.|i8·:·tim | 00009a40:·2d2d·2d2d·2d2b·0a7c·6938·203a·2074·696d··-----+.|i8·:·tim | ||
| 00009a50:·6520·4c4c·4c28·6d2c·2053·7472·6174·6567··e·LLL(m,·Strateg | 00009a50:·6520·4c4c·4c28·6d2c·2053·7472·6174·6567··e·LLL(m,·Strateg | ||
| 00009a60:·793d·3e7b·4769·7665·6e73·2c52·6561·6c58··y=>{Givens,RealX | 00009a60:·793d·3e7b·4769·7665·6e73·2c52·6561·6c58··y=>{Givens,RealX | ||
| 00009a70:·447d·293b·2020·2020·2020·2020·2020·2020··D});············ | 00009a70:·447d·293b·2020·2020·2020·2020·2020·2020··D});············ | ||
| 00009a80:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00009a80:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
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| 00009a | 00009aa0:·3873·2028·6370·7529·3b20·302e·3035·3539··8s·(cpu);·0.0559 | ||
| 00009ab0:·3231·3173·2028·7468·7265·6164·293b·2030··211s·(thread);·0 | |||
| 00009ac0:·2028 | 00009ac0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
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| 00009ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00009b30:·2020·2020·3437·2020·2020·2020·2020·2020······47·········· | 00009b30:·2020·2020·3437·2020·2020·2020·2020·2020······47·········· | ||
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| 00009c00:·6d2c·2053·7472·6174·6567·793d·3e7b·4769··m,·Strategy=>{Gi | 00009c00:·6d2c·2053·7472·6174·6567·793d·3e7b·4769··m,·Strategy=>{Gi | ||
| 00009c10:·7665·6e73·2c52·6561·6c52·527d·293b·2020··vens,RealRR});·· | 00009c10:·7665·6e73·2c52·6561·6c52·527d·293b·2020··vens,RealRR});·· | ||
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| 00009c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000046e0:·6963·2850·2c50·2c73·6d6f·6f74·6854·6573··ic(P,P,smoothTes | 000046e0:·6963·2850·2c50·2c73·6d6f·6f74·6854·6573··ic(P,P,smoothTes | ||
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| 00004720:·7365·6420·322e·3 | 00004720:·7365·6420·322e·3633·3137·3373·2028·6370··sed·2.63173s·(cp | ||
| 00004730:·7529·3b20·302e·353 | 00004730:·7529·3b20·302e·3536·3139·3637·7320·2874··u);·0.561967s·(t | ||
| 00004740:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00004740:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00004750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004760:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | 00004760:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | ||
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| 00008000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00008040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008060:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00008060:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
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| 00008220:·2c66·2c49·6e6e·6572·3d3e·7b7b·312c·327d··,f,Inner=>{{1,2} | 00008220:·2c66·2c49·6e6e·6572·3d3e·7b7b·312c·327d··,f,Inner=>{{1,2} | ||
| 00008230:·2c7b·332c·317d·7d2c·4f75·7465·723d·3e7b··,{3,1}},Outer=>{ | 00008230:·2c7b·332c·317d·7d2c·4f75·7465·723d·3e7b··,{3,1}},Outer=>{ | ||
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| 00008260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00008280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008290:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00008290:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 000082a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000082a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000082b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000082b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000082c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000082c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f430:·6c61·7073·6564·5469·6d65·206c·696e·6561··lapsedTime·linea | 0000f430:·6c61·7073·6564·5469·6d65·206c·696e·6561··lapsedTime·linea | ||
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| 0000f460:·4d29·7c0a·7c20·2d2d·203 | 0000f460:·4d29·7c0a·7c20·2d2d·2034·392e·3439·3131··M)|.|·--·49.4911 | ||
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| 0000f480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f490:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000f490:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000f4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f4b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f4b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f4d0:·2020·2020·2020·2020·7c0a·7c6f·3620·3d20··········|.|o6·=· | 0000f4d0:·2020·2020·2020·2020·7c0a·7c6f·3620·3d20··········|.|o6·=· | ||
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| 0000f590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f5a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f5a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f5c0:·2d2d·2d2d·2b0a·7c69·3720·3a20·656c·6170··----+.|i7·:·elap | 0000f5c0:·2d2d·2d2d·2b0a·7c69·3720·3a20·656c·6170··----+.|i7·:·elap | ||
| 0000f5d0:·7365·6454·696d·6520·6c69·6e65·6172·5472··sedTime·linearTr | 0000f5d0:·7365·6454·696d·6520·6c69·6e65·6172·5472··sedTime·linearTr | ||
| 0000f5e0:·756e·6361·7469·6f6e·7342·6f75·6e64·204d··uncationsBound·M | 0000f5e0:·756e·6361·7469·6f6e·7342·6f75·6e64·204d··uncationsBound·M | ||
| 0000f5f0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000f5f0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000f600:·0a7c·202d·2d20·2e30·3 | 0000f600:·0a7c·202d·2d20·2e30·3234·3435·3331·7320··.|·--·.0244531s· | ||
| 0000f610:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 0000f610:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 0000f620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f630:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0000f630:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0000f640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f670:·2020·2020·207c·0a7c·6f37·203d·207b·7b34·······|.|o7·=·{{4 | 0000f670:·2020·2020·207c·0a7c·6f37·203d·207b·7b34·······|.|o7·=·{{4 |
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| 000095a0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 000095a0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 000095b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000095b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000095c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000095c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000095d0:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2065··-------+.|i5·:·e | 000095d0:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2065··-------+.|i5·:·e | ||
| 000095e0:·6c61·7073·6564·5469·6d65·2068·696c·6265··lapsedTime·hilbe | 000095e0:·6c61·7073·6564·5469·6d65·2068·696c·6265··lapsedTime·hilbe | ||
| 000095f0:·7274·5361·6d75·656c·4675·6e63·7469·6f6e··rtSamuelFunction | 000095f0:·7274·5361·6d75·656c·4675·6e63·7469·6f6e··rtSamuelFunction | ||
| 00009600:·284d·2c20·302c·2036·2920·2020·2020·207c··(M,·0,·6)······| | 00009600:·284d·2c20·302c·2036·2920·2020·2020·207c··(M,·0,·6)······| | ||
| 00009610:·0a7c·202d·2d20·2e3 | 00009610:·0a7c·202d·2d20·2e33·3837·3837·3673·2065··.|·--·.387876s·e | ||
| 00009620:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 00009620:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 00009630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009640:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00009640:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00009650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009670:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00009670:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00009680:·0a7c·6f35·203d·207b·312c·2033·2c20·362c··.|o5·=·{1,·3,·6, | 00009680:·0a7c·6f35·203d·207b·312c·2033·2c20·362c··.|o5·=·{1,·3,·6, | ||
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| 00009e40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009e40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009e50:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3131·203a··--------+.|i11·: | 00009e50:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3131·203a··--------+.|i11·: | ||
| 00009e60:·2065·6c61·7073·6564·5469·6d65·2068·696c···elapsedTime·hil | 00009e60:·2065·6c61·7073·6564·5469·6d65·2068·696c···elapsedTime·hil | ||
| 00009e70:·6265·7274·5361·6d75·656c·4675·6e63·7469··bertSamuelFuncti | 00009e70:·6265·7274·5361·6d75·656c·4675·6e63·7469··bertSamuelFuncti | ||
| 00009e80:·6f6e·284e·2c20·302c·2035·2920·2d2d·206e··on(N,·0,·5)·--·n | 00009e80:·6f6e·284e·2c20·302c·2035·2920·2d2d·206e··on(N,·0,·5)·--·n | ||
| 00009e90:·2b31·202d·2d20·302e·3032·2073·6563·6f6e··+1·--·0.02·secon | 00009e90:·2b31·202d·2d20·302e·3032·2073·6563·6f6e··+1·--·0.02·secon | ||
| 00009ea0:·6473·2020·2020·2020·7c0a·7c20·2d2d·202e··ds······|.|·--·. | 00009ea0:·6473·2020·2020·2020·7c0a·7c20·2d2d·202e··ds······|.|·--·. | ||
| 00009eb0:·303 | 00009eb0:·3031·3334·3337·3173·2065·6c61·7073·6564··0134371s·elapsed | ||
| 00009ec0:· | 00009ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ef0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00009ef0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00009f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000a070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a080:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3132·203a··--------+.|i12·: | 0000a080:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3132·203a··--------+.|i12·: | ||
| 0000a090:·2065·6c61·7073·6564·5469·6d65·2068·696c···elapsedTime·hil | 0000a090:·2065·6c61·7073·6564·5469·6d65·2068·696c···elapsedTime·hil | ||
| 0000a0a0:·6265·7274·5361·6d75·656c·4675·6e63·7469··bertSamuelFuncti | 0000a0a0:·6265·7274·5361·6d75·656c·4675·6e63·7469··bertSamuelFuncti | ||
| 0000a0b0:·6f6e·2871·2c20·4e2c·2030·2c20·3529·202d··on(q,·N,·0,·5)·- | 0000a0b0:·6f6e·2871·2c20·4e2c·2030·2c20·3529·202d··on(q,·N,·0,·5)·- | ||
| 0000a0c0:·2d20·3628·6e2b·3129·202d·2d20·302e·3332··-·6(n+1)·--·0.32 | 0000a0c0:·2d20·3628·6e2b·3129·202d·2d20·302e·3332··-·6(n+1)·--·0.32 | ||
| 0000a0d0:·2073·6563·6f6e·6473·7c0a·7c20·2d2d·202e···seconds|.|·--·. | 0000a0d0:·2073·6563·6f6e·6473·7c0a·7c20·2d2d·202e···seconds|.|·--·. | ||
| 0000a0e0:·3 | 0000a0e0:·3631·3437·3639·7320·656c·6170·7365·6420··614769s·elapsed· | ||
| 0000a0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a120:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 0000a120:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 0000a130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a150:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00002400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00002410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00002420:·0a7c·6938·203a·2074·696d·6520·6e65·744c··.|i8·:·time·netL | 00002420:·0a7c·6938·203a·2074·696d·6520·6e65·744c··.|i8·:·time·netL | ||
| 00002430:·6973·7420·7072·696d·6172·7944·6563·6f6d··ist·primaryDecom | 00002430:·6973·7420·7072·696d·6172·7944·6563·6f6d··ist·primaryDecom | ||
| 00002440:·706f·7369·7469·6f6e·204a·2020·2020·2020··position·J······ | 00002440:·706f·7369·7469·6f6e·204a·2020·2020·2020··position·J······ | ||
| 00002450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002460:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00002460:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00002470:·0a7c·202d·2d20·7573·6564·2032·2e3 | 00002470:·0a7c·202d·2d20·7573·6564·2032·2e38·3431··.|·--·used·2.841 | ||
| 00002480:·3 | 00002480:·3436·7320·2863·7075·293b·2031·2e34·3132··46s·(cpu);·1.412 | ||
| 00002490:·3 | 00002490:·3135·7320·2874·6872·6561·6429·3b20·3073··15s·(thread);·0s | ||
| 000024a0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 000024a0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 000024b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000024b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000024c0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 000024c0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 000024d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000024e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000024f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002500:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00002500:·2020·2020·2020·2020·2020·2020·2020·207c·················| |
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| 000177a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000177a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000177b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000177b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000177c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 000177c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 000177d0:·3220·3a20·7469·6d65·2067·726f·7468·656e··2·:·time·grothen | 000177d0:·3220·3a20·7469·6d65·2067·726f·7468·656e··2·:·time·grothen | ||
| 000177e0:·6469·6563·6b50·6f6c·796e·6f6d·6961·6c20··dieckPolynomial· | 000177e0:·6469·6563·6b50·6f6c·796e·6f6d·6961·6c20··dieckPolynomial· | ||
| 000177f0:·7720·2020·2020·2020·2020·2020·2020·2020··w··············· | 000177f0:·7720·2020·2020·2020·2020·2020·2020·2020··w··············· | ||
| 00017800:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00017800:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00017810:·2075·7365·6420·302e·3030·333 | 00017810:·2075·7365·6420·302e·3030·3339·3939·3436···used·0.00399946 | ||
| 00017820:·7320·2863·7075·293b·2030·2e30·3033·3 | 00017820:·7320·2863·7075·293b·2030·2e30·3033·3839··s·(cpu);·0.00389 | ||
| 00017830:·3 | 00017830:·3736·3873·2028·7468·7265·6164·293b·2030··768s·(thread);·0 | ||
| 00017840:·7320·2867·6329·2020·7c0a·7c20·2020·2020··s·(gc)··|.|····· | 00017840:·7320·2867·6329·2020·7c0a·7c20·2020·2020··s·(gc)··|.|····· | ||
| 00017850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017880:·2020·2020·2020·7c0a·7c20·2020·2020·2032········|.|······2 | 00017880:·2020·2020·2020·7c0a·7c20·2020·2020·2032········|.|······2 | ||
| 00017890:·2020·2020·2020·2020·3220·2020·2020·2032··········2······2 | 00017890:·2020·2020·2020·2020·3220·2020·2020·2032··········2······2 | ||
| 000178a0:·2020·2020·2020·2020·2020·2020·2020·2032·················2 | 000178a0:·2020·2020·2020·2020·2020·2020·2020·2032·················2 | ||
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| 00017a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017a30:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20··--------+.|i3·:· | 00017a30:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20··--------+.|i3·:· | ||
| 00017a40:·7469·6d65·2067·726f·7468·656e·6469·6563··time·grothendiec | 00017a40:·7469·6d65·2067·726f·7468·656e·6469·6563··time·grothendiec | ||
| 00017a50:·6b50·6f6c·796e·6f6d·6961·6c20·2877·2c41··kPolynomial·(w,A | 00017a50:·6b50·6f6c·796e·6f6d·6961·6c20·2877·2c41··kPolynomial·(w,A | ||
| 00017a60:·6c67·6f72·6974·686d·3d3e·2250·6970·6544··lgorithm=>"PipeD | 00017a60:·6c67·6f72·6974·686d·3d3e·2250·6970·6544··lgorithm=>"PipeD | ||
| 00017a70:·7265·616d·2229·7c0a·7c20·2d2d·2075·7365··ream")|.|·--·use | 00017a70:·7265·616d·2229·7c0a·7c20·2d2d·2075·7365··ream")|.|·--·use | ||
| 00017a80:·6420·302e·3030·3 | 00017a80:·6420·302e·3030·3034·3031·3236·3273·2028··d·0.000401262s·( | ||
| 00017a90:·7075·293b·2030·2e30·3031·3839·3135·3373··pu);·0.00189153s | |||
| 00017a | 00017a90:·6370·7529·3b20·302e·3030·3136·3538·3432··cpu);·0.00165842 | ||
| 00017aa0:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | |||
| 00017ab0:·6 | 00017ab0:·6763·2920·7c0a·7c20·2020·2020·2020·2020··gc)·|.|········· | ||
| 00017ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017af0:·2020·7c0a·7c20·2020·2020·2032·2020·2020····|.|······2···· | 00017af0:·2020·7c0a·7c20·2020·2020·2032·2020·2020····|.|······2···· | ||
| 00017b00:·2020·2020·3220·2020·2020·2032·2020·2020······2······2···· | 00017b00:·2020·2020·3220·2020·2020·2032·2020·2020······2······2···· | ||
| 00017b10:·2020·2020·2020·2020·2020·2032·2020·2020·············2···· | 00017b10:·2020·2020·2020·2020·2020·2032·2020·2020·············2···· | ||
| 00017b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00022ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00022b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00022b10:·0a7c·6932·3320·3a20·7469·6d65·2073·6368··.|i23·:·time·sch | 00022b10:·0a7c·6932·3320·3a20·7469·6d65·2073·6368··.|i23·:·time·sch | ||
| 00022b20:·7562·6572·7452·6567·756c·6172·6974·7920··ubertRegularity· | 00022b20:·7562·6572·7452·6567·756c·6172·6974·7920··ubertRegularity· | ||
| 00022b30:·4220·2020·2020·2020·2020·2020·2020·2020··B··············· | 00022b30:·4220·2020·2020·2020·2020·2020·2020·2020··B··············· | ||
| 00022b40:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00022b40:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00022b50:·202d·2d20·7573·6564·2030·2e30·3 | 00022b50:·202d·2d20·7573·6564·2030·2e30·3836·3930···--·used·0.08690 | ||
| 00022b60:·3 | 00022b60:·3339·7320·2863·7075·293b·2030·2e30·3433··39s·(cpu);·0.043 | ||
| 00022b70:·3 | 00022b70:·3739·3933·7320·2874·6872·6561·6429·3b20··7993s·(thread);· | ||
| 00022b80:·3073·2028·6763·2920·2020·207c·0a7c·2020··0s·(gc)····|.|·· | 00022b80:·3073·2028·6763·2920·2020·207c·0a7c·2020··0s·(gc)····|.|·· | ||
| 00022b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022bc0:·2020·2020·2020·2020·207c·0a7c·6f32·3320···········|.|o23· | 00022bc0:·2020·2020·2020·2020·207c·0a7c·6f32·3320···········|.|o23· | ||
| 00022bd0:·3d20·3120·2020·2020·2020·2020·2020·2020··=·1············· | 00022bd0:·3d20·3120·2020·2020·2020·2020·2020·2020··=·1············· | ||
| 00022be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00022c20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022c20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022c40:·2d2d·2d2d·2d2b·0a7c·6932·3420·3a20·7469··-----+.|i24·:·ti | 00022c40:·2d2d·2d2d·2d2b·0a7c·6932·3420·3a20·7469··-----+.|i24·:·ti | ||
| 00022c50:·6d65·2072·6567·756c·6172·6974·7920·636f··me·regularity·co | 00022c50:·6d65·2072·6567·756c·6172·6974·7920·636f··me·regularity·co | ||
| 00022c60:·6d6f·6475·6c65·2073·6368·7562·6572·7444··module·schubertD | 00022c60:·6d6f·6475·6c65·2073·6368·7562·6572·7444··module·schubertD | ||
| 00022c70:·6574·6572·6d69·6e61·6e74·616c·4964·6561··eterminantalIdea | 00022c70:·6574·6572·6d69·6e61·6e74·616c·4964·6561··eterminantalIdea | ||
| 00022c80:·6c20·427c·0a7c·202d·2d20·7573·6564·2030··l·B|.|·--·used·0 | 00022c80:·6c20·427c·0a7c·202d·2d20·7573·6564·2030··l·B|.|·--·used·0 | ||
| 00022c90:·2e30·3 | 00022c90:·2e30·3131·3437·3137·7320·2863·7075·293b··.0114717s·(cpu); | ||
| 00022ca0:·2030·2e30·313 | 00022ca0:·2030·2e30·3133·3132·3236·7320·2874·6872···0.0131226s·(thr | ||
| 00022cb0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | 00022cb0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 00022cc0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00022cc0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00022cd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022cd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022ce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022cf0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00022cf0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00022d00:·0a7c·6f32·3420·3d20·3120·2020·2020·2020··.|o24·=·1······· | 00022d00:·0a7c·6f32·3420·3d20·3120·2020·2020·2020··.|o24·=·1······· | ||
| 00022d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0003ac10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ac10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ac20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ac20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ac30:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3135·203a··--------+.|i15·: | 0003ac30:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3135·203a··--------+.|i15·: | ||
| 0003ac40:·2074·696d·6520·7363·6875·6265·7274·5265···time·schubertRe | 0003ac40:·2074·696d·6520·7363·6875·6265·7274·5265···time·schubertRe | ||
| 0003ac50:·6775·6c61·7269·7479·2070·2020·2020·2020··gularity·p······ | 0003ac50:·6775·6c61·7269·7479·2070·2020·2020·2020··gularity·p······ | ||
| 0003ac60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ac60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ac70:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 0003ac70:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 0003ac80:·2030·2e30·303 | 0003ac80:·2030·2e30·3031·3331·3734·3573·2028·6370···0.00131745s·(cp | ||
| 0003ac90:·7529·3b20·302e·3030·3032·3 | 0003ac90:·7529·3b20·302e·3030·3032·3338·3736·3873··u);·0.000238768s | ||
| 0003aca0:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | 0003aca0:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | ||
| 0003acb0:·6329·7c0a·7c20·2020·2020·2020·2020·2020··c)|.|··········· | 0003acb0:·6329·7c0a·7c20·2020·2020·2020·2020·2020··c)|.|··········· | ||
| 0003acc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003acc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003acd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003acd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ace0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0003ace0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0003acf0:·0a7c·6f31·3520·3d20·3520·2020·2020·2020··.|o15·=·5······· | 0003acf0:·0a7c·6f31·3520·3d20·3520·2020·2020·2020··.|o15·=·5······· | ||
| 0003ad00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ad00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0003ad40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ad40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ad50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ad50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ad60:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3620··---------+.|i16· | 0003ad60:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3620··---------+.|i16· | ||
| 0003ad70:·3a20·7469·6d65·2072·6567·756c·6172·6974··:·time·regularit | 0003ad70:·3a20·7469·6d65·2072·6567·756c·6172·6974··:·time·regularit | ||
| 0003ad80:·7920·636f·6d6f·6475·6c65·2049·2020·2020··y·comodule·I···· | 0003ad80:·7920·636f·6d6f·6475·6c65·2049·2020·2020··y·comodule·I···· | ||
| 0003ad90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ad90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ada0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 0003ada0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 0003adb0:·6420·302e·3031·3 | 0003adb0:·6420·302e·3031·3034·3036·3773·2028·6370··d·0.0104067s·(cp | ||
| 0003adc0:·7529·3b20·302e·3031·3232·3 | 0003adc0:·7529·3b20·302e·3031·3232·3533·3973·2028··u);·0.0122539s·( | ||
| 0003add0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | 0003add0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 0003ade0:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0003ade0:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0003adf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003adf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ae00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ae00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ae10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ae10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ae20:·7c0a·7c6f·3136·203d·2035·2020·2020·2020··|.|o16·=·5······ | 0003ae20:·7c0a·7c6f·3136·203d·2035·2020·2020·2020··|.|o16·=·5······ | ||
| 0003ae30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ae30:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00009f50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009f50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009f70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00009f70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00009f80:·6933·203a·2065·6c61·7073·6564·5469·6d65··i3·:·elapsedTime | 00009f80:·6933·203a·2065·6c61·7073·6564·5469·6d65··i3·:·elapsedTime | ||
| 00009f90:·204c·203d·2061·6c6c·4d69·6e6f·7273·2856···L·=·allMinors(V | 00009f90:·204c·203d·2061·6c6c·4d69·6e6f·7273·2856···L·=·allMinors(V | ||
| 00009fa0:·2c20·5532·3529·3b20·2020·2020·2020·2020··,·U25);········· | 00009fa0:·2c20·5532·3529·3b20·2020·2020·2020·2020··,·U25);········· | ||
| 00009fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fc0:·207c·0a7c·202d·2d20·2e31·3 | 00009fc0:·207c·0a7c·202d·2d20·2e31·3934·3637·3773···|.|·--·.194677s | ||
| 00009fd0:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 00009fd0:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 00009fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a000:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | 0000a000:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
| 0000a010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000253b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000253b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000253c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000253c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000253d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000253d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000253e0:·2d2d·2d2d·2b0a·7c69·3720·3a20·7469·6d65··----+.|i7·:·time | 000253e0:·2d2d·2d2d·2b0a·7c69·3720·3a20·7469·6d65··----+.|i7·:·time | ||
| 000253f0:·2061·7574·4637·203d·2067·6574·4973·6f73···autF7·=·getIsos | 000253f0:·2061·7574·4637·203d·2067·6574·4973·6f73···autF7·=·getIsos | ||
| 00025400:·2846·372c·2046·3729·3b20·2020·2020·2020··(F7,·F7);······· | 00025400:·2846·372c·2046·3729·3b20·2020·2020·2020··(F7,·F7);······· | ||
| 00025410:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00025410:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00025420:·202d·2d20·7573·6564·2030·2e31·3 | 00025420:·202d·2d20·7573·6564·2030·2e31·3930·3730···--·used·0.19070 | ||
| 00025430:·3 | 00025430:·3273·2028·6370·7529·3b20·302e·3036·3635··2s·(cpu);·0.0665 | ||
| 00025440:·3 | 00025440:·3934·3873·2028·7468·7265·6164·293b·2030··948s·(thread);·0 | ||
| 00025450:·7320·2867·6329·7c0a·2b2d·2d2d·2d2d·2d2d··s·(gc)|.+------- | 00025450:·7320·2867·6329·7c0a·2b2d·2d2d·2d2d·2d2d··s·(gc)|.+------- | ||
| 00025460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00025460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00025470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00025480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00025490:·0a7c·6938·203a·2023·6175·7446·3720·2020··.|i8·:·#autF7··· | 00025490:·0a7c·6938·203a·2023·6175·7446·3720·2020··.|i8·:·#autF7··· | ||
| 000254a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000254a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000254b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000254b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0002a600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0002a600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0002a610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0002a610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0002a620:·2b0a·7c69·3320·3a20·7469·6d65·2068·6173··+.|i3·:·time·has | 0002a620:·2b0a·7c69·3320·3a20·7469·6d65·2068·6173··+.|i3·:·time·has | ||
| 0002a630:·4d69·6e6f·7228·4d36·2c20·4d35·2920·2020··Minor(M6,·M5)··· | 0002a630:·4d69·6e6f·7228·4d36·2c20·4d35·2920·2020··Minor(M6,·M5)··· | ||
| 0002a640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a670:·7c0a·7c20·2d2d·2075·7365·6420·312e·3 | 0002a670:·7c0a·7c20·2d2d·2075·7365·6420·312e·3433··|.|·--·used·1.43 | ||
| 0002a680:·3 | 0002a680:·3131·3373·2028·6370·7529·3b20·312e·3033··113s·(cpu);·1.03 | ||
| 0002a690:·3 | 0002a690:·3933·3873·2028·7468·7265·6164·293b·2030··938s·(thread);·0 | ||
| 0002a6a0:· | 0002a6a0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 0002a6b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a6b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a6c0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0002a6c0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 0002a6d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a6d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a6e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a6e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a6f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a6f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002a700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002a710:·7c0a·7c6f·3320·3d20·7472·7565·2020·2020··|.|o3·=·true···· | 0002a710:·7c0a·7c6f·3320·3d20·7472·7565·2020·2020··|.|o3·=·true···· | ||
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| 00037a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00037a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00037aa0:·2d2b·0a7c·6935·203a·2074·696d·6520·6973··-+.|i5·:·time·is | 00037aa0:·2d2b·0a7c·6935·203a·2074·696d·6520·6973··-+.|i5·:·time·is | ||
| 00037ab0:·6f6d·6f72·7068·6973·6d28·4d35·2c20·6d69··omorphism(M5,·mi | 00037ab0:·6f6d·6f72·7068·6973·6d28·4d35·2c20·6d69··omorphism(M5,·mi | ||
| 00037ac0:·6e6f·724d·3629·2020·2020·2020·2020·2020··norM6)·········· | 00037ac0:·6e6f·724d·3629·2020·2020·2020·2020·2020··norM6)·········· | ||
| 00037ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037af0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 00037af0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 00037b00:·3 | 00037b00:·3037·3932·3836·3473·2028·6370·7529·3b20··0792864s·(cpu);· | ||
| 00037b10:·2e30·3130·353 | 00037b10:·302e·3031·3130·3535·3673·2028·7468·7265··0.0110556s·(thre | ||
| 00037b20:·6429 | 00037b20:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00037b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037b40:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00037b40:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00037b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037b60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037b60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00037b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00037b90:·207c·0a7c·6f35·203d·2048·6173·6854·6162···|.|o5·=·HashTab | 00037b90:·207c·0a7c·6f35·203d·2048·6173·6854·6162···|.|o5·=·HashTab | ||
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| 00038610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00038610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00038620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00038620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00038630:·2d2b·0a7c·6938·203a·2074·696d·6520·7068··-+.|i8·:·time·ph | 00038630:·2d2b·0a7c·6938·203a·2074·696d·6520·7068··-+.|i8·:·time·ph | ||
| 00038640:·6920·3d20·6973·6f6d·6f72·7068·6973·6d28··i·=·isomorphism( | 00038640:·6920·3d20·6973·6f6d·6f72·7068·6973·6d28··i·=·isomorphism( | ||
| 00038650:·4e2c·4d36·2920·2020·2020·2020·2020·2020··N,M6)··········· | 00038650:·4e2c·4d36·2920·2020·2020·2020·2020·2020··N,M6)··········· | ||
| 00038660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00038660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00038670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00038670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00038680:·207c·0a7c·202d·2d20·7573·6564·203 | 00038680:·207c·0a7c·202d·2d20·7573·6564·2034·2e30···|.|·--·used·4.0 | ||
| 00038690:·3 | 00038690:·3235·3837·7320·2863·7075·293b·2032·2e34··2587s·(cpu);·2.4 | ||
| 000386a0:·3 | 000386a0:·3239·3039·7320·2874·6872·6561·6429·3b20··2909s·(thread);· | ||
| 000386b0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 000386b0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 000386c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000386c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000386d0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 000386d0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 000386e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000386e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000386f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000386f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00038700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00038700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00038710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00038710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000443a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000443a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000443b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | 000443b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | ||
| 000443c0:·3020·3a20·7469·6d65·2069·7357·656c·6c44··0·:·time·isWellD | 000443c0:·3020·3a20·7469·6d65·2069·7357·656c·6c44··0·:·time·isWellD | ||
| 000443d0:·6566·696e·6564·2052·3130·2020·2020·2020··efined·R10······ | 000443d0:·6566·696e·6564·2052·3130·2020·2020·2020··efined·R10······ | ||
| 000443e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000443e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000443f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000443f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00044400:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 00044400:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 00044410:·2d20·7573·6564·2030·2e31·3 | 00044410:·2d20·7573·6564·2030·2e31·3331·3273·2028··-·used·0.1312s·( | ||
| 00044420:· | 00044420:·6370·7529·3b20·302e·3036·3837·3831·3873··cpu);·0.0687818s | ||
| 00044430:· | 00044430:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | ||
| 00044440:· | 00044440:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | ||
| 00044450:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00044450:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00044460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00044460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00044470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00044470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00044480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00044480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00044490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00044490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000444a0:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 000444a0:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
| 000444b0:·3020·3d20·7472·7565·2020·2020·2020·2020··0·=·true········ | 000444b0:·3020·3d20·7472·7565·2020·2020·2020·2020··0·=·true········ | ||
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| 00044530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00044530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00044540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | 00044540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | ||
| 00044550:·3120·3a20·7469·6d65·2066·5665·6374·6f72··1·:·time·fVector | 00044550:·3120·3a20·7469·6d65·2066·5665·6374·6f72··1·:·time·fVector | ||
| 00044560:·2052·3130·2020·2020·2020·2020·2020·2020···R10············ | 00044560:·2052·3130·2020·2020·2020·2020·2020·2020···R10············ | ||
| 00044570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00044570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00044580:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00044580:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00044590:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 00044590:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 000445a0:·2d20·7573·6564·2030·2e3 | 000445a0:·2d20·7573·6564·2030·2e31·3234·3431·3373··-·used·0.124413s | ||
| 000445b0:·2028·6370·7529·3b20·302e·3035·3 | 000445b0:·2028·6370·7529·3b20·302e·3035·3631·3932···(cpu);·0.056192 | ||
| 000445c0:·3 | 000445c0:·3673·2028·7468·7265·6164·293b·2030·7320··6s·(thread);·0s· | ||
| 000445d0:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | 000445d0:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 000445e0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 000445e0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 000445f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000445f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00044630:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 00044630:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
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| 00004fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004ff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004ff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005010:·2d2d·2d2d·2d2d·2b0a·7c69·3620·3a20·656c··------+.|i6·:·el | 00005010:·2d2d·2d2d·2d2d·2b0a·7c69·3620·3a20·656c··------+.|i6·:·el | ||
| 00005020:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | 00005020:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | ||
| 00005030:·6c28·6964·6561·6c20·495f·2a2c·2053·7472··l(ideal·I_*,·Str | 00005030:·6c28·6964·6561·6c20·495f·2a2c·2053·7472··l(ideal·I_*,·Str | ||
| 00005040:·6174·6567·7920·3d3e·204d·6f6e·6f6d·6961··ategy·=>·Monomia | 00005040:·6174·6567·7920·3d3e·204d·6f6e·6f6d·6961··ategy·=>·Monomia | ||
| 00005050:·6c29·7c0a·7c20·2d2d·202e·3030·303 | 00005050:·6c29·7c0a·7c20·2d2d·202e·3030·3037·3839··l)|.|·--·.000789 | ||
| 00005060:·3 | 00005060:·3933·3173·2065·6c61·7073·6564·2020·2020··931s·elapsed···· | ||
| 00005070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005080:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00005080:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00005090:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00005090:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 000050a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000050a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000050b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000050b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000050c0:·2020·2020·2020·2020·2020·7c0a·7c6f·3620············|.|o6· | 000050c0:·2020·2020·2020·2020·2020·7c0a·7c6f·3620············|.|o6· | ||
| 000050d0:·3d20·6964·6561·6c20·2861·2c20·622c·2063··=·ideal·(a,·b,·c | 000050d0:·3d20·6964·6561·6c20·2861·2c20·622c·2063··=·ideal·(a,·b,·c | ||
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| 00005180:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 00005180:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 00005190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000051a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000051a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000051b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3720··----------+.|i7· | 000051b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3720··----------+.|i7· | ||
| 000051c0:·3a20·656c·6170·7365·6454·696d·6520·7261··:·elapsedTime·ra | 000051c0:·3a20·656c·6170·7365·6454·696d·6520·7261··:·elapsedTime·ra | ||
| 000051d0:·6469·6361·6c28·6964·6561·6c20·495f·2a2c··dical(ideal·I_*, | 000051d0:·6469·6361·6c28·6964·6561·6c20·495f·2a2c··dical(ideal·I_*, | ||
| 000051e0:·2055·6e6d·6978·6564·203d·3e20·7472·7565···Unmixed·=>·true | 000051e0:·2055·6e6d·6978·6564·203d·3e20·7472·7565···Unmixed·=>·true | ||
| 000051f0:·2920·2020·2020·7c0a·7c20·2d2d·202e·303 | 000051f0:·2920·2020·2020·7c0a·7c20·2d2d·202e·3031··)·····|.|·--·.01 | ||
| 00005200:·3 | 00005200:·3535·3836·3373·2065·6c61·7073·6564·2020··55863s·elapsed·· | ||
| 00005210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005230:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00005230:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00005240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005260:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00005260:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00005270:·7c6f·3720·3d20·6964·6561·6c20·2863·2c20··|o7·=·ideal·(c,· | 00005270:·7c6f·3720·3d20·6964·6561·6c20·2863·2c20··|o7·=·ideal·(c,· | ||
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| 00006870:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006870:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006880:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006890:·2b0a·7c69·3720·3a20·656c·6170·7365·6454··+.|i7·:·elapsedT | 00006890:·2b0a·7c69·3720·3a20·656c·6170·7365·6454··+.|i7·:·elapsedT | ||
| 000068a0:·696d·6520·7261·6469·6361·6c43·6f6e·7461··ime·radicalConta | 000068a0:·696d·6520·7261·6469·6361·6c43·6f6e·7461··ime·radicalConta | ||
| 000068b0:·696e·6d65·6e74·2878·5f30·2c20·4929·2020··inment(x_0,·I)·· | 000068b0:·696e·6d65·6e74·2878·5f30·2c20·4929·2020··inment(x_0,·I)·· | ||
| 000068c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000068c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000068d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000068d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000068e0:·7c0a·7c20·2d2d·202e·3 | 000068e0:·7c0a·7c20·2d2d·202e·3131·3133·3935·7320··|.|·--·.111395s· | ||
| 000068f0:· | 000068f0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00006900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006930:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00006930:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00006940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00006a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006a20:·2b0a·7c69·3820·3a20·656c·6170·7365·6454··+.|i8·:·elapsedT | 00006a20:·2b0a·7c69·3820·3a20·656c·6170·7365·6454··+.|i8·:·elapsedT | ||
| 00006a30:·696d·6520·7261·6469·6361·6c43·6f6e·7461··ime·radicalConta | 00006a30:·696d·6520·7261·6469·6361·6c43·6f6e·7461··ime·radicalConta | ||
| 00006a40:·696e·6d65·6e74·2878·5f30·2c20·492c·2053··inment(x_0,·I,·S | 00006a40:·696e·6d65·6e74·2878·5f30·2c20·492c·2053··inment(x_0,·I,·S | ||
| 00006a50:·7472·6174·6567·7920·3d3e·2022·4b6f·6c6c··trategy·=>·"Koll | 00006a50:·7472·6174·6567·7920·3d3e·2022·4b6f·6c6c··trategy·=>·"Koll | ||
| 00006a60:·6172·2229·2020·2020·2020·2020·2020·2020··ar")············ | 00006a60:·6172·2229·2020·2020·2020·2020·2020·2020··ar")············ | ||
| 00006a70:·7c0a·7c20·2d2d·202e·3030·3 | 00006a70:·7c0a·7c20·2d2d·202e·3030·3231·3537·7320··|.|·--·.002157s· | ||
| 00006a80:· | 00006a80:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00006a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ac0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00006ac0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00006ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00006b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006ba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006ba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006bb0:·2b0a·7c69·3920·3a20·656c·6170·7365·6454··+.|i9·:·elapsedT | 00006bb0:·2b0a·7c69·3920·3a20·656c·6170·7365·6454··+.|i9·:·elapsedT | ||
| 00006bc0:·696d·6520·7261·6469·6361·6c43·6f6e·7461··ime·radicalConta | 00006bc0:·696d·6520·7261·6469·6361·6c43·6f6e·7461··ime·radicalConta | ||
| 00006bd0:·696e·6d65·6e74·2878·5f6e·2c20·492c·2053··inment(x_n,·I,·S | 00006bd0:·696e·6d65·6e74·2878·5f6e·2c20·492c·2053··inment(x_n,·I,·S | ||
| 00006be0:·7472·6174·6567·7920·3d3e·2022·4b6f·6c6c··trategy·=>·"Koll | 00006be0:·7472·6174·6567·7920·3d3e·2022·4b6f·6c6c··trategy·=>·"Koll | ||
| 00006bf0:·6172·2229·2020·2020·2020·2020·2020·2020··ar")············ | 00006bf0:·6172·2229·2020·2020·2020·2020·2020·2020··ar")············ | ||
| 00006c00:·7c0a·7c20·2d2d·202e·3030·313 | 00006c00:·7c0a·7c20·2d2d·202e·3030·3138·3939·3832··|.|·--·.00189982 | ||
| 00006c10:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00006c10:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00006c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006c50:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00006c50:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00006c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006c70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00008860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008870:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00008870:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00008880:·2054·696d·6520·7461·6b65·6e20·3a20·3020···Time·taken·:·0· | 00008880:·2054·696d·6520·7461·6b65·6e20·3a20·3020···Time·taken·:·0· | ||
| 00008890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000088a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000088a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000088b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000088b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000088c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000088c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 000088d0:·2e30·3 | 000088d0:·2e30·3238·3836·3732·7320·656c·6170·7365··.0288672s·elapse | ||
| 000088e0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | 000088e0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 000088f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000088f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008910:·2020·2020·2020·2020·207c·0a7c·2874·696d···········|.|(tim | 00008910:·2020·2020·2020·2020·207c·0a7c·2874·696d···········|.|(tim | ||
| 00008920:·6520·3029·2020·2020·2020·2020·2023·7072··e·0)·········#pr | 00008920:·6520·3029·2020·2020·2020·2020·2023·7072··e·0)·········#pr | ||
| 00008930:·696d·6573·203d·2031·2023·2020·2020·2020··imes·=·1·#······ | 00008930:·696d·6573·203d·2031·2023·2020·2020·2020··imes·=·1·#······ | ||
| 00008940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000089a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000089a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000089b0:·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·2869·6465··---------|.|(ide | 000089b0:·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·2869·6465··---------|.|(ide | ||
| 000089c0:·616c·2049·5f2a·2c20·5374·7261·7465·6779··al·I_*,·Strategy | 000089c0:·616c·2049·5f2a·2c20·5374·7261·7465·6779··al·I_*,·Strategy | ||
| 000089d0:·203d·3e20·4879·6272·6964·7b4c·696e·6561···=>·Hybrid{Linea | 000089d0:·203d·3e20·4879·6272·6964·7b4c·696e·6561···=>·Hybrid{Linea | ||
| 000089e0:·722c·4269·7261·7469·6f6e·616c·2c46·6163··r,Birational,Fac | 000089e0:·722c·4269·7261·7469·6f6e·616c·2c46·6163··r,Birational,Fac | ||
| 000089f0:·746f·7269·7a61·7469·6f6e·2c20·2020·2020··torization,····· | 000089f0:·746f·7269·7a61·7469·6f6e·2c20·2020·2020··torization,····· | ||
| 00008a00:·2020·2020·2020·2020·207c·0a7c·2874·696d···········|.|(tim | 00008a00:·2020·2020·2020·2020·207c·0a7c·2874·696d···········|.|(tim | ||
| 00008a10:·6520· | 00008a10:·6520·2e30·3030·3434·3434·3133·2920·2023··e·.000444413)··# | ||
| 00008a20:·696d·6573·203d·2030·2023·7072·756e· | 00008a20:·7072·696d·6573·203d·2030·2023·7072·756e··primes·=·0·#prun | ||
| 00008a30:·5669·6143·6f64·696d·203d·2030·2020· | 00008a30:·6564·5669·6143·6f64·696d·203d·2030·2020··edViaCodim·=·0·· | ||
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| 00008a60:·6520·2e30·3 | 00008a60:·6520·2e30·3133·3333·3329·2020·2023·7072··e·.013333)···#pr | ||
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| 00008a80:· | 00008a80:·5669·6143·6f64·696d·203d·2030·2020·2020··ViaCodim·=·0···· | ||
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| 00008ac0:·696d·6573·203d·2030·2023·7072·756e·6564··imes·=·0·#pruned | 00008ac0:·696d·6573·203d·2030·2023·7072·756e·6564··imes·=·0·#pruned | ||
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| 00008af0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00008af0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· |
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| 00007010:·756c·7469·5265·6573·4964·6561·6c20·4a20··ultiReesIdeal·J· | 00007010:·756c·7469·5265·6573·4964·6561·6c20·4a20··ultiReesIdeal·J· | ||
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| 00007060:·3 | 00007060:·3736·3734·3273·2028·6370·7529·3b20·302e··76742s·(cpu);·0. | ||
| 00007070:·3 | 00007070:·3135·3130·3873·2028·7468·7265·6164·293b··15108s·(thread); | ||
| 00007080:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 00007080:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
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| 00007450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00007470:·756c·7469·5265·6573·4964·6561·6c20·284a··ultiReesIdeal·(J | 00007470:·756c·7469·5265·6573·4964·6561·6c20·284a··ultiReesIdeal·(J | ||
| 00007480:·2c20·6129·2020·2020·2020·2020·2020·2020··,·a)············ | 00007480:·2c20·6129·2020·2020·2020·2020·2020·2020··,·a)············ | ||
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| 000074b0:·207c·0a7c·202d·2d20·7573·6564·2030·2e3 | 000074b0:·207c·0a7c·202d·2d20·7573·6564·2030·2e32···|.|·--·used·0.2 | ||
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| 000074d0:·3033·3 | 000074d0:·3033·3931·3738·7320·2874·6872·6561·6429··039178s·(thread) | ||
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| 00003bb0:·2d2d·2d2d·2d2d·2d2b·0a7c·6938·203a·2028··-------+.|i8·:·( | 00003bb0:·2d2d·2d2d·2d2d·2d2b·0a7c·6938·203a·2028··-------+.|i8·:·( | ||
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| 00003bd0:·726d·4d43·4d4d·6f64·756c·6520·4e30·2020··rmMCMModule·N0·· | 00003bd0:·726d·4d43·4d4d·6f64·756c·6520·4e30·2020··rmMCMModule·N0·· | ||
| 00003be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00003c00:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | 00003c00:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | ||
| 00003c10:·6564·2030·2e3 | 00003c10:·6564·2030·2e34·3031·3438·3873·2028·6370··ed·0.401488s·(cp | ||
| 00003c20:·7529·3b20·302e·323 | 00003c20:·7529·3b20·302e·3237·3536·3135·7320·2874··u);·0.275615s·(t | ||
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| 00003c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00004730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00004760:·6d65·2064·6566·6f72·6d4d·434d·4d6f·6475··me·deformMCMModu | 00004760:·6d65·2064·6566·6f72·6d4d·434d·4d6f·6475··me·deformMCMModu | ||
| 00004770:·6c65·204e·3027·2020·2020·2020·2020·2020··le·N0'·········· | 00004770:·6c65·204e·3027·2020·2020·2020·2020·2020··le·N0'·········· | ||
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| 000047a0:·2d20·7573·6564·2030·2e3 | 000047a0:·2d20·7573·6564·2030·2e35·3338·3238·3873··-·used·0.538288s | ||
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| 000047d0:·6763·2920·2020·2020·2020·2020·2020·2020··gc)············· | 000047d0:·6763·2920·2020·2020·2020·2020·2020·2020··gc)············· | ||
| 000047e0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 000047e0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
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| 00005d70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005d70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005d80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00005d80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
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| 00005df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005e00:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 00005e00:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
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| 00005e40:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00005e40:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00005e50:·202e·3030·3033·3 | 00005e50:·202e·3030·3033·3935·3339·3273·2065·6c61···.000395392s·ela | ||
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| 00005e90:·2e30·303 | 00005e90:·2e30·3032·3539·3331·3373·2065·6c61·7073··.00259313s·elaps | ||
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| 00005ec0:·2020·2020·2020·2020·7c0a·7c20·2d2d·202e··········|.|·--·. | 00005ec0:·2020·2020·2020·2020·7c0a·7c20·2d2d·202e··········|.|·--·. | ||
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| 00005ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f00:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0 | 00005f00:·2020·2020·2020·207c·0a7c·202d·2d20·2e30·········|.|·--·.0 | ||
| 00005f10:·3030·3 | 00005f10:·3030·3339·3336·3738·7320·656c·6170·7365··00393678s·elapse | ||
| 00005f20:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | 00005f20:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 00005f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f40:·2020·2020·2020·7c0a·7c20·2d2d·202e·3030········|.|·--·.00 | 00005f40:·2020·2020·2020·7c0a·7c20·2d2d·202e·3030········|.|·--·.00 | ||
| 00005f50:·323 | 00005f50:·3239·3538·3231·7320·656c·6170·7365·6420··295821s·elapsed· | ||
| 00005f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f80:·2020·2020·207c·0a7c·202d·2d20·2e30·3 | 00005f80:·2020·2020·207c·0a7c·202d·2d20·2e30·3032·······|.|·--·.002 | ||
| 00005f90:·3 | 00005f90:·3932·3533·3173·2065·6c61·7073·6564·2020··92531s·elapsed·· | ||
| 00005fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005fc0:·2020·2020·7c0a·7c20·2d2d·202e·3030·3032······|.|·--·.0002 | 00005fc0:·2020·2020·7c0a·7c20·2d2d·202e·3030·3032······|.|·--·.0002 | ||
| 00005fd0:·3 | 00005fd0:·3532·3937·3473·2065·6c61·7073·6564·2020··52974s·elapsed·· | ||
| 00005fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006000:·2020·207c·0a7c·202d·2d20·2e30·303 | 00006000:·2020·207c·0a7c·202d·2d20·2e30·3033·3538·····|.|·--·.00358 | ||
| 00006010:·3 | 00006010:·3433·3873·2065·6c61·7073·6564·2020·2020··438s·elapsed···· | ||
| 00006020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006040:·2020·7c0a·7c20·2d2d·202e·3030·3 | 00006040:·2020·7c0a·7c20·2d2d·202e·3030·3331·3433····|.|·--·.003143 | ||
| 00006050:·3 | 00006050:·3339·7320·656c·6170·7365·6420·2020·2020··39s·elapsed····· | ||
| 00006060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006080:·207c·0a7c·202d·2d20·2e30·3030·323 | 00006080:·207c·0a7c·202d·2d20·2e30·3030·3237·3837···|.|·--·.0002787 | ||
| 00006090:·3 | 00006090:·3532·7320·656c·6170·7365·6420·2020·2020··52s·elapsed····· | ||
| 000060a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000060a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000060b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000060b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000060c0:·7c0a·7c2d·2d62·6163·6b75·7020·6469·7265··|.|--backup·dire | 000060c0:·7c0a·7c2d·2d62·6163·6b75·7020·6469·7265··|.|--backup·dire | ||
| 000060d0:·6374·6f72·7920·6372·6561·7465·643a·202f··ctory·created:·/ | 000060d0:·6374·6f72·7920·6372·6561·7465·643a·202f··ctory·created:·/ | ||
| 000060e0:·746d·702f·4d32·2d3 | 000060e0:·746d·702f·4d32·2d33·3730·3437·3035·2d30··tmp/M2-3704705-0 | ||
| 000060f0:·2f31·2020·2020·2020·2020·2020·2020·207c··/1·············| | 000060f0:·2f31·2020·2020·2020·2020·2020·2020·207c··/1·············| | ||
| 00006100:·0a7c·2020·4830·313a·2031·2020·2020·2020··.|··H01:·1······ | 00006100:·0a7c·2020·4830·313a·2031·2020·2020·2020··.|··H01:·1······ | ||
| 00006110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006130:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00006130:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00006140:·7c20·2048·3130·3a20·3120·2020·2020·2020··|··H10:·1······· | 00006140:·7c20·2048·3130·3a20·3120·2020·2020·2020··|··H10:·1······· | ||
| 00006150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006150:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00004060:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | 00004060:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | ||
| 00004070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004090:·2d2d·2b0a·7c69·3320·3a20·656c·6170·7365··--+.|i3·:·elapse | 00004090:·2d2d·2b0a·7c69·3320·3a20·656c·6170·7365··--+.|i3·:·elapse | ||
| 000040a0:·6454·696d·6520·6a4d·756c·7420·4920·2020··dTime·jMult·I··· | 000040a0:·6454·696d·6520·6a4d·756c·7420·4920·2020··dTime·jMult·I··· | ||
| 000040b0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000040b0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000040c0:·2d2d·202e·303 | 000040c0:·2d2d·202e·3032·3439·3835·3373·2065·6c61··--·.0249853s·ela | ||
| 000040d0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 000040d0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 000040e0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 000040e0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 000040f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000040f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004110:·7c0a·7c6f·3320·3d20·3220·2020·2020·2020··|.|o3·=·2······· | 00004110:·7c0a·7c6f·3320·3d20·3220·2020·2020·2020··|.|o3·=·2······· | ||
| 00004120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004130:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | 00004130:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | ||
| 00004140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004160:·2d2d·2d2d·2b0a·7c69·3420·3a20·656c·6170··----+.|i4·:·elap | 00004160:·2d2d·2d2d·2b0a·7c69·3420·3a20·656c·6170··----+.|i4·:·elap | ||
| 00004170:·7365·6454·696d·6520·6d6f·6e6a·4d75·6c74··sedTime·monjMult | 00004170:·7365·6454·696d·6520·6d6f·6e6a·4d75·6c74··sedTime·monjMult | ||
| 00004180:·2049·2020·2020·2020·2020·2020·2020·7c0a···I············|. | 00004180:·2049·2020·2020·2020·2020·2020·2020·7c0a···I············|. | ||
| 00004190:·7c20·2d2d·202e·3 | 00004190:·7c20·2d2d·202e·3239·3930·3635·7320·656c··|·--·.299065s·el | ||
| 000041a0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 000041a0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 000041b0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 000041b0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 000041c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000041c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000041d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000041d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000041e0:·2020·7c0a·7c6f·3420·3d20·3220·2020·2020····|.|o4·=·2····· | 000041e0:·2020·7c0a·7c6f·3420·3d20·3220·2020·2020····|.|o4·=·2····· | ||
| 000041f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000041f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004200:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | 00004200:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | ||
| 00004210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004230:·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20·656c··------+.|i5·:·el | 00004230:·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20·656c··------+.|i5·:·el | ||
| 00004240:·6170·7365·6454·696d·6520·6d75·6c74·6970··apsedTime·multip | 00004240:·6170·7365·6454·696d·6520·6d75·6c74·6970··apsedTime·multip | ||
| 00004250:·6c69·6369·7479·5365·7175·656e·6365·2049··licitySequence·I | 00004250:·6c69·6369·7479·5365·7175·656e·6365·2049··licitySequence·I | ||
| 00004260:·7c0a·7c20·2d2d·202e·3 | 00004260:·7c0a·7c20·2d2d·202e·3831·3637·3034·7320··|.|·--·.816704s· | ||
| 00004270:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 00004270:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00004280:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00004280:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00004290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000042a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000042a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000042b0:·2020·2020·7c0a·7c6f·3520·3d20·4861·7368······|.|o5·=·Hash | 000042b0:·2020·2020·7c0a·7c6f·3520·3d20·4861·7368······|.|o5·=·Hash | ||
| 000042c0:·5461·626c·657b·3220·3d3e·2033·7d20·2020··Table{2·=>·3}··· | 000042c0:·5461·626c·657b·3220·3d3e·2033·7d20·2020··Table{2·=>·3}··· | ||
| 000042d0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000042d0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 00004960:·7c6f·3220·3a20·4964·6561·6c20·6f66·2052··|o2·:·Ideal·of·R | 00004960:·7c6f·3220·3a20·4964·6561·6c20·6f66·2052··|o2·:·Ideal·of·R | ||
| 00004970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004980:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | 00004980:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
| 00004990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000049a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 000049a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 000049b0:·3320·3a20·656c·6170·7365·6454·696d·6520··3·:·elapsedTime· | 000049b0:·3320·3a20·656c·6170·7365·6454·696d·6520··3·:·elapsedTime· | ||
| 000049c0:·6d6f·6e41·6e61·6c79·7469·6353·7072·6561··monAnalyticSprea | 000049c0:·6d6f·6e41·6e61·6c79·7469·6353·7072·6561··monAnalyticSprea | ||
| 000049d0:·6420·497c·0a7c·202d·2d20·2e3 | 000049d0:·6420·497c·0a7c·202d·2d20·2e32·3338·3039··d·I|.|·--·.23809 | ||
| 000049e0:· | 000049e0:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 000049f0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 000049f0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00004a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004a20:·207c·0a7c·6f33·203d·2032·2020·2020·2020···|.|o3·=·2······ | 00004a20:·207c·0a7c·6f33·203d·2032·2020·2020·2020···|.|o3·=·2······ | ||
| 00004a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004a40:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | 00004a40:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | ||
| 00004a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00005310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005320:·2d2d·2d2d·2d2b·0a7c·6933·203a·2065·6c61··-----+.|i3·:·ela | 00005320:·2d2d·2d2d·2d2b·0a7c·6933·203a·2065·6c61··-----+.|i3·:·ela | ||
| 00005330:·7073·6564·5469·6d65·206d·6f6e·6a4d·756c··psedTime·monjMul | 00005330:·7073·6564·5469·6d65·206d·6f6e·6a4d·756c··psedTime·monjMul | ||
| 00005340:·7420·4920·2020·2020·2020·2020·2020·2020··t·I············· | 00005340:·7420·4920·2020·2020·2020·2020·2020·2020··t·I············· | ||
| 00005350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00005370:·2020·2020·207c·0a7c·202d·2d20·2e32·3 | 00005370:·2020·2020·207c·0a7c·202d·2d20·2e32·3839·······|.|·--·.289 | ||
| 00005380:·3 | 00005380:·3036·3573·2065·6c61·7073·6564·2020·2020··065s·elapsed···· | ||
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| 000053a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000053a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000054d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00005560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000240d0:·2050·6869·2020·2020·2020·2020·2020·2020···Phi············ | 000240d0:·2050·6869·2020·2020·2020·2020·2020·2020···Phi············ | ||
| 000240e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000240e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000240f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000240f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024100:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00024100:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00024110:·202d·2d20·7573·6564·2030·2e3 | 00024110:·202d·2d20·7573·6564·2030·2e38·3036·3934···--·used·0.80694 | ||
| 00024120:·3773·2028·6370·7529·3b20·302e·3332·3539··7s·(cpu);·0.3259 | |||
| 000241 | 00024120:·7320·2863·7075·293b·2030·2e34·3838·3033··s·(cpu);·0.48803 | ||
| 00024130:·3673·2028·7468·7265·6164·293b·2030·7320··6s·(thread);·0s· | |||
| 00024140:·2 | 00024140:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 00024150:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00024150:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00024160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000241a0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000241a0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 000241b0:·6f33·203d·2031·2020·2020·2020·2020·2020··o3·=·1·········· | 000241b0:·6f33·203d·2031·2020·2020·2020·2020·2020··o3·=·1·········· | ||
| Offset 9454, 16 lines modified | Offset 9454, 16 lines modified | ||
| 00024ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00024ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00024ee0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | 00024ee0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 00024ef0:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | 00024ef0:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | ||
| 00024f00:·2c53·7472·6174·6567·793d·3e22·7261·6e64··,Strategy=>"rand | 00024f00:·2c53·7472·6174·6567·793d·3e22·7261·6e64··,Strategy=>"rand | ||
| 00024f10:·6f6d·2070·6f69·6e74·2229·2020·2020·2020··om·point")······ | 00024f10:·6f6d·2070·6f69·6e74·2229·2020·2020·2020··om·point")······ | ||
| 00024f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024f30:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00024f30:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00024f40:·7573·6564·203 | 00024f40:·7573·6564·2034·2e35·3233·3939·7320·2863··used·4.52399s·(c | ||
| 00024f50:·7075·293b·203 | 00024f50:·7075·293b·2032·2e36·3636·3539·7320·2874··pu);·2.66659s·(t | ||
| 00024f60:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00024f60:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00024f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024f80:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00024f80:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00024f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 9479, 16 lines modified | Offset 9479, 16 lines modified | ||
| 00025060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00025060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025070:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | 00025070:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | ||
| 00025080:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | 00025080:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | ||
| 00025090:·2c53·7472·6174·6567·793d·3e22·302d·7468··,Strategy=>"0-th | 00025090:·2c53·7472·6174·6567·793d·3e22·302d·7468··,Strategy=>"0-th | ||
| 000250a0:·2070·726f·6a65·6374·6976·6520·6465·6772···projective·degr | 000250a0:·2070·726f·6a65·6374·6976·6520·6465·6772···projective·degr | ||
| 000250b0:·6565·2229·2020·2020·2020·2020·2020·2020··ee")············ | 000250b0:·6565·2229·2020·2020·2020·2020·2020·2020··ee")············ | ||
| 000250c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000250c0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 000250d0:·7573·6564·2030·2e3 | 000250d0:·7573·6564·2030·2e34·3233·3036·3773·2028··used·0.423067s·( | ||
| 000250e0:·6370·7529·3b20·302e·3 | 000250e0:·6370·7529·3b20·302e·3334·3636·3334·7320··cpu);·0.346634s· | ||
| 000250f0:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | 000250f0:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 00025100:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 00025100:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00025110:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00025110:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00025120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 9504, 16 lines modified | Offset 9504, 16 lines modified | ||
| 000251f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000251f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025200:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | 00025200:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | ||
| 00025210:·2074·696d·6520·6465·6772·6565·2050·6869···time·degree·Phi | 00025210:·2074·696d·6520·6465·6772·6565·2050·6869···time·degree·Phi | ||
| 00025220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025250:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00025250:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00025260:·7573·6564·2030·2e3 | 00025260:·7573·6564·2030·2e33·3338·3532·3473·2028··used·0.338524s·( | ||
| 00025270:·6370·7529·3b20·302e·3 | 00025270:·6370·7529·3b20·302e·3334·3036·3831·7320··cpu);·0.340681s· | ||
| 00025280:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | 00025280:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 00025290:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 00025290:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 000252a0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000252a0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000252b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000252b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000252c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000252c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000252d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000252d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000252e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000252e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 10141, 16 lines modified | Offset 10141, 16 lines modified | ||
| 000279c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000279c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000279d0:·2d2b·0a7c·6932·203a·2074·696d·6520·3f20··-+.|i2·:·time·?· | 000279d0:·2d2b·0a7c·6932·203a·2074·696d·6520·3f20··-+.|i2·:·time·?· | ||
| 000279e0:·5068·6920·2020·2020·2020·2020·2020·2020··Phi············· | 000279e0:·5068·6920·2020·2020·2020·2020·2020·2020··Phi············· | ||
| 000279f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000279f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027a20:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 00027a20:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 00027a30:·303 | 00027a30:·3031·3030·3939·3673·2028·6370·7529·3b20··0100996s·(cpu);· | ||
| 00027a40:·302e·3030·3031·3 | 00027a40:·302e·3030·3031·3432·3232·3673·2028·7468··0.000142226s·(th | ||
| 00027a50:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 00027a50:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 00027a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027a70:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00027a70:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00027a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 10206, 17 lines modified | Offset 10206, 17 lines modified | ||
| 00027dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00027de0:·2d2b·0a7c·6934·203a·2074·696d·6520·3f20··-+.|i4·:·time·?· | 00027de0:·2d2b·0a7c·6934·203a·2074·696d·6520·3f20··-+.|i4·:·time·?· | ||
| 00027df0:·5068·6920·2020·2020·2020·2020·2020·2020··Phi············· | 00027df0:·5068·6920·2020·2020·2020·2020·2020·2020··Phi············· | ||
| 00027e00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027e00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027e10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027e10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027e20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027e20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027e30:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 00027e30:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 00027e40:·303 | 00027e40:·3031·3838·3238·3373·2028·6370·7529·3b20··0188283s·(cpu);· | ||
| 00027e50:·302e·3030·3032·3 | 00027e50:·302e·3030·3032·3032·3433·3973·2028·7468··0.000202439s·(th | ||
| 00027e60:·6561 | 00027e60:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 00027e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027e80:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00027e80:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00027e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027ed0:·207c·0a7c·6f34·203d·206d·756c·7469·2d72···|.|o4·=·multi-r | 00027ed0:·207c·0a7c·6f34·203d·206d·756c·7469·2d72···|.|o4·=·multi-r | ||
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| 00028220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00028220:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00028230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00028230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00028240:·2d2b·0a7c·6935·203a·2074·696d·6520·6465··-+.|i5·:·time·de | 00028240:·2d2b·0a7c·6935·203a·2074·696d·6520·6465··-+.|i5·:·time·de | ||
| 00028250:·7363·7269·6265·2050·6869·2020·2020·2020··scribe·Phi······ | 00028250:·7363·7269·6265·2050·6869·2020·2020·2020··scribe·Phi······ | ||
| 00028260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00028260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00028290:·207c·0a7c·202d·2d20·7573·6564·203 | 00028290:·207c·0a7c·202d·2d20·7573·6564·2031·2e30···|.|·--·used·1.0 | ||
| 000282a0:·3833·3632·3773·2028·6370·7529·3b20·302e··83627s·(cpu);·0. | |||
| 000282 | 000282a0:·3333·3538·7320·2863·7075·293b·2030·2e38··3358s·(cpu);·0.8 | ||
| 000282b0:·3539·3636·3773·2028·7468·7265·6164·293b··59667s·(thread); | |||
| 000282c0:· | 000282c0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 000282d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000282d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000282e0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 000282e0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
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| 0000b9e0:·206e·292f·327c·0a7c·2020·2020·2020·2020···n)/2|.|········ | 0000b9e0:·206e·292f·327c·0a7c·2020·2020·2020·2020···n)/2|.|········ | ||
| 0000b9f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000b9f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000113e0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000113e0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000113f0:·0a7c·6f32·203d·207b·44 | 000113f0:·0a7c·6f32·203d·207b·4442·732c·2044·665f··.|o2·=·{DBs,·Df_ | ||
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| 00012250:·2020·2020·2020·2020·7c0a·7c6f·3220·3d20··········|.|o2·=· | 00012250:·2020·2020·2020·2020·7c0a·7c6f·3220·3d20··········|.|o2·=· | ||
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| 000124b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000124b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000124c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000124c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00012510:·2c20·7b6 | 00012510:·2c20·7b63·2c20·657d·7d7d·7d20·2020·2020··,·{c,·e}}}}····· | ||
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| 0000aec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000aec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e140:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000e140:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000e150:·0a7c·6f32·203d·207b·44 | 0000e150:·0a7c·6f32·203d·207b·4479·6f2c·2044·6d43··.|o2·=·{Dyo,·DmC | ||
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| 0000ecb0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | 0000ecb0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | ||
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| 00010020:·616b·656e·2061·7320·7468·6520·7265·7475··aken·as·the·retu | 00010020:·616b·656e·2061·7320·7468·6520·7265·7475··aken·as·the·retu | ||
| 00010030:·726e·6564·206c·6973·7420·6973·2065·6e74··rned·list·is·ent | 00010030:·726e·6564·206c·6973·7420·6973·2065·6e74··rned·list·is·ent | ||
| 00010040:·6972·656c·7920·696e·0a47·7261·7068·3620··irely·in.Graph6· | 00010040:·6972·656c·7920·696e·0a47·7261·7068·3620··irely·in.Graph6· | ||
| 00010050:·6f72·2053·7061·7273·6536·2066·6f72·6d61··or·Sparse6·forma | 00010050:·6f72·2053·7061·7273·6536·2066·6f72·6d61··or·Sparse6·forma | ||
| 00010060:·742e·0a0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d··t...+----------- | 00010060:·742e·0a0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d··t...+----------- | ||
| 00010070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | |||
| 000100a0:·0a7c·6933·203a·2047·203d·2067·656e·6572··.|i3·:·G·=·gener | |||
| 000100b0:·6174·6542·6970·6172·7469·7465·4772·6170··ateBipartiteGrap | |||
| 000100c0:·6873·2037·3b20·2020·2020·2020·2020·2020··hs·7;··········· | |||
| 000100d0:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | |||
| 000100 | 000100e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000100a0:·2b0a·7c69·3320·3a20·4720·3d20·6765·6e65··+.|i3·:·G·=·gene | |||
| 000100b0:·7261·7465·4269·7061·7274·6974·6547·7261··rateBipartiteGra | |||
| 000100c0:·7068·7320·373b·2020·2020·2020·2020·2020··phs·7;·········· | |||
| 000100d0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | |||
| 000100e0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | |||
| 000100f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000100f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010100:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010100:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010110:·2d2d·2d2d·2d2d·2d2d·2d2 | 00010110:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 00010120:·3420·3a20·7469·6d65·2067·7261·7068·436f··4·:·time·graphCo | |||
| 000101 | 00010120:·2074·696d·6520·6772·6170·6843·6f6d·706c···time·graphCompl | ||
| 00010130:·656d·656e·7420·473b·2020·2020·2020·2020··ement·G;········ | |||
| 00010140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010150:·2020·2020·2020· | 00010150:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00010160:·6420·302e·3030·3038·3539·3533·3273·2028··d·0.000859532s·( | |||
| 000101 | 00010170:·6370·7529·3b20·302e·3030·3036·3037·3637··cpu);·0.00060767 | ||
| 00010180:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | |||
| 00010190:·6763·297c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d··gc)|.+---------- | |||
| 00010170:·3173·2028·6370·7529·3b20·302e·3030·3034··1s·(cpu);·0.0004 | |||
| 00010180:·3533·3037·3273·2028·7468·7265·6164·293b··53072s·(thread); | |||
| 00010190:·2030·7320·2867·6329·7c0a·2b2d·2d2d·2d2d···0s·(gc)|.+----- | |||
| 000101a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000101a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000101b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000101b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000101c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000101c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000101d0:·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20·7469··------+.|i5·:·ti | |||
| 000101e0:·6d65·2028·6772·6170·6843·6f6d·706c·656d··me·(graphComplem | |||
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| 00034930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00034930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00034940:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3620··----------+.|i6· | 00034940:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3620··----------+.|i6· | ||
| 00034950:·3a20·656c·6170·7365·6454·696d·6520·6e6f··:·elapsedTime·no | 00034950:·3a20·656c·6170·7365·6454·696d·6520·6e6f··:·elapsedTime·no | ||
| 00034960:·6574·6865·7269·616e·4f70·6572·6174·6f72··etherianOperator | 00034960:·6574·6865·7269·616e·4f70·6572·6174·6f72··etherianOperator | ||
| 00034970:·7328·512c·2053·7472·6174·6567·7920·3d3e··s(Q,·Strategy·=> | 00034970:·7328·512c·2053·7472·6174·6567·7920·3d3e··s(Q,·Strategy·=> | ||
| 00034980:·2022·5075·6e63·7475·616c·5175·6f74·2229···"PunctualQuot") | 00034980:·2022·5075·6e63·7475·616c·5175·6f74·2229···"PunctualQuot") | ||
| 00034990:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00034990:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 000349a0:·202e·3 | 000349a0:·202e·3131·3830·3438·7320·656c·6170·7365···.118048s·elapse | ||
| 000349b0:·6 | 000349b0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 000349c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000349c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000349d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000349d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000349e0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 000349e0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 000349f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000349f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00034a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00034a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00034a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00034a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00034a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00034a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 0001f470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f480:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3134··----------+.|i14 | 0001f480:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3134··----------+.|i14 | ||
| 0001f490:·203a·2059·203d·2074·696d·6520·736d·6f6f···:·Y·=·time·smoo | 0001f490:·203a·2059·203d·2074·696d·6520·736d·6f6f···:·Y·=·time·smoo | ||
| 0001f4a0:·7468·4661·6e6f·546f·7269·6356·6172·6965··thFanoToricVarie | 0001f4a0:·7468·4661·6e6f·546f·7269·6356·6172·6965··thFanoToricVarie | ||
| 0001f4b0:·7479·2835·2c31·3030·293b·2020·2020·2020··ty(5,100);······ | 0001f4b0:·7479·2835·2c31·3030·293b·2020·2020·2020··ty(5,100);······ | ||
| 0001f4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001f4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001f4d0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 0001f4d0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 0001f4e0:·2075·7365·6420·302e·313 | 0001f4e0:·2075·7365·6420·302e·3139·3430·3435·7320···used·0.194045s· | ||
| 0001f4f0:·2863·7075·293b·2030·2e31·3 | 0001f4f0:·2863·7075·293b·2030·2e31·3931·3735·3173··(cpu);·0.191751s | ||
| 0001f500:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | 0001f500:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | ||
| 0001f510:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | 0001f510:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | ||
| 0001f520:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | 0001f520:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | ||
| 0001f530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000200a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000200a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000200b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3139··----------+.|i19 | 000200b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3139··----------+.|i19 | ||
| 000200c0:·203a·2066·6f72·2069·2074·6f20·6469·6d20···:·for·i·to·dim· | 000200c0:·203a·2066·6f72·2069·2074·6f20·6469·6d20···:·for·i·to·dim· | ||
| 000200d0:·5920·6c69·7374·2074·696d·6520·6869·6c62··Y·list·time·hilb | 000200d0:·5920·6c69·7374·2074·696d·6520·6869·6c62··Y·list·time·hilb | ||
| 000200e0:·6572·7446·756e·6374·696f·6e20·2869·2c20··ertFunction·(i,· | 000200e0:·6572·7446·756e·6374·696f·6e20·2869·2c20··ertFunction·(i,· | ||
| 000200f0:·4132·2920·2020·2020·2020·2020·2020·2020··A2)············· | 000200f0:·4132·2920·2020·2020·2020·2020·2020·2020··A2)············· | ||
| 00020100:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00020100:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00020110:·2075·7365·6420·302e·3030·3 | 00020110:·2075·7365·6420·302e·3030·3233·3934·3939···used·0.00239499 | ||
| 00020120:· | 00020120:·7320·2863·7075·293b·2030·2e30·3031·3033··s·(cpu);·0.00103 | ||
| 00020130:·3 | 00020130:·3835·3873·2028·7468·7265·6164·293b·2030··858s·(thread);·0 | ||
| 00020140:· | 00020140:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00020150:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00020150:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00020160:·2075·7365·6420·3 | 00020160:·2075·7365·6420·372e·3637·3534·652d·3035···used·7.6754e-05 | ||
| 00020170:·7320·2863·7075·293b·203 | 00020170:·7320·2863·7075·293b·2039·2e38·3738·3665··s·(cpu);·9.8786e | ||
| 00020180:·2d30·3573·2028·7468·7265·6164·293b·2030··-05s·(thread);·0 | 00020180:·2d30·3573·2028·7468·7265·6164·293b·2030··-05s·(thread);·0 | ||
| 00020190:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | 00020190:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 000201a0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 000201a0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 000201b0:·2075·7365·6420·352e·3932·3965·2d30·3673···used·5.929e-06s | |||
| 000201c0:·2028·6370·7529·3b20·342e·3837·3733·652d···(cpu);·4.8773e- | |||
| 000201 | 000201b0:·2075·7365·6420·312e·3337·3635·652d·3035···used·1.3765e-05 | ||
| 000201c0:·7320·2863·7075·293b·2037·2e37·3435·3665··s·(cpu);·7.7456e | |||
| 000201d0:·2d30·3573·2028·7468·7265·6164·293b·2030··-05s·(thread);·0 | |||
| 000201e0:·2028 | 000201e0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 000201f0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 000201f0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00020200:·2075·7365·6420·3 | 00020200:·2075·7365·6420·312e·3235·3133·652d·3035···used·1.2513e-05 | ||
| 00020210:·2028·6370·7529·3b20·342e·3530·3138·652d···(cpu);·4.5018e- | |||
| 000202 | 00020210:·7320·2863·7075·293b·2039·2e32·3430·3465··s·(cpu);·9.2404e | ||
| 00020220:·2d30·3573·2028·7468·7265·6164·293b·2030··-05s·(thread);·0 | |||
| 00020230:·2028 | 00020230:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00020240:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00020240:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00020250:·2075·7365·6420·3 | 00020250:·2075·7365·6420·312e·3532·3738·652d·3035···used·1.5278e-05 | ||
| 00020260:·2028 | 00020260:·7320·2863·7075·293b·2037·2e33·3339·3865··s·(cpu);·7.3398e | ||
| 00020270:·3573·2028·7468·7265·6164·293b·2030· | 00020270:·2d30·3573·2028·7468·7265·6164·293b·2030··-05s·(thread);·0 | ||
| 00020280:·2867·6329·2020·2020·2020·2020·2020· | 00020280:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00020290:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00020290:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 000202a0:·2075·7365·6420·3 | 000202a0:·2075·7365·6420·392e·3837·3865·2d30·3673···used·9.878e-06s | ||
| 000202b0:·2028·6370·7529·3b20·3 | 000202b0:·2028·6370·7529·3b20·362e·3834·3439·652d···(cpu);·6.8449e- | ||
| 000202c0:·3035·7320·2874·6872·6561·6429·3b20·3073··05s·(thread);·0s | 000202c0:·3035·7320·2874·6872·6561·6429·3b20·3073··05s·(thread);·0s | ||
| 000202d0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 000202d0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 000202e0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 000202e0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 000202f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000202f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00020300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00020300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00020310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00020310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00020320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00020320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00066e00:·2d2d·2b0a·7c69·3320·3a20·6120·3d20·736f··--+.|i3·:·a·=·so | 00066e00:·2d2d·2b0a·7c69·3320·3a20·6120·3d20·736f··--+.|i3·:·a·=·so | ||
| 00066e10:·7274·2061·7070·6c79·2028·332c·2069·202d··rt·apply·(3,·i·- | 00066e10:·7274·2061·7070·6c79·2028·332c·2069·202d··rt·apply·(3,·i·- | ||
| 00066e20:·3e20·7261·6e64·6f6d·2028·3729·2920·2020··>·random·(7))··· | 00066e20:·3e20·7261·6e64·6f6d·2028·3729·2920·2020··>·random·(7))··· | ||
| 00066e30:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00066e30:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
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| 00066e70:·7d20·2020·2020·2020·2020·2020·2020·2020··}··············· | 00066e70:·7d20·2020·2020·2020·2020·2020·2020·2020··}··············· | ||
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| 00066eb0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00066eb0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00066ec0:·7c6f·3320·3a20·4c69·7374·2020·2020·2020··|o3·:·List······ | 00066ec0:·7c6f·3320·3a20·4c69·7374·2020·2020·2020··|o3·:·List······ | ||
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| 00067250:·3d20·7b3 | 00067250:·3d20·7b31·2c20·332c·2034·2c20·372c·2038··=·{1,·3,·4,·7,·8 | ||
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| 0007b6f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0007b6f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0007b700:·3320·3a20·4d31·203d·2065·6c61·7073·6564··3·:·M1·=·elapsed | 0007b700:·3320·3a20·4d31·203d·2065·6c61·7073·6564··3·:·M1·=·elapsed | ||
| 0007b710:·5469·6d65·206d·6f6e·6f6d·6961·6c73·2044··Time·monomials·D | 0007b710:·5469·6d65·206d·6f6e·6f6d·6961·6c73·2044··Time·monomials·D | ||
| 0007b720:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | 0007b720:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | ||
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| 0007b750:·2d2d·202e·313 | 0007b750:·2d2d·202e·3135·3231·3734·7320·656c·6170··--·.152174s·elap | ||
| 0007b760:· | 0007b760:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
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| 0007b790:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0007b790:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
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| 0007bb00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0007bb00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0007bb10:·3420·3a20·656c·6170·7365·6454·696d·6520··4·:·elapsedTime· | 0007bb10:·3420·3a20·656c·6170·7365·6454·696d·6520··4·:·elapsedTime· | ||
| 0007bb20:·6173·7365·7274·2028·7365·7420·4d31·203d··assert·(set·M1·= | 0007bb20:·6173·7365·7274·2028·7365·7420·4d31·203d··assert·(set·M1·= | ||
| 0007bb30:·3d3d·2073·6574·2066·6972·7374·2065·6e74··==·set·first·ent | 0007bb30:·3d3d·2073·6574·2066·6972·7374·2065·6e74··==·set·first·ent | ||
| 0007bb40:·7269·6573·2062·6173·6973·2864·6567·7265··ries·basis(degre | 0007bb40:·7269·6573·2062·6173·6973·2864·6567·7265··ries·basis(degre | ||
| 0007bb50:·6520·4431·2c20·7269·6e67·2020·7c0a·7c20··e·D1,·ring··|.|· | 0007bb50:·6520·4431·2c20·7269·6e67·2020·7c0a·7c20··e·D1,·ring··|.|· | ||
| 0007bb60:·2d2d·202e·3030·313 | 0007bb60:·2d2d·202e·3030·3131·3633·3836·7320·656c··--·.00116386s·el | ||
| 0007bb70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 0007bb70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
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| 0007bbb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0007bbb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0007bbc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0007bbc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0007bbd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0007bbd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 0001e530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001e530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001e540:·2b0a·7c69·3420·3a20·7472·7920·7061·7261··+.|i4·:·try·para | 0001e540:·2b0a·7c69·3420·3a20·7472·7920·7061·7261··+.|i4·:·try·para | ||
| 0001e550:·6d65·7465·7248·6f6d·6f74·6f70·7928·7b66··meterHomotopy({f | 0001e550:·6d65·7465·7248·6f6d·6f74·6f70·7928·7b66··meterHomotopy({f | ||
| 0001e560:·312c·6632·7d2c·7b75·312c·7532·2c75·337d··1,f2},{u1,u2,u3} | 0001e560:·312c·6632·7d2c·7b75·312c·7532·2c75·337d··1,f2},{u1,u2,u3} | ||
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| 0001e590:·7c0a·7c73·683a·2031·3a20·6265·7274·696e··|.|sh:·1:·bertin | |||
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| 0001e5e0:·7c0a·7c74·7275·6520·2020·2020·2020·2020··|.|true········· | 0001e5e0:·7c0a·7c74·7275·6520·2020·2020·2020·2020··|.|true········· | ||
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| 000055d0:·2020·2020·2020·2020·207c·0a7c·5361·6d70···········|.|Samp | 000055d0:·2020·2020·2020·2020·207c·0a7c·5361·6d70···········|.|Samp | ||
| 000055e0:·6c69·6e67·2069·6d61·6765·2070·6f69·6e74··ling·image·point | 000055e0:·6c69·6e67·2069·6d61·6765·2070·6f69·6e74··ling·image·point | ||
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| 00005630:·202d·2d20·7573·6564·202e·3030·3 | 00005630:·202d·2d20·7573·6564·202e·3030·3837·3431···--·used·.008741 | ||
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| 00005670:·2020·2020·2020·2020·207c·0a7c·4372·6561···········|.|Crea | 00005670:·2020·2020·2020·2020·207c·0a7c·4372·6561···········|.|Crea | ||
| 00005680:·7469·6e67·2069·6e74·6572·706f·6c61·7469··ting·interpolati | 00005680:·7469·6e67·2069·6e74·6572·706f·6c61·7469··ting·interpolati | ||
| 00005690:·6f6e·206d·6174·7269·7820·2e2e·2e20·2020··on·matrix·...··· | 00005690:·6f6e·206d·6174·7269·7820·2e2e·2e20·2020··on·matrix·...··· | ||
| 000056a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000056a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000056c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000056c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000056d0:·202d·2d20·7573·6564·202e·3030·3 | 000056d0:·202d·2d20·7573·6564·202e·3030·3639·3531···--·used·.006951 | ||
| 000056e0:·3 | 000056e0:·3837·2073·6563·6f6e·6473·2020·2020·2020··87·seconds······ | ||
| 000056f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000056f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005710:·2020·2020·2020·2020·207c·0a7c·5065·7266···········|.|Perf | 00005710:·2020·2020·2020·2020·207c·0a7c·5065·7266···········|.|Perf | ||
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| 00005730:·7469·6f6e·2070·7265·636f·6e64·6974·696f··tion·preconditio | 00005730:·7469·6f6e·2070·7265·636f·6e64·6974·696f··tion·preconditio | ||
| 00005740:·6e69·6e67·202e·2e2e·2020·2020·2020·2020··ning·...········ | 00005740:·6e69·6e67·202e·2e2e·2020·2020·2020·2020··ning·...········ | ||
| 00005750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005760:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00005760:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00005770:·202d·2d20·7573·6564·202e·3030·3339·393 | 00005770:·202d·2d20·7573·6564·202e·3030·3339·3939···--·used·.003999 | ||
| 00005780:·343 | 00005780:·3439·2073·6563·6f6e·6473·2020·2020·2020··49·seconds······ | ||
| 00005790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057b0:·2020·2020·2020·2020·207c·0a7c·436f·6d70···········|.|Comp | 000057b0:·2020·2020·2020·2020·207c·0a7c·436f·6d70···········|.|Comp | ||
| 000057c0:·7574·696e·6720·6e75·6d65·7269·6361·6c20··uting·numerical· | 000057c0:·7574·696e·6720·6e75·6d65·7269·6361·6c20··uting·numerical· | ||
| 000057d0:·6b65·726e·656c·202e·2e2e·2020·2020·2020··kernel·...······ | 000057d0:·6b65·726e·656c·202e·2e2e·2020·2020·2020··kernel·...······ | ||
| 000057e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 1698, 24 lines modified | Offset 1698, 24 lines modified | ||
| 00006a10:·2c20·6964·6561·6c20·305f·522c·2032·2c20··,·ideal·0_R,·2,· | 00006a10:·2c20·6964·6561·6c20·305f·522c·2032·2c20··,·ideal·0_R,·2,· | ||
| 00006a20:·4174·7465·6d70·745a·5a20·3d3e·2074·7275··AttemptZZ·=>·tru | 00006a20:·4174·7465·6d70·745a·5a20·3d3e·2074·7275··AttemptZZ·=>·tru | ||
| 00006a30:·6529·2020·7c0a·7c53·616d·706c·696e·6720··e)··|.|Sampling· | 00006a30:·6529·2020·7c0a·7c53·616d·706c·696e·6720··e)··|.|Sampling· | ||
| 00006a40:·696d·6167·6520·706f·696e·7473·202e·2e2e··image·points·... | 00006a40:·696d·6167·6520·706f·696e·7473·202e·2e2e··image·points·... | ||
| 00006a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006a70:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | 00006a70:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | ||
| 00006a80:·2d20·7573·6564·202e·3030·3 | 00006a80:·2d20·7573·6564·202e·3030·3533·3231·3835··-·used·.00532185 | ||
| 00006a90:·2073·6563·6f6e·6473·2020·2020·2020·2020···seconds········ | 00006a90:·2073·6563·6f6e·6473·2020·2020·2020·2020···seconds········ | ||
| 00006aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ab0:·2020·2020·2020·2020·2020·7c0a·7c43·7265············|.|Cre | 00006ab0:·2020·2020·2020·2020·2020·7c0a·7c43·7265············|.|Cre | ||
| 00006ac0:·6174·696e·6720·696e·7465·7270·6f6c·6174··ating·interpolat | 00006ac0:·6174·696e·6720·696e·7465·7270·6f6c·6174··ating·interpolat | ||
| 00006ad0:·696f·6e20·6d61·7472·6978·202e·2e2e·2020··ion·matrix·...·· | 00006ad0:·696f·6e20·6d61·7472·6978·202e·2e2e·2020··ion·matrix·...·· | ||
| 00006ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006af0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00006af0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00006b00:·2020·2020·202d·2d20·7573·6564·202e·3030·······--·used·.00 | 00006b00:·2020·2020·202d·2d20·7573·6564·202e·3030·······--·used·.00 | ||
| 00006b10:·3 | 00006b10:·3430·3038·3737·2073·6563·6f6e·6473·2020··400877·seconds·· | ||
| 00006b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006b40:·7c0a·7c50·6572·666f·726d·696e·6720·6e6f··|.|Performing·no | 00006b40:·7c0a·7c50·6572·666f·726d·696e·6720·6e6f··|.|Performing·no | ||
| 00006b50:·726d·616c·697a·6174·696f·6e20·7072·6563··rmalization·prec | 00006b50:·726d·616c·697a·6174·696f·6e20·7072·6563··rmalization·prec | ||
| 00006b60:·6f6e·6469·7469·6f6e·696e·6720·2e2e·2e20··onditioning·...· | 00006b60:·6f6e·6469·7469·6f6e·696e·6720·2e2e·2e20··onditioning·...· | ||
| 00006b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006b80:·2020·207c·0a7c·2020·2020·202d·2d20·7573·····|.|·····--·us | 00006b80:·2020·207c·0a7c·2020·2020·202d·2d20·7573·····|.|·····--·us | ||
| Offset 2659, 45 lines modified | Offset 2659, 45 lines modified | ||
| 0000a620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a630:·2020·2020·2020·2020·2020·7c0a·7c53·616d············|.|Sam | 0000a630:·2020·2020·2020·2020·2020·7c0a·7c53·616d············|.|Sam | ||
| 0000a640:·706c·696e·6720·696d·6167·6520·706f·696e··pling·image·poin | 0000a640:·706c·696e·6720·696d·6167·6520·706f·696e··pling·image·poin | ||
| 0000a650:·7473·202e·2e2e·2020·2020·2020·2020·2020··ts·...·········· | 0000a650:·7473·202e·2e2e·2020·2020·2020·2020·2020··ts·...·········· | ||
| 0000a660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a680:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 0000a680:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 0000a690:·2d2d·2075·7365·6420·2e30·3 | 0000a690:·2d2d·2075·7365·6420·2e30·3131·3236·3437··--·used·.0112647 | ||
| 0000a6a0:·2073·6563·6f6e·6473·2020·2020·2020·2020···seconds········ | 0000a6a0:·2073·6563·6f6e·6473·2020·2020·2020·2020···seconds········ | ||
| 0000a6b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a6b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a6c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a6c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a6d0:·2020·2020·2020·7c0a·7c43·7265·6174·696e········|.|Creatin | 0000a6d0:·2020·2020·2020·7c0a·7c43·7265·6174·696e········|.|Creatin | ||
| 0000a6e0:·6720·696e·7465·7270·6f6c·6174·696f·6e20··g·interpolation· | 0000a6e0:·6720·696e·7465·7270·6f6c·6174·696f·6e20··g·interpolation· | ||
| 0000a6f0:·6d61·7472·6978·202e·2e2e·2020·2020·2020··matrix·...······ | 0000a6f0:·6d61·7472·6978·202e·2e2e·2020·2020·2020··matrix·...······ | ||
| 0000a700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a720:·2020·2020·7c0a·7c20·2020·2020·2d2d·2075······|.|·····--·u | 0000a720:·2020·2020·7c0a·7c20·2020·2020·2d2d·2075······|.|·····--·u | ||
| 0000a730:·7365·6420·2e30·303 | 0000a730:·7365·6420·2e30·3039·3530·3836·3720·7365··sed·.00950867·se | ||
| 0000a740:·636f·6e64·7320·2020·2020·2020·2020·2020··conds··········· | 0000a740:·636f·6e64·7320·2020·2020·2020·2020·2020··conds··········· | ||
| 0000a750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a770:·2020·7c0a·7c50·6572·666f·726d·696e·6720····|.|Performing· | 0000a770:·2020·7c0a·7c50·6572·666f·726d·696e·6720····|.|Performing· | ||
| 0000a780:·6e6f·726d·616c·697a·6174·696f·6e20·7072··normalization·pr | 0000a780:·6e6f·726d·616c·697a·6174·696f·6e20·7072··normalization·pr | ||
| 0000a790:·6563·6f6e·6469·7469·6f6e·696e·6720·2e2e··econditioning·.. | 0000a790:·6563·6f6e·6469·7469·6f6e·696e·6720·2e2e··econditioning·.. | ||
| 0000a7a0:·2e20·2020·2020·2020·2020·2020·2020·2020··.··············· | 0000a7a0:·2e20·2020·2020·2020·2020·2020·2020·2020··.··············· | ||
| 0000a7b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a7b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a7c0:·7c0a·7c20·2020·2020·2d2d·2075·7365·6420··|.|·····--·used· | 0000a7c0:·7c0a·7c20·2020·2020·2d2d·2075·7365·6420··|.|·····--·used· | ||
| 0000a7d0:·2e30·3 | 0000a7d0:·2e30·3130·3339·3037·2073·6563·6f6e·6473··.0103907·seconds | ||
| 0000a7e0:· | 0000a7e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a7f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a7f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a800:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000a800:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000a810:·7c43·6f6d·7075·7469·6e67·206e·756d·6572··|Computing·numer | 0000a810:·7c43·6f6d·7075·7469·6e67·206e·756d·6572··|Computing·numer | ||
| 0000a820:·6963·616c·206b·6572·6e65·6c20·2e2e·2e20··ical·kernel·...· | 0000a820:·6963·616c·206b·6572·6e65·6c20·2e2e·2e20··ical·kernel·...· | ||
| 0000a830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a850:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000a850:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0000a860:·2020·2020·2d2d·2075·7365·6420·2e30·303 | 0000a860:·2020·2020·2d2d·2075·7365·6420·2e30·3030······--·used·.000 | ||
| 0000a870:·3 | 0000a870:·3932·3839·3131·2073·6563·6f6e·6473·2020··928911·seconds·· | ||
| 0000a880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a8a0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0000a8a0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0000a8b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a8b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a8c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a8c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a8d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a8d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a8e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a8e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2777, 35 lines modified | Offset 2777, 35 lines modified | ||
| 0000ad80:·7365·534c·5020·3d3e·2074·7275·6529·2020··seSLP·=>·true)·· | 0000ad80:·7365·534c·5020·3d3e·2074·7275·6529·2020··seSLP·=>·true)·· | ||
| 0000ad90:·2020·2020·2020·207c·0a7c·4372·6561·7469·········|.|Creati | 0000ad90:·2020·2020·2020·207c·0a7c·4372·6561·7469·········|.|Creati | ||
| 0000ada0:·6e67·2069·6e74·6572·706f·6c61·7469·6f6e··ng·interpolation | 0000ada0:·6e67·2069·6e74·6572·706f·6c61·7469·6f6e··ng·interpolation | ||
| 0000adb0:·206d·6174·7269·7820·2e2e·2e20·2020·2020···matrix·...····· | 0000adb0:·206d·6174·7269·7820·2e2e·2e20·2020·2020···matrix·...····· | ||
| 0000adc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000adc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000add0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000add0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ade0:·2020·2020·7c0a·7c20·2020·2020·2d2d·2075······|.|·····--·u | 0000ade0:·2020·2020·7c0a·7c20·2020·2020·2d2d·2075······|.|·····--·u | ||
| 0000adf0:·7365·6420·2e30·3033·3 | 0000adf0:·7365·6420·2e30·3033·3738·3939·3420·7365··sed·.00378994·se | ||
| 0000ae00:·636f·6e64·7320·2020·2020·2020·2020·2020··conds··········· | 0000ae00:·636f·6e64·7320·2020·2020·2020·2020·2020··conds··········· | ||
| 0000ae10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ae10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ae20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ae20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ae30:·207c·0a7c·5065·7266·6f72·6d69·6e67·206e···|.|Performing·n | 0000ae30:·207c·0a7c·5065·7266·6f72·6d69·6e67·206e···|.|Performing·n | ||
| 0000ae40:·6f72·6d61·6c69·7a61·7469·6f6e·2070·7265··ormalization·pre | 0000ae40:·6f72·6d61·6c69·7a61·7469·6f6e·2070·7265··ormalization·pre | ||
| 0000ae50:·636f·6e64·6974·696f·6e69·6e67·202e·2e2e··conditioning·... | 0000ae50:·636f·6e64·6974·696f·6e69·6e67·202e·2e2e··conditioning·... | ||
| 0000ae60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ae60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ae70:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000ae70:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000ae80:·7c20·2020·2020·2d2d·2075·7365·6420·2e30··|·····--·used·.0 | 0000ae80:·7c20·2020·2020·2d2d·2075·7365·6420·2e30··|·····--·used·.0 | ||
| 0000ae90:·303 | 0000ae90:·3038·3136·3137·3720·7365·636f·6e64·7320··0816177·seconds· | ||
| 0000aea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000aea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Max diff block lines reached; 3705/13530 bytes (27.38%) of diff not shown. | |||
| Offset 6755, 15 lines modified | Offset 6755, 15 lines modified | ||
| 0001a620:·2020·523d·6b6b·5b73·7570·706f·7274·2063····R=kk[support·c | 0001a620:·2020·523d·6b6b·5b73·7570·706f·7274·2063····R=kk[support·c | ||
| 0001a630:·5d3b·633d·7375·6228·632c·5229·3b20·2020··];c=sub(c,R);··· | 0001a630:·5d3b·633d·7375·6228·632c·5229·3b20·2020··];c=sub(c,R);··· | ||
| 0001a640:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0001a640:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0001a650:·0a7c·2020·2020·2020·2020·2020·2020·2068··.|·············h | 0001a650:·0a7c·2020·2020·2020·2020·2020·2020·2068··.|·············h | ||
| 0001a660:·6575·7269·7374·6963·536d·6f6f·7468·6e65··euristicSmoothne | 0001a660:·6575·7269·7374·6963·536d·6f6f·7468·6e65··euristicSmoothne | ||
| 0001a670:·7373·2063·2929·2020·2020·2020·2020·2020··ss·c))·········· | 0001a670:·7373·2063·2929·2020·2020·2020·2020·2020··ss·c))·········· | ||
| 0001a680:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0001a680:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0001a690:·2d2d·203 | 0001a690:·2d2d·2032·2e38·3736·3734·7320·656c·6170··--·2.87674s·elap | ||
| 0001a6a0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | 0001a6a0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 0001a6b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001a6b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001a6c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 0001a6c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
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| 0001a700:·2020·2020·2020·7c0a·7c6f·3420·3d20·5461········|.|o4·=·Ta | 0001a700:·2020·2020·2020·7c0a·7c6f·3420·3d20·5461········|.|o4·=·Ta | ||
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| 0001cac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001cac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001cad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001cad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001cae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 0001cae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 0001caf0:·6933·203a·2065·6c61·7073·6564·5469·6d65··i3·:·elapsedTime | 0001caf0:·6933·203a·2065·6c61·7073·6564·5469·6d65··i3·:·elapsedTime | ||
| 0001cb00:·2069·7353·6d6f·6f74·6861·626c·6553·656d···isSmoothableSem | 0001cb00:·2069·7353·6d6f·6f74·6861·626c·6553·656d···isSmoothableSem | ||
| 0001cb10:·6967·726f·7570·284c·2c30·2e33·302c·3029··igroup(L,0.30,0) | 0001cb10:·6967·726f·7570·284c·2c30·2e33·302c·3029··igroup(L,0.30,0) | ||
| 0001cb20:·7c0a·7c20·2d2d·202e·3 | 0001cb20:·7c0a·7c20·2d2d·202e·3833·3033·3231·7320··|.|·--·.830321s· | ||
| 0001cb30:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 0001cb30:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
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| 0001cb80:·2020·2020·2020·7c0a·7c6f·3320·3d20·6661········|.|o3·=·fa | 0001cb80:·2020·2020·2020·7c0a·7c6f·3320·3d20·6661········|.|o3·=·fa | ||
| 0001cb90:·6c73·6520·2020·2020·2020·2020·2020·2020··lse············· | 0001cb90:·6c73·6520·2020·2020·2020·2020·2020·2020··lse············· | ||
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| 0001cbc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001cbc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001cbd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001cbd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001cbe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0001cbe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0001cbf0:·3420·3a20·656c·6170·7365·6454·696d·6520··4·:·elapsedTime· | 0001cbf0:·3420·3a20·656c·6170·7365·6454·696d·6520··4·:·elapsedTime· | ||
| 0001cc00:·6973·536d·6f6f·7468·6162·6c65·5365·6d69··isSmoothableSemi | 0001cc00:·6973·536d·6f6f·7468·6162·6c65·5365·6d69··isSmoothableSemi | ||
| 0001cc10:·6772·6f75·7028·4c2c·302e·3134·2c30·297c··group(L,0.14,0)| | 0001cc10:·6772·6f75·7028·4c2c·302e·3134·2c30·297c··group(L,0.14,0)| | ||
| 0001cc20:·0a7c·202d·2d20·3 | 0001cc20:·0a7c·202d·2d20·332e·3131·3039·3573·2065··.|·--·3.11095s·e | ||
| 0001cc30:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 0001cc30:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
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| 0001cc80:·2020·2020·207c·0a7c·6f34·203d·2074·7275·······|.|o4·=·tru | 0001cc80:·2020·2020·207c·0a7c·6f34·203d·2074·7275·······|.|o4·=·tru | ||
| 0001cc90:·6520·2020·2020·2020·2020·2020·2020·2020··e··············· | 0001cc90:·6520·2020·2020·2020·2020·2020·2020·2020··e··············· | ||
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| 0001deb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001deb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001dec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001dec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001ded0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0001ded0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0001dee0:·0a7c·6933·203a·2065·6c61·7073·6564·5469··.|i3·:·elapsedTi | 0001dee0:·0a7c·6933·203a·2065·6c61·7073·6564·5469··.|i3·:·elapsedTi | ||
| 0001def0:·6d65·2069·7357·6569·6572·7374·7261·7373··me·isWeierstrass | 0001def0:·6d65·2069·7357·6569·6572·7374·7261·7373··me·isWeierstrass | ||
| 0001df00:·5365·6d69·6772·6f75·7028·4c2c·302e·3135··Semigroup(L,0.15 | 0001df00:·5365·6d69·6772·6f75·7028·4c2c·302e·3135··Semigroup(L,0.15 | ||
| 0001df10:·297c·0a7c·202d·2d20·3 | 0001df10:·297c·0a7c·202d·2d20·332e·3439·3738·3173··)|.|·--·3.49781s | ||
| 0001df20:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 0001df20:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
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| 0001df70:·2020·2020·207c·0a7c·6f33·203d·2074·7275·······|.|o3·=·tru | 0001df70:·2020·2020·207c·0a7c·6f33·203d·2074·7275·······|.|o3·=·tru | ||
| 0001df80:·6520·2020·2020·2020·2020·2020·2020·2020··e··············· | 0001df80:·6520·2020·2020·2020·2020·2020·2020·2020··e··············· | ||
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| 000215e0:·2020·2020·2020·7c0a·7c75·6e66·6f6c·6469········|.|unfoldi | 000215e0:·2020·2020·2020·7c0a·7c75·6e66·6f6c·6469········|.|unfoldi | ||
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| 00021630:·2020·2020·2020·7c0a·7c20·2d2d·202e·3 | 00021630:·2020·2020·2020·7c0a·7c20·2d2d·202e·3134········|.|·--·.14 | ||
| 00021640:·3334·3 | 00021640:·3334·3937·7320·656c·6170·7365·6420·2020··3497s·elapsed··· | ||
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| 00021680:·2020·2020·2020·7c0a·7c66·6c61·7474·656e········|.|flatten | 00021680:·2020·2020·2020·7c0a·7c66·6c61·7474·656e········|.|flatten | ||
| 00021690:·696e·6752·656c·6174·696f·6e73·2020·2020··ingRelations···· | 00021690:·696e·6752·656c·6174·696f·6e73·2020·2020··ingRelations···· | ||
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| 000216d0:·2020·2020·2020·7c0a·7c20·2d2d·202e·3 | 000216d0:·2020·2020·2020·7c0a·7c20·2d2d·202e·3130········|.|·--·.10 | ||
| 000216e0:·333 | 000216e0:·3331·3534·7320·656c·6170·7365·6420·2020··3154s·elapsed··· | ||
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| 00021720:·2020·2020·2020·7c0a·7c6e·6578·7420·6762········|.|next·gb | 00021720:·2020·2020·2020·7c0a·7c6e·6578·7420·6762········|.|next·gb | ||
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| 00021770:·2020·2020·2020·7c0a·7c20·2d2d·202e·3030········|.|·--·.00 | 00021770:·2020·2020·2020·7c0a·7c20·2d2d·202e·3030········|.|·--·.00 | ||
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| 000217c0:·2020·2020·2020·7c0a·7c74·7275·6520·2020········|.|true··· | 000217c0:·2020·2020·2020·7c0a·7c74·7275·6520·2020········|.|true··· | ||
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| 00021810:·2020·2020·2020·7c0a·7c75·6e66·6f6c·6469········|.|unfoldi | 00021810:·2020·2020·2020·7c0a·7c75·6e66·6f6c·6469········|.|unfoldi | ||
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| 00021860:·2020·2020·2020·7c0a·7c20·2d2d·202e·3039········|.|·--·.09 | 00021860:·2020·2020·2020·7c0a·7c20·2d2d·202e·3039········|.|·--·.09 | ||
| 00021870:·3 | 00021870:·3938·3238·3673·2065·6c61·7073·6564·2020··98286s·elapsed·· | ||
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| 000218b0:·2020·2020·2020·7c0a·7c66·6c61·7474·656e········|.|flatten | 000218b0:·2020·2020·2020·7c0a·7c66·6c61·7474·656e········|.|flatten | ||
| 000218c0:·696e·6752·656c·6174·696f·6e73·2020·2020··ingRelations···· | 000218c0:·696e·6752·656c·6174·696f·6e73·2020·2020··ingRelations···· | ||
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| 00021910:·3 | 00021910:·3031·3538·7320·656c·6170·7365·6420·2020··0158s·elapsed··· | ||
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| 0001a2d0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | 0001a2d0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 0001a2e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001a2e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001a2f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001a2f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001a300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001a300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 0001aa30:·7941·6374·696f·6e3b·2020·2020·2020·2020··yAction;········ | 0001aa30:·7941·6374·696f·6e3b·2020·2020·2020·2020··yAction;········ | ||
| 0001aa40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001aa40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001aa50:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 0001aa50:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 0001aa60:·2020·2023·6431·203e·3d33·206f·7220·2364·····#d1·>=3·or·#d | 0001aa60:·2020·2023·6431·203e·3d33·206f·7220·2364·····#d1·>=3·or·#d | ||
| 0001aa70:·3020·3e3d·3329·2064·6f20·2829·3b20·2020··0·>=3)·do·();··· | 0001aa70:·3020·3e3d·3329·2064·6f20·2829·3b20·2020··0·>=3)·do·();··· | ||
| 0001aa80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001aa80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001aa90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001aa90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001aaa0:·2020·2020·2020·7c0a·7c20·2d2d·202e·333 | 0001aaa0:·2020·2020·2020·7c0a·7c20·2d2d·202e·3335········|.|·--·.35 | ||
| 0001aab0:·3 | 0001aab0:·3138·3035·7320·656c·6170·7365·6420·2020··1805s·elapsed··· | ||
| 0001aac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001aac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001aad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001aad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001aae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001aae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001aaf0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | 0001aaf0:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 0001ab00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001ab00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001ab10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001ab10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001ab20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001ab20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 0001aee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001aee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001aef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001aef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001af00:·2d2d·2d2d·2d2d·2b0a·7c69·3133·203a·2065··------+.|i13·:·e | 0001af00:·2d2d·2d2d·2d2d·2b0a·7c69·3133·203a·2065··------+.|i13·:·e | ||
| 0001af10:·6c61·7073·6564·5469·6d65·2055·6c20·3d20··lapsedTime·Ul·=· | 0001af10:·6c61·7073·6564·5469·6d65·2055·6c20·3d20··lapsedTime·Ul·=· | ||
| 0001af20:·7465·6e73·6f72·5072·6f64·7563·7428·4d2c··tensorProduct(M, | 0001af20:·7465·6e73·6f72·5072·6f64·7563·7428·4d2c··tensorProduct(M, | ||
| 0001af30:·5629·3b20·2d2d·2074·6865·2068·6561·7669··V);·--·the·heavi | 0001af30:·5629·3b20·2d2d·2074·6865·2068·6561·7669··V);·--·the·heavi | ||
| 0001af40:·6573·7420·7061·7274·2063·6f6d·7075·7469··est·part·computi | 0001af40:·6573·7420·7061·7274·2063·6f6d·7075·7469··est·part·computi | ||
| 0001af50:·6e67·2074·6865·7c0a·7c20·2d2d·2031·3 | 0001af50:·6e67·2074·6865·7c0a·7c20·2d2d·2031·352e··ng·the|.|·--·15. | ||
| 0001af60:·3 | 0001af60:·3838·3838·7320·656c·6170·7365·6420·2020··8888s·elapsed··· | ||
| 0001af70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001af70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001af80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001af80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001af90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001af90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001afa0:·2020·2020·2020·7c0a·7c2d·2d2d·2d2d·2d2d········|.|------- | 0001afa0:·2020·2020·2020·7c0a·7c2d·2d2d·2d2d·2d2d········|.|------- | ||
| 0001afb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001afb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001afc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001afc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001afd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001afd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00031240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00031240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00031250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00031250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00031260:·2d2b·0a7c·6931·3220·3a20·656c·6170·7365··-+.|i12·:·elapse | 00031260:·2d2b·0a7c·6931·3220·3a20·656c·6170·7365··-+.|i12·:·elapse | ||
| 00031270:·6454·696d·6520·556c·7220·3d20·7365·6172··dTime·Ulr·=·sear | 00031270:·6454·696d·6520·556c·7220·3d20·7365·6172··dTime·Ulr·=·sear | ||
| 00031280:·6368·556c·7269·6368·284d·2c53·293b·2020··chUlrich(M,S);·· | 00031280:·6368·556c·7269·6368·284d·2c53·293b·2020··chUlrich(M,S);·· | ||
| 00031290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00031290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000312a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000312a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000312b0:·207c·0a7c·202d·2d20·2e3 | 000312b0:·207c·0a7c·202d·2d20·2e37·3130·3438·3373···|.|·--·.710483s | ||
| 000312c0:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 000312c0:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 000312d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000312d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000312e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000312e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000312f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000312f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00031300:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | 00031300:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
| 00031310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00031310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00031320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00031320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000316f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000316f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00031700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00031700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00031710:·2d2b·0a7c·6931·3520·3a20·656c·6170·7365··-+.|i15·:·elapse | 00031710:·2d2b·0a7c·6931·3520·3a20·656c·6170·7365··-+.|i15·:·elapse | ||
| 00031720:·6454·696d·6520·556c·7233·203d·2073·6561··dTime·Ulr3·=·sea | 00031720:·6454·696d·6520·556c·7233·203d·2073·6561··dTime·Ulr3·=·sea | ||
| 00031730:·7263·6855·6c72·6963·6828·4d2c·532c·3329··rchUlrich(M,S,3) | 00031730:·7263·6855·6c72·6963·6828·4d2c·532c·3329··rchUlrich(M,S,3) | ||
| 00031740:·3b20·2020·2020·2020·2020·2020·2020·2020··;··············· | 00031740:·3b20·2020·2020·2020·2020·2020·2020·2020··;··············· | ||
| 00031750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00031750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00031760:·207c·0a7c·202d·2d20·312e·3 | 00031760:·207c·0a7c·202d·2d20·312e·3833·3733·3773···|.|·--·1.83737s | ||
| 00031770:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 00031770:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 00031780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00031780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00031790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00031790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000317a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000317a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000317b0:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | 000317b0:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
| 000317c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000317c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000317d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000317d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00003550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | 00003560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | ||
| 00003570:·3020·3a20·656c·6170·7365·6454·696d·6520··0·:·elapsedTime· | 00003570:·3020·3a20·656c·6170·7365·6454·696d·6520··0·:·elapsedTime· | ||
| 00003580:·2851·2c69·6e47·2c47·2920·3d20·6166·6669··(Q,inG,G)·=·affi | 00003580:·2851·2c69·6e47·2c47·2920·3d20·6166·6669··(Q,inG,G)·=·affi | ||
| 00003590:·6e65·4661·7450·6f69·6e74·7328·4d2c·6d75··neFatPoints(M,mu | 00003590:·6e65·4661·7450·6f69·6e74·7328·4d2c·6d75··neFatPoints(M,mu | ||
| 000035a0:·6c74·732c·5229·3b20·2020·2020·2020·2020··lts,R);········· | 000035a0:·6c74·732c·5229·3b20·2020·2020·2020·2020··lts,R);········· | ||
| 000035b0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 000035b0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 000035c0:·2d20·3 | 000035c0:·2d20·332e·3132·3030·3973·2065·6c61·7073··-·3.12009s·elaps | ||
| 000035d0:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | 000035d0:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | ||
| 000035e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000035e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000035f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000035f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003600:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | 00003600:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | ||
| 00003610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003650:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | 00003650:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931··-----------+.|i1 | ||
| 00003660:·3120·3a20·656c·6170·7365·6454·696d·6520··1·:·elapsedTime· | 00003660:·3120·3a20·656c·6170·7365·6454·696d·6520··1·:·elapsedTime· | ||
| 00003670:·4820·3d20·6166·6669·6e65·4661·7450·6f69··H·=·affineFatPoi | 00003670:·4820·3d20·6166·6669·6e65·4661·7450·6f69··H·=·affineFatPoi | ||
| 00003680:·6e74·7342·7949·6e74·6572·7365·6374·696f··ntsByIntersectio | 00003680:·6e74·7342·7949·6e74·6572·7365·6374·696f··ntsByIntersectio | ||
| 00003690:·6e28·4d2c·6d75·6c74·732c·5229·3b20·2020··n(M,mults,R);··· | 00003690:·6e28·4d2c·6d75·6c74·732c·5229·3b20·2020··n(M,mults,R);··· | ||
| 000036a0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 000036a0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 000036b0:·2d20·3 | 000036b0:·2d20·342e·3437·3436·7320·656c·6170·7365··-·4.4746s·elapse | ||
| 000036c0:·6 | 000036c0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 000036d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000036d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000036e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000036e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000036f0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | 000036f0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | ||
| 00003700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003710:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003710:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003720:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003720:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00022380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022390:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:· | 00022390:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:· | ||
| 000223a0:·7469·6d65·2067·7265·656e·654b·6c65·6974··time·greeneKleit | 000223a0:·7469·6d65·2067·7265·656e·654b·6c65·6974··time·greeneKleit | ||
| 000223b0:·6d61·6e50·6172·7469·7469·6f6e·2844·2c20··manPartition(D,· | 000223b0:·6d61·6e50·6172·7469·7469·6f6e·2844·2c20··manPartition(D,· | ||
| 000223c0:·5374·7261·7465·6779·203d·3e20·2261·6e74··Strategy·=>·"ant | 000223c0:·5374·7261·7465·6779·203d·3e20·2261·6e74··Strategy·=>·"ant | ||
| 000223d0:·6963·6861·696e·7322·297c·0a7c·202d·2d20··ichains")|.|·--· | 000223d0:·6963·6861·696e·7322·297c·0a7c·202d·2d20··ichains")|.|·--· | ||
| 000223e0:·7573·6564·2030·2e3 | 000223e0:·7573·6564·2030·2e32·3833·3630·3773·2028··used·0.283607s·( | ||
| 000223f0:·6370·7529·3b20·302e·3 | 000223f0:·6370·7529·3b20·302e·3136·3530·3839·7320··cpu);·0.165089s· | ||
| 00022400:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | 00022400:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 00022410:·2920·2020·2020·2020·2020·7c0a·7c20·2020··)·········|.|··· | 00022410:·2920·2020·2020·2020·2020·7c0a·7c20·2020··)·········|.|··· | ||
| 00022420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022450:·2020·2020·2020·2020·2020·207c·0a7c·6f34·············|.|o4 | 00022450:·2020·2020·2020·2020·2020·207c·0a7c·6f34·············|.|o4 | ||
| 00022460:·203d·2050·6172·7469·7469·6f6e·7b39·2c20···=·Partition{9,· | 00022460:·203d·2050·6172·7469·7469·6f6e·7b39·2c20···=·Partition{9,· | ||
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| 00022540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00022550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00022560:·0a7c·6935·203a·2074·696d·6520·6772·6565··.|i5·:·time·gree | 00022560:·0a7c·6935·203a·2074·696d·6520·6772·6565··.|i5·:·time·gree | ||
| 00022570:·6e65·4b6c·6569·746d·616e·5061·7274·6974··neKleitmanPartit | 00022570:·6e65·4b6c·6569·746d·616e·5061·7274·6974··neKleitmanPartit | ||
| 00022580:·696f·6e28·442c·2053·7472·6174·6567·7920··ion(D,·Strategy· | 00022580:·696f·6e28·442c·2053·7472·6174·6567·7920··ion(D,·Strategy· | ||
| 00022590:·3d3e·2022·6368·6169·6e73·2229·2020·2020··=>·"chains")···· | 00022590:·3d3e·2022·6368·6169·6e73·2229·2020·2020··=>·"chains")···· | ||
| 000225a0:·7c0a·7c20·2d2d·2075·7365·6420·3 | 000225a0:·7c0a·7c20·2d2d·2075·7365·6420·362e·3538··|.|·--·used·6.58 | ||
| 000225b0:·3031·3635·3432·3973·2028·6370·7529·3b20··0165429s·(cpu);· | |||
| 000225c0:·372e·3237·3165·2d30·3673·2028·7468·7265··7.271e-06s·(thre | |||
| 000225 | 000225b0:·3433·652d·3035·7320·2863·7075·293b·2039··43e-05s·(cpu);·9 | ||
| 000225c0:·2e38·3539·652d·3036·7320·2874·6872·6561··.859e-06s·(threa | |||
| 000225d0:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | |||
| 000225e0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 000225e0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 000225f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000225f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022620:·2020·7c0a·7c6f·3520·3d20·5061·7274·6974····|.|o5·=·Partit | 00022620:·2020·7c0a·7c6f·3520·3d20·5061·7274·6974····|.|o5·=·Partit | ||
| 00022630:·696f·6e7b·392c·2032·7d20·2020·2020·2020··ion{9,·2}······· | 00022630:·696f·6e7b·392c·2032·7d20·2020·2020·2020··ion{9,·2}······· | ||
| 00022640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000483d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000483d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000483e0:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·7469··------+.|i7·:·ti | 000483e0:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·7469··------+.|i7·:·ti | ||
| 000483f0:·6d65·2069·7344·6973·7472·6962·7574·6976··me·isDistributiv | 000483f0:·6d65·2069·7344·6973·7472·6962·7574·6976··me·isDistributiv | ||
| 00048400:·6520·4320·2020·2020·2020·2020·2020·2020··e·C············· | 00048400:·6520·4320·2020·2020·2020·2020·2020·2020··e·C············· | ||
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| 00048430:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00048430:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00048440:·6420·302e·3030·3035·3432·3036·3673·2028··d·0.000542066s·( | |||
| 000484 | 00048440:·6420·312e·3731·3332·652d·3035·7320·2863··d·1.7132e-05s·(c | ||
| 00048450:·7075·293b·2035·2e35·3665·2d30·3673·2028··pu);·5.56e-06s·( | |||
| 00048460:· | 00048460:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 00048470:· | 00048470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00048480:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00048480:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00048490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000484b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000484b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000484d0:·2020·2020·2020·7c0a·7c6f·3720·3d20·7472········|.|o7·=·tr | 000484d0:·2020·2020·2020·7c0a·7c6f·3720·3d20·7472········|.|o7·=·tr | ||
| 000484e0:·7565·2020·2020·2020·2020·2020·2020·2020··ue·············· | 000484e0:·7565·2020·2020·2020·2020·2020·2020·2020··ue·············· | ||
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| 00048560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00048560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00048570:·2d2d·2d2d·2d2d·2b0a·7c69·3820·3a20·7469··------+.|i8·:·ti | 00048570:·2d2d·2d2d·2d2d·2b0a·7c69·3820·3a20·7469··------+.|i8·:·ti | ||
| 00048580:·6d65·2069·7344·6973·7472·6962·7574·6976··me·isDistributiv | 00048580:·6d65·2069·7344·6973·7472·6962·7574·6976··me·isDistributiv | ||
| 00048590:·6520·5020·2020·2020·2020·2020·2020·2020··e·P············· | 00048590:·6520·5020·2020·2020·2020·2020·2020·2020··e·P············· | ||
| 000485a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000485a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000485c0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 000485c0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 000485d0:·6420·342e·3 | 000485d0:·6420·342e·3937·3237·3173·2028·6370·7529··d·4.97271s·(cpu) | ||
| 000485e0:·3b20·3 | 000485e0:·3b20·332e·3436·3337·3473·2028·7468·7265··;·3.46374s·(thre | ||
| 000485f0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | 000485f0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00048600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00048870:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3130··----------+.|i10 | 00048870:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3130··----------+.|i10 | ||
| 00048880:·203a·2074·696d·6520·6973·4469·7374·7269···:·time·isDistri | 00048880:·203a·2074·696d·6520·6973·4469·7374·7269···:·time·isDistri | ||
| 00048890:·6275·7469·7665·2043·2720·2020·2020·2020··butive·C'······· | 00048890:·6275·7469·7665·2043·2720·2020·2020·2020··butive·C'······· | ||
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| 000488b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000488b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000488c0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 000488c0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 000488d0:·2075·7365·6420·302e·3030·303 | 000488d0:·2075·7365·6420·302e·3030·3032·3233·3938···used·0.00022398 | ||
| 000488e0:·3373·2028·6370·7529·3b20·332e·3933·3665··3s·(cpu);·3.936e | |||
| 000488 | 000488e0:·7320·2863·7075·293b·2034·2e32·3438·652d··s·(cpu);·4.248e- | ||
| 000488f0:·3036·7320·2874·6872·6561·6429·3b20·3073··06s·(thread);·0s | |||
| 00048900:· | 00048900:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00048910:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00048910:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
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| 00048960:·2020·2020·2020·2020·2020·7c0a·7c6f·3130············|.|o10 | 00048960:·2020·2020·2020·2020·2020·7c0a·7c6f·3130············|.|o10 | ||
| 00048970:·203d·2074·7275·6520·2020·2020·2020·2020···=·true········· | 00048970:·203d·2074·7275·6520·2020·2020·2020·2020···=·true········· |
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| 0000e2f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e2f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e300:·2d2b·0a7c·6934·203a·2065·6c61·7073·6564··-+.|i4·:·elapsed | 0000e300:·2d2b·0a7c·6934·203a·2065·6c61·7073·6564··-+.|i4·:·elapsed | ||
| 0000e310:·5469·6d65·206b·6572·6e65·6c4f·664c·6f63··Time·kernelOfLoc | 0000e310:·5469·6d65·206b·6572·6e65·6c4f·664c·6f63··Time·kernelOfLoc | ||
| 0000e320:·616c·697a·6174·696f·6e28·4d2c·2049·3129··alization(M,·I1) | 0000e320:·616c·697a·6174·696f·6e28·4d2c·2049·3129··alization(M,·I1) | ||
| 0000e330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e350:·207c·0a7c·202d·2d20·2e31·3 | 0000e350:·207c·0a7c·202d·2d20·2e31·3939·3533·3373···|.|·--·.199533s | ||
| 0000e360:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 0000e360:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 0000e370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e3a0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000e3a0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000e3b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e3b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e3c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e3c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e740:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e740:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e760:·2d2b·0a7c·6935·203a·2065·6c61·7073·6564··-+.|i5·:·elapsed | 0000e760:·2d2b·0a7c·6935·203a·2065·6c61·7073·6564··-+.|i5·:·elapsed | ||
| 0000e770:·5469·6d65·206b·6572·6e65·6c4f·664c·6f63··Time·kernelOfLoc | 0000e770:·5469·6d65·206b·6572·6e65·6c4f·664c·6f63··Time·kernelOfLoc | ||
| 0000e780:·616c·697a·6174·696f·6e28·4d2c·2049·3229··alization(M,·I2) | 0000e780:·616c·697a·6174·696f·6e28·4d2c·2049·3229··alization(M,·I2) | ||
| 0000e790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e7a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e7a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e7b0:·207c·0a7c·202d·2d20·2e30·313 | 0000e7b0:·207c·0a7c·202d·2d20·2e30·3137·3137·3031···|.|·--·.0171701 | ||
| 0000e7c0:·2065 | 0000e7c0:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 0000e7d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e7d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e7e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e7e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e7f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e7f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e800:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000e800:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000e810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000eba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000eba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ebb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ebb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ebc0:·2d2b·0a7c·6936·203a·2065·6c61·7073·6564··-+.|i6·:·elapsed | 0000ebc0:·2d2b·0a7c·6936·203a·2065·6c61·7073·6564··-+.|i6·:·elapsed | ||
| 0000ebd0:·5469·6d65·206b·6572·6e65·6c4f·664c·6f63··Time·kernelOfLoc | 0000ebd0:·5469·6d65·206b·6572·6e65·6c4f·664c·6f63··Time·kernelOfLoc | ||
| 0000ebe0:·616c·697a·6174·696f·6e28·4d2c·2049·3329··alization(M,·I3) | 0000ebe0:·616c·697a·6174·696f·6e28·4d2c·2049·3329··alization(M,·I3) | ||
| 0000ebf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec10:·207c·0a7c·202d·2d20·2e30·3 | 0000ec10:·207c·0a7c·202d·2d20·2e30·3435·3136·3036···|.|·--·.0451606 | ||
| 0000ec20:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 0000ec20:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 0000ec30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec60:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000ec60:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000ec70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00014ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014ae0:·2d2b·0a7c·6933·203a·2065·6c61·7073·6564··-+.|i3·:·elapsed | 00014ae0:·2d2b·0a7c·6933·203a·2065·6c61·7073·6564··-+.|i3·:·elapsed | ||
| 00014af0:·5469·6d65·2072·6567·5365·7149·6e49·6465··Time·regSeqInIde | 00014af0:·5469·6d65·2072·6567·5365·7149·6e49·6465··Time·regSeqInIde | ||
| 00014b00:·616c·2049·2020·2020·2020·2020·2020·2020··al·I············ | 00014b00:·616c·2049·2020·2020·2020·2020·2020·2020··al·I············ | ||
| 00014b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b30:·207c·0a7c·202d·2d20·2e30·3 | 00014b30:·207c·0a7c·202d·2d20·2e30·3932·3436·3032···|.|·--·.0924602 | ||
| 00014b40:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00014b40:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
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| 00014ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000155e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000155e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000155f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000155f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00015600:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·656c··------+.|i7·:·el | 00015600:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·656c··------+.|i7·:·el | ||
| 00015610:·6170·7365·6454·696d·6520·7265·6753·6571··apsedTime·regSeq | 00015610:·6170·7365·6454·696d·6520·7265·6753·6571··apsedTime·regSeq | ||
| 00015620:·496e·4964·6561·6c28·492c·2033·2c20·332c··InIdeal(I,·3,·3, | 00015620:·496e·4964·6561·6c28·492c·2033·2c20·332c··InIdeal(I,·3,·3, | ||
| 00015630:·2031·2920·2020·2020·2020·2020·2020·2020···1)············· | 00015630:·2031·2920·2020·2020·2020·2020·2020·2020···1)············· | ||
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| 00015650:·2020·2020·2020·7c0a·7c20·2d2d·202e·303 | 00015650:·2020·2020·2020·7c0a·7c20·2d2d·202e·3031········|.|·--·.01 | ||
| 00015660:·3 | 00015660:·3233·3839·3473·2065·6c61·7073·6564·2020··23894s·elapsed·· | ||
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| 000156a0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 000156a0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
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| 00009750:·6174·6f72·2078·2020·2020·2020·2020·2020··ator·x·········· | 00009750:·6174·6f72·2078·2020·2020·2020·2020·2020··ator·x·········· | ||
| 00009760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009770:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00009770:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00009780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000097a0:·2020·7c0a·7c6f·3220·3d20·3c72·616e·6765····|.|o2·=·<range | 000097a0:·2020·7c0a·7c6f·3220·3d20·3c72·616e·6765····|.|o2·=·<range | ||
| 000097b0:·5f69·7465·7261·746f·7220·6f62·6a65·6374··_iterator·object | 000097b0:·5f69·7465·7261·746f·7220·6f62·6a65·6374··_iterator·object | ||
| 000097c0:·2061·7420·3078·3766· | 000097c0:·2061·7420·3078·3766·3362·6139·6366·6463···at·0x7f3ba9cfdc | ||
| 000097d0:·3530·3e7c·0a7c·2020·2020·2020·2020·2020··50>|.|·········· | 000097d0:·3530·3e7c·0a7c·2020·2020·2020·2020·2020··50>|.|·········· | ||
| 000097e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000097e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000097f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000097f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009800:·2020·2020·7c0a·7c6f·3220·3a20·5079·7468······|.|o2·:·Pyth | 00009800:·2020·2020·7c0a·7c6f·3220·3a20·5079·7468······|.|o2·:·Pyth | ||
| 00009810:·6f6e·4f62·6a65·6374·206f·6620·636c·6173··onObject·of·clas | 00009810:·6f6e·4f62·6a65·6374·206f·6620·636c·6173··onObject·of·clas | ||
| 00009820:·7320·7261·6e67·655f·6974·6572·6174·6f72··s·range_iterator | 00009820:·7320·7261·6e67·655f·6974·6572·6174·6f72··s·range_iterator | ||
| 00009830:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | 00009830:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
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| 0000a1d0:·2069·7465·7261·746f·7220·7820·2020·2020···iterator·x····· | 0000a1d0:·2069·7465·7261·746f·7220·7820·2020·2020···iterator·x····· | ||
| 0000a1e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a1e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1f0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 0000a1f0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
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| 0000a210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a220:·2020·2020·2020·207c·0a7c·6f32·203d·203c·········|.|o2·=·< | 0000a220:·2020·2020·2020·207c·0a7c·6f32·203d·203c·········|.|o2·=·< | ||
| 0000a230:·7261·6e67·655f·6974·6572·6174·6f72·206f··range_iterator·o | 0000a230:·7261·6e67·655f·6974·6572·6174·6f72·206f··range_iterator·o | ||
| 0000a240:·626a·6563·7420·6174·2030·7837·666 | 0000a240:·626a·6563·7420·6174·2030·7837·6664·3733··bject·at·0x7fd73 | ||
| 0000a250:·3 | 0000a250:·3731·6639·6461·303e·7c0a·7c20·2020·2020··71f9da0>|.|····· | ||
| 0000a260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a280:·2020·2020·2020·2020·207c·0a7c·6f32·203a···········|.|o2·: | 0000a280:·2020·2020·2020·2020·207c·0a7c·6f32·203a···········|.|o2·: | ||
| 0000a290:·2050·7974·686f·6e4f·626a·6563·7420·6f66···PythonObject·of | 0000a290:·2050·7974·686f·6e4f·626a·6563·7420·6f66···PythonObject·of | ||
| 0000a2a0:·2063·6c61·7373·2072·616e·6765·5f69·7465···class·range_ite | 0000a2a0:·2063·6c61·7373·2072·616e·6765·5f69·7465···class·range_ite | ||
| 0000a2b0:·7261·746f·7220·2020·2020·7c0a·2b2d·2d2d··rator·····|.+--- | 0000a2b0:·7261·746f·7220·2020·2020·7c0a·2b2d·2d2d··rator·····|.+--- | ||
| 0000a2c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a2c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000127c0:·2020·2020·2020·7c0a·7c6f·3133·203d·203c········|.|o13·=·< | 000127c0:·2020·2020·2020·7c0a·7c6f·3133·203d·203c········|.|o13·=·< | ||
| 000127d0:·6275·696c·742d·696e·206d·6574·686f·6420··built-in·method· | 000127d0:·6275·696c·742d·696e·206d·6574·686f·6420··built-in·method· | ||
| 000127e0:·6d32·7371·7274·206f·6620·5079·4361·7073··m2sqrt·of·PyCaps | 000127e0:·6d32·7371·7274·206f·6620·5079·4361·7073··m2sqrt·of·PyCaps | ||
| 000127f0:·756c·6520·6f62·6a65·6374·2061·7420·3078··ule·object·at·0x | 000127f0:·756c·6520·6f62·6a65·6374·2061·7420·3078··ule·object·at·0x | ||
| 00012800:·3766· | 00012800:·3766·3637·3434·3566·3966·3530·3e7c·0a7c··7f67445f9f50>|.| | ||
| 00012810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00012840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012850:·2020·2020·7c0a·7c6f·3133·203a·2050·7974······|.|o13·:·Pyt | 00012850:·2020·2020·7c0a·7c6f·3133·203a·2050·7974······|.|o13·:·Pyt | ||
| 00012860:·686f·6e4f·626a·6563·7420·6f66·2063·6c61··honObject·of·cla | 00012860:·686f·6e4f·626a·6563·7420·6f66·2063·6c61··honObject·of·cla | ||
| 00012870:·7373·2062·7569·6c74·696e·5f66·756e·6374··ss·builtin_funct | 00012870:·7373·2062·7569·6c74·696e·5f66·756e·6374··ss·builtin_funct |
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| 000008d0:·6f66·7320·6f66·0a75·6e69·7261·7469·6f6e··ofs·of.uniration | 000008d0:·6f66·7320·6f66·0a75·6e69·7261·7469·6f6e··ofs·of.uniration | ||
| 000008e0:·616c·6974·7920·6f66·2024·4d5f·6724·2062··ality·of·$M_g$·b | 000008e0:·616c·6974·7920·6f66·2024·4d5f·6724·2062··ality·of·$M_g$·b | ||
| 000008f0:·7920·5365·7665·7269·2c20·5365·726e·6573··y·Severi,·Sernes | 000008f0:·7920·5365·7665·7269·2c20·5365·726e·6573··y·Severi,·Sernes | ||
| 00000900:·692c·2043·6861·6e67·2d52·616e·2061·6e64··i,·Chang-Ran·and | 00000900:·692c·2043·6861·6e67·2d52·616e·2061·6e64··i,·Chang-Ran·and | ||
| 00000910:·2056·6572·7261·2e0a·0a2b·2d2d·2d2d·2d2d···Verra...+------ | 00000910:·2056·6572·7261·2e0a·0a2b·2d2d·2d2d·2d2d···Verra...+------ | ||
| 00000920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a | 00000940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00000950:·3120·3a20·7365·7452·616e·646f·6d53·6565··1·:·setRandomSee | |||
| 000009 | 00000950:·6931·203a·2073·6574·5261·6e64·6f6d·5365··i1·:·setRandomSe | ||
| 00000960:·6564·2022·616c·7068·6122·3b20·2020·2020··ed·"alpha";····· | |||
| 00000970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000980:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d· | 00000980:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | ||
| 00000990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000009a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000009a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000009b0:·2d2d·2d2d·2d2d·2b0a | 000009b0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a··---------+.|i2·: | ||
| 000009c0:· | 000009c0:·2067·3d31·343b·2020·2020·2020·2020·2020···g=14;·········· | ||
| 000009d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000009d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000009e0:·2020·2020·2020·2020·2020·20 | 000009e0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000009f0:· | 000009f0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00000a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000a20:·2b0a·7c69·3320·3a20·4646·3d5a·5a2f·3130··+.|i3·:·FF=ZZ/10 | |||
| 00000a | 00000a20:·2d2d·2d2d·2d2b·0a7c·6933·203a·2046·463d··-----+.|i3·:·FF= | ||
| 00000a30:·5a5a·2f31·3030·3037·3b20·2020·2020·2020··ZZ/10007;······· | |||
| 00000a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000a50:·2020·2020·20 | 00000a50:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | ||
| 00000a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000a70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000a70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000a80:·2d2d·2d2d·2d2d·2d2d·2d2d·2 | 00000a80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000a90:·3a20·523d·4646·5b78·5f30·2e2e·785f·2867··:·R=FF[x_0..x_(g | |||
| 00000a | 00000a90:·2d2b·0a7c·6934·203a·2052·3d46·465b·785f··-+.|i4·:·R=FF[x_ | ||
| 00000aa0:·302e·2e78·5f28·672d·3129·5d3b·2020·2020··0..x_(g-1)];···· | |||
| 00000ab0:·2020·2020·2020·2020·2020·2020·2020·20 | 00000ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000ac0:· | 00000ac0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00000ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000af0:·2d2d·2d2d·2b0a·7c69·3520·3a20·7469·6d65··----+.|i5·:·time | |||
| 00000b00:·2062·6574·7469·2849·3d28·7261·6e64·6f6d···betti(I=(random | |||
| 00000b10:·2063·616e·6f6e·6963·616c·4375·7276·6529···canonicalCurve) | |||
| 00000b20:·2867·2c52·2929·2020·207c·0a7c·202d·2d20··(g,R))···|.|·--· | |||
| 00000b30:·7573·6564·2035·2e31·3834·3973·2028·6370··used·5.1849s·(cp | |||
| 00000b40:·7529·3b20·342e·3133·3835·3473·2028·7468··u);·4.13854s·(th | |||
| 00000b50:·7265·6164·293b·2030·7320·2867·6329·7c0a··read);·0s·(gc)|. | |||
| 00000 | 00000af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00000b00:·6935·203a·2074·696d·6520·6265·7474·6928··i5·:·time·betti( | |||
| 00000b10:·493d·2872·616e·646f·6d20·6361·6e6f·6e69··I=(random·canoni | |||
| 00000b20:·6361·6c43·7572·7665·2928·672c·5229·2920··calCurve)(g,R))· | |||
| 00000b30:·2020·207c·0a7c·202d·2d20·7573·6564·2035·····|.|·--·used·5 | |||
| 00000b40:·2e38·3335·3935·7320·2863·7075·293b·2034··.83595s·(cpu);·4 | |||
| 00000b50:·2e36·3633·3834·7320·2874·6872·6561·6429··.66384s·(thread) | |||
| 00000b60:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | |||
| 00000b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000b90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | |||
| 00000ba0:·0a7c·2020·2020·2020·2020·2020·2020·3020··.|············0· | |||
| 00000b | 00000bb0:·2031·2020·2020·2020·2020·2020·2020·2020···1·············· | ||
| 00000ba0:·2020·3020·2031·2020·2020·2020·2020·2020····0··1·········· | |||
| 00000b | 00000bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000bc0:·2020·2020·2020·2020·7c0a·7c6f·3520·3d20··········|.|o5·=· | |||
| 00000bd0:· | 00000bd0:·2020·2020·207c·0a7c·6f35·203d·2074·6f74·······|.|o5·=·tot | ||
| 00000be0:·616c·3a20·3120·3636·2020·2020·2020·2020··al:·1·66········ | |||
| 00000b | 00000bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000 | 00000c00:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00000c | 00000c10:·2020·2020·2020·2030·3a20·3120·202e·2020·········0:·1··.·· | ||
| 00000c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000c30:·2020·7c0a·7c20·2020·2020·2020·2020·313a····|.|·········1: | |||
| 00000c40:·202e·2036·3620·2020·2020·2020·2020·2020···.·66··········· | |||
| 00000c | 00000c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000c40:·207c·0a7c·2020·2020·2020·2020·2031·3a20···|.|·········1:· | |||
| 00000c | 00000c50:·2e20·3636·2020·2020·2020·2020·2020·2020··.·66············ | ||
| 00000c | 00000c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000c70:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | |||
| 00000c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000c90:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | |||
| 00000ca0:·3520·3a20·4265·7474·6954·616c·6c79·2020··5·:·BettiTally·· | |||
| 00000c | 00000c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000ca0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00000cb0:·6f35·203a·2042·6574·7469·5461·6c6c·7920··o5·:·BettiTally· | |||
| 00000cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000cd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000c | 00000ce0:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | ||
| 00000ce0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00000cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00000d | 00000d10:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | ||
| 00000d20:·2067·656e·7573·2049·203d·3d20·6720·616e···genus·I·==·g·an | |||
| 00000d30:·6420·6465·6772·6565·2049·203d·3d32·2a67··d·degree·I·==2*g | |||
| 00000d10:·6e75·7320·4920·3d3d·2067·2061·6e64·2064··nus·I·==·g·and·d | |||
| 00000d20:·6567·7265·6520·4920·3d3d·322a·672d·3220··egree·I·==2*g-2· | |||
| 00000d30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | |||
| 00000d40:·2 | 00000d40:·2d32·2020·2020·2020·2020·2020·2020·207c··-2·············| | ||
| 00000d50:· | 00000d50:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00000d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000d70:·7c0a·7c6f·3620·3d20·7472·7565·2020·2020··|.|o6·=·true···· | |||
| 00000d | 00000d70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000d80:·2020·2020·207c·0a7c·6f36·203d·2074·7275·······|.|o6·=·tru | |||
| 00000d90:·6520·2020·2020·2020·2020·2020·2020·2020··e··············· | |||
| 00000d | 00000da0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000db0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | |||
| 00000da0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | |||
| 00000db0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00000dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2 | 00000dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000de0:·2074·6865·2070·726f·6772·616d·6d65·720a···the·programmer. | |||
| 00000df0:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | |||
| 00000e00:·3d3d·0a0a·5468·6520·6f62·6a65·6374·202a··==..The·object·* | |||
| 00000e10:·6e6f·7465·2063·616e·6f6e·6963·616c·4375··note·canonicalCu | |||
| 00000e20:·7276·653a·2063·616e·6f6e·6963·616c·4375··rve:·canonicalCu | |||
| 00000e30:·7276·652c·2069·7320·616e·2069·6e73·7461··rve,·is·an·insta | |||
| 00000e40:·6e63·6520·6f66·2074·6865·2074·7970·650a··nce·of·the·type. | |||
| 00000e50:·2a6e·6f74·6520·5261·6e64·6f6d·4f62·6a65··*note·RandomObje | |||
| 00000e60:·6374·3a20·2852·616e·646f·6d4f·626a·6563··ct:·(RandomObjec | |||
| 00000e70:·7473·2952·616e·646f·6d4f·626a·6563·742c··ts)RandomObject, | |||
| 00000e80:·2e0a·1f0a·5461·6720·5461·626c·653a·0a4e··....Tag·Table:.N | |||
| 00000e90:·6f64·653a·2054·6f70·7f32·3937·0a4e·6f64··ode:·Top.297.Nod | |||
| 00000ea0:·653a·2063·616e·6f6e·6963·616c·4375·7276··e:·canonicalCurv | |||
| 00000eb0:·657f·3135·3532·0a1f·0a45·6e64·2054·6167··e.1552...End·Tag | |||
| 00000 | 00000de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000df0:·2d2b·0a0a·466f·7220·7468·6520·7072·6f67··-+..For·the·prog | |||
| 00000e00:·7261·6d6d·6572·0a3d·3d3d·3d3d·3d3d·3d3d··rammer.========= | |||
| 00000e10:·3d3d·3d3d·3d3d·3d3d·3d0a·0a54·6865·206f··=========..The·o | |||
| 00000e20:·626a·6563·7420·2a6e·6f74·6520·6361·6e6f··bject·*note·cano | |||
| 00000e30:·6e69·6361·6c43·7572·7665·3a20·6361·6e6f··nicalCurve:·cano | |||
| 00000e40:·6e69·6361·6c43·7572·7665·2c20·6973·2061··nicalCurve,·is·a | |||
| 00000e50:·6e20·696e·7374·616e·6365·206f·6620·7468··n·instance·of·th | |||
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| 00003080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000030a0:·2d2d·2d2d·2d2b·0a7c·6931·203a·2074·696d··-----+.|i1·:·tim | |||
| 000030b0:·6520·4943·616e·203d·2073·6d6f·6f74·6843··e·ICan·=·smoothC | |||
| 000030 | 000030a0:·2d2d·2d2d·2b0a·7c69·3120·3a20·7469·6d65··----+.|i1·:·time | ||
| 000030b0:·2049·4361·6e20·3d20·736d·6f6f·7468·4361···ICan·=·smoothCa | |||
| 000030c0:·6e6f·6e69·6361·6c43·7572·7665·2831·312c··nonicalCurve(11, | |||
| 000030d0:· | 000030d0:·3529·3b20·2020·2020·2020·7c0a·7c20·2d2d··5);·······|.|·-- | ||
| 000030e0:·2 | 000030e0:·2075·7365·6420·312e·3436·3535·3773·2028···used·1.46557s·( | ||
| 000030f0:·2028·6370·7529·3b20·302e·3834·3534·3931···(cpu);·0.845491 | |||
| 00003 | 000030f0:·6370·7529·3b20·312e·3130·3536·3273·2028··cpu);·1.10562s·( | ||
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| 00003110:· | 00003110:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00003120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003140:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | |||
| 000031 | 00003140:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00003150:·2020·2020·2020·205a·5a20·2020·2020·2020·········ZZ······· | |||
| 00003160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003170:·2020·2020·2020·2020·2020·2020· | 00003170:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 00003180:·207c·0a7c·6f31·203a·2049·6465·616c·206f···|.|o1·:·Ideal·o | |||
| 000031 | 00003180:·3120·3a20·4964·6561·6c20·6f66·202d·2d5b··1·:·Ideal·of·--[ | ||
| 00003190:·7420·2e2e·7420·205d·2020·2020·2020·2020··t·..t··]········ | |||
| 000031a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000031a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000031b0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | |||
| 000031c0:·2020·2020·2020·2020·2020·3520·2030·2020············5··0·· | |||
| 000031 | 000031b0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 000031c0:·2020·2020·3520·2030·2020·2031·3020·2020······5··0···10··· | |||
| 000031 | 000031d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000031e0:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | |||
| 000031f0:· | 000031f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2 | 00003210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00003220:·2d2d·2d2d·2d2d·2b0a·7c69·3220·3a20·2864··------+.|i2·:·(d | |||
| 00003230:·696d·2049·4361·6e2c·2067·656e·7573·2049··im·ICan,·genus·I | |||
| 00003240:·4361·6e2c·2064·6567·7265·6520·4943·616e··Can,·degree·ICan | |||
| 000032 | 00003220:·7c69·3220·3a20·2864·696d·2049·4361·6e2c··|i2·:·(dim·ICan, | ||
| 00003230:·2067·656e·7573·2049·4361·6e2c·2064·6567···genus·ICan,·deg | |||
| 00003240:·7265·6520·4943·616e·2920·2020·2020·2020··ree·ICan)······· | |||
| 00003250:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | |||
| 00003260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003280:·2020·2020·2020·2020·2020·7c0a·7c6f·3220············|.|o2· | |||
| 00003290:·3d20·2832·2c20·3131·2c20·3230·2920·2020··=·(2,·11,·20)··· | |||
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| 00003290:·2020·2020·7c0a·7c6f·3220·3d20·2832·2c20······|.|o2·=·(2,· | |||
| 000032a0:·3131·2c20·3230·2920·2020·2020·2020·2020··11,·20)········· | |||
| 000032b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000032b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000032d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000032d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000032e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000032e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000032f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
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| 000033 | 00003300:·7175·656e·6365·2020·2020·2020·2020·2020··quence·········· | ||
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| 00003330:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00003340:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003340:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003350:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003350:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 000033 | 00003360:·2d2d·2b0a·7c69·3320·3a20·6265·7474·6920··--+.|i3·:·betti· | ||
| 000033 | 00003370:·4943·616e·2020·2020·2020·2020·2020·2020··ICan············ | ||
| 000033 | 00003380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000033 | 00003390:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 000033a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000033b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000033b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000033c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000033 | 000033c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000033 | 000033d0:·7c20·2020·2020·2020·2020·2020·2030·2020··|············0·· | ||
| 000033 | 000033e0:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | ||
| 00003400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00003410:·2020·2020·207c·0a7c·6f33·203d·2074·6f74·······|.|o3·=·tot | |||
| 00003420:·616c·3a20·3120·3336·2020·2020·2020·2020··al:·1·36········ | |||
| 00003 | 000033f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003400:·2020·2020·7c0a·7c6f·3320·3d20·746f·7461······|.|o3·=·tota | |||
| 00003410:·6c3a·2031·2033·3620·2020·2020·2020·2020··l:·1·36········· | |||
| 00003420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000034 | 00003430:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 000034 | 00003440:·2020·2020·2020·303a·2031·2020·2e20·2020········0:·1··.··· | ||
| 00003450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00003460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003470:·7c0a·7c20·2020·2020·2020·2020·313a·202e··|.|·········1:·. | |||
| 00003480:·2033·3620·2020·2020·2020·2020·2020·2020···36············· | |||
| 000034 | 00003490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000034 | 000034a0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00003490:·3a20·2e20·3336·2020·2020·2020·2020·2020··:·.·36·········· | |||
| 000034 | 000034b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000034b0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | |||
| 000034c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000034c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000034d0:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | |||
| 000034e0:·3320·3a20·4265·7474·6954·616c·6c79·2020··3·:·BettiTally·· | |||
| 000034 | 000034f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000034e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000034f0:·207c·0a7c·6f33·203a·2042·6574·7469·5461···|.|o3·:·BettiTa | |||
| 00003500:·6c6c·7920·2020·2020·2020·2020·2020·2020··lly············· | |||
| 000035 | 00003500:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000035 | 00003510:·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d····|.+----------- | ||
| 00003520:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00003530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003540:·2d2d·2d2d·2d2d·2d2d·2b0a·0a53·6565·2061··--------+..See·a | |||
| 00003550:·6c73·6f0a·3d3d·3d3d·3d3d·3d3d·0a0a·2020··lso.========..·· | |||
| 00003560:·2a20·2a6e·6f74·6520·736d·6f6f·7468·4361··*·*note·smoothCa | |||
| 00003570:·6e6f·6e69·6361·6c43·7572·7665·5669·6150··nonicalCurveViaP | |||
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| 00003540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
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| 00003560:·0a0a·5365·6520·616c·736f·0a3d·3d3d·3d3d··..See·also.===== | |||
| 00003570:·3d3d·3d0a·0a20·202a·202a·6e6f·7465·2073··===..··*·*note·s | |||
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| 000035b0:·6c43·7572·7665·5669·6150·6c61·6e65·4d6f··lCurveViaPlaneMo | |||
| 000035c0:·6465·6c2c·0a20·2020·202d·2d20·436f·6d70··del,.····--·Comp | |||
| 000035d0:·7574·6573·2074·6865·2069·6465·616c·206f··utes·the·ideal·o | |||
| 000035e0:·6620·6361·6e6f·6e69·6361·6c20·6375·7276··f·canonical·curv | |||
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| 00003610:·6f74·6843·616e·6f6e·6963·616c·4375·7276··othCanonicalCurv | |||
| 00003620:·6556·6961·5370·6163·654d·6f64·656c·3a20··eViaSpaceModel:· | |||
| 00003630:·736d·6f6f·7468·4361·6e6f·6e69·6361·6c43··smoothCanonicalC | |||
| 00003640:·7572·7665·5669·6153·7061·6365·4d6f·6465··urveViaSpaceMode | |||
| 00003650:·6c2c·0a20·2020·202d·2d20·436f·6d70·7574··l,.····--·Comput | |||
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| 00003dc0:·6279·2073·656d·692d·636f·6e74·696e·7569··by·semi-continui | 00003dc0:·6279·2073·656d·692d·636f·6e74·696e·7569··by·semi-continui | ||
| 00003dd0:·7479·2c20·616e·642c·2068·656e·6365·2c20··ty,·and,·hence,· | 00003dd0:·7479·2c20·616e·642c·2068·656e·6365·2c20··ty,·and,·hence,· | ||
| 00003de0:·666f·7220·616c·6c20·6275·7420·6669·6e69··for·all·but·fini | 00003de0:·666f·7220·616c·6c20·6275·7420·6669·6e69··for·all·but·fini | ||
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| 00003e20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003e20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003e30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2 | 00003e30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
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| 00003e60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003e60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00003e90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003e90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00003ed0:·2020·2020·2020·2020·2020·20 | 00003ed0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | ||
| 00003ee0:· | 00003ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003f00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003f00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003f10:·2d2d·2d2d·2d2b·0a7c·6933·203a·2053·3d46··-----+.|i3·:·S=F | |||
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| 00004040:·2020·2020·2020·2020·2020·2020·2020· | 00004040:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 000040e0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
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| 000040f0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | |||
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| 00004130:·2031·2031·3320·3435·2035·3620·3235·2032···1·13·45·56·25·2 | |||
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| 000041 | 00004160:·2020·2030·3a20·3120·202e·2020·2e20·202e·····0:·1··.··.··. | ||
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| 000041 | 000041d0:·2e20·2038·2034·3520·3536·2032·3520·2e20··.··8·45·56·25·.· | ||
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| 00004250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004260:·7c0a·7c6f·3520·3a20·4265·7474·6954·616c··|.|o5·:·BettiTal | |||
| 00004270:·6c79·2020·2020·2020·2020·2020·2020·2020··ly·············· | |||
| 000042 | 00004280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004290:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | |||
| 000042a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00004270:·2020·2020·207c·0a7c·6f35·203a·2042·6574·······|.|o5·:·Bet | |||
| 00004280:·7469·5461·6c6c·7920·2020·2020·2020·2020··tiTally········· | |||
| 00004290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000042a0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | |||
| 000042b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000042b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000042c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 000042d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 000042e0:·2d2b·0a0a·5761·7973·2074·6f20·7573·6520··-+..Ways·to·use· | |||
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| 00004 | 000042c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·0a57·6179··----------+..Way | ||
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| 000042f0:·6531·3869·6e50·363a·0a3d·3d3d·3d3d·3d3d··e18inP6:.======= | |||
| 00004300:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | |||
| 00004310:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | 00004310:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | ||
| 00004320:·3d3d·3d3d·0a0a·2020·2a20·2272·616e·646f··====..··*·"rando | |||
| 00004320:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | |||
| 00004330:·3d3d·3d3d·3d3d·3d3d·3d3d·3d0a·0a20·202a··===========..··* | |||
| 00004340:·2022·7261·6e64·6f6d·4375·7276·6547·656e···"randomCurveGen | |||
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| 00004360:·2850·6f6c·796e·6f6d·6961·6c52·696e·6729··(PolynomialRing) | |||
| 00004370:·220a·0a46·6f72·2074·6865·2070·726f·6772··"..For·the·progr | |||
| 00004380:·616d·6d65·720a·3d3d·3d3d·3d3d·3d3d·3d3d··ammer.========== | |||
| 00004390:·3d3d·3d3d·3d3d·3d3d·0a0a·5468·6520·6f62··========..The·ob | |||
| 000043a0:·6a65·6374·202a·6e6f·7465·2072·616e·646f··ject·*note·rando | |||
| 000043 | 00004330:·6d43·7572·7665·4765·6e75·7331·3444·6567··mCurveGenus14Deg | ||
| 000043 | 00004340:·7265·6531·3869·6e50·3628·506f·6c79·6e6f··ree18inP6(Polyno | ||
| 00004350:·6d69·616c·5269·6e67·2922·0a0a·466f·7220··mialRing)"..For· | |||
| 00004360:·7468·6520·7072·6f67·7261·6d6d·6572·0a3d··the·programmer.= | |||
| 00004370:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | |||
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| 00003790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000037a0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | 000037a0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 000037b0:·2065·6c61·7073·6564·5469·6d65·2064·696d···elapsedTime·dim | 000037b0:·2065·6c61·7073·6564·5469·6d65·2064·696d···elapsedTime·dim | ||
| 000037c0:·5669·6142·657a·6f75·7428·4929·2020·2020··ViaBezout(I)···· | 000037c0:·5669·6142·657a·6f75·7428·4929·2020·2020··ViaBezout(I)···· | ||
| 000037d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000037d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000037e0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 000037e0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 000037f0:·2d20·312e·3 | 000037f0:·2d20·312e·3238·3131·3873·2065·6c61·7073··-·1.28118s·elaps | ||
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| 000038d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000038d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000038f0:·2d2d·2d2b·0a7c·6935·203a·2065·6c61·7073··---+.|i5·:·elaps | 000038f0:·2d2d·2d2b·0a7c·6935·203a·2065·6c61·7073··---+.|i5·:·elaps | ||
| 00003900:·6564·5469·6d65·2064·696d·2049·2020·2020··edTime·dim·I···· | 00003900:·6564·5469·6d65·2064·696d·2049·2020·2020··edTime·dim·I···· | ||
| 00003910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00003930:·2020·2020·207c·0a7c·202d·2d20·3 | 00003930:·2020·2020·207c·0a7c·202d·2d20·342e·3136·······|.|·--·4.16 | ||
| 00003940:·3 | 00003940:·3032·3973·2065·6c61·7073·6564·2020·2020··029s·elapsed···· | ||
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| 000039b0:·2020·2020·2020·2020·207c·0a7c·6f35·203d···········|.|o5·= | 000039b0:·2020·2020·2020·2020·207c·0a7c·6f35·203d···········|.|o5·= | ||
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| 000060f0:·2b0a·7c69·3130·203a·2065·6c61·7073·6564··+.|i10·:·elapsed | 000060f0:·2b0a·7c69·3130·203a·2065·6c61·7073·6564··+.|i10·:·elapsed | ||
| 00006100:·5469·6d65·2877·6869·6c65·2028·6920·3c20··Time(while·(i·<· | 00006100:·5469·6d65·2877·6869·6c65·2028·6920·3c20··Time(while·(i·<· | ||
| 00006110:·3130·2920·616e·6420·6469·6d20·4a20·3e20··10)·and·dim·J·>· | 00006110:·3130·2920·616e·6420·6469·6d20·4a20·3e20··10)·and·dim·J·>· | ||
| 00006120:·3120·646f·2028·6920·3d20·692b·313b·204a··1·do·(i·=·i+1;·J | 00006120:·3120·646f·2028·6920·3d20·692b·313b·204a··1·do·(i·=·i+1;·J | ||
| 00006130:·203d·2020·2020·2020·2020·2020·2020·2020···=·············· | 00006130:·203d·2020·2020·2020·2020·2020·2020·2020···=·············· | ||
| 00006140:·7c0a·7c20·2d2d·2031·2e3 | 00006140:·7c0a·7c20·2d2d·2031·2e39·3635·3934·7320··|.|·--·1.96594s· | ||
| 00006150:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 00006150:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00006160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006190:·7c0a·7c2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.|------------- | 00006190:·7c0a·7c2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.|------------- | ||
| 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000061b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000061b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00011990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000119a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6938··-----------+.|i8 | 000119a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6938··-----------+.|i8 | ||
| 000119b0:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | 000119b0:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | ||
| 000119c0:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | 000119c0:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | ||
| 000119d0:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | 000119d0:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | ||
| 000119e0:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | 000119e0:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | ||
| 000119f0:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | 000119f0:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | ||
| 00011a00:·2d20·332e·3 | 00011a00:·2d20·332e·3531·3430·3473·2065·6c61·7073··-·3.51404s·elaps | ||
| 00011a10:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | 00011a10:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | ||
| 00011a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a40:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00011a40:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00011a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00011d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011d10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6939··-----------+.|i9 | 00011d10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6939··-----------+.|i9 | ||
| 00011d20:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | 00011d20:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | ||
| 00011d30:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | 00011d30:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | ||
| 00011d40:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | 00011d40:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | ||
| 00011d50:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | 00011d50:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | ||
| 00011d60:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | 00011d60:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | ||
| 00011d70:·2d20·3 | 00011d70:·2d20·322e·3232·3133·7320·656c·6170·7365··-·2.2213s·elapse | ||
| 00011d80:·6 | 00011d80:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 00011d90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011d90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011da0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011da0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011db0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00011db0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00011dc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011dc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011dd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011dd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00008b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00008b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00008b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00008b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00008b40:·2d2b·0a7c·6931·3420·3a20·7469·6d65·2069··-+.|i14·:·time·i | 00008b40:·2d2b·0a7c·6931·3420·3a20·7469·6d65·2069··-+.|i14·:·time·i | ||
| 00008b50:·6e76·6572·7365·4f66·4d61·7028·7068·692c··nverseOfMap(phi, | 00008b50:·6e76·6572·7365·4f66·4d61·7028·7068·692c··nverseOfMap(phi, | ||
| 00008b60:·4368·6563·6b42·6972·6174·696f·6e61·6c3d··CheckBirational= | 00008b60:·4368·6563·6b42·6972·6174·696f·6e61·6c3d··CheckBirational= | ||
| 00008b70:·3e66·616c·7365·2c20·5665·7262·6f73·6974··>false,·Verbosit | 00008b70:·3e66·616c·7365·2c20·5665·7262·6f73·6974··>false,·Verbosit | ||
| 00008b80:·793d·3e30·2920·2020·2020·2020·2020·2020··y=>0)··········· | 00008b80:·793d·3e30·2920·2020·2020·2020·2020·2020··y=>0)··········· | ||
| 00008b90:·207c·0a7c·202d·2d20·7573·6564·2032·2e3 | 00008b90:·207c·0a7c·202d·2d20·7573·6564·2032·2e31···|.|·--·used·2.1 | ||
| 00008ba0:·373 | 00008ba0:·3735·3436·7320·2863·7075·293b·2030·2e35··7546s·(cpu);·0.5 | ||
| 00008bb0:·3 | 00008bb0:·3736·3130·3873·2028·7468·7265·6164·293b··76108s·(thread); | ||
| 00008bc0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 00008bc0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 00008bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008be0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00008be0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00008bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00004b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004b60:·2d2d·2d2d·2d2d·2b0a·7c69·3134·203a·2074··------+.|i14·:·t | 00004b60:·2d2d·2d2d·2d2d·2b0a·7c69·3134·203a·2074··------+.|i14·:·t | ||
| 00004b70:·696d·6520·7261·7469·6f6e·616c·506f·696e··ime·rationalPoin | 00004b70:·696d·6520·7261·7469·6f6e·616c·506f·696e··ime·rationalPoin | ||
| 00004b80:·7473·2849·2c20·416d·6f75·6e74·203d·3e20··ts(I,·Amount·=>· | 00004b80:·7473·2849·2c20·416d·6f75·6e74·203d·3e20··ts(I,·Amount·=>· | ||
| 00004b90:·7472·7565·2920·2020·2020·2020·2020·2020··true)··········· | 00004b90:·7472·7565·2920·2020·2020·2020·2020·2020··true)··········· | ||
| 00004ba0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 00004ba0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 00004bb0:·2d20·7573·6564·2030·2e30·303 | 00004bb0:·2d20·7573·6564·2030·2e30·3033·3939·3733··-·used·0.0039973 | ||
| 00004bc0:·3 | 00004bc0:·3373·2028·6370·7529·3b20·302e·3030·3334··3s·(cpu);·0.0034 | ||
| 00004bd0:·303 | 00004bd0:·3039·3638·7320·2874·6872·6561·6429·3b20··0968s·(thread);· | ||
| 00004be0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 00004be0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 00004bf0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00004bf0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00004c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004c30:·2020·2020·207c·0a7c·6f31·3420·3d20·3131·······|.|o14·=·11 | 00004c30:·2020·2020·207c·0a7c·6f31·3420·3d20·3131·······|.|o14·=·11 | ||
| 00004c40:·3034·3632·3231·3235·3431·3132·3034·3531··0462212541120451 | 00004c40:·3034·3632·3231·3235·3431·3132·3034·3531··0462212541120451 | ||
| Offset 1778, 18 lines modified | Offset 1778, 18 lines modified | ||
| 00006f10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006f10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006f20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00006f20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00006f30:·0a7c·6933·3220·3a20·7469·6d65·2072·6174··.|i32·:·time·rat | 00006f30:·0a7c·6933·3220·3a20·7469·6d65·2072·6174··.|i32·:·time·rat | ||
| 00006f40:·696f·6e61·6c50·6f69·6e74·7328·7661·7269··ionalPoints(vari | 00006f40:·696f·6e61·6c50·6f69·6e74·7328·7661·7269··ionalPoints(vari | ||
| 00006f50:·6574·7920·6e6f·6465·732c·2053·706c·6974··ety·nodes,·Split | 00006f50:·6574·7920·6e6f·6465·732c·2053·706c·6974··ety·nodes,·Split | ||
| 00006f60:·3d3e·7472·7565·2c20·5665·7262·6f73·653d··=>true,·Verbose= | 00006f60:·3d3e·7472·7565·2c20·5665·7262·6f73·653d··=>true,·Verbose= | ||
| 00006f70:·3e74·7275·6529·3b20·2020·2020·2020·207c··>true);········| | 00006f70:·3e74·7275·6529·3b20·2020·2020·2020·207c··>true);········| | ||
| 00006f80:·0a7c·202d·2d20·7573·6564·203 | 00006f80:·0a7c·202d·2d20·7573·6564·2031·2e33·3334··.|·--·used·1.334 | ||
| 00006f90:·3338·3973·2028·6370·7529·3b20·302e·3632··389s·(cpu);·0.62 | |||
| 00006f | 00006f90:·3237·7320·2863·7075·293b·2030·2e38·3932··27s·(cpu);·0.892 | ||
| 00006fa0:·3933·3773·2028·7468·7265·6164·293b·2030··937s·(thread);·0 | |||
| 00006fb0:· | 00006fb0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00006fc0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00006fc0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00006fd0:·0a7c·2d2d·2062·6173·6520·6368·616e·6765··.|--·base·change | 00006fd0:·0a7c·2d2d·2062·6173·6520·6368·616e·6765··.|--·base·change | ||
| 00006fe0:·2074·6f20·7468·6520·6669·656c·6420·5151···to·the·field·QQ | 00006fe0:·2074·6f20·7468·6520·6669·656c·6420·5151···to·the·field·QQ | ||
| 00006ff0:·5b61·5d2f·2861·5e38·2d34·302a·615e·362b··[a]/(a^8-40*a^6+ | 00006ff0:·5b61·5d2f·2861·5e38·2d34·302a·615e·362b··[a]/(a^8-40*a^6+ | ||
| 00007000:·3233·302a·615e·342d·3230·302a·615e·322b··230*a^4-200*a^2+ | 00007000:·3233·302a·615e·342d·3230·302a·615e·322b··230*a^4-200*a^2+ | ||
| 00007010:·3235·2920·2020·2020·2020·2020·2020·207c··25)············| | 00007010:·3235·2920·2020·2020·2020·2020·2020·207c··25)············| | ||
| 00007020:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00007020:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
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| 00007340:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007340:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007350:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007350:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007360:·2d2d·2d2d·2b0a·7c69·3335·203a·2074·696d··----+.|i35·:·tim | 00007360:·2d2d·2d2d·2b0a·7c69·3335·203a·2074·696d··----+.|i35·:·tim | ||
| 00007370:·6520·2372·6174·696f·6e61·6c50·6f69·6e74··e·#rationalPoint | 00007370:·6520·2372·6174·696f·6e61·6c50·6f69·6e74··e·#rationalPoint | ||
| 00007380:·7328·7661·7269·6574·7920·6e6f·6465·7327··s(variety·nodes' | 00007380:·7328·7661·7269·6574·7920·6e6f·6465·7327··s(variety·nodes' | ||
| 00007390:·2c20·5370·6c69·743d·3e74·7275·652c·2056··,·Split=>true,·V | 00007390:·2c20·5370·6c69·743d·3e74·7275·652c·2056··,·Split=>true,·V | ||
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| 00002ee0:·3120·3d20·2e30·3 | 00002ee0:·3120·3d20·2e30·3536·3333·3933·3538·3830··1·=·.05633935880 | ||
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| 000030b0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 000030b0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
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| 0000f2e0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 0000f2e0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 0000f2f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f2f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f310:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000f310:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000f320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000197f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000197f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00019800:·2d2d·2d2d·2d2b·0a7c·6935·203a·2065·6c61··-----+.|i5·:·ela | 00019800:·2d2d·2d2d·2d2b·0a7c·6935·203a·2065·6c61··-----+.|i5·:·ela | ||
| 00019810:·7073·6564·5469·6d65·2043·3d72·616e·646f··psedTime·C=rando | 00019810:·7073·6564·5469·6d65·2043·3d72·616e·646f··psedTime·C=rando | ||
| 00019820:·6d43·6861·696e·436f·6d70·6c65·7828·682c··mChainComplex(h, | 00019820:·6d43·6861·696e·436f·6d70·6c65·7828·682c··mChainComplex(h, | ||
| 00019830:·722c·4865·6967·6874·3d3e·352c·5a65·726f··r,Height=>5,Zero | 00019830:·722c·4865·6967·6874·3d3e·352c·5a65·726f··r,Height=>5,Zero | ||
| 00019840:·4d65·616e·3d3e·7472·7565·2920·2020·2020··Mean=>true)····· | 00019840:·4d65·616e·3d3e·7472·7565·2920·2020·2020··Mean=>true)····· | ||
| 00019850:·2020·2020·207c·0a7c·202d·2d20·2e30·3032·······|.|·--·.002 | 00019850:·2020·2020·207c·0a7c·202d·2d20·2e30·3032·······|.|·--·.002 | ||
| 00019860:·3 | 00019860:·3939·3830·3973·2065·6c61·7073·6564·2020··99809s·elapsed·· | ||
| 00019870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00019870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00019880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00019880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00019890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00019890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000198a0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 000198a0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 000198b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000198b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000198c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000198c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000198d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000198d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00025fa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00025fa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00025fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00025fc0:·0a7c·6934·203a·2065·6c61·7073·6564·5469··.|i4·:·elapsedTi | 00025fc0:·0a7c·6934·203a·2065·6c61·7073·6564·5469··.|i4·:·elapsedTi | ||
| 00025fd0:·6d65·2043·3d72·616e·646f·6d43·6861·696e··me·C=randomChain | 00025fd0:·6d65·2043·3d72·616e·646f·6d43·6861·696e··me·C=randomChain | ||
| 00025fe0:·436f·6d70·6c65·7828·682c·722c·4865·6967··Complex(h,r,Heig | 00025fe0:·436f·6d70·6c65·7828·682c·722c·4865·6967··Complex(h,r,Heig | ||
| 00025ff0:·6874·3d3e·3429·2020·2020·2020·2020·2020··ht=>4)·········· | 00025ff0:·6874·3d3e·3429·2020·2020·2020·2020·2020··ht=>4)·········· | ||
| 00026000:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00026000:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00026010:·0a7c·202d·2d20·2e30·313 | 00026010:·0a7c·202d·2d20·2e30·3135·3736·3434·7320··.|·--·.0157644s· | ||
| 00026020:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 00026020:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00026030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026050:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00026050:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00026060:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00026060:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00026070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00026ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00026ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00026af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00026af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00026b00:·0a7c·6937·203a·2065·6c61·7073·6564·5469··.|i7·:·elapsedTi | 00026b00:·0a7c·6937·203a·2065·6c61·7073·6564·5469··.|i7·:·elapsedTi | ||
| 00026b10:·6d65·2028·682c·5529·3d53·5644·436f·6d70··me·(h,U)=SVDComp | 00026b10:·6d65·2028·682c·5529·3d53·5644·436f·6d70··me·(h,U)=SVDComp | ||
| 00026b20:·6c65·7820·4352·3b20·2020·2020·2020·2020··lex·CR;········· | 00026b20:·6c65·7820·4352·3b20·2020·2020·2020·2020··lex·CR;········· | ||
| 00026b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026b40:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00026b40:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00026b50:·0a7c·202d·2d20·2e30·303 | 00026b50:·0a7c·202d·2d20·2e30·3036·3732·3836·3173··.|·--·.00672861s | ||
| 00026b60:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 00026b60:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 00026b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026b90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00026b90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00026ba0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00026ba0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00026bb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00026bb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00026bc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00026bc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00027940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00027950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00027950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00027960:·0a7c·6931·3320·3a20·656c·6170·7365·6454··.|i13·:·elapsedT | 00027960:·0a7c·6931·3320·3a20·656c·6170·7365·6454··.|i13·:·elapsedT | ||
| 00027970:·696d·6520·2868·4c2c·5529·3d53·5644·436f··ime·(hL,U)=SVDCo | 00027970:·696d·6520·2868·4c2c·5529·3d53·5644·436f··ime·(hL,U)=SVDCo | ||
| 00027980:·6d70·6c65·7828·4352·2c53·7472·6174·6567··mplex(CR,Strateg | 00027980:·6d70·6c65·7828·4352·2c53·7472·6174·6567··mplex(CR,Strateg | ||
| 00027990:·793d·3e4c·6170·6c61·6369·616e·293b·2020··y=>Laplacian);·· | 00027990:·793d·3e4c·6170·6c61·6369·616e·293b·2020··y=>Laplacian);·· | ||
| 000279a0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000279a0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000279b0:·0a7c·202d·2d20·2e30·313 | 000279b0:·0a7c·202d·2d20·2e30·3131·3937·3635·7320··.|·--·.0119765s· | ||
| 000279c0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 000279c0:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 000279d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000279d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000279e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000279e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000279f0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000279f0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00027a00:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00027a00:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00027a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00027a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00028fd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00028fd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00028fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00028fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00028ff0:·2b0a·7c69·3420·3a20·656c·6170·7365·6454··+.|i4·:·elapsedT | 00028ff0:·2b0a·7c69·3420·3a20·656c·6170·7365·6454··+.|i4·:·elapsedT | ||
| 00029000:·696d·6520·433d·7261·6e64·6f6d·4368·6169··ime·C=randomChai | 00029000:·696d·6520·433d·7261·6e64·6f6d·4368·6169··ime·C=randomChai | ||
| 00029010:·6e43·6f6d·706c·6578·2868·2c72·2c48·6569··nComplex(h,r,Hei | 00029010:·6e43·6f6d·706c·6578·2868·2c72·2c48·6569··nComplex(h,r,Hei | ||
| 00029020:·6768·743d·3e35·2c5a·6572·6f4d·6561·6e3d··ght=>5,ZeroMean= | 00029020:·6768·743d·3e35·2c5a·6572·6f4d·6561·6e3d··ght=>5,ZeroMean= | ||
| 00029030:·3e74·7275·6529·2020·2020·2020·2020·2020··>true)·········· | 00029030:·3e74·7275·6529·2020·2020·2020·2020·2020··>true)·········· | ||
| 00029040:·7c0a·7c20·2d2d·202e·3030·3 | 00029040:·7c0a·7c20·2d2d·202e·3030·3233·3131·3139··|.|·--·.00231119 | ||
| 00029050:·656c·6170·7365·6420·2020·2020·2020· | 00029050:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00029060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00029090:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00029090:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 000290a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000290a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000299d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000299d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000299e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000299e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000299f0:·2b0a·7c69·3720·3a20·656c·6170·7365·6454··+.|i7·:·elapsedT | 000299f0:·2b0a·7c69·3720·3a20·656c·6170·7365·6454··+.|i7·:·elapsedT | ||
| 00029a00:·696d·6520·2868·2c68·3129·3d53·5644·486f··ime·(h,h1)=SVDHo | 00029a00:·696d·6520·2868·2c68·3129·3d53·5644·486f··ime·(h,h1)=SVDHo | ||
| 00029a10:·6d6f·6c6f·6779·2043·5220·2020·2020·2020··mology·CR······· | 00029a10:·6d6f·6c6f·6779·2043·5220·2020·2020·2020··mology·CR······· | ||
| 00029a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029a40:·7c0a·7c20·2d2d·202e·3030·303 | 00029a40:·7c0a·7c20·2d2d·202e·3030·3036·3638·3830··|.|·--·.00066880 | ||
| 00029a50:·3473·2065·6c61·7073·6564·2020·2020·2020··4s·elapsed······ | 00029a50:·3473·2065·6c61·7073·6564·2020·2020·2020··4s·elapsed······ | ||
| 00029a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00029a90:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00029a90:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
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| 0000e250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e270:·2d2d·2d2d·2b0a·7c69·3720·3a20·7469·6d65··----+.|i7·:·time | 0000e270:·2d2d·2d2d·2b0a·7c69·3720·3a20·7469·6d65··----+.|i7·:·time | ||
| 0000e280:·2071·756f·7469·656e·7428·495e·332c·204a···quotient(I^3,·J | 0000e280:·2071·756f·7469·656e·7428·495e·332c·204a···quotient(I^3,·J | ||
| 0000e290:·5e32·2c20·5374·7261·7465·6779·203d·3e20··^2,·Strategy·=>· | 0000e290:·5e32·2c20·5374·7261·7465·6779·203d·3e20··^2,·Strategy·=>· | ||
| 0000e2a0:·4974·6572·6174·6529·3b20·2020·7c0a·7c20··Iterate);···|.|· | 0000e2a0:·4974·6572·6174·6529·3b20·2020·7c0a·7c20··Iterate);···|.|· | ||
| 0000e2b0:·2d2d·2075·7365·6420·302e·3 | 0000e2b0:·2d2d·2075·7365·6420·302e·3337·3231·3932··--·used·0.372192 | ||
| 0000e2c0:·7320·2863·7075·293b·2030·2e3 | 0000e2c0:·7320·2863·7075·293b·2030·2e33·3733·3937··s·(cpu);·0.37397 | ||
| 0000e2d0:·3 | 0000e2d0:·3173·2028·7468·7265·6164·293b·2030·7320··1s·(thread);·0s· | ||
| 0000e2e0:·2867·6329·7c0a·7c20·2020·2020·2020·2020··(gc)|.|········· | 0000e2e0:·2867·6329·7c0a·7c20·2020·2020·2020·2020··(gc)|.|········· | ||
| 0000e2f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e2f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e310:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | 0000e310:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 0000e320:·3720·3a20·4964·6561·6c20·6f66·2053·2020··7·:·Ideal·of·S·· | 0000e320:·3720·3a20·4964·6561·6c20·6f66·2053·2020··7·:·Ideal·of·S·· | ||
| 0000e330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3639, 16 lines modified | Offset 3639, 16 lines modified | ||
| 0000e360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e370:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e370:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0000e380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0000e390:·3820·3a20·7469·6d65·2071·756f·7469·656e··8·:·time·quotien | 0000e390:·3820·3a20·7469·6d65·2071·756f·7469·656e··8·:·time·quotien | ||
| 0000e3a0:·7428·495e·332c·204a·5e32·2c20·5374·7261··t(I^3,·J^2,·Stra | 0000e3a0:·7428·495e·332c·204a·5e32·2c20·5374·7261··t(I^3,·J^2,·Stra | ||
| 0000e3b0:·7465·6779·203d·3e20·5175·6f74·6965·6e74··tegy·=>·Quotient | 0000e3b0:·7465·6779·203d·3e20·5175·6f74·6965·6e74··tegy·=>·Quotient | ||
| 0000e3c0:·293b·2020·7c0a·7c20·2d2d·2075·7365·6420··);··|.|·--·used· | 0000e3c0:·293b·2020·7c0a·7c20·2d2d·2075·7365·6420··);··|.|·--·used· | ||
| 0000e3d0:·302e·3 | 0000e3d0:·302e·3632·3839·3538·7320·2863·7075·293b··0.628958s·(cpu); | ||
| 0000e3e0:·2030·2e3 | 0000e3e0:·2030·2e35·3735·3333·3973·2028·7468·7265···0.575339s·(thre | ||
| 0000e3f0:·6164·293b·2030·7320·2867·6329·7c0a·7c20··ad);·0s·(gc)|.|· | 0000e3f0:·6164·293b·2030·7320·2867·6329·7c0a·7c20··ad);·0s·(gc)|.|· | ||
| 0000e400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e430:·2020·2020·7c0a·7c6f·3820·3a20·4964·6561······|.|o8·:·Idea | 0000e430:·2020·2020·7c0a·7c6f·3820·3a20·4964·6561······|.|o8·:·Idea | ||
| 0000e440:·6c20·6f66·2053·2020·2020·2020·2020·2020··l·of·S·········· | 0000e440:·6c20·6f66·2053·2020·2020·2020·2020·2020··l·of·S·········· | ||
| 0000e450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3686, 17 lines modified | Offset 3686, 17 lines modified | ||
| 0000e650:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e650:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e670:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3120··---------+.|i11· | 0000e670:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3120··---------+.|i11· | ||
| 0000e680:·3a20·7469·6d65·2071·756f·7469·656e·7428··:·time·quotient( | 0000e680:·3a20·7469·6d65·2071·756f·7469·656e·7428··:·time·quotient( | ||
| 0000e690:·495e·352c·2049·5e33·2c20·5374·7261·7465··I^5,·I^3,·Strate | 0000e690:·495e·352c·2049·5e33·2c20·5374·7261·7465··I^5,·I^3,·Strate | ||
| 0000e6a0:·6779·203d·3e20·4974·6572·6174·6529·3b20··gy·=>·Iterate);· | 0000e6a0:·6779·203d·3e20·4974·6572·6174·6529·3b20··gy·=>·Iterate);· | ||
| 0000e6b0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 0000e6b0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 0000e6c0:·2030·2e30·313 | 0000e6c0:·2030·2e30·3139·3333·3973·2028·6370·7529···0.019339s·(cpu) | ||
| 0000e6d0:·293b·2030·2e30·3136·3436·3532·7320·2874··);·0.0164652s·(t | |||
| 0000e6 | 0000e6d0:·3b20·302e·3032·3134·3331·3673·2028·7468··;·0.0214316s·(th | ||
| 0000e6e0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | |||
| 0000e6f0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000e6f0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000e700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e720:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000e720:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000e730:·6f31·3120·3a20·4964·6561·6c20·6f66·2053··o11·:·Ideal·of·S | 0000e730:·6f31·3120·3a20·4964·6561·6c20·6f66·2053··o11·:·Ideal·of·S | ||
| 0000e740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3705, 16 lines modified | Offset 3705, 16 lines modified | ||
| 0000e780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e7a0:·2d2d·2d2d·2d2b·0a7c·6931·3220·3a20·7469··-----+.|i12·:·ti | 0000e7a0:·2d2d·2d2d·2d2b·0a7c·6931·3220·3a20·7469··-----+.|i12·:·ti | ||
| 0000e7b0:·6d65·2071·756f·7469·656e·7428·495e·352c··me·quotient(I^5, | 0000e7b0:·6d65·2071·756f·7469·656e·7428·495e·352c··me·quotient(I^5, | ||
| 0000e7c0:·2049·5e33·2c20·5374·7261·7465·6779·203d···I^3,·Strategy·= | 0000e7c0:·2049·5e33·2c20·5374·7261·7465·6779·203d···I^3,·Strategy·= | ||
| 0000e7d0:·3e20·5175·6f74·6965·6e74·293b·2020·2020··>·Quotient);···· | 0000e7d0:·3e20·5175·6f74·6965·6e74·293b·2020·2020··>·Quotient);···· | ||
| 0000e7e0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 0000e7e0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 0000e7f0:·303 | 0000e7f0:·3035·3639·3030·3373·2028·6370·7529·3b20··0569003s·(cpu);· | ||
| 0000e800:·302e·3030·363 | 0000e800:·302e·3030·3638·3737·3131·7320·2874·6872··0.00687711s·(thr | ||
| 0000e810:·6561·6429·3b20·3073·2028·6763·297c·0a7c··ead);·0s·(gc)|.| | 0000e810:·6561·6429·3b20·3073·2028·6763·297c·0a7c··ead);·0s·(gc)|.| | ||
| 0000e820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e850:·2020·2020·2020·2020·207c·0a7c·6f31·3220···········|.|o12· | 0000e850:·2020·2020·2020·2020·207c·0a7c·6f31·3220···········|.|o12· | ||
| 0000e860:·3a20·4964·6561·6c20·6f66·2053·2020·2020··:·Ideal·of·S···· | 0000e860:·3a20·4964·6561·6c20·6f66·2053·2020·2020··:·Ideal·of·S···· | ||
| 0000e870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e870:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 2286, 56 lines modified | Offset 2286, 56 lines modified | ||
| 00008ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00008ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00008ee0:·2b0a·7c69·3720·3a20·666f·7220·6e20·6672··+.|i7·:·for·n·fr | 00008ee0:·2b0a·7c69·3720·3a20·666f·7220·6e20·6672··+.|i7·:·for·n·fr | ||
| 00008ef0:·6f6d·2032·2074·6f20·3130·206c·6973·7420··om·2·to·10·list· | 00008ef0:·6f6d·2032·2074·6f20·3130·206c·6973·7420··om·2·to·10·list· | ||
| 00008f00:·7469·6d65·2066·206e·2020·2020·2020·2020··time·f·n········ | 00008f00:·7469·6d65·2066·206e·2020·2020·2020·2020··time·f·n········ | ||
| 00008f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008f30:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | 00008f30:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 00008f40:·3 | 00008f40:·3739·3730·3832·7320·2863·7075·293b·2030··797082s·(cpu);·0 | ||
| 00008f50:·2e30·303 | 00008f50:·2e30·3034·3932·3834·3473·2028·7468·7265··.00492844s·(thre | ||
| 00008f60:·6429 | 00008f60:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00008f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008f80:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | 00008f80:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 00008f90:·3 | 00008f90:·3334·3239·3332·7320·2863·7075·293b·2030··342932s·(cpu);·0 | ||
| 00008fa0:·2e30·303 | 00008fa0:·2e30·3036·3336·3030·3673·2028·7468·7265··.00636006s·(thre | ||
| 00008fb0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | 00008fb0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00008fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008fd0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | 00008fd0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 00008fe0:·3 | 00008fe0:·3930·3339·3935·7320·2863·7075·293b·2030··903995s·(cpu);·0 | ||
| 00008ff0:·2e30·3 | 00008ff0:·2e30·3130·3437·3932·7320·2874·6872·6561··.0104792s·(threa | ||
| 00009000:·6 | 00009000:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 00009010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009020:·7c0a·7c20·2d2d·2075·7365·6420·302e·3031··|.|·--·used·0.01 | 00009020:·7c0a·7c20·2d2d·2075·7365·6420·302e·3031··|.|·--·used·0.01 | ||
| 00009030:·3 | 00009030:·3535·3032·3573·2028·6370·7529·3b20·302e··55025s·(cpu);·0. | ||
| 00009040:·3031·3 | 00009040:·3031·3835·3130·3373·2028·7468·7265·6164··0185103s·(thread | ||
| 00009050:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | 00009050:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | ||
| 00009060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009070:·7c0a·7c20·2d2d·2075·7365·6420·302e·303 | 00009070:·7c0a·7c20·2d2d·2075·7365·6420·302e·3033··|.|·--·used·0.03 | ||
| 00009080:·3335·3538·3573·2028·6370·7529·3b20·302e··35585s·(cpu);·0. | |||
| 000090 | 00009080:·3139·3535·7320·2863·7075·293b·2030·2e30··1955s·(cpu);·0.0 | ||
| 00009090:·3332·3636·3135·7320·2874·6872·6561·6429··326615s·(thread) | |||
| 000090a0:· | 000090a0:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 000090b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000090b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000090c0:·7c0a·7c20·2d2d·2075·7365·6420·302e·303 | 000090c0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3036··|.|·--·used·0.06 | ||
| 000090d0:·3 | 000090d0:·3832·3730·3373·2028·6370·7529·3b20·302e··82703s·(cpu);·0. | ||
| 000090e0:·303 | 000090e0:·3036·3836·3939·3773·2028·7468·7265·6164··0686997s·(thread | ||
| 000090f0:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | 000090f0:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | ||
| 00009100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009110:·7c0a·7c20·2d2d·2075·7365·6420·302e·3 | 00009110:·7c0a·7c20·2d2d·2075·7365·6420·302e·3131··|.|·--·used·0.11 | ||
| 00009120:·3937·3437·3573·2028·6370·7529·3b20·302e··97475s·(cpu);·0. | |||
| 00009130:·3037·3036·3232·3773·2028·7468·7265·6164··0706227s·(thread | |||
| 000091 | 00009120:·3333·3033·7320·2863·7075·293b·2030·2e31··3303s·(cpu);·0.1 | ||
| 00009130:·3137·7320·2874·6872·6561·6429·3b20·3073··17s·(thread);·0s | |||
| 00009140:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | |||
| 00009150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009160:·7c0a·7c20·2d2d·2075·7365·6420·302e·3 | 00009160:·7c0a·7c20·2d2d·2075·7365·6420·302e·3230··|.|·--·used·0.20 | ||
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| 000091d0:·3 | 000091d0:·3735·3134·3773·2028·7468·7265·6164·293b··75147s·(thread); | ||
| 000091e0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 000091e0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 000091f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000091f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00007300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00007330:·6564·2033·3 | 00007330:·6564·2033·302e·3635·3635·7320·2863·7075··ed·30.6565s·(cpu | ||
| 00007340:·293b·203 | 00007340:·293b·2035·2e37·3534·7320·2874·6872·6561··);·5.754s·(threa | ||
| 00007350:·6 | 00007350:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 00007360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007370:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00007370:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00007380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000073c0:·2020·2020·2020·207c·0a7c·6f31·3120·3d20·········|.|o11·=· | 000073c0:·2020·2020·2020·207c·0a7c·6f31·3120·3d20·········|.|o11·=· | ||
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| 000078a0:·7261·7465·2858·2c42·2929·2020·2020·2020··rate(X,B))······ | 000078a0:·7261·7465·2858·2c42·2929·2020·2020·2020··rate(X,B))······ | ||
| 000078b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000078b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000078c0:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | 000078c0:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | ||
| 000078d0:·6564·203 | 000078d0:·6564·2038·302e·3439·3337·7320·2863·7075··ed·80.4937s·(cpu | ||
| 000078e0:·293b·203 | 000078e0:·293b·2035·352e·3732·3433·7320·2874·6872··);·55.7243s·(thr | ||
| 000078f0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | 000078f0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 00007900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000102f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000102f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010310:·2d2d·2d2d·2d2b·0a7c·6936·203a·2074·696d··-----+.|i6·:·tim | 00010310:·2d2d·2d2d·2d2b·0a7c·6936·203a·2074·696d··-----+.|i6·:·tim | ||
| 00010320:·6520·7320·3d20·7365·6772·6544·696d·5828··e·s·=·segreDimX( | 00010320:·6520·7320·3d20·7365·6772·6544·696d·5828··e·s·=·segreDimX( | ||
| 00010330:·582c·592c·4129·2020·2020·2020·2020·2020··X,Y,A)·········· | 00010330:·582c·592c·4129·2020·2020·2020·2020·2020··X,Y,A)·········· | ||
| 00010340:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010340:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010350:·7c20·2d2d·2075·7365·6420·352e·3 | 00010350:·7c20·2d2d·2075·7365·6420·352e·3331·3530··|·--·used·5.3150 | ||
| 00010360:·3 | 00010360:·3473·2028·6370·7529·3b20·302e·3732·3639··4s·(cpu);·0.7269 | ||
| 00010370:·3 | 00010370:·3435·7320·2874·6872·6561·6429·3b20·3073··45s·(thread);·0s | ||
| 00010380:·2028·6763·2920·207c·0a7c·2020·2020·2020···(gc)··|.|······ | 00010380:·2028·6763·2920·207c·0a7c·2020·2020·2020···(gc)··|.|······ | ||
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| 000103c0:·7c0a·7c20·2020·2020·2020·3220·2020·2020··|.|·······2····· | 000103c0:·7c0a·7c20·2020·2020·2020·3220·2020·2020··|.|·······2····· | ||
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| 000104f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000104f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010500:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010510:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·7469··------+.|i7·:·ti | 00010510:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·7469··------+.|i7·:·ti | ||
| 00010520:·6d65·2073·6567·7265·2858·2c59·2c41·2920··me·segre(X,Y,A)· | 00010520:·6d65·2073·6567·7265·2858·2c59·2c41·2920··me·segre(X,Y,A)· | ||
| 00010530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010540:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00010540:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00010550:·0a7c·202d·2d20·7573·6564·2030·2e3 | 00010550:·0a7c·202d·2d20·7573·6564·2030·2e32·3436··.|·--·used·0.246 | ||
| 00010560:·3 | 00010560:·3333·3573·2028·6370·7529·3b20·302e·3039··335s·(cpu);·0.09 | ||
| 00010570:·3 | 00010570:·3832·3134·3473·2028·7468·7265·6164·293b··82144s·(thread); | ||
| 00010580:·2030·7320·2867·6329·7c0a·7c20·2020·2020···0s·(gc)|.|····· | 00010580:·2030·7320·2867·6329·7c0a·7c20·2020·2020···0s·(gc)|.|····· | ||
| 00010590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000105c0:·207c·0a7c·2020·2020·2020·2020·3220·3220···|.|········2·2· | 000105c0:·207c·0a7c·2020·2020·2020·2020·3220·3220···|.|········2·2· | ||
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| 000105e0:·2020·2020·3220·2020·2020·2020·2020·2020······2··········· | 000105e0:·2020·2020·3220·2020·2020·2020·2020·2020······2··········· |
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| 0000a330:·2d2d·2b0a·7c69·3120·3a20·6368·6563·6b20··--+.|i1·:·check· | 0000a330:·2d2d·2b0a·7c69·3120·3a20·6368·6563·6b20··--+.|i1·:·check· | ||
| 0000a340:·5369·6d70·6c65·446f·6320·2020·2020·2020··SimpleDoc······· | 0000a340:·5369·6d70·6c65·446f·6320·2020·2020·2020··SimpleDoc······· | ||
| 0000a350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a370:·2020·2020·2020·207c·0a7c·202d·2d20·6361·········|.|·--·ca | 0000a370:·2020·2020·2020·207c·0a7c·202d·2d20·6361·········|.|·--·ca | ||
| 0000a380:·7074·7572·696e·6720·6368·6563·6b28·302c··pturing·check(0, | 0000a380:·7074·7572·696e·6720·6368·6563·6b28·302c··pturing·check(0, | ||
| 0000a390:·2022·5369·6d70·6c65·446f·6322·2920·2020···"SimpleDoc")··· | 0000a390:·2022·5369·6d70·6c65·446f·6322·2920·2020···"SimpleDoc")··· | ||
| 0000a3a0:·2020·2020·2020·2020·2d2d·202e·303 | 0000a3a0:·2020·2020·2020·2020·2d2d·202e·3037·3436··········--·.0746 | ||
| 0000a3b0:·3 | 0000a3b0:·3131·3873·2065·6c61·7073·6564·7c0a·2b2d··118s·elapsed|.+- | ||
| 0000a3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a3e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a3e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a3f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a3f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a400:·2d2b·0a0a·5365·6520·616c·736f·0a3d·3d3d··-+..See·also.=== | 0000a400:·2d2b·0a0a·5365·6520·616c·736f·0a3d·3d3d··-+..See·also.=== | ||
| 0000a410:·3d3d·3d3d·3d0a·0a20·202a·202a·6e6f·7465··=====..··*·*note | 0000a410:·3d3d·3d3d·3d0a·0a20·202a·202a·6e6f·7465··=====..··*·*note | ||
| 0000a420:·2054·4553·543a·2028·4d61·6361·756c·6179···TEST:·(Macaulay | 0000a420:·2054·4553·543a·2028·4d61·6361·756c·6179···TEST:·(Macaulay |
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| 0002eb00:·302a·7265·6d56·6172·735f·312d·3129·2020··0*remVars_1-1)·· | 0002eb00:·302a·7265·6d56·6172·735f·312d·3129·2020··0*remVars_1-1)·· | ||
| 0002eb10:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0002eb10:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
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| 00004cb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004cb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004cc0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 00004cc0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
| 00004cd0:·302e·323 | 00004cd0:·302e·3239·3233·3831·7320·2863·7075·293b··0.292381s·(cpu); | ||
| 00004ce0:·2030·2e3 | 00004ce0:·2030·2e32·3131·3034·3473·2028·7468·7265···0.211044s·(thre | ||
| 00004cf0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | 00004cf0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00004d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d10:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00004d10:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00004d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00005f20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005f20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005f30:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a·2074··-------+.|i2·:·t | 00005f30:·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a·2074··-------+.|i2·:·t | ||
| 00005f40:·696d·6520·6465·6e73·6552·6573·756c·7461··ime·denseResulta | 00005f40:·696d·6520·6465·6e73·6552·6573·756c·7461··ime·denseResulta | ||
| 00005f50:·6e74·2866·302c·6631·2c66·3229·3b20·2d2d··nt(f0,f1,f2);·-- | 00005f50:·6e74·2866·302c·6631·2c66·3229·3b20·2d2d··nt(f0,f1,f2);·-- | ||
| 00005f60:·2075·7369·6e67·2050·6f69·7373·6f6e·2066···using·Poisson·f | 00005f60:·2075·7369·6e67·2050·6f69·7373·6f6e·2066···using·Poisson·f | ||
| 00005f70:·6f72·6d75·6c61·2020·2020·2020·2020·2020··ormula·········· | 00005f70:·6f72·6d75·6c61·2020·2020·2020·2020·2020··ormula·········· | ||
| 00005f80:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | 00005f80:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | ||
| 00005f90:·6564·2030·2e30·3 | 00005f90:·6564·2030·2e30·3833·3132·3573·2028·6370··ed·0.083125s·(cp | ||
| 00005fa0:·7075·293b·2030·2e30·3633·3534·3836·7320··pu);·0.0635486s· | |||
| 00005f | 00005fa0:·7529·3b20·302e·3038·3234·3331·3473·2028··u);·0.0824314s·( | ||
| 00005fb0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | |||
| 00005fc0:·2 | 00005fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005fd0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 00005fd0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00005fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005ff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005ff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006020:·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a·2074··-------+.|i3·:·t | 00006020:·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a·2074··-------+.|i3·:·t | ||
| 00006030:·696d·6520·6465·6e73·6552·6573·756c·7461··ime·denseResulta | 00006030:·696d·6520·6465·6e73·6552·6573·756c·7461··ime·denseResulta | ||
| 00006040:·6e74·2866·302c·6631·2c66·322c·416c·676f··nt(f0,f1,f2,Algo | 00006040:·6e74·2866·302c·6631·2c66·322c·416c·676f··nt(f0,f1,f2,Algo | ||
| 00006050:·7269·7468·6d3d·3e22·4d61·6361·756c·6179··rithm=>"Macaulay | 00006050:·7269·7468·6d3d·3e22·4d61·6361·756c·6179··rithm=>"Macaulay | ||
| 00006060:·2229·3b20·2d2d·2075·7369·6e67·204d·6163··");·--·using·Mac | 00006060:·2229·3b20·2d2d·2075·7369·6e67·204d·6163··");·--·using·Mac | ||
| 00006070:·6175·6c61·7920·207c·0a7c·202d·2d20·7573··aulay··|.|·--·us | 00006070:·6175·6c61·7920·207c·0a7c·202d·2d20·7573··aulay··|.|·--·us | ||
| 00006080:·6564·2030·2e3 | 00006080:·6564·2030·2e33·3039·3539·3273·2028·6370··ed·0.309592s·(cp | ||
| 00006090:·7529·3b20·302e·3 | 00006090:·7529·3b20·302e·3237·3330·3335·7320·2874··u);·0.273035s·(t | ||
| 000060a0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 000060a0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 000060b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000060b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000060c0:·2020·2020·2020·207c·0a7c·2d2d·2d2d·2d2d·········|.|------ | 000060c0:·2020·2020·2020·207c·0a7c·2d2d·2d2d·2d2d·········|.|------ | ||
| 000060d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000060e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000060f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006100:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006100:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000061b0:·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a·2074··-------+.|i4·:·t | 000061b0:·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a·2074··-------+.|i4·:·t | ||
| 000061c0:·696d·6520·2864·656e·7365·5265·7375·6c74··ime·(denseResult | 000061c0:·696d·6520·2864·656e·7365·5265·7375·6c74··ime·(denseResult | ||
| 000061d0:·616e·7428·312c·322c·3229·2920·2866·302c··ant(1,2,2))·(f0, | 000061d0:·616e·7428·312c·322c·3229·2920·2866·302c··ant(1,2,2))·(f0, | ||
| 000061e0:·6631·2c66·3229·3b20·2d2d·2075·7369·6e67··f1,f2);·--·using | 000061e0:·6631·2c66·3229·3b20·2d2d·2075·7369·6e67··f1,f2);·--·using | ||
| 000061f0:·2073·7061·7273·6552·6573·756c·7461·6e74···sparseResultant | 000061f0:·2073·7061·7273·6552·6573·756c·7461·6e74···sparseResultant | ||
| 00006200:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | 00006200:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | ||
| 00006210:·6564·2030·2e35·3 | 00006210:·6564·2030·2e35·3333·3235·7320·2863·7075··ed·0.53325s·(cpu | ||
| 00006220:·7529·3b20·302e·3235·3631·3539·7320·2874··u);·0.256159s·(t | |||
| 000062 | 00006220:·293b·2030·2e33·3231·3033·3573·2028·7468··);·0.321035s·(th | ||
| 00006230:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | |||
| 00006240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006250:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 00006250:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00006260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000062a0:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2061··-------+.|i5·:·a | 000062a0:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2061··-------+.|i5·:·a | ||
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| 00006e40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006e40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006e50:·2d2d·2d2d·2d2d·2b0a·7c69·3220·3a20·7469··------+.|i2·:·ti | 00006e50:·2d2d·2d2d·2d2d·2b0a·7c69·3220·3a20·7469··------+.|i2·:·ti | ||
| 00006e60:·6d65·2064·6574·204d·2020·2020·2020·2020··me·det·M········ | 00006e60:·6d65·2064·6574·204d·2020·2020·2020·2020··me·det·M········ | ||
| 00006e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ea0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00006ea0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00006eb0:·6420·302e·3 | 00006eb0:·6420·302e·3832·3939·3237·7320·2863·7075··d·0.829927s·(cpu | ||
| 00006ec0:·293b·2030·2e31·3 | 00006ec0:·293b·2030·2e31·3434·3234·7320·2874·6872··);·0.14424s·(thr | ||
| 00006ed0:· | 00006ed0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 00006ee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ef0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00006ef0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00006f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006f40:·2020·2020·2020·7c0a·7c6f·3220·3d20·3936········|.|o2·=·96 | 00006f40:·2020·2020·2020·7c0a·7c6f·3220·3d20·3936········|.|o2·=·96 | ||
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| 00007430:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007430:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007440:·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20·7469··------+.|i4·:·ti | 00007440:·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20·7469··------+.|i4·:·ti | ||
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| 00007610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007620:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·: | 00007620:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·: | ||
| 00007630:·2074·696d·6520·5527·203d·2061·7373·6f63···time·U'·=·assoc | 00007630:·2074·696d·6520·5527·203d·2061·7373·6f63···time·U'·=·assoc | ||
| 00007640:·6961·7465·6443·6173·7465·6c6e·756f·766f··iatedCastelnuovo | 00007640:·6961·7465·6443·6173·7465·6c6e·756f·766f··iatedCastelnuovo | ||
| 00007650:·5375·7266·6163·6520·583b·2020·2020·2020··Surface·X;······ | 00007650:·5375·7266·6163·6520·583b·2020·2020·2020··Surface·X;······ | ||
| 00007660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007670:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00007670:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00007680:·7573·6564·2033·2e3 | 00007680:·7573·6564·2033·2e36·3337·3132·7320·2863··used·3.63712s·(c | ||
| 00007690:·7075·293b·2030·2e39·3431·3731·3973·2028··pu);·0.941719s·( | |||
| 000076 | 00007690:·7075·293b·2031·2e30·3633·3039·7320·2874··pu);·1.06309s·(t | ||
| 000076a0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | |||
| 000076b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000076c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000076d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007710:·2020·2020·2020·2020·207c·0a7c·6f33·203a···········|.|o3·: | 00007710:·2020·2020·2020·2020·207c·0a7c·6f33·203a···········|.|o3·: | ||
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| 00008f10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00008f10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00008f20:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20··--------+.|i3·:· | 00008f20:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20··--------+.|i3·:· | ||
| 00008f30:·7469·6d65·2055·2720·3d20·6173·736f·6369··time·U'·=·associ | 00008f30:·7469·6d65·2055·2720·3d20·6173·736f·6369··time·U'·=·associ | ||
| 00008f40:·6174·6564·4b33·7375·7266·6163·6520·583b··atedK3surface·X; | 00008f40:·6174·6564·4b33·7375·7266·6163·6520·583b··atedK3surface·X; | ||
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| 00008f | 00008f90:·7529·3b20·312e·3131·3930·3573·2028·7468··u);·1.11905s·(th | ||
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| 00008fc0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00008fc0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00008fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000a7f0:·7266·6163·6520·583b·2020·2020·2020·2020··rface·X;········ | 0000a7f0:·7266·6163·6520·583b·2020·2020·2020·2020··rface·X;········ | ||
| 0000a800:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a800:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000a860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a870:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0000a870:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 0000a880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f590:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | 0000f590:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
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| 00010b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010b30:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00010b30:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 00010b80:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00010b80:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 000111f0:·6f6e·6963·2074·6f20·7468·6520·7375·7266··onic·to·the·surf | 000111f0:·6f6e·6963·2074·6f20·7468·6520·7375·7266··onic·to·the·surf | ||
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| 00011210:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00011210:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 00011260:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00011260:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 0000cf10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cf10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cf20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cf20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cf30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cf30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cf40:·2020·2020·2020·2020·7c0a·7c6f·3320·3d20··········|.|o3·=· | 0000cf40:·2020·2020·2020·2020·7c0a·7c6f·3320·3d20··········|.|o3·=· | ||
| 0000cf50:·7b4 | 0000cf50:·7b44·6967·7261·7068·2c20·4269·6772·6170··{Digraph,·Bigrap | ||
| 0000cf60:· | 0000cf60:·682c·2047·7261·7068·7d20·2020·2020·2020··h,·Graph}······· | ||
| 0000cf70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cf70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cf80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cf80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cf90:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 0000cf90:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 0000cfa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cfa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cfb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cfb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cfc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cfc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cfd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cfd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0001c430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c440:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0001c440:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0001c450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c490:·2020·207c·0a7c·6f32·203d·206e·6577·2048·····|.|o2·=·new·H | 0001c490:·2020·207c·0a7c·6f32·203d·206e·6577·2048·····|.|o2·=·new·H | ||
| 0001c4a0:·6173·6854·6162·6c65·2066·726f·6d20·7b4 | 0001c4a0:·6173·6854·6162·6c65·2066·726f·6d20·7b42··ashTable·from·{B | ||
| 0001c4b0:·6967·7261·7068·203d·3e20·6 | 0001c4b0:·6967·7261·7068·203d·3e20·6269·6772·6170··igraph·=>·bigrap | ||
| 0001c4c0:·6820·287b·3 | 0001c4c0:·6820·287b·332c·2034·2c20·327d·2c20·7b7b··h·({3,·4,·2},·{{ | ||
| 0001c4d0:·3 | 0001c4d0:·342c·2033·7d2c·207b·342c·2032·7d7d·292c··4,·3},·{4,·2}}), | ||
| 0001c4e0:·2020·207c·0a7c·2020·2020·204 | 0001c4e0:·2020·207c·0a7c·2020·2020·2047·7261·7068·····|.|·····Graph | ||
| 0001c4f0:·7068·203d·3e20·6269·6772·6170·6820·287b··ph·=>·bigraph·({ | |||
| 0001c500:·332c·2034·2c20·327d·2c20·7b7b·342c·2033··3,·4,·2},·{{4,·3 | |||
| 0001c510:·7d2c·207b·342c·2032·7d7d·292c·2047·7261··},·{4,·2}}),·Gra | |||
| 0001c | 0001c4f0:·203d·3e20·6772·6170·6820·287b·332c·2031···=>·graph·({3,·1 | ||
| 0001c500:·7d2c·207b·7b31·2c20·337d·7d29·2c20·4469··},·{{1,·3}}),·Di | |||
| 0001c510:·6772·6170·6820·3d3e·2064·6967·7261·7068··graph·=>·digraph | |||
| 0001c520:·2028·7b31·2c20·322c·2033·7d2c·207b·7b31···({1,·2,·3},·{{1 | |||
| 0001c530:·2 | 0001c530:·2c20·207c·0a7c·2020·2020·2032·7d2c·207b··,··|.|·····2},·{ | ||
| 0001c540:· | 0001c540:·322c·2033·7d7d·297d·2020·2020·2020·2020··2,·3}})}········ | ||
| 0001c550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c580:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | 0001c580:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | ||
| 0001c590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001c590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001c5a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001c5a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001c5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001c5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00011de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011df0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011df0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011e00:·2d2d·2d2b·0a7c·6937·203a·2074·696d·6520··---+.|i7·:·time· | 00011e00:·2d2d·2d2b·0a7c·6937·203a·2074·696d·6520··---+.|i7·:·time· | ||
| 00011e10:·7379·6d62·6f6c·6963·506f·7765·7228·502c··symbolicPower(P, | 00011e10:·7379·6d62·6f6c·6963·506f·7765·7228·502c··symbolicPower(P, | ||
| 00011e20:·3429·3b20·2020·2020·2020·2020·2020·2020··4);············· | 00011e20:·3429·3b20·2020·2020·2020·2020·2020·2020··4);············· | ||
| 00011e30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011e30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011e40:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00011e40:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00011e50:·7573·6564·2030·2e31·3 | 00011e50:·7573·6564·2030·2e31·3731·3933·3173·2028··used·0.171931s·( | ||
| 00011e60:·6370·7529·3b20·302e·313 | 00011e60:·6370·7529·3b20·302e·3133·3731·7320·2874··cpu);·0.1371s·(t | ||
| 00011e70:· | 00011e70:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00011e80:·2 | 00011e80:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00011e90:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00011e90:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00011ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011ed0:·2020·2020·207c·0a7c·6f37·203a·2049·6465·······|.|o7·:·Ide | 00011ed0:·2020·2020·207c·0a7c·6f37·203a·2049·6465·······|.|o7·:·Ide | ||
| 00011ee0:·616c·206f·6620·5151·5b78·2e2e·7a5d·2020··al·of·QQ[x..z]·· | 00011ee0:·616c·206f·6620·5151·5b78·2e2e·7a5d·2020··al·of·QQ[x..z]·· | ||
| 00011ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00012240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012260:·2d2d·2d2b·0a7c·6931·3020·3a20·7469·6d65··---+.|i10·:·time | 00012260:·2d2d·2d2b·0a7c·6931·3020·3a20·7469·6d65··---+.|i10·:·time | ||
| 00012270:·2073·796d·626f·6c69·6350·6f77·6572·2851···symbolicPower(Q | 00012270:·2073·796d·626f·6c69·6350·6f77·6572·2851···symbolicPower(Q | ||
| 00012280:·2c34·293b·2020·2020·2020·2020·2020·2020··,4);············ | 00012280:·2c34·293b·2020·2020·2020·2020·2020·2020··,4);············ | ||
| 00012290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000122a0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000122a0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 000122b0:·7573·6564·2030·2e30·3 | 000122b0:·7573·6564·2030·2e30·3831·3337·3238·7320··used·0.0813728s· | ||
| 000122c0:·2863·7075·293b·2030·2e30·333 | 000122c0:·2863·7075·293b·2030·2e30·3339·3330·3131··(cpu);·0.0393011 | ||
| 000122d0:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | 000122d0:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | ||
| 000122e0:·6763·2920·2020·2020·2020·2020·2020·207c··gc)············| | 000122e0:·6763·2920·2020·2020·2020·2020·2020·207c··gc)············| | ||
| 000122f0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 000122f0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00012300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012330:·2020·2020·207c·0a7c·6f31·3020·3a20·4964·······|.|o10·:·Id | 00012330:·2020·2020·207c·0a7c·6f31·3020·3a20·4964·······|.|o10·:·Id |
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| 0000fb90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fb90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fbb0:·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20·7469··------+.|i4·:·ti | 0000fbb0:·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20·7469··------+.|i4·:·ti | ||
| 0000fbc0:·6d65·2054·3d74·6174·6545·7874·656e·7369··me·T=tateExtensi | 0000fbc0:·6d65·2054·3d74·6174·6545·7874·656e·7369··me·T=tateExtensi | ||
| 0000fbd0:·6f6e·2057·3b20·2020·2020·2020·2020·2020··on·W;··········· | 0000fbd0:·6f6e·2057·3b20·2020·2020·2020·2020·2020··on·W;··········· | ||
| 0000fbe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fbe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fbf0:·207c·0a7c·202d·2d20·7573·6564·2030·2e33···|.|·--·used·0.3 | 0000fbf0:·207c·0a7c·202d·2d20·7573·6564·2030·2e33···|.|·--·used·0.3 | ||
| 0000fc00:·3 | 0000fc00:·3634·3939·3873·2028·6370·7529·3b20·302e··64998s·(cpu);·0. | ||
| 0000fc10:·313 | 0000fc10:·3136·3835·3935·7320·2874·6872·6561·6429··168595s·(thread) | ||
| 0000fc20:·3b20·3073·2028·6763·2920·2020·7c0a·2b2d··;·0s·(gc)···|.+- | 0000fc20:·3b20·3073·2028·6763·2920·2020·7c0a·2b2d··;·0s·(gc)···|.+- | ||
| 0000fc30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fc30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fc40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fc40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fc50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fc50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fc60:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2063··-------+.|i5·:·c | 0000fc60:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2063··-------+.|i5·:·c | ||
| 0000fc70:·6f68·6f6d·6f6c·6f67·794d·6174·7269·7828··ohomologyMatrix( | 0000fc70:·6f68·6f6d·6f6c·6f67·794d·6174·7269·7828··ohomologyMatrix( | ||
| 0000fc80:·542c·2d7b·332c·337d·2c7b·332c·337d·2920··T,-{3,3},{3,3})· | 0000fc80:·542c·2d7b·332c·337d·2c7b·332c·337d·2920··T,-{3,3},{3,3})· |
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| 000061c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000061c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000061d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420··----------+.|i4· | 000061d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420··----------+.|i4· | ||
| 000061e0:·3a20·7469·6d65·2065·6444·6567·2841·2920··:·time·edDeg(A)· | 000061e0:·3a20·7469·6d65·2065·6444·6567·2841·2920··:·time·edDeg(A)· | ||
| 000061f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000061f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006220:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00006220:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00006230:·2075·7365·6420·302e·3 | 00006230:·2075·7365·6420·302e·3936·3733·3236·7320···used·0.967326s· | ||
| 00006240:·2863·7075·293b·2030·2e3 | 00006240:·2863·7075·293b·2030·2e36·3730·3735·3973··(cpu);·0.670759s | ||
| 00006250:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | 00006250:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | ||
| 00006260:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | 00006260:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | ||
| 00006270:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00006270:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00006280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000062a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000062a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000062b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000062b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000066c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000066c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000066d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3520··----------+.|i5· | 000066d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3520··----------+.|i5· | ||
| 000066e0:·3a20·7469·6d65·2065·6444·6567·2841·2c46··:·time·edDeg(A,F | 000066e0:·3a20·7469·6d65·2065·6444·6567·2841·2c46··:·time·edDeg(A,F | ||
| 000066f0:·6f72·6365·416d·6174·3d3e·7472·7565·2920··orceAmat=>true)· | 000066f0:·6f72·6365·416d·6174·3d3e·7472·7565·2920··orceAmat=>true)· | ||
| 00006700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006720:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00006720:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00006730:·2075·7365·6420·332e·3 | 00006730:·2075·7365·6420·332e·3834·3833·3673·2028···used·3.84836s·( | ||
| 00006740:·6370·7529·3b20·322e·3 | 00006740:·6370·7529·3b20·322e·3638·3531·3773·2028··cpu);·2.68517s·( | ||
| 00006750:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | 00006750:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 00006760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006770:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00006770:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00006780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000067a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000067a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000067b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000067b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 000004a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000004a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000004b0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 000004b0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 000004c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000004c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000004d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000004d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000004e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000004e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000004f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000004f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000500:·2020·2020·2020·2020·7c0a·7c6f·3320·3d20··········|.|o3·=· | 00000500:·2020·2020·2020·2020·7c0a·7c6f·3320·3d20··········|.|o3·=· | ||
| 00000510:·7b7b·632c·2064·2c20·652c·2066·7d2c·207b··{{c,·d,·e,·f},·{ | |||
| 000005 | 00000510:·7b7b·612a·6420·2d20·622a·632c·2065·2c20··{{a*d·-·b*c,·e,· | ||
| 00000530:·2064·2a65·2c20·672c·2068·7d20·2f20·7b64···d*e,·g,·h}·/·{d | |||
| 000005 | 00000520:·667d·202f·2064·2c20·7b61·2a64·202d·2062··f}·/·d,·{a*d·-·b | ||
| 00000530:·2a63·2c20·632a·6620·2d20·642a·652c·2065··*c,·c*f·-·d*e,·e | |||
| 00000540:·2a68·202d·2066·2a67·7d20·2f20·7b64·2c20··*h·-·f*g}·/·{d,· | |||
| 00000550:·6 | 00000550:·662c·2068·7d2c·2020·7c0a·7c20·2020·2020··f,·h},··|.|····· | ||
| 00000560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000005a0:·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020·2020··--------|.|····· | 000005a0:·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020·2020··--------|.|····· | ||
| 000005b0:·642c·2067·2c20·687d·2c20·7b61·2a64·202d··d,·g,·h},·{a*d·- | |||
| 000005c0:·2062·2a63·2c20·652c·2066·7d20·2f20·642c···b*c,·e,·f}·/·d, | |||
| 000005d0:·207b·612a·6420·2d20·622a·632c·2063·2a66···{a*d·-·b*c,·c*f | |||
| 000005 | 000005b0:·7b63·2c20·642c·2066·2c20·687d·2c20·7b63··{c,·d,·f,·h},·{c | ||
| 000005c0:·2c20·642c·2065·2a68·202d·2066·2a67·7d20··,·d,·e*h·-·f*g}· | |||
| 000005d0:·2f20·682c·207b·622c·2064·2c20·652c·2066··/·h,·{b,·d,·e,·f | |||
| 000005e0:·7d2c·207b·632c·2064·2c20·652c·2066·7d2c··},·{c,·d,·e,·f}, | |||
| 000005f0:· | 000005f0:·207b·612a·6420·2d20·7c0a·7c20·2020·2020···{a*d·-·|.|····· | ||
| 00000600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000610:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00000630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00000640:·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020·2020··--------|.|····· | 00000640:·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020·2020··--------|.|····· | ||
| 00000650:·662c·2068·7d2c·207b·632c·2064·2c20·652a··f,·h},·{c,·d,·e* | |||
| 000006 | 00000650:·622a·632c·2063·2a66·202d·2064·2a65·2c20··b*c,·c*f·-·d*e,· | ||
| 00000660:·672c·2068·7d20·2f20·7b64·2c20·667d·2c20··g,·h}·/·{d,·f},· | |||
| 00000670:·2c20·642c·2066·2c20·687d·2c20·7b6 | 00000670:·7b62·2c20·642c·2066·2c20·687d·2c20·7b63··{b,·d,·f,·h},·{c | ||
| 00000680:·642c·206 | 00000680:·2c20·642c·2067·2c20·687d·7d20·2020·2020··,·d,·g,·h}}····· | ||
| 00000690:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00000690:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 000006a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000006a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000006b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000006b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000006c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000006c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000006d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000006d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000006e0:·2020·2020·2020·2020·7c0a·7c6f·3320·3a20··········|.|o3·:· | 000006e0:·2020·2020·2020·2020·7c0a·7c6f·3320·3a20··········|.|o3·:· | ||
| 000006f0:·4c69·7374·2020·2020·2020·2020·2020·2020··List············ | 000006f0:·4c69·7374·2020·2020·2020·2020·2020·2020··List············ | ||
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| 0000d060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d070:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d070:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d080:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 0000d080:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 0000d090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d0c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d0d0:·7c6f·3320·3d20·7b7b·632c·2064·2c20·6 | 0000d0d0:·7c6f·3320·3d20·7b7b·632c·2064·2c20·652c··|o3·=·{{c,·d,·e, | ||
| 0000d0e0:·2068·7d2c·207b·622c·2064·2c20·652c·2066···h},·{b,·d,·e,·f | |||
| 0000d0f0:·7d2c·207b·632c·2064·2c20·652c·2066·7d2c··},·{c,·d,·e,·f}, | |||
| 0000d | 0000d0e0:·2066·7d2c·207b·612a·6420·2d20·622a·632c···f},·{a*d·-·b*c, | ||
| 0000d | 0000d0f0:·2063·2a66·202d·2064·2a65·2c20·672c·2068···c*f·-·d*e,·g,·h | ||
| 0000d100:·7d20·2f20·7b64·2c20·667d·2c20·7b62·2c20··}·/·{d,·f},·{b,· | |||
| 0000d110:·642c·2066·2c20·687d·2c20·7b63·2c20·7c0a··d,·f,·h},·{c,·|. | |||
| 0000d120:·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d·2d2d··|·····---------- | 0000d120:·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d·2d2d··|·····---------- | ||
| 0000d130:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d130:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d140:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|. | 0000d160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|. | ||
| 0000d170:·7c20·2020·2020·622a·632c·2063·2a66·202d··|·····b*c,·c*f·- | |||
| 0000d180:·2064·2a65·2c20·672c·2068·7d20·2f20·7b64···d*e,·g,·h}·/·{d | |||
| 0000d190:·2c20·667d·2c20·7b61·2a64·202d·2062·2a63··,·f},·{a*d·-·b*c | |||
| 0000d1a0:·2c20·632a·6620·2d20·642a·652c·2065·2a68··,·c*f·-·d*e,·e*h | |||
| 0000d1 | 0000d170:·7c20·2020·2020·642c·2067·2c20·687d·2c20··|·····d,·g,·h},· | ||
| 0000d180:·7b61·2a64·202d·2062·2a63·2c20·652c·2066··{a*d·-·b*c,·e,·f | |||
| 0000d190:·7d20·2f20·642c·207b·612a·6420·2d20·622a··}·/·d,·{a*d·-·b* | |||
| 0000d1a0:·632c·2063·2a66·202d·2064·2a65·2c20·652a··c,·c*f·-·d*e,·e* | |||
| 0000d1b0:·6820·2d20·662a·677d·202f·207b·642c·7c0a··h·-·f*g}·/·{d,|. | |||
| 0000d1c0:·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d·2d2d··|·····---------- | 0000d1c0:·7c20·2020·2020·2d2d·2d2d·2d2d·2d2d·2d2d··|·····---------- | ||
| 0000d1d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d1d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d1e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d1e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d1f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d1f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|. | 0000d200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·7c0a··--------------|. | ||
| 0000d210:·7c20·2020·2020·662c·2068·7d2c·207b·6 | 0000d210:·7c20·2020·2020·662c·2068·7d2c·207b·632c··|·····f,·h},·{c, | ||
| 0000d220:·2064·2c20·662c·2068·7d2c·207b·632c·2064···d,·f,·h},·{c,·d | |||
| 0000d2 | 0000d220:·2064·2c20·652a·6820·2d20·662a·677d·202f···d,·e*h·-·f*g}·/ | ||
| 0000d230:·2068·2c20·7b63·2c20·642c·2066·2c20·687d···h,·{c,·d,·f,·h} | |||
| 0000d240:·2c20·7b6 | 0000d240:·2c20·7b62·2c20·642c·2065·2c20·667d·7d20··,·{b,·d,·e,·f}}· | ||
| 0000d250:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d250:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d260:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 0000d260:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 0000d270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d2a0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d2a0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d2b0:·7c6f·3320·3a20·4c69·7374·2020·2020·2020··|o3·:·List······ | 0000d2b0:·7c6f·3320·3a20·4c69·7374·2020·2020·2020··|o3·:·List······ | ||
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| 0000d380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d390:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d390:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d3a0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 0000d3a0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 0000d3b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d3b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d3c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d3c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d3e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d3e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d3f0:·7c6f·3420·3d20·7b63·2c20·642c·206 | 0000d3f0:·7c6f·3420·3d20·7b63·2c20·642c·2065·2c20··|o4·=·{c,·d,·e,· | ||
| 0000d400:·6 | 0000d400:·667d·2020·2020·2020·2020·2020·2020·2020··f}·············· | ||
| 0000d410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d430:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000d430:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000d440:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 0000d440:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 0000d450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d470:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 5275, 2670 lines modified | Offset 5275, 2669 lines modified | ||
| 000149a0:·6d61·7274·4c69·6674·3d3e·7472·7565·2077··martLift=>true·w | 000149a0:·6d61·7274·4c69·6674·3d3e·7472·7565·2077··martLift=>true·w | ||
| 000149b0:·6520·6765·7420·7665·7279·206e·6963·6520··e·get·very·nice· | 000149b0:·6520·6765·7420·7665·7279·206e·6963·6520··e·get·very·nice· | ||
| 000149c0:·6571·7561·7469·6f6e·7320·666f·7220·7468··equations·for·th | 000149c0:·6571·7561·7469·6f6e·7320·666f·7220·7468··equations·for·th | ||
| 000149d0:·650a·6261·7365·2073·7061·6365·3a0a·0a2b··e.base·space:..+ | 000149d0:·650a·6261·7365·2073·7061·6365·3a0a·0a2b··e.base·space:..+ | ||
| 000149e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000149e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000149f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000149f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014a10:·2d2d·2d2d·2d2b·0a7c·6933·203a·2074·696d··-----+.|i3·:·tim | |||
| 00014a20:·6520·2846·2c52·2c47·2c43·293d·6c6f·6361··e·(F,R,G,C)=loca | |||
| 00014a | 00014a10:·2d2d·2d2d·2b0a·7c69·3320·3a20·7469·6d65··----+.|i3·:·time | ||
| 00014a20:·2028·462c·522c·472c·4329·3d6c·6f63·616c···(F,R,G,C)=local | |||
| 00014a30:·4869·6c62·6572·7453·6368·656d·6528·4630··HilbertScheme(F0 | |||
| 00014a40:· | 00014a40:·293b·2020·2020·2020·2020·207c·0a7c·202d··);·········|.|·- | ||
| 00014a50:·2 | 00014a50:·2d20·7573·6564·2030·2e39·3034·3636·7320··-·used·0.90466s· | ||
| 00014a60:·3573·2028·6370·7529·3b20·302e·3534·3533··5s·(cpu);·0.5453 | |||
| 00014a | 00014a60:·2863·7075·293b·2030·2e36·3535·3430·3973··(cpu);·0.655409s | ||
| 00014a70:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | |||
| 00014a80:· | 00014a80:·6329·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d··c)|.+----------- | ||
| 00014a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014aa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014aa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014ab0:·2d2d·2d2d·2d2d·2d2d·2d2 | 00014ab0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 00014ac0:· | 00014ac0:·2054·3d72·696e·6720·6669·7273·7420·473b···T=ring·first·G; | ||
| 00014ad0:· | 00014ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014af0:· | 00014af0:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00014b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | |||
| 00014b | 00014b20:·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a·2073··-------+.|i5·:·s | ||
| 00014b30:·756d·2047·2020·2020·2020·2020·2020·2020··um·G············ | |||
| 00014b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | |||
| 00014b | 00014b60:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00014b60:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | |||
| 00014b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b90:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00014ba0:·6f35·203d·207c·2074·5f31·745f·3136·2020··o5·=·|·t_1t_16·· | |||
| 00014bb0:·2020·2020·2020·2020·2020·207c·2020·2020·············|···· | |||
| 00014bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014b | 00014b90:·2020·2020·207c·0a7c·6f35·203d·207c·2074·······|.|o5·=·|·t | ||
| 00014b | 00014ba0:·5f31·745f·3136·2020·2020·2020·2020·2020··_1t_16·········· | ||
| 00014b | 00014bb0:·2020·207c·2020·2020·2020·2020·2020·2020·····|············ | ||
| 00014 | 00014bc0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00014 | 00014bd0:·2020·2020·7c20·745f·3974·5f31·3620·2020······|·t_9t_16··· | ||
| 00014 | 00014be0:·2020·2020·2020·2020·2020·7c20·2020·2020············|····· | ||
| 00014bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014c00:·2020·207c·0a7c·2020·2020·207c·202d·745f·····|.|·····|·-t_ | |||
| 00014c10:·3474·5f31·3620·2020·2020·2020·2020·2020··4t_16··········· | |||
| 00014c20:·207c·2020·2020·2020·2020·2020·2020·2020···|·············· | |||
| 00014c30:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | |||
| 00014c40:·2020·7c20·2d32·745f·3134·745f·3136·2b74····|·-2t_14t_16+t | |||
| 00014c50:·5f31·3574·5f31·3620·7c20·2020·2020·2020··_15t_16·|······· | |||
| 00014c | 00014c60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014c40:·2020·2020·207c·0a7c·2020·2020·207c·202d·······|.|·····|·- | |||
| 00014c50:·3274·5f31·3474·5f31·362b·745f·3135·745f··2t_14t_16+t_15t_ | |||
| 00014c | 00014c70:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00014c70:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00014c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ca0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | |||
| 00014cb0:·2020·2020·2020·2020·3420·2020·2020·2031··········4······1 | |||
| 00014c | 00014cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014c | 00014cd0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00014ce0:·0a7c·6f35·203a·204d·6174·7269·7820·5420··.|o5·:·Matrix·T· | |||
| 00014c | 00014cf0:·203c·2d2d·2054·2020·2020·2020·2020·2020···<--·T·········· | ||
| 00014 | 00014d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ce0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00014cf0:·6f35·203a·204d·6174·7269·7820·5420·203c··o5·:·Matrix·T··< | |||
| 00014d00:·2d2d·2054·2020·2020·2020·2020·2020·2020··--·T············ | |||
| 00014d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014d | 00014d10:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 00014d20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00014d30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014d30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014d40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00014d | 00014d40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a0a··-------------+.. | ||
| 00014d | 00014d50:·5769·7468·2074·6865·2073·6574·7469·6e67··With·the·setting | ||
| 00014d | 00014d60:·2053·6d61·7274·4c69·6674·3d3e·6661·6c73···SmartLift=>fals | ||
| 00014d | 00014d70:·6520·7468·6520·6361·6c63·756c·6174·696f··e·the·calculatio | ||
| 00014d | 00014d80:·6e20·6973·2066·6173·7465·722c·2062·7574··n·is·faster,·but | ||
| 00014d | 00014d90:·2074·6865·2065·7175·6174·696f·6e73·0a61···the·equations.a | ||
| 00014d | 00014da0:·7265·206e·6f20·6c6f·6e67·6572·2068·6f6d··re·no·longer·hom | ||
| 00014d | 00014db0:·6f67·656e·656f·7573·3a0a·0a2b·2d2d·2d2d··ogeneous:..+---- | ||
| 00014dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00014dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014de0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014df0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014df0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014e00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00014e | 00014e00:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | ||
| 00014e | 00014e10:·2074·696d·6520·2846·2c52·2c47·2c43·293d···time·(F,R,G,C)= | ||
| 00014e | 00014e20:·6c6f·6361·6c48·696c·6265·7274·5363·6865··localHilbertSche | ||
| 00014e | 00014e30:·6d65·2846·302c·536d·6172·744c·6966·743d··me(F0,SmartLift= | ||
| 00014e | 00014e40:·3e66·616c·7365·293b·2020·2020·2020·2020··>false);········ | ||
| 00014e | 00014e50:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00014e | 00014e60:·7573·6564·2030·2e35·3634·3330·3273·2028··used·0.564302s·( | ||
| 00014e | 00014e70:·6370·7529·3b20·302e·3338·3533·3939·7320··cpu);·0.385399s· | ||
| 00014e | 00014e80:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 00014e | 00014e90:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00014e | 00014ea0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 00014eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00014ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00014 | 00014ef0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·: | ||
| 00014f | 00014f00:·2073·756d·2047·2020·2020·2020·2020·2020···sum·G·········· | ||
| 00014f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014f | 00014f40:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00014f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014f | 00014f90:·2020·2020·2020·2020·207c·0a7c·6f37·203d···········|.|o7·= | ||
| 00014f | 00014fa0:·207c·2074·5f31·745f·3136·2020·2020·2020···|·t_1t_16······ | ||
| 00014fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00014f | 00014fe0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 0001 | 00014ff0:·207c·2032·745f·3574·5f31·3074·5f31·3174···|·2t_5t_10t_11t | ||
| 000150 | 00015000:·5f31·362b·745f·3774·5f31·315e·3274·5f31··_16+t_7t_11^2t_1 | ||
| 000150 | 00015010:·362d·3274·5f36·745f·3130·745f·3136·2b33··6-2t_6t_10t_16+3 | ||
| 000150 | 00015020:·745f·3130·5e32·745f·3136·2d74·5f38·745f··t_10^2t_16-t_8t_ | ||
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| 00017fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017fb0:·2020·2020·2020·2020·2020·2020·207c·202 | 00017fb0:·2020·2020·2020·2020·2020·2020·207c·202d···············|·- | ||
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| 00017ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00018010:·3 | 00018010:·3320·7c20·2020·2020·2020·207c·0a7c·2020··3·|········|.|·· | ||
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| 00018030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018040:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018040:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00021260:·2d2d·2d2d·2b0a·7c69·3220·3a20·4c3d·746f··----+.|i2·:·L=to | 00021260:·2d2d·2d2d·2b0a·7c69·3220·3a20·4c3d·746f··----+.|i2·:·L=to | ||
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| 00004dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004dd0:·2d2d·2d2d·2b0a·7c69·3233·203a·2074·696d··----+.|i23·:·tim | 00004dd0:·2d2d·2d2d·2b0a·7c69·3233·203a·2074·696d··----+.|i23·:·tim | ||
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| 00004e00:·2c53·7472·6174·7354·6f46·696e·643d·3e22··,StratsToFind=>" | 00004e00:·2c53·7472·6174·7354·6f46·696e·643d·3e22··,StratsToFind=>" | ||
| 00004e10:·7369·6e67·756c·6172·4f6e·6c79·2229·7c0a··singularOnly")|. | 00004e10:·7369·6e67·756c·6172·4f6e·6c79·2229·7c0a··singularOnly")|. | ||
| 00004e20:·7c20·2d2d·2075·7365·6420·312e·3 | 00004e20:·7c20·2d2d·2075·7365·6420·312e·3836·3238··|·--·used·1.8628 | ||
| 00004e30:·3 | 00004e30:·3473·2028·6370·7529·3b20·312e·3034·3536··4s·(cpu);·1.0456 | ||
| 00004e40:·3 | 00004e40:·3973·2028·7468·7265·6164·293b·2030·7320··9s·(thread);·0s· | ||
| 00004e50:·2 | 00004e50:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 00004e60:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00004e60:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00004e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004eb0:·2020·7c0a·7c6f·3233·203d·207b·4d75·7461····|.|o23·=·{Muta | 00004eb0:·2020·7c0a·7c6f·3233·203d·207b·4d75·7461····|.|o23·=·{Muta | ||
| 00004ec0:·626c·6548·6173·6854·6162·6c65·7b2e·2e2e··bleHashTable{... | 00004ec0:·626c·6548·6173·6854·6162·6c65·7b2e·2e2e··bleHashTable{... | ||
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| 00005180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005190:·2d2d·2d2d·2d2d·2b0a·7c69·3235·203a·2074··------+.|i25·:·t | 00005190:·2d2d·2d2d·2d2d·2b0a·7c69·3235·203a·2074··------+.|i25·:·t | ||
| 000051a0:·696d·6520·6d73·3d6d·6170·5374·7261·7469··ime·ms=mapStrati | 000051a0:·696d·6520·6d73·3d6d·6170·5374·7261·7469··ime·ms=mapStrati | ||
| 000051b0:·6679·2846·2c58·682c·6964·6561·6c28·305f··fy(F,Xh,ideal(0_ | 000051b0:·6679·2846·2c58·682c·6964·6561·6c28·305f··fy(F,Xh,ideal(0_ | ||
| 000051c0:·5329·2c53·7472·6174·7354·6f46·696e·643d··S),StratsToFind= | 000051c0:·5329·2c53·7472·6174·7354·6f46·696e·643d··S),StratsToFind= | ||
| 000051d0:·3e22·6d6f·7374·2229·2020·2020·2020·2020··>"most")········ | 000051d0:·3e22·6d6f·7374·2229·2020·2020·2020·2020··>"most")········ | ||
| 000051e0:·7c0a·7c20·2d2d·2075·7365·6420·3137·2e3 | 000051e0:·7c0a·7c20·2d2d·2075·7365·6420·3137·2e30··|.|·--·used·17.0 | ||
| 000051f0:·3 | 000051f0:·3731·7320·2863·7075·293b·2034·2e30·3733··71s·(cpu);·4.073 | ||
| 00005200:·3 | 00005200:·3439·7320·2874·6872·6561·6429·3b20·3073··49s·(thread);·0s | ||
| 00005210:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 00005210:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00005220:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00005220:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00005230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005270:·2020·2020·7c0a·7c6f·3235·203d·207b·4d75······|.|o25·=·{Mu | 00005270:·2020·2020·7c0a·7c6f·3235·203d·207b·4d75······|.|o25·=·{Mu | ||
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| 00005530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005550:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3237·203a··--------+.|i27·: | 00005550:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3237·203a··--------+.|i27·: | ||
| 00005560:·2074·696d·6520·6d73·3d6d·6170·5374·7261···time·ms=mapStra | 00005560:·2074·696d·6520·6d73·3d6d·6170·5374·7261···time·ms=mapStra | ||
| 00005570:·7469·6679·2846·2c58·682c·6964·6561·6c28··tify(F,Xh,ideal( | 00005570:·7469·6679·2846·2c58·682c·6964·6561·6c28··tify(F,Xh,ideal( | ||
| 00005580:·305f·5329·2c53·7472·6174·7354·6f46·696e··0_S),StratsToFin | 00005580:·305f·5329·2c53·7472·6174·7354·6f46·696e··0_S),StratsToFin | ||
| 00005590:·643d·3e22·616c·6c22·2920·2020·2020·2020··d=>"all")······· | 00005590:·643d·3e22·616c·6c22·2920·2020·2020·2020··d=>"all")······· | ||
| 000055a0:·2020·7c0a·7c20·2d2d·2075·7365·6420·313 | 000055a0:·2020·7c0a·7c20·2d2d·2075·7365·6420·3138····|.|·--·used·18 | ||
| 000055b0:·2e38·3 | 000055b0:·2e38·3033·3773·2028·6370·7529·3b20·342e··.8037s·(cpu);·4. | ||
| 000055c0:·3 | 000055c0:·3430·3735·3173·2028·7468·7265·6164·293b··40751s·(thread); | ||
| 000055d0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 000055d0:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 000055e0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000055e0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000055f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000055f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005630:·2020·2020·2020·7c0a·7c6f·3237·203d·207b········|.|o27·=·{ | 00005630:·2020·2020·2020·7c0a·7c6f·3237·203d·207b········|.|o27·=·{ |
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| 0002d310:·6f61·6450·6163·6b61·6765·2822·6766·616e··oadPackage("gfan | 0002d310:·6f61·6450·6163·6b61·6765·2822·6766·616e··oadPackage("gfan | ||
| 0002d320:·496e·7465·7266·6163·6522·2c20·436f·6e66··Interface",·Conf | 0002d320:·496e·7465·7266·6163·6522·2c20·436f·6e66··Interface",·Conf | ||
| 0002d330:·6967·7572·6174·696f·6e20·3d3e·207b·2022··iguration·=>·{·" | 0002d330:·6967·7572·6174·696f·6e20·3d3e·207b·2022··iguration·=>·{·" | ||
| 0002d340:·6b65·6570·6669·6c65·7322·203d·3e20·7472··keepfiles"·=>·tr | 0002d340:·6b65·6570·6669·6c65·7322·203d·3e20·7472··keepfiles"·=>·tr | ||
| 0002d350:·7565·2c20·2276·657c·0a7c·202d·2d20·7275··ue,·"ve|.|·--·ru | 0002d350:·7565·2c20·2276·657c·0a7c·202d·2d20·7275··ue,·"ve|.|·--·ru | ||
| 0002d360:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | 0002d360:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | ||
| 0002d370:·6766·616e·2067·6661·6e20·2d2d·6865·6c70··gfan·gfan·--help | 0002d370:·6766·616e·2067·6661·6e20·2d2d·6865·6c70··gfan·gfan·--help | ||
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| 0002d390:·3 | 0002d390:·3930·2d30·2f31·3732·2020·2020·2020·2020··90-0/172········ | ||
| 0002d3a0:·2020·2020·2020·207c·0a7c·5468·6973·2069·········|.|This·i | 0002d3a0:·2020·2020·2020·207c·0a7c·5468·6973·2069·········|.|This·i | ||
| 0002d3b0:·7320·6120·7072·6f67·7261·6d20·666f·7220··s·a·program·for· | 0002d3b0:·7320·6120·7072·6f67·7261·6d20·666f·7220··s·a·program·for· | ||
| 0002d3c0:·636f·6d70·7574·696e·6720·616c·6c20·7265··computing·all·re | 0002d3c0:·636f·6d70·7574·696e·6720·616c·6c20·7265··computing·all·re | ||
| 0002d3d0:·6475·6365·6420·4772·6f65·626e·6572·2062··duced·Groebner·b | 0002d3d0:·6475·6365·6420·4772·6f65·626e·6572·2062··duced·Groebner·b | ||
| 0002d3e0:·6173·6573·206f·6620·6120·706f·6c79·6e6f··ases·of·a·polyno | 0002d3e0:·6173·6573·206f·6620·6120·706f·6c79·6e6f··ases·of·a·polyno | ||
| 0002d3f0:·6d69·616c·2069·647c·0a7c·4f70·7469·6f6e··mial·id|.|Option | 0002d3f0:·6d69·616c·2069·647c·0a7c·4f70·7469·6f6e··mial·id|.|Option | ||
| 0002d400:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | 0002d400:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | ||
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| 0002d8f0:·2020·2020·2020·207c·0a7c·2049·6e74·6572·········|.|·Inter | 0002d8f0:·2020·2020·2020·207c·0a7c·2049·6e74·6572·········|.|·Inter | ||
| 0002d900:·7275·7074·2074·6865·2065·6e75·6d65·7261··rupt·the·enumera | 0002d900:·7275·7074·2074·6865·2065·6e75·6d65·7261··rupt·the·enumera | ||
| 0002d910:·7469·6f6e·2061·6674·6572·2061·2073·7065··tion·after·a·spe | 0002d910:·7469·6f6e·2061·6674·6572·2061·2073·7065··tion·after·a·spe | ||
| 0002d920:·6369·6669·6564·206e·756d·6265·7220·6f66··cified·number·of | 0002d920:·6369·6669·6564·206e·756d·6265·7220·6f66··cified·number·of | ||
| 0002d930:·2066·6163·6574·7320·6861·7665·2062·6565···facets·have·bee | 0002d930:·2066·6163·6574·7320·6861·7665·2062·6565···facets·have·bee | ||
| 0002d940:·6e20·636f·6d70·757c·0a7c·7573·696e·6720··n·compu|.|using· | 0002d940:·6e20·636f·6d70·757c·0a7c·7573·696e·6720··n·compu|.|using· | ||
| 0002d950:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | 0002d950:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | ||
| 0002d960:·746d·702f·4d32·2d3 | 0002d960:·746d·702f·4d32·2d33·3630·3436·3930·2d30··tmp/M2-3604690-0 | ||
| 0002d970:·2f31·3732·2020·2020·2020·2020·2020·2020··/172············ | 0002d970:·2f31·3732·2020·2020·2020·2020·2020·2020··/172············ | ||
| 0002d980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002d980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002d990:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | 0002d990:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | ||
| 0002d9a0:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | 0002d9a0:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | ||
| 0002d9b0:·6766·616e·205f·6275·6368·6265·7267·6572··gfan·_buchberger | 0002d9b0:·6766·616e·205f·6275·6368·6265·7267·6572··gfan·_buchberger | ||
| 0002d9c0:·202d·2d68·656c·7020·3c20·2f74·6d70·2f4d···--help·<·/tmp/M | 0002d9c0:·202d·2d68·656c·7020·3c20·2f74·6d70·2f4d···--help·<·/tmp/M | ||
| 0002d9d0:·322d·3 | 0002d9d0:·322d·3336·3034·3639·302d·302f·3137·3420··2-3604690-0/174· | ||
| 0002d9e0:·2020·2020·2020·207c·0a7c·5468·6973·2070·········|.|This·p | 0002d9e0:·2020·2020·2020·207c·0a7c·5468·6973·2070·········|.|This·p | ||
| 0002d9f0:·726f·6772·616d·2063·6f6d·7075·7465·7320··rogram·computes· | 0002d9f0:·726f·6772·616d·2063·6f6d·7075·7465·7320··rogram·computes· | ||
| 0002da00:·6120·7265·6475·6365·6420·6c65·7869·636f··a·reduced·lexico | 0002da00:·6120·7265·6475·6365·6420·6c65·7869·636f··a·reduced·lexico | ||
| 0002da10:·6772·6170·6869·6320·4772·6f65·626e·6572··graphic·Groebner | 0002da10:·6772·6170·6869·6320·4772·6f65·626e·6572··graphic·Groebner | ||
| 0002da20:·2062·6173·6973·206f·6620·7468·6520·706f···basis·of·the·po | 0002da20:·2062·6173·6973·206f·6620·7468·6520·706f···basis·of·the·po | ||
| 0002da30:·6c79·6e6f·6d69·617c·0a7c·4f70·7469·6f6e··lynomia|.|Option | 0002da30:·6c79·6e6f·6d69·617c·0a7c·4f70·7469·6f6e··lynomia|.|Option | ||
| 0002da40:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | 0002da40:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | ||
| Offset 11754, 22 lines modified | Offset 11754, 22 lines modified | ||
| 0002de90:·2020·2020·2020·207c·0a7c·2057·6974·6820·········|.|·With· | 0002de90:·2020·2020·2020·207c·0a7c·2057·6974·6820·········|.|·With· | ||
| 0002dea0:·7468·6973·206f·7074·696f·6e20·796f·7520··this·option·you· | 0002dea0:·7468·6973·206f·7074·696f·6e20·796f·7520··this·option·you· | ||
| 0002deb0:·6361·6e20·7370·6563·6966·7920·686f·7720··can·specify·how· | 0002deb0:·6361·6e20·7370·6563·6966·7920·686f·7720··can·specify·how· | ||
| 0002dec0:·6d61·6e79·2076·6172·6961·626c·6573·2074··many·variables·t | 0002dec0:·6d61·6e79·2076·6172·6961·626c·6573·2074··many·variables·t | ||
| 0002ded0:·6f20·7472·6561·7420·6173·2070·6172·616d··o·treat·as·param | 0002ded0:·6f20·7472·6561·7420·6173·2070·6172·616d··o·treat·as·param | ||
| 0002dee0:·6574·6572·7320·697c·0a7c·7573·696e·6720··eters·i|.|using· | 0002dee0:·6574·6572·7320·697c·0a7c·7573·696e·6720··eters·i|.|using· | ||
| 0002def0:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | 0002def0:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | ||
| 0002df00:·746d·702f·4d32·2d3 | 0002df00:·746d·702f·4d32·2d33·3630·3436·3930·2d30··tmp/M2-3604690-0 | ||
| 0002df10:·2f31·3734·2020·2020·2020·2020·2020·2020··/174············ | 0002df10:·2f31·3734·2020·2020·2020·2020·2020·2020··/174············ | ||
| 0002df20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002df20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002df30:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | 0002df30:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | ||
| 0002df40:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | 0002df40:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | ||
| 0002df50:·6766·616e·205f·646f·6573·6964·6561·6c63··gfan·_doesidealc | 0002df50:·6766·616e·205f·646f·6573·6964·6561·6c63··gfan·_doesidealc | ||
| 0002df60:·6f6e·7461·696e·202d·2d68·656c·7020·3c20··ontain·--help·<· | 0002df60:·6f6e·7461·696e·202d·2d68·656c·7020·3c20··ontain·--help·<· | ||
| 0002df70:·2f74·6d70·2f4d·322d·3 | 0002df70:·2f74·6d70·2f4d·322d·3336·3034·3639·302d··/tmp/M2-3604690- | ||
| 0002df80:·302f·3137·3620·207c·0a7c·5468·6973·2070··0/176··|.|This·p | 0002df80:·302f·3137·3620·207c·0a7c·5468·6973·2070··0/176··|.|This·p | ||
| 0002df90:·726f·6772·616d·2074·616b·6573·2061·206d··rogram·takes·a·m | 0002df90:·726f·6772·616d·2074·616b·6573·2061·206d··rogram·takes·a·m | ||
| 0002dfa0:·6172·6b65·6420·4772·6f65·626e·6572·2062··arked·Groebner·b | 0002dfa0:·6172·6b65·6420·4772·6f65·626e·6572·2062··arked·Groebner·b | ||
| 0002dfb0:·6173·6973·206f·6620·616e·2069·6465·616c··asis·of·an·ideal | 0002dfb0:·6173·6973·206f·6620·616e·2069·6465·616c··asis·of·an·ideal | ||
| 0002dfc0:·2049·2061·6e64·2061·2073·6574·206f·6620···I·and·a·set·of· | 0002dfc0:·2049·2061·6e64·2061·2073·6574·206f·6620···I·and·a·set·of· | ||
| 0002dfd0:·706f·6c79·6e6f·6d7c·0a7c·4f70·7469·6f6e··polynom|.|Option | 0002dfd0:·706f·6c79·6e6f·6d7c·0a7c·4f70·7469·6f6e··polynom|.|Option | ||
| 0002dfe0:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | 0002dfe0:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | ||
| Offset 11794, 23 lines modified | Offset 11794, 23 lines modified | ||
| 0002e110:·2020·2020·2020·207c·0a7c·2052·6561·6473·········|.|·Reads | 0002e110:·2020·2020·2020·207c·0a7c·2052·6561·6473·········|.|·Reads | ||
| 0002e120:·2069·6e20·6120·706f·6c79·6e6f·6d69·616c···in·a·polynomial | 0002e120:·2069·6e20·6120·706f·6c79·6e6f·6d69·616c···in·a·polynomial | ||
| 0002e130:·2074·6861·7420·7769·6c6c·2062·6520·6d75···that·will·be·mu | 0002e130:·2074·6861·7420·7769·6c6c·2062·6520·6d75···that·will·be·mu | ||
| 0002e140:·6c74·6970·6c69·6564·2074·6f20·7468·6520··ltiplied·to·the· | 0002e140:·6c74·6970·6c69·6564·2074·6f20·7468·6520··ltiplied·to·the· | ||
| 0002e150:·706f·6c79·6e6f·6d69·616c·2074·6f20·6265··polynomial·to·be | 0002e150:·706f·6c79·6e6f·6d69·616c·2074·6f20·6265··polynomial·to·be | ||
| 0002e160:·2064·6976·6964·657c·0a7c·7573·696e·6720···divide|.|using· | 0002e160:·2064·6976·6964·657c·0a7c·7573·696e·6720···divide|.|using· | ||
| 0002e170:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | 0002e170:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | ||
| 0002e180:·746d·702f·4d32·2d3 | 0002e180:·746d·702f·4d32·2d33·3630·3436·3930·2d30··tmp/M2-3604690-0 | ||
| 0002e190:·2f31·3736·2020·2020·2020·2020·2020·2020··/176············ | 0002e190:·2f31·3736·2020·2020·2020·2020·2020·2020··/176············ | ||
| 0002e1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e1b0:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | 0002e1b0:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | ||
| 0002e1c0:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | 0002e1c0:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | ||
| 0002e1d0:·6766·616e·205f·6661·6e63·6f6d·6d6f·6e72··gfan·_fancommonr | 0002e1d0:·6766·616e·205f·6661·6e63·6f6d·6d6f·6e72··gfan·_fancommonr | ||
| 0002e1e0:·6566·696e·656d·656e·7420·2d2d·6865·6c70··efinement·--help | 0002e1e0:·6566·696e·656d·656e·7420·2d2d·6865·6c70··efinement·--help | ||
| 0002e1f0:·203c·202f·746d·702f·4d32·2d3 | 0002e1f0:·203c·202f·746d·702f·4d32·2d33·3630·3436···<·/tmp/M2-36046 | ||
| 0002e200:·3 | 0002e200:·3930·2d30·2f31·377c·0a7c·5468·6973·2070··90-0/17|.|This·p | ||
| 0002e210:·726f·6772·616d·2074·616b·6573·2074·776f··rogram·takes·two | 0002e210:·726f·6772·616d·2074·616b·6573·2074·776f··rogram·takes·two | ||
| 0002e220:·2070·6f6c·7968·6564·7261·6c20·6661·6e73···polyhedral·fans | 0002e220:·2070·6f6c·7968·6564·7261·6c20·6661·6e73···polyhedral·fans | ||
| 0002e230:·2061·6e64·2063·6f6d·7075·7465·7320·7468···and·computes·th | 0002e230:·2061·6e64·2063·6f6d·7075·7465·7320·7468···and·computes·th | ||
| 0002e240:·6569·7220·636f·6d6d·6f6e·2072·6566·696e··eir·common·refin | 0002e240:·6569·7220·636f·6d6d·6f6e·2072·6566·696e··eir·common·refin | ||
| 0002e250:·656d·656e·742e·207c·0a7c·4f70·7469·6f6e··ement.·|.|Option | 0002e250:·656d·656e·742e·207c·0a7c·4f70·7469·6f6e··ement.·|.|Option | ||
| 0002e260:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | 0002e260:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | ||
| 0002e270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 11844, 22 lines modified | Offset 11844, 22 lines modified | ||
| 0002e430:·2020·2020·2020·207c·0a7c·2043·6f6d·7075·········|.|·Compu | 0002e430:·2020·2020·2020·207c·0a7c·2043·6f6d·7075·········|.|·Compu | ||
| 0002e440:·7465·2074·6865·2073·7461·626c·6520·696e··te·the·stable·in | 0002e440:·7465·2074·6865·2073·7461·626c·6520·696e··te·the·stable·in | ||
| 0002e450:·7465·7273·6563·7469·6f6e·2e20·2020·2020··tersection.····· | 0002e450:·7465·7273·6563·7469·6f6e·2e20·2020·2020··tersection.····· | ||
| 0002e460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e480:·2020·2020·2020·207c·0a7c·7573·696e·6720·········|.|using· | 0002e480:·2020·2020·2020·207c·0a7c·7573·696e·6720·········|.|using· | ||
| 0002e490:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | 0002e490:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | ||
| 0002e4a0:·746d·702f·4d32·2d3 | 0002e4a0:·746d·702f·4d32·2d33·3630·3436·3930·2d30··tmp/M2-3604690-0 | ||
| 0002e4b0:·2f31·3738·2020·2020·2020·2020·2020·2020··/178············ | 0002e4b0:·2f31·3738·2020·2020·2020·2020·2020·2020··/178············ | ||
| 0002e4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e4d0:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | 0002e4d0:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | ||
| 0002e4e0:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | 0002e4e0:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | ||
| 0002e4f0:·6766·616e·205f·6661·6e6c·696e·6b20·2d2d··gfan·_fanlink·-- | 0002e4f0:·6766·616e·205f·6661·6e6c·696e·6b20·2d2d··gfan·_fanlink·-- | ||
| 0002e500:·6865·6c70·203c·202f·746d·702f·4d32·2d3 | 0002e500:·6865·6c70·203c·202f·746d·702f·4d32·2d33··help·<·/tmp/M2-3 | ||
| 0002e510:·3 | 0002e510:·3630·3436·3930·2d30·2f31·3830·2020·2020··604690-0/180···· | ||
| 0002e520:·2020·2020·2020·207c·0a7c·5468·6973·2070·········|.|This·p | 0002e520:·2020·2020·2020·207c·0a7c·5468·6973·2070·········|.|This·p | ||
| 0002e530:·726f·6772·616d·2074·616b·6573·2061·2070··rogram·takes·a·p | 0002e530:·726f·6772·616d·2074·616b·6573·2061·2070··rogram·takes·a·p | ||
| 0002e540:·6f6c·7968·6564·7261·6c20·6661·6e20·616e··olyhedral·fan·an | 0002e540:·6f6c·7968·6564·7261·6c20·6661·6e20·616e··olyhedral·fan·an | ||
| 0002e550:·6420·6120·7665·6374·6f72·2061·6e64·2063··d·a·vector·and·c | 0002e550:·6420·6120·7665·6374·6f72·2061·6e64·2063··d·a·vector·and·c | ||
| 0002e560:·6f6d·7075·7465·7320·7468·6520·6c69·6e6b··omputes·the·link | 0002e560:·6f6d·7075·7465·7320·7468·6520·6c69·6e6b··omputes·the·link | ||
| 0002e570:·206f·6620·7468·657c·0a7c·4f70·7469·6f6e···of·the|.|Option | 0002e570:·206f·6620·7468·657c·0a7c·4f70·7469·6f6e···of·the|.|Option | ||
| 0002e580:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | 0002e580:·733a·2020·2020·2020·2020·2020·2020·2020··s:·············· | ||
| Offset 11899, 22 lines modified | Offset 11899, 22 lines modified | ||
| 0002e7a0:·2020·2020·2020·207c·0a7c·2043·6f6d·7075·········|.|·Compu | 0002e7a0:·2020·2020·2020·207c·0a7c·2043·6f6d·7075·········|.|·Compu | ||
| 0002e7b0:·7465·7320·7468·6520·7374·6172·2069·6e73··tes·the·star·ins | 0002e7b0:·7465·7320·7468·6520·7374·6172·2069·6e73··tes·the·star·ins | ||
| 0002e7c0:·7465·6164·2e20·5468·6520·7374·6172·2069··tead.·The·star·i | 0002e7c0:·7465·6164·2e20·5468·6520·7374·6172·2069··tead.·The·star·i | ||
| 0002e7d0:·7320·6465·6669·6e65·6420·6173·2074·6865··s·defined·as·the | 0002e7d0:·7320·6465·6669·6e65·6420·6173·2074·6865··s·defined·as·the | ||
| 0002e7e0:·2073·6d61·6c6c·6573·7420·706f·6c79·6865···smallest·polyhe | 0002e7e0:·2073·6d61·6c6c·6573·7420·706f·6c79·6865···smallest·polyhe | ||
| 0002e7f0:·6472·616c·2066·617c·0a7c·7573·696e·6720··dral·fa|.|using· | 0002e7f0:·6472·616c·2066·617c·0a7c·7573·696e·6720··dral·fa|.|using· | ||
| 0002e800:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | 0002e800:·7465·6d70·6f72·6172·7920·6669·6c65·202f··temporary·file·/ | ||
| 0002e810:·746d·702f·4d32·2d3 | 0002e810:·746d·702f·4d32·2d33·3630·3436·3930·2d30··tmp/M2-3604690-0 | ||
| 0002e820:·2f31·3830·2020·2020·2020·2020·2020·2020··/180············ | 0002e820:·2f31·3830·2020·2020·2020·2020·2020·2020··/180············ | ||
| 0002e830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e840:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | 0002e840:·2020·2020·2020·207c·0a7c·202d·2d20·7275·········|.|·--·ru | ||
| 0002e850:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | 0002e850:·6e6e·696e·673a·202f·7573·722f·6269·6e2f··nning:·/usr/bin/ | ||
| 0002e860:·6766·616e·205f·6661·6e70·726f·6475·6374··gfan·_fanproduct | 0002e860:·6766·616e·205f·6661·6e70·726f·6475·6374··gfan·_fanproduct | ||
| 0002e870:·202d·2d68·656c·7020·3c20·2f74·6d70·2f4d···--help·<·/tmp/M | 0002e870:·202d·2d68·656c·7020·3c20·2f74·6d70·2f4d···--help·<·/tmp/M | ||
| 0002e880:·322d·3 | 0002e880:·322d·3336·3034·3639·302d·302f·3138·3220··2-3604690-0/182· | ||
| 0002e890:·2020·2020·2020·207c·0a7c·5468·6973·2070·········|.|This·p | 0002e890:·2020·2020·2020·207c·0a7c·5468·6973·2070·········|.|This·p | ||
| 0002e8a0:·726f·6772·616d·2074·616b·6573·2074·776f··rogram·takes·two | 0002e8a0:·726f·6772·616d·2074·616b·6573·2074·776f··rogram·takes·two | ||
| Max diff block lines reached; 65554/75163 bytes (87.22%) of diff not shown. | |||
| Offset 1, 3 lines modified | Offset 1, 101 lines modified | ||
| 00000000:·6465·7374·696e·6174·696f·6e3a·205f·5f5f··destination:·___ | |||
| 00000010:·4672·6565·5f5f·4f5f·5f49·5f5f·4d6f·6475··Free__O__I__Modu | |||
| 000000 | 00000000:·2d2d·202d·2a2d·204d·322d·636f·6d69·6e74··--·-*-·M2-comint | ||
| 00000010:·202d·2a2d·2068·6173·683a·2031·3734·3434···-*-·hash:·17444 | |||
| 00000020:·3136·3738·3330·3039·3932·3331·3133·320a··167830099231132. | |||
| 00000030:·0a69·3120·3a20·5020·3d20·6d61·6b65·506f··.i1·:·P·=·makePo | |||
| 00000040:·6c79·6e6f·6d69·616c·4f49·416c·6765·6272··lynomialOIAlgebr | |||
| 00000050:·6128·322c·2078·2c20·5151·293b·0a0a·6932··a(2,·x,·QQ);..i2 | |||
| 00000060:·203a·2046·203d·206d·616b·6546·7265·654f···:·F·=·makeFreeO | |||
| 00000070:·494d·6f64·756c·6528·652c·207b·312c·327d··IModule(e,·{1,2} | |||
| 00000080:·2c20·5029·3b0a·0a69·3320·3a20·696e·7374··,·P);..i3·:·inst | |||
| 00000090:·616c·6c47·656e·6572·6174·6f72·7349·6e57··allGeneratorsInW | |||
| 000000a0:·6964·7468·2846·2c20·3329·3b0a·0a69·3420··idth(F,·3);..i4· | |||
| 000000b0:·3a20·6220·3d20·785f·2831·2c32·292a·785f··:·b·=·x_(1,2)*x_ | |||
| 000000c0:·2831·2c31·292a·655f·2833·2c7b·327d·2c31··(1,1)*e_(3,{2},1 | |||
| 000000d0:·292b·785f·2832·2c32·292a·785f·2832·2c31··)+x_(2,2)*x_(2,1 | |||
| 000000e0:·292a·655f·2833·2c7b·312c·337d·2c32·293b··)*e_(3,{1,3},2); | |||
| 000000f0:·0a0a·6935·203a·2043·203d·206f·6952·6573··..i5·:·C·=·oiRes | |||
| 00000100:·287b·627d·2c20·3229·0a0a·6f35·203d·2030··({b},·2)..o5·=·0 | |||
| 00000110:·3a20·2865·302c·207b·337d·2c20·7b2d·327d··:·(e0,·{3},·{-2} | |||
| 00000120:·290a·2020·2020·2031·3a20·2865·312c·207b··).·····1:·(e1,·{ | |||
| 00000130:·352c·2035·7d2c·207b·2d34·2c20·2d33·7d29··5,·5},·{-4,·-3}) | |||
| 00000140:·0a20·2020·2020·323a·2028·6532·2c20·7b36··.·····2:·(e2,·{6 | |||
| 00000150:·2c20·362c·2036·2c20·362c·2036·2c20·362c··,·6,·6,·6,·6,·6, | |||
| 00000160:·2036·2c20·362c·2036·7d2c·207b·2d34·2c20···6,·6,·6},·{-4,· | |||
| 00000170:·2d33·2c20·2d33·2c20·2d32·2c20·2d34·2c20··-3,·-3,·-2,·-4,· | |||
| 00000180:·2d35·2c20·2d34·2c20·2d35·2c20·2d35·7d29··-5,·-4,·-5,·-5}) | |||
| 00000190:·0a0a·6f35·203a·204f·4952·6573·6f6c·7574··..o5·:·OIResolut | |||
| 000001a0:·696f·6e0a·0a69·3620·3a20·7068·6920·3d20··ion..i6·:·phi·=· | |||
| 000001b0:·432e·6464·5f31·0a0a·6f36·203d·2053·6f75··C.dd_1..o6·=·Sou | |||
| 000001c0:·7263·653a·2028·6531·2c20·7b35·2c20·357d··rce:·(e1,·{5,·5} | |||
| 000001d0:·2c20·7b2d·342c·202d·337d·2920·5461·7267··,·{-4,·-3})·Targ | |||
| 000001e0:·6574·3a20·2865·302c·207b·337d·2c20·7b2d··et:·(e0,·{3},·{- | |||
| 000001f0:·327d·290a·0a6f·3620·3a20·4672·6565·4f49··2})..o6·:·FreeOI | |||
| 00000200:·4d6f·6475·6c65·4d61·700a·0a69·3720·3a20··ModuleMap..i7·:· | |||
| 00000210:·4720·3d20·6765·7442·6173·6973·456c·656d··G·=·getBasisElem | |||
| 00000220:·656e·7473·2043·5f31·0a0a·6f37·203d·207b··ents·C_1..o7·=·{ | |||
| 00000230:·3165·3120·2020·2020·2020·2020·2020·2020··1e1············· | |||
| 00000240:·2020·2020·2020·2c20·3165·3120·2020·2020········,·1e1····· | |||
| 00000250:·2020·2020·2020·2020·2020·2020·2020·7d0a················}. | |||
| 00000260:·2020·2020·2020·2020·2035·2c7b·312c·2032···········5,{1,·2 | |||
| 00000270:·2c20·332c·2034·2c20·357d·2c31·2020·2020··,·3,·4,·5},1···· | |||
| 00000280:·2035·2c7b·312c·2032·2c20·332c·2034·2c20···5,{1,·2,·3,·4,· | |||
| 00000290:·357d·2c32·0a0a·6f37·203a·204c·6973·740a··5},2..o7·:·List. | |||
| 000002a0:·0a69·3820·3a20·7068·6920·4723·300a·0a6f··.i8·:·phi·G#0..o | |||
| 000002b0:·3820·3d20·7820·2020·7820·2020·6530·2020··8·=·x···x···e0·· | |||
| 000002c0:·2020·2020·2020·2020·2020·2020·2d20·7820··············-·x· | |||
| 000002d0:·2020·7820·2020·6530·2020·2020·2020·2020····x···e0········ | |||
| 000002e0:·2020·2020·2020·2d20·7820·2020·7820·2020········-·x···x··· | |||
| 000002f0:·6530·2020·2020·2020·2020·2020·2020·2020··e0·············· | |||
| 00000300:·2b20·7820·2020·7820·2020·6530·0a20·2020··+·x···x···e0.··· | |||
| 00000310:·2020·2032·2c33·2031·2c31·2020·352c·7b32·····2,3·1,1··5,{2 | |||
| 00000320:·2c20·342c·2035·7d2c·3120·2020·2032·2c34··,·4,·5},1····2,4 | |||
| 00000330:·2031·2c31·2020·352c·7b32·2c20·332c·2035···1,1··5,{2,·3,·5 | |||
| 00000340:·7d2c·3120·2020·2032·2c33·2031·2c32·2020··},1····2,3·1,2·· | |||
| 00000350:·352c·7b31·2c20·342c·2035·7d2c·3120·2020··5,{1,·4,·5},1··· | |||
| 00000360:·2032·2c34·2031·2c32·2020·352c·7b31·2c20···2,4·1,2··5,{1,· | |||
| 00000370:·332c·2035·7d2c·310a·0a20·2020·2020·2020··3,·5},1..······· | |||
| 00000380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000003a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000003b0:·2020·2020·2020·2020·2020·2020·2020·3130················10 | |||
| 000003c0:·0a6f·3820·3a20·2851·515b·7820·2020·2c20··.o8·:·(QQ[x···,· | |||
| 000003d0:·7820·2020·2c20·7820·2020·2c20·7820·2020··x···,·x···,·x··· | |||
| 000003e0:·2c20·7820·2020·2c20·7820·2020·2c20·7820··,·x···,·x···,·x· | |||
| 000003f0:·2020·2c20·7820·2020·2c20·7820·2020·2c20····,·x···,·x···,· | |||
| 00000400:·7820·2020·5d29·2020·2069·6e20·7769·6474··x···])···in·widt | |||
| 00000410:·6820·352c·2064·6567·7265·6573·207b·322c··h·5,·degrees·{2, | |||
| 00000420:·2032·2c20·322c·2032·2c20·322c·2032·2c20···2,·2,·2,·2,·2,· | |||
| 00000430:·322c·2032·2c20·322c·2032·7d0a·2020·2020··2,·2,·2,·2}.···· | |||
| 00000440:·2020·2020·2020·322c·3520·2020·322c·3420········2,5···2,4· | |||
| 00000450:·2020·322c·3320·2020·322c·3220·2020·322c····2,3···2,2···2, | |||
| 00000460:·3120·2020·312c·3520·2020·312c·3420·2020··1···1,5···1,4··· | |||
| 00000470:·312c·3320·2020·312c·3220·2020·312c·310a··1,3···1,2···1,1. | |||
| 00000480:·0a69·3920·3a20·7068·6920·4723·310a·0a6f··.i9·:·phi·G#1..o | |||
| 00000490:·3920·3d20·2d78·2020·2065·3020·2020·2020··9·=·-x···e0····· | |||
| 000004a0:·2020·2020·2020·2020·202b·2078·2020·2065···········+·x···e | |||
| 000004b0:·3020·2020·2020·2020·2020·2020·2020·202b··0··············+ | |||
| 000004c0:·2078·2020·2065·3020·2020·2020·2020·2020···x···e0········· | |||
| 000004d0:·2020·2020·202d·2078·2020·2065·300a·2020·······-·x···e0.·· | |||
| 000004e0:·2020·2020·2032·2c32·2020·352c·7b31·2c20·······2,2··5,{1,· | |||
| 000004f0:·332c·2035·7d2c·3120·2020·2032·2c32·2020··3,·5},1····2,2·· | |||
| 00000500:·352c·7b31·2c20·332c·2034·7d2c·3120·2020··5,{1,·3,·4},1··· | |||
| 00000510:·2032·2c33·2020·352c·7b31·2c20·322c·2035···2,3··5,{1,·2,·5 | |||
| 00000520:·7d2c·3120·2020·2032·2c33·2020·352c·7b31··},1····2,3··5,{1 | |||
| 00000530:·2c20·322c·2034·7d2c·310a·0a20·2020·2020··,·2,·4},1..····· | |||
| 00000540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00000580:·3130·0a6f·3920·3a20·2851·515b·7820·2020··10.o9·:·(QQ[x··· | |||
| 00000590:·2c20·7820·2020·2c20·7820·2020·2c20·7820··,·x···,·x···,·x· | |||
| 000005a0:·2020·2c20·7820·2020·2c20·7820·2020·2c20····,·x···,·x···,· | |||
| 000005b0:·7820·2020·2c20·7820·2020·2c20·7820·2020··x···,·x···,·x··· | |||
| 000005c0:·2c20·7820·2020·5d29·2020·2069·6e20·7769··,·x···])···in·wi | |||
| 000005d0:·6474·6820·352c·2064·6567·7265·6573·207b··dth·5,·degrees·{ | |||
| 000005e0:·322c·2032·2c20·322c·2032·2c20·322c·2032··2,·2,·2,·2,·2,·2 | |||
| 000005f0:·2c20·322c·2032·2c20·322c·2032·7d0a·2020··,·2,·2,·2,·2}.·· | |||
| 00000600:·2020·2020·2020·2020·322c·3520·2020·322c··········2,5···2, | |||
| 00000610:·3420·2020·322c·3320·2020·322c·3220·2020··4···2,3···2,2··· | |||
| 00000620:·322c·3120·2020·312c·3520·2020·312c·3420··2,1···1,5···1,4· | |||
| 00000630:·2020·312c·3320·2020·312c·3220·2020·312c····1,3···1,2···1, | |||
| 00000640:·310a·0a69·3130·203a·200a·················1..i10·:·. |
| Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
| 1 | -rw-r--r--···0········0········0········4·2024-11-03·00:49:13.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2024-11-03·00:49:13.000000·debian-binary |
| 2 | -rw-r--r--···0········0········0·····2120·2024-11-03·00:49:13.000000·control.tar.xz | 2 | -rw-r--r--···0········0········0·····2120·2024-11-03·00:49:13.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0··257 | 3 | -rw-r--r--···0········0········0··2578492·2024-11-03·00:49:13.000000·data.tar.xz |
| Offset 3498, 42 lines modified | Offset 3498, 42 lines modified | ||
| 3498 | 0000000000849638··0000000000000008·R_X86_64_RELATIVE·························857190 | 3498 | 0000000000849638··0000000000000008·R_X86_64_RELATIVE·························857190 |
| 3499 | 0000000000849640··0000000000000008·R_X86_64_RELATIVE·························857280 | 3499 | 0000000000849640··0000000000000008·R_X86_64_RELATIVE·························857280 |
| 3500 | 0000000000849648··0000000000000008·R_X86_64_RELATIVE·························857118 | 3500 | 0000000000849648··0000000000000008·R_X86_64_RELATIVE·························857118 |
| 3501 | 0000000000849650··0000000000000008·R_X86_64_RELATIVE·························6fc840 | 3501 | 0000000000849650··0000000000000008·R_X86_64_RELATIVE·························6fc840 |
| 3502 | 0000000000849658··0000000000000008·R_X86_64_RELATIVE·························55a2d0 | 3502 | 0000000000849658··0000000000000008·R_X86_64_RELATIVE·························55a2d0 |
| 3503 | 0000000000849660··0000000000000008·R_X86_64_RELATIVE·························55a2f0 | 3503 | 0000000000849660··0000000000000008·R_X86_64_RELATIVE·························55a2f0 |
| 3504 | 0000000000849668··0000000000000008·R_X86_64_RELATIVE·························55cf30 | 3504 | 0000000000849668··0000000000000008·R_X86_64_RELATIVE·························55cf30 |
| 3505 | 0000000000849680··0000000000000008·R_X86_64_RELATIVE·························6d610 | 3505 | 0000000000849680··0000000000000008·R_X86_64_RELATIVE·························6d6102 |
| 3506 | 0000000000849688··0000000000000008·R_X86_64_RELATIVE·························6d610 | 3506 | 0000000000849688··0000000000000008·R_X86_64_RELATIVE·························6d6102 |
| 3507 | 0000000000849690··0000000000000008·R_X86_64_RELATIVE·························6d612 | 3507 | 0000000000849690··0000000000000008·R_X86_64_RELATIVE·························6d6126 |
| 3508 | 0000000000849698··0000000000000008·R_X86_64_RELATIVE·························6d614 | 3508 | 0000000000849698··0000000000000008·R_X86_64_RELATIVE·························6d6146 |
| 3509 | 00000000008496a0··0000000000000008·R_X86_64_RELATIVE·························6d637 | 3509 | 00000000008496a0··0000000000000008·R_X86_64_RELATIVE·························6d6372 |
| 3510 | 00000000008496a8··0000000000000008·R_X86_64_RELATIVE·························6d637 | 3510 | 00000000008496a8··0000000000000008·R_X86_64_RELATIVE·························6d6375 |
| 3511 | 00000000008496b0··0000000000000008·R_X86_64_RELATIVE·························6d637 | 3511 | 00000000008496b0··0000000000000008·R_X86_64_RELATIVE·························6d6379 |
| 3512 | 00000000008496b8··0000000000000008·R_X86_64_RELATIVE·························6d63 | 3512 | 00000000008496b8··0000000000000008·R_X86_64_RELATIVE·························6d637d |
| 3513 | 00000000008496c0··0000000000000008·R_X86_64_RELATIVE·························6d638 | 3513 | 00000000008496c0··0000000000000008·R_X86_64_RELATIVE·························6d6382 |
| 3514 | 00000000008496c8··0000000000000008·R_X86_64_RELATIVE·························6d638 | 3514 | 00000000008496c8··0000000000000008·R_X86_64_RELATIVE·························6d6388 |
| 3515 | 00000000008496d0··0000000000000008·R_X86_64_RELATIVE·························6d63 | 3515 | 00000000008496d0··0000000000000008·R_X86_64_RELATIVE·························6d638f |
| 3516 | 00000000008496d8··0000000000000008·R_X86_64_RELATIVE·························6d639 | 3516 | 00000000008496d8··0000000000000008·R_X86_64_RELATIVE·························6d6397 |
| 3517 | 00000000008496e0··0000000000000008·R_X86_64_RELATIVE·························6d63a | 3517 | 00000000008496e0··0000000000000008·R_X86_64_RELATIVE·························6d63a0 |
| 3518 | 00000000008496e8··0000000000000008·R_X86_64_RELATIVE·························6d63a | 3518 | 00000000008496e8··0000000000000008·R_X86_64_RELATIVE·························6d63aa |
| 3519 | 00000000008496f0··0000000000000008·R_X86_64_RELATIVE·························6d63b | 3519 | 00000000008496f0··0000000000000008·R_X86_64_RELATIVE·························6d63b5 |
| 3520 | 00000000008496f8··0000000000000008·R_X86_64_RELATIVE·························6d63c | 3520 | 00000000008496f8··0000000000000008·R_X86_64_RELATIVE·························6d63c1 |
| 3521 | 0000000000849700··0000000000000008·R_X86_64_RELATIVE·························6d63 | 3521 | 0000000000849700··0000000000000008·R_X86_64_RELATIVE·························6d63cf |
| 3522 | 0000000000849708··0000000000000008·R_X86_64_RELATIVE·························6d63 | 3522 | 0000000000849708··0000000000000008·R_X86_64_RELATIVE·························6d63de |
| 3523 | 0000000000849710··0000000000000008·R_X86_64_RELATIVE·························6d63 | 3523 | 0000000000849710··0000000000000008·R_X86_64_RELATIVE·························6d63ee |
| 3524 | 0000000000849718··0000000000000008·R_X86_64_RELATIVE·························6d6 | 3524 | 0000000000849718··0000000000000008·R_X86_64_RELATIVE·························6d63ff |
| 3525 | 0000000000849720··0000000000000008·R_X86_64_RELATIVE·························6d641 | 3525 | 0000000000849720··0000000000000008·R_X86_64_RELATIVE·························6d6412 |
| 3526 | 0000000000849728··0000000000000008·R_X86_64_RELATIVE·························6d642 | 3526 | 0000000000849728··0000000000000008·R_X86_64_RELATIVE·························6d6426 |
| 3527 | 0000000000849730··0000000000000008·R_X86_64_RELATIVE·························6d643 | 3527 | 0000000000849730··0000000000000008·R_X86_64_RELATIVE·························6d643b |
| 3528 | 0000000000849738··0000000000000008·R_X86_64_RELATIVE·························6d645 | 3528 | 0000000000849738··0000000000000008·R_X86_64_RELATIVE·························6d6452 |
| 3529 | 0000000000849740··0000000000000008·R_X86_64_RELATIVE·························6d646 | 3529 | 0000000000849740··0000000000000008·R_X86_64_RELATIVE·························6d646a |
| 3530 | 0000000000849748··0000000000000008·R_X86_64_RELATIVE·························6d648 | 3530 | 0000000000849748··0000000000000008·R_X86_64_RELATIVE·························6d6483 |
| 3531 | 0000000000849750··0000000000000008·R_X86_64_RELATIVE·························6d64 | 3531 | 0000000000849750··0000000000000008·R_X86_64_RELATIVE·························6d649e |
| 3532 | 0000000000849758··0000000000000008·R_X86_64_RELATIVE·························6d64b | 3532 | 0000000000849758··0000000000000008·R_X86_64_RELATIVE·························6d64ba |
| 3533 | 0000000000849760··0000000000000008·R_X86_64_RELATIVE·························6f3368 | 3533 | 0000000000849760··0000000000000008·R_X86_64_RELATIVE·························6f3368 |
| 3534 | 0000000000849768··0000000000000008·R_X86_64_RELATIVE·························6f3388 | 3534 | 0000000000849768··0000000000000008·R_X86_64_RELATIVE·························6f3388 |
| 3535 | 0000000000849770··0000000000000008·R_X86_64_RELATIVE·························6f33a8 | 3535 | 0000000000849770··0000000000000008·R_X86_64_RELATIVE·························6f33a8 |
| 3536 | 0000000000849778··0000000000000008·R_X86_64_RELATIVE·························6f33d0 | 3536 | 0000000000849778··0000000000000008·R_X86_64_RELATIVE·························6f33d0 |
| 3537 | 0000000000849780··0000000000000008·R_X86_64_RELATIVE·························6f33f8 | 3537 | 0000000000849780··0000000000000008·R_X86_64_RELATIVE·························6f33f8 |
| 3538 | 0000000000849788··0000000000000008·R_X86_64_RELATIVE·························6f3420 | 3538 | 0000000000849788··0000000000000008·R_X86_64_RELATIVE·························6f3420 |
| 3539 | 0000000000849790··0000000000000008·R_X86_64_RELATIVE·························6f3448 | 3539 | 0000000000849790··0000000000000008·R_X86_64_RELATIVE·························6f3448 |
| Offset 9774, 28 lines modified | Offset 9774, 28 lines modified | ||
| 9774 | 000000000085a290··0000000000000008·R_X86_64_RELATIVE·························6d3dea | 9774 | 000000000085a290··0000000000000008·R_X86_64_RELATIVE·························6d3dea |
| 9775 | 000000000085a298··0000000000000008·R_X86_64_RELATIVE·························6d327d | 9775 | 000000000085a298··0000000000000008·R_X86_64_RELATIVE·························6d327d |
| 9776 | 000000000085a2a0··0000000000000008·R_X86_64_RELATIVE·························6d561e | 9776 | 000000000085a2a0··0000000000000008·R_X86_64_RELATIVE·························6d561e |
| 9777 | 000000000085a2a8··0000000000000008·R_X86_64_RELATIVE·························6d5a08 | 9777 | 000000000085a2a8··0000000000000008·R_X86_64_RELATIVE·························6d5a08 |
| 9778 | 000000000085a2b0··0000000000000008·R_X86_64_RELATIVE·························6d5abe | 9778 | 000000000085a2b0··0000000000000008·R_X86_64_RELATIVE·························6d5abe |
| 9779 | 000000000085a2b8··0000000000000008·R_X86_64_RELATIVE·························6d45ae | 9779 | 000000000085a2b8··0000000000000008·R_X86_64_RELATIVE·························6d45ae |
| 9780 | 000000000085a2c0··0000000000000008·R_X86_64_RELATIVE·························6d44f8 | 9780 | 000000000085a2c0··0000000000000008·R_X86_64_RELATIVE·························6d44f8 |
| 9781 | 000000000085a2c8··0000000000000008·R_X86_64_RELATIVE·························6d620 | 9781 | 000000000085a2c8··0000000000000008·R_X86_64_RELATIVE·························6d6204 |
| 9782 | 000000000085a2d0··0000000000000008·R_X86_64_RELATIVE·························6d3d1b | 9782 | 000000000085a2d0··0000000000000008·R_X86_64_RELATIVE·························6d3d1b |
| 9783 | 000000000085a2d8··0000000000000008·R_X86_64_RELATIVE·························6d3d1b | 9783 | 000000000085a2d8··0000000000000008·R_X86_64_RELATIVE·························6d3d1b |
| 9784 | 000000000085a2e0··0000000000000008·R_X86_64_RELATIVE·························6d5a13 | 9784 | 000000000085a2e0··0000000000000008·R_X86_64_RELATIVE·························6d5a13 |
| 9785 | 000000000085a2e8··0000000000000008·R_X86_64_RELATIVE·························6d5a16 | 9785 | 000000000085a2e8··0000000000000008·R_X86_64_RELATIVE·························6d5a16 |
| 9786 | 000000000085a2f0··0000000000000008·R_X86_64_RELATIVE·························6d3d1a | 9786 | 000000000085a2f0··0000000000000008·R_X86_64_RELATIVE·························6d3d1a |
| 9787 | 000000000085a2f8··0000000000000008·R_X86_64_RELATIVE·························6d31b5 | 9787 | 000000000085a2f8··0000000000000008·R_X86_64_RELATIVE·························6d31b5 |
| 9788 | 000000000085a300··0000000000000008·R_X86_64_RELATIVE·························6d5bb3 | 9788 | 000000000085a300··0000000000000008·R_X86_64_RELATIVE·························6d5bb3 |
| 9789 | 000000000085a308··0000000000000008·R_X86_64_RELATIVE·························6d4984 | 9789 | 000000000085a308··0000000000000008·R_X86_64_RELATIVE·························6d4984 |
| 9790 | 000000000085a310··0000000000000008·R_X86_64_RELATIVE·························6d65 | 9790 | 000000000085a310··0000000000000008·R_X86_64_RELATIVE·························6d652d |
| 9791 | 000000000085a318··0000000000000008·R_X86_64_RELATIVE·························6d466a | 9791 | 000000000085a318··0000000000000008·R_X86_64_RELATIVE·························6d466a |
| 9792 | 000000000085a320··0000000000000008·R_X86_64_RELATIVE·························6d4510 | 9792 | 000000000085a320··0000000000000008·R_X86_64_RELATIVE·························6d4510 |
| 9793 | 000000000085a328··0000000000000008·R_X86_64_RELATIVE·························6d5a19 | 9793 | 000000000085a328··0000000000000008·R_X86_64_RELATIVE·························6d5a19 |
| 9794 | 000000000085a330··0000000000000008·R_X86_64_RELATIVE·························6d619 | 9794 | 000000000085a330··0000000000000008·R_X86_64_RELATIVE·························6d619b |
| 9795 | 000000000085a338··0000000000000008·R_X86_64_RELATIVE·························6d5e0c | 9795 | 000000000085a338··0000000000000008·R_X86_64_RELATIVE·························6d5e0c |
| 9796 | 000000000085a340··0000000000000008·R_X86_64_RELATIVE·························6d4ab4 | 9796 | 000000000085a340··0000000000000008·R_X86_64_RELATIVE·························6d4ab4 |
| 9797 | 000000000085a348··0000000000000008·R_X86_64_RELATIVE·························6d5251 | 9797 | 000000000085a348··0000000000000008·R_X86_64_RELATIVE·························6d5251 |
| 9798 | 000000000085a350··0000000000000008·R_X86_64_RELATIVE·························6d5308 | 9798 | 000000000085a350··0000000000000008·R_X86_64_RELATIVE·························6d5308 |
| 9799 | 000000000085a358··0000000000000008·R_X86_64_RELATIVE·························6d3d1b | 9799 | 000000000085a358··0000000000000008·R_X86_64_RELATIVE·························6d3d1b |
| 9800 | 000000000085a360··0000000000000008·R_X86_64_RELATIVE·························6d3d1b | 9800 | 000000000085a360··0000000000000008·R_X86_64_RELATIVE·························6d3d1b |
| 9801 | 000000000085a368··0000000000000008·R_X86_64_RELATIVE·························6d3d1b | 9801 | 000000000085a368··0000000000000008·R_X86_64_RELATIVE·························6d3d1b |
| Offset 9807, 15 lines modified | Offset 9807, 15 lines modified | ||
| 9807 | 000000000085a398··0000000000000008·R_X86_64_RELATIVE·························6d5a50 | 9807 | 000000000085a398··0000000000000008·R_X86_64_RELATIVE·························6d5a50 |
| 9808 | 000000000085a3a0··0000000000000008·R_X86_64_RELATIVE·························6d5a95 | 9808 | 000000000085a3a0··0000000000000008·R_X86_64_RELATIVE·························6d5a95 |
| 9809 | 000000000085a3a8··0000000000000008·R_X86_64_RELATIVE·························6d4650 | 9809 | 000000000085a3a8··0000000000000008·R_X86_64_RELATIVE·························6d4650 |
| 9810 | 000000000085a3b0··0000000000000008·R_X86_64_RELATIVE·························6d58d7 | 9810 | 000000000085a3b0··0000000000000008·R_X86_64_RELATIVE·························6d58d7 |
| 9811 | 000000000085a3b8··0000000000000008·R_X86_64_RELATIVE·························6d5a74 | 9811 | 000000000085a3b8··0000000000000008·R_X86_64_RELATIVE·························6d5a74 |
| 9812 | 000000000085a3c0··0000000000000008·R_X86_64_RELATIVE·························6d5a1b | 9812 | 000000000085a3c0··0000000000000008·R_X86_64_RELATIVE·························6d5a1b |
| 9813 | 000000000085a3c8··0000000000000008·R_X86_64_RELATIVE·························6d3e9b | 9813 | 000000000085a3c8··0000000000000008·R_X86_64_RELATIVE·························6d3e9b |
| 9814 | 000000000085a3d0··0000000000000008·R_X86_64_RELATIVE·························6d618 | 9814 | 000000000085a3d0··0000000000000008·R_X86_64_RELATIVE·························6d6182 |
| 9815 | 000000000085a3d8··0000000000000008·R_X86_64_RELATIVE·························6d59d7 | 9815 | 000000000085a3d8··0000000000000008·R_X86_64_RELATIVE·························6d59d7 |
| 9816 | 000000000085a3e0··0000000000000008·R_X86_64_RELATIVE·························6d5b02 | 9816 | 000000000085a3e0··0000000000000008·R_X86_64_RELATIVE·························6d5b02 |
| 9817 | 000000000085a3e8··0000000000000008·R_X86_64_RELATIVE·························6d5a1d | 9817 | 000000000085a3e8··0000000000000008·R_X86_64_RELATIVE·························6d5a1d |
| 9818 | 000000000085a3f0··0000000000000008·R_X86_64_RELATIVE·························6d5af6 | 9818 | 000000000085a3f0··0000000000000008·R_X86_64_RELATIVE·························6d5af6 |
| 9819 | 000000000085a3f8··0000000000000008·R_X86_64_RELATIVE·························6d4660 | 9819 | 000000000085a3f8··0000000000000008·R_X86_64_RELATIVE·························6d4660 |
| 9820 | 000000000085a400··0000000000000008·R_X86_64_RELATIVE·························6d5a49 | 9820 | 000000000085a400··0000000000000008·R_X86_64_RELATIVE·························6d5a49 |
| 9821 | 000000000085a408··0000000000000008·R_X86_64_RELATIVE·························6d5a4c | 9821 | 000000000085a408··0000000000000008·R_X86_64_RELATIVE·························6d5a4c |
| Offset 9945, 26 lines modified | Offset 9945, 26 lines modified | ||
| 9945 | 000000000085a7f8··0000000000000008·R_X86_64_RELATIVE·························6d4c7a | 9945 | 000000000085a7f8··0000000000000008·R_X86_64_RELATIVE·························6d4c7a |
| 9946 | 000000000085a800··0000000000000008·R_X86_64_RELATIVE·························6d5a53 | 9946 | 000000000085a800··0000000000000008·R_X86_64_RELATIVE·························6d5a53 |
| 9947 | 000000000085a808··0000000000000008·R_X86_64_RELATIVE·························6d58bc | 9947 | 000000000085a808··0000000000000008·R_X86_64_RELATIVE·························6d58bc |
| 9948 | 000000000085a810··0000000000000008·R_X86_64_RELATIVE·························6d5a7a | 9948 | 000000000085a810··0000000000000008·R_X86_64_RELATIVE·························6d5a7a |
| 9949 | 000000000085a818··0000000000000008·R_X86_64_RELATIVE·························6d5a1e | 9949 | 000000000085a818··0000000000000008·R_X86_64_RELATIVE·························6d5a1e |
| 9950 | 000000000085a820··0000000000000008·R_X86_64_RELATIVE·························6d5a59 | 9950 | 000000000085a820··0000000000000008·R_X86_64_RELATIVE·························6d5a59 |
| 9951 | 000000000085a828··0000000000000008·R_X86_64_RELATIVE·························6d5e2d | 9951 | 000000000085a828··0000000000000008·R_X86_64_RELATIVE·························6d5e2d |
| 9952 | 000000000085a830··0000000000000008·R_X86_64_RELATIVE·························6d65 | 9952 | 000000000085a830··0000000000000008·R_X86_64_RELATIVE·························6d652d |
| 9953 | 000000000085a838··0000000000000008·R_X86_64_RELATIVE·························6d4571 | 9953 | 000000000085a838··0000000000000008·R_X86_64_RELATIVE·························6d4571 |
| 9954 | 000000000085a840··0000000000000008·R_X86_64_RELATIVE·························6d618 | 9954 | 000000000085a840··0000000000000008·R_X86_64_RELATIVE·························6d6182 |
| 9955 | 000000000085a848··0000000000000008·R_X86_64_RELATIVE·························6d618 | 9955 | 000000000085a848··0000000000000008·R_X86_64_RELATIVE·························6d6189 |
| 9956 | 000000000085a850··0000000000000008·R_X86_64_RELATIVE·························6d466a | 9956 | 000000000085a850··0000000000000008·R_X86_64_RELATIVE·························6d466a |
| 9957 | 000000000085a858··0000000000000008·R_X86_64_RELATIVE·························6d4166 | 9957 | 000000000085a858··0000000000000008·R_X86_64_RELATIVE·························6d4166 |
| 9958 | 000000000085a860··0000000000000008·R_X86_64_RELATIVE·························6d4510 | 9958 | 000000000085a860··0000000000000008·R_X86_64_RELATIVE·························6d4510 |
| 9959 | 000000000085a868··0000000000000008·R_X86_64_RELATIVE·························6d498c | 9959 | 000000000085a868··0000000000000008·R_X86_64_RELATIVE·························6d498c |
| 9960 | 000000000085a870··0000000000000008·R_X86_64_RELATIVE·························6d5a19 | 9960 | 000000000085a870··0000000000000008·R_X86_64_RELATIVE·························6d5a19 |
| 9961 | 000000000085a878··0000000000000008·R_X86_64_RELATIVE·························6d5d7d | 9961 | 000000000085a878··0000000000000008·R_X86_64_RELATIVE·························6d5d7d |
| 9962 | 000000000085a880··0000000000000008·R_X86_64_RELATIVE·························6d619 | 9962 | 000000000085a880··0000000000000008·R_X86_64_RELATIVE·························6d619b |
| 9963 | 000000000085a888··0000000000000008·R_X86_64_RELATIVE·························6d617 | 9963 | 000000000085a888··0000000000000008·R_X86_64_RELATIVE·························6d6176 |
| 9964 | 000000000085a890··0000000000000008·R_X86_64_RELATIVE·························6d5a71 | 9964 | 000000000085a890··0000000000000008·R_X86_64_RELATIVE·························6d5a71 |
| 9965 | 000000000085a898··0000000000000008·R_X86_64_RELATIVE·························6d5ca1 | 9965 | 000000000085a898··0000000000000008·R_X86_64_RELATIVE·························6d5ca1 |
| 9966 | 000000000085a8a0··0000000000000008·R_X86_64_RELATIVE·························6d5cb4 | 9966 | 000000000085a8a0··0000000000000008·R_X86_64_RELATIVE·························6d5cb4 |
| 9967 | 000000000085a8a8··0000000000000008·R_X86_64_RELATIVE·························6d5cc2 | 9967 | 000000000085a8a8··0000000000000008·R_X86_64_RELATIVE·························6d5cc2 |
| 9968 | 000000000085a8b0··0000000000000008·R_X86_64_RELATIVE·························6d5cd6 | 9968 | 000000000085a8b0··0000000000000008·R_X86_64_RELATIVE·························6d5cd6 |
| 9969 | 000000000085a8b8··0000000000000008·R_X86_64_RELATIVE·························6d5cdc | 9969 | 000000000085a8b8··0000000000000008·R_X86_64_RELATIVE·························6d5cdc |
| 9970 | 000000000085a8c0··0000000000000008·R_X86_64_RELATIVE·························6d3d1b | 9970 | 000000000085a8c0··0000000000000008·R_X86_64_RELATIVE·························6d3d1b |
| Offset 9972, 36 lines modified | Offset 9972, 36 lines modified | ||
| 9972 | 000000000085a9c8··0000000000000008·R_X86_64_RELATIVE·························6d5e2a | 9972 | 000000000085a9c8··0000000000000008·R_X86_64_RELATIVE·························6d5e2a |
| 9973 | 000000000085a9e0··0000000000000008·R_X86_64_RELATIVE·························85aa20 | 9973 | 000000000085a9e0··0000000000000008·R_X86_64_RELATIVE·························85aa20 |
| 9974 | 000000000085aa20··0000000000000008·R_X86_64_RELATIVE·························6d5e2f | 9974 | 000000000085aa20··0000000000000008·R_X86_64_RELATIVE·························6d5e2f |
| 9975 | 000000000085aa28··0000000000000008·R_X86_64_RELATIVE·························542860 | 9975 | 000000000085aa28··0000000000000008·R_X86_64_RELATIVE·························542860 |
| 9976 | 000000000085aa38··0000000000000008·R_X86_64_RELATIVE·························6d5e36 | 9976 | 000000000085aa38··0000000000000008·R_X86_64_RELATIVE·························6d5e36 |
| 9977 | 000000000085aa70··0000000000000008·R_X86_64_RELATIVE·························6f32c8 | 9977 | 000000000085aa70··0000000000000008·R_X86_64_RELATIVE·························6f32c8 |
| 9978 | 000000000085aa78··0000000000000008·R_X86_64_RELATIVE·························6f32f0 | 9978 | 000000000085aa78··0000000000000008·R_X86_64_RELATIVE·························6f32f0 |
| 9979 | 000000000085aa80··0000000000000008·R_X86_64_RELATIVE·························6d655 | 9979 | 000000000085aa80··0000000000000008·R_X86_64_RELATIVE·························6d6553 |
| 9980 | 000000000085aa88··0000000000000008·R_X86_64_RELATIVE·························6d62 | 9980 | 000000000085aa88··0000000000000008·R_X86_64_RELATIVE·························6d626e |
| 9981 | 000000000085aa90··0000000000000008·R_X86_64_RELATIVE·························6d635 | 9981 | 000000000085aa90··0000000000000008·R_X86_64_RELATIVE·························6d635b |
| 9982 | 000000000085aa98··0000000000000008·R_X86_64_RELATIVE·························6f2af8 | 9982 | 000000000085aa98··0000000000000008·R_X86_64_RELATIVE·························6f2af8 |
| 9983 | 000000000085aaa0··0000000000000008·R_X86_64_RELATIVE·························6f3318 | 9983 | 000000000085aaa0··0000000000000008·R_X86_64_RELATIVE·························6f3318 |
| Max diff block lines reached; 2593/16653 bytes (15.57%) of diff not shown. | |||
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | Displaying·notes·found·in:·.note.gnu.property | 1 | Displaying·notes·found·in:·.note.gnu.property |
| 2 | ··Owner················Data·size·» Description | 2 | ··Owner················Data·size·» Description |
| 3 | ··GNU··················0x00000010» NT_GNU_PROPERTY_TYPE_0» ······Properties:·x86·ISA·needed:·x86-64-baseline | 3 | ··GNU··················0x00000010» NT_GNU_PROPERTY_TYPE_0» ······Properties:·x86·ISA·needed:·x86-64-baseline |
| 4 | Displaying·notes·found·in:·.note.gnu.build-id | 4 | Displaying·notes·found·in:·.note.gnu.build-id |
| 5 | ··Owner················Data·size·» Description | 5 | ··Owner················Data·size·» Description |
| 6 | ··GNU··················0x00000014» NT_GNU_BUILD_ID·(unique·build·ID·bitstring)» ····Build·ID:·7 | 6 | ··GNU··················0x00000014» NT_GNU_BUILD_ID·(unique·build·ID·bitstring)» ····Build·ID:·a9722da9714e39e4e5a4d717c943ae4df094d501 |
| 7 | Displaying·notes·found·in:·.note.ABI-tag | 7 | Displaying·notes·found·in:·.note.ABI-tag |
| 8 | ··Owner················Data·size·» Description | 8 | ··Owner················Data·size·» Description |
| 9 | ··GNU··················0x00000010» NT_GNU_ABI_TAG·(ABI·version·tag)» ····OS:·Linux,·ABI:·3.2.0 | 9 | ··GNU··················0x00000010» NT_GNU_ABI_TAG·(ABI·version·tag)» ····OS:·Linux,·ABI:·3.2.0 |
| Offset 12678, 15 lines modified | Offset 12678, 15 lines modified | ||
| 12678 | evaluate_evalSequenceHadError | 12678 | evaluate_evalSequenceHadError |
| 12679 | errorreturn | 12679 | errorreturn |
| 12680 | evaluate_backtrace | 12680 | evaluate_backtrace |
| 12681 | lastCode | 12681 | lastCode |
| 12682 | tryEvalSuccess | 12682 | tryEvalSuccess |
| 12683 | gcc·14.2.0 | 12683 | gcc·14.2.0 |
| 12684 | x86_64-Linux-Debian-trixie | 12684 | x86_64-Linux-Debian-trixie |
| 12685 | 6.1 | 12685 | 6.10.11+bpo-amd64 |
| 12686 | m2-compile-node | 12686 | m2-compile-node |
| 12687 | %d.%d.%d | 12687 | %d.%d.%d |
| 12688 | not·present | 12688 | not·present |
| 12689 | x86_64-pc-linux-gnu | 12689 | x86_64-pc-linux-gnu |
| 12690 | 1.24.11-bin | 12690 | 1.24.11-bin |
| 12691 | whichway | 12691 | whichway |
| 12692 | sortlist | 12692 | sortlist |
| Offset 71311, 15 lines modified | Offset 71311, 15 lines modified | ||
| 71311 | » endbr64 | 71311 | » endbr64 |
| 71312 | » push···%rbp | 71312 | » push···%rbp |
| 71313 | » mov····$0x10,%edi | 71313 | » mov····$0x10,%edi |
| 71314 | » push···%rbx | 71314 | » push···%rbx |
| 71315 | » push···%rax | 71315 | » push···%rax |
| 71316 | » call···5b080·<__cxa_allocate_exception@plt> | 71316 | » call···5b080·<__cxa_allocate_exception@plt> |
| 71317 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1) | 71317 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1) |
| 71318 | » lea····0x642d8 | 71318 | » lea····0x642d8b(%rip),%rsi········ |
| 71319 | » mov····%rax,%rdi | 71319 | » mov····%rax,%rdi |
| 71320 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40 | 71320 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40 |
| 71321 | » mov····%rax,%rbx | 71321 | » mov····%rax,%rbx |
| 71322 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1) | 71322 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·1) |
| 71323 | » call···58840·<std::runtime_error::runtime_error(char·const*)@plt> | 71323 | » call···58840·<std::runtime_error::runtime_error(char·const*)@plt> |
| 71324 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·2) | 71324 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:40·(discriminator·2) |
| 71325 | » mov····0x7c6b97(%rip),%rdx········ | 71325 | » mov····0x7c6b97(%rip),%rdx········ |
| Offset 71377, 15 lines modified | Offset 71377, 15 lines modified | ||
| 71377 | /usr/include/c++/14/bits/basic_string.h:2032 | 71377 | /usr/include/c++/14/bits/basic_string.h:2032 |
| 71378 | » push···%rax | 71378 | » push···%rax |
| 71379 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::_M_check(unsigned·long,·char·const*)·const: | 71379 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::_M_check(unsigned·long,·char·const*)·const: |
| 71380 | /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1) | 71380 | /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1) |
| 71381 | » mov····%rsi,%rdx | 71381 | » mov····%rsi,%rdx |
| 71382 | » lea····0x65a343(%rip),%rdi········ | 71382 | » lea····0x65a343(%rip),%rdi········ |
| 71383 | » xor····%eax,%eax | 71383 | » xor····%eax,%eax |
| 71384 | » lea····0x642ce | 71384 | » lea····0x642ce1(%rip),%rsi········ |
| 71385 | » call···583e0·<std::__throw_out_of_range_fmt(char·const*,·...)@plt> | 71385 | » call···583e0·<std::__throw_out_of_range_fmt(char·const*,·...)@plt> |
| 71386 | std::basic_ostream<char,·std::char_traits<char>·>&·std::endl<char,·std::char_traits<char>·>(std::basic_ostream<char,·std::char_traits<char>·>&): | 71386 | std::basic_ostream<char,·std::char_traits<char>·>&·std::endl<char,·std::char_traits<char>·>(std::basic_ostream<char,·std::char_traits<char>·>&): |
| 71387 | /usr/include/c++/14/ostream:741 | 71387 | /usr/include/c++/14/ostream:741 |
| 71388 | » push···%rbp | 71388 | » push···%rbp |
| 71389 | » push···%rbx | 71389 | » push···%rbx |
| 71390 | » push···%rdx | 71390 | » push···%rdx |
| 71391 | /usr/include/c++/14/ostream:742 | 71391 | /usr/include/c++/14/ostream:742 |
| Offset 131546, 15 lines modified | Offset 131546, 15 lines modified | ||
| 131546 | » mov····0xb8204b(%rip),%rdi········ | 131546 | » mov····0xb8204b(%rip),%rdi········ |
| 131547 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 | 131547 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 |
| 131548 | » movw···$0x7,(%rbx) | 131548 | » movw···$0x7,(%rbx) |
| 131549 | » movl···$0x2,0x4(%rbx) | 131549 | » movl···$0x2,0x4(%rbx) |
| 131550 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 131550 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 131551 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131551 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| 131552 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131552 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131553 | » lea····0x612b | 131553 | » lea····0x612b7e(%rip),%rdi········ |
| 131554 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 131554 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 131555 | » mov····%rax,0x8(%rbx) | 131555 | » mov····%rax,0x8(%rbx) |
| 131556 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131556 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131557 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> | 131557 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> |
| 131558 | » mov····%rax,%rdi | 131558 | » mov····%rax,%rdi |
| 131559 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 131559 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 131560 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131560 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| Offset 131590, 15 lines modified | Offset 131590, 15 lines modified | ||
| 131590 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:78 | 131590 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:78 |
| 131591 | » shr····$0x10,%r9d | 131591 | » shr····$0x10,%r9d |
| 131592 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:81 | 131592 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:81 |
| 131593 | » cmp····$0xff,%eax | 131593 | » cmp····$0xff,%eax |
| 131594 | » je·····c43ec·<std::runtime_error::~runtime_error()@plt+0x67b04> | 131594 | » je·····c43ec·<std::runtime_error::~runtime_error()@plt+0x67b04> |
| 131595 | /usr/include/x86_64-linux-gnu/bits/stdio2.h:68·(discriminator·1) | 131595 | /usr/include/x86_64-linux-gnu/bits/stdio2.h:68·(discriminator·1) |
| 131596 | » push···%rax | 131596 | » push···%rax |
| 131597 | » lea····0x612b1 | 131597 | » lea····0x612b1b(%rip),%r8········ |
| 131598 | » push···%rdx | 131598 | » push···%rdx |
| 131599 | » lea····0xb82070(%rip),%rbx········ | 131599 | » lea····0xb82070(%rip),%rbx········ |
| 131600 | » mov····$0x1,%edx | 131600 | » mov····$0x1,%edx |
| 131601 | » mov····$0x28,%ecx | 131601 | » mov····$0x28,%ecx |
| 131602 | » xor····%eax,%eax | 131602 | » xor····%eax,%eax |
| 131603 | » mov····$0x28,%esi | 131603 | » mov····$0x28,%esi |
| 131604 | » mov····%rbx,%rdi | 131604 | » mov····%rbx,%rdi |
| Offset 131627, 15 lines modified | Offset 131627, 15 lines modified | ||
| 131627 | » test···%rax,%rax | 131627 | » test···%rax,%rax |
| 131628 | » je·····c43ff·<std::runtime_error::~runtime_error()@plt+0x67b17> | 131628 | » je·····c43ff·<std::runtime_error::~runtime_error()@plt+0x67b17> |
| 131629 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:156 | 131629 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:156 |
| 131630 | » mov····0x60(%rsp),%r14 | 131630 | » mov····0x60(%rsp),%r14 |
| 131631 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 131631 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 131632 | » mov····0xb81f50(%rip),%rdi········ | 131632 | » mov····0xb81f50(%rip),%rdi········ |
| 131633 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131633 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131634 | » lea····0x612a | 131634 | » lea····0x612abd(%rip),%rbx········ |
| 131635 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:156 | 131635 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:156 |
| 131636 | » movw···$0x7,(%r14) | 131636 | » movw···$0x7,(%r14) |
| 131637 | » movl···$0x2,0x4(%r14) | 131637 | » movl···$0x2,0x4(%r14) |
| 131638 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 131638 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 131639 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131639 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| 131640 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131640 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131641 | » mov····%rbx,%rdi | 131641 | » mov····%rbx,%rdi |
| Offset 131662, 15 lines modified | Offset 131662, 15 lines modified | ||
| 131662 | » mov····0xb81ef2(%rip),%rdi········ | 131662 | » mov····0xb81ef2(%rip),%rdi········ |
| 131663 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 | 131663 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 |
| 131664 | » movw···$0x7,(%r15) | 131664 | » movw···$0x7,(%r15) |
| 131665 | » movl···$0x2,0x4(%r15) | 131665 | » movl···$0x2,0x4(%r15) |
| 131666 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 131666 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 131667 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131667 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| 131668 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 131668 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 131669 | » lea····0x612a6 | 131669 | » lea····0x612a60(%rip),%rdi········ |
| 131670 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 131670 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 131671 | » mov····%rax,0x8(%r15) | 131671 | » mov····%rax,0x8(%r15) |
| 131672 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 131672 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 131673 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> | 131673 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> |
| 131674 | » mov····%rax,%rdi | 131674 | » mov····%rax,%rdi |
| 131675 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·2) | 131675 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·2) |
| 131676 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131676 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| Offset 131690, 15 lines modified | Offset 131690, 15 lines modified | ||
| 131690 | » mov····0xb81e97(%rip),%rdi········ | 131690 | » mov····0xb81e97(%rip),%rdi········ |
| 131691 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:164 | 131691 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:164 |
| 131692 | » movw···$0x7,(%r14) | 131692 | » movw···$0x7,(%r14) |
| 131693 | » movl···$0x2,0x4(%r14) | 131693 | » movl···$0x2,0x4(%r14) |
| 131694 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 131694 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 131695 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131695 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| 131696 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131696 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131697 | » lea····0x612a1 | 131697 | » lea····0x612a13(%rip),%rdi········ |
| 131698 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 131698 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 131699 | » mov····%rax,0x8(%r14) | 131699 | » mov····%rax,0x8(%r14) |
| 131700 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131700 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131701 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> | 131701 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> |
| 131702 | » mov····%rax,%rdi | 131702 | » mov····%rax,%rdi |
| 131703 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 131703 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 131704 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131704 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| Offset 131718, 15 lines modified | Offset 131718, 15 lines modified | ||
| 131718 | » mov····0xb81e3c(%rip),%rdi········ | 131718 | » mov····0xb81e3c(%rip),%rdi········ |
| 131719 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 | 131719 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 |
| 131720 | » movw···$0x7,(%r15) | 131720 | » movw···$0x7,(%r15) |
| 131721 | » movl···$0x2,0x4(%r15) | 131721 | » movl···$0x2,0x4(%r15) |
| 131722 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 131722 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 131723 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131723 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| 131724 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131724 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131725 | » lea····0x6129c | 131725 | » lea····0x6129c6(%rip),%rdi········ |
| 131726 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 131726 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 131727 | » mov····%rax,0x8(%r15) | 131727 | » mov····%rax,0x8(%r15) |
| 131728 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 131728 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 131729 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> | 131729 | » call···542d40·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xea20> |
| 131730 | » mov····%rax,%rdi | 131730 | » mov····%rax,%rdi |
| 131731 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 131731 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 131732 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> | 131732 | » call···56d710·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x393f0> |
| Max diff block lines reached; 242590/248742 bytes (97.53%) of diff not shown. | |||
| Offset 776, 90 lines modified | Offset 776, 90 lines modified | ||
| 776 | ··0x006d6050·7475726e·00657661·6c756174·655f6261·turn.evaluate_ba | 776 | ··0x006d6050·7475726e·00657661·6c756174·655f6261·turn.evaluate_ba |
| 777 | ··0x006d6060·636b7472·61636500·6c617374·436f6465·cktrace.lastCode | 777 | ··0x006d6060·636b7472·61636500·6c617374·436f6465·cktrace.lastCode |
| 778 | ··0x006d6070·00747279·4576616c·53756363·65737300·.tryEvalSuccess. | 778 | ··0x006d6070·00747279·4576616c·53756363·65737300·.tryEvalSuccess. |
| 779 | ··0x006d6080·312e3234·2e313100·342e342e·30006763·1.24.11.4.4.0.gc | 779 | ··0x006d6080·312e3234·2e313100·342e342e·30006763·1.24.11.4.4.0.gc |
| 780 | ··0x006d6090·63203134·2e322e30·00783836·5f363400·c·14.2.0.x86_64. | 780 | ··0x006d6090·63203134·2e322e30·00783836·5f363400·c·14.2.0.x86_64. |
| 781 | ··0x006d60a0·7838365f·36342d4c·696e7578·2d446562·x86_64-Linux-Deb | 781 | ··0x006d60a0·7838365f·36342d4c·696e7578·2d446562·x86_64-Linux-Deb |
| 782 | ··0x006d60b0·69616e2d·74726978·6965004c·696e7578·ian-trixie.Linux | 782 | ··0x006d60b0·69616e2d·74726978·6965004c·696e7578·ian-trixie.Linux |
| 783 | ··0x006d60c0·00362e31· | 783 | ··0x006d60c0·00362e31·302e3131·2b62706f·2d616d64·.6.10.11+bpo-amd |
| 784 | ··0x006d60d0· | 784 | ··0x006d60d0·3634006d·322d636f·6d70696c·652d6e6f·64.m2-compile-no |
| 785 | ··0x006d60e0· | 785 | ··0x006d60e0·64650025·642e2564·2e256400·6e6f7420·de.%d.%d.%d.not· |
| 786 | ··0x006d60f0· | 786 | ··0x006d60f0·70726573·656e7400·322e352e·3000332e·present.2.5.0.3. |
| 787 | ··0x006d6100· | 787 | ··0x006d6100·322e3100·332e3132·2e370033·2e31302e·2.1.3.12.7.3.10. |
| 788 | ··0x006d6110·3 | 788 | ··0x006d6110·34003131·2e352e31·00332e31·2e300031·4.11.5.1.3.1.0.1 |
| 789 | ··0x006d6120· | 789 | ··0x006d6120·5f383300·382e3200·342e322e·3100312e·_83.8.2.4.2.1.1. |
| 790 | ··0x006d6130· | 790 | ··0x006d6130·352e3400·32303231·2e313200·332e342e·5.4.2021.12.3.4. |
| 791 | ··0x006d6140· | 791 | ··0x006d6140·3000332e·342e3600·7838365f·36342d70·0.3.4.6.x86_64-p |
| 792 | ··0x006d6150· | 792 | ··0x006d6150·632d6c69·6e75782d·676e7500·312e3234·c-linux-gnu.1.24 |
| 793 | ··0x006d6160·2e3 | 793 | ··0x006d6160·2e31312d·62696e00·4d325461·736b0077·.11-bin.M2Task.w |
| 794 | ··0x006d6170·6 | 794 | ··0x006d6170·68696368·77617900·736f7274·6c697374·hichway.sortlist |
| 795 | ··0x006d6180· | 795 | ··0x006d6180·00257000·68616473·65710064·65657073·.%p.hadseq.deeps |
| 796 | ··0x006d6190·657 | 796 | ··0x006d6190·65710064·65657069·6e646578·00726573·eq.deepindex.res |
| 797 | ··0x006d61a0· | 797 | ··0x006d61a0·65747661·72730077·72617070·6564204d·etvars.wrapped·M |
| 798 | ··0x006d61b0·6 | 798 | ··0x006d61b0·61636175·6c617932·2066756e·6374696f·acaulay2·functio |
| 799 | ··0x006d61c0· | 799 | ··0x006d61c0·6e007465·73740062·61736963·5f737472·n.test.basic_str |
| 800 | ··0x006d61d0· | 800 | ··0x006d61d0·696e673a·3a696e73·65727400·4f766572·ing::insert.Over |
| 801 | ··0x006d61e0· | 801 | ··0x006d61e0·666c6f77·20457272·6f720063·6272743c·flow·Error.cbrt< |
| 802 | ··0x006d61f0· | 802 | ··0x006d61f0·2531253e·28253125·29006c67·616d6d61·%1%>(%1%).lgamma |
| 803 | ··0x006d6200· | 803 | ··0x006d6200·3c253125·3e00626f·6f73743a·3a6d6174·<%1%>.boost::mat |
| 804 | ··0x006d6210·6 | 804 | ··0x006d6210·683a3a65·78706d31·3c253125·3e282531·h::expm1<%1%>(%1 |
| 805 | ··0x006d6220·2 | 805 | ··0x006d6220·2529006e·756d6572·6963206f·76657266·%).numeric·overf |
| 806 | ··0x006d6230·6 | 806 | ··0x006d6230·6c6f7700·626f6f73·743a3a6d·6174683a·low.boost::math: |
| 807 | ··0x006d6240· | 807 | ··0x006d6240·3a6c6f67·31703c25·31253e28·25312529·:log1p<%1%>(%1%) |
| 808 | ··0x006d6250·31252900·4576616c·75617469·6f6e206f·1%).Evaluation·o | ||
| 809 | ··0x006d6260·66206c67·616d6d61·20617420·2531252e·f·lgamma·at·%1%. | ||
| 810 | ··0x006d6270·00626f6f·73743a3a·6d617468·3a3a6c67·.boost::math::lg | ||
| 811 | ··0x006d6280·616d6d61·3c253125·3e282531·2529006f·amma<%1%>(%1%).o | ||
| 812 | ··0x006d6290·70657261·746f723d·00556e61·626c6520·perator=.Unable· | ||
| 813 | ··0x006d62a0·746f2070·61727365·20737472·696e6720·to·parse·string· | ||
| 814 | ··0x006d62 | 808 | ··0x006d6250·00457661·6c756174·696f6e20·6f66206c·.Evaluation·of·l |
| 815 | ··0x006d62 | 809 | ··0x006d6260·67616d6d·61206174·20253125·2e00626f·gamma·at·%1%..bo |
| 810 | ··0x006d6270·6f73743a·3a6d6174·683a3a6c·67616d6d·ost::math::lgamm | ||
| 811 | ··0x006d6280·613c2531·253e2825·31252900·6f706572·a<%1%>(%1%).oper | ||
| 812 | ··0x006d6290·61746f72·3d00556e·61626c65·20746f20·ator=.Unable·to· | ||
| 813 | ··0x006d62a0·70617273·65207374·72696e67·20220045·parse·string·".E | ||
| 814 | ··0x006d62b0·76616c75·6174696f·6e206f66·20746761·valuation·of·tga | ||
| 815 | ··0x006d62c0·6d6d6120·61742025·31252e00·626f6f73·mma·at·%1%..boos | ||
| 816 | ··0x006d62d0· | 816 | ··0x006d62d0·743a3a6d·6174683a·3a697472·756e633c·t::math::itrunc< |
| 817 | ··0x006d62e0· | 817 | ··0x006d62e0·2531253e·28253125·29002061·6e642078·%1%>(%1%).·and·x |
| 818 | ··0x006d62f0· | 818 | ··0x006d62f0·203d2025·31250062·6f6f7374·3a3a6d61··=·%1%.boost::ma |
| 819 | ··0x006d6300·74683a3a·7a657461·3c253125·3e282531·th::zeta<%1%>(%1 | ||
| 820 | ··0x006d6310·25290062·6f6f7374·3a3a6d61·74683a3a·%).boost::math:: | ||
| 821 | ··0x006d6320·6572665f·696e763c·2531253e·0067616d·erf_inv<%1%>.gam | ||
| 822 | ··0x006d6330·6d615f71·3c253125·3e282531·252c2025·ma_q<%1%>(%1%,·% | ||
| 823 | ··0x006d6340·31252900·67616d6d·615f703c·2531253e·1%).gamma_p<%1%> | ||
| 824 | ··0x006d6350·28253125·2c202531·25290062·6f6f7374·(%1%,·%1%).boost | ||
| 819 | ··0x006d63 | 825 | ··0x006d6360·3a3a6d61·74683a3a·7a657461·3c253125·::math::zeta<%1% |
| 820 | ··0x006d6310·28253125·2900626f·6f73743a·3a6d6174·(%1%).boost::mat | ||
| 821 | ··0x006d6320·683a3a65·72665f69·6e763c25·31253e00·h::erf_inv<%1%>. | ||
| 822 | ··0x006d6330·67616d6d·615f713c·2531253e·28253125·gamma_q<%1%>(%1% | ||
| 823 | ··0x006d6340·2c202531·25290067·616d6d61·5f703c25·,·%1%).gamma_p<% | ||
| 824 | ··0x006d6350·31253e28·2531252c·20253125·2900626f·1%>(%1%,·%1%).bo | ||
| 825 | ··0x006d6360·6f73743a·3a6d6174·683a3a7a·6574613c·ost::math::zeta< | ||
| 826 | ··0x006d6370· | 826 | ··0x006d6370·3e003234·00313230·00373230·00353034·>.24.120.720.504 |
| 827 | ··0x006d6380·3 | 827 | ··0x006d6380·30003430·33323000·33363238·38300033·0.40320.362880.3 |
| 828 | ··0x006d6390·3 | 828 | ··0x006d6390·36323838·30300033·39393136·38303000·628800.39916800. |
| 829 | ··0x006d63a0·3 | 829 | ··0x006d63a0·34373930·30313630·30003632·32373032·479001600.622702 |
| 830 | ··0x006d63b0·3 | 830 | ··0x006d63b0·30383030·00383731·37383239·31323030·0800.87178291200 |
| 831 | ··0x006d63c0· | 831 | ··0x006d63c0·00313330·37363734·33363830·30300032·.1307674368000.2 |
| 832 | ··0x006d63d0·30 | 832 | ··0x006d63d0·30393232·37383938·38383030·30003335·0922789888000.35 |
| 833 | ··0x006d63e0· | 833 | ··0x006d63e0·35363837·34323830·39363030·30003634·5687428096000.64 |
| 834 | ··0x006d63f0· | 834 | ··0x006d63f0·30323337·33373035·37323830·30300031·02373705728000.1 |
| 835 | ··0x006d6400·3 | 835 | ··0x006d6400·32313634·35313030·34303838·33323030·2164510040883200 |
| 836 | ··0x006d6410·3 | 836 | ··0x006d6410·30003234·33323930·32303038·31373636·0.24329020081766 |
| 837 | ··0x006d6420·3 | 837 | ··0x006d6420·34303030·30003531·30393039·34323137·40000.5109094217 |
| 838 | ··0x006d6430·3 | 838 | ··0x006d6430·31373039·34343030·30300031·31323430·1709440000.11240 |
| 839 | ··0x006d6440·3 | 839 | ··0x006d6440·30303732·37373737·36303736·38303030·0072777760768000 |
| 840 | ··0x006d6450·30 | 840 | ··0x006d6450·30003235·38353230·31363733·38383834·0.25852016738884 |
| 841 | ··0x006d6460·3 | 841 | ··0x006d6460·39373636·34303030·30003632·30343438·976640000.620448 |
| 842 | ··0x006d6470·343 | 842 | ··0x006d6470·34303137·33333233·39343339·33363030·4017332394393600 |
| 843 | ··0x006d6480·3 | 843 | ··0x006d6480·30300031·35353131·32313030·34333333·00.1551121004333 |
| 844 | ··0x006d6490·3 | 844 | ··0x006d6490·30393835·39383430·30303030·30003430·0985984000000.40 |
| 845 | ··0x006d64a0· | 845 | ··0x006d64a0·33323931·34363131·32363630·35363335·3291461126605635 |
| 846 | ··0x006d64b0·3 | 846 | ··0x006d64b0·35383430·30303030·30003130·38383838·584000000.108888 |
| 847 | ··0x006d64c0·3 | 847 | ··0x006d64c0·36393435·30343138·33353231·36303736·6945041835216076 |
| 848 | ··0x006d64d0·3 | 848 | ··0x006d64d0·38303030·30303000·666c6f61·745f7072·8000000.float_pr |
| 849 | ··0x006d64e0· | 849 | ··0x006d64e0·696f723c·2531253e·28253125·2900666c·ior<%1%>(%1%).fl |
| 850 | ··0x006d64f0· | 850 | ··0x006d64f0·6f61745f·6e657874·3c253125·3e282531·oat_next<%1%>(%1 |
| 851 | ··0x006d6500·2 | 851 | ··0x006d6500·25290062·61736963·5f737472·696e673a·%).basic_string: |
| 852 | ··0x006d6510· | 852 | ··0x006d6510·3a726570·6c616365·00652b30·3000302e·:replace.e+00.0. |
| 853 | ··0x006d6520·00 | 853 | ··0x006d6520·002d696e·66002b69·6e66006e·616e002d·.-inf.+inf.nan.- |
| 854 | ··0x006d6530· | 854 | ··0x006d6530·30004361·75736520·756e6b6e·6f776e00·0.Cause·unknown. |
| 855 | ··0x006d6540· | 855 | ··0x006d6540·4572726f·7220696e·2066756e·6374696f·Error·in·functio |
| 856 | ··0x006d6550· | 856 | ··0x006d6550·6e200062·6f6f7374·3a3a6d61·74683a3a·n·.boost::math:: |
| 857 | ··0x006d6560· | 857 | ··0x006d6560·7467616d·6d613c25·31253e28·25312529·tgamma<%1%>(%1%) |
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| 859 | ··0x006d6580·01000000·00000000·00000000·00000000·................ | 859 | ··0x006d6580·01000000·00000000·00000000·00000000·................ |
| 860 | ··0x006d6590·30303031·30323033·30343035·30363037·0001020304050607 | 860 | ··0x006d6590·30303031·30323033·30343035·30363037·0001020304050607 |
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| Offset 1816, 28 lines modified | Offset 1816, 28 lines modified | ||
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| Offset 40, 32 lines modified | Offset 40, 32 lines modified | ||
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| 44 | ··0x0085a290·ea3d6d00·00000000·7d326d00·00000000·.=m.....}2m..... | 44 | ··0x0085a290·ea3d6d00·00000000·7d326d00·00000000·.=m.....}2m..... |
| 45 | ··0x0085a2a0·1e566d00·00000000·085a6d00·00000000·.Vm......Zm..... | 45 | ··0x0085a2a0·1e566d00·00000000·085a6d00·00000000·.Vm......Zm..... |
| 46 | ··0x0085a2b0·be5a6d00·00000000·ae456d00·00000000·.Zm......Em..... | 46 | ··0x0085a2b0·be5a6d00·00000000·ae456d00·00000000·.Zm......Em..... |
| 47 | ··0x0085a2c0·f8446d00·00000000·0 | 47 | ··0x0085a2c0·f8446d00·00000000·04626d00·00000000·.Dm......bm..... |
| 48 | ··0x0085a2d0·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... | 48 | ··0x0085a2d0·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... |
| 49 | ··0x0085a2e0·135a6d00·00000000·165a6d00·00000000·.Zm......Zm..... | 49 | ··0x0085a2e0·135a6d00·00000000·165a6d00·00000000·.Zm......Zm..... |
| 50 | ··0x0085a2f0·1a3d6d00·00000000·b5316d00·00000000·.=m......1m..... | 50 | ··0x0085a2f0·1a3d6d00·00000000·b5316d00·00000000·.=m......1m..... |
| 51 | ··0x0085a300·b35b6d00·00000000·84496d00·00000000·.[m......Im..... | 51 | ··0x0085a300·b35b6d00·00000000·84496d00·00000000·.[m......Im..... |
| 52 | ··0x0085a310· | 52 | ··0x0085a310·2d656d00·00000000·6a466d00·00000000·-em.....jFm..... |
| 53 | ··0x0085a320·10456d00·00000000·195a6d00·00000000·.Em......Zm..... | 53 | ··0x0085a320·10456d00·00000000·195a6d00·00000000·.Em......Zm..... |
| 54 | ··0x0085a330·9 | 54 | ··0x0085a330·9b616d00·00000000·0c5e6d00·00000000·.am......^m..... |
| 55 | ··0x0085a340·b44a6d00·00000000·51526d00·00000000·.Jm.....QRm..... | 55 | ··0x0085a340·b44a6d00·00000000·51526d00·00000000·.Jm.....QRm..... |
| 56 | ··0x0085a350·08536d00·00000000·1b3d6d00·00000000·.Sm......=m..... | 56 | ··0x0085a350·08536d00·00000000·1b3d6d00·00000000·.Sm......=m..... |
| 57 | ··0x0085a360·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... | 57 | ··0x0085a360·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... |
| 58 | ··0x0085a370·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... | 58 | ··0x0085a370·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... |
| 59 | ··0x0085a380·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... | 59 | ··0x0085a380·1b3d6d00·00000000·1b3d6d00·00000000·.=m......=m..... |
| 60 | ··0x0085a390·1b3d6d00·00000000·505a6d00·00000000·.=m.....PZm..... | 60 | ··0x0085a390·1b3d6d00·00000000·505a6d00·00000000·.=m.....PZm..... |
| 61 | ··0x0085a3a0·955a6d00·00000000·50466d00·00000000·.Zm.....PFm..... | 61 | ··0x0085a3a0·955a6d00·00000000·50466d00·00000000·.Zm.....PFm..... |
| 62 | ··0x0085a3b0·d7586d00·00000000·745a6d00·00000000·.Xm.....tZm..... | 62 | ··0x0085a3b0·d7586d00·00000000·745a6d00·00000000·.Xm.....tZm..... |
| 63 | ··0x0085a3c0·1b5a6d00·00000000·9b3e6d00·00000000·.Zm......>m..... | 63 | ··0x0085a3c0·1b5a6d00·00000000·9b3e6d00·00000000·.Zm......>m..... |
| 64 | ··0x0085a3d0·8 | 64 | ··0x0085a3d0·82616d00·00000000·d7596d00·00000000·.am......Ym..... |
| 65 | ··0x0085a3e0·025b6d00·00000000·1d5a6d00·00000000·.[m......Zm..... | 65 | ··0x0085a3e0·025b6d00·00000000·1d5a6d00·00000000·.[m......Zm..... |
| 66 | ··0x0085a3f0·f65a6d00·00000000·60466d00·00000000·.Zm.....`Fm..... | 66 | ··0x0085a3f0·f65a6d00·00000000·60466d00·00000000·.Zm.....`Fm..... |
| 67 | ··0x0085a400·495a6d00·00000000·4c5a6d00·00000000·IZm.....LZm..... | 67 | ··0x0085a400·495a6d00·00000000·4c5a6d00·00000000·IZm.....LZm..... |
| 68 | ··0x0085a410·4f5a6d00·00000000·e65c6d00·00000000·OZm......\m..... | 68 | ··0x0085a410·4f5a6d00·00000000·e65c6d00·00000000·OZm......\m..... |
| 69 | ··0x0085a420·525a6d00·00000000·555a6d00·00000000·RZm.....UZm..... | 69 | ··0x0085a420·525a6d00·00000000·555a6d00·00000000·RZm.....UZm..... |
| 70 | ··0x0085a430·81386d00·00000000·585a6d00·00000000·.8m.....XZm..... | 70 | ··0x0085a430·81386d00·00000000·585a6d00·00000000·.8m.....XZm..... |
| 71 | ··0x0085a440·5b5a6d00·00000000·2d326d00·00000000·[Zm.....-2m..... | 71 | ··0x0085a440·5b5a6d00·00000000·2d326d00·00000000·[Zm.....-2m..... |
| Offset 127, 20 lines modified | Offset 127, 20 lines modified | ||
| 127 | ··0x0085a7c0·945c6d00·00000000·b35b6d00·00000000·.\m......[m..... | 127 | ··0x0085a7c0·945c6d00·00000000·b35b6d00·00000000·.\m......[m..... |
| 128 | ··0x0085a7d0·be5a6d00·00000000·0c5e6d00·00000000·.Zm......^m..... | 128 | ··0x0085a7d0·be5a6d00·00000000·0c5e6d00·00000000·.Zm......^m..... |
| 129 | ··0x0085a7e0·0f366d00·00000000·08536d00·00000000·.6m......Sm..... | 129 | ··0x0085a7e0·0f366d00·00000000·08536d00·00000000·.6m......Sm..... |
| 130 | ··0x0085a7f0·84496d00·00000000·7a4c6d00·00000000·.Im.....zLm..... | 130 | ··0x0085a7f0·84496d00·00000000·7a4c6d00·00000000·.Im.....zLm..... |
| 131 | ··0x0085a800·535a6d00·00000000·bc586d00·00000000·SZm......Xm..... | 131 | ··0x0085a800·535a6d00·00000000·bc586d00·00000000·SZm......Xm..... |
| 132 | ··0x0085a810·7a5a6d00·00000000·1e5a6d00·00000000·zZm......Zm..... | 132 | ··0x0085a810·7a5a6d00·00000000·1e5a6d00·00000000·zZm......Zm..... |
| 133 | ··0x0085a820·595a6d00·00000000·2d5e6d00·00000000·YZm.....-^m..... | 133 | ··0x0085a820·595a6d00·00000000·2d5e6d00·00000000·YZm.....-^m..... |
| 134 | ··0x0085a830· | 134 | ··0x0085a830·2d656d00·00000000·71456d00·00000000·-em.....qEm..... |
| 135 | ··0x0085a840·8 | 135 | ··0x0085a840·82616d00·00000000·89616d00·00000000·.am......am..... |
| 136 | ··0x0085a850·6a466d00·00000000·66416d00·00000000·jFm.....fAm..... | 136 | ··0x0085a850·6a466d00·00000000·66416d00·00000000·jFm.....fAm..... |
| 137 | ··0x0085a860·10456d00·00000000·8c496d00·00000000·.Em......Im..... | 137 | ··0x0085a860·10456d00·00000000·8c496d00·00000000·.Em......Im..... |
| 138 | ··0x0085a870·195a6d00·00000000·7d5d6d00·00000000·.Zm.....}]m..... | 138 | ··0x0085a870·195a6d00·00000000·7d5d6d00·00000000·.Zm.....}]m..... |
| 139 | ··0x0085a880·9 | 139 | ··0x0085a880·9b616d00·00000000·76616d00·00000000·.am.....vam..... |
| 140 | ··0x0085a890·715a6d00·00000000·a15c6d00·00000000·qZm......\m..... | 140 | ··0x0085a890·715a6d00·00000000·a15c6d00·00000000·qZm......\m..... |
| 141 | ··0x0085a8a0·b45c6d00·00000000·c25c6d00·00000000·.\m......\m..... | 141 | ··0x0085a8a0·b45c6d00·00000000·c25c6d00·00000000·.\m......\m..... |
| 142 | ··0x0085a8b0·d65c6d00·00000000·dc5c6d00·00000000·.\m......\m..... | 142 | ··0x0085a8b0·d65c6d00·00000000·dc5c6d00·00000000·.\m......\m..... |
| 143 | ··0x0085a8c0·1b3d6d00·00000000·00000000·00000000·.=m............. | 143 | ··0x0085a8c0·1b3d6d00·00000000·00000000·00000000·.=m............. |
| 144 | ··0x0085a8d0·25733a25·643a2065·72726f72·3a202573·%s:%d:·error:·%s | 144 | ··0x0085a8d0·25733a25·643a2065·72726f72·3a202573·%s:%d:·error:·%s |
| 145 | ··0x0085a8e0·00000000·00000000·00000000·00000000·................ | 145 | ··0x0085a8e0·00000000·00000000·00000000·00000000·................ |
| 146 | ··0x0085a8f0·25733a25·643a2564·3a206572·726f723a·%s:%d:%d:·error: | 146 | ··0x0085a8f0·25733a25·643a2564·3a206572·726f723a·%s:%d:%d:·error: |
| Offset 164, 22 lines modified | Offset 164, 22 lines modified | ||
| 164 | ··0x0085aa10·00000000·00000000·00000000·00000000·................ | 164 | ··0x0085aa10·00000000·00000000·00000000·00000000·................ |
| 165 | ··0x0085aa20·2f5e6d00·00000000·60285400·00000000·/^m.....`(T..... | 165 | ··0x0085aa20·2f5e6d00·00000000·60285400·00000000·/^m.....`(T..... |
| 166 | ··0x0085aa30·01000000·00000000·365e6d00·00000000·........6^m..... | 166 | ··0x0085aa30·01000000·00000000·365e6d00·00000000·........6^m..... |
| 167 | ··0x0085aa40·00000000·00000000·00000000·00000000·................ | 167 | ··0x0085aa40·00000000·00000000·00000000·00000000·................ |
| 168 | ··0x0085aa50·00000000·00000000·00000000·00000000·................ | 168 | ··0x0085aa50·00000000·00000000·00000000·00000000·................ |
| 169 | ··0x0085aa60·0a000000·00000000·64636261·00000000·........dcba.... | 169 | ··0x0085aa60·0a000000·00000000·64636261·00000000·........dcba.... |
| 170 | ··0x0085aa70·c8326f00·00000000·f0326f00·00000000·.2o......2o..... | 170 | ··0x0085aa70·c8326f00·00000000·f0326f00·00000000·.2o......2o..... |
| 171 | ··0x0085aa80·5 | 171 | ··0x0085aa80·53656d00·00000000·6e626d00·00000000·Sem.....nbm..... |
| 172 | ··0x0085aa90·5 | 172 | ··0x0085aa90·5b636d00·00000000·f82a6f00·00000000·[cm......*o..... |
| 173 | ··0x0085aaa0·18336f00·00000000·40336f00·00000000·.3o.....@3o..... | 173 | ··0x0085aaa0·18336f00·00000000·40336f00·00000000·.3o.....@3o..... |
| 174 | ··0x0085aab0·a04e6f00·00000000·f0326f00·00000000·.No......2o..... | 174 | ··0x0085aab0·a04e6f00·00000000·f0326f00·00000000·.No......2o..... |
| 175 | ··0x0085aac0·e04e6f00·00000000·e04e6f00·00000000·.No......No..... | 175 | ··0x0085aac0·e04e6f00·00000000·e04e6f00·00000000·.No......No..... |
| 176 | ··0x0085aad0·d | 176 | ··0x0085aad0·d8646d00·00000000·ee646d00·00000000·.dm......dm..... |
| 177 | ··0x0085aae0·084f6f00·00000000·5 | 177 | ··0x0085aae0·084f6f00·00000000·53656d00·00000000·.Oo.....Sem..... |
| 178 | ··0x0085aaf0· | 178 | ··0x0085aaf0·6e626d00·00000000·88316f00·00000000·nbm......1o..... |
| 179 | ··0x0085ab00·304f6f00·00000000·584f6f00·00000000·0Oo.....XOo..... | 179 | ··0x0085ab00·304f6f00·00000000·584f6f00·00000000·0Oo.....XOo..... |
| 180 | ··0x0085ab10·804f6f00·00000000·e04e6f00·00000000·.Oo......No..... | 180 | ··0x0085ab10·804f6f00·00000000·e04e6f00·00000000·.Oo......No..... |
| 181 | ··0x0085ab20·18336f00·00000000·3 | 181 | ··0x0085ab20·18336f00·00000000·34626d00·00000000·.3o.....4bm..... |
| 182 | ··0x0085ab30·e04e6f00·00000000·584f6f00·00000000·.No.....XOo..... | 182 | ··0x0085ab30·e04e6f00·00000000·584f6f00·00000000·.No.....XOo..... |
| 183 | ··0x0085ab40·b04f6f00·00000000·03000000·14000000·.Oo............. | 183 | ··0x0085ab40·b04f6f00·00000000·03000000·14000000·.Oo............. |
| 184 | ··0x0085ab50·98738500·00000000·00000000·00000000·.s.............. | 184 | ··0x0085ab50·98738500·00000000·00000000·00000000·.s.............. |
| Offset 1, 7 lines modified | Offset 1, 7 lines modified | ||
| 1 | Hex·dump·of·section·'.gnu_debuglink': | 1 | Hex·dump·of·section·'.gnu_debuglink': |
| 2 | ··0x00000000·35643139·30393432·62346336·66653132·5d190942b4c6fe12 | ||
| 3 | ··0x000000 | 2 | ··0x00000000·37323264·61393731·34653339·65346535·722da9714e39e4e5 |
| 3 | ··0x00000010·61346437·31376339·34336165·34646630·a4d717c943ae4df0 | ||
| 4 | ··0x00000020· | 4 | ··0x00000020·39346435·30312e64·65627567·00000000·94d501.debug.... |
| 5 | ··0x00000030· | 5 | ··0x00000030·8ec69ea8····························.... |
| Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
| 1 | -rw-r--r--···0········0········0········4·2024-11-03·00:49:13.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2024-11-03·00:49:13.000000·debian-binary |
| 2 | -rw-r--r--···0········0········0······53 | 2 | -rw-r--r--···0········0········0······536·2024-11-03·00:49:13.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0·489 | 3 | -rw-r--r--···0········0········0·48960392·2024-11-03·00:49:13.000000·data.tar.xz |
| Offset 5, 8 lines modified | Offset 5, 8 lines modified | ||
| 5 | Architecture:·amd64 | 5 | Architecture:·amd64 |
| 6 | Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org> | 6 | Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org> |
| 7 | Installed-Size:·50168 | 7 | Installed-Size:·50168 |
| 8 | Depends:·macaulay2·(=·1.24.11+ds-3) | 8 | Depends:·macaulay2·(=·1.24.11+ds-3) |
| 9 | Section:·debug | 9 | Section:·debug |
| 10 | Priority:·optional | 10 | Priority:·optional |
| 11 | Description:·debug·symbols·for·macaulay2 | 11 | Description:·debug·symbols·for·macaulay2 |
| 12 | Build-Ids:·7 | 12 | Build-Ids:·a9722da9714e39e4e5a4d717c943ae4df094d501 |
| Offset 1, 10 lines modified | Offset 1, 10 lines modified | ||
| 1 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./ | 1 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./ |
| 2 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/ | 2 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/ |
| 3 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/ | 3 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/ |
| 4 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/debug/ | 4 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/debug/ |
| 5 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/debug/.build-id/ | 5 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/debug/.build-id/ |
| 6 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/debug/.build-id/ | 6 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/lib/debug/.build-id/a9/ |
| 7 | -rw-r--r--···0·root·········(0)·root·········(0)·51361 | 7 | -rw-r--r--···0·root·········(0)·root·········(0)·51361632·2024-11-03·00:49:13.000000·./usr/lib/debug/.build-id/a9/722da9714e39e4e5a4d717c943ae4df094d501.debug |
| 8 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/ | 8 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/ |
| 9 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/ | 9 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/ |
| 10 | lrwxrwxrwx···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/macaulay2-dbgsym·->·macaulay2 | 10 | lrwxrwxrwx···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/macaulay2-dbgsym·->·macaulay2 |
| Offset 6, 15 lines modified | Offset 6, 15 lines modified | ||
| 6 | ··OS/ABI:····························UNIX·-·GNU | 6 | ··OS/ABI:····························UNIX·-·GNU |
| 7 | ··ABI·Version:·······················0 | 7 | ··ABI·Version:·······················0 |
| 8 | ··Type:······························DYN·(Shared·object·file) | 8 | ··Type:······························DYN·(Shared·object·file) |
| 9 | ··Machine:···························Advanced·Micro·Devices·X86-64 | 9 | ··Machine:···························Advanced·Micro·Devices·X86-64 |
| 10 | ··Version:···························0x1 | 10 | ··Version:···························0x1 |
| 11 | ··Entry·point·address:···············0xee990 | 11 | ··Entry·point·address:···············0xee990 |
| 12 | ··Start·of·program·headers:··········64·(bytes·into·file) | 12 | ··Start·of·program·headers:··········64·(bytes·into·file) |
| 13 | ··Start·of·section·headers:··········51358 | 13 | ··Start·of·section·headers:··········51358944·(bytes·into·file) |
| 14 | ··Flags:·····························0x0 | 14 | ··Flags:·····························0x0 |
| 15 | ··Size·of·this·header:···············64·(bytes) | 15 | ··Size·of·this·header:···············64·(bytes) |
| 16 | ··Size·of·program·headers:···········56·(bytes) | 16 | ··Size·of·program·headers:···········56·(bytes) |
| 17 | ··Number·of·program·headers:·········14 | 17 | ··Number·of·program·headers:·········14 |
| 18 | ··Size·of·section·headers:···········64·(bytes) | 18 | ··Size·of·section·headers:···········64·(bytes) |
| 19 | ··Number·of·section·headers:·········42 | 19 | ··Number·of·section·headers:·········42 |
| 20 | ··Section·header·string·table·index:·41 | 20 | ··Section·header·string·table·index:·41 |
| Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
| 1 | There·are·42·section·headers,·starting·at·offset·0x30fac | 1 | There·are·42·section·headers,·starting·at·offset·0x30face0: |
| 2 | Section·Headers: | 2 | Section·Headers: |
| 3 | ··[Nr]·Name··············Type············Address··········Off····Size···ES·Flg·Lk·Inf·Al | 3 | ··[Nr]·Name··············Type············Address··········Off····Size···ES·Flg·Lk·Inf·Al |
| 4 | ··[·0]···················NULL············0000000000000000·000000·000000·00······0···0··0 | 4 | ··[·0]···················NULL············0000000000000000·000000·000000·00······0···0··0 |
| 5 | ··[·1]·.interp···········NOBITS··········0000000000000350·000350·00001c·00···A··0···0··1 | 5 | ··[·1]·.interp···········NOBITS··········0000000000000350·000350·00001c·00···A··0···0··1 |
| 6 | ··[·2]·.note.gnu.property·NOTE············0000000000000370·000370·000020·00···A··0···0··8 | 6 | ··[·2]·.note.gnu.property·NOTE············0000000000000370·000370·000020·00···A··0···0··8 |
| 7 | ··[·3]·.note.gnu.build-id·NOTE············0000000000000390·000390·000024·00···A··0···0··4 | 7 | ··[·3]·.note.gnu.build-id·NOTE············0000000000000390·000390·000024·00···A··0···0··4 |
| Offset 29, 23 lines modified | Offset 29, 23 lines modified | ||
| 29 | ··[24]·.data.rel.ro······NOBITS··········00000000008424c0·001140·015248·00··WA··0···0·32 | 29 | ··[24]·.data.rel.ro······NOBITS··········00000000008424c0·001140·015248·00··WA··0···0·32 |
| 30 | ··[25]·.dynamic··········NOBITS··········0000000000857708·001140·0003c0·10··WA··7···0··8 | 30 | ··[25]·.dynamic··········NOBITS··········0000000000857708·001140·0003c0·10··WA··7···0··8 |
| 31 | ··[26]·.got··············NOBITS··········0000000000857ac8·001140·002528·08··WA··0···0··8 | 31 | ··[26]·.got··············NOBITS··········0000000000857ac8·001140·002528·08··WA··0···0··8 |
| 32 | ··[27]·.data·············NOBITS··········000000000085a000·001140·000b60·00··WA··0···0·32 | 32 | ··[27]·.data·············NOBITS··········000000000085a000·001140·000b60·00··WA··0···0·32 |
| 33 | ··[28]·.bss··············NOBITS··········000000000085ab80·001140·3f01d0·00··WA··0···0·64 | 33 | ··[28]·.bss··············NOBITS··········000000000085ab80·001140·3f01d0·00··WA··0···0·64 |
| 34 | ··[29]·.comment··········PROGBITS········0000000000000000·0003d4·00001e·01··MS··0···0··1 | 34 | ··[29]·.comment··········PROGBITS········0000000000000000·0003d4·00001e·01··MS··0···0··1 |
| 35 | ··[30]·.debug_aranges····PROGBITS········0000000000000000·0003f8·0098bc·00···C··0···0··8 | 35 | ··[30]·.debug_aranges····PROGBITS········0000000000000000·0003f8·0098bc·00···C··0···0··8 |
| 36 | ··[31]·.debug_info·······PROGBITS········0000000000000000·009cb8·1ae8 | 36 | ··[31]·.debug_info·······PROGBITS········0000000000000000·009cb8·1ae8c16·00···C··0···0··8 |
| 37 | ··[32]·.debug_abbrev·····PROGBITS········0000000000000000·1af28 | 37 | ··[32]·.debug_abbrev·····PROGBITS········0000000000000000·1af28d0·03ace9·00···C··0···0··8 |
| 38 | ··[33]·.debug_line·······PROGBITS········0000000000000000·1b2d | 38 | ··[33]·.debug_line·······PROGBITS········0000000000000000·1b2d5c0·2951d0·00···C··0···0··8 |
| 39 | ··[34]·.debug_str········PROGBITS········0000000000000000·1dc2 | 39 | ··[34]·.debug_str········PROGBITS········0000000000000000·1dc2790·9007c9·01·MSC··0···0··8 |
| 40 | ··[35]·.debug_line_str···PROGBITS········0000000000000000·26c2 | 40 | ··[35]·.debug_line_str···PROGBITS········0000000000000000·26c2f60·0035e6·01·MSC··0···0··8 |
| 41 | ··[36]·.debug_loclists···PROGBITS········0000000000000000·26c6 | 41 | ··[36]·.debug_loclists···PROGBITS········0000000000000000·26c6548·5a61ed·00···C··0···0··8 |
| 42 | ··[37]·.debug_macro······PROGBITS········0000000000000000·2c6c | 42 | ··[37]·.debug_macro······PROGBITS········0000000000000000·2c6c738·0e089c·00···C··0···0··8 |
| 43 | ··[38]·.debug_rnglists···PROGBITS········0000000000000000·2d4cf | 43 | ··[38]·.debug_rnglists···PROGBITS········0000000000000000·2d4cfd8·13f785·00···C··0···0··8 |
| 44 | ··[39]·.symtab···········SYMTAB··········0000000000000000·2e8c | 44 | ··[39]·.symtab···········SYMTAB··········0000000000000000·2e8c760·08f3a0·18·····40·8679··8 |
| 45 | ··[40]·.strtab···········STRTAB··········0000000000000000·2f1b | 45 | ··[40]·.strtab···········STRTAB··········0000000000000000·2f1bb00·1df02c·00······0···0··1 |
| 46 | ··[41]·.shstrtab·········STRTAB··········0000000000000000·30fa | 46 | ··[41]·.shstrtab·········STRTAB··········0000000000000000·30fab2c·0001b3·00······0···0··1 |
| 47 | Key·to·Flags: | 47 | Key·to·Flags: |
| 48 | ··W·(write),·A·(alloc),·X·(execute),·M·(merge),·S·(strings),·I·(info), | 48 | ··W·(write),·A·(alloc),·X·(execute),·M·(merge),·S·(strings),·I·(info), |
| 49 | ··L·(link·order),·O·(extra·OS·processing·required),·G·(group),·T·(TLS), | 49 | ··L·(link·order),·O·(extra·OS·processing·required),·G·(group),·T·(TLS), |
| 50 | ··C·(compressed),·x·(unknown),·o·(OS·specific),·E·(exclude), | 50 | ··C·(compressed),·x·(unknown),·o·(OS·specific),·E·(exclude), |
| 51 | ··R·(retain),·D·(mbind),·l·(large),·p·(processor·specific) | 51 | ··R·(retain),·D·(mbind),·l·(large),·p·(processor·specific) |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | Displaying·notes·found·in:·.note.gnu.property | 1 | Displaying·notes·found·in:·.note.gnu.property |
| 2 | ··Owner················Data·size·» Description | 2 | ··Owner················Data·size·» Description |
| 3 | ··GNU··················0x00000010» NT_GNU_PROPERTY_TYPE_0» ······Properties:·x86·ISA·needed:·x86-64-baseline | 3 | ··GNU··················0x00000010» NT_GNU_PROPERTY_TYPE_0» ······Properties:·x86·ISA·needed:·x86-64-baseline |
| 4 | Displaying·notes·found·in:·.note.gnu.build-id | 4 | Displaying·notes·found·in:·.note.gnu.build-id |
| 5 | ··Owner················Data·size·» Description | 5 | ··Owner················Data·size·» Description |
| 6 | ··GNU··················0x00000014» NT_GNU_BUILD_ID·(unique·build·ID·bitstring)» ····Build·ID:·7 | 6 | ··GNU··················0x00000014» NT_GNU_BUILD_ID·(unique·build·ID·bitstring)» ····Build·ID:·a9722da9714e39e4e5a4d717c943ae4df094d501 |
| 7 | Displaying·notes·found·in:·.note.ABI-tag | 7 | Displaying·notes·found·in:·.note.ABI-tag |
| 8 | ··Owner················Data·size·» Description | 8 | ··Owner················Data·size·» Description |
| 9 | ··GNU··················0x00000010» NT_GNU_ABI_TAG·(ABI·version·tag)» ····OS:·Linux,·ABI:·3.2.0 | 9 | ··GNU··················0x00000010» NT_GNU_ABI_TAG·(ABI·version·tag)» ····OS:·Linux,·ABI:·3.2.0 |
| Offset 11507, 15 lines modified | Offset 11507, 15 lines modified | ||
| 11507 | ·DW_MACRO_define_strp·-·lineno·:·310·macro·:·PACKAGE_BUGREPORT·"https://github.com/Macaulay2/M2/issues" | 11507 | ·DW_MACRO_define_strp·-·lineno·:·310·macro·:·PACKAGE_BUGREPORT·"https://github.com/Macaulay2/M2/issues" |
| 11508 | ·DW_MACRO_define_strp·-·lineno·:·313·macro·:·PACKAGE_NAME·"Macaulay2" | 11508 | ·DW_MACRO_define_strp·-·lineno·:·313·macro·:·PACKAGE_NAME·"Macaulay2" |
| 11509 | ·DW_MACRO_define_strp·-·lineno·:·316·macro·:·PACKAGE_STRING·"Macaulay2·1.24.11" | 11509 | ·DW_MACRO_define_strp·-·lineno·:·316·macro·:·PACKAGE_STRING·"Macaulay2·1.24.11" |
| 11510 | ·DW_MACRO_define_strp·-·lineno·:·319·macro·:·PACKAGE_TARNAME·"Macaulay2" | 11510 | ·DW_MACRO_define_strp·-·lineno·:·319·macro·:·PACKAGE_TARNAME·"Macaulay2" |
| 11511 | ·DW_MACRO_define_strp·-·lineno·:·322·macro·:·PACKAGE_URL·"https://macaulay2.com/" | 11511 | ·DW_MACRO_define_strp·-·lineno·:·322·macro·:·PACKAGE_URL·"https://macaulay2.com/" |
| 11512 | ·DW_MACRO_define_strp·-·lineno·:·325·macro·:·PACKAGE_VERSION·"1.24.11" | 11512 | ·DW_MACRO_define_strp·-·lineno·:·325·macro·:·PACKAGE_VERSION·"1.24.11" |
| 11513 | ·DW_MACRO_define_strp·-·lineno·:·328·macro·:·PROFILING·0 | 11513 | ·DW_MACRO_define_strp·-·lineno·:·328·macro·:·PROFILING·0 |
| 11514 | ·DW_MACRO_define_strp·-·lineno·:·331·macro·:·REL·"6.1 | 11514 | ·DW_MACRO_define_strp·-·lineno·:·331·macro·:·REL·"6.10.11+bpo-amd64" |
| 11515 | ·DW_MACRO_define_strp·-·lineno·:·334·macro·:·SIZEOF_INT_P·8 | 11515 | ·DW_MACRO_define_strp·-·lineno·:·334·macro·:·SIZEOF_INT_P·8 |
| 11516 | ·DW_MACRO_define_strp·-·lineno·:·337·macro·:·SIZEOF_LONG·8 | 11516 | ·DW_MACRO_define_strp·-·lineno·:·337·macro·:·SIZEOF_LONG·8 |
| 11517 | ·DW_MACRO_define_strp·-·lineno·:·350·macro·:·STDC_HEADERS·1 | 11517 | ·DW_MACRO_define_strp·-·lineno·:·350·macro·:·STDC_HEADERS·1 |
| 11518 | ·DW_MACRO_define_strp·-·lineno·:·356·macro·:·WITH_NEWLINE_CR·0 | 11518 | ·DW_MACRO_define_strp·-·lineno·:·356·macro·:·WITH_NEWLINE_CR·0 |
| 11519 | ·DW_MACRO_define_strp·-·lineno·:·359·macro·:·WITH_NEWLINE_CRLF·0 | 11519 | ·DW_MACRO_define_strp·-·lineno·:·359·macro·:·WITH_NEWLINE_CRLF·0 |
| 11520 | ·DW_MACRO_define_strp·-·lineno·:·362·macro·:·WITH_PYTHON·1 | 11520 | ·DW_MACRO_define_strp·-·lineno·:·362·macro·:·WITH_PYTHON·1 |
| 11521 | ·DW_MACRO_define_strp·-·lineno·:·365·macro·:·WITH_TBB·1 | 11521 | ·DW_MACRO_define_strp·-·lineno·:·365·macro·:·WITH_TBB·1 |
| Offset 2640748, 15 lines modified | Offset 2640748, 15 lines modified | ||
| 2640748 | ····00779336·v000000000000001·v000000000000000·views·at·00779334·for: | 2640748 | ····00779336·v000000000000001·v000000000000000·views·at·00779334·for: |
| 2640749 | ·············00000000002c76fd·00000000002c771b·(DW_OP_reg6·(rbp)) | 2640749 | ·············00000000002c76fd·00000000002c771b·(DW_OP_reg6·(rbp)) |
| 2640750 | ····00779342·<End·of·list> | 2640750 | ····00779342·<End·of·list> |
| 2640751 | ····00779343·v000000000000001·v000000000000000·location·view·pair | 2640751 | ····00779343·v000000000000001·v000000000000000·location·view·pair |
| 2640752 | ····00779345·v000000000000001·v000000000000000·views·at·00779343·for: | 2640752 | ····00779345·v000000000000001·v000000000000000·views·at·00779343·for: |
| 2640753 | ·············00000000002c76fd·00000000002c771b·(DW_OP_addr:·6d610 | 2640753 | ·············00000000002c76fd·00000000002c771b·(DW_OP_addr:·6d6102;·DW_OP_stack_value) |
| 2640754 | ····0077935a·<End·of·list> | 2640754 | ····0077935a·<End·of·list> |
| 2640755 | ····0077935b·v000000000000002·v000000000000001·location·view·pair | 2640755 | ····0077935b·v000000000000002·v000000000000001·location·view·pair |
| 2640756 | ····0077935d·v000000000000002·v000000000000001·views·at·0077935b·for: | 2640756 | ····0077935d·v000000000000002·v000000000000001·views·at·0077935b·for: |
| 2640757 | ·············00000000002c77b4·00000000002c77c5·(DW_OP_reg6·(rbp)) | 2640757 | ·············00000000002c77b4·00000000002c77c5·(DW_OP_reg6·(rbp)) |
| 2640758 | ····00779369·<End·of·list> | 2640758 | ····00779369·<End·of·list> |
| Offset 2710541, 15 lines modified | Offset 2710541, 15 lines modified | ||
| 2710541 | ····007acff9·v000000000000001·v000000000000001·views·at·007acff7·for: | 2710541 | ····007acff9·v000000000000001·v000000000000001·views·at·007acff7·for: |
| 2710542 | ·············00000000002db058·00000000002db067·(DW_OP_reg3·(rbx)) | 2710542 | ·············00000000002db058·00000000002db067·(DW_OP_reg3·(rbx)) |
| 2710543 | ····007ad005·<End·of·list> | 2710543 | ····007ad005·<End·of·list> |
| 2710544 | ····007ad006·v000000000000001·v000000000000001·location·view·pair | 2710544 | ····007ad006·v000000000000001·v000000000000001·location·view·pair |
| 2710545 | ····007ad008·v000000000000001·v000000000000001·views·at·007ad006·for: | 2710545 | ····007ad008·v000000000000001·v000000000000001·views·at·007ad006·for: |
| 2710546 | ·············00000000002db058·00000000002db067·(DW_OP_addr:·6d619 | 2710546 | ·············00000000002db058·00000000002db067·(DW_OP_addr:·6d619b;·DW_OP_stack_value) |
| 2710547 | ····007ad01d·<End·of·list> | 2710547 | ····007ad01d·<End·of·list> |
| 2710548 | ····007ad01e·v000000000000001·v000000000000001·location·view·pair | 2710548 | ····007ad01e·v000000000000001·v000000000000001·location·view·pair |
| 2710549 | ····007ad020·v000000000000001·v000000000000001·views·at·007ad01e·for: | 2710549 | ····007ad020·v000000000000001·v000000000000001·views·at·007ad01e·for: |
| 2710550 | ·············00000000002db067·00000000002db073·(DW_OP_reg3·(rbx)) | 2710550 | ·············00000000002db067·00000000002db073·(DW_OP_reg3·(rbx)) |
| 2710551 | ····007ad02c·<End·of·list> | 2710551 | ····007ad02c·<End·of·list> |
| Offset 3224092, 15 lines modified | Offset 3224092, 15 lines modified | ||
| 3224092 | ····00929330·v000000000000001·v000000000000001·views·at·0092932e·for: | 3224092 | ····00929330·v000000000000001·v000000000000001·views·at·0092932e·for: |
| 3224093 | ·············000000000036ff14·000000000036ff23·(DW_OP_reg6·(rbp)) | 3224093 | ·············000000000036ff14·000000000036ff23·(DW_OP_reg6·(rbp)) |
| 3224094 | ····0092933c·<End·of·list> | 3224094 | ····0092933c·<End·of·list> |
| 3224095 | ····0092933d·v000000000000001·v000000000000001·location·view·pair | 3224095 | ····0092933d·v000000000000001·v000000000000001·location·view·pair |
| 3224096 | ····0092933f·v000000000000001·v000000000000001·views·at·0092933d·for: | 3224096 | ····0092933f·v000000000000001·v000000000000001·views·at·0092933d·for: |
| 3224097 | ·············000000000036ff14·000000000036ff23·(DW_OP_addr:·6d620 | 3224097 | ·············000000000036ff14·000000000036ff23·(DW_OP_addr:·6d6204;·DW_OP_stack_value) |
| 3224098 | ····00929354·<End·of·list> | 3224098 | ····00929354·<End·of·list> |
| 3224099 | ····00929355·v000000000000001·v000000000000000·location·view·pair | 3224099 | ····00929355·v000000000000001·v000000000000000·location·view·pair |
| 3224100 | ····00929357·v000000000000000·v000000000000000·location·view·pair | 3224100 | ····00929357·v000000000000000·v000000000000000·location·view·pair |
| 3224101 | ····00929359·v000000000000000·v000000000000000·location·view·pair | 3224101 | ····00929359·v000000000000000·v000000000000000·location·view·pair |
| 3224102 | ····0092935b·000000000036ff8f·(base·address) | 3224102 | ····0092935b·000000000036ff8f·(base·address) |
| Offset 3251957, 15 lines modified | Offset 3251957, 15 lines modified | ||
| 3251957 | ····0093eda0·v000000000000001·v000000000000001·views·at·0093ed9e·for: | 3251957 | ····0093eda0·v000000000000001·v000000000000001·views·at·0093ed9e·for: |
| 3251958 | ·············0000000000377f73·0000000000377f82·(DW_OP_reg6·(rbp)) | 3251958 | ·············0000000000377f73·0000000000377f82·(DW_OP_reg6·(rbp)) |
| 3251959 | ····0093edac·<End·of·list> | 3251959 | ····0093edac·<End·of·list> |
| 3251960 | ····0093edad·v000000000000001·v000000000000001·location·view·pair | 3251960 | ····0093edad·v000000000000001·v000000000000001·location·view·pair |
| 3251961 | ····0093edaf·v000000000000001·v000000000000001·views·at·0093edad·for: | 3251961 | ····0093edaf·v000000000000001·v000000000000001·views·at·0093edad·for: |
| 3251962 | ·············0000000000377f73·0000000000377f82·(DW_OP_addr:·6d620 | 3251962 | ·············0000000000377f73·0000000000377f82·(DW_OP_addr:·6d6204;·DW_OP_stack_value) |
| 3251963 | ····0093edc4·<End·of·list> | 3251963 | ····0093edc4·<End·of·list> |
| 3251964 | ····0093edc5·v000000000000001·v000000000000000·location·view·pair | 3251964 | ····0093edc5·v000000000000001·v000000000000000·location·view·pair |
| 3251965 | ····0093edc7·v000000000000000·v000000000000000·location·view·pair | 3251965 | ····0093edc7·v000000000000000·v000000000000000·location·view·pair |
| 3251966 | ····0093edc9·v000000000000000·v000000000000000·location·view·pair | 3251966 | ····0093edc9·v000000000000000·v000000000000000·location·view·pair |
| 3251967 | ····0093edcb·0000000000377fef·(base·address) | 3251967 | ····0093edcb·0000000000377fef·(base·address) |
| Offset 3539896, 15 lines modified | Offset 3539896, 15 lines modified | ||
| 3539896 | ····00a1945b·v000000000000001·v000000000000001·views·at·00a19459·for: | 3539896 | ····00a1945b·v000000000000001·v000000000000001·views·at·00a19459·for: |
| 3539897 | ·············00000000003b55ac·00000000003b55bb·(DW_OP_reg6·(rbp)) | 3539897 | ·············00000000003b55ac·00000000003b55bb·(DW_OP_reg6·(rbp)) |
| 3539898 | ····00a19467·<End·of·list> | 3539898 | ····00a19467·<End·of·list> |
| 3539899 | ····00a19468·v000000000000001·v000000000000001·location·view·pair | 3539899 | ····00a19468·v000000000000001·v000000000000001·location·view·pair |
| 3539900 | ····00a1946a·v000000000000001·v000000000000001·views·at·00a19468·for: | 3539900 | ····00a1946a·v000000000000001·v000000000000001·views·at·00a19468·for: |
| 3539901 | ·············00000000003b55ac·00000000003b55bb·(DW_OP_addr:·6d620 | 3539901 | ·············00000000003b55ac·00000000003b55bb·(DW_OP_addr:·6d6204;·DW_OP_stack_value) |
| 3539902 | ····00a1947f·<End·of·list> | 3539902 | ····00a1947f·<End·of·list> |
| 3539903 | ····00a19480·v000000000000001·v000000000000000·location·view·pair | 3539903 | ····00a19480·v000000000000001·v000000000000000·location·view·pair |
| 3539904 | ····00a19482·v000000000000001·v000000000000000·views·at·00a19480·for: | 3539904 | ····00a19482·v000000000000001·v000000000000000·views·at·00a19480·for: |
| 3539905 | ·············00000000003b5614·00000000003b561f·(DW_OP_reg6·(rbp)) | 3539905 | ·············00000000003b5614·00000000003b561f·(DW_OP_reg6·(rbp)) |
| 3539906 | ····00a1948e·<End·of·list> | 3539906 | ····00a1948e·<End·of·list> |
| Offset 3626751, 15 lines modified | Offset 3626751, 15 lines modified | ||
| 3626751 | ····00a5a55b·v000000000000001·v000000000000000·views·at·00a5a559·for: | 3626751 | ····00a5a55b·v000000000000001·v000000000000000·views·at·00a5a559·for: |
| 3626752 | ·············00000000003caccc·00000000003cacd3·(DW_OP_reg6·(rbp)) | 3626752 | ·············00000000003caccc·00000000003cacd3·(DW_OP_reg6·(rbp)) |
| 3626753 | ····00a5a567·<End·of·list> | 3626753 | ····00a5a567·<End·of·list> |
| 3626754 | ····00a5a568·v000000000000001·v000000000000000·location·view·pair | 3626754 | ····00a5a568·v000000000000001·v000000000000000·location·view·pair |
| 3626755 | ····00a5a56a·v000000000000001·v000000000000000·views·at·00a5a568·for: | 3626755 | ····00a5a56a·v000000000000001·v000000000000000·views·at·00a5a568·for: |
| 3626756 | ·············00000000003caccc·00000000003cacd3·(DW_OP_addr:·6d610 | 3626756 | ·············00000000003caccc·00000000003cacd3·(DW_OP_addr:·6d6102;·DW_OP_stack_value) |
| 3626757 | ····00a5a57f·<End·of·list> | 3626757 | ····00a5a57f·<End·of·list> |
| 3626758 | ····00a5a580·v000000000000000·v000000000000000·location·view·pair | 3626758 | ····00a5a580·v000000000000000·v000000000000000·location·view·pair |
| 3626759 | ····00a5a582·v000000000000000·v000000000000000·location·view·pair | 3626759 | ····00a5a582·v000000000000000·v000000000000000·location·view·pair |
| 3626760 | ····00a5a584·v000000000000000·v000000000000000·location·view·pair | 3626760 | ····00a5a584·v000000000000000·v000000000000000·location·view·pair |
| 3626761 | ····00a5a586·00000000003cb200·(base·address) | 3626761 | ····00a5a586·00000000003cb200·(base·address) |
| Offset 3628127, 15 lines modified | Offset 3628127, 15 lines modified | ||
| 3628127 | ····00a5b46f·v000000000000000·v000000000000000·views·at·00a5b46d·for: | 3628127 | ····00a5b46f·v000000000000000·v000000000000000·views·at·00a5b46d·for: |
| 3628128 | ·············00000000003ca469·00000000003ca478·(DW_OP_reg6·(rbp)) | 3628128 | ·············00000000003ca469·00000000003ca478·(DW_OP_reg6·(rbp)) |
| 3628129 | ····00a5b47b·<End·of·list> | 3628129 | ····00a5b47b·<End·of·list> |
| 3628130 | ····00a5b47c·v000000000000000·v000000000000000·location·view·pair | 3628130 | ····00a5b47c·v000000000000000·v000000000000000·location·view·pair |
| 3628131 | ····00a5b47e·v000000000000000·v000000000000000·views·at·00a5b47c·for: | 3628131 | ····00a5b47e·v000000000000000·v000000000000000·views·at·00a5b47c·for: |
| 3628132 | ·············00000000003ca469·00000000003ca478·(DW_OP_addr:·6d610 | 3628132 | ·············00000000003ca469·00000000003ca478·(DW_OP_addr:·6d6102;·DW_OP_stack_value) |
| 3628133 | ····00a5b493·<End·of·list> | 3628133 | ····00a5b493·<End·of·list> |
| 3628134 | ····00a5b494·v000000000000000·v000000000000000·location·view·pair | 3628134 | ····00a5b494·v000000000000000·v000000000000000·location·view·pair |
| 3628135 | ····00a5b496·v000000000000000·v000000000000000·location·view·pair | 3628135 | ····00a5b496·v000000000000000·v000000000000000·location·view·pair |
| 3628136 | ····00a5b498·v000000000000000·v000000000000000·location·view·pair | 3628136 | ····00a5b498·v000000000000000·v000000000000000·location·view·pair |
| 3628137 | ····00a5b49a·00000000003ca4b4·(base·address) | 3628137 | ····00a5b49a·00000000003ca4b4·(base·address) |
| Offset 3648377, 15 lines modified | Offset 3648377, 15 lines modified | ||
| 3648377 | ····00a6a800·v000000000000001·v000000000000001·views·at·00a6a7fe·for: | 3648377 | ····00a6a800·v000000000000001·v000000000000001·views·at·00a6a7fe·for: |
| 3648378 | ·············00000000003cf4d6·00000000003cf4f3·(DW_OP_fbreg:·-152) | 3648378 | ·············00000000003cf4d6·00000000003cf4f3·(DW_OP_fbreg:·-152) |
| 3648379 | ····00a6a80e·<End·of·list> | 3648379 | ····00a6a80e·<End·of·list> |
| 3648380 | ····00a6a80f·v000000000000001·v000000000000001·location·view·pair | 3648380 | ····00a6a80f·v000000000000001·v000000000000001·location·view·pair |
| 3648381 | ····00a6a811·v000000000000001·v000000000000001·views·at·00a6a80f·for: | 3648381 | ····00a6a811·v000000000000001·v000000000000001·views·at·00a6a80f·for: |
| 3648382 | ·············00000000003cf4d6·00000000003cf4f3·(DW_OP_addr:·6d610 | 3648382 | ·············00000000003cf4d6·00000000003cf4f3·(DW_OP_addr:·6d6102;·DW_OP_stack_value) |
| 3648383 | ····00a6a826·<End·of·list> | 3648383 | ····00a6a826·<End·of·list> |
| 3648384 | ····00a6a827·v000000000000000·v000000000000000·location·view·pair | 3648384 | ····00a6a827·v000000000000000·v000000000000000·location·view·pair |
| 3648385 | ····00a6a829·v000000000000000·v000000000000000·location·view·pair | 3648385 | ····00a6a829·v000000000000000·v000000000000000·location·view·pair |
| 3648386 | ····00a6a82b·v000000000000000·v000000000000000·location·view·pair | 3648386 | ····00a6a82b·v000000000000000·v000000000000000·location·view·pair |
| 3648387 | ····00a6a82d·v000000000000000·v000000000000000·location·view·pair | 3648387 | ····00a6a82d·v000000000000000·v000000000000000·location·view·pair |
| 3648388 | ····00a6a82f·v000000000000000·v000000000000000·location·view·pair | 3648388 | ····00a6a82f·v000000000000000·v000000000000000·location·view·pair |
| Max diff block lines reached; 2130/8549 bytes (24.92%) of diff not shown. | |||
| Offset 1, 6573 lines modified | Offset 1, 6505 lines modified | ||
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| Max diff block lines reached; 202143/206598 bytes (97.84%) of diff not shown. | |||