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| 1 | ·b912f785ba7885d26c5016893842df0b·59952·editors·optional·elpa-macaulay2_1.24.05+ds-5_all.deb | 1 | ·b912f785ba7885d26c5016893842df0b·59952·editors·optional·elpa-macaulay2_1.24.05+ds-5_all.deb |
| 2 | · | 2 | ·9da5d9fae7c7138a4508b9b3d2d0edc0·29641648·math·optional·macaulay2-common_1.24.05+ds-5_all.deb |
| 3 | · | 3 | ·02382528763406841e5f7cb61a24afe4·48522520·debug·optional·macaulay2-dbgsym_1.24.05+ds-5_amd64.deb |
| 4 | · | 4 | ·053588e7e134ed0dfd36677d38e15882·2567020·math·optional·macaulay2_1.24.05+ds-5_amd64.deb |
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| 1 | Package:·macaulay2-common | 1 | Package:·macaulay2-common |
| 2 | Source:·macaulay2 | 2 | Source:·macaulay2 |
| 3 | Version:·1.24.05+ds-5 | 3 | Version:·1.24.05+ds-5 |
| 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:·2853 | 6 | Installed-Size:·285362 |
| 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),·libjs-underscore·(>=·1.13.4~dfsg+~1.11.4),·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),·libjs-underscore·(>=·1.13.4~dfsg+~1.11.4),·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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| 3347 | -rw-r--r--···0·root·········(0)·root·········(0)·····5429·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/BettiCharacters/html/___Character_sp__Array.html | 3347 | -rw-r--r--···0·root·········(0)·root·········(0)·····5429·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/BettiCharacters/html/___Character_sp__Array.html |
| 3348 | -rw-r--r--···0·root·········(0)·root·········(0)·····4188·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/BettiCharacters/html/___Character_spoperations.html | 3348 | -rw-r--r--···0·root·········(0)·root·········(0)·····4188·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/BettiCharacters/html/___Character_spoperations.html |
| 3349 | -rw-r--r--···0·root·········(0)·root·········(0)·····6458·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/BettiCharacters/html/___Equality_spchecks.html | 3349 | -rw-r--r--···0·root·········(0)·root·········(0)·····6458·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/BettiCharacters/html/___Equality_spchecks.html |
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| 3619 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/dump/ | 3619 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/dump/ |
| 3620 | -rw-r--r--···0·root·········(0)·root·········(0)···125939·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/dump/rawdocumentation.dump | 3620 | -rw-r--r--···0·root·········(0)·root·········(0)···125939·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/dump/rawdocumentation.dump |
| 3621 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/example-output/ | 3621 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/example-output/ |
| 3622 | -rw-r--r--···0·root·········(0)·root·········(0)······917·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/example-output/___H__H^__Z__Z_sp__Cell__Complex.out | 3622 | -rw-r--r--···0·root·········(0)·root·········(0)······917·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/example-output/___H__H^__Z__Z_sp__Cell__Complex.out |
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| 3625 | -rw-r--r--···0·root·········(0)·root·········(0)······47 | 3625 | -rw-r--r--···0·root·········(0)·root·········(0)······475·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/example-output/___Ring__Map_sp_st_st_sp__Cell__Complex.out |
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| 3653 | -rw-r--r--···0·root·········(0)·root·········(0)······73 | 3653 | -rw-r--r--···0·root·········(0)·root·········(0)······730·2024-09-09·00:38:13.000000·./usr/share/doc/Macaulay2/CellularResolutions/example-output/_relabel__Cell__Complex.out |
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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=347 | 9 | #:len=347 |
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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=35 | 7 | #:len=35 |
| 8 | aGFzTWluaW1hbE11bHQoUmluZyxJbmZpbml0ZU51bWJlcik= | 8 | aGFzTWluaW1hbE11bHQoUmluZyxJbmZpbml0ZU51bWJlcik= |
| 9 | #:len=285 | 9 | #:len=285 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTQ4Nywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTQ4Nywgc3ltYm9sIERvY3VtZW50VGFn |
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| Offset 10, 25 lines modified | Offset 10, 25 lines modified | ||
| 10 | o2·=·cokernel·|·a·b·c·| | 10 | o2·=·cokernel·|·a·b·c·| |
| 11 | ····························1 | 11 | ····························1 |
| 12 | o2·:·R-module,·quotient·of·R | 12 | o2·:·R-module,·quotient·of·R |
| 13 | i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) | 13 | i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) |
| 14 | ·--· | 14 | ·--·1.44633·seconds·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 | ·--·1.73605·seconds·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 87, 26 lines modified | Offset 87, 26 lines modified | ||
| 87 | o2·=·cokernel·|·a·b·c·| | 87 | o2·=·cokernel·|·a·b·c·| |
| 88 | ····························1 | 88 | ····························1 |
| 89 | o2·:·R-module,·quotient·of·R</code></pre> | 89 | o2·:·R-module,·quotient·of·R</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false) |
| 93 | ·--· | 93 | ·--·1.44633·seconds·elapsed |
| 94 | ······1······3······9······27······81······243······729······2187 | 94 | ······1······3······9······27······81······243······729······2187 |
| 95 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 95 | o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 96 | ····························································· | 96 | ····························································· |
| 97 | ·····0······1······2······3·······4·······5········6········7 | 97 | ·····0······1······2······3·······4·······5········6········7 |
| 98 | o3·:·Complex</code></pre> | 98 | o3·:·Complex</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true) |
| 102 | ·--· | 102 | ·--·1.73605·seconds·elapsed |
| 103 | ······1······3······9······27······81······243······729······2187 | 103 | ······1······3······9······27······81······243······729······2187 |
| 104 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R | 104 | o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R |
| 105 | ····························································· | 105 | ····························································· |
| 106 | ·····0······1······2······3·······4·······5········6········7 | 106 | ·····0······1······2······3·······4·······5········6········7 |
| 107 | o4·:·Complex</code></pre> | 107 | 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 | ·--· | 29 | ·--·1.44633·seconds·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 | ·--·1.73605·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | QWJzdHJhY3RUb3JpY1ZhcmlldGllcw== | 8 | QWJzdHJhY3RUb3JpY1ZhcmlldGllcw== |
| 9 | #:len=379 | 9 | #:len=379 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibGlua3MgYWJzdHJhY3Qgc2ltcGxpY2lh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibGlua3MgYWJzdHJhY3Qgc2ltcGxpY2lh |
| 11 | bCAobm9ybWFsKSB0b3JpYyB2YXJpZXRpZXMgdG8gU2NodWJlcnQyIiwgRGVzY3JpcHRpb24gPT4g | 11 | bCAobm9ybWFsKSB0b3JpYyB2YXJpZXRpZXMgdG8gU2NodWJlcnQyIiwgRGVzY3JpcHRpb24gPT4g |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.0 | 53 | ·--·0.0170346·seconds·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 | ·--·0. | 91 | ·--·0.394243·seconds·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 | ·--·3.99616·seconds·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 | ·--·0.10 | 84 | ·--·0.0107638·seconds·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 | ·--·0.0441086·seconds·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 | ·--· | 99 | ·--·1.31903·seconds·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 131, 15 lines modified | Offset 131, 15 lines modified | ||
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i9·:·c=codim·I | 132 | <td>··············<pre><code·class="language-macaulay2">i9·:·c=codim·I |
| 133 | o9·=·4</code></pre> | 133 | o9·=·4</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I | 136 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I |
| 137 | ·--·0.0 | 137 | ·--·0.0170346·seconds·elapsed |
| 138 | ········1·······14·······33·······28·······8 | 138 | ········1·······14·······33·······28·······8 |
| 139 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 | 139 | o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0 |
| 140 | ·················································· | 140 | ·················································· |
| 141 | ······0·······1········2········3········4·······5 | 141 | ······0·······1········2········3········4·······5 |
| 142 | o10·:·ChainComplex</code></pre> | 142 | 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 | ·--·0.0 | 60 | ·--·0.0170346·seconds·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 193, 15 lines modified | Offset 193, 15 lines modified | ||
| 193 | ··········<tr> | 193 | ··········<tr> |
| 194 | <td>··············<pre><code·class="language-macaulay2">i14·:·phi=map(P2,Pn,H); | 194 | <td>··············<pre><code·class="language-macaulay2">i14·:·phi=map(P2,Pn,H); |
| 195 | o14·:·RingMap·P2·<--·Pn</code></pre> | 195 | o14·:·RingMap·P2·<--·Pn</code></pre> |
| 196 | </td>··········</tr> | 196 | </td>··········</tr> |
| 197 | ··········<tr> | 197 | ··········<tr> |
| 198 | <td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi) | 198 | <td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi) |
| 199 | ·--·0. | 199 | ·--·0.394243·seconds·elapsed |
| 200 | ·············0··1 | 200 | ·············0··1 |
| 201 | o15·=·total:·1·11 | 201 | o15·=·total:·1·11 |
| 202 | ··········0:·1··. | 202 | ··········0:·1··. |
| 203 | ··········1:·.··3 | 203 | ··········1:·.··3 |
| 204 | ··········2:·.··8 | 204 | ··········2:·.··8 |
| Offset 210, 15 lines modified | Offset 210, 15 lines modified | ||
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i16·:·I'==·I | 211 | <td>··············<pre><code·class="language-macaulay2">i16·:·I'==·I |
| 212 | o16·=·true</code></pre> | 212 | o16·=·true</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ··········<tr> | 214 | ··········<tr> |
| 215 | <td>··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 215 | <td>··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 216 | ·--· | 216 | ·--·3.99616·seconds·elapsed</code></pre> |
| 217 | </td>··········</tr> | 217 | </td>··········</tr> |
| 218 | ··········<tr> | 218 | ··········<tr> |
| 219 | <td>··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 219 | <td>··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 220 | ··························0·1 | 220 | ··························0·1 |
| 221 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} | 221 | o18·=·Tally{(1,·1,·total:·1·2)·=>·5} |
| 222 | ·······················0:·1·2 | 222 | ·······················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 | ·--·0. | 116 | ·--·0.394243·seconds·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 | ·--·3.99616·seconds·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 168, 28 lines modified | Offset 168, 28 lines modified | ||
| 168 | ··········2:·.·. | 168 | ··········2:·.·. |
| 169 | ··········3:·.·8 | 169 | ··········3:·.·8 |
| 170 | o13·:·BettiTally</code></pre> | 170 | o13·:·BettiTally</code></pre> |
| 171 | </td>··········</tr> | 171 | </td>··········</tr> |
| 172 | ··········<tr> | 172 | ··········<tr> |
| 173 | <td>··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H) | 173 | <td>··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H) |
| 174 | ·--·0.10 | 174 | ·--·0.0107638·seconds·elapsed |
| 175 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) | 175 | o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0) |
| 176 | o14·:·Ideal·of·P2</code></pre> | 176 | o14·:·Ideal·of·P2</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ··········<tr> | 178 | ··········<tr> |
| 179 | <td>··············<pre><code·class="language-macaulay2">i15·:·phi=map(P2,Pn,H); | 179 | <td>··············<pre><code·class="language-macaulay2">i15·:·phi=map(P2,Pn,H); |
| 180 | o15·:·RingMap·P2·<--·Pn</code></pre> | 180 | o15·:·RingMap·P2·<--·Pn</code></pre> |
| 181 | </td>··········</tr> | 181 | </td>··········</tr> |
| 182 | ··········<tr> | 182 | ··········<tr> |
| 183 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi) | 183 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi) |
| 184 | ·--·0. | 184 | ·--·0.0441086·seconds·elapsed |
| 185 | ·············0··1 | 185 | ·············0··1 |
| 186 | o16·=·total:·1·12 | 186 | o16·=·total:·1·12 |
| 187 | ··········0:·1··. | 187 | ··········0:·1··. |
| 188 | ··········1:·.·12 | 188 | ··········1:·.·12 |
| 189 | o16·:·BettiTally</code></pre> | 189 | o16·:·BettiTally</code></pre> |
| Offset 197, 15 lines modified | Offset 197, 15 lines modified | ||
| 197 | ··········<tr> | 197 | ··········<tr> |
| 198 | <td>··············<pre><code·class="language-macaulay2">i17·:·I'==·I | 198 | <td>··············<pre><code·class="language-macaulay2">i17·:·I'==·I |
| 199 | o17·=·true</code></pre> | 199 | o17·=·true</code></pre> |
| 200 | </td>··········</tr> | 200 | </td>··········</tr> |
| 201 | ··········<tr> | 201 | ··········<tr> |
| 202 | <td>··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; | 202 | <td>··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H; |
| 203 | ·--· | 203 | ·--·1.31903·seconds·elapsed</code></pre> |
| 204 | </td>··········</tr> | 204 | </td>··········</tr> |
| 205 | ··········<tr> | 205 | ··········<tr> |
| 206 | <td>··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) | 206 | <td>··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c)) |
| 207 | ···························0··1 | 207 | ···························0··1 |
| 208 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} | 208 | o19·=·Tally{(0,·34,·total:·1·15)·=>·1} |
| 209 | ························0:·1··. | 209 | ························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 | ·--·0.10 | 89 | ·--·0.0107638·seconds·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 | ·--·0.0441086·seconds·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 | ·--· | 104 | ·--·1.31903·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.493988s·(cpu);·0.314954s·(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·0.4 | 127 | ·--·used·0.472162s·(cpu);·0.333546s·(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 229, 15 lines modified | Offset 229, 15 lines modified | ||
| 229 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| | 229 | ······|·-10a-29b·39a+21b··-43a-15b·45a-34b··| |
| 230 | ··············4······4 | 230 | ··············4······4 |
| 231 | o13·:·Matrix·A··<--·A</code></pre> | 231 | o13·:·Matrix·A··<--·A</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| 233 | ··········<tr> | 233 | ··········<tr> |
| 234 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) | 234 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4})) |
| 235 | ·--·used·0. | 235 | ·--·used·0.493988s·(cpu);·0.314954s·(thread);·0s·(gc) |
| 236 | ·············0·1·2 | 236 | ·············0·1·2 |
| 237 | o14·=·total:·3·6·3 | 237 | o14·=·total:·3·6·3 |
| 238 | ··········0:·3·.·. | 238 | ··········0:·3·.·. |
| 239 | ··········1:·.·6·. | 239 | ··········1:·.·6·. |
| 240 | ··········2:·.·.·3 | 240 | ··········2:·.·.·3 |
| Offset 246, 15 lines modified | Offset 246, 15 lines modified | ||
| 246 | ········</table> | 246 | ········</table> |
| 247 | ········<div> | 247 | ········<div> |
| 248 | ··········<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 | ··········<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> |
| 249 | ········</div> | 249 | ········</div> |
| 250 | ········<table·class="examples"> | 250 | ········<table·class="examples"> |
| 251 | ··········<tr> | 251 | ··········<tr> |
| 252 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) | 252 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4})) |
| 253 | ·--·used·0.4 | 253 | ·--·used·0.472162s·(cpu);·0.333546s·(thread);·0s·(gc) |
| 254 | ·············0·1·2 | 254 | ·············0·1·2 |
| 255 | o15·=·total:·3·6·3 | 255 | o15·=·total:·3·6·3 |
| 256 | ··········0:·3·.·. | 256 | ··········0:·3·.·. |
| 257 | ··········1:·.·6·. | 257 | ··········1:·.·6·. |
| 258 | ··········2:·.·.·3 | 258 | ··········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·0.493988s·(cpu);·0.314954s·(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·0.4 | 181 | ·--·used·0.472162s·(cpu);·0.333546s·(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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| 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, 10 lines modified | Offset 1, 10 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-894285193 | 1 | --·-*-·M2-comint·-*-·hash:·-894285193 |
| 2 | i1·:·runBenchmarks·"res39" | 2 | i1·:·runBenchmarks·"res39" |
| 3 | --·beginning·computation· | 3 | --·beginning·computation·Wed·Oct·16·04:21:46·+14·2024 |
| 4 | --·Linux·i | 4 | --·Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·x86_64·GNU/Linux |
| 5 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz· | 5 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·2196.688·· |
| 6 | --·Macaulay2·1.24.05,·compiled·with·gcc·14.2.0 | 6 | --·Macaulay2·1.24.05,·compiled·with·gcc·14.2.0 |
| 7 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.1 | 7 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.118286·seconds |
| 8 | i2·:· | 8 | i2·:· |
| Offset 74, 19 lines modified | Offset 74, 19 lines modified | ||
| 74 | ········<h2>Description</h2> | 74 | ········<h2>Description</h2> |
| 75 | ········<div> | 75 | ········<div> |
| 76 | ··········<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 | ··········<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> |
| 77 | ········</div> | 77 | ········</div> |
| 78 | ········<table·class="examples"> | 78 | ········<table·class="examples"> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·"res39" | 80 | <td>··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·"res39" |
| 81 | --·beginning·computation· | 81 | --·beginning·computation·Wed·Oct·16·04:21:46·+14·2024 |
| 82 | --·Linux·i | 82 | --·Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·x86_64·GNU/Linux |
| 83 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz· | 83 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·2196.688·· |
| 84 | --·Macaulay2·1.24.05,·compiled·with·gcc·14.2.0 | 84 | --·Macaulay2·1.24.05,·compiled·with·gcc·14.2.0 |
| 85 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.1 | 85 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.118286·seconds</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>For·the·programmer</h2> | 90 | ········<h2>For·the·programmer</h2> |
| 91 | ········<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 | ········<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> |
| 92 | ······</div> | 92 | ······</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·Mon·Nov·17·06:10:00·-12·2025 | ||
| 32 | --· | 31 | --·beginning·computation·Wed·Oct·16·04:21:46·+14·2024 |
| 32 | --·Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC | ||
| 33 | 33 | Debian·6.1.112-1·(2024-09-30)·x86_64·GNU/Linux | |
| 34 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz· | 34 | --·AMD·EPYC-Rome·Processor··AuthenticAMD··cpu·MHz·2196.688 |
| 35 | --·Macaulay2·1.24.05,·compiled·with·gcc·14.2.0 | 35 | --·Macaulay2·1.24.05,·compiled·with·gcc·14.2.0 |
| 36 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.1 | 36 | --·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.118286·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 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]--> | 83 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]--> |
| 84 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> | 84 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> |
| 85 | ··············<li> | 85 | ··············<li> |
| 86 | <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 | <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> |
| 87 | ··············<li> | 87 | ··············<li> |
| 88 | <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 | <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> |
| 89 | ··············<li> | 89 | ··············<li> |
| 90 | <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- | 90 | <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/M2-2335887-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li> |
| 91 | ··············<li> | 91 | ··············<li> |
| 92 | <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 | <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> |
| 93 | ············</ul> | 93 | ············</ul> |
| 94 | ··········</li> | 94 | ··········</li> |
| 95 | ··········<li> | 95 | ··········<li> |
| 96 | Outputs:············<ul> | 96 | Outputs:············<ul> |
| 97 | ··············<li> | 97 | ··············<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/M2-2335887-0/0",·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 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | ··············<li> | 89 | ··············<li> |
| 90 | <span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]--> | 90 | <span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]--> |
| 91 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> | 91 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> |
| 92 | ··············<li> | 92 | ··············<li> |
| 93 | <span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]--> | 93 | <span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]--> |
| 94 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> | 94 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li> |
| 95 | ··············<li> | 95 | ··············<li> |
| 96 | <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- | 96 | <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/M2-2335887-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li> |
| 97 | ··············<li> | 97 | ··············<li> |
| 98 | <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 | <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> |
| 99 | ············</ul> | 99 | ············</ul> |
| 100 | ··········</li> | 100 | ··········</li> |
| 101 | ··········<li> | 101 | ··········<li> |
| 102 | Outputs:············<ul> | 102 | Outputs:············<ul> |
| 103 | ··············<li> | 103 | ··············<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/M2-2335887-0/0",·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 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]--> | 92 | <span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]--> |
| 93 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> | 93 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li> |
| 94 | ··············<li> | 94 | ··············<li> |
| 95 | <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 | <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> |
| 96 | ··············<li> | 96 | ··············<li> |
| 97 | <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 | <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> |
| 98 | ··············<li> | 98 | ··············<li> |
| 99 | <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- | 99 | <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/M2-2335887-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li> |
| 100 | ··············<li> | 100 | ··············<li> |
| 101 | <span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]--> | 101 | <span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]--> |
| 102 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span>··············</li> | 102 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span>··············</li> |
| 103 | ··············<li> | 103 | ··············<li> |
| 104 | <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 | <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> |
| 105 | ············</ul> | 105 | ············</ul> |
| 106 | ··········</li> | 106 | ··········</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/M2-2335887-0/0",·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjg1Miwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjg1Miwgc3ltYm9sIERvY3VtZW50VGFn |
| 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 | ·--·0. | 80 | ·--·0.324355·seconds·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 | ·--·0. | 104 | ·--·0.607698·seconds·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 | ·--·0. | 191 | ·--·0.839791·seconds·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 | ·--· | 200 | ·--·45.494·seconds·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 | ·--·18.7888·seconds·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 139, 15 lines modified | Offset 139, 15 lines modified | ||
| 139 | o8·=·ChainComplex·with·15·actors | 139 | o8·=·ChainComplex·with·15·actors |
| 140 | o8·:·ActionOnComplex</code></pre> | 140 | o8·:·ActionOnComplex</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·c·=·character·A | 143 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·c·=·character·A |
| 144 | ·--·0. | 144 | ·--·0.324355·seconds·elapsed |
| 145 | o9·=·Character·over·R | 145 | o9·=·Character·over·R |
| 146 | ······ | 146 | ······ |
| 147 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| | 147 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·1·1·1·1·| |
| 148 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| | 148 | ·····(1,·{2})·=>·|·0·-1·1·-1·0·0·0·-1·2·0·2·2·2·6·14·| |
| 149 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| | 149 | ·····(2,·{3})·=>·|·0·1·0·0·-1·1·-1·-1·-1·-1·-1·1·-1·5·35·| |
| 150 | ·····(3,·{4})·=>·|·0·-1·0·0·1·1·1·-1·-1·1·-1·-1·-1·-5·35·| | 150 | ·····(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 | ·--·0. | 96 | ·--·0.324355·seconds·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 161, 15 lines modified | Offset 161, 15 lines modified | ||
| 161 | o6·=·ChainComplex·with·11·actors | 161 | o6·=·ChainComplex·with·11·actors |
| 162 | o6·:·ActionOnComplex</code></pre> | 162 | o6·:·ActionOnComplex</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·c=character·A | 165 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·c=character·A |
| 166 | ·--·0. | 166 | ·--·0.607698·seconds·elapsed |
| 167 | o7·=·Character·over·R | 167 | o7·=·Character·over·R |
| 168 | ······ | 168 | ······ |
| 169 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| | 169 | ·····(0,·{0})·=>·|·1·1·1·1·1·1·1·1·1·1·1·| |
| 170 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| | 170 | ·····(1,·{5})·=>·|·0·1·0·2·0·1·3·0·2·4·6·| |
| 171 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| | 171 | ·····(1,·{7})·=>·|·0·0·0·0·0·1·3·0·4·16·60·| |
| 172 | ·····(1,·{9})·=>·|·0·0·0·0·2·2·2·0·4·8·20·| | 172 | ·····(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 | ·--·0. | 118 | ·--·0.607698·seconds·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 265, 28 lines modified | Offset 265, 28 lines modified | ||
| 265 | o19·=·ChainComplex·with·6·actors | 265 | o19·=·ChainComplex·with·6·actors |
| 266 | o19·:·ActionOnComplex</code></pre> | 266 | o19·:·ActionOnComplex</code></pre> |
| 267 | </td>··········</tr> | 267 | </td>··········</tr> |
| 268 | ··········<tr> | 268 | ··········<tr> |
| 269 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·a1·=·character·A1 | 269 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·a1·=·character·A1 |
| 270 | ·--·0. | 270 | ·--·0.839791·seconds·elapsed |
| 271 | o20·=·Character·over·R | 271 | o20·=·Character·over·R |
| 272 | ······· | 272 | ······· |
| 273 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 273 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 274 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 274 | ······(1,·{8})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 275 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| | 275 | ······(2,·{11})·=>·|·1·1·1·1·1·1·| |
| 276 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| | 276 | ······(2,·{13})·=>·|·1·1·1·1·1·1·| |
| 277 | o20·:·Character</code></pre> | 277 | o20·:·Character</code></pre> |
| 278 | </td>··········</tr> | 278 | </td>··········</tr> |
| 279 | ··········<tr> | 279 | ··········<tr> |
| 280 | <td>··············<pre><code·class="language-macaulay2">i21·:·elapsedTime·a2·=·character·A2 | 280 | <td>··············<pre><code·class="language-macaulay2">i21·:·elapsedTime·a2·=·character·A2 |
| 281 | ·--· | 281 | ·--·45.494·seconds·elapsed |
| 282 | o21·=·Character·over·R | 282 | o21·=·Character·over·R |
| 283 | ······· | 283 | ······· |
| 284 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| | 284 | ······(0,·{0})·=>·|·1·1·1·1·1·1·| |
| 285 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| | 285 | ······(1,·{16})·=>·|·6·2·0·0·-1·-1·| |
| 286 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 286 | ······(2,·{19})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| 287 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| | 287 | ······(2,·{21})·=>·|·3·-1·0·1·a4+a2+a·-a4-a2-a-1·| |
| Offset 398, 15 lines modified | Offset 398, 15 lines modified | ||
| 398 | o31·=·Module·with·6·actors | 398 | o31·=·Module·with·6·actors |
| 399 | o31·:·ActionOnGradedModule</code></pre> | 399 | o31·:·ActionOnGradedModule</code></pre> |
| 400 | </td>··········</tr> | 400 | </td>··········</tr> |
| 401 | ··········<tr> | 401 | ··········<tr> |
| 402 | <td>··············<pre><code·class="language-macaulay2">i32·:·elapsedTime·b·=·character(B,21) | 402 | <td>··············<pre><code·class="language-macaulay2">i32·:·elapsedTime·b·=·character(B,21) |
| 403 | ·--·1 | 403 | ·--·18.7888·seconds·elapsed |
| 404 | o32·=·Character·over·R | 404 | o32·=·Character·over·R |
| 405 | ······· | 405 | ······· |
| 406 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| | 406 | ······(0,·{21})·=>·|·1·1·1·1·1·1·| |
| 407 | o32·:·Character</code></pre> | 407 | o32·:·Character</code></pre> |
| 408 | </td>··········</tr> | 408 | </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 | ·--·0. | 197 | ·--·0.839791·seconds·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 | ·--· | 205 | ·--·45.494·seconds·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 | ·--·18.7888·seconds·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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| 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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| 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·0.197984s·(cpu);·0.163591s·(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 337, 15 lines modified | Offset 337, 15 lines modified | ||
| 337 | ··········1:·.·4·2·.·. | 337 | ··········1:·.·4·2·.·. |
| 338 | ··········2:·.·1·6·5·1 | 338 | ··········2:·.·1·6·5·1 |
| 339 | o22·:·BettiTally</code></pre> | 339 | o22·:·BettiTally</code></pre> |
| 340 | </td>··········</tr> | 340 | </td>··········</tr> |
| 341 | ··········<tr> | 341 | ··········<tr> |
| 342 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·j=bruns·F.dd_3; | 342 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·j=bruns·F.dd_3; |
| 343 | ·--·used·0. | 343 | ·--·used·0.197984s·(cpu);·0.163591s·(thread);·0s·(gc) |
| 344 | o23·:·Ideal·of·S</code></pre> | 344 | o23·:·Ideal·of·S</code></pre> |
| 345 | </td>··········</tr> | 345 | </td>··········</tr> |
| 346 | ··········<tr> | 346 | ··········<tr> |
| 347 | <td>··············<pre><code·class="language-macaulay2">i24·:·betti·res·j | 347 | <td>··············<pre><code·class="language-macaulay2">i24·:·betti·res·j |
| 348 | ·············0·1·2·3·4 | 348 | ·············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·0.197984s·(cpu);·0.163591s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTUwNiwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTUwNiwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ViY29tcGxleCxDZWxsQ29tcGxleCxMaXN0KSwi | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc3ViY29tcGxleCxDZWxsQ29tcGxleCxMaXN0KSwi |
| Offset 26, 13 lines modified | Offset 26, 13 lines modified | ||
| 26 | o10·:·List | 26 | o10·:·List |
| 27 | i11·:·D·=·f·**·C; | 27 | i11·:·D·=·f·**·C; |
| 28 | i12·:·cells(1,D)/cellLabel | 28 | i12·:·cells(1,D)/cellLabel |
| 29 | ··········2 | 29 | ···············2 |
| 30 | o12·=·{ | 30 | o12·=·{a*b,·b*c·} |
| 31 | o12·:·List | 31 | o12·:·List |
| 32 | i13·:· | 32 | i13·:· |
| Offset 34, 14 lines modified | Offset 34, 14 lines modified | ||
| 34 | i12·:·f·=·(cells(2,C))#0; | 34 | i12·:·f·=·(cells(2,C))#0; |
| 35 | i13·:·boundary(f) | 35 | i13·:·boundary(f) |
| 36 | o13·=·{(Cell·of·dimension·1·with·label·1,·1),·(Cell·of·dimension·1·with·label | 36 | o13·=·{(Cell·of·dimension·1·with·label·1,·1),·(Cell·of·dimension·1·with·label |
| 37 | ······----------------------------------------------------------------------- | 37 | ······----------------------------------------------------------------------- |
| 38 | ······1,·1),·(Cell·of·dimension·1·with·label·1,·-1),·(Cell·of·dimension·1 | 38 | ······1,·-1),·(Cell·of·dimension·1·with·label·1,·-1),·(Cell·of·dimension·1 |
| 39 | ······----------------------------------------------------------------------- | 39 | ······----------------------------------------------------------------------- |
| 40 | ······with·label·1,· | 40 | ······with·label·1,·1)} |
| 41 | o13·:·List | 41 | o13·:·List |
| 42 | i14·:· | 42 | i14·:· |
| Offset 16, 24 lines modified | Offset 16, 24 lines modified | ||
| 16 | i8·:·f·=·newSimplexCell·{exy,exz,eyz}; | 16 | i8·:·f·=·newSimplexCell·{exy,exz,eyz}; |
| 17 | i9·:·C·=·cellComplex(R,{f}); | 17 | i9·:·C·=·cellComplex(R,{f}); |
| 18 | i10·:·d1·=·boundaryMap_1·C | 18 | i10·:·d1·=·boundaryMap_1·C |
| 19 | o10·=·{1}·|·- | 19 | o10·=·{1}·|·-y·-x·0··| |
| 20 | ······{1}·|· | 20 | ······{1}·|·0··z··y··| |
| 21 | ······{1}·|· | 21 | ······{1}·|·z··0··-x·| |
| 22 | o10·:·Matrix | 22 | o10·:·Matrix |
| 23 | i11·:·d2·=·boundaryMap_2·C | 23 | i11·:·d2·=·boundaryMap_2·C |
| 24 | o11·=·{2}·|· | 24 | o11·=·{2}·|·x··| |
| 25 | ······{2}·|·-y·| | ||
| 25 | ······{2}·|·z··| | 26 | ······{2}·|·z··| |
| 26 | ······{2}·|·x··| | ||
| 27 | o11·:·Matrix | 27 | o11·:·Matrix |
| 28 | i12·:·assert(d1*d2==0) | 28 | i12·:·assert(d1*d2==0) |
| 29 | i13·:· | 29 | i13·:· |
| Offset 12, 27 lines modified | Offset 12, 27 lines modified | ||
| 12 | i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4}; | 12 | i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4}; |
| 13 | i7·:·C·=·cellComplex(R,F); | 13 | i7·:·C·=·cellComplex(R,F); |
| 14 | i8·:·facePoset·C | 14 | i8·:·facePoset·C |
| 15 | o8·=·Relation·Matrix:·|·1·0·0·0·0· | 15 | o8·=·Relation·Matrix:·|·1·0·0·0·0·0·1·0·1·1·1·0·0·1·1·1·1·| |
| 16 | ······················|·0·1·0·0·0· | 16 | ······················|·0·1·0·0·0·0·1·0·0·0·0·1·1·1·1·0·0·| |
| 17 | ······················|·0·0·1·0·0·0·0·1·0·0·1·0 | 17 | ······················|·0·0·1·0·0·1·0·0·1·0·0·1·0·1·0·1·0·| |
| 18 | ······················|·0·0·0·1·0·0·1·0·1·0·0·1 | 18 | ······················|·0·0·0·1·0·0·0·1·0·1·0·0·1·0·1·0·1·| |
| 19 | ······················|·0·0·0·0·1·0·1·0·0·1·0·0 | 19 | ······················|·0·0·0·0·1·1·0·1·0·0·1·0·0·0·0·1·1·| |
| 20 | ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·1·1·0·0·| | ||
| 21 | ······················|·0·0·0·0·0· | 20 | ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·0·1·0·| |
| 21 | ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·1·1·0·0·| | ||
| 22 | ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·| | ||
| 22 | ······················|·0·0·0·0·0·0·0· | 23 | ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·1·0·1·0·| |
| 23 | ······················|·0·0·0·0·0·0·0·0· | 24 | ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·0·1·0·1·| |
| 24 | ······················|·0·0·0·0·0·0·0·0·0· | 25 | ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·0·1·1·| |
| 25 | ······················|·0·0·0·0·0·0·0·0·0·0· | 26 | ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·1·0·0·0·| |
| 26 | ······················|·0·0·0·0·0·0·0·0·0·0·0· | 27 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·1·0·1·0·0·| |
| 27 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·1·0·| | ||
| 28 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·| | 28 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·| |
| 29 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·| | 29 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·| |
| 30 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·| | 30 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·| |
| 31 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·| | 31 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·| |
| 32 | o8·:·Poset | 32 | o8·:·Poset |
| Offset 32, 12 lines modified | Offset 32, 12 lines modified | ||
| 32 | i8·:·H·=·hashTable·{v_0·=>·x*y,·v_1·=>·y*z,·v_2·=>·x*w,·v_3·=>·y*z}; | 32 | i8·:·H·=·hashTable·{v_0·=>·x*y,·v_1·=>·y*z,·v_2·=>·x*w,·v_3·=>·y*z}; |
| 33 | i9·:·labeledC·=·cellComplex(S,·P,·Labels·=>·H); | 33 | i9·:·labeledC·=·cellComplex(S,·P,·Labels·=>·H); |
| 34 | i10·:·for·i·to·dim·labeledC·list·cells(i,labeledC)/cellLabel | 34 | i10·:·for·i·to·dim·labeledC·list·cells(i,labeledC)/cellLabel |
| 35 | o10·=·{{x* | 35 | o10·=·{{x*w,·x*y,·y*z,·y*z},·{y*z,·x*y*z,·x*y*z*w,·x*y*w},·{x*y*z*w}} |
| 36 | o10·:·List | 36 | o10·:·List |
| 37 | i11·:· | 37 | i11·:· |
| Offset 22, 16 lines modified | Offset 22, 16 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·······2·····2····2···2···2·2 | 29 | ········2·2·······2·····2····2···2···2·2 |
| 30 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} | 30 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} |
| Offset 114, 16 lines modified | Offset 114, 16 lines modified | ||
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i11·:·D·=·f·**·C;</code></pre> | 116 | <td>··············<pre><code·class="language-macaulay2">i11·:·D·=·f·**·C;</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i12·:·cells(1,D)/cellLabel | 119 | <td>··············<pre><code·class="language-macaulay2">i12·:·cells(1,D)/cellLabel |
| 120 | ··········2 | 120 | ···············2 |
| 121 | o12·=·{ | 121 | o12·=·{a*b,·b*c·} |
| 122 | o12·:·List</code></pre> | 122 | o12·:·List</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ········</table> | 124 | ········</table> |
| 125 | ······</div> | 125 | ······</div> |
| 126 | ······<div> | 126 | ······<div> |
| 127 | ········<h2>See·also</h2> | 127 | ········<h2>See·also</h2> |
| Offset 32, 15 lines modified | Offset 32, 15 lines modified | ||
| 32 | o10·=·{y*z,·x*y} | 32 | o10·=·{y*z,·x*y} |
| 33 | o10·:·List | 33 | o10·:·List |
| 34 | i11·:·D·=·f·**·C; | 34 | i11·:·D·=·f·**·C; |
| 35 | i12·:·cells(1,D)/cellLabel | 35 | i12·:·cells(1,D)/cellLabel |
| 36 | ··········2 | 36 | ···············2 |
| 37 | o12·=·{ | 37 | o12·=·{a*b,·b*c·} |
| 38 | o12·:·List | 38 | o12·:·List |
| 39 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 39 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 40 | ····*·_\x8r_\x8e_\x8l_\x8a_\x8b_\x8e_\x8l_\x8C_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·--·relabels·a·cell·complex | 40 | ····*·_\x8r_\x8e_\x8l_\x8a_\x8b_\x8e_\x8l_\x8C_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·--·relabels·a·cell·complex |
| 41 | *\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* | 41 | *\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* |
| 42 | ····*·_\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 | 42 | ····*·_\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 |
| Offset 121, 17 lines modified | Offset 121, 17 lines modified | ||
| 121 | <td>··············<pre><code·class="language-macaulay2">i12·:·f·=·(cells(2,C))#0;</code></pre> | 121 | <td>··············<pre><code·class="language-macaulay2">i12·:·f·=·(cells(2,C))#0;</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i13·:·boundary(f) | 124 | <td>··············<pre><code·class="language-macaulay2">i13·:·boundary(f) |
| 125 | o13·=·{(Cell·of·dimension·1·with·label·1,·1),·(Cell·of·dimension·1·with·label | 125 | o13·=·{(Cell·of·dimension·1·with·label·1,·1),·(Cell·of·dimension·1·with·label |
| 126 | ······----------------------------------------------------------------------- | 126 | ······----------------------------------------------------------------------- |
| 127 | ······1,·1),·(Cell·of·dimension·1·with·label·1,·-1),·(Cell·of·dimension·1 | 127 | ······1,·-1),·(Cell·of·dimension·1·with·label·1,·-1),·(Cell·of·dimension·1 |
| 128 | ······----------------------------------------------------------------------- | 128 | ······----------------------------------------------------------------------- |
| 129 | ······with·label·1,· | 129 | ······with·label·1,·1)} |
| 130 | o13·:·List</code></pre> | 130 | o13·:·List</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ········</table> | 132 | ········</table> |
| 133 | ······</div> | 133 | ······</div> |
| 134 | ······<div> | 134 | ······<div> |
| 135 | ········<h2>See·also</h2> | 135 | ········<h2>See·also</h2> |
| Offset 43, 17 lines modified | Offset 43, 17 lines modified | ||
| 43 | i10·:·P·=·convexHull·matrix·{{1,1,-1,-1},{1,-1,1,-1}}; | 43 | i10·:·P·=·convexHull·matrix·{{1,1,-1,-1},{1,-1,1,-1}}; |
| 44 | i11·:·C·=·cellComplex(R,P); | 44 | i11·:·C·=·cellComplex(R,P); |
| 45 | i12·:·f·=·(cells(2,C))#0; | 45 | i12·:·f·=·(cells(2,C))#0; |
| 46 | i13·:·boundary(f) | 46 | i13·:·boundary(f) |
| 47 | o13·=·{(Cell·of·dimension·1·with·label·1,·1),·(Cell·of·dimension·1·with·label | 47 | o13·=·{(Cell·of·dimension·1·with·label·1,·1),·(Cell·of·dimension·1·with·label |
| 48 | ······----------------------------------------------------------------------- | 48 | ······----------------------------------------------------------------------- |
| 49 | ······1,·1),·(Cell·of·dimension·1·with·label·1,·-1),·(Cell·of·dimension·1 | 49 | ······1,·-1),·(Cell·of·dimension·1·with·label·1,·-1),·(Cell·of·dimension·1 |
| 50 | ······----------------------------------------------------------------------- | 50 | ······----------------------------------------------------------------------- |
| 51 | ······with·label·1,· | 51 | ······with·label·1,·1)} |
| 52 | o13·:·List | 52 | o13·:·List |
| 53 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 53 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 54 | ····*·_\x8b_\x8o_\x8u_\x8n_\x8d_\x8a_\x8r_\x8y_\x8C_\x8e_\x8l_\x8l_\x8s_\x8(_\x8C_\x8e_\x8l_\x8l_\x8)·--·returns·the·boundary·cells·of·the·given·cell | 54 | ····*·_\x8b_\x8o_\x8u_\x8n_\x8d_\x8a_\x8r_\x8y_\x8C_\x8e_\x8l_\x8l_\x8s_\x8(_\x8C_\x8e_\x8l_\x8l_\x8)·--·returns·the·boundary·cells·of·the·given·cell |
| 55 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·b\x8bo\x8ou\x8un\x8nd\x8da\x8ar\x8ry\x8y·:\x8:·*\x8**\x8**\x8**\x8**\x8* | 55 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·b\x8bo\x8ou\x8un\x8nd\x8da\x8ar\x8ry\x8y·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 56 | ····*·boundary(Cell) | 56 | ····*·boundary(Cell) |
| 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 111, 26 lines modified | Offset 111, 26 lines modified | ||
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i9·:·C·=·cellComplex(R,{f});</code></pre> | 113 | <td>··············<pre><code·class="language-macaulay2">i9·:·C·=·cellComplex(R,{f});</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i10·:·d1·=·boundaryMap_1·C | 116 | <td>··············<pre><code·class="language-macaulay2">i10·:·d1·=·boundaryMap_1·C |
| 117 | o10·=·{1}·|·- | 117 | o10·=·{1}·|·-y·-x·0··| |
| 118 | ······{1}·|· | 118 | ······{1}·|·0··z··y··| |
| 119 | ······{1}·|· | 119 | ······{1}·|·z··0··-x·| |
| 120 | o10·:·Matrix</code></pre> | 120 | o10·:·Matrix</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i11·:·d2·=·boundaryMap_2·C | 123 | <td>··············<pre><code·class="language-macaulay2">i11·:·d2·=·boundaryMap_2·C |
| 124 | o11·=·{2}·|· | 124 | o11·=·{2}·|·x··| |
| 125 | ······{2}·|·-y·| | ||
| 125 | ······{2}·|·z··| | 126 | ······{2}·|·z··| |
| 126 | ······{2}·|·x··| | ||
| 127 | o11·:·Matrix</code></pre> | 127 | o11·:·Matrix</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i12·:·assert(d1*d2==0)</code></pre> | 130 | <td>··············<pre><code·class="language-macaulay2">i12·:·assert(d1*d2==0)</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ········</table> | 132 | ········</table> |
| Offset 28, 24 lines modified | Offset 28, 24 lines modified | ||
| 28 | i5·:·exy·=·newSimplexCell·{vx,vy}; | 28 | i5·:·exy·=·newSimplexCell·{vx,vy}; |
| 29 | i6·:·exz·=·newSimplexCell·{vx,vz}; | 29 | i6·:·exz·=·newSimplexCell·{vx,vz}; |
| 30 | i7·:·eyz·=·newSimplexCell·{vy,vz}; | 30 | i7·:·eyz·=·newSimplexCell·{vy,vz}; |
| 31 | i8·:·f·=·newSimplexCell·{exy,exz,eyz}; | 31 | i8·:·f·=·newSimplexCell·{exy,exz,eyz}; |
| 32 | i9·:·C·=·cellComplex(R,{f}); | 32 | i9·:·C·=·cellComplex(R,{f}); |
| 33 | i10·:·d1·=·boundaryMap_1·C | 33 | i10·:·d1·=·boundaryMap_1·C |
| 34 | o10·=·{1}·|·- | 34 | o10·=·{1}·|·-y·-x·0··| |
| 35 | ······{1}·|· | 35 | ······{1}·|·0··z··y··| |
| 36 | ······{1}·|· | 36 | ······{1}·|·z··0··-x·| |
| 37 | o10·:·Matrix | 37 | o10·:·Matrix |
| 38 | i11·:·d2·=·boundaryMap_2·C | 38 | i11·:·d2·=·boundaryMap_2·C |
| 39 | o11·=·{2}·|· | 39 | o11·=·{2}·|·x··| |
| 40 | ······{2}·|·-y·| | ||
| 40 | ······{2}·|·z··| | 41 | ······{2}·|·z··| |
| 41 | ······{2}·|·x··| | ||
| 42 | o11·:·Matrix | 42 | o11·:·Matrix |
| 43 | i12·:·assert(d1*d2==0) | 43 | i12·:·assert(d1*d2==0) |
| 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 | ····*·_\x8c_\x8h_\x8a_\x8i_\x8n_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8C_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8)·--·compute·the·cellular·chain·complex·for·a | 45 | ····*·_\x8c_\x8h_\x8a_\x8i_\x8n_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8C_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8)·--·compute·the·cellular·chain·complex·for·a |
| 46 | ······cell·complex | 46 | ······cell·complex |
| 47 | ····*·_\x8c_\x8h_\x8a_\x8i_\x8n_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8S_\x8i_\x8m_\x8p_\x8l_\x8i_\x8c_\x8i_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8)·--·create·the·chain·complex·associated·to | 47 | ····*·_\x8c_\x8h_\x8a_\x8i_\x8n_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8S_\x8i_\x8m_\x8p_\x8l_\x8i_\x8c_\x8i_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8)·--·create·the·chain·complex·associated·to |
| Offset 102, 27 lines modified | Offset 102, 27 lines modified | ||
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·C·=·cellComplex(R,F);</code></pre> | 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·C·=·cellComplex(R,F);</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i8·:·facePoset·C | 107 | <td>··············<pre><code·class="language-macaulay2">i8·:·facePoset·C |
| 108 | o8·=·Relation·Matrix:·|·1·0·0·0·0· | 108 | o8·=·Relation·Matrix:·|·1·0·0·0·0·0·1·0·1·1·1·0·0·1·1·1·1·| |
| 109 | ······················|·0·1·0·0·0· | 109 | ······················|·0·1·0·0·0·0·1·0·0·0·0·1·1·1·1·0·0·| |
| 110 | ······················|·0·0·1·0·0·0·0·1·0·0·1·0 | 110 | ······················|·0·0·1·0·0·1·0·0·1·0·0·1·0·1·0·1·0·| |
| 111 | ······················|·0·0·0·1·0·0·1·0·1·0·0·1 | 111 | ······················|·0·0·0·1·0·0·0·1·0·1·0·0·1·0·1·0·1·| |
| 112 | ······················|·0·0·0·0·1·0·1·0·0·1·0·0 | 112 | ······················|·0·0·0·0·1·1·0·1·0·0·1·0·0·0·0·1·1·| |
| 113 | ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·1·1·0·0·| | ||
| 114 | ······················|·0·0·0·0·0· | 113 | ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·0·1·0·| |
| 114 | ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·1·1·0·0·| | ||
| 115 | ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·| | ||
| 115 | ······················|·0·0·0·0·0·0·0· | 116 | ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·1·0·1·0·| |
| 116 | ······················|·0·0·0·0·0·0·0·0· | 117 | ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·0·1·0·1·| |
| 117 | ······················|·0·0·0·0·0·0·0·0·0· | 118 | ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·0·1·1·| |
| 118 | ······················|·0·0·0·0·0·0·0·0·0·0· | 119 | ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·1·0·0·0·| |
| 119 | ······················|·0·0·0·0·0·0·0·0·0·0·0· | 120 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·1·0·1·0·0·| |
| 120 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·1·0·| | ||
| 121 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·| | 121 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·| |
| 122 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·| | 122 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·| |
| 123 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·| | 123 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·| |
| 124 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·| | 124 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·| |
| 125 | o8·:·Poset</code></pre> | 125 | o8·:·Poset</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| Offset 27, 27 lines modified | Offset 27, 27 lines modified | ||
| 27 | i3·:·P2·=·convexHull·matrix·{{2,-2,0},{1,1,0}}; | 27 | i3·:·P2·=·convexHull·matrix·{{2,-2,0},{1,1,0}}; |
| 28 | i4·:·P3·=·convexHull·matrix·{{-2,-2,0},{1,-1,0}}; | 28 | i4·:·P3·=·convexHull·matrix·{{-2,-2,0},{1,-1,0}}; |
| 29 | i5·:·P4·=·convexHull·matrix·{{-2,2,0},{-1,-1,0}}; | 29 | i5·:·P4·=·convexHull·matrix·{{-2,2,0},{-1,-1,0}}; |
| 30 | i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4}; | 30 | i6·:·F·=·polyhedralComplex·{P1,P2,P3,P4}; |
| 31 | i7·:·C·=·cellComplex(R,F); | 31 | i7·:·C·=·cellComplex(R,F); |
| 32 | i8·:·facePoset·C | 32 | i8·:·facePoset·C |
| 33 | o8·=·Relation·Matrix:·|·1·0·0·0·0· | 33 | o8·=·Relation·Matrix:·|·1·0·0·0·0·0·1·0·1·1·1·0·0·1·1·1·1·| |
| 34 | ······················|·0·1·0·0·0· | 34 | ······················|·0·1·0·0·0·0·1·0·0·0·0·1·1·1·1·0·0·| |
| 35 | ······················|·0·0·1·0·0·0·0·1·0·0·1·0 | 35 | ······················|·0·0·1·0·0·1·0·0·1·0·0·1·0·1·0·1·0·| |
| 36 | ······················|·0·0·0·1·0·0·1·0·1·0·0·1 | 36 | ······················|·0·0·0·1·0·0·0·1·0·1·0·0·1·0·1·0·1·| |
| 37 | ······················|·0·0·0·0·1·0·1·0·0·1·0·0 | 37 | ······················|·0·0·0·0·1·1·0·1·0·0·1·0·0·0·0·1·1·| |
| 38 | ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·1·1·0·0·| | ||
| 39 | ······················|·0·0·0·0·0· | 38 | ······················|·0·0·0·0·0·1·0·0·0·0·0·0·0·0·0·1·0·| |
| 39 | ······················|·0·0·0·0·0·0·1·0·0·0·0·0·0·1·1·0·0·| | ||
| 40 | ······················|·0·0·0·0·0·0·0·1·0·0·0·0·0·0·0·0·1·| | ||
| 40 | ······················|·0·0·0·0·0·0·0· | 41 | ······················|·0·0·0·0·0·0·0·0·1·0·0·0·0·1·0·1·0·| |
| 41 | ······················|·0·0·0·0·0·0·0·0· | 42 | ······················|·0·0·0·0·0·0·0·0·0·1·0·0·0·0·1·0·1·| |
| 42 | ······················|·0·0·0·0·0·0·0·0·0· | 43 | ······················|·0·0·0·0·0·0·0·0·0·0·1·0·0·0·0·1·1·| |
| 43 | ······················|·0·0·0·0·0·0·0·0·0·0· | 44 | ······················|·0·0·0·0·0·0·0·0·0·0·0·1·0·1·0·0·0·| |
| 44 | ······················|·0·0·0·0·0·0·0·0·0·0·0· | 45 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·1·0·1·0·0·| |
| 45 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·1·0·| | ||
| 46 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·| | 46 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·0·| |
| 47 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·| | 47 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·0·| |
| 48 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·| | 48 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·0·| |
| 49 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·| | 49 | ······················|·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·0·1·| |
| 50 | o8·:·Poset | 50 | o8·:·Poset |
| 51 | The·labels·on·the·vertices·can·be·controlled·via·the·optional·parameter·Labels | 51 | The·labels·on·the·vertices·can·be·controlled·via·the·optional·parameter·Labels |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·labeledC·=·cellComplex(S,·P,·Labels·=>·H);</code></pre> | 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·labeledC·=·cellComplex(S,·P,·Labels·=>·H);</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i10·:·for·i·to·dim·labeledC·list·cells(i,labeledC)/cellLabel | 134 | <td>··············<pre><code·class="language-macaulay2">i10·:·for·i·to·dim·labeledC·list·cells(i,labeledC)/cellLabel |
| 135 | o10·=·{{x* | 135 | o10·=·{{x*w,·x*y,·y*z,·y*z},·{y*z,·x*y*z,·x*y*z*w,·x*y*w},·{x*y*z*w}} |
| 136 | o10·:·List</code></pre> | 136 | o10·:·List</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| 139 | ······</div> | 139 | ······</div> |
| 140 | ······<div> | 140 | ······<div> |
| 141 | ········<h2>See·also</h2> | 141 | ········<h2>See·also</h2> |
| Offset 48, 15 lines modified | Offset 48, 15 lines modified | ||
| 48 | ··············2·······4 | 48 | ··············2·······4 |
| 49 | o7·:·Matrix·QQ··<--·QQ | 49 | o7·:·Matrix·QQ··<--·QQ |
| 50 | i8·:·H·=·hashTable·{v_0·=>·x*y,·v_1·=>·y*z,·v_2·=>·x*w,·v_3·=>·y*z}; | 50 | i8·:·H·=·hashTable·{v_0·=>·x*y,·v_1·=>·y*z,·v_2·=>·x*w,·v_3·=>·y*z}; |
| 51 | i9·:·labeledC·=·cellComplex(S,·P,·Labels·=>·H); | 51 | i9·:·labeledC·=·cellComplex(S,·P,·Labels·=>·H); |
| 52 | i10·:·for·i·to·dim·labeledC·list·cells(i,labeledC)/cellLabel | 52 | i10·:·for·i·to·dim·labeledC·list·cells(i,labeledC)/cellLabel |
| 53 | o10·=·{{x* | 53 | o10·=·{{x*w,·x*y,·y*z,·y*z},·{y*z,·x*y*z,·x*y*z*w,·x*y*w},·{x*y*z*w}} |
| 54 | o10·:·List | 54 | o10·:·List |
| 55 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 55 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 56 | ····*·_\x8c_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8R_\x8i_\x8n_\x8g_\x8,_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8)·--·creates·cell·complex·from·given | 56 | ····*·_\x8c_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8R_\x8i_\x8n_\x8g_\x8,_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8)·--·creates·cell·complex·from·given |
| 57 | ······polyhedral·complex | 57 | ······polyhedral·complex |
| 58 | *\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* | 58 | *\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* |
| 59 | ····*·_\x8c_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8R_\x8i_\x8n_\x8g_\x8,_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8o_\x8n_\x8)·--·creates·cell·complex·from·given | 59 | ····*·_\x8c_\x8e_\x8l_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x_\x8(_\x8R_\x8i_\x8n_\x8g_\x8,_\x8P_\x8o_\x8l_\x8y_\x8h_\x8e_\x8d_\x8r_\x8o_\x8n_\x8)·--·creates·cell·complex·from·given |
| Offset 115, 16 lines modified | Offset 115, 16 lines modified | ||
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i12·:·relabeledC·=·relabelCellComplex(C,T);</code></pre> | 117 | <td>··············<pre><code·class="language-macaulay2">i12·:·relabeledC·=·relabelCellComplex(C,T);</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) | 120 | <td>··············<pre><code·class="language-macaulay2">i13·:·for·c·in·cells(0,relabeledC)·list·cellLabel(c) |
| 121 | ········ | 121 | ··········2···2········2 |
| 122 | o13·=·{b·,· | 122 | o13·=·{b*c·,·b·,·a*c,·a·b} |
| 123 | o13·:·List</code></pre> | 123 | o13·:·List</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) | 126 | <td>··············<pre><code·class="language-macaulay2">i14·:·for·c·in·cells(1,relabeledC)·list·cellLabel(c) |
| 127 | ········2·2·······2·····2····2···2···2·2 | 127 | ········2·2·······2·····2····2···2···2·2 |
| Offset 32, 16 lines modified | Offset 32, 16 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·······2·····2····2···2···2·2 | 42 | ········2·2·······2·····2····2···2···2·2 |
| 43 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} | 43 | o14·=·{b·c·,·a*b*c·,·a*b·c,·a·b*c·,·a·b·} |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=1466 | 9 | #:len=1466 |
| 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·0.238132s·(cpu);·0.183872s·(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·0.14 | 31 | ·--·used·0.143821s·(cpu);·0.0942773s·(thread);·0s·(gc) |
| 32 | i9·:·time·n·=·cartanEilenbergResolution·C; | 32 | i9·:·time·n·=·cartanEilenbergResolution·C; |
| 33 | ·--·used·0.1 | 33 | ·--·used·0.102043s·(cpu);·0.102591s·(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 156, 15 lines modified | Offset 156, 15 lines modified | ||
| 156 | ········</table> | 156 | ········</table> |
| 157 | ········<div> | 157 | ········<div> |
| 158 | ··········<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 | ··········<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> |
| 159 | ········</div> | 159 | ········</div> |
| 160 | ········<table·class="examples"> | 160 | ········<table·class="examples"> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| 162 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·m·=·minimize·(E[1]); | 162 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·m·=·minimize·(E[1]); |
| 163 | ·--·used·0.2 | 163 | ·--·used·0.238132s·(cpu);·0.183872s·(thread);·0s·(gc)</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i14·:·isQuasiIsomorphism·m | 166 | <td>··············<pre><code·class="language-macaulay2">i14·:·isQuasiIsomorphism·m |
| 167 | o14·=·true</code></pre> | 167 | o14·=·true</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<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·0.238132s·(cpu);·0.183872s·(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 117, 19 lines modified | Offset 117, 19 lines modified | ||
| 117 | <td>··············<pre><code·class="language-macaulay2">i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);</code></pre> | 117 | <td>··············<pre><code·class="language-macaulay2">i6·:·mods·=·for·i·from·0·to·max·C·list·pushForward(f,·C_i);</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <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>··············<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> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·m·=·resolutionOfChainComplex·C; | 123 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·m·=·resolutionOfChainComplex·C; |
| 124 | ·--·used·0.14 | 124 | ·--·used·0.143821s·(cpu);·0.0942773s·(thread);·0s·(gc)</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·n·=·cartanEilenbergResolution·C; | 127 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·n·=·cartanEilenbergResolution·C; |
| 128 | ·--·used·0.1 | 128 | ·--·used·0.102043s·(cpu);·0.102591s·(thread);·0s·(gc)</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i10·:·betti·source·m | 131 | <td>··············<pre><code·class="language-macaulay2">i10·:·betti·source·m |
| 132 | ·············0··1··2···3···4···5···6···7 | 132 | ·············0··1··2···3···4···5···6···7 |
| 133 | o10·=·total:·1·19·80·181·312·484·447·156 | 133 | o10·=·total:·1·19·80·181·312·484·447·156 |
| 134 | ··········0:·1··3··3···1···.···.···.···. | 134 | ··········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·0.14 | 56 | ·--·used·0.143821s·(cpu);·0.0942773s·(thread);·0s·(gc) |
| 57 | i9·:·time·n·=·cartanEilenbergResolution·C; | 57 | i9·:·time·n·=·cartanEilenbergResolution·C; |
| 58 | ·--·used·0.1 | 58 | ·--·used·0.102043s·(cpu);·0.102591s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0. | 88 | ·--·used·0.577063s·(cpu);·0.312208s·(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·0.0964433s·(cpu);·0.0644933s·(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. | 13 | ·--·used·0.186936s·(cpu);·0.105635s·(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·0.4 | 23 | ·--·used·0.482281s·(cpu);·0.254977s·(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·0. | 22 | ·--·used·0.503105s·(cpu);·0.286512s·(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·1. | 33 | ·--·used·1.76108s·(cpu);·1.52311s·(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·0.299288s·(cpu);·0.184393s·(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·0.20 | 68 | ·--·used·0.202298s·(cpu);·0.1121s·(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·0.1 | 26 | ·--·used·0.102982s·(cpu);·0.0536714s·(thread);·0s·(gc) |
| 27 | o4·=·4 | 27 | o4·=·4 |
| 28 | i5·:·time·Euler·I | 28 | i5·:·time·Euler·I |
| 29 | ·--·used·0. | 29 | ·--·used·0.220801s·(cpu);·0.134626s·(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·0.201357s·(cpu);·0.104716s·(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·0.124972s·(cpu);·0.0826059s·(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·1.95865s·(cpu);·1.03997s·(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·1.73322s·(cpu);·1.06009s·(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·0. | 7 | ·--·used·0.775404s·(cpu);·0.41112s·(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·0.0991104s·(cpu);·0.0466439s·(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·0.0296291s·(cpu);·0.0310443s·(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·1.43358s·(cpu);·0.816708s·(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·0.272276s·(cpu);·0.170507s·(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 222, 15 lines modified | Offset 222, 15 lines modified | ||
| 222 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) | 222 | o14·=·ideal·(x·x··-·x·x·x·,·x·x·) |
| 223 | ··············0·3····1·2·4···2·5 | 223 | ··············0·3····1·2·4···2·5 |
| 224 | o14·:·Ideal·of·R</code></pre> | 224 | o14·:·Ideal·of·R</code></pre> |
| 225 | </td>··········</tr> | 225 | </td>··········</tr> |
| 226 | ··········<tr> | 226 | ··········<tr> |
| 227 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·csmK=CSM(A,K) | 227 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·csmK=CSM(A,K) |
| 228 | ·--·used·0. | 228 | ·--·used·0.577063s·(cpu);·0.312208s·(thread);·0s·(gc) |
| 229 | ········2·2·····2·········2····2············2 | 229 | ········2·2·····2·········2····2············2 |
| 230 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 230 | o15·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 231 | ········1·2·····1·2·····1·2····1·····1·2····2 | 231 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 232 | o15·:·A</code></pre> | 232 | o15·:·A</code></pre> |
| 233 | </td>··········</tr> | 233 | </td>··········</tr> |
| Offset 275, 15 lines modified | Offset 275, 15 lines modified | ||
| 275 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h | 275 | o21·=·9h·h··+·9h·h··+·9h·h··+·3h··+·7h·h··+·3h··+·3h··+·2h |
| 276 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 | 276 | ········1·2·····1·2·····1·2·····1·····1·2·····2·····1·····2 |
| 277 | o21·:·A</code></pre> | 277 | o21·:·A</code></pre> |
| 278 | </td>··········</tr> | 278 | </td>··········</tr> |
| 279 | ··········<tr> | 279 | ··········<tr> |
| 280 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·CSM(A,K,m) | 280 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·CSM(A,K,m) |
| 281 | ·--·used·0. | 281 | ·--·used·0.0964433s·(cpu);·0.0644933s·(thread);·0s·(gc) |
| 282 | ········2·2·····2·········2····2············2 | 282 | ········2·2·····2·········2····2············2 |
| 283 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h | 283 | o22·=·7h·h··+·5h·h··+·4h·h··+·h··+·3h·h··+·h |
| 284 | ········1·2·····1·2·····1·2····1·····1·2····2 | 284 | ········1·2·····1·2·····1·2····1·····1·2····2 |
| 285 | o22·:·A</code></pre> | 285 | o22·:·A</code></pre> |
| 286 | </td>··········</tr> | 286 | </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·0. | 166 | ·--·used·0.577063s·(cpu);·0.312208s·(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·0.0964433s·(cpu);·0.0644933s·(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 61, 29 lines modified | Offset 61, 29 lines modified | ||
| 61 | o2·=·U | 61 | o2·=·U |
| 62 | o2·:·NormalToricVariety</code></pre> | 62 | o2·:·NormalToricVariety</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·U | 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·U |
| 66 | ·--·used·0. | 66 | ·--·used·0.186936s·(cpu);·0.105635s·(thread);·0s·(gc) |
| 67 | ·······7······6······5······4······3······2 | 67 | ·······7······6······5······4······3······2 |
| 68 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 68 | o3·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 69 | ·······7······7······7······7······7······7·····7 | 69 | ·······7······7······7······7······7······7·····7 |
| 70 | ················································ZZ[x·..x·] | 70 | ················································ZZ[x·..x·] |
| 71 | ····················································0···7 | 71 | ····················································0···7 |
| 72 | o3·:·----------------------------------------------------------------------------------------------- | 72 | o3·:·----------------------------------------------------------------------------------------------- |
| 73 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·) | 73 | ·····(x·x·x·x·x·x·x·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·,·-·x··+·x·) |
| 74 | ·······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 | ·······0·1·2·3·4·5·6·7·····0····1·····0····2·····0····3·····0····4·····0····5·····0····6·····0····7</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(U,CheckSmooth=>false) | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(U,CheckSmooth=>false) |
| 78 | ·--·used·0.4 | 78 | ·--·used·0.482281s·(cpu);·0.254977s·(thread);·0s·(gc) |
| 79 | ·······7······6······5······4······3······2 | 79 | ·······7······6······5······4······3······2 |
| 80 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 | 80 | o4·=·8x··+·28x··+·56x··+·70x··+·56x··+·28x··+·8x··+·1 |
| 81 | ·······7······7······7······7······7······7·····7 | 81 | ·······7······7······7······7······7······7·····7 |
| 82 | ················································ZZ[x·..x·] | 82 | ················································ZZ[x·..x·] |
| 83 | ····················································0···7 | 83 | ····················································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. | 21 | ·--·used·0.186936s·(cpu);·0.105635s·(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·0.4 | 34 | ·--·used·0.482281s·(cpu);·0.254977s·(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 77, 30 lines modified | Offset 77, 30 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <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 | <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)); |
| 79 | o4·:·Ideal·of·R</code></pre> | 79 | o4·:·Ideal·of·R</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) | 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·CSM(I,CompMethod=>ProjectiveDegree) |
| 83 | ·--·used·0. | 83 | ·--·used·0.503105s·(cpu);·0.286512s·(thread);·0s·(gc) |
| 84 | ·······5······4······3······2 | 84 | ·······5······4······3······2 |
| 85 | o5·=·6h··+·14h··+·14h··+·10h | 85 | o5·=·6h··+·14h··+·14h··+·10h |
| 86 | ·······1······1······1······1 | 86 | ·······1······1······1······1 |
| 87 | ·····ZZ[h·] | 87 | ·····ZZ[h·] |
| 88 | ·········1 | 88 | ·········1 |
| 89 | o5·:·------ | 89 | o5·:·------ |
| 90 | ········6 | 90 | ········6 |
| 91 | ·······h | 91 | ·······h |
| 92 | ········1</code></pre> | 92 | ········1</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·CSM(I,CompMethod=>PnResidual) | 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·CSM(I,CompMethod=>PnResidual) |
| 96 | ·--·used·1. | 96 | ·--·used·1.76108s·(cpu);·1.52311s·(thread);·0s·(gc) |
| 97 | ·······5······4······3······2 | 97 | ·······5······4······3······2 |
| 98 | o6·=·6H··+·14H··+·14H··+·10H | 98 | o6·=·6H··+·14H··+·14H··+·10H |
| 99 | ·····ZZ[H] | 99 | ·····ZZ[H] |
| 100 | o6·:·----- | 100 | o6·:·----- |
| 101 | ········6 | 101 | ········6 |
| Offset 117, 30 lines modified | Offset 117, 30 lines modified | ||
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <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 | <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)); |
| 119 | o9·:·Ideal·of·S</code></pre> | 119 | o9·:·Ideal·of·S</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) | 122 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·CSM(K,CompMethod=>ProjectiveDegree) |
| 123 | ·--·used·0. | 123 | ·--·used·0.299288s·(cpu);·0.184393s·(thread);·0s·(gc) |
| 124 | ········3·····2 | 124 | ········3·····2 |
| 125 | o10·=·3h··+·5h | 125 | o10·=·3h··+·5h |
| 126 | ········1·····1 | 126 | ········1·····1 |
| 127 | ······ZZ[h·] | 127 | ······ZZ[h·] |
| 128 | ··········1 | 128 | ··········1 |
| 129 | o10·:·------ | 129 | o10·:·------ |
| 130 | ·········4 | 130 | ·········4 |
| 131 | ········h | 131 | ········h |
| 132 | ·········1</code></pre> | 132 | ·········1</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·CSM(K,CompMethod=>PnResidual) | 135 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·CSM(K,CompMethod=>PnResidual) |
| 136 | ·--·used·0.20 | 136 | ·--·used·0.202298s·(cpu);·0.1121s·(thread);·0s·(gc) |
| 137 | ········3·····2 | 137 | ········3·····2 |
| 138 | o11·=·3H··+·5H | 138 | o11·=·3H··+·5H |
| 139 | ······ZZ[H] | 139 | ······ZZ[H] |
| 140 | o11·:·----- | 140 | o11·:·----- |
| 141 | ·········4 | 141 | ·········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·0. | 38 | ·--·used·0.503105s·(cpu);·0.286512s·(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·1. | 49 | ·--·used·1.76108s·(cpu);·1.52311s·(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·0.299288s·(cpu);·0.184393s·(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·0.20 | 78 | ·--·used·0.202298s·(cpu);·0.1121s·(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 131, 21 lines modified | Offset 131, 21 lines modified | ||
| 131 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) | 131 | ·····-·14254x··-·11226x·x··+·2653x·x··+·12365x·x··-·10226x·x··-·12696x·) |
| 132 | ·············3·········0·4········1·4·········2·4·········3·4·········4 | 132 | ·············3·········0·4········1·4·········2·4·········3·4·········4 |
| 133 | o3·:·Ideal·of·R</code></pre> | 133 | o3·:·Ideal·of·R</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Euler(I,InputIsSmooth=>true) | 136 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Euler(I,InputIsSmooth=>true) |
| 137 | ·--·used·0.1 | 137 | ·--·used·0.102982s·(cpu);·0.0536714s·(thread);·0s·(gc) |
| 138 | o4·=·4</code></pre> | 138 | o4·=·4</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Euler·I | 141 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Euler·I |
| 142 | ·--·used·0. | 142 | ·--·used·0.220801s·(cpu);·0.134626s·(thread);·0s·(gc) |
| 143 | o5·=·4</code></pre> | 143 | o5·=·4</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i6·:·EulerIHash=Euler(I,Output=>HashForm);</code></pre> | 146 | <td>··············<pre><code·class="language-macaulay2">i6·:·EulerIHash=Euler(I,Output=>HashForm);</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| Offset 183, 21 lines modified | Offset 183, 21 lines modified | ||
| 183 | ········</table> | 183 | ········</table> |
| 184 | ········<div> | 184 | ········<div> |
| 185 | ··········<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 | ··········<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> |
| 186 | ········</div> | 186 | ········</div> |
| 187 | ········<table·class="examples"> | 187 | ········<table·class="examples"> |
| 188 | ··········<tr> | 188 | ··········<tr> |
| 189 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Euler(J,Method=>DirectCompleteInt) | 189 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Euler(J,Method=>DirectCompleteInt) |
| 190 | ·--·used·0. | 190 | ·--·used·0.201357s·(cpu);·0.104716s·(thread);·0s·(gc) |
| 191 | o10·=·2</code></pre> | 191 | o10·=·2</code></pre> |
| 192 | </td>··········</tr> | 192 | </td>··········</tr> |
| 193 | ··········<tr> | 193 | ··········<tr> |
| 194 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) | 194 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·Euler(J,Method=>DirectCompleteInt,IndsOfSmooth=>{0,1}) |
| 195 | ·--·used·0. | 195 | ·--·used·0.124972s·(cpu);·0.0826059s·(thread);·0s·(gc) |
| 196 | o11·=·2</code></pre> | 196 | o11·=·2</code></pre> |
| 197 | </td>··········</tr> | 197 | </td>··········</tr> |
| 198 | ········</table> | 198 | ········</table> |
| 199 | ········<div> | 199 | ········<div> |
| 200 | ··········<p>Now·consider·an·example·in·\PP^2·\times·\PP^2.</p> | 200 | ··········<p>Now·consider·an·example·in·\PP^2·\times·\PP^2.</p> |
| 201 | ········</div> | 201 | ········</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·0.1 | 81 | ·--·used·0.102982s·(cpu);·0.0536714s·(thread);·0s·(gc) |
| 82 | o4·=·4 | 82 | o4·=·4 |
| 83 | i5·:·time·Euler·I | 83 | i5·:·time·Euler·I |
| 84 | ·--·used·0. | 84 | ·--·used·0.220801s·(cpu);·0.134626s·(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·0.201357s·(cpu);·0.104716s·(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·0.124972s·(cpu);·0.0826059s·(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 59, 30 lines modified | Offset 59, 30 lines modified | ||
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <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 | <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)); |
| 61 | o2·:·Ideal·of·R</code></pre> | 61 | o2·:·Ideal·of·R</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM(I,Method=>DirectCompletInt) | 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM(I,Method=>DirectCompletInt) |
| 65 | ·--·used· | 65 | ·--·used·1.95865s·(cpu);·1.03997s·(thread);·0s·(gc) |
| 66 | ·······2·2·····2·········2 | 66 | ·······2·2·····2·········2 |
| 67 | o3·=·2h·h··+·2h·h··+·5h·h | 67 | o3·=·2h·h··+·2h·h··+·5h·h |
| 68 | ·······1·2·····1·2·····1·2 | 68 | ·······1·2·····1·2·····1·2 |
| 69 | ·····ZZ[h·..h·] | 69 | ·····ZZ[h·..h·] |
| 70 | ·········1···2 | 70 | ·········1···2 |
| 71 | o3·:·---------- | 71 | o3·:·---------- |
| 72 | ········3···3 | 72 | ········3···3 |
| 73 | ······(h·,·h·) | 73 | ······(h·,·h·) |
| 74 | ········1···2</code></pre> | 74 | ········1···2</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompletInt,IndsOfSmooth=>{1,2}) |
| 78 | ·--·used· | 78 | ·--·used·1.73322s·(cpu);·1.06009s·(thread);·0s·(gc) |
| 79 | ·······2·2·····2·········2 | 79 | ·······2·2·····2·········2 |
| 80 | o4·=·2h·h··+·2h·h··+·5h·h | 80 | o4·=·2h·h··+·2h·h··+·5h·h |
| 81 | ·······1·2·····1·2·····1·2 | 81 | ·······1·2·····1·2·····1·2 |
| 82 | ·····ZZ[h·..h·] | 82 | ·····ZZ[h·..h·] |
| 83 | ·········1···2 | 83 | ·········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·1.95865s·(cpu);·1.03997s·(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·1.73322s·(cpu);·1.06009s·(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 55, 30 lines modified | Offset 55, 30 lines modified | ||
| 55 | ··········<tr> | 55 | ··········<tr> |
| 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); | 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(2,R),random(1,R)); |
| 57 | o2·:·Ideal·of·R</code></pre> | 57 | o2·:·Ideal·of·R</code></pre> |
| 58 | </td>··········</tr> | 58 | </td>··········</tr> |
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I | 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I |
| 61 | ·--·used·0. | 61 | ·--·used·0.775404s·(cpu);·0.41112s·(thread);·0s·(gc) |
| 62 | ·······3 | 62 | ·······3 |
| 63 | o3·=·4h | 63 | o3·=·4h |
| 64 | ·······1 | 64 | ·······1 |
| 65 | ·····ZZ[h·] | 65 | ·····ZZ[h·] |
| 66 | ·········1 | 66 | ·········1 |
| 67 | o3·:·------ | 67 | o3·:·------ |
| 68 | ········5 | 68 | ········5 |
| 69 | ·······h | 69 | ·······h |
| 70 | ········1</code></pre> | 70 | ········1</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,InputIsSmooth=>true) | 73 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,InputIsSmooth=>true) |
| 74 | ·--·used·0. | 74 | ·--·used·0.0991104s·(cpu);·0.0466439s·(thread);·0s·(gc) |
| 75 | ·······3 | 75 | ·······3 |
| 76 | o4·=·4h | 76 | o4·=·4h |
| 77 | ·······1 | 77 | ·······1 |
| 78 | ·····ZZ[h·] | 78 | ·····ZZ[h·] |
| 79 | ·········1 | 79 | ·········1 |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ········</table> | 90 | ········</table> |
| 91 | ········<div> | 91 | ········<div> |
| 92 | ··········<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 | ··········<p>Note·that·one·could,·equivalently,·use·the·command·<a·title="The·Chern·class"·href="___Chern.html">Chern</a>·instead·in·this·case.</p> |
| 93 | ········</div> | 93 | ········</div> |
| 94 | ········<table·class="examples"> | 94 | ········<table·class="examples"> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Chern·I | 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Chern·I |
| 97 | ·--·used·0.0 | 97 | ·--·used·0.0296291s·(cpu);·0.0310443s·(thread);·0s·(gc) |
| 98 | ·······3 | 98 | ·······3 |
| 99 | o5·=·4h | 99 | o5·=·4h |
| 100 | ·······1 | 100 | ·······1 |
| 101 | ·····ZZ[h·] | 101 | ·····ZZ[h·] |
| 102 | ·········1 | 102 | ·········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·0. | 15 | ·--·used·0.775404s·(cpu);·0.41112s·(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·0.0991104s·(cpu);·0.0466439s·(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·0.0296291s·(cpu);·0.0310443s·(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 59, 30 lines modified | Offset 59, 30 lines modified | ||
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <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 | <td>··············<pre><code·class="language-macaulay2">i2·:·I=ideal(random(2,R),random(1,R),R_0*R_1*R_6-R_0^3); |
| 61 | o2·:·Ideal·of·R</code></pre> | 61 | o2·:·Ideal·of·R</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I | 64 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·CSM·I |
| 65 | ·--·used· | 65 | ·--·used·1.43358s·(cpu);·0.816708s·(thread);·0s·(gc) |
| 66 | ········5······4·····3 | 66 | ········5······4·····3 |
| 67 | o3·=·12h··+·10h··+·6h | 67 | o3·=·12h··+·10h··+·6h |
| 68 | ········1······1·····1 | 68 | ········1······1·····1 |
| 69 | ·····ZZ[h·] | 69 | ·····ZZ[h·] |
| 70 | ·········1 | 70 | ·········1 |
| 71 | o3·:·------ | 71 | o3·:·------ |
| 72 | ········7 | 72 | ········7 |
| 73 | ·······h | 73 | ·······h |
| 74 | ········1</code></pre> | 74 | ········1</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompleteInt) | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·CSM(I,Method=>DirectCompleteInt) |
| 78 | ·--·used·0. | 78 | ·--·used·0.272276s·(cpu);·0.170507s·(thread);·0s·(gc) |
| 79 | ········5······4·····3 | 79 | ········5······4·····3 |
| 80 | o4·=·12h··+·10h··+·6h | 80 | o4·=·12h··+·10h··+·6h |
| 81 | ········1······1·····1 | 81 | ········1······1·····1 |
| 82 | ·····ZZ[h·] | 82 | ·····ZZ[h·] |
| 83 | ·········1 | 83 | ·········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·1.43358s·(cpu);·0.816708s·(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·0.272276s·(cpu);·0.170507s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 16, 32 lines modified | Offset 16, 32 lines modified | ||
| 16 | o2·:·Digraph | 16 | o2·:·Digraph |
| 17 | i3·:·G·=·chordalGraph·digraph·hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}}; | 17 | i3·:·G·=·chordalGraph·digraph·hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}}; |
| 18 | i4·:·tree·=·elimTree·G | 18 | i4·:·tree·=·elimTree·G |
| 19 | o4·=·ElimTree{a·=>· | 19 | o4·=·ElimTree{a·=>·b···} |
| 20 | ··············b·=>·c | 20 | ··············b·=>·c |
| 21 | ··············c·=>·d | 21 | ··············c·=>·d |
| 22 | ··············d·=>· | 22 | ··············d·=>·null |
| 23 | o4·:·ElimTree | 23 | o4·:·ElimTree |
| 24 | i5·:·rnk·=·hashTable{"a0"=>a,·"a1"=>a,·"b0"=>b,·"b1"=>b,·"b2"=>b, | 24 | i5·:·rnk·=·hashTable{"a0"=>a,·"a1"=>a,·"b0"=>b,·"b1"=>b,·"b2"=>b, |
| 25 | ·····················"c0"=>c,·"d0"=>d,·"c1"=>c,·"d1"=>d}; | 25 | ·····················"c0"=>c,·"d0"=>d,·"c1"=>c,·"d1"=>d}; |
| 26 | i6·:·eqs·=·hashTable{"a0"·=>·({a},{}),·"a1"·=>·({},{}), | 26 | i6·:·eqs·=·hashTable{"a0"·=>·({a},{}),·"a1"·=>·({},{}), |
| 27 | ·····················"b0"·=>·({b},{}),·"b1"·=>·({},{}),·"b2"·=>·({b},{}), | 27 | ·····················"b0"·=>·({b},{}),·"b1"·=>·({},{}),·"b2"·=>·({b},{}), |
| 28 | ·····················"c0"·=>·({c},{}),·"c1"·=>·({},{}), | 28 | ·····················"c0"·=>·({c},{}),·"c1"·=>·({},{}), |
| 29 | ·····················"d0"·=>·({},{}),·"d1"·=>·({d},{})·}; | 29 | ·····················"d0"·=>·({},{}),·"d1"·=>·({d},{})·}; |
| 30 | i7·:·chordalNet(eqs,rnk,tree,DG) | 30 | i7·:·chordalNet(eqs,rnk,tree,DG) |
| 31 | o7·=·ChordalNet{· | 31 | o7·=·ChordalNet{·d·=>·{·,·d}····} |
| 32 | ·················c·=>·{·,·c} | ||
| 33 | ·················d·=>·{·,·d} | ||
| 34 | ·················b·=>·{b,··,·b} | 32 | ·················b·=>·{b,··,·b} |
| 33 | ·················a·=>·{a,··} | ||
| 34 | ·················c·=>·{·,·c} | ||
| 35 | o7·:·ChordalNet | 35 | o7·:·ChordalNet |
| 36 | i8·:· | 36 | i8·:· |
| Offset 27, 15 lines modified | Offset 27, 15 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···3···4···6···7···········1···2···4···6···7···········1···2···4···5···7···········2···4···5···7···8···········2···3···5···7···8···········1···3··· | 32 | ·····························1···3···4···6···7···········1···2···4···6···7···········1···2···4···5···7···········2···4···5···7···8···········2···3···5···7···8···········1···3···5···6···8···········1···3···4···6···8···········2···3···5···6···8 |
| 33 | ···············6·=>·{} | 33 | ···············6·=>·{} |
| 34 | ···············7·=>·{} | 34 | ···············7·=>·{} |
| 35 | o6·:·HashTable | 35 | o6·:·HashTable |
| 36 | i7·:· | 36 | i7·:· |
| 37 | dmat·lu·qq·PLU | 37 | dmat·lu·qq·PLU |
| Offset 100, 18 lines modified | Offset 100, 18 lines modified | ||
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·G·=·chordalGraph·digraph·hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}};</code></pre> | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·G·=·chordalGraph·digraph·hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}};</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·tree·=·elimTree·G | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·tree·=·elimTree·G |
| 106 | o4·=·ElimTree{a·=>· | 106 | o4·=·ElimTree{a·=>·b···} |
| 107 | ··············b·=>·c | 107 | ··············b·=>·c |
| 108 | ··············c·=>·d | 108 | ··············c·=>·d |
| 109 | ··············d·=>· | 109 | ··············d·=>·null |
| 110 | o4·:·ElimTree</code></pre> | 110 | o4·:·ElimTree</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·rnk·=·hashTable{"a0"=>a,·"a1"=>a,·"b0"=>b,·"b1"=>b,·"b2"=>b, | 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·rnk·=·hashTable{"a0"=>a,·"a1"=>a,·"b0"=>b,·"b1"=>b,·"b2"=>b, |
| 114 | ·····················"c0"=>c,·"d0"=>d,·"c1"=>c,·"d1"=>d};</code></pre> | 114 | ·····················"c0"=>c,·"d0"=>d,·"c1"=>c,·"d1"=>d};</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| Offset 120, 18 lines modified | Offset 120, 18 lines modified | ||
| 120 | ·····················"b0"·=>·({b},{}),·"b1"·=>·({},{}),·"b2"·=>·({b},{}), | 120 | ·····················"b0"·=>·({b},{}),·"b1"·=>·({},{}),·"b2"·=>·({b},{}), |
| 121 | ·····················"c0"·=>·({c},{}),·"c1"·=>·({},{}), | 121 | ·····················"c0"·=>·({c},{}),·"c1"·=>·({},{}), |
| 122 | ·····················"d0"·=>·({},{}),·"d1"·=>·({d},{})·};</code></pre> | 122 | ·····················"d0"·=>·({},{}),·"d1"·=>·({d},{})·};</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i7·:·chordalNet(eqs,rnk,tree,DG) | 125 | <td>··············<pre><code·class="language-macaulay2">i7·:·chordalNet(eqs,rnk,tree,DG) |
| 126 | o7·=·ChordalNet{· | 126 | o7·=·ChordalNet{·d·=>·{·,·d}····} |
| 127 | ·················c·=>·{·,·c} | ||
| 128 | ·················d·=>·{·,·d} | ||
| 129 | ·················b·=>·{b,··,·b} | 127 | ·················b·=>·{b,··,·b} |
| 128 | ·················a·=>·{a,··} | ||
| 129 | ·················c·=>·{·,·c} | ||
| 130 | o7·:·ChordalNet</code></pre> | 130 | o7·:·ChordalNet</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ········</table> | 132 | ········</table> |
| 133 | ········<pre></pre> | 133 | ········<pre></pre> |
| 134 | ······</div> | 134 | ······</div> |
| 135 | ······<div> | 135 | ······<div> |
| Offset 33, 32 lines modified | Offset 33, 32 lines modified | ||
| 33 | ·············d0·=>·{} | 33 | ·············d0·=>·{} |
| 34 | ·············d1·=>·{} | 34 | ·············d1·=>·{} |
| 35 | o2·:·Digraph | 35 | o2·:·Digraph |
| 36 | i3·:·G·=·chordalGraph·digraph·hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}}; | 36 | i3·:·G·=·chordalGraph·digraph·hashTable{a=>{b,c},b=>{c},c=>{d},d=>{}}; |
| 37 | i4·:·tree·=·elimTree·G | 37 | i4·:·tree·=·elimTree·G |
| 38 | o4·=·ElimTree{a·=>· | 38 | o4·=·ElimTree{a·=>·b···} |
| 39 | ··············b·=>·c | 39 | ··············b·=>·c |
| 40 | ··············c·=>·d | 40 | ··············c·=>·d |
| 41 | ··············d·=>· | 41 | ··············d·=>·null |
| 42 | o4·:·ElimTree | 42 | o4·:·ElimTree |
| 43 | i5·:·rnk·=·hashTable{"a0"=>a,·"a1"=>a,·"b0"=>b,·"b1"=>b,·"b2"=>b, | 43 | i5·:·rnk·=·hashTable{"a0"=>a,·"a1"=>a,·"b0"=>b,·"b1"=>b,·"b2"=>b, |
| 44 | ·····················"c0"=>c,·"d0"=>d,·"c1"=>c,·"d1"=>d}; | 44 | ·····················"c0"=>c,·"d0"=>d,·"c1"=>c,·"d1"=>d}; |
| 45 | i6·:·eqs·=·hashTable{"a0"·=>·({a},{}),·"a1"·=>·({},{}), | 45 | i6·:·eqs·=·hashTable{"a0"·=>·({a},{}),·"a1"·=>·({},{}), |
| 46 | ·····················"b0"·=>·({b},{}),·"b1"·=>·({},{}),·"b2"·=>·({b},{}), | 46 | ·····················"b0"·=>·({b},{}),·"b1"·=>·({},{}),·"b2"·=>·({b},{}), |
| 47 | ·····················"c0"·=>·({c},{}),·"c1"·=>·({},{}), | 47 | ·····················"c0"·=>·({c},{}),·"c1"·=>·({},{}), |
| 48 | ·····················"d0"·=>·({},{}),·"d1"·=>·({d},{})·}; | 48 | ·····················"d0"·=>·({},{}),·"d1"·=>·({d},{})·}; |
| 49 | i7·:·chordalNet(eqs,rnk,tree,DG) | 49 | i7·:·chordalNet(eqs,rnk,tree,DG) |
| 50 | o7·=·ChordalNet{· | 50 | o7·=·ChordalNet{·d·=>·{·,·d}····} |
| 51 | ·················c·=>·{·,·c} | ||
| 52 | ·················d·=>·{·,·d} | ||
| 53 | ·················b·=>·{b,··,·b} | 51 | ·················b·=>·{b,··,·b} |
| 52 | ·················a·=>·{a,··} | ||
| 53 | ·················c·=>·{·,·c} | ||
| 54 | o7·:·ChordalNet | 54 | o7·:·ChordalNet |
| 55 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 55 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 56 | ····*·_\x8d_\x8i_\x8s_\x8p_\x8l_\x8a_\x8y_\x8N_\x8e_\x8t·--·displays·a·chordal·network·using·Graphivz | 56 | ····*·_\x8d_\x8i_\x8s_\x8p_\x8l_\x8a_\x8y_\x8N_\x8e_\x8t·--·displays·a·chordal·network·using·Graphivz |
| 57 | ····*·_\x8d_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h_\x8(_\x8C_\x8h_\x8o_\x8r_\x8d_\x8a_\x8l_\x8N_\x8e_\x8t_\x8)·--·digraph·associated·to·a·chordal·network | 57 | ····*·_\x8d_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h_\x8(_\x8C_\x8h_\x8o_\x8r_\x8d_\x8a_\x8l_\x8N_\x8e_\x8t_\x8)·--·digraph·associated·to·a·chordal·network |
| 58 | *\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* | 58 | *\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* |
| 59 | ····*·_\x8c_\x8h_\x8o_\x8r_\x8d_\x8a_\x8l_\x8N_\x8e_\x8t_\x8(_\x8H_\x8a_\x8s_\x8h_\x8T_\x8a_\x8b_\x8l_\x8e_\x8,_\x8H_\x8a_\x8s_\x8h_\x8T_\x8a_\x8b_\x8l_\x8e_\x8,_\x8E_\x8l_\x8i_\x8m_\x8T_\x8r_\x8e_\x8e_\x8,_\x8D_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h_\x8)·--·construct·chordal | 59 | ····*·_\x8c_\x8h_\x8o_\x8r_\x8d_\x8a_\x8l_\x8N_\x8e_\x8t_\x8(_\x8H_\x8a_\x8s_\x8h_\x8T_\x8a_\x8b_\x8l_\x8e_\x8,_\x8H_\x8a_\x8s_\x8h_\x8T_\x8a_\x8b_\x8l_\x8e_\x8,_\x8E_\x8l_\x8i_\x8m_\x8T_\x8r_\x8e_\x8e_\x8,_\x8D_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h_\x8)·--·construct·chordal |
| Offset 110, 15 lines modified | Offset 110, 15 lines modified | ||
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i6·:·components(N) | 112 | <td>··············<pre><code·class="language-macaulay2">i6·:·components(N) |
| 113 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)}················································································································································································} | 113 | o6·=·HashTable{4·=>·{ideal·(x·,·x·,·x·,·x·),·ideal·(x·,·x·,·x·,·x·)}················································································································································································} |
| 114 | ·····························1···3···5···7···········2···4···6···8 | 114 | ·····························1···3···5···7···········2···4···6···8 |
| 115 | ···············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 | ···············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·)} |
| 116 | ·····························1···3···4···6···7···········1···2···4···6···7···········1···2···4···5···7···········2···4···5···7···8···········2···3···5···7···8···········1···3··· | 116 | ·····························1···3···4···6···7···········1···2···4···6···7···········1···2···4···5···7···········2···4···5···7···8···········2···3···5···7···8···········1···3···5···6···8···········1···3···4···6···8···········2···3···5···6···8 |
| 117 | ···············6·=>·{} | 117 | ···············6·=>·{} |
| 118 | ···············7·=>·{} | 118 | ···············7·=>·{} |
| 119 | o6·:·HashTable</code></pre> | 119 | o6·:·HashTable</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ········</table> | 121 | ········</table> |
| 122 | ········<pre></pre> | 122 | ········<pre></pre> |
| Offset 46, 15 lines modified | Offset 46, 15 lines modified | ||
| 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···3···4···6···7···········1···2···4···6···7 | 51 | ·····························1···3···4···6···7···········1···2···4···6···7 |
| 52 | 1···2···4···5···7···········2···4···5···7···8···········2···3···5···7···8 | 52 | 1···2···4···5···7···········2···4···5···7···8···········2···3···5···7···8 |
| 53 | 1···3··· | 53 | 1···3···5···6···8···········1···3···4···6···8···········2···3···5···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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=1235 | 9 | #:len=1235 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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, 40 lines modified | Offset 2, 40 lines modified | ||
| 2 | i1·:·F=GF(4); | 2 | i1·:·F=GF(4); |
| 3 | i2·:·R=F[x,y]; | 3 | i2·:·R=F[x,y]; |
| 4 | i3·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y}) | 4 | i3·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y}) |
| 5 | o3·=·EvaluationCode{cache·=>·CacheTable{}···········································································································································································································································} | 5 | o3·=·EvaluationCode{cache·=>·CacheTable{}···············································································································································································································································} |
| 6 | ·······························································9 | 6 | ·······························································9 |
| 7 | ····················LinearCode·=>·LinearCode{AmbientModule·=>·F····················································································································································································································} | 7 | ····················LinearCode·=>·LinearCode{AmbientModule·=>·F························································································································································································································} |
| 8 | ·············································BaseField·=>·F | 8 | ·············································BaseField·=>·F |
| 9 | ·············································cache·=>·CacheTable{} | 9 | ·············································cache·=>·CacheTable{} |
| 10 | ·············································Code·=>·image·|· | 10 | ·············································Code·=>·image·|·a+1·0···| |
| 11 | ···························································|·a+1·0···| | ||
| 12 | ···························································|·a···a···| | ||
| 13 | ···························································|·a···a···| | ||
| 14 | ···························································|·1···a+1·| | ||
| 11 | ···························································|·1···0···| | 15 | ···························································|·1···0···| |
| 12 | ···························································|·0···0···| | 16 | ···························································|·0···0···| |
| 13 | ···························································|·0···0···| | 17 | ···························································|·0···0···| |
| 14 | ···························································|·1···1···| | 18 | ···························································|·1···1···| |
| 19 | ·············································GeneratorMatrix·=>·|·a+1·a+1·a·a·1···1·0·0·1·| | ||
| 15 | ···························································|·a+1·0···| | 20 | ································································|·0···0···a·a·a+1·0·0·0·1·| |
| 16 | ···························································|·a+1·0···| | ||
| 17 | ···························································|·a···a···| | ||
| 18 | ···························································|·a···a···| | ||
| 19 | ·············································GeneratorMatrix·=>·|·1···1·0·0·1·a+1·a+1·a·a·| | ||
| 20 | ································································|·a+1·0·0·0·1·0···0···a·a·| | ||
| 21 | ·············································Generators·=>·{{ | 21 | ·············································Generators·=>·{{a·+·1,·a·+·1,·a,·a,·1,·1,·0,·0,·1},·{0,·0,·a,·a,·a·+·1,·0,·0,·0,·1}} |
| 22 | ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·a+1·0· | 22 | ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·a+1·0·0·0···| |
| 23 | ··································································|·0·1·0·0·0·a | 23 | ··································································|·0·1·0·0·0·a+1·0·0·0···| |
| 24 | ··································································|·0·0·1·0·0·0···0·0· | 24 | ··································································|·0·0·1·0·0·0···0·0·a···| |
| 25 | ··································································|·0·0·0·1·0·0···0·0· | 25 | ··································································|·0·0·0·1·0·0···0·0·a···| |
| 26 | ··································································|·0·0·0·0·1· | 26 | ··································································|·0·0·0·0·1·a···0·0·a+1·| |
| 27 | ··································································|·0·0·0·0·0· | 27 | ··································································|·0·0·0·0·0·0···1·0·0···| |
| 28 | ··································································|·0·0·0·0·0·0···0·1· | 28 | ··································································|·0·0·0·0·0·0···0·1·0···| |
| 29 | ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·0,·a·+·1,·0,·a,·0},·{0,·1,·0,·0,·0,·a,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,·a·+·1,·0},·{0,·0,·0,·0,·0,·1,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·1}} | ||
| 30 | ····················P | 29 | ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·0,·a·+·1,·0,·0,·0},·{0,·1,·0,·0,·0,·a·+·1,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·a},·{0,·0,·0,·1,·0,·0,·0,·0,·a},·{0,·0,·0,·0,·1,·a,·0,·0,·a·+·1},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·[·...·truncated·by·diffoscope;·len:·1,·SHA:·5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9·...·]}} |
| 30 | ····················Points·=>·{{0,·a},·{a,·0},·{1,·a},·{a,·1},·{a,·a},·{0,·0},·{0,·1},·{1,·0},·{1,·1}} | ||
| 31 | ····················PolynomialSet·=>·{x·+·y·+·1,·x*y} | 31 | ····················PolynomialSet·=>·{x·+·y·+·1,·x*y} |
| 32 | ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}} | 32 | ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}} |
| 33 | ··············································3···········2·········3···········2 | 33 | ··············································3···········2·········3···········2 |
| 34 | ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y) | 34 | ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y) |
| 35 | o3·:·EvaluationCode | 35 | o3·:·EvaluationCode |
| 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·|·1·1· | 7 | ················Code·=>·image·|·1·1·0·1·| |
| 8 | ······························|·1·0·1·1·| | 8 | ······························|·1·0·1·1·| |
| 9 | ······························|·1·1· | 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 | ···································|·1·0·1·0·1·0·0·| | 15 | ···································|·1·0·1·0·1·0·0·| |
| 16 | ···································|· | 16 | ···································|·0·1·1·0·0·1·0·| |
| 17 | ···································|· | 17 | ···································|·1·1·0·0·0·0·1·| |
| 18 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{ | 18 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{0,·1,·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· | 20 | ·····································|·0·0·1·1·1·1·0·| |
| 21 | ·····································|·0·1·0·1·0·1·1·| | 21 | ·····································|·0·1·0·1·0·1·1·| |
| 22 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,· | 22 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}} |
| 23 | o1·:·LinearCode | 23 | o1·:·LinearCode |
| 24 | i2·:·ring(C) | 24 | i2·:·ring(C) |
| 25 | o2·=·GF·2 | 25 | o2·=·GF·2 |
| Offset 55, 31 lines modified | Offset 55, 31 lines modified | ||
| 55 | ···············|·0·|····|·0·| | 55 | ···············|·0·|····|·0·| |
| 56 | ···············|·0·|····|·0·| | 56 | ···············|·0·|····|·0·| |
| 57 | ························|·0·| | 57 | ························|·0·| |
| 58 | ························|·0·| | 58 | ························|·0·| |
| 59 | ························|·0·| | 59 | ························|·0·| |
| 60 | ························|·0·| | 60 | ························|·0·| |
| 61 | ···············|·1·|·=>·|·0·| | 61 | ···············|·1·|·=>·|·0·| |
| 62 | ···············|·0·|····|· | 62 | ···············|·0·|····|·1·| |
| 63 | ···············|·1·|····|·0·| | 63 | ···············|·1·|····|·0·| |
| 64 | ························|· | 64 | ························|·0·| |
| 65 | ························|·0·| | 65 | ························|·0·| |
| 66 | ························|·0·| | 66 | ························|·0·| |
| 67 | ························|·0·| | 67 | ························|·0·| |
| 68 | ···············|·1·|·=>·|·0·| | 68 | ···············|·1·|·=>·|·0·| |
| 69 | ···············|·1·|····|·0·| | 69 | ···············|·1·|····|·0·| |
| 70 | ···············|·0·|····|·1·| | 70 | ···············|·0·|····|·1·| |
| 71 | ························|·0·| | 71 | ························|·0·| |
| 72 | ························|·0·| | 72 | ························|·0·| |
| 73 | ························|·0·| | 73 | ························|·0·| |
| 74 | ························|·0·| | 74 | ························|·0·| |
| 75 | ···············|·1·|·=>·|·0·| | 75 | ···············|·1·|·=>·|·0·| |
| 76 | ···············|·1·|····|·1·| | ||
| 77 | ···············|·1·|····|·0·| | 76 | ···············|·1·|····|·0·| |
| 77 | ···············|·1·|····|·0·| | ||
| 78 | ························|· | 78 | ························|·1·| |
| 79 | ························|·0·| | 79 | ························|·0·| |
| 80 | ························|·0·| | 80 | ························|·0·| |
| 81 | ························|·0·| | 81 | ························|·0·| |
| 82 | o7·:·HashTable | 82 | o7·:·HashTable |
| 83 | i8·:· | 83 | i8·:· |
| Offset 30, 35 lines modified | Offset 30, 35 lines modified | ||
| 30 | i5·:·T.LinearCode | 30 | i5·:·T.LinearCode |
| 31 | ·······································9 | 31 | ·······································9 |
| 32 | o5·=·LinearCode{AmbientModule·=>·(GF·4)·············································································································································································································································} | 32 | o5·=·LinearCode{AmbientModule·=>·(GF·4)·············································································································································································································································} |
| 33 | ················BaseField·=>·GF·4 | 33 | ················BaseField·=>·GF·4 |
| 34 | ················cache·=>·CacheTable{} | 34 | ················cache·=>·CacheTable{} |
| 35 | ················Code·=>·image·|· | 35 | ················Code·=>·image·|·a···a···1···a+1·a···a+1·| |
| 36 | ······························|·a···1···a+1·a+1·a+1·a+1·| | ||
| 37 | ······························|·a+1·a···a+1·a···1···a···| | 36 | ······························|·a+1·a···a+1·a···1···a···| |
| 38 | ······························|·a··· | 37 | ······························|·a···1···a+1·a+1·a+1·a+1·| |
| 39 | ······························|· | 38 | ······························|·1···1···1···1···1···1···| |
| 40 | ······························|·a+1·a+1·1···a···a+1·a···| | 39 | ······························|·a+1·a+1·1···a···a+1·a···| |
| 41 | ······························|·1···a+1·a+1·1···a···1···| | 40 | ······························|·1···a+1·a+1·1···a···1···| |
| 42 | ······························|·1···a···a···1···a+1·1···| | 41 | ······························|·1···a···a···1···a+1·1···| |
| 42 | ······························|·a+1·1···a···a···a···a···| | ||
| 43 | ······························|·a···a+1·a···a+1·1···a+1·| | 43 | ······························|·a···a+1·a···a+1·1···a+1·| |
| 44 | ················GeneratorMatrix·=>·|· | 44 | ················GeneratorMatrix·=>·|·a···a+1·a···1·a+1·1···1···a+1·a···| |
| 45 | ···································|· | 45 | ···································|·a···a···1···1·a+1·a+1·a···1···a+1·| |
| 46 | ···································|·1·a+1·a+1·1 | 46 | ···································|·1···a+1·a+1·1·1···a+1·a···a···a···| |
| 47 | ···································|· | 47 | ···································|·a+1·a···a+1·1·a···1···1···a···a+1·| |
| 48 | ···································|· | 48 | ···································|·a···1···a+1·1·a+1·a···a+1·a···1···| |
| 49 | ···································|· | 49 | ···································|·a+1·a···a+1·1·a···1···1···a···a+1·| |
| 50 | ················Generators·=>·{{ | 50 | ················Generators·=>·{{a,·a·+·1,·a,·1,·a·+·1,·1,·1,·a·+·1,·a},·{a,·a,·1,·1,·a·+·1,·a·+·1,·a,·1,·a·+·1},·{1,·a·+·1,·a·+·1,·1,·1,·a·+·1,·a,·a,·a},·{a·+·1,·a,·a·+·1,·1,·a,·1,·1,·a,·a·+·1},·{a,·1,·a·+·1,·1,·a·+·1,·a,·a·+·1,·a,·1},·{a·+·1,·a,·a·+·1,·1,·a,·1,·1,·a,·a·+·1}} |
| 51 | ················ParityCheckMatrix·=>·|·1·0·0·0·a+1· | 51 | ················ParityCheckMatrix·=>·|·1·0·0·0·a+1·0···a+1·0···a···| |
| 52 | ·····································|·0·1·0·0·a···0···a···0···a+1·| | ||
| 53 | ·····································|·0· | 52 | ·····································|·0·1·0·0·0···a+1·a···0···1···| |
| 53 | ·····································|·0·0·1·0·0···a···0···a···a+1·| | ||
| 54 | ·····································|·0·0·0·1· | 54 | ·····································|·0·0·0·1·a···0···0···a+1·1···| |
| 55 | ················ParityCheckRows·=>·{{1,·0,·0,·0,·a·+·1,·a | 55 | ················ParityCheckRows·=>·{{1,·0,·0,·0,·a·+·1,·0,·a·+·1,·0,·a},·{0,·1,·0,·0,·0,·a·+·1,·a,·0,·1},·{0,·0,·1,·0,·0,·a,·0,·a,·a·+·1},·{0,·0,·0,·1,·a,·0,·0,·a·+·1,·1}} |
| 56 | o5·:·LinearCode | 56 | o5·:·LinearCode |
| 57 | i6·:·length·T.LinearCode | 57 | i6·:·length·T.LinearCode |
| 58 | o6·=·9 | 58 | o6·=·9 |
| Offset 80, 40 lines modified | Offset 80, 40 lines modified | ||
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·R=F[x,y];</code></pre> | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·R=F[x,y];</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y}) | 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·C=cartesianCode(F,{{0,1,a},{0,1,a}},{1+x+y,x*y}) |
| 86 | o3·=·EvaluationCode{cache·=>·CacheTable{}···········································································································································································································································} | 86 | o3·=·EvaluationCode{cache·=>·CacheTable{}···············································································································································································································································} |
| 87 | ·······························································9 | 87 | ·······························································9 |
| 88 | ····················LinearCode·=>·LinearCode{AmbientModule·=>·F····················································································································································································································} | 88 | ····················LinearCode·=>·LinearCode{AmbientModule·=>·F························································································································································································································} |
| 89 | ·············································BaseField·=>·F | 89 | ·············································BaseField·=>·F |
| 90 | ·············································cache·=>·CacheTable{} | 90 | ·············································cache·=>·CacheTable{} |
| 91 | ·············································Code·=>·image·|· | 91 | ·············································Code·=>·image·|·a+1·0···| |
| 92 | ···························································|·a+1·0···| | ||
| 93 | ···························································|·a···a···| | ||
| 94 | ···························································|·a···a···| | ||
| 95 | ···························································|·1···a+1·| | ||
| 92 | ···························································|·1···0···| | 96 | ···························································|·1···0···| |
| 93 | ···························································|·0···0···| | 97 | ···························································|·0···0···| |
| 94 | ···························································|·0···0···| | 98 | ···························································|·0···0···| |
| 95 | ···························································|·1···1···| | 99 | ···························································|·1···1···| |
| 100 | ·············································GeneratorMatrix·=>·|·a+1·a+1·a·a·1···1·0·0·1·| | ||
| 96 | ···························································|·a+1·0···| | 101 | ································································|·0···0···a·a·a+1·0·0·0·1·| |
| 97 | ···························································|·a+1·0···| | ||
| 98 | ···························································|·a···a···| | ||
| 99 | ···························································|·a···a···| | ||
| 100 | ·············································GeneratorMatrix·=>·|·1···1·0·0·1·a+1·a+1·a·a·| | ||
| 101 | ································································|·a+1·0·0·0·1·0···0···a·a·| | ||
| 102 | ·············································Generators·=>·{{ | 102 | ·············································Generators·=>·{{a·+·1,·a·+·1,·a,·a,·1,·1,·0,·0,·1},·{0,·0,·a,·a,·a·+·1,·0,·0,·0,·1}} |
| 103 | ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·a+1·0· | 103 | ·············································ParityCheckMatrix·=>·|·1·0·0·0·0·a+1·0·0·0···| |
| 104 | ··································································|·0·1·0·0·0·a | 104 | ··································································|·0·1·0·0·0·a+1·0·0·0···| |
| 105 | ··································································|·0·0·1·0·0·0···0·0· | 105 | ··································································|·0·0·1·0·0·0···0·0·a···| |
| 106 | ··································································|·0·0·0·1·0·0···0·0· | 106 | ··································································|·0·0·0·1·0·0···0·0·a···| |
| 107 | ··································································|·0·0·0·0·1· | 107 | ··································································|·0·0·0·0·1·a···0·0·a+1·| |
| 108 | ··································································|·0·0·0·0·0· | 108 | ··································································|·0·0·0·0·0·0···1·0·0···| |
| 109 | ··································································|·0·0·0·0·0·0···0·1· | 109 | ··································································|·0·0·0·0·0·0···0·1·0···| |
| 110 | ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·0,·a·+·1,·0,·a,·0},·{0,·1,·0,·0,·0,·a,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·0},·{0,·0,·0,·1,·0,·0,·0,·0,·0},·{0,·0,·0,·0,·1,·0,·0,·a·+·1,·0},·{0,·0,·0,·0,·0,·1,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·1}} | ||
| 111 | ····················P | 110 | ·············································ParityCheckRows·=>·{{1,·0,·0,·0,·0,·a·+·1,·0,·0,·0},·{0,·1,·0,·0,·0,·a·+·1,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0,·a},·{0,·0,·0,·1,·0,·0,·0,·0,·a},·{0,·0,·0,·0,·1,·a,·0,·0,·a·+·1},·{0,·0,·0,·0,·0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·[·...·truncated·by·diffoscope;·len:·1,·SHA:·5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9·...·]}} |
| 111 | ····················Points·=>·{{0,·a},·{a,·0},·{1,·a},·{a,·1},·{a,·a},·{0,·0},·{0,·1},·{1,·0},·{1,·1}} | ||
| 112 | ····················PolynomialSet·=>·{x·+·y·+·1,·x*y} | 112 | ····················PolynomialSet·=>·{x·+·y·+·1,·x*y} |
| 113 | ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}} | 113 | ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}} |
| 114 | ··············································3···········2·········3···········2 | 114 | ··············································3···········2·········3···········2 |
| 115 | ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y) | 115 | ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+·1)y··+·a*y) |
| 116 | o3·:·EvaluationCode</code></pre> | 116 | o3·:·EvaluationCode</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| Offset 23, 49 lines modified | Offset 23, 49 lines modified | ||
| 23 | o3·=·EvaluationCode{cache·=>·CacheTable{} | 23 | o3·=·EvaluationCode{cache·=>·CacheTable{} |
| 24 | } | 24 | } |
| 25 | ·······························································9 | 25 | ·······························································9 |
| 26 | ····················LinearCode·=>·LinearCode{AmbientModule·=>·F | 26 | ····················LinearCode·=>·LinearCode{AmbientModule·=>·F |
| 27 | } | 27 | } |
| 28 | ·············································BaseField·=>·F | 28 | ·············································BaseField·=>·F |
| 29 | ·············································cache·=>·CacheTable{} | 29 | ·············································cache·=>·CacheTable{} |
| 30 | ·············································Code·=>·image·|· | 30 | ·············································Code·=>·image·|·a+1·0···| |
| 31 | ···························································|·a+1·0···| | ||
| 32 | ···························································|·a···a···| | ||
| 33 | ···························································|·a···a···| | ||
| 34 | ···························································|·1···a+1·| | ||
| 31 | ···························································|·1···0···| | 35 | ···························································|·1···0···| |
| 32 | ···························································|·0···0···| | 36 | ···························································|·0···0···| |
| 33 | ···························································|·0···0···| | 37 | ···························································|·0···0···| |
| 34 | ···························································|·1···1···| | 38 | ···························································|·1···1···| |
| 35 | ···························································|·a+1·0···| | ||
| 36 | ···························································|·a+1·0···| | ||
| 37 | ···························································|·a···a···| | ||
| 38 | ···························································|·a···a···| | ||
| 39 | ·············································GeneratorMatrix·=>·|·1· | 39 | ·············································GeneratorMatrix·=>·|·a+1·a+1·a·a·1 |
| 40 | 40 | 1·0·0·1·| | |
| 41 | ································································|· | 41 | ································································|·0···0···a·a |
| 42 | 0· | 42 | a+1·0·0·0·1·| |
| 43 | ·············································Generators·=>·{{ | 43 | ·············································Generators·=>·{{a·+·1,·a·+·1,·a, |
| 44 | 44 | a,·1,·1,·0,·0,·1},·{0,·0,·a,·a,·a·+·1,·0,·0,·0,·1}} | |
| 45 | ·············································ParityCheckMatrix·=>·|·1·0·0·0·0 | 45 | ·············································ParityCheckMatrix·=>·|·1·0·0·0·0 |
| 46 | a+1·0· | 46 | a+1·0·0·0···| |
| 47 | ··································································|·0·1·0·0·0 | 47 | ··································································|·0·1·0·0·0 |
| 48 | 0·0· | 48 | a+1·0·0·0···| |
| 49 | ··································································|·0·0·1·0·0·0 | 49 | ··································································|·0·0·1·0·0·0 |
| 50 | 0·0· | 50 | 0·0·a···| |
| 51 | ··································································|·0·0·0·1·0·0 | 51 | ··································································|·0·0·0·1·0·0 |
| 52 | 0·0· | 52 | 0·0·a···| |
| 53 | ··································································|·0·0·0·0·1· | 53 | ··································································|·0·0·0·0·1·a |
| 54 | 0·a+1 | 54 | 0·0·a+1·| |
| 55 | ··································································|·0·0·0·0·0· | 55 | ··································································|·0·0·0·0·0·0 |
| 56 | 1·0· | 56 | 1·0·0···| |
| 57 | ··································································|·0·0·0·0·0·0 | 57 | ··································································|·0·0·0·0·0·0 |
| 58 | 0·1· | 58 | 0·1·0···| |
| 59 | ·············································ParityCheckRows·=>·{{1,·0,·0,·0, | 59 | ·············································ParityCheckRows·=>·{{1,·0,·0,·0, |
| 60 | 0,·a·+·1,·0,· | 60 | 0,·a·+·1,·0,·0,·0},·{0,·1,·0,·0,·0,·a·+·1,·0,·0,·0},·{0,·0,·1,·0,·0,·0,·0,·0, |
| 61 | {0,·0,·0,·1,·0,·0,·0,·0,· | 61 | a},·{0,·0,·0,·1,·0,·0,·0,·0,·a},·{0,·0,·0,·0,·1,·a,·0,·0,·a·+·1},·{0,·0,·0,·0, |
| 62 | 62 | 0,·0,·1,·0,·0},·{0,·0,·0,·0,·0,·0,·0,·1,·0}} | |
| 63 | ····················Points·=>·{{a,·a},·{0,·0},·{1,·0},·{0,·1},·{1,·1},·{0,·a}, | ||
| 64 | {a,·0},·{a,·1},·{ | 63 | ····················Points·=>·{{0,·a},·{a,·0},·{1,·a},·{a,·1},·{a,·a},·{0,·0}, |
| 64 | {0,·1},·{1,·0},·{1,·1}} | ||
| 65 | ····················PolynomialSet·=>·{x·+·y·+·1,·x*y} | 65 | ····················PolynomialSet·=>·{x·+·y·+·1,·x*y} |
| 66 | ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}} | 66 | ····················Sets·=>·{{0,·1,·a},·{0,·1,·a}} |
| 67 | ··············································3···········2·········3 | 67 | ··············································3···········2·········3 |
| 68 | 2 | 68 | 2 |
| 69 | ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+ | 69 | ····················VanishingIdeal·=>·ideal·(x··+·(a·+·1)x··+·a*x,·y··+·(a·+ |
| 70 | 1)y··+·a*y) | 70 | 1)y··+·a*y) |
| Offset 77, 30 lines modified | Offset 77, 30 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·C·=·hammingCode(2,·3) | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·C·=·hammingCode(2,·3) |
| 79 | ·······································7 | 79 | ·······································7 |
| 80 | o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································} | 80 | o1·=·LinearCode{AmbientModule·=>·(GF·2)···················································································} |
| 81 | ················BaseField·=>·GF·2 | 81 | ················BaseField·=>·GF·2 |
| 82 | ················cache·=>·CacheTable{} | 82 | ················cache·=>·CacheTable{} |
| 83 | ················Code·=>·image·|·1·1· | 83 | ················Code·=>·image·|·1·1·0·1·| |
| 84 | ······························|·1·0·1·1·| | 84 | ······························|·1·0·1·1·| |
| 85 | ······························|·1·1· | 85 | ······························|·1·1·1·0·| |
| 86 | ······························|·1·0·0·0·| | 86 | ······························|·1·0·0·0·| |
| 87 | ······························|·0·1·0·0·| | 87 | ······························|·0·1·0·0·| |
| 88 | ······························|·0·0·1·0·| | 88 | ······························|·0·0·1·0·| |
| 89 | ······························|·0·0·0·1·| | 89 | ······························|·0·0·0·1·| |
| 90 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| | 90 | ················GeneratorMatrix·=>·|·1·1·1·1·0·0·0·| |
| 91 | ···································|·1·0·1·0·1·0·0·| | 91 | ···································|·1·0·1·0·1·0·0·| |
| 92 | ···································|· | 92 | ···································|·0·1·1·0·0·1·0·| |
| 93 | ···································|· | 93 | ···································|·1·1·0·0·0·0·1·| |
| 94 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{ | 94 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0},·{0,·1,·1,·0,·0,·1,·0},·{1,·1,·0,·0,·0,·0,·1}} |
| 95 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| | 95 | ················ParityCheckMatrix·=>·|·1·1·1·1·0·0·0·| |
| 96 | ·····································|·0· | 96 | ·····································|·0·0·1·1·1·1·0·| |
| 97 | ·····································|·0·1·0·1·0·1·1·| | 97 | ·····································|·0·1·0·1·0·1·1·| |
| 98 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,· | 98 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1,·0},·{0,·1,·0,·1,·0,·1,·1}} |
| 99 | o1·:·LinearCode</code></pre> | 99 | o1·:·LinearCode</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i2·:·ring(C) | 102 | <td>··············<pre><code·class="language-macaulay2">i2·:·ring(C) |
| 103 | o2·=·GF·2 | 103 | o2·=·GF·2 |
| Offset 18, 31 lines modified | Offset 18, 31 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·|·1·1· | 24 | ················Code·=>·image·|·1·1·0·1·| |
| 25 | ······························|·1·0·1·1·| | 25 | ······························|·1·0·1·1·| |
| 26 | ······························|·1·1· | 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 | ···································|·1·0·1·0·1·0·0·| | 32 | ···································|·1·0·1·0·1·0·0·| |
| 33 | ···································|· | 33 | ···································|·0·1·1·0·0·1·0·| |
| 34 | ···································|· | 34 | ···································|·1·1·0·0·0·0·1·| |
| 35 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0}, | 35 | ················Generators·=>·{{1,·1,·1,·1,·0,·0,·0},·{1,·0,·1,·0,·1,·0,·0}, |
| 36 | { | 36 | {0,·1,·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· | 38 | ·····································|·0·0·1·1·1·1·0·| |
| 39 | ·····································|·0·1·0·1·0·1·1·| | 39 | ·····································|·0·1·0·1·0·1·1·| |
| 40 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,· | 40 | ················ParityCheckRows·=>·{{1,·1,·1,·1,·0,·0,·0},·{0,·0,·1,·1,·1,·1, |
| 41 | 0},·{0,·1,·0,·1,·0,·1,·1}} | 41 | 0},·{0,·1,·0,·1,·0,·1,·1}} |
| 42 | o1·:·LinearCode | 42 | o1·:·LinearCode |
| 43 | i2·:·ring(C) | 43 | i2·:·ring(C) |
| 44 | o2·=·GF·2 | 44 | o2·=·GF·2 |
| Offset 138, 31 lines modified | Offset 138, 31 lines modified | ||
| 138 | ···············|·0·|····|·0·| | 138 | ···············|·0·|····|·0·| |
| 139 | ···············|·0·|····|·0·| | 139 | ···············|·0·|····|·0·| |
| 140 | ························|·0·| | 140 | ························|·0·| |
| 141 | ························|·0·| | 141 | ························|·0·| |
| 142 | ························|·0·| | 142 | ························|·0·| |
| 143 | ························|·0·| | 143 | ························|·0·| |
| 144 | ···············|·1·|·=>·|·0·| | 144 | ···············|·1·|·=>·|·0·| |
| 145 | ···············|·0·|····|· | 145 | ···············|·0·|····|·1·| |
| 146 | ···············|·1·|····|·0·| | 146 | ···············|·1·|····|·0·| |
| 147 | ························|· | 147 | ························|·0·| |
| 148 | ························|·0·| | 148 | ························|·0·| |
| 149 | ························|·0·| | 149 | ························|·0·| |
| 150 | ························|·0·| | 150 | ························|·0·| |
| 151 | ···············|·1·|·=>·|·0·| | 151 | ···············|·1·|·=>·|·0·| |
| 152 | ···············|·1·|····|·0·| | 152 | ···············|·1·|····|·0·| |
| 153 | ···············|·0·|····|·1·| | 153 | ···············|·0·|····|·1·| |
| 154 | ························|·0·| | 154 | ························|·0·| |
| 155 | ························|·0·| | 155 | ························|·0·| |
| 156 | ························|·0·| | 156 | ························|·0·| |
| 157 | ························|·0·| | 157 | ························|·0·| |
| 158 | ···············|·1·|·=>·|·0·| | 158 | ···············|·1·|·=>·|·0·| |
| 159 | ···············|·1·|····|·1·| | ||
| 160 | ···············|·1·|····|·0·| | 159 | ···············|·1·|····|·0·| |
| 160 | ···············|·1·|····|·0·| | ||
| 161 | ························|· | 161 | ························|·1·| |
| 162 | ························|·0·| | 162 | ························|·0·| |
| 163 | ························|·0·| | 163 | ························|·0·| |
| 164 | ························|·0·| | 164 | ························|·0·| |
| 165 | o7·:·HashTable</code></pre> | 165 | o7·:·HashTable</code></pre> |
| 166 | </td>··········</tr> | 166 | </td>··········</tr> |
| 167 | ········</table> | 167 | ········</table> |
| Offset 70, 31 lines modified | Offset 70, 31 lines modified | ||
| 70 | ···············|·0·|····|·0·| | 70 | ···············|·0·|····|·0·| |
| 71 | ···············|·0·|····|·0·| | 71 | ···············|·0·|····|·0·| |
| 72 | ························|·0·| | 72 | ························|·0·| |
| 73 | ························|·0·| | 73 | ························|·0·| |
| 74 | ························|·0·| | 74 | ························|·0·| |
| 75 | ························|·0·| | 75 | ························|·0·| |
| 76 | ···············|·1·|·=>·|·0·| | 76 | ···············|·1·|·=>·|·0·| |
| 77 | ···············|·0·|····|· | 77 | ···············|·0·|····|·1·| |
| 78 | ···············|·1·|····|·0·| | 78 | ···············|·1·|····|·0·| |
| 79 | ························|· | 79 | ························|·0·| |
| 80 | ························|·0·| | 80 | ························|·0·| |
| 81 | ························|·0·| | 81 | ························|·0·| |
| 82 | ························|·0·| | 82 | ························|·0·| |
| 83 | ···············|·1·|·=>·|·0·| | 83 | ···············|·1·|·=>·|·0·| |
| 84 | ···············|·1·|····|·0·| | 84 | ···············|·1·|····|·0·| |
| 85 | ···············|·0·|····|·1·| | 85 | ···············|·0·|····|·1·| |
| 86 | ························|·0·| | 86 | ························|·0·| |
| 87 | ························|·0·| | 87 | ························|·0·| |
| 88 | ························|·0·| | 88 | ························|·0·| |
| 89 | ························|·0·| | 89 | ························|·0·| |
| 90 | ···············|·1·|·=>·|·0·| | 90 | ···············|·1·|·=>·|·0·| |
| 91 | ···············|·1·|····|·1·| | ||
| 92 | ···············|·1·|····|·0·| | 91 | ···············|·1·|····|·0·| |
| 92 | ···············|·1·|····|·0·| | ||
| 93 | ························|· | 93 | ························|·1·| |
| 94 | ························|·0·| | 94 | ························|·0·| |
| 95 | ························|·0·| | 95 | ························|·0·| |
| 96 | ························|·0·| | 96 | ························|·0·| |
| 97 | o7·:·HashTable | 97 | o7·:·HashTable |
| 98 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8yn\x8nd\x8dr\x8ro\x8om\x8me\x8eD\x8De\x8ec\x8co\x8od\x8de\x8e·:\x8:·*\x8**\x8**\x8**\x8**\x8* | 98 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sy\x8yn\x8nd\x8dr\x8ro\x8om\x8me\x8eD\x8De\x8ec\x8co\x8od\x8de\x8e·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 99 | ····*·syndromeDecode(LinearCode,Matrix,ZZ) | 99 | ····*·syndromeDecode(LinearCode,Matrix,ZZ) |
| Offset 110, 35 lines modified | Offset 110, 35 lines modified | ||
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·T.LinearCode | 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·T.LinearCode |
| 112 | ·······································9 | 112 | ·······································9 |
| 113 | o5·=·LinearCode{AmbientModule·=>·(GF·4)·············································································································································································································································} | 113 | o5·=·LinearCode{AmbientModule·=>·(GF·4)·············································································································································································································································} |
| 114 | ················BaseField·=>·GF·4 | 114 | ················BaseField·=>·GF·4 |
| 115 | ················cache·=>·CacheTable{} | 115 | ················cache·=>·CacheTable{} |
| 116 | ················Code·=>·image·|· | 116 | ················Code·=>·image·|·a···a···1···a+1·a···a+1·| |
| 117 | ······························|·a···1···a+1·a+1·a+1·a+1·| | ||
| 118 | ······························|·a+1·a···a+1·a···1···a···| | 117 | ······························|·a+1·a···a+1·a···1···a···| |
| 119 | ······························|·a··· | 118 | ······························|·a···1···a+1·a+1·a+1·a+1·| |
| 120 | ······························|· | 119 | ······························|·1···1···1···1···1···1···| |
| 121 | ······························|·a+1·a+1·1···a···a+1·a···| | 120 | ······························|·a+1·a+1·1···a···a+1·a···| |
| 122 | ······························|·1···a+1·a+1·1···a···1···| | 121 | ······························|·1···a+1·a+1·1···a···1···| |
| 123 | ······························|·1···a···a···1···a+1·1···| | 122 | ······························|·1···a···a···1···a+1·1···| |
| 123 | ······························|·a+1·1···a···a···a···a···| | ||
| 124 | ······························|·a···a+1·a···a+1·1···a+1·| | 124 | ······························|·a···a+1·a···a+1·1···a+1·| |
| 125 | ················GeneratorMatrix·=>·|· | 125 | ················GeneratorMatrix·=>·|·a···a+1·a···1·a+1·1···1···a+1·a···| |
| 126 | ···································|· | 126 | ···································|·a···a···1···1·a+1·a+1·a···1···a+1·| |
| 127 | ···································|·1·a+1·a+1·1 | 127 | ···································|·1···a+1·a+1·1·1···a+1·a···a···a···| |
| 128 | ···································|· | 128 | ···································|·a+1·a···a+1·1·a···1···1···a···a+1·| |
| 129 | ···································|· | 129 | ···································|·a···1···a+1·1·a+1·a···a+1·a···1···| |
| 130 | ···································|· | 130 | ···································|·a+1·a···a+1·1·a···1···1···a···a+1·| |
| 131 | ················Generators·=>·{{ | 131 | ················Generators·=>·{{a,·a·+·1,·a,·1,·a·+·1,·1,·1,·a·+·1,·a},·{a,·a,·1,·1,·a·+·1,·a·+·1,·a,·1,·a·+·1},·{1,·a·+·1,·a·+·1,·1,·1,·a·+·1,·a,·a,·a},·{a·+·1,·a,·a·+·1,·1,·a,·1,·1,·a,·a·+·1},·{a,·1,·a·+·1,·1,·a·+·1,·a,·a·+·1,·a,·1},·{a·+·1,·a,·a·+·1,·1,·a,·1,·1,·a,·a·+·1}} |
| 132 | ················ParityCheckMatrix·=>·|·1·0·0·0·a+1· | 132 | ················ParityCheckMatrix·=>·|·1·0·0·0·a+1·0···a+1·0···a···| |
| 133 | ·····································|·0·1·0·0·a···0···a···0···a+1·| | ||
| 134 | ·····································|·0· | 133 | ·····································|·0·1·0·0·0···a+1·a···0···1···| |
| 134 | ·····································|·0·0·1·0·0···a···0···a···a+1·| | ||
| 135 | ·····································|·0·0·0·1· | 135 | ·····································|·0·0·0·1·a···0···0···a+1·1···| |
| 136 | ················ParityCheckRows·=>·{{1,·0,·0,·0,·a·+·1,·a | 136 | ················ParityCheckRows·=>·{{1,·0,·0,·0,·a·+·1,·0,·a·+·1,·0,·a},·{0,·1,·0,·0,·0,·a·+·1,·a,·0,·1},·{0,·0,·1,·0,·0,·a,·0,·a,·a·+·1},·{0,·0,·0,·1,·a,·0,·0,·a·+·1,·1}} |
| 137 | o5·:·LinearCode</code></pre> | 137 | o5·:·LinearCode</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i6·:·length·T.LinearCode | 140 | <td>··············<pre><code·class="language-macaulay2">i6·:·length·T.LinearCode |
| 141 | o6·=·9</code></pre> | 141 | o6·=·9</code></pre> |
| Offset 45, 40 lines modified | Offset 45, 40 lines modified | ||
| 45 | i5·:·T.LinearCode | 45 | i5·:·T.LinearCode |
| 46 | ·······································9 | 46 | ·······································9 |
| 47 | o5·=·LinearCode{AmbientModule·=>·(GF·4) | 47 | o5·=·LinearCode{AmbientModule·=>·(GF·4) |
| 48 | } | 48 | } |
| 49 | ················BaseField·=>·GF·4 | 49 | ················BaseField·=>·GF·4 |
| 50 | ················cache·=>·CacheTable{} | 50 | ················cache·=>·CacheTable{} |
| 51 | ················Code·=>·image·|· | 51 | ················Code·=>·image·|·a···a···1···a+1·a···a+1·| |
| 52 | ······························|·a···1···a+1·a+1·a+1·a+1·| | ||
| 53 | ······························|·a+1·a···a+1·a···1···a···| | 52 | ······························|·a+1·a···a+1·a···1···a···| |
| 54 | ······························|·a··· | 53 | ······························|·a···1···a+1·a+1·a+1·a+1·| |
| 55 | ······························|· | 54 | ······························|·1···1···1···1···1···1···| |
| 56 | ······························|·a+1·a+1·1···a···a+1·a···| | 55 | ······························|·a+1·a+1·1···a···a+1·a···| |
| 57 | ······························|·1···a+1·a+1·1···a···1···| | 56 | ······························|·1···a+1·a+1·1···a···1···| |
| 58 | ······························|·1···a···a···1···a+1·1···| | 57 | ······························|·1···a···a···1···a+1·1···| |
| 58 | ······························|·a+1·1···a···a···a···a···| | ||
| 59 | ······························|·a···a+1·a···a+1·1···a+1·| | 59 | ······························|·a···a+1·a···a+1·1···a+1·| |
| 60 | ················GeneratorMatrix·=>·|· | 60 | ················GeneratorMatrix·=>·|·a···a+1·a···1·a+1·1···1···a+1·a···| |
| 61 | ···································|· | 61 | ···································|·a···a···1···1·a+1·a+1·a···1···a+1·| |
| 62 | ···································|·1·a+1·a+1·1 | 62 | ···································|·1···a+1·a+1·1·1···a+1·a···a···a···| |
| 63 | ···································|· | 63 | ···································|·a+1·a···a+1·1·a···1···1···a···a+1·| |
| 64 | ···································|· | 64 | ···································|·a···1···a+1·1·a+1·a···a+1·a···1···| |
| 65 | ···································|· | 65 | ···································|·a+1·a···a+1·1·a···1···1···a···a+1·| |
| 66 | ················Generators·=>·{{ | 66 | ················Generators·=>·{{a,·a·+·1,·a,·1,·a·+·1,·1,·1,·a·+·1,·a},·{a,·a, |
| 67 | 67 | 1,·1,·a·+·1,·a·+·1,·a,·1,·a·+·1},·{1,·a·+·1,·a·+·1,·1,·1,·a·+·1,·a,·a,·a},·{a·+ | |
| 68 | 68 | 1,·a,·a·+·1,·1,·a,·1,·1,·a,·a·+·1},·{a,·1,·a·+·1,·1,·a·+·1,·a,·a·+·1,·a,·1},·{a | |
| 69 | 69 | +·1,·a,·a·+·1,·1,·a,·1,·1,·a,·a·+·1}} | |
| 70 | ················ParityCheckMatrix·=>·|·1·0·0·0·a+1· | 70 | ················ParityCheckMatrix·=>·|·1·0·0·0·a+1·0···a+1·0···a···| |
| 71 | ·····································|·0·1·0·0·a···0···a···0···a+1·| | ||
| 72 | ·····································|·0· | 71 | ·····································|·0·1·0·0·0···a+1·a···0···1···| |
| 72 | ·····································|·0·0·1·0·0···a···0···a···a+1·| | ||
| 73 | ·····································|·0·0·0·1· | 73 | ·····································|·0·0·0·1·a···0···0···a+1·1···| |
| 74 | ················ParityCheckRows·=>·{{1,·0,·0,·0,·a·+·1,·a | 74 | ················ParityCheckRows·=>·{{1,·0,·0,·0,·a·+·1,·0,·a·+·1,·0,·a},·{0,·1, |
| 75 | 0,· | 75 | 0,·0,·0,·a·+·1,·a,·0,·1},·{0,·0,·1,·0,·0,·a,·0,·a,·a·+·1},·{0,·0,·0,·1,·a,·0, |
| 76 | 0,·a·+·1,· | 76 | 0,·a·+·1,·1}} |
| 77 | o5·:·LinearCode | 77 | o5·:·LinearCode |
| 78 | i6·:·length·T.LinearCode | 78 | i6·:·length·T.LinearCode |
| 79 | o6·=·9 | 79 | o6·=·9 |
| 80 | i7·:·dim·T.LinearCode | 80 | i7·:·dim·T.LinearCode |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·4.22947·seconds·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 | ·--·0. | 269 | ·--·0.393572·seconds·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 | ·--·1 | 273 | ·--·13.5372·seconds·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 | ·--·0.476119·seconds·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 | ·--·0. | 285 | ·--·0.454943·seconds·elapsed |
| 286 | ·--·0. | 286 | ·--·0.455011·seconds·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 264, 15 lines modified | Offset 264, 15 lines modified | ||
| 264 | ······----------------------------------------------------------------------- | 264 | ······----------------------------------------------------------------------- |
| 265 | ······0,·0,·0,·-1,·-1}} | 265 | ······0,·0,·0,·-1,·-1}} |
| 266 | o19·:·List</code></pre> | 266 | o19·:·List</code></pre> |
| 267 | </td>··········</tr> | 267 | </td>··········</tr> |
| 268 | ··········<tr> | 268 | ··········<tr> |
| 269 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) | 269 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·hvecs·=·cohomCalg(X,·D2) |
| 270 | ·--· | 270 | ·--·4.22947·seconds·elapsed |
| 271 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, | 271 | o20·=·{{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0}, |
| 272 | ······----------------------------------------------------------------------- | 272 | ······----------------------------------------------------------------------- |
| 273 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, | 273 | ······{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·1,·0,·0,·0},·{0,·0,·0,·0,·0},·{0, |
| 274 | ······----------------------------------------------------------------------- | 274 | ······----------------------------------------------------------------------- |
| 275 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, | 275 | ······0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0,·0,·0,·0},·{0,·0, |
| 276 | ······----------------------------------------------------------------------- | 276 | ······----------------------------------------------------------------------- |
| Offset 348, 23 lines modified | Offset 348, 23 lines modified | ||
| 348 | o22·=·{0,·0,·1,·2,·0,·-1} | 348 | o22·=·{0,·0,·1,·2,·0,·-1} |
| 349 | o22·:·List</code></pre> | 349 | o22·:·List</code></pre> |
| 350 | </td>··········</tr> | 350 | </td>··········</tr> |
| 351 | ··········<tr> | 351 | ··········<tr> |
| 352 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) | 352 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·+·X_8) |
| 353 | ·--·0. | 353 | ·--·0.393572·seconds·elapsed |
| 354 | o23·=·{1,·0,·0,·0,·0} | 354 | o23·=·{1,·0,·0,·0,·0} |
| 355 | o23·:·List</code></pre> | 355 | o23·:·List</code></pre> |
| 356 | </td>··········</tr> | 356 | </td>··········</tr> |
| 357 | ··········<tr> | 357 | ··········<tr> |
| 358 | <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 | <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)) |
| 359 | ·--·1 | 359 | ·--·13.5372·seconds·elapsed |
| 360 | o24·=·{1,·0,·0,·0,·0} | 360 | o24·=·{1,·0,·0,·0,·0} |
| 361 | o24·:·List</code></pre> | 361 | o24·:·List</code></pre> |
| 362 | </td>··········</tr> | 362 | </td>··········</tr> |
| 363 | ··········<tr> | 363 | ··········<tr> |
| 364 | <td>··············<pre><code·class="language-macaulay2">i25·:·assert(cohomvec1·==·cohomvec2)</code></pre> | 364 | <td>··············<pre><code·class="language-macaulay2">i25·:·assert(cohomvec1·==·cohomvec2)</code></pre> |
| Offset 374, 24 lines modified | Offset 374, 24 lines modified | ||
| 374 | o26·=·{0,·0,·1,·2,·-2,·-1} | 374 | o26·=·{0,·0,·1,·2,·-2,·-1} |
| 375 | o26·:·List</code></pre> | 375 | o26·:·List</code></pre> |
| 376 | </td>··········</tr> | 376 | </td>··········</tr> |
| 377 | ··········<tr> | 377 | ··········<tr> |
| 378 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) | 378 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·cohomvec1·=·cohomCalg(X_3·+·X_7·-·X_8) |
| 379 | ·--· | 379 | ·--·0.476119·seconds·elapsed |
| 380 | o27·=·{0,·0,·0,·0,·0} | 380 | o27·=·{0,·0,·0,·0,·0} |
| 381 | o27·:·List</code></pre> | 381 | o27·:·List</code></pre> |
| 382 | </td>··········</tr> | 382 | </td>··········</tr> |
| 383 | ··········<tr> | 383 | ··········<tr> |
| 384 | <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 | <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)) |
| 385 | ·--·0. | 385 | ·--·0.454943·seconds·elapsed |
| 386 | ·--·0. | 386 | ·--·0.455011·seconds·elapsed |
| 387 | o28·=·{0,·0,·0,·0,·0} | 387 | o28·=·{0,·0,·0,·0,·0} |
| 388 | o28·:·List</code></pre> | 388 | o28·:·List</code></pre> |
| 389 | </td>··········</tr> | 389 | </td>··········</tr> |
| 390 | ··········<tr> | 390 | ··········<tr> |
| 391 | <td>··············<pre><code·class="language-macaulay2">i29·:·assert(cohomvec1·==·cohomvec2)</code></pre> | 391 | <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 | ·--·4.22947·seconds·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 | ·--·0. | 267 | ·--·0.393572·seconds·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 | ·--·1 | 272 | ·--·13.5372·seconds·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 | ·--·0.476119·seconds·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 | ·--·0. | 285 | ·--·0.454943·seconds·elapsed |
| 286 | ·--·0. | 286 | ·--·0.455011·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·6.41 | 39 | ·--·used·6.14194s·(cpu);·4.16469s·(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·0.117494s·(cpu);·0.083619s·(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· | 151 | ·--·used·1.01881s·(cpu);·0.655087s·(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·1.0 | 160 | ·--·used·1.05788s·(cpu);·0.707776s·(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:·-1049534658 | 1 | --·-*-·M2-comint·-*-·hash:·-1049534658 |
| 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·0. | 5 | ·--·used·0.574935s·(cpu);·0.353635s·(thread);·0s·(gc) |
| 6 | ·--·used·0.1 | 6 | ·--·used·0.1298s·(cpu);·0.106982s·(thread);·0s·(gc) |
| 7 | ·--·used· | 7 | ·--·used·0.000125789s·(cpu);·7.81e-07s·(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:·402513481 | 1 | --·-*-·M2-comint·-*-·hash:·402513481 |
| 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·0.9 | 5 | ·--·used·0.938182s·(cpu);·0.61898s·(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·0. | 9 | ·--·used·0.61704s·(cpu);·0.401574s·(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. | 13 | ·--·used·0.207061s·(cpu);·0.128487s·(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 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·len·=·10 | 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·len·=·10 |
| 124 | o6·=·10</code></pre> | 124 | o6·=·10</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·G·=·EisenbudShamash(ff,F,len) | 127 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·G·=·EisenbudShamash(ff,F,len) |
| 128 | ·--·used·6.41 | 128 | ·--·used·6.14194s·(cpu);·4.16469s·(thread);·0s·(gc) |
| 129 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76 | 129 | ·····/····S···\1·····/····S···\5·····/····S···\12·····/····S···\20·····/····S···\28·····/····S···\36·····/····S···\44·····/····S···\52·····/····S···\60·····/····S···\68·····/····S···\76 |
| 130 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------| | 130 | o7·=·|--------|··<--·|--------|··<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------|···<--·|--------| |
| 131 | ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·| | 131 | ·····|··2···3·|······|··2···3·|······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·|·······|··2···3·| |
| 132 | ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)| | 132 | ·····|(x·,·x·)|······|(x·,·x·)|······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)|·······|(x·,·x·)| |
| 133 | ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/ | 133 | ·····\··0···1·/······\··0···1·/······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/·······\··0···1·/ |
| 134 | ·············································································································································································· | 134 | ·············································································································································································· |
| Offset 260, 26 lines modified | Offset 260, 26 lines modified | ||
| 260 | o19·=·R1 | 260 | o19·=·R1 |
| 261 | o19·:·QuotientRing</code></pre> | 261 | o19·:·QuotientRing</code></pre> |
| 262 | </td>··········</tr> | 262 | </td>··········</tr> |
| 263 | ··········<tr> | 263 | ··········<tr> |
| 264 | <td>··············<pre><code·class="language-macaulay2">i20·:·FF·=·time·Shamash(R1,F,4) | 264 | <td>··············<pre><code·class="language-macaulay2">i20·:·FF·=·time·Shamash(R1,F,4) |
| 265 | ·--·used·0.1 | 265 | ·--·used·0.117494s·(cpu);·0.083619s·(thread);·0s·(gc) |
| 266 | ········1·······6·······18·······38·······66 | 266 | ········1·······6·······18·······38·······66 |
| 267 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 267 | o20·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 268 | ········································· | 268 | ········································· |
| 269 | ······0·······1·······2········3········4 | 269 | ······0·······1·······2········3········4 |
| 270 | o20·:·ChainComplex</code></pre> | 270 | o20·:·ChainComplex</code></pre> |
| 271 | </td>··········</tr> | 271 | </td>··········</tr> |
| 272 | ··········<tr> | 272 | ··········<tr> |
| 273 | <td>··············<pre><code·class="language-macaulay2">i21·:·GG·=·time·EisenbudShamash(ff,F,4) | 273 | <td>··············<pre><code·class="language-macaulay2">i21·:·GG·=·time·EisenbudShamash(ff,F,4) |
| 274 | ·--·used· | 274 | ·--·used·1.01881s·(cpu);·0.655087s·(thread);·0s·(gc) |
| 275 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 | 275 | ······/·R\1·····/·R\6·····/·R\18·····/·R\38·····/·R\66 |
| 276 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| | 276 | o21·=·|--|··<--·|--|··<--·|--|···<--·|--|···<--·|--| |
| 277 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| | 277 | ······|·3|······|·3|······|·3|·······|·3|·······|·3| |
| 278 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ | 278 | ······\c·/······\c·/······\c·/·······\c·/·······\c·/ |
| 279 | ················································· | 279 | ················································· |
| 280 | ······0·········1·········2··········3··········4 | 280 | ······0·········1·········2··········3··········4 |
| Offset 289, 15 lines modified | Offset 289, 15 lines modified | ||
| 289 | ········</table> | 289 | ········</table> |
| 290 | ········<div> | 290 | ········<div> |
| 291 | ··········<p>The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:</p> | 291 | ··········<p>The·function·also·deals·correctly·with·complexes·F·where·min·F·is·not·0:</p> |
| 292 | ········</div> | 292 | ········</div> |
| 293 | ········<table·class="examples"> | 293 | ········<table·class="examples"> |
| 294 | ··········<tr> | 294 | ··········<tr> |
| 295 | <td>··············<pre><code·class="language-macaulay2">i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) | 295 | <td>··············<pre><code·class="language-macaulay2">i22·:·GG·=·time·EisenbudShamash(R1,F[2],4) |
| 296 | ·--·used·1.0 | 296 | ·--·used·1.05788s·(cpu);·0.707776s·(thread);·0s·(gc) |
| 297 | ········1·······6·······18·······38·······66 | 297 | ········1·······6·······18·······38·······66 |
| 298 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 | 298 | o22·=·R1··<--·R1··<--·R1···<--·R1···<--·R1 |
| 299 | ········································· | 299 | ········································· |
| 300 | ······-2······-1······0········1········2 | 300 | ······-2······-1······0········1········2 |
| 301 | o22·:·ChainComplex</code></pre> | 301 | 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·6.41 | 56 | ·--·used·6.14194s·(cpu);·4.16469s·(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·0.117494s·(cpu);·0.083619s·(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· | 178 | ·--·used·1.01881s·(cpu);·0.655087s·(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·1.0 | 187 | ·--·used·1.05788s·(cpu);·0.707776s·(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 77, 17 lines modified | Offset 77, 17 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 |
| 79 | o1·=·0</code></pre> | 79 | o1·=·0</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·sumTwoMonomials(2,3) | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·sumTwoMonomials(2,3) |
| 83 | ·--·used·0. | 83 | ·--·used·0.574935s·(cpu);·0.353635s·(thread);·0s·(gc) |
| 84 | ·--·used·0.1 | 84 | ·--·used·0.1298s·(cpu);·0.106982s·(thread);·0s·(gc) |
| 85 | ·--·used· | 85 | ·--·used·0.000125789s·(cpu);·7.81e-07s·(thread);·0s·(gc) |
| 86 | 2 | 86 | 2 |
| 87 | Tally{{{2,·2},·{1,·2}}·=>·3} | 87 | Tally{{{2,·2},·{1,·2}}·=>·3} |
| 88 | 3 | 88 | 3 |
| 89 | Tally{{{2,·2},·{1,·2}}·=>·1} | 89 | Tally{{{2,·2},·{1,·2}}·=>·1} |
| 90 | 4 | 90 | 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·0. | 24 | ·--·used·0.574935s·(cpu);·0.353635s·(thread);·0s·(gc) |
| 25 | ·--·used·0.1 | 25 | ·--·used·0.1298s·(cpu);·0.106982s·(thread);·0s·(gc) |
| 26 | ·--·used· | 26 | ·--·used·0.000125789s·(cpu);·7.81e-07s·(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 83, 25 lines modified | Offset 83, 25 lines modified | ||
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 | 84 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed·0 |
| 85 | o1·=·0</code></pre> | 85 | o1·=·0</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·twoMonomials(2,3) | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·twoMonomials(2,3) |
| 89 | ·--·used·0.9 | 89 | ·--·used·0.938182s·(cpu);·0.61898s·(thread);·0s·(gc) |
| 90 | 2 | 90 | 2 |
| 91 | Tally{{{1,·1}}·=>·2········} | 91 | Tally{{{1,·1}}·=>·2········} |
| 92 | ······{{2,·2},·{1,·2}}·=>·4 | 92 | ······{{2,·2},·{1,·2}}·=>·4 |
| 93 | ·--·used·0. | 93 | ·--·used·0.61704s·(cpu);·0.401574s·(thread);·0s·(gc) |
| 94 | 3 | 94 | 3 |
| 95 | Tally{{{2,·2},·{1,·2}}·=>·2} | 95 | Tally{{{2,·2},·{1,·2}}·=>·2} |
| 96 | ······{{3,·3},·{2,·3}}·=>·1 | 96 | ······{{3,·3},·{2,·3}}·=>·1 |
| 97 | ·--·used·0. | 97 | ·--·used·0.207061s·(cpu);·0.128487s·(thread);·0s·(gc) |
| 98 | 4 | 98 | 4 |
| 99 | Tally{{{2,·2},·{1,·2}}·=>·1}</code></pre> | 99 | Tally{{{2,·2},·{1,·2}}·=>·1}</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 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·0.9 | 26 | ·--·used·0.938182s·(cpu);·0.61898s·(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·0. | 30 | ·--·used·0.61704s·(cpu);·0.401574s·(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. | 34 | ·--·used·0.207061s·(cpu);·0.128487s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTI3MCwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTI3MCwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoSG9tLE1hdHJpeCxDb21wbGV4KSwiSG9tKE1hdHJp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoSG9tLE1hdHJpeCxDb21wbGV4KSwiSG9tKE1hdHJp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | Y2Fub25pY2FsRGl2aXNvck0wbmJhcg== | 8 | Y2Fub25pY2FsRGl2aXNvck0wbmJhcg== |
| 9 | #:len=1172 | 9 | #:len=1172 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgY2xhc3Mgb2YgdGhl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgY2xhc3Mgb2YgdGhl |
| 11 | IGNhbm9uaWNhbCBkaXZpc29yIG9uIHRoZSBtb2R1bGkgc3BhY2Ugb2Ygc3RhYmxlIG4tcG9pbnRl | 11 | IGNhbm9uaWNhbCBkaXZpc29yIG9uIHRoZSBtb2R1bGkgc3BhY2Ugb2Ygc3RhYmxlIG4tcG9pbnRl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bUNvbnZleEh1bGxGYWNlcyguLi4sdG9GaWxlPT4uLi4p | 8 | bUNvbnZleEh1bGxGYWNlcyguLi4sdG9GaWxlPT4uLi4p |
| 9 | #:len=273 | 9 | #:len=273 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzU3LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzU3LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1ttQ29udmV4SHVsbEZhY2VzLHRvRmlsZV0sIm1Db252 | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1ttQ29udmV4SHVsbEZhY2VzLHRvRmlsZV0sIm1Db252 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | Y29ud2F5UG9seW5vbWlhbA== | 8 | Y29ud2F5UG9seW5vbWlhbA== |
| 9 | #:len=1873 | 9 | #:len=1873 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJvdmlkZSBhIENvbndheSBwb2x5bm9t | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJvdmlkZSBhIENvbndheSBwb2x5bm9t |
| 11 | aWFsIiwgImxpbmVudW0iID0+IDEwMiwgImZpbGVuYW1lIiA9PiAiQ29ud2F5UG9seW5vbWlhbHMu | 11 | aWFsIiwgImxpbmVudW0iID0+IDEwMiwgImZpbGVuYW1lIiA9PiAiQ29ud2F5UG9seW5vbWlhbHMu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1twcm9kdWN0T2ZQcm9qZWN0aXZlU3BhY2VzLENvZWZm | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1twcm9kdWN0T2ZQcm9qZWN0aXZlU3BhY2VzLENvZWZm |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | TGFiZWxz | 8 | TGFiZWxz |
| 9 | #:len=183 | 9 | #:len=183 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA3LCAidW5kb2N1bWVudGVkIiA9PiB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDA3LCAidW5kb2N1bWVudGVkIiA9PiB0 |
| 11 | cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJMYWJlbHMi | 11 | cnVlLCBzeW1ib2wgRG9jdW1lbnRUYWcgPT4gbmV3IERvY3VtZW50VGFnIGZyb20geyJMYWJlbHMi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·1.1 | 18 | ·--·used·1.12481s·(cpu);·0.757571s·(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·0.82 | 26 | ·--·used·0.825176s·(cpu);·0.686781s·(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·0.17 | 67 | ·--·used·0.172827s·(cpu);·0.126271s·(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·0.0 | 75 | ·--·used·0.00924994s·(cpu);·0.0127465s·(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:·1545107905 | 1 | --·-*-·M2-comint·-*-·hash:·1545107905 |
| 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·0.00 | 4 | ·--·used·0.00399969s·(cpu);·0.0035176s·(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·0.0387384s·(cpu);·0.0375771s·(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·0.02 | 22 | ·--·used·0.0258274s·(cpu);·0.0252749s·(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·0.338828s·(cpu);·0.298263s·(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·0.0421524s·(cpu);·0.0456074s·(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·0.00 | 33 | ·--·used·0.000418389s·(cpu);·0.00242235s·(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·0.3 | 65 | ·--·used·0.305823s·(cpu);·0.30518s·(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·0.0070353s·(cpu);·0.00729468s·(thread);·0s·(gc) |
| 83 | o9·=·true | 83 | o9·=·true |
| 84 | i10·:·time·degreeMap·psi | 84 | i10·:·time·degreeMap·psi |
| 85 | ·--·used·0. | 85 | ·--·used·0.200765s·(cpu);·0.163676s·(thread);·0s·(gc) |
| 86 | o10·=·1 | 86 | o10·=·1 |
| 87 | i11·:·time·projectiveDegrees·psi | 87 | i11·:·time·projectiveDegrees·psi |
| 88 | ·--·used· | 88 | ·--·used·3.96925s·(cpu);·3.67784s·(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·0.000 | 92 | ·--·used·0.000706854s·(cpu);·0.00190851s·(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·0.117052s·(cpu);·0.070352s·(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·0.1 | 8 | ·--·used·0.170217s·(cpu);·0.124707s·(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·0.010 | 11 | ·--·used·0.010587s·(cpu);·0.0124171s·(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·0.0 | 13 | ·--·used·0.0434191s·(cpu);·0.0452526s·(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·0.088 | 42 | ·--·used·0.0880645s·(cpu);·0.046015s·(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·0.1 | 72 | ·--·used·0.191778s·(cpu);·0.151296s·(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·0.378632s·(cpu);·0.33976s·(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·0.3 | 61 | ·--·used·0.319255s·(cpu);·0.246278s·(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·0.0 | 69 | ·--·used·0.0196689s·(cpu);·0.0234299s·(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·0.0 | 78 | ·--·used·0.0899729s·(cpu);·0.0933357s·(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·0.11 | 110 | ·--·used·0.114921s·(cpu);·0.0698991s·(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·0.2 | 128 | ·--·used·0.23249s·(cpu);·0.194658s·(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·0.3 | 156 | ·--·used·0.314221s·(cpu);·0.229513s·(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·0.7 | 165 | ·--·used·0.739914s·(cpu);·0.600007s·(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·0.00163226s·(cpu);·0.000368785s·(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·0.169773s·(cpu);·0.127262s·(thread);·0s·(gc) |
| 31 | o5·=·2 | 31 | o5·=·2 |
| 32 | i6·:·time·rationalMap·psi | 32 | i6·:·time·rationalMap·psi |
| 33 | ·--·used·0.3 | 33 | ·--·used·0.335894s·(cpu);·0.291662s·(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·0.10 | 118 | ·--·used·0.108479s·(cpu);·0.0643053s·(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·2.25649s·(cpu);·1.39659s·(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·0.000149185s·(cpu);·2.3835e-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·3.5 | 143 | ·--·used·3.56932s·(cpu);·2.31037s·(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·2.9 | 173 | ·--·used·2.90677s·(cpu);·1.94741s·(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·0.8 | 49 | ·--·used·0.86198s·(cpu);·0.725435s·(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·0.4 | 110 | ·--·used·0.482746s·(cpu);·0.392192s·(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·1.55227s·(cpu);·1.36223s·(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·2.47494s·(cpu);·2.20227s·(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·0.0 | 14 | ·--·used·0.039396s·(cpu);·0.0387109s·(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·0.493674s·(cpu);·0.409671s·(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·0.00 | 9 | ·--·used·0.00105338s·(cpu);·0.000409015s·(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·0.0 | 40 | ·--·used·0.0181784s·(cpu);·0.0174531s·(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·0.1 | 177 | ·--·used·0.106546s·(cpu);·0.0534625s·(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·0.00 | 38 | ·--·used·0.00299451s·(cpu);·0.00316629s·(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·0.0 | 113 | ·--·used·0.0712451s·(cpu);·0.0699223s·(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·0.11424s·(cpu);·0.0721033s·(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. | 163 | ·--·used·0.171979s·(cpu);·0.124007s·(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·0.0 | 33 | ·--·used·0.0479462s·(cpu);·0.0461476s·(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·0.01 | 45 | ·--·used·0.0162857s·(cpu);·0.0153186s·(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·0.0 | 48 | ·--·used·0.010866s·(cpu);·0.0142216s·(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·1. | 7 | ·--·used·1.57781s·(cpu);·1.49835s·(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·2.25936s·(cpu);·1.83224s·(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·0.0144278s·(cpu);·0.015842s·(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. | 16 | ·--·used·0.275113s·(cpu);·0.23088s·(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·0.003 | 31 | ·--·used·0.00384248s·(cpu);·0.00512669s·(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. | 121 | ·--·used·0.379222s·(cpu);·0.312856s·(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:·-843041710 | 1 | --·-*-·M2-comint·-*-·hash:·-843041710 |
| 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·0.2 | 5 | ·--·used·0.21777s·(cpu);·0.136511s·(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·0.08 | 26 | ·--·used·0.0870562s·(cpu);·0.0877114s·(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·0.01 | 12 | ·--·used·0.0160087s·(cpu);·0.0136984s·(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·0.01 | 35 | ·--·used·0.0110654s·(cpu);·0.0122336s·(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·0.00196016s·(cpu);·3.9329e-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·7.3481e-05s·(cpu);·1.3691e-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·0.0834682s·(cpu);·0.0833077s·(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·0.02 | 22 | ·--·used·0.0239055s·(cpu);·0.0219475s·(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·0.7 | 128 | ·--·used·0.741182s·(cpu);·0.497531s·(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:·-593220679 | 1 | --·-*-·M2-comint·-*-·hash:·-593220679 |
| 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·0.8 | 3 | ·--·used·0.804218s·(cpu);·0.719267s·(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:·-81960144 | 1 | --·-*-·M2-comint·-*-·hash:·-81960144 |
| 2 | i1·:·time·specialCubicTransformation·9 | 2 | i1·:·time·specialCubicTransformation·9 |
| 3 | ·--·used·0.0 | 3 | ·--·used·0.0783795s·(cpu);·0.0770635s·(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·0.01605s·(cpu);·0.0161688s·(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:·-1711938255 | 1 | --·-*-·M2-comint·-*-·hash:·-1711938255 |
| 2 | i1·:·time·specialQuadraticTransformation·4 | 2 | i1·:·time·specialQuadraticTransformation·4 |
| 3 | ·--·used·0.0 | 3 | ·--·used·0.0573645s·(cpu);·0.057115s·(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·0.00798778s·(cpu);·0.00528424s·(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·0.02 | 11 | ·--·used·0.0201272s·(cpu);·0.0189493s·(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·0.002 | 14 | ·--·used·0.00228344s·(cpu);·0.00445355s·(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·0.00145355s·(cpu);·0.00409456s·(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 97, 27 lines modified | Offset 97, 27 lines modified | ||
| 97 | ···············1····0·2·····1·2····0·3·····2····1·3 | 97 | ···············1····0·2·····1·2····0·3·····2····1·3 |
| 98 | o2·:·Ideal·of·GF·78125[x·..x·] | 98 | o2·:·Ideal·of·GF·78125[x·..x·] |
| 99 | ························0···4</code></pre> | 99 | ························0···4</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ChernSchwartzMacPherson·C | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ChernSchwartzMacPherson·C |
| 103 | ·--·used·1.1 | 103 | ·--·used·1.12481s·(cpu);·0.757571s·(thread);·0s·(gc) |
| 104 | ·······4·····3·····2 | 104 | ·······4·····3·····2 |
| 105 | o3·=·3H··+·5H··+·3H | 105 | o3·=·3H··+·5H··+·3H |
| 106 | ·····ZZ[H] | 106 | ·····ZZ[H] |
| 107 | o3·:·----- | 107 | o3·:·----- |
| 108 | ········5 | 108 | ········5 |
| 109 | ·······H</code></pre> | 109 | ·······H</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) | 112 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·ChernSchwartzMacPherson(C,Certify=>true) |
| 113 | ·--·used·0.82 | 113 | ·--·used·0.825176s·(cpu);·0.686781s·(thread);·0s·(gc) |
| 114 | Certify:·output·certified! | 114 | Certify:·output·certified! |
| 115 | ·······4·····3·····2 | 115 | ·······4·····3·····2 |
| 116 | o4·=·3H··+·5H··+·3H | 116 | o4·=·3H··+·5H··+·3H |
| 117 | ·····ZZ[H] | 117 | ·····ZZ[H] |
| 118 | o4·:·----- | 118 | o4·:·----- |
| Offset 155, 27 lines modified | Offset 155, 27 lines modified | ||
| 155 | ················ZZ | 155 | ················ZZ |
| 156 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] | 156 | o8·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] |
| 157 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> | 157 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·ChernClass·G | 160 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·ChernClass·G |
| 161 | ·--·used·0.17 | 161 | ·--·used·0.172827s·(cpu);·0.126271s·(thread);·0s·(gc) |
| 162 | ········9······8······7······6······5······4·····3 | 162 | ········9······8······7······6······5······4·····3 |
| 163 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 163 | o9·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 164 | ·····ZZ[H] | 164 | ·····ZZ[H] |
| 165 | o9·:·----- | 165 | o9·:·----- |
| 166 | ·······10 | 166 | ·······10 |
| 167 | ······H</code></pre> | 167 | ······H</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·ChernClass(G,Certify=>true) | 170 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·ChernClass(G,Certify=>true) |
| 171 | ·--·used·0.0 | 171 | ·--·used·0.00924994s·(cpu);·0.0127465s·(thread);·0s·(gc) |
| 172 | Certify:·output·certified! | 172 | Certify:·output·certified! |
| 173 | ·········9······8······7······6······5······4·····3 | 173 | ·········9······8······7······6······5······4·····3 |
| 174 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H | 174 | o10·=·10H··+·30H··+·60H··+·75H··+·57H··+·25H··+·5H |
| 175 | ······ZZ[H] | 175 | ······ZZ[H] |
| 176 | o10·:·----- | 176 | 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·1.1 | 46 | ·--·used·1.12481s·(cpu);·0.757571s·(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·0.82 | 54 | ·--·used·0.825176s·(cpu);·0.686781s·(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·0.17 | 95 | ·--·used·0.172827s·(cpu);·0.126271s·(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·0.0 | 103 | ·--·used·0.00924994s·(cpu);·0.0127465s·(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 87, 21 lines modified | Offset 87, 21 lines modified | ||
| 87 | ················ZZ | 87 | ················ZZ |
| 88 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] | 88 | o1·:·Ideal·of·------[p···..p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···,·p···] |
| 89 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> | 89 | ··············190181··0,1···0,2···1,2···0,3···1,3···2,3···0,4···1,4···2,4···3,4</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·EulerCharacteristic·I | 92 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·EulerCharacteristic·I |
| 93 | ·--·used·0.1 | 93 | ·--·used·0.170217s·(cpu);·0.124707s·(thread);·0s·(gc) |
| 94 | o2·=·10</code></pre> | 94 | o2·=·10</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·EulerCharacteristic(I,Certify=>true) | 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·EulerCharacteristic(I,Certify=>true) |
| 98 | ·--·used·0.010 | 98 | ·--·used·0.010587s·(cpu);·0.0124171s·(thread);·0s·(gc) |
| 99 | Certify:·output·certified! | 99 | Certify:·output·certified! |
| 100 | o3·=·10</code></pre> | 100 | o3·=·10</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ········</table> | 102 | ········</table> |
| 103 | ······</div> | 103 | ······</div> |
| 104 | ······<div> | 104 | ······<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·0.1 | 38 | ·--·used·0.170217s·(cpu);·0.124707s·(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·0.010 | 41 | ·--·used·0.010587s·(cpu);·0.0124171s·(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 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | o3·=·rational·map·defined·by·forms·of·degree·2 | 83 | o3·=·rational·map·defined·by·forms·of·degree·2 |
| 84 | ·····source·variety:·PP^5 | 84 | ·····source·variety:·PP^5 |
| 85 | ·····target·variety:·PP^5 | 85 | ·····target·variety:·PP^5 |
| 86 | ·····coefficient·ring:·QQ</code></pre> | 86 | ·····coefficient·ring:·QQ</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi!·; | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi!·; |
| 90 | ·--·used·0.0 | 90 | ·--·used·0.0434191s·(cpu);·0.0452526s·(thread);·0s·(gc) |
| 91 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))</code></pre> | 91 | o4·:·RationalMap·(Cremona·transformation·of·PP^5·of·type·(2,2))</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·describe·phi | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·describe·phi |
| 95 | o5·=·rational·map·defined·by·forms·of·degree·2 | 95 | o5·=·rational·map·defined·by·forms·of·degree·2 |
| Offset 116, 15 lines modified | Offset 116, 15 lines modified | ||
| 116 | o8·=·rational·map·defined·by·forms·of·degree·2 | 116 | o8·=·rational·map·defined·by·forms·of·degree·2 |
| 117 | ·····source·variety:·PP^4 | 117 | ·····source·variety:·PP^4 |
| 118 | ·····target·variety:·PP^5 | 118 | ·····target·variety:·PP^5 |
| 119 | ·····coefficient·ring:·QQ</code></pre> | 119 | ·····coefficient·ring:·QQ</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·phi!·; | 122 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·phi!·; |
| 123 | ·--·used·0.088 | 123 | ·--·used·0.0880645s·(cpu);·0.046015s·(thread);·0s·(gc) |
| 124 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)</code></pre> | 124 | o9·:·RationalMap·(quadratic·rational·map·from·PP^4·to·PP^5)</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i10·:·describe·phi | 127 | <td>··············<pre><code·class="language-macaulay2">i10·:·describe·phi |
| 128 | o10·=·rational·map·defined·by·forms·of·degree·2 | 128 | 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·0.0 | 28 | ·--·used·0.0434191s·(cpu);·0.0452526s·(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·0.088 | 54 | ·--·used·0.0880645s·(cpu);·0.046015s·(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 147, 15 lines modified | Offset 147, 15 lines modified | ||
| 147 | ·····----------*v,·x·+·----------*v) | 147 | ·····----------*v,·x·+·----------*v) |
| 148 | ······d*e·-·a*f·········d*e·-·a*f | 148 | ······d*e·-·a*f·········d*e·-·a*f |
| 149 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> | 149 | o5·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi^**·q | 152 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi^**·q |
| 153 | ·--·used·0.1 | 153 | ·--·used·0.191778s·(cpu);·0.151296s·(thread);·0s·(gc) |
| 154 | ················-e········-d········-c········-b········-a | 154 | ················-e········-d········-c········-b········-a |
| 155 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) | 155 | o6·=·ideal·(u·+·--*v,·t·+·--*v,·z·+·--*v,·y·+·--*v,·x·+·--*v) |
| 156 | ·················f·········f·········f·········f·········f | 156 | ·················f·········f·········f·········f·········f |
| 157 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> | 157 | o6·:·Ideal·of·frac(QQ[a..f])[x,·y,·z,·t,·u,·v]</code></pre> |
| 158 | </td>··········</tr> | 158 | </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·0.1 | 89 | ·--·used·0.191778s·(cpu);·0.151296s·(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 132, 52 lines modified | Offset 132, 52 lines modified | ||
| 132 | o3·:·Ideal·of·------------------------------------------------------------------------------------------------------------------------- | 132 | o3·:·Ideal·of·------------------------------------------------------------------------------------------------------------------------- |
| 133 | ···············2·2················2·2········································2·2····················································2·2 | 133 | ···············2·2················2·2········································2·2····················································2·2 |
| 134 | ··············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 | ··············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 |
| 135 | ···············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 | ···············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> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·SegreClass·X | 138 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·SegreClass·X |
| 139 | ·--·used·0. | 139 | ·--·used·0.378632s·(cpu);·0.33976s·(thread);·0s·(gc) |
| 140 | ··········7········6·······5·······4······3 | 140 | ··········7········6·······5·······4······3 |
| 141 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H | 141 | o4·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 142 | ·····ZZ[H] | 142 | ·····ZZ[H] |
| 143 | o4·:·----- | 143 | o4·:·----- |
| 144 | ········8 | 144 | ········8 |
| 145 | ·······H</code></pre> | 145 | ·······H</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·SegreClass·lift(X,P7) | 148 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·SegreClass·lift(X,P7) |
| 149 | ·--·used·0.3 | 149 | ·--·used·0.319255s·(cpu);·0.246278s·(thread);·0s·(gc) |
| 150 | ··········7········6·······5······4······3 | 150 | ··········7········6·······5······4······3 |
| 151 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H | 151 | o5·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 152 | ·····ZZ[H] | 152 | ·····ZZ[H] |
| 153 | o5·:·----- | 153 | o5·:·----- |
| 154 | ········8 | 154 | ········8 |
| 155 | ·······H</code></pre> | 155 | ·······H</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·SegreClass(X,Certify=>true) | 158 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·SegreClass(X,Certify=>true) |
| 159 | ·--·used·0.0 | 159 | ·--·used·0.0196689s·(cpu);·0.0234299s·(thread);·0s·(gc) |
| 160 | Certify:·output·certified! | 160 | Certify:·output·certified! |
| 161 | ··········7········6·······5·······4······3 | 161 | ··········7········6·······5·······4······3 |
| 162 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H | 162 | o6·=·3240H··-·1188H··+·396H··-·114H··+·24H |
| 163 | ·····ZZ[H] | 163 | ·····ZZ[H] |
| 164 | o6·:·----- | 164 | o6·:·----- |
| 165 | ········8 | 165 | ········8 |
| 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">i7·:·time·SegreClass(lift(X,P7),Certify=>true) | 169 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·SegreClass(lift(X,P7),Certify=>true) |
| 170 | ·--·used·0.0 | 170 | ·--·used·0.0899729s·(cpu);·0.0933357s·(thread);·0s·(gc) |
| 171 | Certify:·output·certified! | 171 | Certify:·output·certified! |
| 172 | ··········7········6·······5······4······3 | 172 | ··········7········6·······5······4······3 |
| 173 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H | 173 | o7·=·2816H··-·1056H··+·324H··-·78H··+·12H |
| 174 | ·····ZZ[H] | 174 | ·····ZZ[H] |
| 175 | o7·:·----- | 175 | o7·:·----- |
| Offset 199, 15 lines modified | Offset 199, 15 lines modified | ||
| 199 | o9·=·------[x·..x·] | 199 | o9·=·------[x·..x·] |
| 200 | ·····100003··0···6 | 200 | ·····100003··0···6 |
| 201 | o9·:·PolynomialRing</code></pre> | 201 | o9·:·PolynomialRing</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <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 | <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) |
| 205 | ·--·used·0.11 | 205 | ·--·used·0.114921s·(cpu);·0.0698991s·(thread);·0s·(gc) |
| 206 | ························································ZZ | 206 | ························································ZZ |
| 207 | ······················································------[y·..y·] | 207 | ······················································------[y·..y·] |
| 208 | ······················································100003··0···9················································ZZ··············2······························2 | 208 | ······················································100003··0···9················································ZZ··············2······························2 |
| 209 | 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 | 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·}) |
| 210 | ···········(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 | ···········(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 |
| 211 | ·············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 | 211 | ·············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 217, 15 lines modified | Offset 217, 15 lines modified | ||
| 217 | ·························································100003··0···9···················································ZZ | 217 | ·························································100003··0···9···················································ZZ |
| 218 | o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·] | 218 | o10·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[x·..x·] |
| 219 | ··············(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 | ··············(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 |
| 220 | ················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 | ················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> |
| 221 | </td>··········</tr> | 221 | </td>··········</tr> |
| 222 | ··········<tr> | 222 | ··········<tr> |
| 223 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·SegreClass·phi | 223 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·SegreClass·phi |
| 224 | ·--·used·0.2 | 224 | ·--·used·0.23249s·(cpu);·0.194658s·(thread);·0s·(gc) |
| 225 | ·········9······8······7······6·····5 | 225 | ·········9······8······7······6·····5 |
| 226 | o11·=·23H··-·42H··+·36H··-·22H··+·9H | 226 | o11·=·23H··-·42H··+·36H··-·22H··+·9H |
| 227 | ······ZZ[H] | 227 | ······ZZ[H] |
| 228 | o11·:·----- | 228 | o11·:·----- |
| 229 | ········10 | 229 | ········10 |
| Offset 247, 28 lines modified | Offset 247, 28 lines modified | ||
| 247 | o12·:·Ideal·of·---------------------------------------------------------------------------------------------------- | 247 | o12·:·Ideal·of·---------------------------------------------------------------------------------------------------- |
| 248 | ···············(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 | ···············(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·) |
| 249 | ·················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 | ·················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> |
| 250 | </td>··········</tr> | 250 | </td>··········</tr> |
| 251 | ··········<tr> | 251 | ··········<tr> |
| 252 | <td>··············<pre><code·class="language-macaulay2">i13·:·--·Segre·class·of·B·in·G(1,4) | 252 | <td>··············<pre><code·class="language-macaulay2">i13·:·--·Segre·class·of·B·in·G(1,4) |
| 253 | ······time·SegreClass·B | 253 | ······time·SegreClass·B |
| 254 | ·--·used·0.3 | 254 | ·--·used·0.314221s·(cpu);·0.229513s·(thread);·0s·(gc) |
| 255 | ·········9······8······7······6·····5 | 255 | ·········9······8······7······6·····5 |
| 256 | o13·=·23H··-·42H··+·36H··-·22H··+·9H | 256 | o13·=·23H··-·42H··+·36H··-·22H··+·9H |
| 257 | ······ZZ[H] | 257 | ······ZZ[H] |
| 258 | o13·:·----- | 258 | o13·:·----- |
| 259 | ········10 | 259 | ········10 |
| 260 | ·······H</code></pre> | 260 | ·······H</code></pre> |
| 261 | </td>··········</tr> | 261 | </td>··········</tr> |
| 262 | ··········<tr> | 262 | ··········<tr> |
| 263 | <td>··············<pre><code·class="language-macaulay2">i14·:·--·Segre·class·of·B·in·P^9 | 263 | <td>··············<pre><code·class="language-macaulay2">i14·:·--·Segre·class·of·B·in·P^9 |
| 264 | ······time·SegreClass·lift(B,ambient·ring·B) | 264 | ······time·SegreClass·lift(B,ambient·ring·B) |
| 265 | ·--·used·0.7 | 265 | ·--·used·0.739914s·(cpu);·0.600007s·(thread);·0s·(gc) |
| 266 | ···········9·······8·······7······6·····5 | 266 | ···········9·······8·······7······6·····5 |
| 267 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H | 267 | o14·=·2764H··-·984H··+·294H··-·67H··+·9H |
| 268 | ······ZZ[H] | 268 | ······ZZ[H] |
| 269 | o14·:·----- | 269 | o14·:·----- |
| 270 | ········10 | 270 | ········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·0.378632s·(cpu);·0.33976s·(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·0.3 | 97 | ·--·used·0.319255s·(cpu);·0.246278s·(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·0.0 | 105 | ·--·used·0.0196689s·(cpu);·0.0234299s·(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·0.0 | 114 | ·--·used·0.0899729s·(cpu);·0.0933357s·(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·0.11 | 148 | ·--·used·0.114921s·(cpu);·0.0698991s·(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·0.2 | 177 | ·--·used·0.23249s·(cpu);·0.194658s·(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·0.3 | 206 | ·--·used·0.314221s·(cpu);·0.229513s·(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·0.7 | 215 | ·--·used·0.739914s·(cpu);·0.600007s·(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 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | o3·=·QQ[u·..u·] | 98 | o3·=·QQ[u·..u·] |
| 99 | ·········0···5 | 99 | ·········0···5 |
| 100 | o3·:·PolynomialRing</code></pre> | 100 | o3·:·PolynomialRing</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·psi·=·abstractRationalMap(P4,P5,f) | 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·psi·=·abstractRationalMap(P4,P5,f) |
| 104 | ·--·used·0.00 | 104 | ·--·used·0.00163226s·(cpu);·0.000368785s·(thread);·0s·(gc) |
| 105 | o4·=·--·rational·map·-- | 105 | o4·=·--·rational·map·-- |
| 106 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 106 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 107 | ······················0···1···2···3···4 | 107 | ······················0···1···2···3···4 |
| 108 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 108 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 109 | ······················0···1···2···3···4···5 | 109 | ······················0···1···2···3···4···5 |
| 110 | ·····defining·forms:·given·by·a·function | 110 | ·····defining·forms:·given·by·a·function |
| Offset 114, 21 lines modified | Offset 114, 21 lines modified | ||
| 114 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)</code></pre> | 114 | o4·:·AbstractRationalMap·(rational·map·from·PP^4·to·PP^5)</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ········</table> | 116 | ········</table> |
| 117 | ········<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 | ········<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> |
| 118 | ········<table·class="examples"> | 118 | ········<table·class="examples"> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,3) | 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,3) |
| 121 | ·--·used·0.1 | 121 | ·--·used·0.169773s·(cpu);·0.127262s·(thread);·0s·(gc) |
| 122 | o5·=·2</code></pre> | 122 | o5·=·2</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·rationalMap·psi | 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·rationalMap·psi |
| 126 | ·--·used·0.3 | 126 | ·--·used·0.335894s·(cpu);·0.291662s·(thread);·0s·(gc) |
| 127 | o6·=·--·rational·map·-- | 127 | o6·=·--·rational·map·-- |
| 128 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) | 128 | ·····source:·Proj(QQ[t·,·t·,·t·,·t·,·t·]) |
| 129 | ······················0···1···2···3···4 | 129 | ······················0···1···2···3···4 |
| 130 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) | 130 | ·····target:·Proj(QQ[u·,·u·,·u·,·u·,·u·,·u·]) |
| 131 | ······················0···1···2···3···4···5 | 131 | ······················0···1···2···3···4···5 |
| 132 | ·····defining·forms:·{ | 132 | ·····defining·forms:·{ |
| Offset 212, 15 lines modified | Offset 212, 15 lines modified | ||
| 212 | ·················ZZ | 212 | ·················ZZ |
| 213 | o13·:·Ideal·of·-----[x·..x·] | 213 | o13·:·Ideal·of·-----[x·..x·] |
| 214 | ···············65521··0···3</code></pre> | 214 | ···············65521··0···3</code></pre> |
| 215 | </td>··········</tr> | 215 | </td>··········</tr> |
| 216 | ··········<tr> | 216 | ··········<tr> |
| 217 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·T·=·abstractRationalMap(I,"OADP") | 217 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·T·=·abstractRationalMap(I,"OADP") |
| 218 | ·--·used·0.10 | 218 | ·--·used·0.108479s·(cpu);·0.0643053s·(thread);·0s·(gc) |
| 219 | o14·=·--·rational·map·-- | 219 | o14·=·--·rational·map·-- |
| 220 | ·····················ZZ | 220 | ·····················ZZ |
| 221 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 221 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 222 | ···················65521··0···1···2···3 | 222 | ···················65521··0···1···2···3 |
| 223 | ·····················ZZ | 223 | ·····················ZZ |
| 224 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 224 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| Offset 230, 39 lines modified | Offset 230, 39 lines modified | ||
| 230 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> | 230 | o14·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> |
| 231 | </td>··········</tr> | 231 | </td>··········</tr> |
| 232 | ········</table> | 232 | ········</table> |
| 233 | ········<p>The·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">T</span>·can·be·obtained·by·the·following·command:</p> | 233 | ········<p>The·degree·of·the·forms·defining·the·abstract·map·<span·class="tt">T</span>·can·be·obtained·by·the·following·command:</p> |
| 234 | ········<table·class="examples"> | 234 | ········<table·class="examples"> |
| 235 | ··········<tr> | 235 | ··········<tr> |
| 236 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·projectiveDegrees(T,2) | 236 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·projectiveDegrees(T,2) |
| 237 | ·--·used·2. | 237 | ·--·used·2.25649s·(cpu);·1.39659s·(thread);·0s·(gc) |
| 238 | o15·=·3</code></pre> | 238 | o15·=·3</code></pre> |
| 239 | </td>··········</tr> | 239 | </td>··········</tr> |
| 240 | ········</table> | 240 | ········</table> |
| 241 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·is·defined·by·linear·forms:</p> | 241 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·is·defined·by·linear·forms:</p> |
| 242 | ········<table·class="examples"> | 242 | ········<table·class="examples"> |
| 243 | ··········<tr> | 243 | ··········<tr> |
| 244 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·T2·=·T·*·T | 244 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·T2·=·T·*·T |
| 245 | ·--·used·0.0001 | 245 | ·--·used·0.000149185s·(cpu);·2.3835e-05s·(thread);·0s·(gc) |
| 246 | o16·=·--·rational·map·-- | 246 | o16·=·--·rational·map·-- |
| 247 | ·····················ZZ | 247 | ·····················ZZ |
| 248 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 248 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 249 | ···················65521··0···1···2···3 | 249 | ···················65521··0···1···2···3 |
| 250 | ·····················ZZ | 250 | ·····················ZZ |
| 251 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 251 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) |
| 252 | ···················65521··0···1···2···3 | 252 | ···················65521··0···1···2···3 |
| 253 | ······defining·forms:·given·by·a·function | 253 | ······defining·forms:·given·by·a·function |
| 254 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> | 254 | o16·:·AbstractRationalMap·(rational·map·from·PP^3·to·PP^3)</code></pre> |
| 255 | </td>··········</tr> | 255 | </td>··········</tr> |
| 256 | ··········<tr> | 256 | ··········<tr> |
| 257 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·projectiveDegrees(T2,2) | 257 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·projectiveDegrees(T2,2) |
| 258 | ·--·used·3.5 | 258 | ·--·used·3.56932s·(cpu);·2.31037s·(thread);·0s·(gc) |
| 259 | o17·=·1</code></pre> | 259 | o17·=·1</code></pre> |
| 260 | </td>··········</tr> | 260 | </td>··········</tr> |
| 261 | ········</table> | 261 | ········</table> |
| 262 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·leaves·a·random·point·fixed:</p> | 262 | ········<p>We·verify·that·the·composition·of·<span·class="tt">T</span>·with·itself·leaves·a·random·point·fixed:</p> |
| 263 | ········<table·class="examples"> | 263 | ········<table·class="examples"> |
| 264 | ··········<tr> | 264 | ··········<tr> |
| Offset 287, 15 lines modified | Offset 287, 15 lines modified | ||
| 287 | o20·:·List</code></pre> | 287 | o20·:·List</code></pre> |
| 288 | </td>··········</tr> | 288 | </td>··········</tr> |
| 289 | ········</table> | 289 | ········</table> |
| 290 | ········<p>We·now·compute·the·concrete·rational·map·corresponding·to·<span·class="tt">T</span>:</p> | 290 | ········<p>We·now·compute·the·concrete·rational·map·corresponding·to·<span·class="tt">T</span>:</p> |
| 291 | ········<table·class="examples"> | 291 | ········<table·class="examples"> |
| 292 | ··········<tr> | 292 | ··········<tr> |
| 293 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f·=·rationalMap·T | 293 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f·=·rationalMap·T |
| 294 | ·--·used·2.9 | 294 | ·--·used·2.90677s·(cpu);·1.94741s·(thread);·0s·(gc) |
| 295 | o21·=·--·rational·map·-- | 295 | o21·=·--·rational·map·-- |
| 296 | ·····················ZZ | 296 | ·····················ZZ |
| 297 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) | 297 | ······source:·Proj(-----[x·,·x·,·x·,·x·]) |
| 298 | ···················65521··0···1···2···3 | 298 | ···················65521··0···1···2···3 |
| 299 | ·····················ZZ | 299 | ·····················ZZ |
| 300 | ······target:·Proj(-----[x·,·x·,·x·,·x·]) | 300 | ······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·0.00163226s·(cpu);·0.000368785s·(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·0.169773s·(cpu);·0.127262s·(thread);·0s·(gc) |
| 53 | o5·=·2 | 53 | o5·=·2 |
| 54 | i6·:·time·rationalMap·psi | 54 | i6·:·time·rationalMap·psi |
| 55 | ·--·used·0.3 | 55 | ·--·used·0.335894s·(cpu);·0.291662s·(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·0.10 | 146 | ·--·used·0.108479s·(cpu);·0.0643053s·(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·2.25649s·(cpu);·1.39659s·(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·0.000149185s·(cpu);·2.3835e-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·3.5 | 174 | ·--·used·3.56932s·(cpu);·2.31037s·(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·2.9 | 199 | ·--·used·2.90677s·(cpu);·1.94741s·(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 130, 15 lines modified | Offset 130, 15 lines modified | ||
| 130 | ·······················1·2····0·4 | 130 | ·······················1·2····0·4 |
| 131 | ·····················} | 131 | ·····················} |
| 132 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)</code></pre> | 132 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^9·to·PP^8)</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·psi·=·approximateInverseMap·phi | 135 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·psi·=·approximateInverseMap·phi |
| 136 | ·--·used·0.8 | 136 | ·--·used·0.86198s·(cpu);·0.725435s·(thread);·0s·(gc) |
| 137 | --·approximateInverseMap:·step·1·of·10 | 137 | --·approximateInverseMap:·step·1·of·10 |
| 138 | --·approximateInverseMap:·step·2·of·10 | 138 | --·approximateInverseMap:·step·2·of·10 |
| 139 | --·approximateInverseMap:·step·3·of·10 | 139 | --·approximateInverseMap:·step·3·of·10 |
| 140 | --·approximateInverseMap:·step·4·of·10 | 140 | --·approximateInverseMap:·step·4·of·10 |
| 141 | --·approximateInverseMap:·step·5·of·10 | 141 | --·approximateInverseMap:·step·5·of·10 |
| 142 | --·approximateInverseMap:·step·6·of·10 | 142 | --·approximateInverseMap:·step·6·of·10 |
| 143 | --·approximateInverseMap:·step·7·of·10 | 143 | --·approximateInverseMap:·step·7·of·10 |
| Offset 194, 15 lines modified | Offset 194, 15 lines modified | ||
| 194 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> | 194 | o3·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)</code></pre> | 197 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(phi·*·psi·==·1·and·psi·*·phi·==·1)</code></pre> |
| 198 | </td>··········</tr> | 198 | </td>··········</tr> |
| 199 | ··········<tr> | 199 | ··········<tr> |
| 200 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); | 200 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi'·=·approximateInverseMap(phi,CodimBsInv=>5); |
| 201 | ·--·used·0.4 | 201 | ·--·used·0.482746s·(cpu);·0.392192s·(thread);·0s·(gc) |
| 202 | --·approximateInverseMap:·step·1·of·3 | 202 | --·approximateInverseMap:·step·1·of·3 |
| 203 | --·approximateInverseMap:·step·2·of·3 | 203 | --·approximateInverseMap:·step·2·of·3 |
| 204 | --·approximateInverseMap:·step·3·of·3 | 204 | --·approximateInverseMap:·step·3·of·3 |
| 205 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> | 205 | o5·:·RationalMap·(quadratic·rational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> |
| 206 | </td>··········</tr> | 206 | </td>··········</tr> |
| 207 | ··········<tr> | 207 | ··········<tr> |
| Offset 283, 15 lines modified | Offset 283, 15 lines modified | ||
| 283 | ·····················} | 283 | ·····················} |
| 284 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)</code></pre> | 284 | o7·:·RationalMap·(quadratic·rational·map·from·PP^8·to·8-dimensional·subvariety·of·PP^11)</code></pre> |
| 285 | </td>··········</tr> | 285 | </td>··········</tr> |
| 286 | ··········<tr> | 286 | ··········<tr> |
| 287 | <td>··············<pre><code·class="language-macaulay2">i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time· | 287 | <td>··············<pre><code·class="language-macaulay2">i8·:·--·without·the·option·'CodimBsInv=>4',·it·takes·about·triple·time· |
| 288 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) | 288 | ·····time·psi=approximateInverseMap(phi,CodimBsInv=>4) |
| 289 | ·--·used·1. | 289 | ·--·used·1.55227s·(cpu);·1.36223s·(thread);·0s·(gc) |
| 290 | --·approximateInverseMap:·step·1·of·3 | 290 | --·approximateInverseMap:·step·1·of·3 |
| 291 | --·approximateInverseMap:·step·2·of·3 | 291 | --·approximateInverseMap:·step·2·of·3 |
| 292 | --·approximateInverseMap:·step·3·of·3 | 292 | --·approximateInverseMap:·step·3·of·3 |
| 293 | o8·=·--·rational·map·-- | 293 | o8·=·--·rational·map·-- |
| 294 | ································ZZ | 294 | ································ZZ |
| 295 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by | 295 | ·····source:·subvariety·of·Proj(--[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x··,·x··])·defined·by |
| Offset 350, 15 lines modified | Offset 350, 15 lines modified | ||
| 350 | ·····phi·*·psi·==·1 | 350 | ·····phi·*·psi·==·1 |
| 351 | o9·=·false</code></pre> | 351 | o9·=·false</code></pre> |
| 352 | </td>··········</tr> | 352 | </td>··········</tr> |
| 353 | ··········<tr> | 353 | ··········<tr> |
| 354 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify | 354 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·in·this·case·we·can·remedy·enabling·the·option·Certify |
| 355 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) | 355 | ······time·psi·=·approximateInverseMap(phi,CodimBsInv=>4,Certify=>true) |
| 356 | ·--·used·2. | 356 | ·--·used·2.47494s·(cpu);·2.20227s·(thread);·0s·(gc) |
| 357 | --·approximateInverseMap:·step·1·of·3 | 357 | --·approximateInverseMap:·step·1·of·3 |
| 358 | --·approximateInverseMap:·step·2·of·3 | 358 | --·approximateInverseMap:·step·2·of·3 |
| 359 | --·approximateInverseMap:·step·3·of·3 | 359 | --·approximateInverseMap:·step·3·of·3 |
| 360 | Certify:·output·certified! | 360 | Certify:·output·certified! |
| 361 | o10·=·--·rational·map·-- | 361 | o10·=·--·rational·map·-- |
| 362 | ·································ZZ | 362 | ·································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·0.8 | 131 | ·--·used·0.86198s·(cpu);·0.725435s·(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·0.4 | 256 | ·--·used·0.482746s·(cpu);·0.392192s·(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·1.55227s·(cpu);·1.36223s·(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·2.47494s·(cpu);·2.20227s·(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 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | 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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·}) | 92 | 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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| 93 | 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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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| 94 | o4·:·RingMap·ringP8·<--·ringP14</code></pre> | 94 | o4·:·RingMap·ringP8·<--·ringP14</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degreeMap·phi | 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degreeMap·phi |
| 98 | ·--·used·0.0 | 98 | ·--·used·0.039396s·(cpu);·0.0387109s·(thread);·0s·(gc) |
| 99 | o5·=·1</code></pre> | 99 | o5·=·1</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <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 | <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· |
| 103 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14) | 103 | ·····--·of·dimension·5·(so·that·the·composition·phi':P^8--->P^8·must·have·degree·equal·to·deg(G(1,5))=14) |
| 104 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) | 104 | ·····phi'=phi*map(ringP14,ringP8,for·i·to·8·list·random(1,ringP14)) |
| Offset 109, 15 lines modified | Offset 109, 15 lines modified | ||
| 109 | 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·}) | 109 | 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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|
| 111 | o6·:·RingMap·ringP8·<--·ringP8</code></pre> | 111 | o6·:·RingMap·ringP8·<--·ringP8</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·degreeMap·phi' | 114 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·degreeMap·phi' |
| 115 | ·--·used·0. | 115 | ·--·used·0.493674s·(cpu);·0.409671s·(thread);·0s·(gc) |
| 116 | o7·=·14</code></pre> | 116 | o7·=·14</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ········</table> | 118 | ········</table> |
| 119 | ······</div> | 119 | ······</div> |
| 120 | ······<div> | 120 | ······<div> |
| 121 | ········<h2>See·also</h2> | 121 | ········<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·0.0 | 273 | ·--·used·0.039396s·(cpu);·0.0387109s·(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·0.493674s·(cpu);·0.409671s·(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 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap(X,Dominant=>2); | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap(X,Dominant=>2); |
| 82 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> | 82 | o3·:·RationalMap·(cubic·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·forceImage(Phi,ideal·0_(target·Phi)) |
| 86 | ·--·used·0.00 | 86 | ·--·used·0.00105338s·(cpu);·0.000409015s·(thread);·0s·(gc)</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi; | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi; |
| 90 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> | 90 | o5·:·RationalMap·(cubic·dominant·rational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ········</table> | 92 | ········</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·0.00 | 25 | ·--·used·0.00105338s·(cpu);·0.000409015s·(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 114, 15 lines modified | Offset 114, 15 lines modified | ||
| 114 | ·························3····2·4 | 114 | ·························3····2·4 |
| 115 | ·····················} | 115 | ·····················} |
| 116 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 116 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(p1,p2)·=·graph·phi; | 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(p1,p2)·=·graph·phi; |
| 120 | ·--·used·0.0 | 120 | ·--·used·0.0181784s·(cpu);·0.0174531s·(thread);·0s·(gc)</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·p1 | 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·p1 |
| 124 | o4·=·--·rational·map·-- | 124 | o4·=·--·rational·map·-- |
| 125 | ··································ZZ·································ZZ | 125 | ··································ZZ·································ZZ |
| 126 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by | 126 | ·····source:·subvariety·of·Proj(------[x·,·x·,·x·,·x·,·x·])·x·Proj(------[y·,·y·,·y·,·y·,·y·,·y·])·defined·by |
| Offset 261, 15 lines modified | Offset 261, 15 lines modified | ||
| 261 | o8·:·List</code></pre> | 261 | o8·:·List</code></pre> |
| 262 | </td>··········</tr> | 262 | </td>··········</tr> |
| 263 | ········</table> | 263 | ········</table> |
| 264 | ········<p>When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method·returns·all·the·projections.</p> | 264 | ········<p>When·the·source·of·the·rational·map·is·a·multi-projective·variety,·the·method·returns·all·the·projections.</p> |
| 265 | ········<table·class="examples"> | 265 | ········<table·class="examples"> |
| 266 | ··········<tr> | 266 | ··········<tr> |
| 267 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·g·=·graph·p2; | 267 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·g·=·graph·p2; |
| 268 | ·--·used·0.1 | 268 | ·--·used·0.106546s·(cpu);·0.0534625s·(thread);·0s·(gc)</code></pre> |
| 269 | </td>··········</tr> | 269 | </td>··········</tr> |
| 270 | ··········<tr> | 270 | ··········<tr> |
| 271 | <td>··············<pre><code·class="language-macaulay2">i10·:·g_0; | 271 | <td>··············<pre><code·class="language-macaulay2">i10·:·g_0; |
| 272 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)</code></pre> | 272 | o10·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·x·PP^5·to·PP^4)</code></pre> |
| 273 | </td>··········</tr> | 273 | </td>··········</tr> |
| 274 | ··········<tr> | 274 | ··········<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·0.0 | 57 | ·--·used·0.0181784s·(cpu);·0.0174531s·(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·0.1 | 198 | ·--·used·0.106546s·(cpu);·0.0534625s·(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 108, 15 lines modified | Offset 108, 15 lines modified | ||
| 108 | ·······················1····0·3 | 108 | ·······················1····0·3 |
| 109 | ·····················} | 109 | ·····················} |
| 110 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> | 110 | o2·:·RationalMap·(quadratic·rational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ideal·phi | 113 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·ideal·phi |
| 114 | ·--·used·0.00 | 114 | ·--·used·0.00299451s·(cpu);·0.00316629s·(thread);·0s·(gc) |
| 115 | ·············2·····································2······················ | 115 | ·············2·····································2······················ |
| 116 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ | 116 | o3·=·ideal·(x··-·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x··+·x·x·,·x·x··-·x·x··+ |
| 117 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3·· | 117 | ·············4····3·5···2·4····3·4····1·5···2·3····3····1·4···1·2····1·3·· |
| 118 | ·····------------------------------------------------------------------------ | 118 | ·····------------------------------------------------------------------------ |
| 119 | ············2 | 119 | ············2 |
| 120 | ·····x·x·,·x··-·x·x·) | 120 | ·····x·x·,·x··-·x·x·) |
| Offset 186, 15 lines modified | Offset 186, 15 lines modified | ||
| 186 | ·······················4 | 186 | ·······················4 |
| 187 | ·····················} | 187 | ·····················} |
| 188 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)</code></pre> | 188 | o5·:·MultihomogeneousRationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^5·x·PP^4·to·PP^4)</code></pre> |
| 189 | </td>··········</tr> | 189 | </td>··········</tr> |
| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·phi' | 191 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·phi' |
| 192 | ·--·used·0.0 | 192 | ·--·used·0.0712451s·(cpu);·0.0699223s·(thread);·0s·(gc) |
| 193 | o6·=·ideal·1 | 193 | o6·=·ideal·1 |
| 194 | ············································································································QQ[x·..x·,·y·..y·] | 194 | ············································································································QQ[x·..x·,·y·..y·] |
| 195 | ················································································································0···5···0···4 | 195 | ················································································································0···5···0···4 |
| 196 | o6·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 196 | o6·:·Ideal·of·-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 197 | ·····································································································································································································2 | 197 | ·····································································································································································································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·0.00 | 53 | ·--·used·0.00299451s·(cpu);·0.00316629s·(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·0.0 | 128 | ·--·used·0.0712451s·(cpu);·0.0699223s·(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 155, 15 lines modified | Offset 155, 15 lines modified | ||
| 155 | ·······················2·4····1·5····0·6 | 155 | ·······················2·4····1·5····0·6 |
| 156 | ·····················} | 156 | ·····················} |
| 157 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)</code></pre> | 157 | o1·:·RationalMap·(quadratic·Cremona·transformation·of·PP^20)</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·psi·=·inverseMap·phi | 160 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·psi·=·inverseMap·phi |
| 161 | ·--·used·0.1 | 161 | ·--·used·0.11424s·(cpu);·0.0721033s·(thread);·0s·(gc) |
| 162 | o2·=·--·rational·map·-- | 162 | o2·=·--·rational·map·-- |
| 163 | ·····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 | ·····source:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 164 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 | 164 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 |
| 165 | ·····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 | ·····target:·Proj(QQ[w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w·,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··,·w··]) |
| 166 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 | 166 | ······················0···1···2···3···4···5···6···7···8···9···10···11···12···13···14···15···16···17···18···19···20 |
| 167 | ·····defining·forms:·{ | 167 | ·····defining·forms:·{ |
| Offset 247, 15 lines modified | Offset 247, 15 lines modified | ||
| 247 | ··············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 | ··············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 |
| 248 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 248 | o4·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 249 | ·················0···26··········0···26</code></pre> | 249 | ·················0···26··········0···26</code></pre> |
| 250 | </td>··········</tr> | 250 | </td>··········</tr> |
| 251 | ··········<tr> | 251 | ··········<tr> |
| 252 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi·=·inverseMap·phi | 252 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·psi·=·inverseMap·phi |
| 253 | ·--·used·0. | 253 | ·--·used·0.171979s·(cpu);·0.124007s·(thread);·0s·(gc) |
| 254 | 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 | 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··}) |
| 255 | ··············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 | ··············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 |
| 256 | o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] | 256 | o5·:·RingMap·QQ[w·..w··]·<--·QQ[w·..w··] |
| 257 | ·················0···26··········0···26</code></pre> | 257 | ·················0···26··········0···26</code></pre> |
| 258 | </td>··········</tr> | 258 | </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·0.11424s·(cpu);·0.0721033s·(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. | 223 | ·--·used·0.171979s·(cpu);·0.124007s·(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 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | ·························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 | ·························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 |
| 104 | ·····················} | 104 | ·····················} |
| 105 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)</code></pre> | 105 | o2·:·RationalMap·(rational·map·from·PP^4·to·PP^4)</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·phi | 108 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·phi |
| 109 | ·--·used·0.0 | 109 | ·--·used·0.0479462s·(cpu);·0.0461476s·(thread);·0s·(gc) |
| 110 | o3·=·--·rational·map·-- | 110 | o3·=·--·rational·map·-- |
| 111 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 111 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 112 | ······················0···1···2···3···4 | 112 | ······················0···1···2···3···4 |
| 113 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) | 113 | ·····target:·Proj(QQ[x·,·x·,·x·,·x·,·x·]) |
| 114 | ······················0···1···2···3···4 | 114 | ······················0···1···2···3···4 |
| 115 | ·····defining·forms:·{ | 115 | ·····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·0.0 | 288 | ·--·used·0.0479462s·(cpu);·0.0461476s·(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 123, 21 lines modified | Offset 123, 21 lines modified | ||
| 123 | ·························3····2·4 | 123 | ·························3····2·4 |
| 124 | ·····················} | 124 | ·····················} |
| 125 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 125 | o2·:·RationalMap·(quadratic·dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isBirational·phi | 128 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isBirational·phi |
| 129 | ·--·used·0.01 | 129 | ·--·used·0.0162857s·(cpu);·0.0153186s·(thread);·0s·(gc) |
| 130 | o3·=·true</code></pre> | 130 | o3·=·true</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isBirational(phi,Certify=>true) | 133 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isBirational(phi,Certify=>true) |
| 134 | ·--·used·0.0 | 134 | ·--·used·0.010866s·(cpu);·0.0142216s·(thread);·0s·(gc) |
| 135 | Certify:·output·certified! | 135 | Certify:·output·certified! |
| 136 | o4·=·true</code></pre> | 136 | o4·=·true</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| 139 | ······</div> | 139 | ······</div> |
| 140 | ······<div> | 140 | ······<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·0.01 | 65 | ·--·used·0.0162857s·(cpu);·0.0153186s·(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·0.0 | 68 | ·--·used·0.010866s·(cpu);·0.0142216s·(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 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <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 | <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}}; |
| 86 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)</code></pre> | 86 | o2·:·RationalMap·(rational·map·from·PP^8·to·PP^8)</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isDominant(phi,Certify=>true) | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isDominant(phi,Certify=>true) |
| 90 | ·--·used·1. | 90 | ·--·used·1.57781s·(cpu);·1.49835s·(thread);·0s·(gc) |
| 91 | Certify:·output·certified! | 91 | Certify:·output·certified! |
| 92 | o3·=·true</code></pre> | 92 | o3·=·true</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·P7·=·ZZ/101[x_0..x_7];</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·P7·=·ZZ/101[x_0..x_7];</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·rationalMap(C,3,2); | 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·rationalMap(C,3,2); |
| 107 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)</code></pre> | 107 | o6·:·RationalMap·(cubic·rational·map·from·PP^7·to·PP^7)</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDominant(phi,Certify=>true) | 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDominant(phi,Certify=>true) |
| 111 | ·--·used·2. | 111 | ·--·used·2.25936s·(cpu);·1.83224s·(thread);·0s·(gc) |
| 112 | Certify:·output·certified! | 112 | Certify:·output·certified! |
| 113 | o7·=·false</code></pre> | 113 | o7·=·false</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ········</table> | 115 | ········</table> |
| 116 | ······</div> | 116 | ······</div> |
| 117 | ······<div> | 117 | ······<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·1. | 26 | ·--·used·1.57781s·(cpu);·1.49835s·(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·2.25936s·(cpu);·1.83224s·(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 88, 24 lines modified | Offset 88, 24 lines modified | ||
| 88 | ··············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 | ··············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 |
| 89 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] | 89 | o1·:·RingMap·QQ[x·..x·]·<--·QQ[y·..y··] |
| 90 | ·················0···8··········0···11</code></pre> | 90 | ·················0···8··········0···11</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·kernel(phi,1) | 93 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·kernel(phi,1) |
| 94 | ·--·used·0.01 | 94 | ·--·used·0.0144278s·(cpu);·0.015842s·(thread);·0s·(gc) |
| 95 | o2·=·ideal·() | 95 | o2·=·ideal·() |
| 96 | o2·:·Ideal·of·QQ[y·..y··] | 96 | o2·:·Ideal·of·QQ[y·..y··] |
| 97 | ··················0···11</code></pre> | 97 | ··················0···11</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·kernel(phi,2) | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·kernel(phi,2) |
| 101 | ·--·used·0. | 101 | ·--·used·0.275113s·(cpu);·0.23088s·(thread);·0s·(gc) |
| 102 | ···························2················································ | 102 | ···························2················································ |
| 103 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- | 103 | o3·=·ideal·(y·y··+·y·y··+·y··+·5y·y··+·y·y··+·5y·y··-·y·y··-·4y·y··-·5y·y··- |
| 104 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6·· | 104 | ·············2·4····3·4····4·····2·5····3·5·····4·5····1·6·····2·6·····5·6·· |
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ··········································································· | 106 | ··········································································· |
| 107 | ·····4y·y··-·2y·y··-·y·y··+·4y·y··-·5y·y··-·4y·y··+·3y·y··-·4y·y··-·y·y···- | 107 | ·····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·0.0144278s·(cpu);·0.015842s·(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. | 79 | ·--·used·0.275113s·(cpu);·0.23088s·(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 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | ·················ZZ | 102 | ·················ZZ |
| 103 | o2·:·Ideal·of·--------[x·..x·] | 103 | o2·:·Ideal·of·--------[x·..x·] |
| 104 | ··············10000019··0···9</code></pre> | 104 | ··············10000019··0···9</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·parametrize·L | 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·parametrize·L |
| 108 | ·--·used·0.003 | 108 | ·--·used·0.00384248s·(cpu);·0.00512669s·(thread);·0s·(gc) |
| 109 | o3·=·--·rational·map·-- | 109 | o3·=·--·rational·map·-- |
| 110 | ·····················ZZ | 110 | ·····················ZZ |
| 111 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) | 111 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·]) |
| 112 | ··················10000019··0···1···2···3···4···5 | 112 | ··················10000019··0···1···2···3···4···5 |
| 113 | ·····················ZZ | 113 | ·····················ZZ |
| 114 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 114 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 194, 15 lines modified | Offset 194, 15 lines modified | ||
| 194 | ·················ZZ | 194 | ·················ZZ |
| 195 | o4·:·Ideal·of·--------[x·..x·] | 195 | o4·:·Ideal·of·--------[x·..x·] |
| 196 | ··············10000019··0···9</code></pre> | 196 | ··············10000019··0···9</code></pre> |
| 197 | </td>··········</tr> | 197 | </td>··········</tr> |
| 198 | ··········<tr> | 198 | ··········<tr> |
| 199 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·parametrize·Q | 199 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·parametrize·Q |
| 200 | ·--·used·0. | 200 | ·--·used·0.379222s·(cpu);·0.312856s·(thread);·0s·(gc) |
| 201 | o5·=·--·rational·map·-- | 201 | o5·=·--·rational·map·-- |
| 202 | ·····················ZZ | 202 | ·····················ZZ |
| 203 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 203 | ·····source:·Proj(--------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 204 | ··················10000019··0···1···2···3···4···5···6 | 204 | ··················10000019··0···1···2···3···4···5···6 |
| 205 | ·····················ZZ | 205 | ·····················ZZ |
| 206 | ·····target:·Proj(--------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 206 | ·····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·0.003 | 47 | ·--·used·0.00384248s·(cpu);·0.00512669s·(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. | 143 | ·--·used·0.379222s·(cpu);·0.312856s·(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 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·inverseMap·specialQuadraticTransformation(9,ZZ/33331); |
| 79 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)</code></pre> | 79 | o1·:·RationalMap·(cubic·rational·map·from·8-dimensional·subvariety·of·PP^11·to·PP^8)</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·p·=·point·source·f | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·p·=·point·source·f |
| 83 | ·--·used·0.2 | 83 | ·--·used·0.21777s·(cpu);·0.136511s·(thread);·0s·(gc) |
| 84 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ | 84 | o2·=·ideal·(y···-·9235y··,·y··+·11075y··,·y··-·5847y··,·y··+·7396y··,·y··+ |
| 85 | ·············10········11···9·········11···8········11···7········11···6·· | 85 | ·············10········11···9·········11···8········11···7········11···6·· |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| 87 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- | 87 | ·····13530y··,·y··+·4359y··,·y··-·2924y··,·y··+·13040y··,·y··+·6904y··,·y··- |
| 88 | ···········11···5········11···4········11···3·········11···2········11···1·· | 88 | ···········11···5········11···4········11···3·········11···2········11···1·· |
| 89 | ·····------------------------------------------------------------------------ | 89 | ·····------------------------------------------------------------------------ |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | ···························································33331··0···11 | 97 | ···························································33331··0···11 |
| 98 | o2·:·Ideal·of·------------------------------------------------------------------------------------------------------- | 98 | o2·:·Ideal·of·------------------------------------------------------------------------------------------------------- |
| 99 | ··············(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 | ··············(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·) |
| 100 | ················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 | ················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> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·==·f^*·f·p | 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·==·f^*·f·p |
| 104 | ·--·used·0.08 | 104 | ·--·used·0.0870562s·(cpu);·0.0877114s·(thread);·0s·(gc) |
| 105 | o3·=·true</code></pre> | 105 | o3·=·true</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ········</table> | 107 | ········</table> |
| 108 | ······</div> | 108 | ······</div> |
| 109 | ······<div> | 109 | ······<div> |
| 110 | ········<h2>See·also</h2> | 110 | ········<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·0.2 | 26 | ·--·used·0.21777s·(cpu);·0.136511s·(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·0.08 | 48 | ·--·used·0.0870562s·(cpu);·0.0877114s·(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 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ·····················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 | ·····················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 |
| 92 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] | 92 | o2·:·RingMap·GF·109561[t·..t·]·<--·GF·109561[x·..x·] |
| 93 | ························0···4·················0···5</code></pre> | 93 | ························0···4·················0···5</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·projectiveDegrees(phi,Certify=>true) | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·projectiveDegrees(phi,Certify=>true) |
| 97 | ·--·used·0.01 | 97 | ·--·used·0.0160087s·(cpu);·0.0136984s·(thread);·0s·(gc) |
| 98 | Certify:·output·certified! | 98 | Certify:·output·certified! |
| 99 | o3·=·{1,·2,·4,·4,·2} | 99 | o3·=·{1,·2,·4,·4,·2} |
| 100 | o3·:·List</code></pre> | 100 | o3·:·List</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| Offset 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | ·························0···5 | 115 | ·························0···5 |
| 116 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] | 116 | o4·:·RingMap·------------------·<--·GF·109561[t·..t·] |
| 117 | ·············x·x··-·x·x··+·x·x·················0···4 | 117 | ·············x·x··-·x·x··+·x·x·················0···4 |
| 118 | ··············2·3····1·4····0·5</code></pre> | 118 | ··············2·3····1·4····0·5</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,Certify=>true) | 121 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees(psi,Certify=>true) |
| 122 | ·--·used·0.01 | 122 | ·--·used·0.0110654s·(cpu);·0.0122336s·(thread);·0s·(gc) |
| 123 | Certify:·output·certified! | 123 | Certify:·output·certified! |
| 124 | o5·=·{2,·4,·4,·2,·1} | 124 | o5·=·{2,·4,·4,·2,·1} |
| 125 | o5·:·List</code></pre> | 125 | o5·:·List</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ········</table> | 127 | ········</table> |
| Offset 138, 23 lines modified | Offset 138, 23 lines modified | ||
| 138 | ···············ZZ·················ZZ | 138 | ···············ZZ·················ZZ |
| 139 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] | 139 | o6·:·RingMap·------[x·..x·]·<--·------[x·..x·] |
| 140 | ·············300007··0···6······300007··0···6</code></pre> | 140 | ·············300007··0···6······300007··0···6</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·projectiveDegrees·phi | 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·projectiveDegrees·phi |
| 144 | ·--·used·0.00 | 144 | ·--·used·0.00196016s·(cpu);·3.9329e-05s·(thread);·0s·(gc) |
| 145 | o7·=·{1,·2,·4,·8,·8,·4,·1} | 145 | o7·=·{1,·2,·4,·8,·8,·4,·1} |
| 146 | o7·:·List</code></pre> | 146 | o7·:·List</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·projectiveDegrees(phi,NumDegrees=>1) | 149 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·projectiveDegrees(phi,NumDegrees=>1) |
| 150 | ·--·used· | 150 | ·--·used·7.3481e-05s·(cpu);·1.3691e-05s·(thread);·0s·(gc) |
| 151 | o8·=·{4,·1} | 151 | o8·=·{4,·1} |
| 152 | o8·:·List</code></pre> | 152 | o8·:·List</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ········</table> | 154 | ········</table> |
| 155 | ········<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> | 155 | ········<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·0.01 | 59 | ·--·used·0.0160087s·(cpu);·0.0136984s·(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·0.01 | 82 | ·--·used·0.0110654s·(cpu);·0.0122336s·(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·0.00196016s·(cpu);·3.9329e-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·7.3481e-05s·(cpu);·1.3691e-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 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ················ZZ | 91 | ················ZZ |
| 92 | o2·:·Ideal·of·-----[x·..x·] | 92 | o2·:·Ideal·of·-----[x·..x·] |
| 93 | ··············33331··0···6</code></pre> | 93 | ··············33331··0···6</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·phi·=·rationalMap(V,3,2) | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·phi·=·rationalMap(V,3,2) |
| 97 | ·--·used·0.0 | 97 | ·--·used·0.0834682s·(cpu);·0.0833077s·(thread);·0s·(gc) |
| 98 | o3·=·--·rational·map·-- | 98 | o3·=·--·rational·map·-- |
| 99 | ····················ZZ | 99 | ····················ZZ |
| 100 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 100 | ·····source:·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 101 | ··················33331··0···1···2···3···4···5···6 | 101 | ··················33331··0···1···2···3···4···5···6 |
| 102 | ····················ZZ | 102 | ····················ZZ |
| 103 | ·····target:·Proj(-----[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y··,·y··,·y··,·y··]) | 103 | ·····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·0.0834682s·(cpu);·0.0833077s·(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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| 105 | o4·:·Ideal·of·X</code></pre> | 105 | o4·:·Ideal·of·X</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};</code></pre> | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·D·=·new·Tally·from·{H·=>·2,C·=>·1};</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi·=·rationalMap·D | 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·phi·=·rationalMap·D |
| 112 | ·--·used·0.02 | 112 | ·--·used·0.0239055s·(cpu);·0.0219475s·(thread);·0s·(gc) |
| 113 | o6·=·--·rational·map·-- | 113 | o6·=·--·rational·map·-- |
| 114 | ··································ZZ | 114 | ··································ZZ |
| 115 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by | 115 | ·····source:·subvariety·of·Proj(-----[x·,·x·,·x·,·x·,·x·,·x·])·defined·by |
| 116 | ································65521··0···1···2···3···4···5 | 116 | ································65521··0···1···2···3···4···5 |
| 117 | ·············{ | 117 | ·············{ |
| 118 | ·················2··················2 | 118 | ·················2··················2 |
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| 211 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 | 211 | ·······················0·1·5····0·2·5····1·2·5····2·5····1·4·5·····2·4·5····4·5 |
| 212 | ·····················} | 212 | ·····················} |
| 213 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)</code></pre> | 213 | o6·:·RationalMap·(cubic·rational·map·from·surface·in·PP^5·to·PP^20)</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ··········<tr> | 215 | ··········<tr> |
| 216 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·?·image(phi,"F4") | 216 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·?·image(phi,"F4") |
| 217 | ·--·used·0.7 | 217 | ·--·used·0.741182s·(cpu);·0.497531s·(thread);·0s·(gc) |
| 218 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 | 218 | o7·=·surface·of·degree·38·and·sectional·genus·20·in·PP^20·cut·out·by·153 |
| 219 | ·····hypersurfaces·of·degree·2</code></pre> | 219 | ·····hypersurfaces·of·degree·2</code></pre> |
| 220 | </td>··········</tr> | 220 | </td>··········</tr> |
| 221 | ········</table> | 221 | ········</table> |
| 222 | ········<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 | ········<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> |
| 223 | ······</div> | 223 | ······</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·0.02 | 46 | ·--·used·0.0239055s·(cpu);·0.0219475s·(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·0.7 | 176 | ·--·used·0.741182s·(cpu);·0.497531s·(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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| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>Description</h2> | 73 | ········<h2>Description</h2> |
| 74 | ········<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 | ········<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> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·apply(1..12,i·->·describe·specialCremonaTransformation(i,ZZ/3331)) |
| 78 | ·--·used·0.8 | 78 | ·--·used·0.804218s·(cpu);·0.719267s·(thread);·0s·(gc) |
| 79 | o1·=·(rational·map·defined·by·forms·of·degree·3, | 79 | o1·=·(rational·map·defined·by·forms·of·degree·3, |
| 80 | ······source·variety:·PP^3······················ | 80 | ······source·variety:·PP^3······················ |
| 81 | ······target·variety:·PP^3······················ | 81 | ······target·variety:·PP^3······················ |
| 82 | ······dominance:·true··························· | 82 | ······dominance:·true··························· |
| 83 | ······birationality:·true······················· | 83 | ······birationality:·true······················· |
| 84 | ······projective·degrees:·{1,·3,·3,·1}·········· | 84 | ······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·0.8 | 24 | ·--·used·0.804218s·(cpu);·0.719267s·(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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| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>Description</h2> | 73 | ········<h2>Description</h2> |
| 74 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> | 74 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialCubicTransformation·9 | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialCubicTransformation·9 |
| 78 | ·--·used·0.0 | 78 | ·--·used·0.0783795s·(cpu);·0.0770635s·(thread);·0s·(gc) |
| 79 | o1·=·--·rational·map·-- | 79 | o1·=·--·rational·map·-- |
| 80 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 80 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 81 | ······················0···1···2···3···4···5···6 | 81 | ······················0···1···2···3···4···5···6 |
| 82 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by | 82 | ·····target:·subvariety·of·Proj(QQ[t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·,·t·])·defined·by |
| 83 | ····································0···1···2···3···4···5···6···7···8···9 | 83 | ····································0···1···2···3···4···5···6···7···8···9 |
| 84 | ·············{ | 84 | ·············{ |
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| 137 | ························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 | ························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 |
| 138 | ·····················} | 138 | ·····················} |
| 139 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> | 139 | o1·:·RationalMap·(cubic·birational·map·from·PP^6·to·6-dimensional·subvariety·of·PP^9)</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo | 142 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo |
| 143 | ·--·used·0.01 | 143 | ·--·used·0.01605s·(cpu);·0.0161688s·(thread);·0s·(gc) |
| 144 | o2·=·rational·map·defined·by·forms·of·degree·3 | 144 | o2·=·rational·map·defined·by·forms·of·degree·3 |
| 145 | ·····source·variety:·PP^6 | 145 | ·····source·variety:·PP^6 |
| 146 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 | 146 | ·····target·variety:·complete·intersection·of·type·(2,2,2)·in·PP^9 |
| 147 | ·····dominance:·true | 147 | ·····dominance:·true |
| 148 | ·····birationality:·true | 148 | ·····birationality:·true |
| 149 | ·····projective·degrees:·{1,·3,·9,·17,·21,·16,·8} | 149 | ·····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·0.0783795s·(cpu);·0.0770635s·(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·0.01605s·(cpu);·0.0161688s·(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} |
| 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 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> | 74 | ········<p>The·field·<span·class="tt">K</span>·is·required·to·be·large·enough.</p> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialQuadraticTransformation·4 | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·specialQuadraticTransformation·4 |
| 78 | ·--·used·0.0 | 78 | ·--·used·0.0573645s·(cpu);·0.057115s·(thread);·0s·(gc) |
| 79 | o1·=·--·rational·map·-- | 79 | o1·=·--·rational·map·-- |
| 80 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 80 | ·····source:·Proj(QQ[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| 81 | ······················0···1···2···3···4···5···6···7···8 | 81 | ······················0···1···2···3···4···5···6···7···8 |
| 82 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by | 82 | ·····target:·subvariety·of·Proj(QQ[y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·])·defined·by |
| 83 | ····································0···1···2···3···4···5···6···7···8···9 | 83 | ····································0···1···2···3···4···5···6···7···8···9 |
| 84 | ·············{ | 84 | ·············{ |
| Offset 125, 15 lines modified | Offset 125, 15 lines modified | ||
| 125 | ·······················0·1····0·4····3·6····4·6····6····5·7 | 125 | ·······················0·1····0·4····3·6····4·6····6····5·7 |
| 126 | ·····················} | 126 | ·····················} |
| 127 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> | 127 | o1·:·RationalMap·(quadratic·birational·map·from·PP^8·to·hypersurface·in·PP^9)</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo | 130 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·oo |
| 131 | ·--·used·0.00 | 131 | ·--·used·0.00798778s·(cpu);·0.00528424s·(thread);·0s·(gc) |
| 132 | o2·=·rational·map·defined·by·forms·of·degree·2 | 132 | o2·=·rational·map·defined·by·forms·of·degree·2 |
| 133 | ·····source·variety:·PP^8 | 133 | ·····source·variety:·PP^8 |
| 134 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 | 134 | ·····target·variety:·hypersurface·of·degree·3·in·PP^9 |
| 135 | ·····dominance:·true | 135 | ·····dominance:·true |
| 136 | ·····birationality:·true | 136 | ·····birationality:·true |
| 137 | ·····projective·degrees:·{1,·2,·4,·8,·16,·21,·17,·9,·3} | 137 | ·····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·0.0 | 23 | ·--·used·0.0573645s·(cpu);·0.057115s·(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·0.00798778s·(cpu);·0.00528424s·(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 83, 36 lines modified | Offset 83, 36 lines modified | ||
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·#str | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·#str |
| 85 | o3·=·6927</code></pre> | 85 | o3·=·6927</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi'·=·value·str; | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·phi'·=·value·str; |
| 89 | ·--·used·0.02 | 89 | ·--·used·0.0201272s·(cpu);·0.0189493s·(thread);·0s·(gc) |
| 90 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)</code></pre> | 90 | o4·:·RationalMap·(cubic·birational·map·from·PP^3·to·hypersurface·in·PP^4)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·phi' | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·phi' |
| 94 | ·--·used·0.002 | 94 | ·--·used·0.00228344s·(cpu);·0.00445355s·(thread);·0s·(gc) |
| 95 | o5·=·rational·map·defined·by·forms·of·degree·3 | 95 | o5·=·rational·map·defined·by·forms·of·degree·3 |
| 96 | ·····source·variety:·PP^3 | 96 | ·····source·variety:·PP^3 |
| 97 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 | 97 | ·····target·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 98 | ·····dominance:·true | 98 | ·····dominance:·true |
| 99 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 99 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 100 | ·····projective·degrees:·{1,·3,·4,·2} | 100 | ·····projective·degrees:·{1,·3,·4,·2} |
| 101 | ·····number·of·minimal·representatives:·1 | 101 | ·····number·of·minimal·representatives:·1 |
| 102 | ·····dimension·base·locus:·1 | 102 | ·····dimension·base·locus:·1 |
| 103 | ·····degree·base·locus:·5 | 103 | ·····degree·base·locus:·5 |
| 104 | ·····coefficient·ring:·ZZ/33331</code></pre> | 104 | ·····coefficient·ring:·ZZ/33331</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·inverse·phi' | 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·inverse·phi' |
| 108 | ·--·used·0.00 | 108 | ·--·used·0.00145355s·(cpu);·0.00409456s·(thread);·0s·(gc) |
| 109 | o6·=·rational·map·defined·by·forms·of·degree·2 | 109 | o6·=·rational·map·defined·by·forms·of·degree·2 |
| 110 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 | 110 | ·····source·variety:·smooth·quadric·hypersurface·in·PP^4 |
| 111 | ·····target·variety:·PP^3 | 111 | ·····target·variety:·PP^3 |
| 112 | ·····dominance:·true | 112 | ·····dominance:·true |
| 113 | ·····birationality:·true·(the·inverse·map·is·already·calculated) | 113 | ·····birationality:·true·(the·inverse·map·is·already·calculated) |
| 114 | ·····projective·degrees:·{2,·4,·3,·1} | 114 | ·····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·0.02 | 25 | ·--·used·0.0201272s·(cpu);·0.0189493s·(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·0.002 | 28 | ·--·used·0.00228344s·(cpu);·0.00445355s·(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·0.00145355s·(cpu);·0.00409456s·(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 49, 63 lines modified | Offset 49, 63 lines modified | ||
| 49 | ········<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 | ········<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> |
| 50 | ········<table·class="examples"> | 50 | ········<table·class="examples"> |
| 51 | ··········<tr> | 51 | ··········<tr> |
| 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·ZZ/300007[t_0..t_6];</code></pre> | 52 | <td>··············<pre><code·class="language-macaulay2">i1·:·ZZ/300007[t_0..t_6];</code></pre> |
| 53 | </td>··········</tr> | 53 | </td>··········</tr> |
| 54 | ··········<tr> | 54 | ··········<tr> |
| 55 | <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 | <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}}) |
| 56 | ·--·used·0.00 | 56 | ·--·used·0.00399969s·(cpu);·0.0035176s·(thread);·0s·(gc) |
| 57 | ············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 | ············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 |
| 58 | 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 | 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·}) |
| 59 | ··········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 | ··········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 |
| 60 | ···············ZZ·················ZZ | 60 | ···············ZZ·················ZZ |
| 61 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] | 61 | o2·:·RingMap·------[t·..t·]·<--·------[x·..x·] |
| 62 | ·············300007··0···6······300007··0···9</code></pre> | 62 | ·············300007··0···6······300007··0···9</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·J·=·kernel(phi,2) | 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·J·=·kernel(phi,2) |
| 66 | ·--·used·0.03 | 66 | ·--·used·0.0387384s·(cpu);·0.0375771s·(thread);·0s·(gc) |
| 67 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x· | 67 | o3·=·ideal·(x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·,·x·x· |
| 68 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 | 68 | ·············6·7····5·8····4·9···3·7····2·8····1·9···3·5····2·6····0·9···3·4 |
| 69 | ·····------------------------------------------------------------------------ | 69 | ·····------------------------------------------------------------------------ |
| 70 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) | 70 | ·····-·x·x··+·x·x·,·x·x··-·x·x··+·x·x·) |
| 71 | ········1·6····0·8···2·4····1·5····0·7 | 71 | ········1·6····0·8···2·4····1·5····0·7 |
| 72 | ················ZZ | 72 | ················ZZ |
| 73 | o3·:·Ideal·of·------[x·..x·] | 73 | o3·:·Ideal·of·------[x·..x·] |
| 74 | ··············300007··0···9</code></pre> | 74 | ··············300007··0···9</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degreeMap·phi | 77 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degreeMap·phi |
| 78 | ·--·used·0.02 | 78 | ·--·used·0.0258274s·(cpu);·0.0252749s·(thread);·0s·(gc) |
| 79 | o4·=·1</code></pre> | 79 | o4·=·1</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees·phi | 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projectiveDegrees·phi |
| 83 | ·--·used·0.3 | 83 | ·--·used·0.338828s·(cpu);·0.298263s·(thread);·0s·(gc) |
| 84 | o5·=·{1,·3,·9,·17,·21,·15,·5} | 84 | o5·=·{1,·3,·9,·17,·21,·15,·5} |
| 85 | o5·:·List</code></pre> | 85 | o5·:·List</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·projectiveDegrees(phi,NumDegrees=>0) | 88 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·projectiveDegrees(phi,NumDegrees=>0) |
| 89 | ·--·used·0.0 | 89 | ·--·used·0.0421524s·(cpu);·0.0456074s·(thread);·0s·(gc) |
| 90 | o6·=·{5} | 90 | o6·=·{5} |
| 91 | o6·:·List</code></pre> | 91 | o6·:·List</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·phi·=·toMap(phi,Dominant=>J) | 94 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·phi·=·toMap(phi,Dominant=>J) |
| 95 | ·--·used·0.00 | 95 | ·--·used·0.000418389s·(cpu);·0.00242235s·(thread);·0s·(gc) |
| 96 | ·······································································ZZ | 96 | ·······································································ZZ |
| 97 | ·····································································------[x·..x·] | 97 | ·····································································------[x·..x·] |
| 98 | ············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 | ············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 |
| 99 | 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 | 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·}) |
| 100 | ··········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 | ··········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 |
| 101 | ····························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 | 101 | ····························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 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | ···············ZZ··························································300007··0···9 | 115 | ···············ZZ··························································300007··0···9 |
| 116 | o7·:·RingMap·------[t·..t·]·<--·---------------------------------------------------------------------------------------------------- | 116 | o7·:·RingMap·------[t·..t·]·<--·---------------------------------------------------------------------------------------------------- |
| 117 | ·············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 | ·············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·) |
| 118 | ··································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 | ··································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> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·psi·=·inverseMap·phi | 121 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·psi·=·inverseMap·phi |
| 122 | ·--·used·0.3 | 122 | ·--·used·0.305823s·(cpu);·0.30518s·(thread);·0s·(gc) |
| 123 | ·······················································ZZ | 123 | ·······················································ZZ |
| 124 | ·····················································------[x·..x·] | 124 | ·····················································------[x·..x·] |
| 125 | ·····················································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 | ·····················································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 |
| 126 | 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 | 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·}) |
| 127 | ··········(x·x··-·x·x··+·x·x·,·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 | ··········(x·x··-·x·x··+·x·x·,·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 |
| 128 | ············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 | 128 | ············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 133, 38 lines modified | Offset 133, 38 lines modified | ||
| 133 | ························································300007··0···9···················································ZZ | 133 | ························································300007··0···9···················································ZZ |
| 134 | o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·] | 134 | o8·:·RingMap·----------------------------------------------------------------------------------------------------·<--·------[t·..t·] |
| 135 | ·············(x·x··-·x·x··+·x·x·,·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 | ·············(x·x··-·x·x··+·x·x·,·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 |
| 136 | ···············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 | ···············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> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isInverseMap(phi,psi) | 139 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isInverseMap(phi,psi) |
| 140 | ·--·used·0.00 | 140 | ·--·used·0.0070353s·(cpu);·0.00729468s·(thread);·0s·(gc) |
| 141 | o9·=·true</code></pre> | 141 | o9·=·true</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·degreeMap·psi | 144 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·degreeMap·psi |
| 145 | ·--·used·0. | 145 | ·--·used·0.200765s·(cpu);·0.163676s·(thread);·0s·(gc) |
| 146 | o10·=·1</code></pre> | 146 | o10·=·1</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·projectiveDegrees·psi | 149 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·projectiveDegrees·psi |
| 150 | ·--·used· | 150 | ·--·used·3.96925s·(cpu);·3.67784s·(thread);·0s·(gc) |
| 151 | o11·=·{5,·15,·21,·17,·9,·3,·1} | 151 | o11·=·{5,·15,·21,·17,·9,·3,·1} |
| 152 | o11·:·List</code></pre> | 152 | o11·:·List</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ········</table> | 154 | ········</table> |
| 155 | ········<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 | ········<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> |
| 156 | ········<table·class="examples"> | 156 | ········<table·class="examples"> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <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 | <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}}) |
| 159 | ·--·used·0.000 | 159 | ·--·used·0.000706854s·(cpu);·0.00190851s·(thread);·0s·(gc) |
| 160 | o12·=·--·rational·map·-- | 160 | o12·=·--·rational·map·-- |
| 161 | ·····················ZZ | 161 | ·····················ZZ |
| 162 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) | 162 | ······source:·Proj(------[t·,·t·,·t·,·t·,·t·,·t·,·t·]) |
| 163 | ···················300007··0···1···2···3···4···5···6 | 163 | ···················300007··0···1···2···3···4···5···6 |
| 164 | ·····················ZZ | 164 | ·····················ZZ |
| 165 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) | 165 | ······target:·Proj(------[x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·,·x·]) |
| Offset 211, 15 lines modified | Offset 211, 15 lines modified | ||
| 211 | ··························4·····3·4·5····2·5····3·6····2·4·6 | 211 | ··························4·····3·4·5····2·5····3·6····2·4·6 |
| 212 | ······················} | 212 | ······················} |
| 213 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)</code></pre> | 213 | o12·:·RationalMap·(cubic·rational·map·from·PP^6·to·PP^9)</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ··········<tr> | 215 | ··········<tr> |
| 216 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·phi·=·rationalMap(phi,Dominant=>2) | 216 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·phi·=·rationalMap(phi,Dominant=>2) |
| 217 | ·--·used·0.1 | 217 | ·--·used·0.117052s·(cpu);·0.070352s·(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·0.00 | 32 | ·--·used·0.00399969s·(cpu);·0.0035176s·(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·0.0387384s·(cpu);·0.0375771s·(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·0.02 | 68 | ·--·used·0.0258274s·(cpu);·0.0252749s·(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·0.338828s·(cpu);·0.298263s·(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·0.0421524s·(cpu);·0.0456074s·(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·0.00 | 79 | ·--·used·0.000418389s·(cpu);·0.00242235s·(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·0.3 | 130 | ·--·used·0.305823s·(cpu);·0.30518s·(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·0.0070353s·(cpu);·0.00729468s·(thread);·0s·(gc) |
| 172 | o9·=·true | 172 | o9·=·true |
| 173 | i10·:·time·degreeMap·psi | 173 | i10·:·time·degreeMap·psi |
| 174 | ·--·used·0. | 174 | ·--·used·0.200765s·(cpu);·0.163676s·(thread);·0s·(gc) |
| 175 | o10·=·1 | 175 | o10·=·1 |
| 176 | i11·:·time·projectiveDegrees·psi | 176 | i11·:·time·projectiveDegrees·psi |
| 177 | ·--·used· | 177 | ·--·used·3.96925s·(cpu);·3.67784s·(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·0.000 | 183 | ·--·used·0.000706854s·(cpu);·0.00190851s·(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·0.117052s·(cpu);·0.070352s·(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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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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+IDMxMDIsIElucHV0cyA9PiB7U1BBTntUVHsicGhp | 11 | REdBbGdlYnJhTWFwIiwgImxpbmVudW0iID0+IDMxMDIsIElucHV0cyA9PiB7U1BBTntUVHsicGhp |
| 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·0.01 | 160 | ·--·used·0.018054s·(cpu);·0.0155849s·(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·0.0 | 35 | ·--·used·0.0199661s·(cpu);·0.0183738s·(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·0.0 | 73 | ·--·used·0.0209853s·(cpu);·0.0191715s·(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·0.0119 | 60 | ·--·used·0.0119878s·(cpu);·0.0126056s·(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·0.0 | 65 | ·--·used·0.0699531s·(cpu);·0.0328535s·(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·0.5 | 84 | ·--·used·0.450498s·(cpu);·0.451366s·(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·0.01 | 22 | ·--·used·0.0154059s·(cpu);·0.0174428s·(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·0.01 | 22 | ·--·used·0.017227s·(cpu);·0.0185067s·(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·0.1 | 50 | ·--·used·0.125512s·(cpu);·0.0946989s·(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·0.0 | 118 | ·--·used·0.0443013s·(cpu);·0.0463048s·(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·0.0 | 156 | ·--·used·0.0182637s·(cpu);·0.0170846s·(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·0.0 | 48 | ·--·used·0.0606897s·(cpu);·0.0272446s·(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·0. | 39 | ·--·used·0.0951711s·(cpu);·0.0941606s·(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·0.4 | 73 | ·--·used·0.433427s·(cpu);·0.433057s·(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·0.1 | 32 | ·--·used·0.124147s·(cpu);·0.124242s·(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·0.4 | 15 | ·--·used·0.411236s·(cpu);·0.372693s·(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 250, 15 lines modified | Offset 250, 15 lines modified | ||
| 250 | ········</table> | 250 | ········</table> |
| 251 | ········<div> | 251 | ········<div> |
| 252 | ··········<p>One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.</p> | 252 | ··········<p>One·can·also·obtain·the·map·on·homology·induced·by·a·DGAlgebra·map.</p> |
| 253 | ········</div> | 253 | ········</div> |
| 254 | ········<table·class="examples"> | 254 | ········<table·class="examples"> |
| 255 | ··········<tr> | 255 | ··········<tr> |
| 256 | <td>··············<pre><code·class="language-macaulay2">i17·:·HHg·=·HH·g | 256 | <td>··············<pre><code·class="language-macaulay2">i17·:·HHg·=·HH·g |
| 257 | ·--·used·0.01 | 257 | ·--·used·0.018054s·(cpu);·0.0155849s·(thread);·0s·(gc) |
| 258 | Finding·easy·relations···········:· | 258 | Finding·easy·relations···········:· |
| 259 | ··························ZZ | 259 | ··························ZZ |
| 260 | ·························---[a..c] | 260 | ·························---[a..c] |
| 261 | ············ZZ···········101 | 261 | ············ZZ···········101 |
| 262 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 262 | o17·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 263 | ···········101··1···2···········3···1·····1 | 263 | ···········101··1···2···········3···1·····1 |
| 264 | ························(c,·b,·a·) | 264 | ························(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·0.01 | 216 | ·--·used·0.018054s·(cpu);·0.0155849s·(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 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | ········</table> | 98 | ········</table> |
| 99 | ········<div> | 99 | ········<div> |
| 100 | ··········<p>One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)·command.</p> | 100 | ··········<p>One·can·compute·the·homology·algebra·of·a·DGAlgebra·using·the·homology·(or·HH)·command.</p> |
| 101 | ········</div> | 101 | ········</div> |
| 102 | ········<table·class="examples"> | 102 | ········<table·class="examples"> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·HB·=·HH·B | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·HB·=·HH·B |
| 105 | ·--·used·0.0 | 105 | ·--·used·0.0199661s·(cpu);·0.0183738s·(thread);·0s·(gc) |
| 106 | Finding·easy·relations···········:· | 106 | Finding·easy·relations···········:· |
| 107 | o5·=·HB | 107 | o5·=·HB |
| 108 | o5·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 108 | o5·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·HB | 111 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·HB |
| Offset 149, 15 lines modified | Offset 149, 15 lines modified | ||
| 149 | ······Differential·=>·{a,·b,·c,·d,·a·T·} | 149 | ······Differential·=>·{a,·b,·c,·d,·a·T·} |
| 150 | ······································1 | 150 | ······································1 |
| 151 | o9·:·DGAlgebra</code></pre> | 151 | o9·:·DGAlgebra</code></pre> |
| 152 | </td>··········</tr> | 152 | </td>··········</tr> |
| 153 | ··········<tr> | 153 | ··········<tr> |
| 154 | <td>··············<pre><code·class="language-macaulay2">i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) | 154 | <td>··············<pre><code·class="language-macaulay2">i10·:·homologyAlgebra(C,GenDegreeLimit=>4,RelDegreeLimit=>4) |
| 155 | ·--·used·0.0 | 155 | ·--·used·0.0209853s·(cpu);·0.0191715s·(thread);·0s·(gc) |
| 156 | Finding·easy·relations···········:· | 156 | Finding·easy·relations···········:· |
| 157 | ·······ZZ | 157 | ·······ZZ |
| 158 | o10·=·---[X·..X·] | 158 | o10·=·---[X·..X·] |
| 159 | ······101··1···3 | 159 | ······101··1···3 |
| 160 | o10·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> | 160 | o10·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> |
| 161 | </td>··········</tr> | 161 | </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·0.0 | 48 | ·--·used·0.0199661s·(cpu);·0.0183738s·(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·0.0 | 92 | ·--·used·0.0209853s·(cpu);·0.0191715s·(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 133, 15 lines modified | Offset 133, 15 lines modified | ||
| 133 | ···············{2}·|·0·| | 133 | ···············{2}·|·0·| |
| 134 | ···············{2}·|·1·| | 134 | ···············{2}·|·1·| |
| 135 | o6·:·ChainComplexMap</code></pre> | 135 | o6·:·ChainComplexMap</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i7·:·HHg·=·HH·g | 138 | <td>··············<pre><code·class="language-macaulay2">i7·:·HHg·=·HH·g |
| 139 | ·--·used·0.0119 | 139 | ·--·used·0.0119878s·(cpu);·0.0126056s·(thread);·0s·(gc) |
| 140 | Finding·easy·relations···········:· | 140 | Finding·easy·relations···········:· |
| 141 | ·························ZZ | 141 | ·························ZZ |
| 142 | ························---[a..c] | 142 | ························---[a..c] |
| 143 | ···········ZZ···········101 | 143 | ···········ZZ···········101 |
| 144 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) | 144 | o7·=·map·(---[X·..X·],·----------[X·],·{X·,·0,·0,·0}) |
| 145 | ··········101··1···2···········3···1·····1 | 145 | ··········101··1···2···········3···1·····1 |
| 146 | ·······················(c,·b,·a·) | 146 | ·······················(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·0.0119 | 69 | ·--·used·0.0119878s·(cpu);·0.0126056s·(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 131, 15 lines modified | Offset 131, 15 lines modified | ||
| 131 | ········</table> | 131 | ········</table> |
| 132 | ········<div> | 132 | ········<div> |
| 133 | ··········<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 | ··········<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> |
| 134 | ········</div> | 134 | ········</div> |
| 135 | ········<table·class="examples"> | 135 | ········<table·class="examples"> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i7·:·HKR·=·HH·KR | 137 | <td>··············<pre><code·class="language-macaulay2">i7·:·HKR·=·HH·KR |
| 138 | ·--·used·0.0 | 138 | ·--·used·0.0699531s·(cpu);·0.0328535s·(thread);·0s·(gc) |
| 139 | Finding·easy·relations···········:· | 139 | Finding·easy·relations···········:· |
| 140 | o7·=·HKR | 140 | o7·=·HKR |
| 141 | o7·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 141 | o7·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i8·:·ideal·HKR | 144 | <td>··············<pre><code·class="language-macaulay2">i8·:·ideal·HKR |
| Offset 153, 15 lines modified | Offset 153, 15 lines modified | ||
| 153 | o9·=·R' | 153 | o9·=·R' |
| 154 | o9·:·QuotientRing</code></pre> | 154 | o9·:·QuotientRing</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i10·:·HKR'·=·HH·koszulComplexDGA·R' | 157 | <td>··············<pre><code·class="language-macaulay2">i10·:·HKR'·=·HH·koszulComplexDGA·R' |
| 158 | ·--·used·0.5 | 158 | ·--·used·0.450498s·(cpu);·0.451366s·(thread);·0s·(gc) |
| 159 | Finding·easy·relations···········:· | 159 | Finding·easy·relations···········:· |
| 160 | o10·=·HKR' | 160 | o10·=·HKR' |
| 161 | o10·:·QuotientRing</code></pre> | 161 | o10·:·QuotientRing</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·HKR' | 164 | <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·0.0 | 81 | ·--·used·0.0699531s·(cpu);·0.0328535s·(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·0.5 | 97 | ·--·used·0.450498s·(cpu);·0.451366s·(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 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | o3·=·{1,·4,·6,·4,·1} | 79 | o3·=·{1,·4,·6,·4,·1} |
| 80 | o3·:·List</code></pre> | 80 | o3·:·List</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) | 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) |
| 84 | ·--·used·0.01 | 84 | ·--·used·0.0154059s·(cpu);·0.0174428s·(thread);·0s·(gc) |
| 85 | Finding·easy·relations···········:· | 85 | Finding·easy·relations···········:· |
| 86 | o4·=·HA | 86 | o4·=·HA |
| 87 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 87 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·numgens·HA | 90 | <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·0.01 | 29 | ·--·used·0.0154059s·(cpu);·0.0174428s·(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 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | o3·=·{1,·4,·6,·4,·1} | 101 | o3·=·{1,·4,·6,·4,·1} |
| 102 | o3·:·List</code></pre> | 102 | o3·:·List</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·HA·=·homologyAlgebra(A) |
| 106 | ·--·used·0.01 | 106 | ·--·used·0.017227s·(cpu);·0.0185067s·(thread);·0s·(gc) |
| 107 | Finding·easy·relations···········:· | 107 | Finding·easy·relations···········:· |
| 108 | o4·=·HA | 108 | o4·=·HA |
| 109 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 109 | o4·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| 112 | ········<div> | 112 | ········<div> |
| Offset 138, 15 lines modified | Offset 138, 15 lines modified | ||
| 138 | o7·=·{1,·5,·10,·10,·4} | 138 | o7·=·{1,·5,·10,·10,·4} |
| 139 | o7·:·List</code></pre> | 139 | o7·:·List</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i8·:·HA·=·homologyAlgebra(A) | 142 | <td>··············<pre><code·class="language-macaulay2">i8·:·HA·=·homologyAlgebra(A) |
| 143 | ·--·used·0.1 | 143 | ·--·used·0.125512s·(cpu);·0.0946989s·(thread);·0s·(gc) |
| 144 | Finding·easy·relations···········:· | 144 | Finding·easy·relations···········:· |
| 145 | o8·=·HA | 145 | o8·=·HA |
| 146 | o8·:·QuotientRing</code></pre> | 146 | o8·:·QuotientRing</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i9·:·numgens·HA | 149 | <td>··············<pre><code·class="language-macaulay2">i9·:·numgens·HA |
| Offset 216, 15 lines modified | Offset 216, 15 lines modified | ||
| 216 | o15·=·{1,·7,·7,·1} | 216 | o15·=·{1,·7,·7,·1} |
| 217 | o15·:·List</code></pre> | 217 | o15·:·List</code></pre> |
| 218 | </td>··········</tr> | 218 | </td>··········</tr> |
| 219 | ··········<tr> | 219 | ··········<tr> |
| 220 | <td>··············<pre><code·class="language-macaulay2">i16·:·HA·=·homologyAlgebra(A) | 220 | <td>··············<pre><code·class="language-macaulay2">i16·:·HA·=·homologyAlgebra(A) |
| 221 | ·--·used·0.0 | 221 | ·--·used·0.0443013s·(cpu);·0.0463048s·(thread);·0s·(gc) |
| 222 | Finding·easy·relations···········:· | 222 | Finding·easy·relations···········:· |
| 223 | o16·=·HA | 223 | o16·=·HA |
| 224 | o16·:·QuotientRing</code></pre> | 224 | o16·:·QuotientRing</code></pre> |
| 225 | </td>··········</tr> | 225 | </td>··········</tr> |
| 226 | ········</table> | 226 | ········</table> |
| 227 | ········<div> | 227 | ········<div> |
| Offset 266, 15 lines modified | Offset 266, 15 lines modified | ||
| 266 | ································1···4 | 266 | ································1···4 |
| 267 | ·······Differential·=>·{a,·b,·c,·d} | 267 | ·······Differential·=>·{a,·b,·c,·d} |
| 268 | o20·:·DGAlgebra</code></pre> | 268 | o20·:·DGAlgebra</code></pre> |
| 269 | </td>··········</tr> | 269 | </td>··········</tr> |
| 270 | ··········<tr> | 270 | ··········<tr> |
| 271 | <td>··············<pre><code·class="language-macaulay2">i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) | 271 | <td>··············<pre><code·class="language-macaulay2">i21·:·HB·=·homologyAlgebra(B,GenDegreeLimit=>7,RelDegreeLimit=>14) |
| 272 | ·--·used·0.0 | 272 | ·--·used·0.0182637s·(cpu);·0.0170846s·(thread);·0s·(gc) |
| 273 | Finding·easy·relations···········:· | 273 | Finding·easy·relations···········:· |
| 274 | o21·=·HB | 274 | o21·=·HB |
| 275 | o21·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> | 275 | o21·:·PolynomialRing,·4·skew·commutative·variable(s)</code></pre> |
| 276 | </td>··········</tr> | 276 | </td>··········</tr> |
| 277 | ········</table> | 277 | ········</table> |
| 278 | ······</div> | 278 | ······</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·0.01 | 39 | ·--·used·0.017227s·(cpu);·0.0185067s·(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·0.1 | 65 | ·--·used·0.125512s·(cpu);·0.0946989s·(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·0.0 | 126 | ·--·used·0.0443013s·(cpu);·0.0463048s·(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·0.0 | 162 | ·--·used·0.0182637s·(cpu);·0.0170846s·(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 124, 15 lines modified | Offset 124, 15 lines modified | ||
| 124 | ········2 | 124 | ········2 |
| 125 | o6·:·R[T·..T·] | 125 | o6·:·R[T·..T·] |
| 126 | ········1···3</code></pre> | 126 | ········1···3</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i7·:·H·=·HH(KR) | 129 | <td>··············<pre><code·class="language-macaulay2">i7·:·H·=·HH(KR) |
| 130 | ·--·used·0.0 | 130 | ·--·used·0.0606897s·(cpu);·0.0272446s·(thread);·0s·(gc) |
| 131 | Finding·easy·relations···········:· | 131 | Finding·easy·relations···········:· |
| 132 | o7·=·H | 132 | o7·=·H |
| 133 | o7·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> | 133 | o7·:·PolynomialRing,·3·skew·commutative·variable(s)</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i8·:·homologyClass(KR,z1*z2) | 136 | <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·0.0 | 60 | ·--·used·0.0606897s·(cpu);·0.0272446s·(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 120, 15 lines modified | Offset 120, 15 lines modified | ||
| 120 | ·································· | 120 | ·································· |
| 121 | ·····0······1······2······3······4 | 121 | ·····0······1······2······3······4 |
| 122 | o5·:·ChainComplex</code></pre> | 122 | o5·:·ChainComplex</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·HKR·=·HH(KR) | 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·HKR·=·HH(KR) |
| 126 | ·--·used·0. | 126 | ·--·used·0.0951711s·(cpu);·0.0941606s·(thread);·0s·(gc) |
| 127 | Finding·easy·relations···········:· | 127 | Finding·easy·relations···········:· |
| 128 | o6·=·HKR | 128 | o6·=·HKR |
| 129 | o6·:·QuotientRing</code></pre> | 129 | o6·:·QuotientRing</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ········</table> | 131 | ········</table> |
| 132 | ········<div> | 132 | ········<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·0. | 60 | ·--·used·0.0951711s·(cpu);·0.0941606s·(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 177, 15 lines modified | Offset 177, 15 lines modified | ||
| 177 | ········</div> | 177 | ········</div> |
| 178 | ········<div> | 178 | ········<div> |
| 179 | ··········<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 | ··········<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> |
| 180 | ········</div> | 180 | ········</div> |
| 181 | ········<table·class="examples"> | 181 | ········<table·class="examples"> |
| 182 | ··········<tr> | 182 | ··········<tr> |
| 183 | <td>··············<pre><code·class="language-macaulay2">i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) | 183 | <td>··············<pre><code·class="language-macaulay2">i10·:·z123·=·masseyTripleProduct(KR,z1,z2,z3) |
| 184 | ·--·used·0.4 | 184 | ·--·used·0.433427s·(cpu);·0.433057s·(thread);·0s·(gc) |
| 185 | Finding·easy·relations···········:· | 185 | Finding·easy·relations···········:· |
| 186 | ·············2 | 186 | ·············2 |
| 187 | o10·=·x·x·y·z·T·T·T·T | 187 | o10·=·x·x·y·z·T·T·T·T |
| 188 | ·······1·2·2···2·3·4·5 | 188 | ·······1·2·2···2·3·4·5 |
| 189 | o10·:·R[T·..T·] | 189 | o10·:·R[T·..T·] |
| 190 | ·········1···5</code></pre> | 190 | ·········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·0.4 | 98 | ·--·used·0.433427s·(cpu);·0.433057s·(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 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | ······Differential·=>·{t·,·t·,·t·,·t·} | 115 | ······Differential·=>·{t·,·t·,·t·,·t·} |
| 116 | ························1···2···3···4 | 116 | ························1···2···3···4 |
| 117 | o4·:·DGAlgebra</code></pre> | 117 | o4·:·DGAlgebra</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·H·=·HH(KR) | 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·H·=·HH(KR) |
| 121 | ·--·used·0.1 | 121 | ·--·used·0.124147s·(cpu);·0.124242s·(thread);·0s·(gc) |
| 122 | Finding·easy·relations···········:· | 122 | Finding·easy·relations···········:· |
| 123 | o5·=·H | 123 | o5·=·H |
| 124 | o5·:·QuotientRing</code></pre> | 124 | o5·:·QuotientRing</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i6·:·masseys·=·masseyTripleProduct(KR,1,1,1); | 127 | <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·0.1 | 56 | ·--·used·0.124147s·(cpu);·0.124242s·(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 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | o3·=·S | 96 | o3·=·S |
| 97 | o3·:·QuotientRing</code></pre> | 97 | o3·:·QuotientRing</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·HB·=·torAlgebra(R,S,GenDegreeLimit=>4,RelDegreeLimit=>8) |
| 101 | ·--·used·0.4 | 101 | ·--·used·0.411236s·(cpu);·0.372693s·(thread);·0s·(gc) |
| 102 | Finding·easy·relations···········:· | 102 | Finding·easy·relations···········:· |
| 103 | o4·=·HB | 103 | o4·=·HB |
| 104 | o4·:·QuotientRing</code></pre> | 104 | o4·:·QuotientRing</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·numgens·HB | 107 | <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·0.4 | 33 | ·--·used·0.411236s·(cpu);·0.372693s·(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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| 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 | bGluZWFyQ29tYg== | 8 | bGluZWFyQ29tYg== |
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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=29 | 7 | #:len=29 |
| 8 | aXNWZXJ5QW1wbGUoLi4uLFZlcmJvc2U9Pi4uLik= | 8 | aXNWZXJ5QW1wbGUoLi4uLFZlcmJvc2U9Pi4uLik= |
| 9 | #:len=252 | 9 | #:len=252 |
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| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaXNWZXJ5QW1wbGUsVmVyYm9zZV0sImlzVmVyeUFt | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbaXNWZXJ5QW1wbGUsVmVyYm9zZV0sImlzVmVyeUFt |
| Offset 1, 14 lines modified | Offset 1, 14 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-1576409255 | 1 | --·-*-·M2-comint·-*-·hash:·-1576409255 |
| 2 | i1·:·R·=·QQ[x,y,z]; | 2 | i1·:·R·=·QQ[x,y,z]; |
| 3 | i2·:·D·=·divisor(x*y^2*z^3) | 3 | i2·:·D·=·divisor(x*y^2*z^3) |
| 4 | o2·=· | 4 | o2·=·Div(x)·+·2*Div(y)·+·3*Div(z) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·H·=·new·HashTable·from·D | 6 | i3·:·H·=·new·HashTable·from·D |
| 7 | o3·=·HashTable{{x}·=>·{1}··················} | 7 | o3·=·HashTable{{x}·=>·{1}··················} |
| 8 | ···············{y}·=>·{2} | 8 | ···············{y}·=>·{2} |
| Offset 16, 18 lines modified | Offset 16, 18 lines modified | ||
| 16 | ···············cache·=>·CacheTable{...1...} | 16 | ···············cache·=>·CacheTable{...1...} |
| 17 | ···············ring·=>·R | 17 | ···············ring·=>·R |
| 18 | o3·:·HashTable | 18 | o3·:·HashTable |
| 19 | i4·:·(2/3)*D | 19 | i4·:·(2/3)*D |
| 20 | o4·=·2*Div( | 20 | o4·=·2/3*Div(x)·+·2*Div(z)·+·4/3*Div(y) |
| 21 | o4·:·QWeilDivisor·on·R | 21 | o4·:·QWeilDivisor·on·R |
| 22 | i5·:·0.6*D | 22 | i5·:·0.6*D |
| 23 | o5·=· | 23 | o5·=·.6*Div(x)·+·1.8*Div(z)·+·1.2*Div(y) |
| 24 | o5·:·RWeilDivisor·on·R | 24 | o5·:·RWeilDivisor·on·R |
| 25 | i6·:· | 25 | i6·:· |
| 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·=·-Div(x+y)·+·Div( | 94 | o17·=·-Div(x+y)·+·Div(x)·+·Div(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, 32 lines modified | Offset 1, 32 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·594689672 | 1 | --·-*-·M2-comint·-*-·hash:·594689672 |
| 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,·4/3},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 3 | i2·:·D·=·divisor({1/2,·4/3},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 4 | o2·=· | 4 | o2·=·1/2*Div(x,·z)·+·4/3*Div(y,·z) |
| 5 | o2·:·QWeilDivisor·on·R | 5 | o2·:·QWeilDivisor·on·R |
| 6 | i3·:·ceiling(·D·) | 6 | i3·:·ceiling(·D·) |
| 7 | o3·=· | 7 | o3·=·Div(x,·z)·+·2*Div(y,·z) |
| 8 | o3·:·WeilDivisor·on·R | 8 | o3·:·WeilDivisor·on·R |
| 9 | i4·:·floor(·D·) | 9 | i4·:·floor(·D·) |
| 10 | o4·=·Div(y,·z) | 10 | o4·=·Div(y,·z) |
| 11 | o4·:·WeilDivisor·on·R | 11 | o4·:·WeilDivisor·on·R |
| 12 | i5·:·E·=·divisor({0.3,·-0.7},·{ideal(x,·z),·ideal(y,z)},·CoefficientType·=>·RR) | 12 | i5·:·E·=·divisor({0.3,·-0.7},·{ideal(x,·z),·ideal(y,z)},·CoefficientType·=>·RR) |
| 13 | o5·=· | 13 | o5·=·.3*Div(x,·z)·+·-.7*Div(y,·z) |
| 14 | o5·:·RWeilDivisor·on·R | 14 | o5·:·RWeilDivisor·on·R |
| 15 | i6·:·ceiling(·E·) | 15 | i6·:·ceiling(·E·) |
| 16 | o6·=·Div(x,·z) | 16 | o6·=·Div(x,·z) |
| Offset 1, 17 lines modified | Offset 1, 17 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·503842787 | 1 | --·-*-·M2-comint·-*-·hash:·503842787 |
| 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·=· | 4 | o2·=·Div(x)·+·0*Div(y)·+·-2*Div(z) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·cleanSupport(D) | 6 | i3·:·cleanSupport(D) |
| 7 | o3·=· | 7 | o3·=·Div(x)·+·-2*Div(z) |
| 8 | o3·:·WeilDivisor·on·R | 8 | o3·:·WeilDivisor·on·R |
| 9 | i4·:· | 9 | i4·:· |
| Offset 1, 38 lines modified | Offset 1, 38 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-9127469 | 1 | --·-*-·M2-comint·-*-·hash:·-9127469 |
| 2 | i1·:·R·=·QQ[x,y,z]; | 2 | i1·:·R·=·QQ[x,y,z]; |
| 3 | i2·:·D·=·divisor({1,2,3},·{ideal(x),·ideal(y),·ideal(z)}) | 3 | i2·:·D·=·divisor({1,2,3},·{ideal(x),·ideal(y),·ideal(z)}) |
| 4 | o2·=·Div( | 4 | o2·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·E·=·divisor(x*y^2*z^3) | 6 | i3·:·E·=·divisor(x*y^2*z^3) |
| 7 | o3·=·Div( | 7 | o3·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 8 | o3·:·WeilDivisor·on·R | 8 | o3·:·WeilDivisor·on·R |
| 9 | i4·:·F·=·divisor(ideal(x*y^2*z^3)) | 9 | i4·:·F·=·divisor(ideal(x*y^2*z^3)) |
| 10 | o4·=·Div( | 10 | o4·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 11 | o4·:·WeilDivisor·on·R | 11 | o4·:·WeilDivisor·on·R |
| 12 | i5·:·G·=·divisor({{1,·ideal(x)},·{2,·ideal(y)},·{3,·ideal(z)}}) | 12 | i5·:·G·=·divisor({{1,·ideal(x)},·{2,·ideal(y)},·{3,·ideal(z)}}) |
| 13 | o5·=·Div( | 13 | o5·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 14 | o5·:·WeilDivisor·on·R | 14 | o5·:·WeilDivisor·on·R |
| 15 | i6·:·H·=·divisor(x)·+·2*divisor(y)·+·3*divisor(z) | 15 | i6·:·H·=·divisor(x)·+·2*divisor(y)·+·3*divisor(z) |
| 16 | o6·=·Div( | 16 | o6·=·3*Div(z)·+·2*Div(y)·+·Div(x) |
| 17 | o6·:·WeilDivisor·on·R | 17 | o6·:·WeilDivisor·on·R |
| 18 | i7·:·R·=·QQ[x,y,z]/ideal(x^2-y*z); | 18 | i7·:·R·=·QQ[x,y,z]/ideal(x^2-y*z); |
| 19 | i8·:·D·=·divisor({2},·{ideal(x,y)}) | 19 | i8·:·D·=·divisor({2},·{ideal(x,y)}) |
| Offset 68, 21 lines modified | Offset 68, 21 lines modified | ||
| 68 | o15·:·WeilDivisor·on·A | 68 | o15·:·WeilDivisor·on·A |
| 69 | i16·:·R·=·ZZ/7[x,y]; | 69 | i16·:·R·=·ZZ/7[x,y]; |
| 70 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) | 70 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) |
| 71 | o17·=· | 71 | o17·=·2*Div(x)·+·-1/2*Div(-x^3+y^2) |
| 72 | o17·:·QWeilDivisor·on·R | 72 | o17·:·QWeilDivisor·on·R |
| 73 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) | 73 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) |
| 74 | o18·=· | 74 | o18·=·2*Div(x)·+·-1/2*Div(-x^3+y^2) |
| 75 | o18·:·QWeilDivisor·on·R | 75 | o18·:·QWeilDivisor·on·R |
| 76 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); | 76 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); |
| 77 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)},·CoefficientType=>RR) | 77 | 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·0.0867955s·(cpu);·0.0500834s·(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·0.355413s·(cpu);·0.356183s·(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·0.369571s·(cpu);·0.372327s·(thread);·0s·(gc) |
| 55 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); | 55 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); |
| 56 | ·--·used·0.002 | 56 | ·--·used·0.000279119s·(cpu);·0.00243976s·(thread);·0s·(gc) |
| 57 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); | 57 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); |
| 58 | ·--·used· | 58 | ·--·used·0.00163478s·(cpu);·0.00181563s·(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·0.182193s·(cpu);·0.0927599s·(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·0.00 | 69 | ·--·used·0.0060663s·(cpu);·0.00597311s·(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:·1008317510 | 1 | --·-*-·M2-comint·-*-·hash:·1008317510 |
| 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·=·-8*Div(x)·+·2*Div(y)·+·0*Div(x^2+z) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·getPrimeDivisors(·D·) | 6 | i3·:·getPrimeDivisors(·D·) |
| 7 | o3·=·{Div( | 7 | o3·=·{Div(x),·Div(y),·Div(x^2+z)} |
| 8 | o3·:·List | 8 | o3·:·List |
| 9 | i4·:·getPrimeDivisors(·cleanSupport·D·) | 9 | i4·:·getPrimeDivisors(·cleanSupport·D·) |
| 10 | o4·=·{Div( | 10 | o4·=·{Div(x),·Div(y)} |
| 11 | o4·:·List | 11 | o4·:·List |
| 12 | i5·:· | 12 | i5·:· |
| Offset 1, 14 lines modified | Offset 1, 14 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1670778332 | 1 | --·-*-·M2-comint·-*-·hash:·1670778332 |
| 2 | i1·:·R·=·QQ[x,·y,·z]; | 2 | i1·:·R·=·QQ[x,·y,·z]; |
| 3 | i2·:·D·=·divisor({1,·2,·3},·{ideal(x·*·y·-·z^2),·ideal(y·*·z·-·x^2),·ideal(x·*·z·-·y^2)}) | 3 | i2·:·D·=·divisor({1,·2,·3},·{ideal(x·*·y·-·z^2),·ideal(y·*·z·-·x^2),·ideal(x·*·z·-·y^2)}) |
| 4 | o2·=· | 4 | o2·=·Div(x*y-z^2)·+·2*Div(-x^2+y*z)·+·3*Div(-y^2+x*z) |
| 5 | o2·:·WeilDivisor·on·R | 5 | o2·:·WeilDivisor·on·R |
| 6 | i3·:·isHomogeneous(·D·) | 6 | i3·:·isHomogeneous(·D·) |
| 7 | o3·=·true | 7 | o3·=·true |
| Offset 1, 14 lines modified | Offset 1, 14 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-562598002 | 1 | --·-*-·M2-comint·-*-·hash:·-562598002 |
| 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},·{ideal(x,·z),·ideal(y,·z)}) | 3 | i2·:·D·=·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·:·isSNC(·D·) | 6 | i3·:·isSNC(·D·) |
| 7 | o3·=·false | 7 | o3·=·false |
| 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·0.1 | 107 | ·--·used·0.129371s·(cpu);·0.12711s·(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·0.3 | 110 | ·--·used·0.308069s·(cpu);·0.267614s·(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·0.1 | 118 | ·--·used·0.132441s·(cpu);·0.0901738s·(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·4. | 123 | ·--·used·4.92606s·(cpu);·3.70073s·(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·5.0 | 130 | ·--·used·5.03995s·(cpu);·4.01795s·(thread);·0s·(gc) |
| 131 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 131 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 132 | ·--·used·0. | 132 | ·--·used·0.609443s·(cpu);·0.309426s·(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·0.697877s·(cpu);·0.234957s·(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. | 151 | ·--·used·0.211058s·(cpu);·0.0447583s·(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·0.1 | 162 | ·--·used·0.0319051s·(cpu);·0.0315516s·(thread);·0s·(gc) |
| 163 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 163 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 164 | ·--·used·0.00 | 164 | ·--·used·0.00188358s·(cpu);·0.00514914s·(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·0.02 | 27 | ·--·used·0.0237094s·(cpu);·0.0224293s·(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·0.1 | 32 | ·--·used·0.152776s·(cpu);·0.112704s·(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·0.02 | 40 | ·--·used·0.0238286s·(cpu);·0.0245194s·(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·0.0 | 43 | ·--·used·0.0476995s·(cpu);·0.0502523s·(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 16, 12 lines modified | Offset 16, 12 lines modified | ||
| 16 | o4·=·Div(x) | 16 | o4·=·Div(x) |
| 17 | o4·:·QWeilDivisor·on·R | 17 | o4·:·QWeilDivisor·on·R |
| 18 | i5·:·F·=·divisor({3,·0,·-2},·{ideal(x),·ideal(y),·ideal(x+y)}) | 18 | i5·:·F·=·divisor({3,·0,·-2},·{ideal(x),·ideal(y),·ideal(x+y)}) |
| 19 | o5·=· | 19 | o5·=·-2*Div(x+y)·+·3*Div(x)·+·0*Div(y) |
| 20 | o5·:·WeilDivisor·on·R | 20 | o5·:·WeilDivisor·on·R |
| 21 | i6·:· | 21 | i6·:· |
| Offset 63, 15 lines modified | Offset 63, 15 lines modified | ||
| 63 | ········<table·class="examples"> | 63 | ········<table·class="examples"> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> | 65 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> |
| 66 | </td>··········</tr> | 66 | </td>··········</tr> |
| 67 | ··········<tr> | 67 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor(x*y^2*z^3) | 68 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor(x*y^2*z^3) |
| 69 | o2·=· | 69 | o2·=·Div(x)·+·2*Div(y)·+·3*Div(z) |
| 70 | o2·:·WeilDivisor·on·R</code></pre> | 70 | o2·:·WeilDivisor·on·R</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i3·:·H·=·new·HashTable·from·D | 73 | <td>··············<pre><code·class="language-macaulay2">i3·:·H·=·new·HashTable·from·D |
| 74 | o3·=·HashTable{{x}·=>·{1}··················} | 74 | o3·=·HashTable{{x}·=>·{1}··················} |
| Offset 81, 22 lines modified | Offset 81, 22 lines modified | ||
| 81 | ···············ring·=>·R | 81 | ···············ring·=>·R |
| 82 | o3·:·HashTable</code></pre> | 82 | o3·:·HashTable</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·(2/3)*D | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·(2/3)*D |
| 86 | o4·=·2*Div( | 86 | o4·=·2/3*Div(x)·+·2*Div(z)·+·4/3*Div(y) |
| 87 | o4·:·QWeilDivisor·on·R</code></pre> | 87 | o4·:·QWeilDivisor·on·R</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·0.6*D | 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·0.6*D |
| 91 | o5·=· | 91 | o5·=·.6*Div(x)·+·1.8*Div(z)·+·1.2*Div(y) |
| 92 | o5·:·RWeilDivisor·on·R</code></pre> | 92 | o5·:·RWeilDivisor·on·R</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ········</table> | 94 | ········</table> |
| 95 | ······</div> | 95 | ······</div> |
| 96 | ······<div·class="waystouse"> | 96 | ······<div·class="waystouse"> |
| 97 | ········<h2>Types·of·<span·class="tt">BasicDivisor</span>·:</h2> | 97 | ········<h2>Types·of·<span·class="tt">BasicDivisor</span>·:</h2> |
| Offset 15, 34 lines modified | Offset 15, 34 lines modified | ||
| 15 | specifies·the·ambient·ring.·Another·key·is·cache·which·points·to·a·CacheTable. | 15 | specifies·the·ambient·ring.·Another·key·is·cache·which·points·to·a·CacheTable. |
| 16 | The·remaining·keys·are·a·Groebner·basis·$L$·for·each·prime·ideal·$P$·in·the | 16 | The·remaining·keys·are·a·Groebner·basis·$L$·for·each·prime·ideal·$P$·in·the |
| 17 | support·with·corresponding·value·a·list·with·one·entry·{$n$}·where·$n$·is·the | 17 | support·with·corresponding·value·a·list·with·one·entry·{$n$}·where·$n$·is·the |
| 18 | coefficient·of·the·height·one·prime. | 18 | coefficient·of·the·height·one·prime. |
| 19 | i1·:·R·=·QQ[x,y,z]; | 19 | i1·:·R·=·QQ[x,y,z]; |
| 20 | i2·:·D·=·divisor(x*y^2*z^3) | 20 | i2·:·D·=·divisor(x*y^2*z^3) |
| 21 | o2·=· | 21 | o2·=·Div(x)·+·2*Div(y)·+·3*Div(z) |
| 22 | o2·:·WeilDivisor·on·R | 22 | o2·:·WeilDivisor·on·R |
| 23 | i3·:·H·=·new·HashTable·from·D | 23 | i3·:·H·=·new·HashTable·from·D |
| 24 | o3·=·HashTable{{x}·=>·{1}··················} | 24 | o3·=·HashTable{{x}·=>·{1}··················} |
| 25 | ···············{y}·=>·{2} | 25 | ···············{y}·=>·{2} |
| 26 | ···············{z}·=>·{3} | 26 | ···············{z}·=>·{3} |
| 27 | ···············cache·=>·CacheTable{...1...} | 27 | ···············cache·=>·CacheTable{...1...} |
| 28 | ···············ring·=>·R | 28 | ···············ring·=>·R |
| 29 | o3·:·HashTable | 29 | o3·:·HashTable |
| 30 | i4·:·(2/3)*D | 30 | i4·:·(2/3)*D |
| 31 | o4·=·2*Div( | 31 | o4·=·2/3*Div(x)·+·2*Div(z)·+·4/3*Div(y) |
| 32 | o4·:·QWeilDivisor·on·R | 32 | o4·:·QWeilDivisor·on·R |
| 33 | i5·:·0.6*D | 33 | i5·:·0.6*D |
| 34 | o5·=· | 34 | o5·=·.6*Div(x)·+·1.8*Div(z)·+·1.2*Div(y) |
| 35 | o5·:·RWeilDivisor·on·R | 35 | o5·:·RWeilDivisor·on·R |
| 36 | *\x8**\x8**\x8**\x8**\x8*·T\x8Ty\x8yp\x8pe\x8es\x8s·o\x8of\x8f·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r·:\x8:·*\x8**\x8**\x8**\x8**\x8* | 36 | *\x8**\x8**\x8**\x8**\x8*·T\x8Ty\x8yp\x8pe\x8es\x8s·o\x8of\x8f·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 37 | ····*·RWeilDivisor | 37 | ····*·RWeilDivisor |
| 38 | *\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\x8an\x8n·o\x8ob\x8bj\x8je\x8ec\x8ct\x8t·o\x8of\x8f·c\x8cl\x8la\x8as\x8ss\x8s·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r·:\x8:·*\x8**\x8**\x8**\x8**\x8* | 38 | *\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\x8an\x8n·o\x8ob\x8bj\x8je\x8ec\x8ct\x8t·o\x8of\x8f·c\x8cl\x8la\x8as\x8ss\x8s·B\x8Ba\x8as\x8si\x8ic\x8cD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 39 | ····*·applyToCoefficients(BasicDivisor,Function)·--·see·_\x8a_\x8p_\x8p_\x8l_\x8y_\x8T_\x8o_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8s·- | 39 | ····*·applyToCoefficients(BasicDivisor,Function)·--·see·_\x8a_\x8p_\x8p_\x8l_\x8y_\x8T_\x8o_\x8C_\x8o_\x8e_\x8f_\x8f_\x8i_\x8c_\x8i_\x8e_\x8n_\x8t_\x8s·- |
| 40 | ······-·apply·a·function·to·the·coefficients·of·a·divisor | 40 | ······-·apply·a·function·to·the·coefficients·of·a·divisor |
| Offset 196, 15 lines modified | Offset 196, 15 lines modified | ||
| 196 | ········<table·class="examples"> | 196 | ········<table·class="examples"> |
| 197 | ··········<tr> | 197 | ··········<tr> |
| 198 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/11[x,y];</code></pre> | 198 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/11[x,y];</code></pre> |
| 199 | </td>··········</tr> | 199 | </td>··········</tr> |
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor(x*y/(x+y)) | 201 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor(x*y/(x+y)) |
| 202 | o17·=·-Div(x+y)·+·Div( | 202 | o17·=·-Div(x+y)·+·Div(x)·+·Div(y) |
| 203 | o17·:·WeilDivisor·on·R</code></pre> | 203 | o17·:·WeilDivisor·on·R</code></pre> |
| 204 | </td>··········</tr> | 204 | </td>··········</tr> |
| 205 | ··········<tr> | 205 | ··········<tr> |
| 206 | <td>··············<pre><code·class="language-macaulay2">i18·:·divisor(OO(D)) | 206 | <td>··············<pre><code·class="language-macaulay2">i18·:·divisor(OO(D)) |
| 207 | o18·=·0,·the·zero·divisor | 207 | 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·=·-Div(x+y)·+·Div( | 107 | o17·=·-Div(x+y)·+·Div(x)·+·Div(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 |
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| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*y·-·z^2);</code></pre> | 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*y·-·z^2);</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1/2,·4/3},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1/2,·4/3},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 83 | o2·=· | 83 | o2·=·1/2*Div(x,·z)·+·4/3*Div(y,·z) |
| 84 | o2·:·QWeilDivisor·on·R</code></pre> | 84 | o2·:·QWeilDivisor·on·R</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·ceiling(·D·) | 87 | <td>··············<pre><code·class="language-macaulay2">i3·:·ceiling(·D·) |
| 88 | o3·=· | 88 | o3·=·Div(x,·z)·+·2*Div(y,·z) |
| 89 | o3·:·WeilDivisor·on·R</code></pre> | 89 | o3·:·WeilDivisor·on·R</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·floor(·D·) | 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·floor(·D·) |
| 93 | o4·=·Div(y,·z) | 93 | o4·=·Div(y,·z) |
| 94 | o4·:·WeilDivisor·on·R</code></pre> | 94 | o4·:·WeilDivisor·on·R</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·E·=·divisor({0.3,·-0.7},·{ideal(x,·z),·ideal(y,z)},·CoefficientType·=>·RR) | 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·E·=·divisor({0.3,·-0.7},·{ideal(x,·z),·ideal(y,z)},·CoefficientType·=>·RR) |
| 98 | o5·=· | 98 | o5·=·.3*Div(x,·z)·+·-.7*Div(y,·z) |
| 99 | o5·:·RWeilDivisor·on·R</code></pre> | 99 | o5·:·RWeilDivisor·on·R</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i6·:·ceiling(·E·) | 102 | <td>··············<pre><code·class="language-macaulay2">i6·:·ceiling(·E·) |
| 103 | o6·=·Div(x,·z) | 103 | o6·=·Div(x,·z) |
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| 16 | ··········o·an·instance·of·the·type·_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r, | 16 | ··········o·an·instance·of·the·type·_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r, |
| 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 | Start·with·a·rational·or·real·Weil·divisor.·We·form·a·new·divisor·whose | 18 | Start·with·a·rational·or·real·Weil·divisor.·We·form·a·new·divisor·whose |
| 19 | coefficients·are·obtained·by·applying·the·ceiling·or·floor·function·to·them. | 19 | coefficients·are·obtained·by·applying·the·ceiling·or·floor·function·to·them. |
| 20 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*y·-·z^2); | 20 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*y·-·z^2); |
| 21 | i2·:·D·=·divisor({1/2,·4/3},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) | 21 | i2·:·D·=·divisor({1/2,·4/3},·{ideal(x,·z),·ideal(y,·z)},·CoefficientType·=>·QQ) |
| 22 | o2·=· | 22 | o2·=·1/2*Div(x,·z)·+·4/3*Div(y,·z) |
| 23 | o2·:·QWeilDivisor·on·R | 23 | o2·:·QWeilDivisor·on·R |
| 24 | i3·:·ceiling(·D·) | 24 | i3·:·ceiling(·D·) |
| 25 | o3·=· | 25 | o3·=·Div(x,·z)·+·2*Div(y,·z) |
| 26 | o3·:·WeilDivisor·on·R | 26 | o3·:·WeilDivisor·on·R |
| 27 | i4·:·floor(·D·) | 27 | i4·:·floor(·D·) |
| 28 | o4·=·Div(y,·z) | 28 | o4·=·Div(y,·z) |
| 29 | o4·:·WeilDivisor·on·R | 29 | o4·:·WeilDivisor·on·R |
| 30 | i5·:·E·=·divisor({0.3,·-0.7},·{ideal(x,·z),·ideal(y,z)},·CoefficientType·=>·RR) | 30 | i5·:·E·=·divisor({0.3,·-0.7},·{ideal(x,·z),·ideal(y,z)},·CoefficientType·=>·RR) |
| 31 | o5·=· | 31 | o5·=·.3*Div(x,·z)·+·-.7*Div(y,·z) |
| 32 | o5·:·RWeilDivisor·on·R | 32 | o5·:·RWeilDivisor·on·R |
| 33 | i6·:·ceiling(·E·) | 33 | i6·:·ceiling(·E·) |
| 34 | o6·=·Div(x,·z) | 34 | o6·=·Div(x,·z) |
| 35 | o6·:·WeilDivisor·on·R | 35 | o6·:·WeilDivisor·on·R |
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| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,0,-2},·{ideal(x),·ideal(y),·ideal(z)}) |
| 80 | o2·=· | 80 | o2·=·Div(x)·+·0*Div(y)·+·-2*Div(z) |
| 81 | o2·:·WeilDivisor·on·R</code></pre> | 81 | o2·:·WeilDivisor·on·R</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·cleanSupport(D) | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·cleanSupport(D) |
| 85 | o3·=· | 85 | o3·=·Div(x)·+·-2*Div(z) |
| 86 | o3·:·WeilDivisor·on·R</code></pre> | 86 | o3·:·WeilDivisor·on·R</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·<span·class="tt">cleanSupport</span>·:</h2> | 91 | ········<h2>Ways·to·use·<span·class="tt">cleanSupport</span>·:</h2> |
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| 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·=· | 20 | o2·=·Div(x)·+·0*Div(y)·+·-2*Div(z) |
| 21 | o2·:·WeilDivisor·on·R | 21 | o2·:·WeilDivisor·on·R |
| 22 | i3·:·cleanSupport(D) | 22 | i3·:·cleanSupport(D) |
| 23 | o3·=· | 23 | o3·=·Div(x)·+·-2*Div(z) |
| 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. |
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| 105 | ········<table·class="examples"> | 105 | ········<table·class="examples"> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> | 107 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,y,z];</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,2,3},·{ideal(x),·ideal(y),·ideal(z)}) | 110 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,2,3},·{ideal(x),·ideal(y),·ideal(z)}) |
| 111 | o2·=·Div( | 111 | o2·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 112 | o2·:·WeilDivisor·on·R</code></pre> | 112 | o2·:·WeilDivisor·on·R</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·E·=·divisor(x*y^2*z^3) | 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·E·=·divisor(x*y^2*z^3) |
| 116 | o3·=·Div( | 116 | o3·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 117 | o3·:·WeilDivisor·on·R</code></pre> | 117 | o3·:·WeilDivisor·on·R</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·F·=·divisor(ideal(x*y^2*z^3)) | 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·F·=·divisor(ideal(x*y^2*z^3)) |
| 121 | o4·=·Div( | 121 | o4·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 122 | o4·:·WeilDivisor·on·R</code></pre> | 122 | o4·:·WeilDivisor·on·R</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i5·:·G·=·divisor({{1,·ideal(x)},·{2,·ideal(y)},·{3,·ideal(z)}}) | 125 | <td>··············<pre><code·class="language-macaulay2">i5·:·G·=·divisor({{1,·ideal(x)},·{2,·ideal(y)},·{3,·ideal(z)}}) |
| 126 | o5·=·Div( | 126 | o5·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 127 | o5·:·WeilDivisor·on·R</code></pre> | 127 | o5·:·WeilDivisor·on·R</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i6·:·H·=·divisor(x)·+·2*divisor(y)·+·3*divisor(z) | 130 | <td>··············<pre><code·class="language-macaulay2">i6·:·H·=·divisor(x)·+·2*divisor(y)·+·3*divisor(z) |
| 131 | o6·=·Div( | 131 | o6·=·3*Div(z)·+·2*Div(y)·+·Div(x) |
| 132 | o6·:·WeilDivisor·on·R</code></pre> | 132 | o6·:·WeilDivisor·on·R</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ········</table> | 134 | ········</table> |
| 135 | ········<div> | 135 | ········<div> |
| 136 | ··········<p>Next·we·construct·the·same·divisor·in·two·different·ways.··We·are·working·on·the·quadric·cone,·and·we·are·working·with·a·divisor·of·a·ruling·of·the·cone.··This·divisor·is·not·Cartier,·but·2·times·it·is.</p> | 136 | ··········<p>Next·we·construct·the·same·divisor·in·two·different·ways.··We·are·working·on·the·quadric·cone,·and·we·are·working·with·a·divisor·of·a·ruling·of·the·cone.··This·divisor·is·not·Cartier,·but·2·times·it·is.</p> |
| 137 | ········</div> | 137 | ········</div> |
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| 203 | ········<table·class="examples"> | 203 | ········<table·class="examples"> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/7[x,y];</code></pre> | 205 | <td>··············<pre><code·class="language-macaulay2">i16·:·R·=·ZZ/7[x,y];</code></pre> |
| 206 | </td>··········</tr> | 206 | </td>··········</tr> |
| 207 | ··········<tr> | 207 | ··········<tr> |
| 208 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) | 208 | <td>··············<pre><code·class="language-macaulay2">i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) |
| 209 | o17·=· | 209 | o17·=·2*Div(x)·+·-1/2*Div(-x^3+y^2) |
| 210 | o17·:·QWeilDivisor·on·R</code></pre> | 210 | o17·:·QWeilDivisor·on·R</code></pre> |
| 211 | </td>··········</tr> | 211 | </td>··········</tr> |
| 212 | ··········<tr> | 212 | ··········<tr> |
| 213 | <td>··············<pre><code·class="language-macaulay2">i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) | 213 | <td>··············<pre><code·class="language-macaulay2">i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) |
| 214 | o18·=· | 214 | o18·=·2*Div(x)·+·-1/2*Div(-x^3+y^2) |
| 215 | o18·:·QWeilDivisor·on·R</code></pre> | 215 | o18·:·QWeilDivisor·on·R</code></pre> |
| 216 | </td>··········</tr> | 216 | </td>··········</tr> |
| 217 | ········</table> | 217 | ········</table> |
| 218 | ········<div> | 218 | ········<div> |
| 219 | ··········<p>Or·an·R-divisor.··This·time·we·work·in·the·cone·over·$P^1·\times·P^1$.</p> | 219 | ··········<p>Or·an·R-divisor.··This·time·we·work·in·the·cone·over·$P^1·\times·P^1$.</p> |
| 220 | ········</div> | 220 | ········</div> |
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| 44 | call·it.·In·our·first·example,·we·construct·divisors·on·$A^3$·(which·can·also | 44 | call·it.·In·our·first·example,·we·construct·divisors·on·$A^3$·(which·can·also |
| 45 | be·viewed·as·divisors·on·$P^2$·since·the·ideals·are·homogeneous).·The·following | 45 | be·viewed·as·divisors·on·$P^2$·since·the·ideals·are·homogeneous).·The·following |
| 46 | creates·the·same·Weil·divisor·with·coefficients·1,·2·and·3·in·five·different | 46 | creates·the·same·Weil·divisor·with·coefficients·1,·2·and·3·in·five·different |
| 47 | ways. | 47 | ways. |
| 48 | i1·:·R·=·QQ[x,y,z]; | 48 | i1·:·R·=·QQ[x,y,z]; |
| 49 | i2·:·D·=·divisor({1,2,3},·{ideal(x),·ideal(y),·ideal(z)}) | 49 | i2·:·D·=·divisor({1,2,3},·{ideal(x),·ideal(y),·ideal(z)}) |
| 50 | o2·=·Div( | 50 | o2·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 51 | o2·:·WeilDivisor·on·R | 51 | o2·:·WeilDivisor·on·R |
| 52 | i3·:·E·=·divisor(x*y^2*z^3) | 52 | i3·:·E·=·divisor(x*y^2*z^3) |
| 53 | o3·=·Div( | 53 | o3·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 54 | o3·:·WeilDivisor·on·R | 54 | o3·:·WeilDivisor·on·R |
| 55 | i4·:·F·=·divisor(ideal(x*y^2*z^3)) | 55 | i4·:·F·=·divisor(ideal(x*y^2*z^3)) |
| 56 | o4·=·Div( | 56 | o4·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 57 | o4·:·WeilDivisor·on·R | 57 | o4·:·WeilDivisor·on·R |
| 58 | i5·:·G·=·divisor({{1,·ideal(x)},·{2,·ideal(y)},·{3,·ideal(z)}}) | 58 | i5·:·G·=·divisor({{1,·ideal(x)},·{2,·ideal(y)},·{3,·ideal(z)}}) |
| 59 | o5·=·Div( | 59 | o5·=·2*Div(y)·+·3*Div(z)·+·Div(x) |
| 60 | o5·:·WeilDivisor·on·R | 60 | o5·:·WeilDivisor·on·R |
| 61 | i6·:·H·=·divisor(x)·+·2*divisor(y)·+·3*divisor(z) | 61 | i6·:·H·=·divisor(x)·+·2*divisor(y)·+·3*divisor(z) |
| 62 | o6·=·Div( | 62 | o6·=·3*Div(z)·+·2*Div(y)·+·Div(x) |
| 63 | o6·:·WeilDivisor·on·R | 63 | o6·:·WeilDivisor·on·R |
| 64 | Next·we·construct·the·same·divisor·in·two·different·ways.·We·are·working·on·the | 64 | Next·we·construct·the·same·divisor·in·two·different·ways.·We·are·working·on·the |
| 65 | quadric·cone,·and·we·are·working·with·a·divisor·of·a·ruling·of·the·cone.·This | 65 | quadric·cone,·and·we·are·working·with·a·divisor·of·a·ruling·of·the·cone.·This |
| 66 | divisor·is·not·Cartier,·but·2·times·it·is. | 66 | divisor·is·not·Cartier,·but·2·times·it·is. |
| 67 | i7·:·R·=·QQ[x,y,z]/ideal(x^2-y*z); | 67 | i7·:·R·=·QQ[x,y,z]/ideal(x^2-y*z); |
| 68 | i8·:·D·=·divisor({2},·{ideal(x,y)}) | 68 | i8·:·D·=·divisor({2},·{ideal(x,y)}) |
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| 104 | o15·:·WeilDivisor·on·A | 104 | o15·:·WeilDivisor·on·A |
| 105 | We·can·construct·a·Q-divisor·as·well.·Here·are·two·ways·to·do·it·(we·work·in | 105 | We·can·construct·a·Q-divisor·as·well.·Here·are·two·ways·to·do·it·(we·work·in |
| 106 | $A^2$·this·time). | 106 | $A^2$·this·time). |
| 107 | i16·:·R·=·ZZ/7[x,y]; | 107 | i16·:·R·=·ZZ/7[x,y]; |
| 108 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) | 108 | i17·:·D·=·divisor({-1/2,·2/1},·{ideal(y^2-x^3),·ideal(x)},·CoefficientType=>QQ) |
| 109 | o17·=· | 109 | o17·=·2*Div(x)·+·-1/2*Div(-x^3+y^2) |
| 110 | o17·:·QWeilDivisor·on·R | 110 | o17·:·QWeilDivisor·on·R |
| 111 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) | 111 | i18·:·D·=·(-1/2)*divisor(y^2-x^3)·+·(2/1)*divisor(x) |
| 112 | o18·=· | 112 | o18·=·2*Div(x)·+·-1/2*Div(-x^3+y^2) |
| 113 | o18·:·QWeilDivisor·on·R | 113 | o18·:·QWeilDivisor·on·R |
| 114 | Or·an·R-divisor.·This·time·we·work·in·the·cone·over·$P^1·\times·P^1$. | 114 | Or·an·R-divisor.·This·time·we·work·in·the·cone·over·$P^1·\times·P^1$. |
| 115 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); | 115 | i19·:·R·=·ZZ/11[x,y,u,v]/ideal(x*y-u*v); |
| 116 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)}, | 116 | i20·:·D·=·divisor({1.1,·-3.14159},·{ideal(x,u),·ideal(x,·v)}, |
| 117 | CoefficientType=>RR) | 117 | CoefficientType=>RR) |
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| 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·:·M·=·J*R^1;</code></pre> | 149 | <td>··············<pre><code·class="language-macaulay2">i11·:·M·=·J*R^1;</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·dualize(J,·Strategy=>IdealStrategy); | 152 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 153 | ·--·used·0.0 | 153 | ·--·used·0.0867955s·(cpu);·0.0500834s·(thread);·0s·(gc) |
| 154 | o12·:·Ideal·of·R</code></pre> | 154 | o12·:·Ideal·of·R</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·dualize(J,·Strategy=>ModuleStrategy); | 157 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 158 | ·--·used·0. | 158 | ·--·used·0.355413s·(cpu);·0.356183s·(thread);·0s·(gc) |
| 159 | o13·:·Ideal·of·R</code></pre> | 159 | o13·:·Ideal·of·R</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| 162 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·dualize(M,·Strategy=>IdealStrategy); | 162 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·dualize(M,·Strategy=>IdealStrategy); |
| 163 | ·--·used·0. | 163 | ·--·used·0.369571s·(cpu);·0.372327s·(thread);·0s·(gc)</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·dualize(M,·Strategy=>ModuleStrategy); | 166 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·dualize(M,·Strategy=>ModuleStrategy); |
| 167 | ·--·used·0.002 | 167 | ·--·used·0.000279119s·(cpu);·0.00243976s·(thread);·0s·(gc)</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); | 170 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); |
| 171 | ·--·used· | 171 | ·--·used·0.00163478s·(cpu);·0.00181563s·(thread);·0s·(gc) |
| 172 | o16·:·Ideal·of·R</code></pre> | 172 | o16·:·Ideal·of·R</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ········</table> | 174 | ········</table> |
| 175 | ········<div> | 175 | ········<div> |
| 176 | ··········<p>For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.</p> | 176 | ··········<p>For·monomial·ideals·in·toric·rings,·frequently·ModuleStrategy·appears·faster.</p> |
| 177 | ········</div> | 177 | ········</div> |
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| 190 | ··········<tr> | 190 | ··········<tr> |
| 191 | <td>··············<pre><code·class="language-macaulay2">i19·:·J·=·I^15; | 191 | <td>··············<pre><code·class="language-macaulay2">i19·:·J·=·I^15; |
| 192 | o19·:·Ideal·of·R</code></pre> | 192 | o19·:·Ideal·of·R</code></pre> |
| 193 | </td>··········</tr> | 193 | </td>··········</tr> |
| 194 | ··········<tr> | 194 | ··········<tr> |
| 195 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·dualize(J,·Strategy=>IdealStrategy); | 195 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·dualize(J,·Strategy=>IdealStrategy); |
| 196 | ·--·used·0.1 | 196 | ·--·used·0.182193s·(cpu);·0.0927599s·(thread);·0s·(gc) |
| 197 | o20·:·Ideal·of·R</code></pre> | 197 | o20·:·Ideal·of·R</code></pre> |
| 198 | </td>··········</tr> | 198 | </td>··········</tr> |
| 199 | ··········<tr> | 199 | ··········<tr> |
| 200 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·dualize(J,·Strategy=>ModuleStrategy); | 200 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·dualize(J,·Strategy=>ModuleStrategy); |
| 201 | ·--·used·0.00 | 201 | ·--·used·0.0060663s·(cpu);·0.00597311s·(thread);·0s·(gc) |
| 202 | o21·:·Ideal·of·R</code></pre> | 202 | o21·:·Ideal·of·R</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ········</table> | 204 | ········</table> |
| 205 | ········<div> | 205 | ········<div> |
| 206 | ··········<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 | ··········<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> |
| 207 | ········</div> | 207 | ········</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·0.0867955s·(cpu);·0.0500834s·(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·0.355413s·(cpu);·0.356183s·(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·0.369571s·(cpu);·0.372327s·(thread);·0s·(gc) |
| 73 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); | 73 | i15·:·time·dualize(M,·Strategy=>ModuleStrategy); |
| 74 | ·--·used·0.002 | 74 | ·--·used·0.000279119s·(cpu);·0.00243976s·(thread);·0s·(gc) |
| 75 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); | 75 | i16·:·time·embedAsIdeal·dualize(M,·Strategy=>ModuleStrategy); |
| 76 | ·--·used· | 76 | ·--·used·0.00163478s·(cpu);·0.00181563s·(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·0.182193s·(cpu);·0.0927599s·(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·0.00 | 88 | ·--·used·0.0060663s·(cpu);·0.00597311s·(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); |
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| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre> | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({-8,·2,·0},·{ideal(x),·ideal(y),·ideal(x^2+z)}) |
| 80 | o2·=· | 80 | o2·=·-8*Div(x)·+·2*Div(y)·+·0*Div(x^2+z) |
| 81 | o2·:·WeilDivisor·on·R</code></pre> | 81 | o2·:·WeilDivisor·on·R</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·getPrimeDivisors(·D·) | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·getPrimeDivisors(·D·) |
| 85 | o3·=·{Div( | 85 | o3·=·{Div(x),·Div(y),·Div(x^2+z)} |
| 86 | o3·:·List</code></pre> | 86 | o3·:·List</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·getPrimeDivisors(·cleanSupport·D·) | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·getPrimeDivisors(·cleanSupport·D·) |
| 90 | o4·=·{Div( | 90 | o4·=·{Div(x),·Div(y)} |
| 91 | o4·:·List</code></pre> | 91 | o4·:·List</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>Ways·to·use·<span·class="tt">getPrimeDivisors</span>·:</h2> | 96 | ········<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·=·-8*Div(x)·+·2*Div(y)·+·0*Div(x^2+z) |
| 22 | o2·:·WeilDivisor·on·R | 22 | o2·:·WeilDivisor·on·R |
| 23 | i3·:·getPrimeDivisors(·D·) | 23 | i3·:·getPrimeDivisors(·D·) |
| 24 | o3·=·{Div( | 24 | o3·=·{Div(x),·Div(y),·Div(x^2+z)} |
| 25 | o3·:·List | 25 | o3·:·List |
| 26 | i4·:·getPrimeDivisors(·cleanSupport·D·) | 26 | i4·:·getPrimeDivisors(·cleanSupport·D·) |
| 27 | o4·=·{Div( | 27 | o4·=·{Div(x),·Div(y)} |
| 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. |
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| 76 | ········<table·class="examples"> | 76 | ········<table·class="examples"> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre> | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z];</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,·2,·3},·{ideal(x·*·y·-·z^2),·ideal(y·*·z·-·x^2),·ideal(x·*·z·-·y^2)}) | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,·2,·3},·{ideal(x·*·y·-·z^2),·ideal(y·*·z·-·x^2),·ideal(x·*·z·-·y^2)}) |
| 82 | o2·=· | 82 | o2·=·Div(x*y-z^2)·+·2*Div(-x^2+y*z)·+·3*Div(-y^2+x*z) |
| 83 | o2·:·WeilDivisor·on·R</code></pre> | 83 | o2·:·WeilDivisor·on·R</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·isHomogeneous(·D·) | 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·isHomogeneous(·D·) |
| 87 | o3·=·true</code></pre> | 87 | o3·=·true</code></pre> |
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| 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 | This·function·returns·true·if·the·divisor·is·graded·(homogeneous),·otherwise·it | 17 | This·function·returns·true·if·the·divisor·is·graded·(homogeneous),·otherwise·it |
| 18 | returns·false. | 18 | returns·false. |
| 19 | i1·:·R·=·QQ[x,·y,·z]; | 19 | i1·:·R·=·QQ[x,·y,·z]; |
| 20 | i2·:·D·=·divisor({1,·2,·3},·{ideal(x·*·y·-·z^2),·ideal(y·*·z·-·x^2),·ideal(x·* | 20 | i2·:·D·=·divisor({1,·2,·3},·{ideal(x·*·y·-·z^2),·ideal(y·*·z·-·x^2),·ideal(x·* |
| 21 | z·-·y^2)}) | 21 | z·-·y^2)}) |
| 22 | o2·=· | 22 | o2·=·Div(x*y-z^2)·+·2*Div(-x^2+y*z)·+·3*Div(-y^2+x*z) |
| 23 | o2·:·WeilDivisor·on·R | 23 | o2·:·WeilDivisor·on·R |
| 24 | i3·:·isHomogeneous(·D·) | 24 | i3·:·isHomogeneous(·D·) |
| 25 | o3·=·true | 25 | o3·=·true |
| 26 | i4·:·R·=·QQ[x,·y,·z]; | 26 | i4·:·R·=·QQ[x,·y,·z]; |
| 27 | i5·:·D·=·divisor({1,·2},·{ideal(x·*·y·-·z^2),·ideal(y^2·-·z^3)}) | 27 | i5·:·D·=·divisor({1,·2},·{ideal(x·*·y·-·z^2),·ideal(y^2·-·z^3)}) |
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| 80 | ········<table·class="examples"> | 80 | ········<table·class="examples"> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·);</code></pre> | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·);</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,·-2},·{ideal(x,·z),·ideal(y,·z)}) | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·D·=·divisor({1,·-2},·{ideal(x,·z),·ideal(y,·z)}) |
| 86 | o2·=·Div( | 86 | o2·=·-2*Div(y,·z)·+·Div(x,·z) |
| 87 | o2·:·WeilDivisor·on·R</code></pre> | 87 | o2·:·WeilDivisor·on·R</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·isSNC(·D·) | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·isSNC(·D·) |
| 91 | o3·=·false</code></pre> | 91 | o3·=·false</code></pre> |
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| 16 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e, | 16 | ··········o·a·_\x8B_\x8o_\x8o_\x8l_\x8e_\x8a_\x8n_\x8·_\x8v_\x8a_\x8l_\x8u_\x8e, |
| 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·function·returns·true·if·the·divisor·is·simple·normal·crossings,·this | 18 | This·function·returns·true·if·the·divisor·is·simple·normal·crossings,·this |
| 19 | includes·checking·that·the·ambient·ring·is·regular. | 19 | includes·checking·that·the·ambient·ring·is·regular. |
| 20 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); | 20 | i1·:·R·=·QQ[x,·y,·z]·/·ideal(x·*·y·-·z^2·); |
| 21 | i2·:·D·=·divisor({1,·-2},·{ideal(x,·z),·ideal(y,·z)}) | 21 | i2·:·D·=·divisor({1,·-2},·{ideal(x,·z),·ideal(y,·z)}) |
| 22 | o2·=·Div( | 22 | o2·=·-2*Div(y,·z)·+·Div(x,·z) |
| 23 | o2·:·WeilDivisor·on·R | 23 | o2·:·WeilDivisor·on·R |
| 24 | i3·:·isSNC(·D·) | 24 | i3·:·isSNC(·D·) |
| 25 | o3·=·false | 25 | o3·=·false |
| 26 | i4·:·R·=·QQ[x,·y]; | 26 | i4·:·R·=·QQ[x,·y]; |
| 27 | i5·:·D·=·divisor(x*y*(x+y)) | 27 | i5·:·D·=·divisor(x*y*(x+y)) |
| Offset 230, 21 lines modified | Offset 230, 21 lines modified | ||
| 230 | ··········<tr> | 230 | ··········<tr> |
| 231 | <td>··············<pre><code·class="language-macaulay2">i22·:·J·=·I^21; | 231 | <td>··············<pre><code·class="language-macaulay2">i22·:·J·=·I^21; |
| 232 | o22·:·Ideal·of·R</code></pre> | 232 | o22·:·Ideal·of·R</code></pre> |
| 233 | </td>··········</tr> | 233 | </td>··········</tr> |
| 234 | ··········<tr> | 234 | ··········<tr> |
| 235 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·reflexify(J); | 235 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·reflexify(J); |
| 236 | ·--·used·0.1 | 236 | ·--·used·0.129371s·(cpu);·0.12711s·(thread);·0s·(gc) |
| 237 | o23·:·Ideal·of·R</code></pre> | 237 | o23·:·Ideal·of·R</code></pre> |
| 238 | </td>··········</tr> | 238 | </td>··········</tr> |
| 239 | ··········<tr> | 239 | ··········<tr> |
| 240 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·reflexify(J*R^1); | 240 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·reflexify(J*R^1); |
| 241 | ·--·used·0.3 | 241 | ·--·used·0.308069s·(cpu);·0.267614s·(thread);·0s·(gc)</code></pre> |
| 242 | </td>··········</tr> | 242 | </td>··········</tr> |
| 243 | ········</table> | 243 | ········</table> |
| 244 | ········<div> | 244 | ········<div> |
| 245 | ··········<p>Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at·least·if·the·module·embeds·as·an·ideal).</p> | 245 | ··········<p>Because·of·this,·there·are·two·strategies·for·computing·a·reflexification·(at·least·if·the·module·embeds·as·an·ideal).</p> |
| 246 | ········</div> | 246 | ········</div> |
| 247 | ········<div> | 247 | ········<div> |
| 248 | ··········<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> | 248 | ··········<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 270, 42 lines modified | Offset 270, 42 lines modified | ||
| 270 | o27·:·Ideal·of·R</code></pre> | 270 | o27·:·Ideal·of·R</code></pre> |
| 271 | </td>··········</tr> | 271 | </td>··········</tr> |
| 272 | ··········<tr> | 272 | ··········<tr> |
| 273 | <td>··············<pre><code·class="language-macaulay2">i28·:·M·=·J*R^1;</code></pre> | 273 | <td>··············<pre><code·class="language-macaulay2">i28·:·M·=·J*R^1;</code></pre> |
| 274 | </td>··········</tr> | 274 | </td>··········</tr> |
| 275 | ··········<tr> | 275 | ··········<tr> |
| 276 | <td>··············<pre><code·class="language-macaulay2">i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) | 276 | <td>··············<pre><code·class="language-macaulay2">i29·:·J1·=·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 277 | ·--·used·0.1 | 277 | ·--·used·0.132441s·(cpu);·0.0901738s·(thread);·0s·(gc) |
| 278 | ··············2············2·····9·······9···11 | 278 | ··············2············2·····9·······9···11 |
| 279 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 279 | o29·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 280 | o29·:·Ideal·of·R</code></pre> | 280 | o29·:·Ideal·of·R</code></pre> |
| 281 | </td>··········</tr> | 281 | </td>··········</tr> |
| 282 | ··········<tr> | 282 | ··········<tr> |
| 283 | <td>··············<pre><code·class="language-macaulay2">i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 283 | <td>··············<pre><code·class="language-macaulay2">i30·:·J2·=·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 284 | ·--·used·4. | 284 | ·--·used·4.92606s·(cpu);·3.70073s·(thread);·0s·(gc) |
| 285 | ··············2············2·····9·······9···11 | 285 | ··············2············2·····9·······9···11 |
| 286 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) | 286 | o30·=·ideal·(x··+·5x*y·+·3y·,·x*z··-·4y*z·,·z···+·x·-·4y) |
| 287 | o30·:·Ideal·of·R</code></pre> | 287 | o30·:·Ideal·of·R</code></pre> |
| 288 | </td>··········</tr> | 288 | </td>··········</tr> |
| 289 | ··········<tr> | 289 | ··········<tr> |
| 290 | <td>··············<pre><code·class="language-macaulay2">i31·:·J1·==·J2 | 290 | <td>··············<pre><code·class="language-macaulay2">i31·:·J1·==·J2 |
| 291 | o31·=·true</code></pre> | 291 | o31·=·true</code></pre> |
| 292 | </td>··········</tr> | 292 | </td>··········</tr> |
| 293 | ··········<tr> | 293 | ··········<tr> |
| 294 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 294 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 295 | ·--·used·5.0 | 295 | ·--·used·5.03995s·(cpu);·4.01795s·(thread);·0s·(gc)</code></pre> |
| 296 | </td>··········</tr> | 296 | </td>··········</tr> |
| 297 | ··········<tr> | 297 | ··········<tr> |
| 298 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 298 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 299 | ·--·used·0. | 299 | ·--·used·0.609443s·(cpu);·0.309426s·(thread);·0s·(gc)</code></pre> |
| 300 | </td>··········</tr> | 300 | </td>··········</tr> |
| 301 | ········</table> | 301 | ········</table> |
| 302 | ········<div> | 302 | ········<div> |
| 303 | ··········<p>However,·sometimes·<span·class="tt">ModuleStrategy</span>·is·faster,·especially·for·Monomial·ideals.</p> | 303 | ··········<p>However,·sometimes·<span·class="tt">ModuleStrategy</span>·is·faster,·especially·for·Monomial·ideals.</p> |
| 304 | ········</div> | 304 | ········</div> |
| 305 | ········<table·class="examples"> | 305 | ········<table·class="examples"> |
| 306 | ··········<tr> | 306 | ··········<tr> |
| Offset 322, 49 lines modified | Offset 322, 49 lines modified | ||
| 322 | o36·:·Ideal·of·R</code></pre> | 322 | o36·:·Ideal·of·R</code></pre> |
| 323 | </td>··········</tr> | 323 | </td>··········</tr> |
| 324 | ··········<tr> | 324 | ··········<tr> |
| 325 | <td>··············<pre><code·class="language-macaulay2">i37·:·M·=·I^20*R^1;</code></pre> | 325 | <td>··············<pre><code·class="language-macaulay2">i37·:·M·=·I^20*R^1;</code></pre> |
| 326 | </td>··········</tr> | 326 | </td>··········</tr> |
| 327 | ··········<tr> | 327 | ··········<tr> |
| 328 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) | 328 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·reflexify(·J,·Strategy=>IdealStrategy·) |
| 329 | ·--·used·0. | 329 | ·--·used·0.697877s·(cpu);·0.234957s·(thread);·0s·(gc) |
| 330 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· | 330 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· |
| 331 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 331 | o38·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 332 | ······----------------------------------------------------------------------- | 332 | ······----------------------------------------------------------------------- |
| 333 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· | 333 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· |
| 334 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 334 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 335 | ······----------------------------------------------------------------------- | 335 | ······----------------------------------------------------------------------- |
| 336 | ·······19····20 | 336 | ·······19····20 |
| 337 | ······x··u,·x··) | 337 | ······x··u,·x··) |
| 338 | o38·:·Ideal·of·R</code></pre> | 338 | o38·:·Ideal·of·R</code></pre> |
| 339 | </td>··········</tr> | 339 | </td>··········</tr> |
| 340 | ··········<tr> | 340 | ··········<tr> |
| 341 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) | 341 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·reflexify(·J,·Strategy=>ModuleStrategy·) |
| 342 | ·--·used·0. | 342 | ·--·used·0.211058s·(cpu);·0.0447583s·(thread);·0s·(gc) |
| 343 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· | 343 | ··············20·····19···2·18···3·17···4·16···5·15···6·14···7·13···8·12· |
| 344 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, | 344 | o39·=·ideal·(u··,·x*u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··,·x·u··, |
| 345 | ······----------------------------------------------------------------------- | 345 | ······----------------------------------------------------------------------- |
| 346 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· | 346 | ·······9·11···10·10···11·9···12·8···13·7···14·6···15·5···16·4···17·3···18·2· |
| 347 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, | 347 | ······x·u··,·x··u··,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·,·x··u·, |
| 348 | ······----------------------------------------------------------------------- | 348 | ······----------------------------------------------------------------------- |
| 349 | ·······19····20 | 349 | ·······19····20 |
| 350 | ······x··u,·x··) | 350 | ······x··u,·x··) |
| 351 | o39·:·Ideal·of·R</code></pre> | 351 | o39·:·Ideal·of·R</code></pre> |
| 352 | </td>··········</tr> | 352 | </td>··········</tr> |
| 353 | ··········<tr> | 353 | ··········<tr> |
| 354 | <td>··············<pre><code·class="language-macaulay2">i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); | 354 | <td>··············<pre><code·class="language-macaulay2">i40·:·time·reflexify(·M,·Strategy=>IdealStrategy·); |
| 355 | ·--·used·0.1 | 355 | ·--·used·0.0319051s·(cpu);·0.0315516s·(thread);·0s·(gc)</code></pre> |
| 356 | </td>··········</tr> | 356 | </td>··········</tr> |
| 357 | ··········<tr> | 357 | ··········<tr> |
| 358 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 358 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 359 | ·--·used·0.00 | 359 | ·--·used·0.00188358s·(cpu);·0.00514914s·(thread);·0s·(gc)</code></pre> |
| 360 | </td>··········</tr> | 360 | </td>··········</tr> |
| 361 | ········</table> | 361 | ········</table> |
| 362 | ········<div> | 362 | ········<div> |
| 363 | ··········<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 | ··········<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> |
| 364 | ········</div> | 364 | ········</div> |
| 365 | ········<div> | 365 | ········<div> |
| 366 | ··········<p>Consider·the·following·example·showing·the·importance·of·making·the·correct·assumption·about·the·ring·being·a·domain.</p> | 366 | ··········<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·0.1 | 120 | ·--·used·0.129371s·(cpu);·0.12711s·(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·0.3 | 123 | ·--·used·0.308069s·(cpu);·0.267614s·(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·0.1 | 145 | ·--·used·0.132441s·(cpu);·0.0901738s·(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·4. | 150 | ·--·used·4.92606s·(cpu);·3.70073s·(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·5.0 | 157 | ·--·used·5.03995s·(cpu);·4.01795s·(thread);·0s·(gc) |
| 158 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 158 | i33·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 159 | ·--·used·0. | 159 | ·--·used·0.609443s·(cpu);·0.309426s·(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·0.697877s·(cpu);·0.234957s·(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. | 179 | ·--·used·0.211058s·(cpu);·0.0447583s·(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·0.1 | 190 | ·--·used·0.0319051s·(cpu);·0.0315516s·(thread);·0s·(gc) |
| 191 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); | 191 | i41·:·time·reflexify(·M,·Strategy=>ModuleStrategy·); |
| 192 | ·--·used·0.00 | 192 | ·--·used·0.00188358s·(cpu);·0.00514914s·(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 115, 26 lines modified | Offset 115, 26 lines modified | ||
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal(x-z,y-2*z); | 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal(x-z,y-2*z); |
| 117 | o6·:·Ideal·of·R</code></pre> | 117 | o6·:·Ideal·of·R</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·J20a·=·reflexivePower(20,·I); | 120 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·J20a·=·reflexivePower(20,·I); |
| 121 | ·--·used·0.02 | 121 | ·--·used·0.0237094s·(cpu);·0.0224293s·(thread);·0s·(gc) |
| 122 | o7·:·Ideal·of·R</code></pre> | 122 | o7·:·Ideal·of·R</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i8·:·I20·=·I^20; | 125 | <td>··············<pre><code·class="language-macaulay2">i8·:·I20·=·I^20; |
| 126 | o8·:·Ideal·of·R</code></pre> | 126 | o8·:·Ideal·of·R</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J20b·=·reflexify(I20); | 129 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J20b·=·reflexify(I20); |
| 130 | ·--·used·0.1 | 130 | ·--·used·0.152776s·(cpu);·0.112704s·(thread);·0s·(gc) |
| 131 | o9·:·Ideal·of·R</code></pre> | 131 | o9·:·Ideal·of·R</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i10·:·J20a·==·J20b | 134 | <td>··············<pre><code·class="language-macaulay2">i10·:·J20a·==·J20b |
| 135 | o10·=·true</code></pre> | 135 | o10·=·true</code></pre> |
| Offset 150, 21 lines modified | Offset 150, 21 lines modified | ||
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal(x-z,y-2*z); | 151 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal(x-z,y-2*z); |
| 152 | o12·:·Ideal·of·R</code></pre> | 152 | o12·:·Ideal·of·R</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); | 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·J1·=·reflexivePower(20,·I,·Strategy=>IdealStrategy); |
| 156 | ·--·used·0.02 | 156 | ·--·used·0.0238286s·(cpu);·0.0245194s·(thread);·0s·(gc) |
| 157 | o13·:·Ideal·of·R</code></pre> | 157 | o13·:·Ideal·of·R</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); | 160 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·J2·=·reflexivePower(20,·I,·Strategy=>ModuleStrategy); |
| 161 | ·--·used·0.0 | 161 | ·--·used·0.0476995s·(cpu);·0.0502523s·(thread);·0s·(gc) |
| 162 | o14·:·Ideal·of·R</code></pre> | 162 | o14·:·Ideal·of·R</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i15·:·J1·==·J2 | 165 | <td>··············<pre><code·class="language-macaulay2">i15·:·J1·==·J2 |
| 166 | o15·=·true</code></pre> | 166 | 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·0.02 | 47 | ·--·used·0.0237094s·(cpu);·0.0224293s·(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·0.1 | 52 | ·--·used·0.152776s·(cpu);·0.112704s·(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·0.02 | 62 | ·--·used·0.0238286s·(cpu);·0.0245194s·(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·0.0 | 65 | ·--·used·0.0476995s·(cpu);·0.0502523s·(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, |
| Offset 93, 15 lines modified | Offset 93, 15 lines modified | ||
| 93 | o4·=·Div(x) | 93 | o4·=·Div(x) |
| 94 | o4·:·QWeilDivisor·on·R</code></pre> | 94 | o4·:·QWeilDivisor·on·R</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·F·=·divisor({3,·0,·-2},·{ideal(x),·ideal(y),·ideal(x+y)}) | 97 | <td>··············<pre><code·class="language-macaulay2">i5·:·F·=·divisor({3,·0,·-2},·{ideal(x),·ideal(y),·ideal(x+y)}) |
| 98 | o5·=· | 98 | o5·=·-2*Div(x+y)·+·3*Div(x)·+·0*Div(y) |
| 99 | o5·:·WeilDivisor·on·R</code></pre> | 99 | o5·:·WeilDivisor·on·R</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, 15 lines modified | Offset 25, 15 lines modified | ||
| 25 | i4·:·toQWeilDivisor(E) | 25 | i4·:·toQWeilDivisor(E) |
| 26 | o4·=·Div(x) | 26 | o4·=·Div(x) |
| 27 | o4·:·QWeilDivisor·on·R | 27 | o4·:·QWeilDivisor·on·R |
| 28 | i5·:·F·=·divisor({3,·0,·-2},·{ideal(x),·ideal(y),·ideal(x+y)}) | 28 | i5·:·F·=·divisor({3,·0,·-2},·{ideal(x),·ideal(y),·ideal(x+y)}) |
| 29 | o5·=· | 29 | o5·=·-2*Div(x+y)·+·3*Div(x)·+·0*Div(y) |
| 30 | o5·:·WeilDivisor·on·R | 30 | o5·:·WeilDivisor·on·R |
| 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 | ····*·_\x8t_\x8o_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·create·a·Weil·divisor·from·a·Q·or·R-divisor | 32 | ····*·_\x8t_\x8o_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·create·a·Weil·divisor·from·a·Q·or·R-divisor |
| 33 | ····*·_\x8t_\x8o_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·create·a·R-divisor·from·a·Q·or·Weil·divisor | 33 | ····*·_\x8t_\x8o_\x8R_\x8W_\x8e_\x8i_\x8l_\x8D_\x8i_\x8v_\x8i_\x8s_\x8o_\x8r·--·create·a·R-divisor·from·a·Q·or·Weil·divisor |
| 34 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·t\x8to\x8oQ\x8QW\x8We\x8ei\x8il\x8lD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r·:\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\x8to\x8oQ\x8QW\x8We\x8ei\x8il\x8lD\x8Di\x8iv\x8vi\x8is\x8so\x8or\x8r·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 35 | ····*·toQWeilDivisor(QWeilDivisor) | 35 | ····*·toQWeilDivisor(QWeilDivisor) |
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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=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 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"·=>·{{b,·c},·{a,·e},·{c,·d}}} |
| 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 2, 18 lines modified | Offset 2, 26 lines modified | ||
| 2 | i1·:·R·=·QQ[x_1..x_5]; | 2 | i1·:·R·=·QQ[x_1..x_5]; |
| 3 | i2·:·randomHyperGraph(R,{3,2,4}) | 3 | i2·:·randomHyperGraph(R,{3,2,4}) |
| 4 | i3·:·randomHyperGraph(R,{3,2,4}) | 4 | i3·:·randomHyperGraph(R,{3,2,4}) |
| 5 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | ||
| 6 | ······························1···2···5·····1···3·····2···3···4···5 | ||
| 7 | ················"ring"·=>·R | ||
| 8 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | ||
| 9 | ································1···2···3···4···5 | ||
| 10 | o3·:·HyperGraph | ||
| 5 | i4·:·randomHyperGraph(R,{3,2,4}) | 11 | i4·:·randomHyperGraph(R,{3,2,4}) |
| 6 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | 12 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} |
| 7 | ······························1··· | 13 | ······························1···4···5·····3···5·····1···2···3···4 |
| 8 | ················"ring"·=>·R | 14 | ················"ring"·=>·R |
| 9 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | 15 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} |
| 10 | ································1···2···3···4···5 | 16 | ································1···2···3···4···5 |
| 11 | o4·:·HyperGraph | 17 | o4·:·HyperGraph |
| 12 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached | 18 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch·limit·reached |
| Offset 3, 15 lines modified | Offset 3, 15 lines modified | ||
| 3 | i1·:·R·=·QQ[x_1..x_6]; | 3 | i1·:·R·=·QQ[x_1..x_6]; |
| 4 | i2·:·C·=·cycle·R;·--·a·6-cycle | 4 | i2·:·C·=·cycle·R;·--·a·6-cycle |
| 5 | i3·:·spanningTree·C | 5 | i3·:·spanningTree·C |
| 6 | o3·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} | 6 | o3·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} |
| 7 | ·························1···2····· | 7 | ·························1···2·····3···4·····4···5·····1···6·····5···6 |
| 8 | ···········"ring"·=>·R | 8 | ···········"ring"·=>·R |
| 9 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} | 9 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} |
| 10 | ···························1···2···3···4···5···6 | 10 | ···························1···2···3···4···5···6 |
| 11 | o3·:·Graph | 11 | o3·:·Graph |
| 12 | i4·:·T·=·graph·{x_1*x_2,x_2*x_3,·x_1*x_4,x_1*x_5,x_5*x_6};·--·a·tree·(no·cycles) | 12 | i4·:·T·=·graph·{x_1*x_2,x_2*x_3,·x_1*x_4,x_1*x_5,x_5*x_6};·--·a·tree·(no·cycles) |
| Offset 21, 15 lines modified | Offset 21, 15 lines modified | ||
| 21 | o5·=·true | 21 | o5·=·true |
| 22 | i6·:·G·=·graph·{x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4};·--·two·three·cycles | 22 | i6·:·G·=·graph·{x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4};·--·two·three·cycles |
| 23 | i7·:·spanningTree·G | 23 | i7·:·spanningTree·G |
| 24 | o7·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} | 24 | o7·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} |
| 25 | ·························1··· | 25 | ·························1···3·····2···3·····4···6·····5···6 |
| 26 | ···········"ring"·=>·R | 26 | ···········"ring"·=>·R |
| 27 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} | 27 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} |
| 28 | ···························1···2···3···4···5···6 | 28 | ···························1···2···3···4···5···6 |
| 29 | o7·:·Graph | 29 | o7·:·Graph |
| 30 | i8·:· | 30 | i8·:· |
| Offset 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | o3·=·{{a,·b},·{d,·e}} | 92 | o3·=·{{a,·b},·{d,·e}} |
| 93 | o3·:·List</code></pre> | 93 | o3·:·List</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·gprime·=·deleteEdges·(g,T) | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·gprime·=·deleteEdges·(g,T) |
| 97 | o4·=·HyperGraph{"edges"·=>·{{ | 97 | o4·=·HyperGraph{"edges"·=>·{{b,·c},·{a,·e},·{c,·d}}} |
| 98 | ················"ring"·=>·S | 98 | ················"ring"·=>·S |
| 99 | ················"vertices"·=>·{a,·b,·c,·d,·e} | 99 | ················"vertices"·=>·{a,·b,·c,·d,·e} |
| 100 | o4·:·HyperGraph</code></pre> | 100 | o4·:·HyperGraph</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·h·=·hyperGraph·{a*b*c,c*d*e,a*e} | 103 | <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"·=>·{{b,·c},·{a,·e},·{c,·d}}} |
| 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 85, 21 lines modified | Offset 85, 29 lines modified | ||
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x_1..x_5];</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[x_1..x_5];</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·randomHyperGraph(R,{3,2,4})</code></pre> | 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·randomHyperGraph(R,{3,2,4})</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·randomHyperGraph(R,{3,2,4}) | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·randomHyperGraph(R,{3,2,4}) |
| 93 | o3·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | ||
| 94 | ······························1···2···5·····1···3·····2···3···4···5 | ||
| 95 | ················"ring"·=>·R | ||
| 96 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | ||
| 97 | ································1···2···3···4···5 | ||
| 98 | o3·:·HyperGraph</code></pre> | ||
| 93 | </td>··········</tr> | 99 | </td>··········</tr> |
| 94 | ··········<tr> | 100 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomHyperGraph(R,{3,2,4}) | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomHyperGraph(R,{3,2,4}) |
| 96 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | 102 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} |
| 97 | ······························1··· | 103 | ······························1···4···5·····3···5·····1···2···3···4 |
| 98 | ················"ring"·=>·R | 104 | ················"ring"·=>·R |
| 99 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | 105 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} |
| 100 | ································1···2···3···4···5 | 106 | ································1···2···3···4···5 |
| 101 | o4·:·HyperGraph</code></pre> | 107 | o4·:·HyperGraph</code></pre> |
| 102 | </td>··········</tr> | 108 | </td>··········</tr> |
| 103 | ··········<tr> | 109 | ··········<tr> |
| Offset 24, 18 lines modified | Offset 24, 26 lines modified | ||
| 24 | sizes·using·a·random·recursive·algorithm.·Limits·can·be·placed·on·the·both | 24 | sizes·using·a·random·recursive·algorithm.·Limits·can·be·placed·on·the·both |
| 25 | number·of·recursive·steps·taken·(see·_\x8B_\x8r_\x8a_\x8n_\x8c_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t)·and·on·the·time·taken·(see | 25 | number·of·recursive·steps·taken·(see·_\x8B_\x8r_\x8a_\x8n_\x8c_\x8h_\x8L_\x8i_\x8m_\x8i_\x8t)·and·on·the·time·taken·(see |
| 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·}}} | ||
| 32 | ······························1···2···5·····1···3·····2···3···4···5 | ||
| 33 | ················"ring"·=>·R | ||
| 34 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | ||
| 35 | ································1···2···3···4···5 | ||
| 36 | o3·:·HyperGraph | ||
| 31 | i4·:·randomHyperGraph(R,{3,2,4}) | 37 | i4·:·randomHyperGraph(R,{3,2,4}) |
| 32 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} | 38 | o4·=·HyperGraph{"edges"·=>·{{x·,·x·,·x·},·{x·,·x·},·{x·,·x·,·x·,·x·}}} |
| 33 | ······························1··· | 39 | ······························1···4···5·····3···5·····1···2···3···4 |
| 34 | ················"ring"·=>·R | 40 | ················"ring"·=>·R |
| 35 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} | 41 | ················"vertices"·=>·{x·,·x·,·x·,·x·,·x·} |
| 36 | ································1···2···3···4···5 | 42 | ································1···2···3···4···5 |
| 37 | o4·:·HyperGraph | 43 | o4·:·HyperGraph |
| 38 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch | 44 | i5·:·randomHyperGraph(R,{4,4,2,2})·--·impossible,·returns·null·when·time/branch |
| 39 | limit·reached | 45 | limit·reached |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·C·=·cycle·R;·--·a·6-cycle</code></pre> | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·C·=·cycle·R;·--·a·6-cycle</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·spanningTree·C | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·spanningTree·C |
| 83 | o3·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} | 83 | o3·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} |
| 84 | ·························1···2····· | 84 | ·························1···2·····3···4·····4···5·····1···6·····5···6 |
| 85 | ···········"ring"·=>·R | 85 | ···········"ring"·=>·R |
| 86 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} | 86 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} |
| 87 | ···························1···2···3···4···5···6 | 87 | ···························1···2···3···4···5···6 |
| 88 | o3·:·Graph</code></pre> | 88 | o3·:·Graph</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| Offset 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·G·=·graph·{x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4};·--·two·three·cycles</code></pre> | 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·G·=·graph·{x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4};·--·two·three·cycles</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·spanningTree·G | 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·spanningTree·G |
| 105 | o7·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} | 105 | o7·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} |
| 106 | ·························1··· | 106 | ·························1···3·····2···3·····4···6·····5···6 |
| 107 | ···········"ring"·=>·R | 107 | ···········"ring"·=>·R |
| 108 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} | 108 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} |
| 109 | ···························1···2···3···4···5···6 | 109 | ···························1···2···3···4···5···6 |
| 110 | o7·:·Graph</code></pre> | 110 | o7·:·Graph</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| Offset 14, 15 lines modified | Offset 14, 15 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 | This·function·returns·a·breadth·first·spanning·tree·of·a·graph. | 15 | This·function·returns·a·breadth·first·spanning·tree·of·a·graph. |
| 16 | i1·:·R·=·QQ[x_1..x_6]; | 16 | i1·:·R·=·QQ[x_1..x_6]; |
| 17 | i2·:·C·=·cycle·R;·--·a·6-cycle | 17 | i2·:·C·=·cycle·R;·--·a·6-cycle |
| 18 | i3·:·spanningTree·C | 18 | i3·:·spanningTree·C |
| 19 | o3·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} | 19 | o3·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} |
| 20 | ·························1···2····· | 20 | ·························1···2·····3···4·····4···5·····1···6·····5···6 |
| 21 | ···········"ring"·=>·R | 21 | ···········"ring"·=>·R |
| 22 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} | 22 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} |
| 23 | ···························1···2···3···4···5···6 | 23 | ···························1···2···3···4···5···6 |
| 24 | o3·:·Graph | 24 | o3·:·Graph |
| 25 | i4·:·T·=·graph·{x_1*x_2,x_2*x_3,·x_1*x_4,x_1*x_5,x_5*x_6};·--·a·tree·(no | 25 | i4·:·T·=·graph·{x_1*x_2,x_2*x_3,·x_1*x_4,x_1*x_5,x_5*x_6};·--·a·tree·(no |
| 26 | cycles) | 26 | cycles) |
| Offset 30, 15 lines modified | Offset 30, 15 lines modified | ||
| 30 | o5·=·true | 30 | o5·=·true |
| 31 | i6·:·G·=·graph·{x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4};·--·two·three | 31 | i6·:·G·=·graph·{x_1*x_2,x_2*x_3,x_3*x_1,x_4*x_5,x_5*x_6,x_6*x_4};·--·two·three |
| 32 | cycles | 32 | cycles |
| 33 | i7·:·spanningTree·G | 33 | i7·:·spanningTree·G |
| 34 | o7·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} | 34 | o7·=·Graph{"edges"·=>·{{x·,·x·},·{x·,·x·},·{x·,·x·},·{x·,·x·}}} |
| 35 | ·························1··· | 35 | ·························1···3·····2···3·····4···6·····5···6 |
| 36 | ···········"ring"·=>·R | 36 | ···········"ring"·=>·R |
| 37 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} | 37 | ···········"vertices"·=>·{x·,·x·,·x·,·x·,·x·,·x·} |
| 38 | ···························1···2···3···4···5···6 | 38 | ···························1···2···3···4···5···6 |
| 39 | o7·:·Graph | 39 | o7·:·Graph |
| 40 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sp\x8pa\x8an\x8nn\x8ni\x8in\x8ng\x8gT\x8Tr\x8re\x8ee\x8e·:\x8:·*\x8**\x8**\x8**\x8**\x8* | 40 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·s\x8sp\x8pa\x8an\x8nn\x8ni\x8in\x8ng\x8gT\x8Tr\x8re\x8ee\x8e·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 41 | ····*·spanningTree(Graph) | 41 | ····*·spanningTree(Graph) |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0. | 20 | ·--·0.209902·seconds·elapsed |
| 21 | i4·:·#sols·--·156·solutions | 21 | i4·:·#sols·--·156·solutions |
| 22 | o4·=·156 | 22 | o4·=·156 |
| 23 | i5·:· | 23 | i5·:· |
| Offset 69, 15 lines modified | Offset 69, 15 lines modified | ||
| 69 | ·····------------------------------------------------------------------------ | 69 | ·····------------------------------------------------------------------------ |
| 70 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) | 70 | ·····a*b*d*e*f·+·a*c*d*e*f·+·b*c*d*e*f,·a*b*c*d*e*f·-·1) |
| 71 | o2·:·Ideal·of·QQ[a..f]</code></pre> | 71 | o2·:·Ideal·of·QQ[a..f]</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·sols·=·zeroDimSolve·I; | 74 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·sols·=·zeroDimSolve·I; |
| 75 | ·--·0. | 75 | ·--·0.209902·seconds·elapsed</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·#sols·--·156·solutions | 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·#sols·--·156·solutions |
| 79 | o4·=·156</code></pre> | 79 | o4·=·156</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ········</table> | 81 | ········</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 | ·--·0. | 35 | ·--·0.209902·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00401342s·(cpu);·0.00275838s·(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·0.00150306s·(cpu);·0.00128135s·(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·0.00 | 21 | ·--·used·0.00637996s·(cpu);·0.0032604s·(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·0.000 | 26 | ·--·used·0.00035257s·(cpu);·0.00133325s·(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. | 21 | ·--·used·1.36831s·(cpu);·1.23433s·(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·0.0118706s·(cpu);·0.0128323s·(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. | 23 | ·--·used·1.32327s·(cpu);·1.1905s·(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·0.015114s·(cpu);·0.0130378s·(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 101, 24 lines modified | Offset 101, 24 lines modified | ||
| 101 | ······2 | 101 | ······2 |
| 102 | o3·=·x··+·x*c·+·d | 102 | o3·=·x··+·x*c·+·d |
| 103 | o3·:·R</code></pre> | 103 | o3·:·R</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) |
| 107 | ·--·used·0.00 | 107 | ·--·used·0.00401342s·(cpu);·0.00275838s·(thread);·0s·(gc) |
| 108 | ······················2····2·············2···········2 | 108 | ······················2····2·············2···········2 |
| 109 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 109 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 110 | o4·:·Ideal·of·R</code></pre> | 110 | o4·:·Ideal·of·R</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) | 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) |
| 114 | ·--·used·0.00 | 114 | ·--·used·0.00150306s·(cpu);·0.00128135s·(thread);·0s·(gc) |
| 115 | ························2····2·············2···········2 | 115 | ························2····2·············2···········2 |
| 116 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 116 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 117 | o5·:·Ideal·of·R</code></pre> | 117 | o5·:·Ideal·of·R</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<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·0.00401342s·(cpu);·0.00275838s·(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·0.00150306s·(cpu);·0.00128135s·(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 92, 24 lines modified | Offset 92, 24 lines modified | ||
| 92 | ······2 | 92 | ······2 |
| 93 | o3·=·x··+·x*c·+·d | 93 | o3·=·x··+·x*c·+·d |
| 94 | o3·:·R</code></pre> | 94 | o3·:·R</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(x,ideal(f,g)) |
| 98 | ·--·used·0.00 | 98 | ·--·used·0.00637996s·(cpu);·0.0032604s·(thread);·0s·(gc) |
| 99 | ······················2····2·············2···········2 | 99 | ······················2····2·············2···········2 |
| 100 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) | 100 | o4·=·ideal(a*b*c·-·b*c··-·a·d·+·a*c*d·-·b··+·2b*d·-·d·) |
| 101 | o4·:·Ideal·of·R</code></pre> | 101 | o4·:·Ideal·of·R</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) |
| 105 | ·--·used·0.000 | 105 | ·--·used·0.00035257s·(cpu);·0.00133325s·(thread);·0s·(gc) |
| 106 | ························2····2·············2···········2 | 106 | ························2····2·············2···········2 |
| 107 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) | 107 | o5·=·ideal(-·a*b*c·+·b*c··+·a·d·-·a*c*d·+·b··-·2b*d·+·d·) |
| 108 | o5·:·Ideal·of·R</code></pre> | 108 | o5·:·Ideal·of·R</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<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·0.00 | 36 | ·--·used·0.00637996s·(cpu);·0.0032604s·(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·0.000 | 41 | ·--·used·0.00035257s·(cpu);·0.00133325s·(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 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | ······8····5 | 104 | ······8····5 |
| 105 | o3·=·x··+·x··+·x*c·+·d | 105 | o3·=·x··+·x··+·x*c·+·d |
| 106 | o3·:·R</code></pre> | 106 | o3·:·R</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(ideal(f,g),x) | 109 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·eliminate(ideal(f,g),x) |
| 110 | ·--·used·1. | 110 | ·--·used·1.36831s·(cpu);·1.23433s·(thread);·0s·(gc) |
| 111 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 111 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 112 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 112 | o4·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 113 | ·····------------------------------------------------------------------------ | 113 | ·····------------------------------------------------------------------------ |
| 114 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 114 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 115 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 115 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 116 | ·····------------------------------------------------------------------------ | 116 | ·····------------------------------------------------------------------------ |
| Offset 161, 15 lines modified | Offset 161, 15 lines modified | ||
| 161 | ···············3··········4········4 | 161 | ···············3··········4········4 |
| 162 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 162 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 163 | o4·:·Ideal·of·R</code></pre> | 163 | o4·:·Ideal·of·R</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) | 166 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·ideal·resultant(f,g,x) |
| 167 | ·--·used·0.01 | 167 | ·--·used·0.0118706s·(cpu);·0.0128323s·(thread);·0s·(gc) |
| 168 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 168 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 169 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 169 | o5·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 170 | ·····------------------------------------------------------------------------ | 170 | ·····------------------------------------------------------------------------ |
| 171 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 171 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 172 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 172 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 173 | ·····------------------------------------------------------------------------ | 173 | ·····------------------------------------------------------------------------ |
| 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. | 41 | ·--·used·1.36831s·(cpu);·1.23433s·(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·0.0118706s·(cpu);·0.0128323s·(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 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | ······8····5 | 99 | ······8····5 |
| 100 | o4·=·x··+·x··+·x*c·+·d | 100 | o4·=·x··+·x··+·x*c·+·d |
| 101 | o4·:·R</code></pre> | 101 | o4·:·R</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·eliminate(ideal(f,g),x) | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·eliminate(ideal(f,g),x) |
| 105 | ·--·used·1. | 105 | ·--·used·1.32327s·(cpu);·1.1905s·(thread);·0s·(gc) |
| 106 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 106 | ············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 107 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- | 107 | o5·=·ideal(a·b*c·-·a·d·+·a·b··-·b··-·6a·b*c·-·18a·b·c·+·7b·c·+·48a·b·c··- |
| 108 | ·····------------------------------------------------------------------------ | 108 | ·····------------------------------------------------------------------------ |
| 109 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 109 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 110 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ | 110 | ·····21b·c··-·46a·b·c··+·35b·c··+·15a·b*c··-·35b·c··+·21b·c··-·7b·c··+·b*c··+ |
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| Offset 156, 15 lines modified | Offset 156, 15 lines modified | ||
| 156 | ···············3··········4········4 | 156 | ···············3··········4········4 |
| 157 | ·····-·216b*c*d··+·2052a*d··-·1944d·) | 157 | ·····-·216b*c*d··+·2052a*d··-·1944d·) |
| 158 | o5·:·Ideal·of·R</code></pre> | 158 | o5·:·Ideal·of·R</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ··········<tr> | 160 | ··········<tr> |
| 161 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·resultant(f,g,x) | 161 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·ideal·resultant(f,g,x) |
| 162 | ·--·used·0.01 | 162 | ·--·used·0.015114s·(cpu);·0.0130378s·(thread);·0s·(gc) |
| 163 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· | 163 | ··············7·······8·····3·5····8·····6·········3·4······7·······3·3·2·· |
| 164 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ | 164 | o6·=·ideal(-·a·b*c·+·a·d·-·a·b··+·b··+·6a·b*c·+·18a·b·c·-·7b·c·-·48a·b·c··+ |
| 165 | ·····------------------------------------------------------------------------ | 165 | ·····------------------------------------------------------------------------ |
| 166 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· | 166 | ········6·2······3·2·3······5·3······3···4······4·4······3·5·····2·6······7·· |
| 167 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- | 167 | ·····21b·c··+·46a·b·c··-·35b·c··-·15a·b*c··+·35b·c··-·21b·c··+·7b·c··-·b*c··- |
| 168 | ·····------------------------------------------------------------------------ | 168 | ·····------------------------------------------------------------------------ |
| 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. | 36 | ·--·used·1.32327s·(cpu);·1.1905s·(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·0.015114s·(cpu);·0.0130378s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtEZXNjcmlwdGlvbiA9PiAxOihESVZ7UEFSQXtURVh7IlRoaXMg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtEZXNjcmlwdGlvbiA9PiAxOihESVZ7UEFSQXtURVh7IlRoaXMg |
| 11 | cGFja2FnZSBwcm92aWRlcyBzb21lIGZ1bmN0aW9ucyBmb3IgY29tcHV0aW5nIGVsbGlwdGljIGlu | 11 | cGFja2FnZSBwcm92aWRlcyBzb21lIGZ1bmN0aW9ucyBmb3IgY29tcHV0aW5nIGVsbGlwdGljIGlu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
| 11 | YXVsYXkyIGVuZ2luZSIsICJsaW5lbnVtIiA9PiA0NzcsICJmaWxlbmFtZSIgPT4gIkVuZ2luZVRl | 11 | YXVsYXkyIGVuZ2luZSIsICJsaW5lbnVtIiA9PiA0NzcsICJmaWxlbmFtZSIgPT4gIkVuZ2luZVRl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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:·535811417 | 1 | --·-*-·M2-comint·-*-·hash:·535811417 |
| 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·0.0166573s·(cpu);·0.019383s·(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·0.248599s·(cpu);·0.231056s·(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·0.0929804s·(cpu);·0.0965723s·(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·3. | 51 | ·--·used·3.56651s·(cpu);·3.18372s·(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·0.09 | 57 | ·--·used·0.0947383s·(cpu);·0.0951559s·(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·3. | 61 | ·--·used·3.609s·(cpu);·3.21848s·(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·1.1495s·(cpu);·1.01505s·(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·5.42 | 71 | ·--·used·5.04299s·(cpu);·4.14941s·(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·1.22768s·(cpu);·1.07359s·(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·5. | 79 | ·--·used·5.19427s·(cpu);·4.33975s·(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·4.90846s·(cpu);·4.21886s·(thread);·0s·(gc) |
| 84 | o16·=·1139448384 | 84 | o16·=·1139448384 |
| 85 | o16·:·QQ | 85 | o16·:·QQ |
| 86 | i17·:· | 86 | i17·:· |
| Offset 71, 15 lines modified | Offset 71, 15 lines modified | ||
| 71 | ········<div> | 71 | ········<div> |
| 72 | ··········<p>Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in·\mathbb·P^n.</p> | 72 | ··········<p>Computes·the·number·of·lines·on·a·general·hypersurface·of·degree·2n·-·3·in·\mathbb·P^n.</p> |
| 73 | ··········<p></p> | 73 | ··········<p></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·:·time·for·n·from·2·to·10·list·linesHypersurface(n) | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·for·n·from·2·to·10·list·linesHypersurface(n) |
| 78 | ·--·used·0.0 | 78 | ·--·used·0.0166573s·(cpu);·0.019383s·(thread);·0s·(gc) |
| 79 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 79 | o1·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 80 | ·····------------------------------------------------------------------------ | 80 | ·····------------------------------------------------------------------------ |
| 81 | ·····289139638632755625,·520764738758073845321} | 81 | ·····289139638632755625,·520764738758073845321} |
| 82 | o1·:·List</code></pre> | 82 | o1·:·List</code></pre> |
| 83 | </td>··········</tr> | 83 | </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·0.0166573s·(cpu);·0.019383s·(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 141, 39 lines modified | Offset 141, 39 lines modified | ||
| 141 | ········<div> | 141 | ········<div> |
| 142 | ··········<p>The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> | 142 | ··········<p>The·numbers·of·conics·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> |
| 143 | ··········<p></p> | 143 | ··········<p></p> |
| 144 | ········</div> | 144 | ········</div> |
| 145 | ········<table·class="examples"> | 145 | ········<table·class="examples"> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 | 147 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·for·D·in·T·list·rationalCurve(2,D)·-·rationalCurve(1,D)/8 |
| 148 | ·--·used·0.2 | 148 | ·--·used·0.248599s·(cpu);·0.231056s·(thread);·0s·(gc) |
| 149 | o7·=·{609250,·92288,·52812,·22428,·9728} | 149 | o7·=·{609250,·92288,·52812,·22428,·9728} |
| 150 | o7·:·List</code></pre> | 150 | o7·:·List</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| 152 | ········</table> | 152 | ········</table> |
| 153 | ········<div> | 153 | ········<div> |
| 154 | ··········<p>For·rational·curves·of·degree·3:</p> | 154 | ··········<p>For·rational·curves·of·degree·3:</p> |
| 155 | ··········<p></p> | 155 | ··········<p></p> |
| 156 | ········</div> | 156 | ········</div> |
| 157 | ········<table·class="examples"> | 157 | ········<table·class="examples"> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·rationalCurve(3) | 159 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·rationalCurve(3) |
| 160 | ·--·used·0. | 160 | ·--·used·0.0929804s·(cpu);·0.0965723s·(thread);·0s·(gc) |
| 161 | ·····8564575000 | 161 | ·····8564575000 |
| 162 | o8·=·---------- | 162 | o8·=·---------- |
| 163 | ·········27 | 163 | ·········27 |
| 164 | o8·:·QQ</code></pre> | 164 | o8·:·QQ</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·for·D·in·T·list·rationalCurve(3,D) | 167 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·for·D·in·T·list·rationalCurve(3,D) |
| 168 | ·--·used·3. | 168 | ·--·used·3.56651s·(cpu);·3.18372s·(thread);·0s·(gc) |
| 169 | ······8564575000··422690816···········4834592··11239424 | 169 | ······8564575000··422690816···········4834592··11239424 |
| 170 | o9·=·{----------,·---------,·6424365,·-------,·--------} | 170 | o9·=·{----------,·---------,·6424365,·-------,·--------} |
| 171 | ··········27··········27·················3········27 | 171 | ··········27··········27·················3········27 |
| 172 | o9·:·List</code></pre> | 172 | o9·:·List</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| Offset 181, 89 lines modified | Offset 181, 89 lines modified | ||
| 181 | ········<div> | 181 | ········<div> |
| 182 | ··········<p>The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> | 182 | ··········<p>The·number·of·rational·curves·of·degree·3·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> |
| 183 | ··········<p></p> | 183 | ··········<p></p> |
| 184 | ········</div> | 184 | ········</div> |
| 185 | ········<table·class="examples"> | 185 | ········<table·class="examples"> |
| 186 | ··········<tr> | 186 | ··········<tr> |
| 187 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 | 187 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·rationalCurve(3)·-·rationalCurve(1)/27 |
| 188 | ·--·used·0.09 | 188 | ·--·used·0.0947383s·(cpu);·0.0951559s·(thread);·0s·(gc) |
| 189 | o10·=·317206375 | 189 | o10·=·317206375 |
| 190 | o10·:·QQ</code></pre> | 190 | o10·:·QQ</code></pre> |
| 191 | </td>··········</tr> | 191 | </td>··········</tr> |
| 192 | ········</table> | 192 | ········</table> |
| 193 | ········<div> | 193 | ········<div> |
| 194 | ··········<p>The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> | 194 | ··········<p>The·numbers·of·rational·curves·of·degree·3·on·general·complete·intersection·Calabi-Yau·threefolds·can·be·computed·as·follows:</p> |
| 195 | ··········<p></p> | 195 | ··········<p></p> |
| 196 | ········</div> | 196 | ········</div> |
| 197 | ········<table·class="examples"> | 197 | ········<table·class="examples"> |
| 198 | ··········<tr> | 198 | ··········<tr> |
| 199 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 | 199 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·for·D·in·T·list·rationalCurve(3,D)·-·rationalCurve(1,D)/27 |
| 200 | ·--·used·3. | 200 | ·--·used·3.609s·(cpu);·3.21848s·(thread);·0s·(gc) |
| 201 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} | 201 | o11·=·{317206375,·15655168,·6424326,·1611504,·416256} |
| 202 | o11·:·List</code></pre> | 202 | o11·:·List</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ········</table> | 204 | ········</table> |
| 205 | ········<div> | 205 | ········<div> |
| 206 | ··········<p>For·rational·curves·of·degree·4:</p> | 206 | ··········<p>For·rational·curves·of·degree·4:</p> |
| 207 | ··········<p></p> | 207 | ··········<p></p> |
| 208 | ········</div> | 208 | ········</div> |
| 209 | ········<table·class="examples"> | 209 | ········<table·class="examples"> |
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·rationalCurve(4) | 211 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·rationalCurve(4) |
| 212 | ·--·used·1. | 212 | ·--·used·1.1495s·(cpu);·1.01505s·(thread);·0s·(gc) |
| 213 | ······15517926796875 | 213 | ······15517926796875 |
| 214 | o12·=·-------------- | 214 | o12·=·-------------- |
| 215 | ············64 | 215 | ············64 |
| 216 | o12·:·QQ</code></pre> | 216 | o12·:·QQ</code></pre> |
| 217 | </td>··········</tr> | 217 | </td>··········</tr> |
| 218 | ··········<tr> | 218 | ··········<tr> |
| 219 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·rationalCurve(4,{4,2}) | 219 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·rationalCurve(4,{4,2}) |
| 220 | ·--·used·5.42 | 220 | ·--·used·5.04299s·(cpu);·4.14941s·(thread);·0s·(gc) |
| 221 | o13·=·3883914084 | 221 | o13·=·3883914084 |
| 222 | o13·:·QQ</code></pre> | 222 | o13·:·QQ</code></pre> |
| 223 | </td>··········</tr> | 223 | </td>··········</tr> |
| 224 | ········</table> | 224 | ········</table> |
| 225 | ········<div> | 225 | ········<div> |
| 226 | ··········<p>The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> | 226 | ··········<p>The·number·of·rational·curves·of·degree·4·on·a·general·quintic·threefold·can·be·computed·as·follows:</p> |
| 227 | ··········<p></p> | 227 | ··········<p></p> |
| 228 | ········</div> | 228 | ········</div> |
| 229 | ········<table·class="examples"> | 229 | ········<table·class="examples"> |
| 230 | ··········<tr> | 230 | ··········<tr> |
| 231 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 | 231 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalCurve(4)·-·rationalCurve(2)/8 |
| 232 | ·--·used·1. | 232 | ·--·used·1.22768s·(cpu);·1.07359s·(thread);·0s·(gc) |
| 233 | o14·=·242467530000 | 233 | o14·=·242467530000 |
| 234 | o14·:·QQ</code></pre> | 234 | o14·:·QQ</code></pre> |
| 235 | </td>··········</tr> | 235 | </td>··········</tr> |
| 236 | ········</table> | 236 | ········</table> |
| 237 | ········<div> | 237 | ········<div> |
| 238 | ··········<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>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> |
| 239 | ··········<p></p> | 239 | ··········<p></p> |
| 240 | ········</div> | 240 | ········</div> |
| 241 | ········<table·class="examples"> | 241 | ········<table·class="examples"> |
| 242 | ··········<tr> | 242 | ··········<tr> |
| 243 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 | 243 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·rationalCurve(4,{4,2})·-·rationalCurve(2,{4,2})/8 |
| 244 | ·--·used·5. | 244 | ·--·used·5.19427s·(cpu);·4.33975s·(thread);·0s·(gc) |
| 245 | o15·=·3883902528 | 245 | o15·=·3883902528 |
| 246 | o15·:·QQ</code></pre> | 246 | o15·:·QQ</code></pre> |
| 247 | </td>··········</tr> | 247 | </td>··········</tr> |
| 248 | ··········<tr> | 248 | ··········<tr> |
| 249 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 | 249 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·rationalCurve(4,{3,3})·-·rationalCurve(2,{3,3})/8 |
| 250 | ·--·used· | 250 | ·--·used·4.90846s·(cpu);·4.21886s·(thread);·0s·(gc) |
| 251 | o16·=·1139448384 | 251 | o16·=·1139448384 |
| 252 | o16·:·QQ</code></pre> | 252 | o16·:·QQ</code></pre> |
| 253 | </td>··········</tr> | 253 | </td>··········</tr> |
| Max diff block lines reached; 14/4775 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·0.248599s·(cpu);·0.231056s·(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·0.0929804s·(cpu);·0.0965723s·(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·3. | 76 | ·--·used·3.56651s·(cpu);·3.18372s·(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·0.09 | 84 | ·--·used·0.0947383s·(cpu);·0.0951559s·(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·3. | 90 | ·--·used·3.609s·(cpu);·3.21848s·(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·1.1495s·(cpu);·1.01505s·(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·5.42 | 101 | ·--·used·5.04299s·(cpu);·4.14941s·(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·1.22768s·(cpu);·1.07359s·(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·5. | 113 | ·--·used·5.19427s·(cpu);·4.33975s·(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·4.90846s·(cpu);·4.21886s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·.00 | 15 | ·····--·used·.00363182·seconds |
| 16 | ·····--·used·0·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·.00273228·seconds | ||
| 20 | ·····--·used·.00 | 21 | ·····--·used·.00519296·seconds |
| 21 | ·····--·used·.00400402·seconds | ||
| 22 | (16,·26) | 22 | (16,·26) |
| 23 | new·stuff·found | 23 | new·stuff·found |
| 24 | 5 | 24 | 5 |
| 25 | ·····--·used·.00 | 25 | ·····--·used·.00885913·seconds |
| 26 | ·····--·used·.0 | 26 | ·····--·used·.0184731·seconds |
| 27 | (25,·60) | 27 | (25,·60) |
| 28 | 6 | 28 | 6 |
| 29 | ·····--·used·.0152 | 29 | ·····--·used·.0152395·seconds |
| 30 | ·····--·used·.1 | 30 | ·····--·used·.143426·seconds |
| 31 | (36,·120) | 31 | (36,·120) |
| 32 | 7 | 32 | 7 |
| 33 | ·····--·used·.0 | 33 | ·····--·used·.0311025·seconds |
| 34 | ·····--·used·.6 | 34 | ·····--·used·.609062·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 97, 34 lines modified | Offset 97, 34 lines modified | ||
| 97 | ··················1···1·0···1·0···0 | 97 | ··················1···1·0···1·0···0 |
| 98 | o3·:·RingMap·R·<--·S</code></pre> | 98 | o3·:·RingMap·R·<--·S</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·egbToric(m,·OutFile=>stdio) | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·egbToric(m,·OutFile=>stdio) |
| 102 | 3 | 102 | 3 |
| 103 | ·····--·used·.00 | 103 | ·····--·used·.00363182·seconds |
| 104 | ·····--·used·0·seconds | 104 | ·····--·used·0·seconds |
| 105 | (9,·9) | 105 | (9,·9) |
| 106 | new·stuff·found | 106 | new·stuff·found |
| 107 | 4 | 107 | 4 |
| 108 | ·····--·used·.00273228·seconds | ||
| 108 | ·····--·used·.00 | 109 | ·····--·used·.00519296·seconds |
| 109 | ·····--·used·.00400402·seconds | ||
| 110 | (16,·26) | 110 | (16,·26) |
| 111 | new·stuff·found | 111 | new·stuff·found |
| 112 | 5 | 112 | 5 |
| 113 | ·····--·used·.00 | 113 | ·····--·used·.00885913·seconds |
| 114 | ·····--·used·.0 | 114 | ·····--·used·.0184731·seconds |
| 115 | (25,·60) | 115 | (25,·60) |
| 116 | 6 | 116 | 6 |
| 117 | ·····--·used·.0152 | 117 | ·····--·used·.0152395·seconds |
| 118 | ·····--·used·.1 | 118 | ·····--·used·.143426·seconds |
| 119 | (36,·120) | 119 | (36,·120) |
| 120 | 7 | 120 | 7 |
| 121 | ·····--·used·.0 | 121 | ·····--·used·.0311025·seconds |
| 122 | ·····--·used·.6 | 122 | ·····--·used·.609062·seconds |
| 123 | (49,·217) | 123 | (49,·217) |
| 124 | ···································2 | 124 | ···································2 |
| 125 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ | 125 | o4·=·{-·y····+·y···,·-·y···y····+·y···,·-·y···y····+·y···y···,·-·y···y····+ |
| 126 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0·· | 126 | ·········1,0····0,1·····1,1·0,0····1,0·····2,1·0,0····2,0·1,0·····2,1·1,0·· |
| 127 | ·····------------------------------------------------------------------------ | 127 | ·····------------------------------------------------------------------------ |
| 128 | ·····y···y···,·-·y···y····+·y···y···,·-·y···y····+·y···y···,·-·y···y····+ | 128 | ·····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·.00 | 40 | ·····--·used·.00363182·seconds |
| 41 | ·····--·used·0·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·.00273228·seconds | ||
| 45 | ·····--·used·.00 | 46 | ·····--·used·.00519296·seconds |
| 46 | ·····--·used·.00400402·seconds | ||
| 47 | (16,·26) | 47 | (16,·26) |
| 48 | new·stuff·found | 48 | new·stuff·found |
| 49 | 5 | 49 | 5 |
| 50 | ·····--·used·.00 | 50 | ·····--·used·.00885913·seconds |
| 51 | ·····--·used·.0 | 51 | ·····--·used·.0184731·seconds |
| 52 | (25,·60) | 52 | (25,·60) |
| 53 | 6 | 53 | 6 |
| 54 | ·····--·used·.0152 | 54 | ·····--·used·.0152395·seconds |
| 55 | ·····--·used·.1 | 55 | ·····--·used·.143426·seconds |
| 56 | (36,·120) | 56 | (36,·120) |
| 57 | 7 | 57 | 7 |
| 58 | ·····--·used·.0 | 58 | ·····--·used·.0311025·seconds |
| 59 | ·····--·used·.6 | 59 | ·····--·used·.609062·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=7 | 7 | #:len=7 |
| 8 | VGhyZWFkcw== | 8 | VGhyZWFkcw== |
| 9 | #:len=679 | 9 | #:len=679 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gb3B0aW9uIGZvciB2YXJpb3VzIGZ1 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gb3B0aW9uIGZvciB2YXJpb3VzIGZ1 |
| 11 | bmN0aW9ucyIsICJsaW5lbnVtIiA9PiAyMTIwLCBTZWVBbHNvID0+IERJVntIRUFERVIyeyJTZWUg | 11 | bmN0aW9ucyIsICJsaW5lbnVtIiA9PiAyMTIwLCBTZWVBbHNvID0+IERJVntIRUFERVIyeyJTZWUg |
| 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·0.09 | 467 | ·--·used·0.0926647s·(cpu);·0.0913073s·(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·0.295783s·(cpu);·0.1785s·(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·0.32 | 473 | ·--·used·0.329401s·(cpu);·0.240018s·(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·0.23 | 476 | ·--·used·0.23319s·(cpu);·0.165047s·(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·0.237 | 479 | ·--·used·0.237015s·(cpu);·0.150739s·(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. | 482 | ·--·used·0.198512s·(cpu);·0.165398s·(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·0.274583s·(cpu);·0.168375s·(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·1 | 488 | ·--·used·11.7549s·(cpu);·8.16996s·(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·0.281795s·(cpu);·0.258025s·(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·0.466464s·(cpu);·0.408424s·(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·0.38 | 609 | ·--·used·0.308804s·(cpu);·0.267869s·(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· | 612 | ·--·used·2.86051s·(cpu);·2.57045s·(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·0.5 | 614 | ·--·used·0.53384s·(cpu);·0.492477s·(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·2.4 | 617 | ·--·used·2.45237s·(cpu);·2.27144s·(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·1.8 | 619 | ·--·used·1.82772s·(cpu);·1.55502s·(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·0.699402s·(cpu);·0.612712s·(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·2. | 624 | ·--·used·2.06508s·(cpu);·1.75116s·(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·2.4 | 626 | ·--·used·2.44508s·(cpu);·2.13326s·(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·6.78766s·(cpu);·5.68746s·(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·5.48683s·(cpu);·4.60829s·(thread);·0s·(gc) |
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| 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·0.644332s·(cpu);·0.494877s·(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·8. | 14 | ·--·used·8.29738s·(cpu);·6.28396s·(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·1.0 | 94 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.05593s·(cpu);·0.785987s·(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·0.1 | 98 | ·--·used·0.135862s·(cpu);·0.10264s·(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·0.1 | 121 | ·--·used·0.107905s·(cpu);·0.0858087s·(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·0.4 | 143 | ·--·used·0.459622s·(cpu);·0.366591s·(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·0.5 | 171 | ·--·used·0.530465s·(cpu);·0.40864s·(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·0.3 | 220 | ·--·used·0.300366s·(cpu);·0.241727s·(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:·1976012015 | 1 | --·-*-·M2-comint·-*-·hash:·1976012015 |
| 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 | ·--·1.43601·seconds·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 | ·--· | 22 | ·--·0.816981·seconds·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·0.003 | 20 | ·--·used·0.000302355s·(cpu);·0.00225645s·(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·0.00 | 27 | ·--·used·0.00143862s·(cpu);·0.00195208s·(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· | 31 | ·--·used·5.5463e-05s·(cpu);·0.00165724s·(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·0.15 | 11 | ·--·used·0.152643s·(cpu);·0.109336s·(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·0.011 | 14 | ·--·used·0.011221s·(cpu);·0.0113486s·(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·0.331626s·(cpu);·0.334452s·(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·1.16743s·(cpu);·1.0458s·(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·1.21346s·(cpu);·0.996398s·(thread);·0s·(gc) |
| 22 | o8·=·true | 22 | o8·=·true |
| 23 | i9·:·time·regularInCodimension(2,·S) | 23 | i9·:·time·regularInCodimension(2,·S) |
| 24 | ·--·used·5.26 | 24 | ·--·used·5.26304s·(cpu);·4.19769s·(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·0.13 | 29 | ·--·used·0.132359s·(cpu);·0.131444s·(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·0.400783s·(cpu);·0.297457s·(thread);·0s·(gc) |
| 33 | o13·=·true | 33 | o13·=·true |
| 34 | i14·:·time·regularInCodimension(2,·R) | 34 | i14·:·time·regularInCodimension(2,·R) |
| 35 | ·--·used·0.6 | 35 | ·--·used·0.670672s·(cpu);·0.487833s·(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·0.265479s·(cpu);·0.182623s·(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·5. | 393 | internalChooseMinor:·Choosing·--·used·5.3412s·(cpu);·4.15577s·(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·1.09 | 436 | ·--·used·1.09184s·(cpu);·0.913607s·(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·0.1 | 494 | ·--·used·0.105472s·(cpu);·0.0738162s·(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·0.2 | 497 | ·--·used·0.215444s·(cpu);·0.139735s·(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·1.17744s·(cpu);·0.948932s·(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·0.9 | 503 | ·--·used·0.93812s·(cpu);·0.735867s·(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·0.3 | 508 | ·--·used·0.376813s·(cpu);·0.263105s·(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·1.79 | 511 | ·--·used·1.79424s·(cpu);·1.35742s·(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·0.137147s·(cpu);·0.105093s·(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·0.1 | 516 | ·--·used·0.165322s·(cpu);·0.127653s·(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·1.26608s·(cpu);·1.02607s·(thread);·0s·(gc) |
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| Offset 559, 57 lines modified | Offset 559, 57 lines modified | ||
| 559 | ········</table> | 559 | ········</table> |
| 560 | ········<div> | 560 | ········<div> |
| 561 | ··········<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 | ··········<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> |
| 562 | ········</div> | 562 | ········</div> |
| 563 | ········<table·class="examples"> | 563 | ········<table·class="examples"> |
| 564 | ··········<tr> | 564 | ··········<tr> |
| 565 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) | 565 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Random)) |
| 566 | ·--·used·0.09 | 566 | ·--·used·0.0926647s·(cpu);·0.0913073s·(thread);·0s·(gc) |
| 567 | o28·=·2</code></pre> | 567 | o28·=·2</code></pre> |
| 568 | </td>··········</tr> | 568 | </td>··········</tr> |
| 569 | ··········<tr> | 569 | ··········<tr> |
| 570 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) | 570 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallest)) |
| 571 | ·--·used·0.2 | 571 | ·--·used·0.295783s·(cpu);·0.1785s·(thread);·0s·(gc) |
| 572 | o29·=·3</code></pre> | 572 | o29·=·3</code></pre> |
| 573 | </td>··········</tr> | 573 | </td>··········</tr> |
| 574 | ··········<tr> | 574 | ··········<tr> |
| 575 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) | 575 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexSmallestTerm)) |
| 576 | ·--·used·0.32 | 576 | ·--·used·0.329401s·(cpu);·0.240018s·(thread);·0s·(gc) |
| 577 | o30·=·1</code></pre> | 577 | o30·=·1</code></pre> |
| 578 | </td>··········</tr> | 578 | </td>··········</tr> |
| 579 | ··········<tr> | 579 | ··········<tr> |
| 580 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) | 580 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>LexLargest)) |
| 581 | ·--·used·0.23 | 581 | ·--·used·0.23319s·(cpu);·0.165047s·(thread);·0s·(gc) |
| 582 | o31·=·2</code></pre> | 582 | o31·=·2</code></pre> |
| 583 | </td>··········</tr> | 583 | </td>··········</tr> |
| 584 | ··········<tr> | 584 | ··········<tr> |
| 585 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) | 585 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallest)) |
| 586 | ·--·used·0.237 | 586 | ·--·used·0.237015s·(cpu);·0.150739s·(thread);·0s·(gc) |
| 587 | o32·=·3</code></pre> | 587 | o32·=·3</code></pre> |
| 588 | </td>··········</tr> | 588 | </td>··········</tr> |
| 589 | ··········<tr> | 589 | ··········<tr> |
| 590 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm)) | 590 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexSmallestTerm)) |
| 591 | ·--·used·0. | 591 | ·--·used·0.198512s·(cpu);·0.165398s·(thread);·0s·(gc) |
| 592 | o33·=·3</code></pre> | 592 | o33·=·3</code></pre> |
| 593 | </td>··········</tr> | 593 | </td>··········</tr> |
| 594 | ··········<tr> | 594 | ··········<tr> |
| 595 | <td>··············<pre><code·class="language-macaulay2">i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) | 595 | <td>··············<pre><code·class="language-macaulay2">i34·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>GRevLexLargest)) |
| 596 | ·--·used·0.2 | 596 | ·--·used·0.274583s·(cpu);·0.168375s·(thread);·0s·(gc) |
| 597 | o34·=·3</code></pre> | 597 | o34·=·3</code></pre> |
| 598 | </td>··········</tr> | 598 | </td>··········</tr> |
| 599 | ··········<tr> | 599 | ··········<tr> |
| 600 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) | 600 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·dim·(J·+·chooseGoodMinors(8,·6,·M,·J,·Strategy=>Points)) |
| 601 | ·--·used·1 | 601 | ·--·used·11.7549s·(cpu);·8.16996s·(thread);·0s·(gc) |
| 602 | o35·=·1</code></pre> | 602 | o35·=·1</code></pre> |
| 603 | </td>··········</tr> | 603 | </td>··········</tr> |
| 604 | ········</table> | 604 | ········</table> |
| 605 | ········<div> | 605 | ········<div> |
| 606 | ··········<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 | ··········<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> |
| 607 | ········</div> | 607 | ········</div> |
| Offset 630, 15 lines modified | Offset 630, 15 lines modified | ||
| 630 | ········</table> | 630 | ········</table> |
| 631 | ········<div> | 631 | ········<div> |
| 632 | ··········<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 | ··········<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> |
| 633 | ········</div> | 633 | ········</div> |
| 634 | ········<table·class="examples"> | 634 | ········<table·class="examples"> |
| 635 | ··········<tr> | 635 | ··········<tr> |
| 636 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true); | 636 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·chooseGoodMinors(20,·6,·M,·J,·Strategy=>StrategyDefault,·Verbose=>true); |
| 637 | ·--·used·0. | 637 | ·--·used·0.281795s·(cpu);·0.258025s·(thread);·0s·(gc) |
| 638 | internalChooseMinor:·Choosing·Random | 638 | internalChooseMinor:·Choosing·Random |
| 639 | internalChooseMinor:·Choosing·LexSmallest | 639 | internalChooseMinor:·Choosing·LexSmallest |
| 640 | internalChooseMinor:·Choosing·Random | 640 | internalChooseMinor:·Choosing·Random |
| 641 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 641 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 642 | internalChooseMinor:·Choosing·RandomNonZero | 642 | internalChooseMinor:·Choosing·RandomNonZero |
| 643 | internalChooseMinor:·Choosing·RandomNonZero | 643 | internalChooseMinor:·Choosing·RandomNonZero |
| 644 | internalChooseMinor:·Choosing·LexSmallest | 644 | internalChooseMinor:·Choosing·LexSmallest |
| Offset 729, 15 lines modified | Offset 729, 15 lines modified | ||
| 729 | ··········<tr> | 729 | ··········<tr> |
| 730 | <td>··············<pre><code·class="language-macaulay2">i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value | 730 | <td>··············<pre><code·class="language-macaulay2">i42·:·ptsStratGeometric#ExtendField·--look·at·the·default·value |
| 731 | o42·=·true</code></pre> | 731 | o42·=·true</code></pre> |
| 732 | </td>··········</tr> | 732 | </td>··········</tr> |
| 733 | ··········<tr> | 733 | ··········<tr> |
| 734 | <td>··············<pre><code·class="language-macaulay2">i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric)) | 734 | <td>··············<pre><code·class="language-macaulay2">i43·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratGeometric)) |
| 735 | ·--·used·0. | 735 | ·--·used·0.466464s·(cpu);·0.408424s·(thread);·0s·(gc) |
| 736 | o43·=·2</code></pre> | 736 | o43·=·2</code></pre> |
| 737 | </td>··········</tr> | 737 | </td>··········</tr> |
| 738 | ··········<tr> | 738 | ··········<tr> |
| 739 | <td>··············<pre><code·class="language-macaulay2">i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value | 739 | <td>··············<pre><code·class="language-macaulay2">i44·:·ptsStratRational·=·ptsStratGeometric++{ExtendField=>false}·--change·that·value |
| 740 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} | 740 | o44·=·OptionTable{DecompositionStrategy·=>·Decompose} |
| Offset 755, 67 lines modified | Offset 755, 67 lines modified | ||
| 755 | ··········<tr> | 755 | ··········<tr> |
| 756 | <td>··············<pre><code·class="language-macaulay2">i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value | 756 | <td>··············<pre><code·class="language-macaulay2">i45·:·ptsStratRational.ExtendField·--look·at·our·changed·value |
| 757 | o45·=·false</code></pre> | 757 | o45·=·false</code></pre> |
| 758 | </td>··········</tr> | 758 | </td>··········</tr> |
| 759 | ··········<tr> | 759 | ··········<tr> |
| 760 | <td>··············<pre><code·class="language-macaulay2">i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational)) | 760 | <td>··············<pre><code·class="language-macaulay2">i46·:·time·dim·(J·+·chooseGoodMinors(1,·6,·M,·J,·Strategy=>Points,·PointOptions=>ptsStratRational)) |
| 761 | ·--·used·0.38 | 761 | ·--·used·0.308804s·(cpu);·0.267869s·(thread);·0s·(gc) |
| 762 | o46·=·2</code></pre> | 762 | o46·=·2</code></pre> |
| 763 | </td>··········</tr> | 763 | </td>··········</tr> |
| 764 | ········</table> | 764 | ········</table> |
| 765 | ········<div> | 765 | ········<div> |
| 766 | ··········<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 | ··········<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> |
| 767 | ········</div> | 767 | ········</div> |
| 768 | ········<div> | 768 | ········<div> |
| 769 | ··········<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 | ··········<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> |
| 770 | ········</div> | 770 | ········</div> |
| 771 | ········<table·class="examples"> | 771 | ········<table·class="examples"> |
| 772 | ··········<tr> | 772 | ··········<tr> |
| 773 | <td>··············<pre><code·class="language-macaulay2">i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault) | 773 | <td>··············<pre><code·class="language-macaulay2">i47·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefault) |
| 774 | ·--·used· | 774 | ·--·used·2.86051s·(cpu);·2.57045s·(thread);·0s·(gc)</code></pre> |
| 775 | </td>··········</tr> | 775 | </td>··········</tr> |
| 776 | ··········<tr> | 776 | ··········<tr> |
| 777 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom) | 777 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>StrategyDefaultNonRandom) |
| 778 | ·--·used·0.5 | 778 | ·--·used·0.53384s·(cpu);·0.492477s·(thread);·0s·(gc) |
| 779 | o48·=·true</code></pre> | 779 | o48·=·true</code></pre> |
| 780 | </td>··········</tr> | 780 | </td>··········</tr> |
| 781 | ··········<tr> | 781 | ··········<tr> |
| 782 | <td>··············<pre><code·class="language-macaulay2">i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) | 782 | <td>··············<pre><code·class="language-macaulay2">i49·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>Random) |
| 783 | ·--·used·2.4 | 783 | ·--·used·2.45237s·(cpu);·2.27144s·(thread);·0s·(gc)</code></pre> |
| 784 | </td>··········</tr> | 784 | </td>··········</tr> |
| 785 | ··········<tr> | 785 | ··········<tr> |
| 786 | <td>··············<pre><code·class="language-macaulay2">i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest) | 786 | <td>··············<pre><code·class="language-macaulay2">i50·:·time·regularInCodimension(1,·S/J,·MaxMinors·=>·100,·Strategy=>LexSmallest) |
| 787 | ·--·used·1.8 | 787 | ·--·used·1.82772s·(cpu);·1.55502s·(thread);·0s·(gc)</code></pre> |
| 788 | </td>··········</tr> | 788 | </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·0.09 | 493 | ·--·used·0.0926647s·(cpu);·0.0913073s·(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·0.295783s·(cpu);·0.1785s·(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·0.32 | 499 | ·--·used·0.329401s·(cpu);·0.240018s·(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·0.23 | 502 | ·--·used·0.23319s·(cpu);·0.165047s·(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·0.237 | 505 | ·--·used·0.237015s·(cpu);·0.150739s·(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. | 509 | ·--·used·0.198512s·(cpu);·0.165398s·(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·0.274583s·(cpu);·0.168375s·(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·1 | 515 | ·--·used·11.7549s·(cpu);·8.16996s·(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·0.281795s·(cpu);·0.258025s·(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·0.466464s·(cpu);·0.408424s·(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·0.38 | 660 | ·--·used·0.308804s·(cpu);·0.267869s·(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· | 674 | ·--·used·2.86051s·(cpu);·2.57045s·(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·0.5 | 677 | ·--·used·0.53384s·(cpu);·0.492477s·(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·2.4 | 680 | ·--·used·2.45237s·(cpu);·2.27144s·(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·1.8 | 683 | ·--·used·1.82772s·(cpu);·1.55502s·(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·0.699402s·(cpu);·0.612712s·(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·2. | 690 | ·--·used·2.06508s·(cpu);·1.75116s·(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·2.4 | 693 | ·--·used·2.44508s·(cpu);·2.13326s·(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·6.78766s·(cpu);·5.68746s·(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 68, 21 lines modified | Offset 68, 21 lines modified | ||
| 68 | ········</table> | 68 | ········</table> |
| 69 | ········<div> | 69 | ········<div> |
| 70 | ··········<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 | ··········<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> |
| 71 | ········</div> | 71 | ········</div> |
| 72 | ········<table·class="examples"> | 72 | ········<table·class="examples"> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·regularInCodimension(1,·S/J) | 74 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·regularInCodimension(1,·S/J) |
| 75 | ·--·used·0. | 75 | ·--·used·0.644332s·(cpu);·0.494877s·(thread);·0s·(gc) |
| 76 | o4·=·true</code></pre> | 76 | o4·=·true</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·regularInCodimension(2,·S/J) | 79 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·regularInCodimension(2,·S/J) |
| 80 | ·--·used·8. | 80 | ·--·used·8.29738s·(cpu);·6.28396s·(thread);·0s·(gc)</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ········</table> | 82 | ········</table> |
| 83 | ········<div> | 83 | ········<div> |
| 84 | ··········<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 | ··········<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> |
| 85 | ········</div> | 85 | ········</div> |
| 86 | ········<table·class="examples"> | 86 | ········<table·class="examples"> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| Offset 155, 27 lines modified | Offset 155, 27 lines modified | ||
| 155 | internalChooseMinor:·Choosing·LexSmallest | 155 | internalChooseMinor:·Choosing·LexSmallest |
| 156 | internalChooseMinor:·Choosing·LexSmallestTerm | 156 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 157 | internalChooseMinor:·Choosing·LexSmallest | 157 | internalChooseMinor:·Choosing·LexSmallest |
| 158 | internalChooseMinor:·Choosing·Random | 158 | internalChooseMinor:·Choosing·Random |
| 159 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39 | 159 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·49,·and·computed·=·39 |
| 160 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast | 160 | regularInCodimension:··singularLocus·dimension·verified·by·isCodimAtLeast |
| 161 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 | 161 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·2 |
| 162 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.0 | 162 | regularInCodimension:··Loop·completed,·submatrices·considered·=·49,·and·compute·--·used·1.05593s·(cpu);·0.785987s·(thread);·0s·(gc) |
| 163 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 | 163 | d·=·39.··singular·locus·dimension·appears·to·be·=·2 |
| 164 | o6·=·true</code></pre> | 164 | o6·=·true</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ········</table> | 166 | ········</table> |
| 167 | ········<div> | 167 | ········<div> |
| 168 | ··········<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 | ··········<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> |
| 169 | ········</div> | 169 | ········</div> |
| 170 | ········<table·class="examples"> | 170 | ········<table·class="examples"> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) | 172 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Verbose=>true) |
| 173 | ·--·used·0.1 | 173 | ·--·used·0.135862s·(cpu);·0.10264s·(thread);·0s·(gc) |
| 174 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 174 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 175 | regularInCodimension:·About·to·enter·loop | 175 | regularInCodimension:·About·to·enter·loop |
| 176 | internalChooseMinor:·Choosing·Random | 176 | internalChooseMinor:·Choosing·Random |
| 177 | internalChooseMinor:·Choosing·RandomNonZero | 177 | internalChooseMinor:·Choosing·RandomNonZero |
| 178 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 178 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 179 | internalChooseMinor:·Choosing·Random | 179 | internalChooseMinor:·Choosing·Random |
| 180 | internalChooseMinor:·Choosing·Random | 180 | internalChooseMinor:·Choosing·Random |
| Offset 198, 15 lines modified | Offset 198, 15 lines modified | ||
| 198 | ········</div> | 198 | ········</div> |
| 199 | ········<div> | 199 | ········<div> |
| 200 | ··········<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 | ··········<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> |
| 201 | ········</div> | 201 | ········</div> |
| 202 | ········<table·class="examples"> | 202 | ········<table·class="examples"> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true) | 204 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·Strategy=>StrategyRandom,·Verbose=>true) |
| 205 | ·--·used·0.1 | 205 | ·--·used·0.107905s·(cpu);·0.0858087s·(thread);·0s·(gc) |
| 206 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 206 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 207 | regularInCodimension:·About·to·enter·loop | 207 | regularInCodimension:·About·to·enter·loop |
| 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 |
| 212 | internalChooseMinor:·Choosing·Random | 212 | internalChooseMinor:·Choosing·Random |
| Offset 229, 15 lines modified | Offset 229, 15 lines modified | ||
| 229 | ········</div> | 229 | ········</div> |
| 230 | ········<div> | 230 | ········<div> |
| 231 | ··········<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 | ··········<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> |
| 232 | ········</div> | 232 | ········</div> |
| 233 | ········<table·class="examples"> | 233 | ········<table·class="examples"> |
| 234 | ··········<tr> | 234 | ··········<tr> |
| 235 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true) | 235 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(1,·S/J,·MaxMinors=>10,·MinMinorsFunction·=>·t->3,·Verbose=>true) |
| 236 | ·--·used·0.4 | 236 | ·--·used·0.459622s·(cpu);·0.366591s·(thread);·0s·(gc) |
| 237 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. | 237 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·10·of·them. |
| 238 | regularInCodimension:·About·to·enter·loop | 238 | regularInCodimension:·About·to·enter·loop |
| 239 | internalChooseMinor:·Choosing·RandomNonZero | 239 | internalChooseMinor:·Choosing·RandomNonZero |
| 240 | internalChooseMinor:·Choosing·Random | 240 | internalChooseMinor:·Choosing·Random |
| 241 | internalChooseMinor:·Choosing·LexSmallest | 241 | internalChooseMinor:·Choosing·LexSmallest |
| 242 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3 | 242 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·3,·and·computed·=·3 |
| 243 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 243 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| Offset 266, 15 lines modified | Offset 266, 15 lines modified | ||
| 266 | ········</div> | 266 | ········</div> |
| 267 | ········<div> | 267 | ········<div> |
| 268 | ··········<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 | ··········<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> |
| 269 | ········</div> | 269 | ········</div> |
| 270 | ········<table·class="examples"> | 270 | ········<table·class="examples"> |
| 271 | ··········<tr> | 271 | ··········<tr> |
| 272 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) | 272 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·CodimCheckFunction·=>·t->t/5,·MinMinorsFunction·=>·t->2,·Verbose=>true) |
| 273 | ·--·used·0.5 | 273 | ·--·used·0.530465s·(cpu);·0.40864s·(thread);·0s·(gc) |
| 274 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. | 274 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. |
| 275 | regularInCodimension:·About·to·enter·loop | 275 | regularInCodimension:·About·to·enter·loop |
| 276 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 276 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 277 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 277 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 278 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2 | 278 | regularInCodimension:··Loop·step,·about·to·compute·dimension.··Submatrices·considered:·2,·and·computed·=·2 |
| 279 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. | 279 | regularInCodimension:··isCodimAtLeast·failed,·computing·codim. |
| 280 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·4 | 280 | regularInCodimension:··partial·singular·locus·dimension·computed,·=·4 |
| Offset 321, 15 lines modified | Offset 321, 15 lines modified | ||
| 321 | ········</table> | 321 | ········</table> |
| 322 | ········<div> | 322 | ········<div> |
| 323 | ··········<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 | ··········<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> |
| 324 | ········</div> | 324 | ········</div> |
| 325 | ········<table·class="examples"> | 325 | ········<table·class="examples"> |
| 326 | ··········<tr> | 326 | ··········<tr> |
| 327 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true) | 327 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·regularInCodimension(1,·S/J,·MaxMinors=>25,·UseOnlyFastCodim·=>·true,·Verbose=>true) |
| 328 | ·--·used·0.3 | 328 | ·--·used·0.300366s·(cpu);·0.241727s·(thread);·0s·(gc) |
| 329 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. | 329 | regularInCodimension:·ring·dimension·=4,·there·are·1465128·possible·5·by·5·minors,·we·will·compute·up·to·25·of·them. |
| 330 | regularInCodimension:·About·to·enter·loop | 330 | regularInCodimension:·About·to·enter·loop |
| 331 | internalChooseMinor:·Choosing·GRevLexSmallest | 331 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 332 | internalChooseMinor:·Choosing·LexSmallest | 332 | internalChooseMinor:·Choosing·LexSmallest |
| 333 | internalChooseMinor:·Choosing·RandomNonZero | 333 | internalChooseMinor:·Choosing·RandomNonZero |
| 334 | internalChooseMinor:·Choosing·RandomNonZero | 334 | internalChooseMinor:·Choosing·RandomNonZero |
| 335 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 335 | 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·0.644332s·(cpu);·0.494877s·(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·8. | 33 | ·--·used·8.29738s·(cpu);·6.28396s·(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·1.0 | 128 | --·used·1.05593s·(cpu);·0.785987s·(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·0.1 | 134 | ·--·used·0.135862s·(cpu);·0.10264s·(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·0.1 | 166 | ·--·used·0.107905s·(cpu);·0.0858087s·(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·0.4 | 204 | ·--·used·0.459622s·(cpu);·0.366591s·(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·0.5 | 250 | ·--·used·0.530465s·(cpu);·0.40864s·(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·0.3 | 315 | ·--·used·0.300366s·(cpu);·0.241727s·(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 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | ········</ul> | 67 | ········</ul> |
| 68 | 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 | 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"> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <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>··············<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> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) | 73 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>StrategyDefault) |
| 74 | ·--·1. | 74 | ·--·1.43601·seconds·elapsed |
| 75 | o2·=·true</code></pre> | 75 | o2·=·true</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ········</table> | 77 | ········</table> |
| 78 | In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion·of·each·of·the·above·strategies·after·100·runs.········<ul> | 78 | In·this·particular·example,·on·one·machine,·we·list·average·time·to·completion·of·each·of·the·above·strategies·after·100·runs.········<ul> |
| 79 | ··········<li> | 79 | ··········<li> |
| 80 | <span·class="tt">StrategyDefault</span>:·1.65·seconds··········</li> | 80 | <span·class="tt">StrategyDefault</span>:·1.65·seconds··········</li> |
| Offset 138, 15 lines modified | Offset 138, 15 lines modified | ||
| 138 | <span·class="tt">StrategyPoints</span>:·choose·all·submatrices·via·Points.··········</li> | 138 | <span·class="tt">StrategyPoints</span>:·choose·all·submatrices·via·Points.··········</li> |
| 139 | ··········<li> | 139 | ··········<li> |
| 140 | <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 | <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> |
| 141 | ········</ul> | 141 | ········</ul> |
| 142 | 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 | 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"> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) | 144 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·regularInCodimension(1,·T,·Strategy=>LexSmallestTerm) |
| 145 | ·--· | 145 | ·--·0.816981·seconds·elapsed |
| 146 | o4·=·true</code></pre> | 146 | o4·=·true</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ········</table> | 148 | ········</table> |
| 149 | ······</div> | 149 | ······</div> |
| 150 | ······<div·class="waystouse"> | 150 | ······<div·class="waystouse"> |
| 151 | ········<h2>For·the·programmer</h2> | 151 | ········<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 | ·--·1.43601·seconds·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 | ·--· | 141 | ·--·0.816981·seconds·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 107, 15 lines modified | Offset 107, 15 lines modified | ||
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); | 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·chooseGoodMinors(15,·r,·myDiff,·Strategy=>StrategyDefaultNonRandom); |
| 109 | o6·:·Ideal·of·R</code></pre> | 109 | o6·:·Ideal·of·R</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isCodimAtLeast(3,·J) | 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isCodimAtLeast(3,·J) |
| 113 | ·--·used·0.003 | 113 | ·--·used·0.000302355s·(cpu);·0.00225645s·(thread);·0s·(gc) |
| 114 | o7·=·true</code></pre> | 114 | o7·=·true</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ········</table> | 116 | ········</table> |
| 117 | ········<div> | 117 | ········<div> |
| 118 | ··········<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 | ··········<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> |
| 119 | ········</div> | 119 | ········</div> |
| Offset 125, 22 lines modified | Offset 125, 22 lines modified | ||
| 125 | ···············ZZ | 125 | ···············ZZ |
| 126 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] | 126 | o8·:·Ideal·of·---[x··,·x·,·x·,·x·,·x··,·x·,·x·,·x··,·x·,·x·,·x·,·x·] |
| 127 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7</code></pre> | 127 | ··············127··11···8···1···9···12···6···5···10···2···4···3···7</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) | 130 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·5,·Verbose=>true) |
| 131 | ·--·used·0.00 | 131 | ·--·used·0.00143862s·(cpu);·0.00195208s·(thread);·0s·(gc) |
| 132 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. | 132 | isCodimAtLeast:·Computing·codim·of·monomials·based·on·ideal·generators. |
| 133 | o9·=·true</code></pre> | 133 | o9·=·true</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ··········<tr> | 135 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) | 136 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isCodimAtLeast(5,·I,·PairLimit·=>·200,·Verbose=>false) |
| 137 | ·--·used· | 137 | ·--·used·5.5463e-05s·(cpu);·0.00165724s·(thread);·0s·(gc) |
| 138 | o10·=·true</code></pre> | 138 | o10·=·true</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ········</table> | 140 | ········</table> |
| 141 | ········<div> | 141 | ········<div> |
| 142 | ··········<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 | ··········<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> |
| 143 | ········</div> | 143 | ········</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·0.003 | 45 | ·--·used·0.000302355s·(cpu);·0.00225645s·(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·0.00 | 79 | ·--·used·0.00143862s·(cpu);·0.00195208s·(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· | 83 | ·--·used·5.5463e-05s·(cpu);·0.00165724s·(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 101, 21 lines modified | Offset 101, 21 lines modified | ||
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·pdim(module·I) | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·pdim(module·I) |
| 103 | o3·=·2</code></pre> | 103 | o3·=·2</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·projDim(module·I,·Strategy=>StrategyRandom) |
| 107 | ·--·used·0.15 | 107 | ·--·used·0.152643s·(cpu);·0.109336s·(thread);·0s·(gc) |
| 108 | o4·=·1</code></pre> | 108 | o4·=·1</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) | 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·projDim(module·I,·Strategy=>StrategyRandom,·MinDimension·=>·1) |
| 112 | ·--·used·0.011 | 112 | ·--·used·0.011221s·(cpu);·0.0113486s·(thread);·0s·(gc) |
| 113 | o5·=·1</code></pre> | 113 | o5·=·1</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ········</table> | 115 | ········</table> |
| 116 | ········<div> | 116 | ········<div> |
| 117 | ··········<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 | ··········<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> |
| 118 | ········</div> | 118 | ········</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·0.15 | 50 | ·--·used·0.152643s·(cpu);·0.109336s·(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·0.011 | 53 | ·--·used·0.011221s·(cpu);·0.0113486s·(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 95, 21 lines modified | Offset 95, 21 lines modified | ||
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·M·=·random(R^{5,5,5,5,5,5},·R^7); |
| 96 | ·············6······7 | 96 | ·············6······7 |
| 97 | o2·:·Matrix·R··<--·R</code></pre> | 97 | o2·:·Matrix·R··<--·R</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·I2·=·recursiveMinors(4,·M,·Threads=>0); |
| 101 | ·--·used·0. | 101 | ·--·used·0.331626s·(cpu);·0.334452s·(thread);·0s·(gc) |
| 102 | o3·:·Ideal·of·R</code></pre> | 102 | o3·:·Ideal·of·R</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); | 105 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I1·=·minors(4,·M,·Strategy=>Cofactor); |
| 106 | ·--·used·1. | 106 | ·--·used·1.16743s·(cpu);·1.0458s·(thread);·0s·(gc) |
| 107 | o4·:·Ideal·of·R</code></pre> | 107 | o4·:·Ideal·of·R</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·I1·==·I2 | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·I1·==·I2 |
| 111 | o5·=·true</code></pre> | 111 | 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·0.331626s·(cpu);·0.334452s·(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·1.16743s·(cpu);·1.0458s·(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 130, 21 lines modified | Offset 130, 21 lines modified | ||
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i7·:·dim·S | 131 | <td>··············<pre><code·class="language-macaulay2">i7·:·dim·S |
| 132 | o7·=·3</code></pre> | 132 | o7·=·3</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S) | 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·regularInCodimension(1,·S) |
| 136 | ·--·used·1. | 136 | ·--·used·1.21346s·(cpu);·0.996398s·(thread);·0s·(gc) |
| 137 | o8·=·true</code></pre> | 137 | o8·=·true</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(2,·S) | 140 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·regularInCodimension(2,·S) |
| 141 | ·--·used·5.26 | 141 | ·--·used·5.26304s·(cpu);·4.19769s·(thread);·0s·(gc)</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ········</table> | 143 | ········</table> |
| 144 | ········<div> | 144 | ········<div> |
| 145 | ··········<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 | ··········<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> |
| 146 | ········</div> | 146 | ········</div> |
| 147 | ········<div> | 147 | ········<div> |
| 148 | ··········<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> | 148 | ··········<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 156, 33 lines modified | Offset 156, 33 lines modified | ||
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim(R) | 157 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim(R) |
| 158 | o11·=·2</code></pre> | 158 | o11·=·2</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ··········<tr> | 160 | ··········<tr> |
| 161 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(dim·singularLocus·(R)) | 161 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(dim·singularLocus·(R)) |
| 162 | ·--·used·0.13 | 162 | ·--·used·0.132359s·(cpu);·0.131444s·(thread);·0s·(gc) |
| 163 | o12·=·-1</code></pre> | 163 | o12·=·-1</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·regularInCodimension(2,·R) | 166 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·regularInCodimension(2,·R) |
| 167 | ·--·used·0. | 167 | ·--·used·0.400783s·(cpu);·0.297457s·(thread);·0s·(gc) |
| 168 | o13·=·true</code></pre> | 168 | o13·=·true</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·regularInCodimension(2,·R) | 171 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·regularInCodimension(2,·R) |
| 172 | ·--·used·0.6 | 172 | ·--·used·0.670672s·(cpu);·0.487833s·(thread);·0s·(gc) |
| 173 | o14·=·true</code></pre> | 173 | o14·=·true</code></pre> |
| 174 | </td>··········</tr> | 174 | </td>··········</tr> |
| 175 | ··········<tr> | 175 | ··········<tr> |
| 176 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·regularInCodimension(2,·R) | 176 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·regularInCodimension(2,·R) |
| 177 | ·--·used·0.2 | 177 | ·--·used·0.265479s·(cpu);·0.182623s·(thread);·0s·(gc) |
| 178 | o15·=·true</code></pre> | 178 | o15·=·true</code></pre> |
| 179 | </td>··········</tr> | 179 | </td>··········</tr> |
| 180 | ········</table> | 180 | ········</table> |
| 181 | ········<div> | 181 | ········<div> |
| 182 | ··········<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 | ··········<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> |
| 183 | ········</div> | 183 | ········</div> |
| Offset 520, 15 lines modified | Offset 520, 15 lines modified | ||
| 520 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 520 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 521 | internalChooseMinor:·Choosing·RandomNonZero | 521 | internalChooseMinor:·Choosing·RandomNonZero |
| 522 | internalChooseMinor:·Choosing·LexSmallest | 522 | internalChooseMinor:·Choosing·LexSmallest |
| 523 | internalChooseMinor:·Choosing·Random | 523 | internalChooseMinor:·Choosing·Random |
| 524 | internalChooseMinor:·Choosing·Random | 524 | internalChooseMinor:·Choosing·Random |
| 525 | internalChooseMinor:·Choosing·LexSmallestTerm | 525 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 526 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 526 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| 527 | internalChooseMinor:·Choosing·--·used·5. | 527 | internalChooseMinor:·Choosing·--·used·5.3412s·(cpu);·4.15577s·(thread);·0s·(gc) |
| 528 | ·LexSmallestTerm | 528 | ·LexSmallestTerm |
| 529 | internalChooseMinor:·Choosing·Random | 529 | internalChooseMinor:·Choosing·Random |
| 530 | internalChooseMinor:·Choosing·Random | 530 | internalChooseMinor:·Choosing·Random |
| 531 | internalChooseMinor:·Choosing·GRevLexSmallest | 531 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 532 | internalChooseMinor:·Choosing·RandomNonZero | 532 | internalChooseMinor:·Choosing·RandomNonZero |
| 533 | internalChooseMinor:·Choosing·GRevLexSmallest | 533 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 534 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 534 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 570, 15 lines modified | Offset 570, 15 lines modified | ||
| 570 | ········</table> | 570 | ········</table> |
| 571 | ········<div> | 571 | ········<div> |
| 572 | ··········<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 | ··········<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> |
| 573 | ········</div> | 573 | ········</div> |
| 574 | ········<table·class="examples"> | 574 | ········<table·class="examples"> |
| 575 | ··········<tr> | 575 | ··········<tr> |
| 576 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) | 576 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) |
| 577 | ·--·used·1.09 | 577 | ·--·used·1.09184s·(cpu);·0.913607s·(thread);·0s·(gc) |
| 578 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them. | 578 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4·minors,·we·will·compute·up·to·30·of·them. |
| 579 | regularInCodimension:·About·to·enter·loop | 579 | regularInCodimension:·About·to·enter·loop |
| 580 | internalChooseMinor:·Choosing·Random | 580 | internalChooseMinor:·Choosing·Random |
| 581 | internalChooseMinor:·Choosing·Random | 581 | internalChooseMinor:·Choosing·Random |
| 582 | internalChooseMinor:·Choosing·RandomNonZero | 582 | internalChooseMinor:·Choosing·RandomNonZero |
| 583 | internalChooseMinor:·Choosing·LexSmallestTerm | 583 | internalChooseMinor:·Choosing·LexSmallestTerm |
| 584 | internalChooseMinor:·Choosing·RandomNonZero | 584 | internalChooseMinor:·Choosing·RandomNonZero |
| Offset 639, 73 lines modified | Offset 639, 73 lines modified | ||
| 639 | <td>··············<pre><code·class="language-macaulay2">i19·:·StrategyCurrent#LexSmallest·=·100;</code></pre> | 639 | <td>··············<pre><code·class="language-macaulay2">i19·:·StrategyCurrent#LexSmallest·=·100;</code></pre> |
| 640 | </td>··········</tr> | 640 | </td>··········</tr> |
| 641 | ··········<tr> | 641 | ··········<tr> |
| 642 | <td>··············<pre><code·class="language-macaulay2">i20·:·StrategyCurrent#LexSmallestTerm·=·0;</code></pre> | 642 | <td>··············<pre><code·class="language-macaulay2">i20·:·StrategyCurrent#LexSmallestTerm·=·0;</code></pre> |
| 643 | </td>··········</tr> | 643 | </td>··········</tr> |
| 644 | ··········<tr> | 644 | ··········<tr> |
| 645 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 645 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 646 | ·--·used·0.1 | 646 | ·--·used·0.105472s·(cpu);·0.0738162s·(thread);·0s·(gc) |
| 647 | o21·=·true</code></pre> | 647 | o21·=·true</code></pre> |
| 648 | </td>··········</tr> | 648 | </td>··········</tr> |
| 649 | ··········<tr> | 649 | ··········<tr> |
| 650 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 650 | <td>··············<pre><code·class="language-macaulay2">i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 651 | ·--·used·0.2 | 651 | ·--·used·0.215444s·(cpu);·0.139735s·(thread);·0s·(gc) |
| 652 | o22·=·true</code></pre> | 652 | o22·=·true</code></pre> |
| 653 | </td>··········</tr> | 653 | </td>··········</tr> |
| 654 | ··········<tr> | 654 | ··········<tr> |
| 655 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 655 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 656 | ·--·used·1. | 656 | ·--·used·1.17744s·(cpu);·0.948932s·(thread);·0s·(gc) |
| 657 | o23·=·true</code></pre> | 657 | o23·=·true</code></pre> |
| 658 | </td>··········</tr> | 658 | </td>··········</tr> |
| 659 | ··········<tr> | 659 | ··········<tr> |
| 660 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 660 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 661 | ·--·used·0.9 | 661 | ·--·used·0.93812s·(cpu);·0.735867s·(thread);·0s·(gc) |
| 662 | o24·=·true</code></pre> | 662 | o24·=·true</code></pre> |
| 663 | </td>··········</tr> | 663 | </td>··········</tr> |
| 664 | ··········<tr> | 664 | ··········<tr> |
| 665 | <td>··············<pre><code·class="language-macaulay2">i25·:·StrategyCurrent#LexSmallest·=·0;</code></pre> | 665 | <td>··············<pre><code·class="language-macaulay2">i25·:·StrategyCurrent#LexSmallest·=·0;</code></pre> |
| 666 | </td>··········</tr> | 666 | </td>··········</tr> |
| 667 | ··········<tr> | 667 | ··········<tr> |
| 668 | <td>··············<pre><code·class="language-macaulay2">i26·:·StrategyCurrent#LexSmallestTerm·=·100;</code></pre> | 668 | <td>··············<pre><code·class="language-macaulay2">i26·:·StrategyCurrent#LexSmallestTerm·=·100;</code></pre> |
| 669 | </td>··········</tr> | 669 | </td>··········</tr> |
| 670 | ··········<tr> | 670 | ··········<tr> |
| 671 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 671 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 672 | ·--·used·0.3 | 672 | ·--·used·0.376813s·(cpu);·0.263105s·(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·1.21346s·(cpu);·0.996398s·(thread);·0s·(gc) |
| 79 | o8·=·true | 79 | o8·=·true |
| 80 | i9·:·time·regularInCodimension(2,·S) | 80 | i9·:·time·regularInCodimension(2,·S) |
| 81 | ·--·used·5.26 | 81 | ·--·used·5.26304s·(cpu);·4.19769s·(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·0.13 | 99 | ·--·used·0.132359s·(cpu);·0.131444s·(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·0.400783s·(cpu);·0.297457s·(thread);·0s·(gc) |
| 103 | o13·=·true | 103 | o13·=·true |
| 104 | i14·:·time·regularInCodimension(2,·R) | 104 | i14·:·time·regularInCodimension(2,·R) |
| 105 | ·--·used·0.6 | 105 | ·--·used·0.670672s·(cpu);·0.487833s·(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·0.265479s·(cpu);·0.182623s·(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, 16 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·5. | 469 | internalChooseMinor:·Choosing·--·used·5.3412s·(cpu);·4.15577s·(thread);·0s·(gc) |
| 470 | (gc) | ||
| 471 | ·LexSmallestTerm | 470 | ·LexSmallestTerm |
| 472 | internalChooseMinor:·Choosing·Random | 471 | internalChooseMinor:·Choosing·Random |
| 473 | internalChooseMinor:·Choosing·Random | 472 | internalChooseMinor:·Choosing·Random |
| 474 | internalChooseMinor:·Choosing·GRevLexSmallest | 473 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 475 | internalChooseMinor:·Choosing·RandomNonZero | 474 | internalChooseMinor:·Choosing·RandomNonZero |
| 476 | internalChooseMinor:·Choosing·GRevLexSmallest | 475 | internalChooseMinor:·Choosing·GRevLexSmallest |
| 477 | internalChooseMinor:·Choosing·GRevLexSmallestTerm | 476 | internalChooseMinor:·Choosing·GRevLexSmallestTerm |
| Offset 517, 15 lines modified | Offset 516, 15 lines modified | ||
| 517 | a·function·to·the·option·MaxMinors.·This·function·should·have·two·inputs;·the | 516 | 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 | 517 | 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 | 518 | regular·in·codimension·n,·and·the·second·is·the·total·number·of·minors |
| 520 | available·in·the·Jacobian.·The·function·regularInCodimension·does·not·recompute | 519 | 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 | 520 | determinants,·so·MaxMinors·or·is·only·an·upper·bound·on·the·number·of·minors |
| 522 | computed. | 521 | computed. |
| 523 | i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) | 522 | i17·:·time·regularInCodimension(2,·S,·Verbose=>true,·MaxMinors=>30) |
| 524 | ·--·used·1.09 | 523 | ·--·used·1.09184s·(cpu);·0.913607s·(thread);·0s·(gc) |
| 525 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4 | 524 | regularInCodimension:·ring·dimension·=3,·there·are·17325·possible·4·by·4 |
| 526 | minors,·we·will·compute·up·to·30·of·them. | 525 | minors,·we·will·compute·up·to·30·of·them. |
| 527 | regularInCodimension:·About·to·enter·loop | 526 | regularInCodimension:·About·to·enter·loop |
| 528 | internalChooseMinor:·Choosing·Random | 527 | internalChooseMinor:·Choosing·Random |
| 529 | internalChooseMinor:·Choosing·Random | 528 | internalChooseMinor:·Choosing·Random |
| 530 | internalChooseMinor:·Choosing·RandomNonZero | 529 | internalChooseMinor:·Choosing·RandomNonZero |
| 531 | internalChooseMinor:·Choosing·LexSmallestTerm | 530 | internalChooseMinor:·Choosing·LexSmallestTerm |
| Offset 592, 51 lines modified | Offset 591, 51 lines modified | ||
| 592 | because·there·are·a·small·number·of·entries·with·nonzero·constant·terms,·which | 591 | 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 | 592 | are·selected·repeatedly).·However,·in·our·first·example,·the·LexSmallestTerm·is |
| 594 | much·faster,·and·Random·does·not·perform·well·at·all. | 593 | much·faster,·and·Random·does·not·perform·well·at·all. |
| 595 | i18·:·StrategyCurrent#Random·=·0; | 594 | i18·:·StrategyCurrent#Random·=·0; |
| 596 | i19·:·StrategyCurrent#LexSmallest·=·100; | 595 | i19·:·StrategyCurrent#LexSmallest·=·100; |
| 597 | i20·:·StrategyCurrent#LexSmallestTerm·=·0; | 596 | i20·:·StrategyCurrent#LexSmallestTerm·=·0; |
| 598 | i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 597 | i21·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 599 | ·--·used·0.1 | 598 | ·--·used·0.105472s·(cpu);·0.0738162s·(thread);·0s·(gc) |
| 600 | o21·=·true | 599 | o21·=·true |
| 601 | i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 600 | i22·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 602 | ·--·used·0.2 | 601 | ·--·used·0.215444s·(cpu);·0.139735s·(thread);·0s·(gc) |
| 603 | o22·=·true | 602 | o22·=·true |
| 604 | i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 603 | i23·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 605 | ·--·used·1. | 604 | ·--·used·1.17744s·(cpu);·0.948932s·(thread);·0s·(gc) |
| 606 | o23·=·true | 605 | o23·=·true |
| 607 | i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 606 | i24·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 608 | ·--·used·0.9 | 607 | ·--·used·0.93812s·(cpu);·0.735867s·(thread);·0s·(gc) |
| 609 | o24·=·true | 608 | o24·=·true |
| 610 | i25·:·StrategyCurrent#LexSmallest·=·0; | 609 | i25·:·StrategyCurrent#LexSmallest·=·0; |
| 611 | i26·:·StrategyCurrent#LexSmallestTerm·=·100; | 610 | i26·:·StrategyCurrent#LexSmallestTerm·=·100; |
| 612 | i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 611 | i27·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 613 | ·--·used·0.3 | 612 | ·--·used·0.376813s·(cpu);·0.263105s·(thread);·0s·(gc) |
| 614 | o27·=·true | 613 | o27·=·true |
| 615 | i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) | 614 | i28·:·time·regularInCodimension(2,·R,·Strategy=>StrategyCurrent) |
| 616 | ·--·used·1.79 | 615 | ·--·used·1.79424s·(cpu);·1.35742s·(thread);·0s·(gc) |
| 617 | i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 616 | i29·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 618 | ·--·used·0.1 | 617 | ·--·used·0.137147s·(cpu);·0.105093s·(thread);·0s·(gc) |
| 619 | o29·=·true | 618 | o29·=·true |
| 620 | i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) | 619 | i30·:·time·regularInCodimension(1,·S,·Strategy=>StrategyCurrent) |
| 621 | ·--·used·0.1 | 620 | ·--·used·0.165322s·(cpu);·0.127653s·(thread);·0s·(gc) |
| 622 | o30·=·true | 621 | o30·=·true |
| 623 | i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) | 622 | i31·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) |
| 624 | ·--·used·1. | 623 | ·--·used·1.26608s·(cpu);·1.02607s·(thread);·0s·(gc) |
| 625 | o31·=·true | 624 | o31·=·true |
| 626 | i32·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) | 625 | i32·:·time·regularInCodimension(1,·S,·Strategy=>StrategyRandom) |
| 627 | ·--·used·1.2 | 626 | ·--·used·1.22142s·(cpu);·1.04303s·(thread);·0s·(gc) |
| 628 | o32·=·true | 627 | o32·=·true |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00400582s·(cpu);·0.00214903s·(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·0.00258967s·(cpu);·0.00493058s·(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 167, 24 lines modified | Offset 167, 24 lines modified | ||
| 167 | <td>··············<pre><code·class="language-macaulay2">i14·:·K3=nextDegree(gens·ker·Q2,2,S); | 167 | <td>··············<pre><code·class="language-macaulay2">i14·:·K3=nextDegree(gens·ker·Q2,2,S); |
| 168 | ··············8······8 | 168 | ··············8······8 |
| 169 | o14·:·Matrix·R··<--·R</code></pre> | 169 | o14·:·Matrix·R··<--·R</code></pre> |
| 170 | </td>··········</tr> | 170 | </td>··········</tr> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·I=co1Fitting(K3) | 172 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·I=co1Fitting(K3) |
| 173 | ·--·used·0.00 | 173 | ·--·used·0.00400582s·(cpu);·0.00214903s·(thread);·0s·(gc) |
| 174 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) | 174 | o15·=·ideal·(a·a···+·a··-·a··,·a·a···-·a·,·a·a···+·a··-·a··,·a·a···-·a·) |
| 175 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 | 175 | ··············9·11····5····12···3·11····6···9·10····4····11···3·10····5 |
| 176 | o15·:·Ideal·of·R</code></pre> | 176 | o15·:·Ideal·of·R</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ··········<tr> | 178 | ··········<tr> |
| 179 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·J=fittingIdeal(2-1,coker·K3); | 179 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·J=fittingIdeal(2-1,coker·K3); |
| 180 | ·--·used·0.00 | 180 | ·--·used·0.00258967s·(cpu);·0.00493058s·(thread);·0s·(gc) |
| 181 | o16·:·Ideal·of·R</code></pre> | 181 | o16·:·Ideal·of·R</code></pre> |
| 182 | </td>··········</tr> | 182 | </td>··········</tr> |
| 183 | ··········<tr> | 183 | ··········<tr> |
| 184 | <td>··············<pre><code·class="language-macaulay2">i17·:·I==J | 184 | <td>··············<pre><code·class="language-macaulay2">i17·:·I==J |
| 185 | o17·=·true</code></pre> | 185 | 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·0.00400582s·(cpu);·0.00214903s·(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·0.00258967s·(cpu);·0.00493058s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTYwMiwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTYwMiwgc3ltYm9sIERvY3VtZW50VGFn |
| 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·=>·0x7f3b6e475ad0} |
| 8 | i3·:·address·x | 8 | i3·:·address·x |
| 9 | o3·=·0x7f | 9 | o3·=·0x7f3b6e475ad0 |
| 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·=·{0x7fdae24821d0,·0x7fdae24821c0,·0x7fdae24821b0} |
| 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·=·{0x7ffb78c8a750,·0x7ffb78c8a740,·0x7ffb78c8a730} |
| 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:·-1443663782 | 1 | --·-*-·M2-comint·-*-·hash:·-1443663782 |
| 2 | i1·:·ptr·=·address·int·0 | 2 | i1·:·ptr·=·address·int·0 |
| 3 | o1·=·0x7f | 3 | o1·=·0x7fbbf4762b50 |
| 4 | o1·:·Pointer | 4 | o1·:·Pointer |
| 5 | i2·:·voidstar·ptr | 5 | i2·:·voidstar·ptr |
| 6 | o2·=·0x7f | 6 | o2·=·0x7fbbf4762b50 |
| 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·=·0x7f7a2cc77af0 |
| 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:·1169345882 | 1 | --·-*-·M2-comint·-*-·hash:·1169345882 |
| 2 | i1·:·ptr·=·voidstar·address·int·5 | 2 | i1·:·ptr·=·voidstar·address·int·5 |
| 3 | o1·=·0x7f | 3 | o1·=·0x7f706247ca30 |
| 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"·=>·6.94657e-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·=>·0x7fd | 7 | o2·=·int32{Address·=>·0x7efd4083aa90} |
| 8 | i3·:·ptr·=·address·x | 8 | i3·:·ptr·=·address·x |
| 9 | o3·=·0x7fd | 9 | o3·=·0x7efd4083aa90 |
| 10 | o3·:·Pointer | 10 | o3·:·Pointer |
| 11 | i4·:·ptr·+·5 | 11 | i4·:·ptr·+·5 |
| 12 | o4·=·0x7fd | 12 | o4·=·0x7efd4083aa95 |
| 13 | o4·:·Pointer | 13 | o4·:·Pointer |
| 14 | i5·:·ptr·-·3 | 14 | i5·:·ptr·-·3 |
| 15 | o5·=·0x7fd | 15 | o5·=·0x7efd4083aa8d |
| 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{0x7f170643f550,·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·=·0x7f69e1457a80 |
| 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:·-954131557 | 1 | --·-*-·M2-comint·-*-·hash:·-954131557 |
| 2 | i1·:·address·int | 2 | i1·:·address·int |
| 3 | o1·=·0x5 | 3 | o1·=·0x55f234d681e0 |
| 4 | o1·:·Pointer | 4 | o1·:·Pointer |
| 5 | i2·:·address·int·5 | 5 | i2·:·address·int·5 |
| 6 | o2·=·0x7f | 6 | o2·=·0x7f93974a1930 |
| 7 | o2·:·Pointer | 7 | o2·:·Pointer |
| 8 | i3·:· | 8 | i3·:· |
| Offset 96, 14 lines modified | Offset 96, 14 lines modified | ||
| 96 | o19·=·free | 96 | o19·=·free |
| 97 | o19·:·ForeignFunction | 97 | o19·:·ForeignFunction |
| 98 | i20·:·x·=·malloc·8 | 98 | i20·:·x·=·malloc·8 |
| 99 | o20·=·0x7f | 99 | o20·=·0x7fa278066810 |
| 100 | o20·:·ForeignObject·of·type·void* | 100 | o20·:·ForeignObject·of·type·void* |
| 101 | i21·:·registerFinalizer(x,·free) | 101 | i21·:·registerFinalizer(x,·free) |
| 102 | i22·:· | 102 | i22·:· |
| Offset 1, 21 lines modified | Offset 1, 21 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-1015538506 | 1 | --·-*-·M2-comint·-*-·hash:·-1015538506 |
| 2 | i1·:·ptr·=·getMemory·8 | 2 | i1·:·ptr·=·getMemory·8 |
| 3 | o1·=·0x7f | 3 | o1·=·0x7f6c60804370 |
| 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·=·0x7f6c60886910 |
| 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·=·0x7f6c60886800 |
| 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·0x7fb1300688a0 | ||
| 22 | freeing·memory·at·0x7fb1300521e0 | ||
| 23 | freeing·memory·at·0x7fb130004f20 | ||
| 24 | freeing·memory·at·0x7f | 21 | freeing·memory·at·0x7f829c068150 |
| 25 | freeing·memory·at·0x7f | 22 | freeing·memory·at·0x7f829c0521e0 |
| 26 | freeing·memory·at·0x7fb130066830 | ||
| 27 | freeing·memory·at·0x7f | 23 | freeing·memory·at·0x7f829c004f20 |
| 28 | freeing·memory·at·0x7f | 24 | freeing·memory·at·0x7f829c068880 |
| 25 | freeing·memory·at·0x7f829c0688a0 | ||
| 29 | freeing·memory·at·0x7f | 26 | freeing·memory·at·0x7f829c066810 |
| 27 | freeing·memory·at·0x7f829c05e150 | ||
| 28 | freeing·memory·at·0x7f829c0687f0 | ||
| 29 | freeing·memory·at·0x7f829c066830 | ||
| 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·=·0x7ff | 23 | o5·=·0x7ffa45c523c0 |
| 24 | o5·:·ForeignObject·of·type·void* | 24 | o5·:·ForeignObject·of·type·void* |
| 25 | i6·:·value·x | 25 | i6·:·value·x |
| 26 | o6·=·0x7ff | 26 | o6·=·0x7ffa45c523c0 |
| 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 55, 25 lines modified | Offset 55, 25 lines modified | ||
| 55 | o1·=·5 | 55 | o1·=·5 |
| 56 | o1·:·ForeignObject·of·type·int32</code></pre> | 56 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x | 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x |
| 60 | o2·=·int32{Address·=>·0x7f | 60 | o2·=·int32{Address·=>·0x7f3b6e475ad0}</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ········</table> | 62 | ········</table> |
| 63 | ········<div> | 63 | ········<div> |
| 64 | ··········<p>To·get·this,·use·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> | 64 | ··········<p>To·get·this,·use·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> |
| 65 | ········</div> | 65 | ········</div> |
| 66 | ········<table·class="examples"> | 66 | ········<table·class="examples"> |
| 67 | ··········<tr> | 67 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·address·x | 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·address·x |
| 69 | o3·=·0x7f | 69 | o3·=·0x7f3b6e475ad0 |
| 70 | o3·:·Pointer</code></pre> | 70 | o3·:·Pointer</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ········</table> | 72 | ········</table> |
| 73 | ········<div> | 73 | ········<div> |
| 74 | ··········<p>Use·<a·title="class·of·an·object"·href="../../Macaulay2Doc/html/_class.html">class</a>·to·determine·the·type·of·the·object.</p> | 74 | ··········<p>Use·<a·title="class·of·an·object"·href="../../Macaulay2Doc/html/_class.html">class</a>·to·determine·the·type·of·the·object.</p> |
| 75 | ········</div> | 75 | ········</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·=>·0x7f3b6e475ad0} |
| 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·=·0x7f3b6e475ad0 |
| 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 63, 15 lines modified | Offset 63, 15 lines modified | ||
| 63 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} | 63 | o2·=·{the,·quick,·brown,·fox,·jumps,·over,·the,·lazy,·dog} |
| 64 | o2·:·ForeignObject·of·type·char**</code></pre> | 64 | o2·:·ForeignObject·of·type·char**</code></pre> |
| 65 | </td>··········</tr> | 65 | </td>··········</tr> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 68 | o3·=·{0x7f | 68 | o3·=·{0x7fdae24821d0,·0x7fdae24821c0,·0x7fdae24821b0} |
| 69 | o3·:·ForeignObject·of·type·void**</code></pre> | 69 | o3·:·ForeignObject·of·type·void**</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ········</table> | 71 | ········</table> |
| 72 | ········<div> | 72 | ········<div> |
| 73 | ··········<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 | ··········<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> |
| 74 | ········</div> | 74 | ········</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·=·{0x7fdae24821d0,·0x7fdae24821c0,·0x7fdae24821b0} |
| 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 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | o1·=·{foo,·bar} | 82 | o1·=·{foo,·bar} |
| 83 | o1·:·ForeignObject·of·type·char**</code></pre> | 83 | o1·:·ForeignObject·of·type·char**</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 87 | o2·=·{0x7f | 87 | o2·=·{0x7ffb78c8a750,·0x7ffb78c8a740,·0x7ffb78c8a730} |
| 88 | o2·:·ForeignObject·of·type·void**</code></pre> | 88 | o2·:·ForeignObject·of·type·void**</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·int2star·=·foreignPointerArrayType(2·*·int) | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·int2star·=·foreignPointerArrayType(2·*·int) |
| 92 | o3·=·int32[2]* | 92 | o3·=·int32[2]* |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | i1·:·charstarstar·{"foo",·"bar"} | 20 | i1·:·charstarstar·{"foo",·"bar"} |
| 21 | o1·=·{foo,·bar} | 21 | o1·=·{foo,·bar} |
| 22 | o1·:·ForeignObject·of·type·char** | 22 | o1·:·ForeignObject·of·type·char** |
| 23 | i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} | 23 | i2·:·voidstarstar·{address·int·0,·address·int·1,·address·int·2} |
| 24 | o2·=·{0x7f | 24 | o2·=·{0x7ffb78c8a750,·0x7ffb78c8a740,·0x7ffb78c8a730} |
| 25 | o2·:·ForeignObject·of·type·void** | 25 | o2·:·ForeignObject·of·type·void** |
| 26 | i3·:·int2star·=·foreignPointerArrayType(2·*·int) | 26 | i3·:·int2star·=·foreignPointerArrayType(2·*·int) |
| 27 | o3·=·int32[2]* | 27 | o3·=·int32[2]* |
| 28 | o3·:·ForeignPointerArrayType | 28 | o3·:·ForeignPointerArrayType |
| Offset 75, 22 lines modified | Offset 75, 22 lines modified | ||
| 75 | ········<div> | 75 | ········<div> |
| 76 | ··········<p>To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the·type·followed·by·the·pointer.</p> | 76 | ··········<p>To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the·type·followed·by·the·pointer.</p> |
| 77 | ········</div> | 77 | ········</div> |
| 78 | ········<table·class="examples"> | 78 | ········<table·class="examples"> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·address·int·0 | 80 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·address·int·0 |
| 81 | o1·=·0x7f | 81 | o1·=·0x7fbbf4762b50 |
| 82 | o1·:·Pointer</code></pre> | 82 | o1·:·Pointer</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstar·ptr | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·voidstar·ptr |
| 86 | o2·=·0x7f | 86 | o2·=·0x7fbbf4762b50 |
| 87 | o2·:·ForeignObject·of·type·void*</code></pre> | 87 | o2·:·ForeignObject·of·type·void*</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·this·method:</h2> | 92 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 15, 18 lines modified | Offset 15, 18 lines modified | ||
| 15 | ····*·Outputs: | 15 | ····*·Outputs: |
| 16 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t, | 16 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t, |
| 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 | To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the | 18 | To·cast·a·Macaulay2·pointer·to·a·foreign·object·with·a·pointer·type,·give·the |
| 19 | type·followed·by·the·pointer. | 19 | type·followed·by·the·pointer. |
| 20 | i1·:·ptr·=·address·int·0 | 20 | i1·:·ptr·=·address·int·0 |
| 21 | o1·=·0x7f | 21 | o1·=·0x7fbbf4762b50 |
| 22 | o1·:·Pointer | 22 | o1·:·Pointer |
| 23 | i2·:·voidstar·ptr | 23 | i2·:·voidstar·ptr |
| 24 | o2·=·0x7f | 24 | o2·=·0x7fbbf4762b50 |
| 25 | o2·:·ForeignObject·of·type·void* | 25 | o2·:·ForeignObject·of·type·void* |
| 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 | ····*·_\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 | 27 | ····*·_\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 | ······pointer | 28 | ······pointer |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | o1·=·5 | 82 | o1·=·5 |
| 83 | o1·:·ForeignObject·of·type·int32</code></pre> | 83 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x |
| 87 | o2·=·0x7f | 87 | o2·=·0x7f7a2cc77af0 |
| 88 | o2·:·Pointer</code></pre> | 88 | o2·:·Pointer</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·int·ptr | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·int·ptr |
| 92 | o3·=·5 | 92 | 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·=·0x7f7a2cc77af0 |
| 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 75, 15 lines modified | Offset 75, 15 lines modified | ||
| 75 | ········<div> | 75 | ········<div> |
| 76 | ··········<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 | ··········<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> |
| 77 | ········</div> | 77 | ········</div> |
| 78 | ········<table·class="examples"> | 78 | ········<table·class="examples"> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·voidstar·address·int·5 | 80 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·voidstar·address·int·5 |
| 81 | o1·=·0x7f | 81 | o1·=·0x7f706247ca30 |
| 82 | o1·:·ForeignObject·of·type·void*</code></pre> | 82 | o1·:·ForeignObject·of·type·void*</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·int·*·ptr | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·int·*·ptr |
| 86 | o2·=·5 | 86 | o2·=·5 |
| Offset 14, 15 lines modified | Offset 14, 15 lines modified | ||
| 14 | ····*·Outputs: | 14 | ····*·Outputs: |
| 15 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,·of·type·T; | 15 | ··········o·a·_\x8f_\x8o_\x8r_\x8e_\x8i_\x8g_\x8n_\x8·_\x8o_\x8b_\x8j_\x8e_\x8c_\x8t,·of·type·T; |
| 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 | 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 | 17 | 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 | dereferencing·pointers. | 18 | dereferencing·pointers. |
| 19 | i1·:·ptr·=·voidstar·address·int·5 | 19 | i1·:·ptr·=·voidstar·address·int·5 |
| 20 | o1·=·0x7f | 20 | o1·=·0x7f706247ca30 |
| 21 | o1·:·ForeignObject·of·type·void* | 21 | o1·:·ForeignObject·of·type·void* |
| 22 | i2·:·int·*·ptr | 22 | i2·:·int·*·ptr |
| 23 | o2·=·5 | 23 | o2·=·5 |
| 24 | o2·:·ForeignObject·of·type·int32 | 24 | o2·:·ForeignObject·of·type·int32 |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | o1·=·myunion | 82 | o1·=·myunion |
| 83 | o1·:·ForeignUnionType</code></pre> | 83 | o1·:·ForeignUnionType</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·myunion·27 | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·myunion·27 |
| 87 | o2·=·HashTable{"bar"·=>·6.9 | 87 | o2·=·HashTable{"bar"·=>·6.94657e-310} |
| 88 | ···············"foo"·=>·27 | 88 | ···············"foo"·=>·27 |
| 89 | o2·:·ForeignObject·of·type·myunion</code></pre> | 89 | o2·:·ForeignObject·of·type·myunion</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·myunion·pi | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·myunion·pi |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 20 | i1·:·myunion·=·foreignUnionType("myunion",·{"foo"·=>·int,·"bar"·=>·double}) | 20 | i1·:·myunion·=·foreignUnionType("myunion",·{"foo"·=>·int,·"bar"·=>·double}) |
| 21 | o1·=·myunion | 21 | o1·=·myunion |
| 22 | o1·:·ForeignUnionType | 22 | o1·:·ForeignUnionType |
| 23 | i2·:·myunion·27 | 23 | i2·:·myunion·27 |
| 24 | o2·=·HashTable{"bar"·=>·6.9 | 24 | o2·=·HashTable{"bar"·=>·6.94657e-310} |
| 25 | ···············"foo"·=>·27 | 25 | ···············"foo"·=>·27 |
| 26 | o2·:·ForeignObject·of·type·myunion | 26 | o2·:·ForeignObject·of·type·myunion |
| 27 | i3·:·myunion·pi | 27 | i3·:·myunion·pi |
| 28 | o3·=·HashTable{"bar"·=>·3.14159···} | 28 | o3·=·HashTable{"bar"·=>·3.14159···} |
| 29 | ···············"foo"·=>·1413754136 | 29 | ···············"foo"·=>·1413754136 |
| Offset 55, 44 lines modified | Offset 55, 44 lines modified | ||
| 55 | o1·=·20 | 55 | o1·=·20 |
| 56 | o1·:·ForeignObject·of·type·int32</code></pre> | 56 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x | 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·x |
| 60 | o2·=·int32{Address·=>·0x7fd | 60 | o2·=·int32{Address·=>·0x7efd4083aa90}</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ········</table> | 62 | ········</table> |
| 63 | ········<div> | 63 | ········<div> |
| 64 | ··········<p>These·pointers·can·be·accessed·using·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> | 64 | ··········<p>These·pointers·can·be·accessed·using·<a·title="pointer·to·type·or·object"·href="_address.html">address</a>.</p> |
| 65 | ········</div> | 65 | ········</div> |
| 66 | ········<table·class="examples"> | 66 | ········<table·class="examples"> |
| 67 | ··········<tr> | 67 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·address·x | 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·address·x |
| 69 | o3·=·0x7fd | 69 | o3·=·0x7efd4083aa90 |
| 70 | o3·:·Pointer</code></pre> | 70 | o3·:·Pointer</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ········</table> | 72 | ········</table> |
| 73 | ········<div> | 73 | ········<div> |
| 74 | ··········<p>Simple·arithmetic·can·be·performed·on·pointers.</p> | 74 | ··········<p>Simple·arithmetic·can·be·performed·on·pointers.</p> |
| 75 | ········</div> | 75 | ········</div> |
| 76 | ········<table·class="examples"> | 76 | ········<table·class="examples"> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·ptr·+·5 | 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·ptr·+·5 |
| 79 | o4·=·0x7fd | 79 | o4·=·0x7efd4083aa95 |
| 80 | o4·:·Pointer</code></pre> | 80 | o4·:·Pointer</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i5·:·ptr·-·3 | 83 | <td>··············<pre><code·class="language-macaulay2">i5·:·ptr·-·3 |
| 84 | o5·=·0x7fd | 84 | o5·=·0x7efd4083aa8d |
| 85 | o5·:·Pointer</code></pre> | 85 | o5·:·Pointer</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>Functions·and·methods·returning·a·pointer·:</h2> | 90 | ········<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·=>·0x7fd | 14 | o2·=·int32{Address·=>·0x7efd4083aa90} |
| 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·=·0x7fd | 17 | o3·=·0x7efd4083aa90 |
| 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·=·0x7fd | 21 | o4·=·0x7efd4083aa95 |
| 22 | o4·:·Pointer | 22 | o4·:·Pointer |
| 23 | i5·:·ptr·-·3 | 23 | i5·:·ptr·-·3 |
| 24 | o5·=·0x7fd | 24 | o5·=·0x7efd4083aa8d |
| 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 55, 15 lines modified | Offset 55, 15 lines modified | ||
| 55 | o1·=·mpfr | 55 | o1·=·mpfr |
| 56 | o1·:·SharedLibrary</code></pre> | 56 | o1·:·SharedLibrary</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·mpfr | 59 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·mpfr |
| 60 | o2·=·SharedLibrary{0x7f | 60 | o2·=·SharedLibrary{0x7f170643f550,·mpfr}</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ········</table> | 62 | ········</table> |
| 63 | ······</div> | 63 | ······</div> |
| 64 | ······<div·class="waystouse"> | 64 | ······<div·class="waystouse"> |
| 65 | ········<h2>Functions·and·methods·returning·a·shared·library·:</h2> | 65 | ········<h2>Functions·and·methods·returning·a·shared·library·:</h2> |
| 66 | ········<ul> | 66 | ········<ul> |
| 67 | ··········<li> | 67 | ··········<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{0x7f170643f550,·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 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | o1·=·5 | 76 | o1·=·5 |
| 77 | o1·:·ForeignObject·of·type·int32</code></pre> | 77 | o1·:·ForeignObject·of·type·int32</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·address·x |
| 81 | o2·=·0x7f | 81 | o2·=·0x7f69e1457a80 |
| 82 | o2·:·Pointer</code></pre> | 82 | o2·:·Pointer</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·*ptr·=·int·6 | 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·*ptr·=·int·6 |
| 86 | o3·=·6 | 86 | 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·=·0x7f69e1457a80 |
| 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 71, 27 lines modified | Offset 71, 27 lines modified | ||
| 71 | ········<div> | 71 | ········<div> |
| 72 | ··········<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 | ··········<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> |
| 73 | ········</div> | 73 | ········</div> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·address·int | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·address·int |
| 77 | o1·=·0x5 | 77 | o1·=·0x55f234d681e0 |
| 78 | o1·:·Pointer</code></pre> | 78 | o1·:·Pointer</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ········</table> | 80 | ········</table> |
| 81 | ········<div> | 81 | ········<div> |
| 82 | ··········<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 | ··········<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> |
| 83 | ········</div> | 83 | ········</div> |
| 84 | ········<table·class="examples"> | 84 | ········<table·class="examples"> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·address·int·5 | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·address·int·5 |
| 87 | o2·=·0x7f | 87 | o2·=·0x7f93974a1930 |
| 88 | o2·:·Pointer</code></pre> | 88 | o2·:·Pointer</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ········</table> | 90 | ········</table> |
| 91 | ······</div> | 91 | ······</div> |
| 92 | ······<div·class="waystouse"> | 92 | ······<div·class="waystouse"> |
| 93 | ········<h2>Ways·to·use·<span·class="tt">address</span>·:</h2> | 93 | ········<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·=·0x55f234d681e0 |
| 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·=·0x7f93974a1930 |
| 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 231, 15 lines modified | Offset 231, 15 lines modified | ||
| 231 | o19·=·free | 231 | o19·=·free |
| 232 | o19·:·ForeignFunction</code></pre> | 232 | o19·:·ForeignFunction</code></pre> |
| 233 | </td>··········</tr> | 233 | </td>··········</tr> |
| 234 | ··········<tr> | 234 | ··········<tr> |
| 235 | <td>··············<pre><code·class="language-macaulay2">i20·:·x·=·malloc·8 | 235 | <td>··············<pre><code·class="language-macaulay2">i20·:·x·=·malloc·8 |
| 236 | o20·=·0x7f | 236 | o20·=·0x7fa278066810 |
| 237 | o20·:·ForeignObject·of·type·void*</code></pre> | 237 | o20·:·ForeignObject·of·type·void*</code></pre> |
| 238 | </td>··········</tr> | 238 | </td>··········</tr> |
| 239 | ··········<tr> | 239 | ··········<tr> |
| 240 | <td>··············<pre><code·class="language-macaulay2">i21·:·registerFinalizer(x,·free)</code></pre> | 240 | <td>··············<pre><code·class="language-macaulay2">i21·:·registerFinalizer(x,·free)</code></pre> |
| 241 | </td>··········</tr> | 241 | </td>··········</tr> |
| 242 | ········</table> | 242 | ········</table> |
| Offset 113, 15 lines modified | Offset 113, 15 lines modified | ||
| 113 | i19·:·free·=·foreignFunction("free",·void,·voidstar) | 113 | i19·:·free·=·foreignFunction("free",·void,·voidstar) |
| 114 | o19·=·free | 114 | o19·=·free |
| 115 | o19·:·ForeignFunction | 115 | o19·:·ForeignFunction |
| 116 | i20·:·x·=·malloc·8 | 116 | i20·:·x·=·malloc·8 |
| 117 | o20·=·0x7f | 117 | o20·=·0x7fa278066810 |
| 118 | o20·:·ForeignObject·of·type·void* | 118 | o20·:·ForeignObject·of·type·void* |
| 119 | i21·:·registerFinalizer(x,·free) | 119 | i21·:·registerFinalizer(x,·free) |
| 120 | *\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* | 120 | *\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* |
| 121 | ····*·foreignFunction(Pointer,String,ForeignType,VisibleList) | 121 | ····*·foreignFunction(Pointer,String,ForeignType,VisibleList) |
| 122 | ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType) | 122 | ····*·foreignFunction(SharedLibrary,String,ForeignType,ForeignType) |
| 123 | ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList) | 123 | ····*·foreignFunction(SharedLibrary,String,ForeignType,VisibleList) |
| Offset 80, 39 lines modified | Offset 80, 39 lines modified | ||
| 80 | ········<div> | 80 | ········<div> |
| 81 | ··········<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 | ··········<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> |
| 82 | ········</div> | 82 | ········</div> |
| 83 | ········<table·class="examples"> | 83 | ········<table·class="examples"> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·getMemory·8 | 85 | <td>··············<pre><code·class="language-macaulay2">i1·:·ptr·=·getMemory·8 |
| 86 | o1·=·0x7f | 86 | o1·=·0x7f6c60804370 |
| 87 | o1·:·ForeignObject·of·type·void*</code></pre> | 87 | o1·:·ForeignObject·of·type·void*</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ········</table> | 89 | ········</table> |
| 90 | ········<div> | 90 | ········<div> |
| 91 | ··········<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 | ··········<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> |
| 92 | ········</div> | 92 | ········</div> |
| 93 | ········<table·class="examples"> | 93 | ········<table·class="examples"> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·getMemory(8,·Atomic·=>·true) | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·ptr·=·getMemory(8,·Atomic·=>·true) |
| 96 | o2·=·0x7f | 96 | o2·=·0x7f6c60886910 |
| 97 | o2·:·ForeignObject·of·type·void*</code></pre> | 97 | o2·:·ForeignObject·of·type·void*</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ········</table> | 99 | ········</table> |
| 100 | ········<div> | 100 | ········<div> |
| 101 | ··········<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 | ··········<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> |
| 102 | ········</div> | 102 | ········</div> |
| 103 | ········<table·class="examples"> | 103 | ········<table·class="examples"> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·getMemory·int | 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·ptr·=·getMemory·int |
| 106 | o3·=·0x7f | 106 | o3·=·0x7f6c60886800 |
| 107 | o3·:·ForeignObject·of·type·void*</code></pre> | 107 | o3·:·ForeignObject·of·type·void*</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ······</div> | 110 | ······</div> |
| 111 | ······<div·class="waystouse"> | 111 | ······<div·class="waystouse"> |
| 112 | ········<h2>Ways·to·use·<span·class="tt">getMemory</span>·:</h2> | 112 | ········<h2>Ways·to·use·<span·class="tt">getMemory</span>·:</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·=·0x7f6c60804370 |
| 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·=·0x7f6c60886910 |
| 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·=·0x7f6c60886800 |
| 33 | o3·:·ForeignObject·of·type·void* | 33 | o3·:·ForeignObject·of·type·void* |
| 34 | *\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* | 34 | *\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* |
| 35 | ····*·getMemory(ForeignType) | 35 | ····*·getMemory(ForeignType) |
| 36 | ····*·getMemory(ForeignVoidType) | 36 | ····*·getMemory(ForeignVoidType) |
| 37 | ····*·getMemory(ZZ) | 37 | ····*·getMemory(ZZ) |
| 38 | *\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 | *\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 92, 23 lines modified | Offset 92, 23 lines modified | ||
| 92 | o3·:·FunctionClosure</code></pre> | 92 | o3·:·FunctionClosure</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer))</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·collectGarbage() | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·collectGarbage() |
| 99 | freeing·memory·at·0x7fb1300688a0 | ||
| 100 | freeing·memory·at·0x7fb1300521e0 | ||
| 101 | freeing·memory·at·0x7fb130004f20 | ||
| 102 | freeing·memory·at·0x7f | 99 | freeing·memory·at·0x7f829c068150 |
| 103 | freeing·memory·at·0x7f | 100 | freeing·memory·at·0x7f829c0521e0 |
| 104 | freeing·memory·at·0x7fb130066830 | ||
| 105 | freeing·memory·at·0x7f | 101 | freeing·memory·at·0x7f829c004f20 |
| 106 | freeing·memory·at·0x7f | 102 | freeing·memory·at·0x7f829c068880 |
| 103 | freeing·memory·at·0x7f829c0688a0 | ||
| 104 | freeing·memory·at·0x7f829c066810 | ||
| 105 | freeing·memory·at·0x7f829c05e150 | ||
| 106 | freeing·memory·at·0x7f829c0687f0 | ||
| 107 | freeing·memory·at·0x7f | 107 | freeing·memory·at·0x7f829c066830</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ······</div> | 110 | ······</div> |
| 111 | ······<div·class="waystouse"> | 111 | ······<div·class="waystouse"> |
| 112 | ········<h2>Ways·to·use·this·method:</h2> | 112 | ········<h2>Ways·to·use·this·method:</h2> |
| 113 | ········<ul> | 113 | ········<ul> |
| 114 | ··········<li> | 114 | ··········<li> |
| Offset 31, 19 lines modified | Offset 31, 19 lines modified | ||
| 31 | i3·:·finalizer·=·x·->·(print("freeing·memory·at·"·|·net·x);·free·x) | 31 | i3·:·finalizer·=·x·->·(print("freeing·memory·at·"·|·net·x);·free·x) |
| 32 | o3·=·finalizer | 32 | o3·=·finalizer |
| 33 | o3·:·FunctionClosure | 33 | o3·:·FunctionClosure |
| 34 | i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer)) | 34 | i4·:·for·i·to·9·do·(x·:=·malloc·8;·registerFinalizer(x,·finalizer)) |
| 35 | i5·:·collectGarbage() | 35 | i5·:·collectGarbage() |
| 36 | freeing·memory·at·0x7fb1300688a0 | ||
| 37 | freeing·memory·at·0x7fb1300521e0 | ||
| 38 | freeing·memory·at·0x7fb130004f20 | ||
| 39 | freeing·memory·at·0x7f | 36 | freeing·memory·at·0x7f829c068150 |
| 40 | freeing·memory·at·0x7f | 37 | freeing·memory·at·0x7f829c0521e0 |
| 41 | freeing·memory·at·0x7fb130066830 | ||
| 42 | freeing·memory·at·0x7f | 38 | freeing·memory·at·0x7f829c004f20 |
| 43 | freeing·memory·at·0x7f | 39 | freeing·memory·at·0x7f829c068880 |
| 40 | freeing·memory·at·0x7f829c0688a0 | ||
| 44 | freeing·memory·at·0x7f | 41 | freeing·memory·at·0x7f829c066810 |
| 42 | freeing·memory·at·0x7f829c05e150 | ||
| 43 | freeing·memory·at·0x7f829c0687f0 | ||
| 44 | freeing·memory·at·0x7f829c066830 | ||
| 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* |
| 46 | ····*·_\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 | 46 | ····*·_\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 |
| 47 | ······foreign·object | 47 | ······foreign·object |
| Offset 109, 22 lines modified | Offset 109, 22 lines modified | ||
| 109 | ········<div> | 109 | ········<div> |
| 110 | ··········<p>Foreign·pointer·objects·are·converted·to·<a·title="pointer·to·memory·address"·href="___Pointer.html">Pointer</a>·objects.</p> | 110 | ··········<p>Foreign·pointer·objects·are·converted·to·<a·title="pointer·to·memory·address"·href="___Pointer.html">Pointer</a>·objects.</p> |
| 111 | ········</div> | 111 | ········</div> |
| 112 | ········<table·class="examples"> | 112 | ········<table·class="examples"> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i5·:·x·=·voidstar·address·int·5 | 114 | <td>··············<pre><code·class="language-macaulay2">i5·:·x·=·voidstar·address·int·5 |
| 115 | o5·=·0x7ff | 115 | o5·=·0x7ffa45c523c0 |
| 116 | o5·:·ForeignObject·of·type·void*</code></pre> | 116 | o5·:·ForeignObject·of·type·void*</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·value·x | 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·value·x |
| 120 | o6·=·0x7ff | 120 | o6·=·0x7ffa45c523c0 |
| 121 | o6·:·Pointer</code></pre> | 121 | o6·:·Pointer</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ········</table> | 123 | ········</table> |
| 124 | ········<div> | 124 | ········<div> |
| 125 | ··········<p>Foreign·string·objects·are·converted·to·strings.</p> | 125 | ··········<p>Foreign·string·objects·are·converted·to·strings.</p> |
| 126 | ········</div> | 126 | ········</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·=·0x7ff | 39 | o5·=·0x7ffa45c523c0 |
| 40 | o5·:·ForeignObject·of·type·void* | 40 | o5·:·ForeignObject·of·type·void* |
| 41 | i6·:·value·x | 41 | i6·:·value·x |
| 42 | o6·=·0x7ff | 42 | o6·=·0x7ffa45c523c0 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=2537 | 9 | #:len=2537 |
| 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/M2-2138884-0/0 |
| 11 | i3·:·F·=·openOut(s) | 11 | i3·:·F·=·openOut(s) |
| 12 | o3·=·/tmp/M2- | 12 | o3·=·/tmp/M2-2138884-0/0 |
| 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/M2-2138884-0/0 |
| 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 76, 30 lines modified | Offset 76, 30 lines modified | ||
| 76 | ··············2·······4 | 76 | ··············2·······4 |
| 77 | o1·:·Matrix·ZZ··<--·ZZ</code></pre> | 77 | o1·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·s·=·temporaryFileName() | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·s·=·temporaryFileName() |
| 81 | o2·=·/tmp/M2- | 81 | o2·=·/tmp/M2-2138884-0/0</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·F·=·openOut(s) | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·F·=·openOut(s) |
| 85 | o3·=·/tmp/M2- | 85 | o3·=·/tmp/M2-2138884-0/0 |
| 86 | o3·:·File</code></pre> | 86 | o3·:·File</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·putMatrix(F,A)</code></pre> | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·putMatrix(F,A)</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·close(F) | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·close(F) |
| 93 | o5·=·/tmp/M2- | 93 | o5·=·/tmp/M2-2138884-0/0 |
| 94 | o5·:·File</code></pre> | 94 | o5·:·File</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·getMatrix(s) | 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·getMatrix(s) |
| 98 | o6·=·|·1·1·1·1·| | 98 | 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/M2-2138884-0/0 |
| 23 | i3·:·F·=·openOut(s) | 23 | i3·:·F·=·openOut(s) |
| 24 | o3·=·/tmp/M2- | 24 | o3·=·/tmp/M2-2138884-0/0 |
| 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/M2-2138884-0/0 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=3374 | 9 | #:len=3374 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·1.7 | 159 | ·--·used·1.77169s·(cpu);·1.03971s·(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·1.0 | 163 | ·--·used·1.00214s·(cpu);·0.637969s·(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·0.8 | 169 | ·--·used·0.845766s·(cpu);·0.541732s·(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·0.00414154s·(cpu);·0.00376324s·(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·0.33 | 50 | ·--·used·0.333673s·(cpu);·0.214543s·(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·0.240851s·(cpu);·0.160544s·(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·1.0 | 58 | ·--·used·1.02209s·(cpu);·0.85645s·(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·0.7 | 89 | ·--·used·0.700982s·(cpu);·0.47891s·(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·1.1 | 92 | ·--·used·1.11995s·(cpu);·0.720978s·(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·1.18275s·(cpu);·1.03325s·(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·0.4 | 100 | ·--·used·0.454417s·(cpu);·0.388873s·(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 325, 33 lines modified | Offset 325, 33 lines modified | ||
| 325 | ········</table> | 325 | ········</table> |
| 326 | ········<div> | 326 | ········<div> |
| 327 | ··········<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 | ··········<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> |
| 328 | ········</div> | 328 | ········</div> |
| 329 | ········<table·class="examples"> | 329 | ········<table·class="examples"> |
| 330 | ··········<tr> | 330 | ··········<tr> |
| 331 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) | 331 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·numeric·fpt(f,·DepthOfSearch·=>·3,·FinalAttempt·=>·true) |
| 332 | ·--·used·1.7 | 332 | ·--·used·1.77169s·(cpu);·1.03971s·(thread);·0s·(gc) |
| 333 | o27·=·{.142067,·.144} | 333 | o27·=·{.142067,·.144} |
| 334 | o27·:·List</code></pre> | 334 | o27·:·List</code></pre> |
| 335 | </td>··········</tr> | 335 | </td>··········</tr> |
| 336 | ··········<tr> | 336 | ··········<tr> |
| 337 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) | 337 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·fpt(f,·DepthOfSearch·=>·3,·Attempts·=>·7) |
| 338 | ·--·used·1.0 | 338 | ·--·used·1.00214s·(cpu);·0.637969s·(thread);·0s·(gc) |
| 339 | ······1 | 339 | ······1 |
| 340 | o28·=·- | 340 | o28·=·- |
| 341 | ······7 | 341 | ······7 |
| 342 | o28·:·QQ</code></pre> | 342 | o28·:·QQ</code></pre> |
| 343 | </td>··········</tr> | 343 | </td>··········</tr> |
| 344 | ··········<tr> | 344 | ··········<tr> |
| 345 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·fpt(f,·DepthOfSearch·=>·4) | 345 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·fpt(f,·DepthOfSearch·=>·4) |
| 346 | ·--·used·0.8 | 346 | ·--·used·0.845766s·(cpu);·0.541732s·(thread);·0s·(gc) |
| 347 | ······1 | 347 | ······1 |
| 348 | o29·=·- | 348 | o29·=·- |
| 349 | ······7 | 349 | ······7 |
| 350 | o29·:·QQ</code></pre> | 350 | o29·:·QQ</code></pre> |
| 351 | </td>··········</tr> | 351 | </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·1.7 | 235 | ·--·used·1.77169s·(cpu);·1.03971s·(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·1.0 | 239 | ·--·used·1.00214s·(cpu);·0.637969s·(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·0.8 | 245 | ·--·used·0.845766s·(cpu);·0.541732s·(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 176, 21 lines modified | Offset 176, 21 lines modified | ||
| 176 | <td>··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/17[x,y,z];</code></pre> | 176 | <td>··············<pre><code·class="language-macaulay2">i13·:·R·=·ZZ/17[x,y,z];</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ··········<tr> | 178 | ··········<tr> |
| 179 | <td>··············<pre><code·class="language-macaulay2">i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial</code></pre> | 179 | <td>··············<pre><code·class="language-macaulay2">i14·:·f·=·x^3·+·y^4·+·z^5;·--·a·diagonal·polynomial</code></pre> |
| 180 | </td>··········</tr> | 180 | </td>··········</tr> |
| 181 | ··········<tr> | 181 | ··········<tr> |
| 182 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·frobeniusNu(3,·f) | 182 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·frobeniusNu(3,·f) |
| 183 | ·--·used·0.00 | 183 | ·--·used·0.00414154s·(cpu);·0.00376324s·(thread);·0s·(gc) |
| 184 | o15·=·3756</code></pre> | 184 | o15·=·3756</code></pre> |
| 185 | </td>··········</tr> | 185 | </td>··········</tr> |
| 186 | ··········<tr> | 186 | ··········<tr> |
| 187 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) | 187 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·frobeniusNu(3,·f,·UseSpecialAlgorithms·=>·false) |
| 188 | ·--·used·0.33 | 188 | ·--·used·0.333673s·(cpu);·0.214543s·(thread);·0s·(gc) |
| 189 | o16·=·3756</code></pre> | 189 | o16·=·3756</code></pre> |
| 190 | </td>··········</tr> | 190 | </td>··········</tr> |
| 191 | ········</table> | 191 | ········</table> |
| 192 | ········<div> | 192 | ········<div> |
| 193 | ··········<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>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> |
| 194 | ··········<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> | 194 | ··········<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 201, 21 lines modified | Offset 201, 21 lines modified | ||
| 201 | <td>··············<pre><code·class="language-macaulay2">i17·:·R·=·ZZ/5[x,y,z];</code></pre> | 201 | <td>··············<pre><code·class="language-macaulay2">i17·:·R·=·ZZ/5[x,y,z];</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;</code></pre> | 204 | <td>··············<pre><code·class="language-macaulay2">i18·:·f·=·x^3·+·y^3·+·z^3·+·x*y*z;</code></pre> |
| 205 | </td>··········</tr> | 205 | </td>··········</tr> |
| 206 | ··········<tr> | 206 | ··········<tr> |
| 207 | <td>··············<pre><code·class="language-macaulay2">i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default | 207 | <td>··············<pre><code·class="language-macaulay2">i19·:·time·frobeniusNu(4,·f)·--·ContainmentTest·is·set·to·FrobeniusRoot,·by·default |
| 208 | ·--·used·0.2 | 208 | ·--·used·0.240851s·(cpu);·0.160544s·(thread);·0s·(gc) |
| 209 | o19·=·499</code></pre> | 209 | o19·=·499</code></pre> |
| 210 | </td>··········</tr> | 210 | </td>··········</tr> |
| 211 | ··········<tr> | 211 | ··········<tr> |
| 212 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) | 212 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·frobeniusNu(4,·f,·ContainmentTest·=>·StandardPower) |
| 213 | ·--·used·1.0 | 213 | ·--·used·1.02209s·(cpu);·0.85645s·(thread);·0s·(gc) |
| 214 | o20·=·499</code></pre> | 214 | o20·=·499</code></pre> |
| 215 | </td>··········</tr> | 215 | </td>··········</tr> |
| 216 | ········</table> | 216 | ········</table> |
| 217 | ········<div> | 217 | ········<div> |
| 218 | ··········<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 | ··········<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> |
| 219 | ········</div> | 219 | ········</div> |
| Offset 247, 38 lines modified | Offset 247, 38 lines modified | ||
| 247 | <td>··············<pre><code·class="language-macaulay2">i25·:·R·=·ZZ/5[x,y,z];</code></pre> | 247 | <td>··············<pre><code·class="language-macaulay2">i25·:·R·=·ZZ/5[x,y,z];</code></pre> |
| 248 | </td>··········</tr> | 248 | </td>··········</tr> |
| 249 | ··········<tr> | 249 | ··········<tr> |
| 250 | <td>··············<pre><code·class="language-macaulay2">i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;</code></pre> | 250 | <td>··············<pre><code·class="language-macaulay2">i26·:·f·=·x^2*y^4·+·y^2*z^7·+·z^2*x^8;</code></pre> |
| 251 | </td>··········</tr> | 251 | </td>··········</tr> |
| 252 | ··········<tr> | 252 | ··········<tr> |
| 253 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) | 253 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·frobeniusNu(5,·f)·--·uses·binary·search·(default) |
| 254 | ·--·used·0.7 | 254 | ·--·used·0.700982s·(cpu);·0.47891s·(thread);·0s·(gc) |
| 255 | o27·=·1124</code></pre> | 255 | o27·=·1124</code></pre> |
| 256 | </td>··········</tr> | 256 | </td>··········</tr> |
| 257 | ··········<tr> | 257 | ··········<tr> |
| 258 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) | 258 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·frobeniusNu(5,·f,·Search·=>·Linear) |
| 259 | ·--·used·1.1 | 259 | ·--·used·1.11995s·(cpu);·0.720978s·(thread);·0s·(gc) |
| 260 | o28·=·1124</code></pre> | 260 | o28·=·1124</code></pre> |
| 261 | </td>··········</tr> | 261 | </td>··········</tr> |
| 262 | ··········<tr> | 262 | ··········<tr> |
| 263 | <td>··············<pre><code·class="language-macaulay2">i29·:·M·=·ideal(x,·y,·z); | 263 | <td>··············<pre><code·class="language-macaulay2">i29·:·M·=·ideal(x,·y,·z); |
| 264 | o29·:·Ideal·of·R</code></pre> | 264 | o29·:·Ideal·of·R</code></pre> |
| 265 | </td>··········</tr> | 265 | </td>··········</tr> |
| 266 | ··········<tr> | 266 | ··········<tr> |
| 267 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) | 267 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·frobeniusNu(2,·M,·M^2)·--·uses·binary·search·(default) |
| 268 | ·--·used·1. | 268 | ·--·used·1.18275s·(cpu);·1.03325s·(thread);·0s·(gc) |
| 269 | o30·=·97</code></pre> | 269 | o30·=·97</code></pre> |
| 270 | </td>··········</tr> | 270 | </td>··········</tr> |
| 271 | ··········<tr> | 271 | ··········<tr> |
| 272 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier | 272 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·frobeniusNu(2,·M,·M^2,·Search·=>·Linear)·--·but·linear·search·gets·luckier |
| 273 | ·--·used·0.4 | 273 | ·--·used·0.454417s·(cpu);·0.388873s·(thread);·0s·(gc) |
| 274 | o31·=·97</code></pre> | 274 | o31·=·97</code></pre> |
| 275 | </td>··········</tr> | 275 | </td>··········</tr> |
| 276 | ········</table> | 276 | ········</table> |
| 277 | ········<div> | 277 | ········<div> |
| 278 | ··········<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 | ··········<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> |
| 279 | ········</div> | 279 | ········</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·0.00414154s·(cpu);·0.00376324s·(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·0.33 | 117 | ·--·used·0.333673s·(cpu);·0.214543s·(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·0.240851s·(cpu);·0.160544s·(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·1.0 | 144 | ·--·used·1.02209s·(cpu);·0.85645s·(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·0.7 | 175 | ·--·used·0.700982s·(cpu);·0.47891s·(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·1.1 | 178 | ·--·used·1.11995s·(cpu);·0.720978s·(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·1.18275s·(cpu);·1.03325s·(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·0.4 | 187 | ·--·used·0.454417s·(cpu);·0.388873s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | YXJjcw== | 8 | YXJjcw== |
| 9 | #:len=3082 | 9 | #:len=3082 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJpbnRzIG5vZGUgbGFiZWxzIGZvciB0 | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJpbnRzIG5vZGUgbGFiZWxzIGZvciB0 |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | UlJFRk1ldGhvZA== | 8 | UlJFRk1ldGhvZA== |
| 9 | #:len=209 | 9 | #:len=209 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjEzMCwgInVuZG9jdW1lbnRlZCIgPT4g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjEzMCwgInVuZG9jdW1lbnRlZCIgPT4g |
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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·0.56 | 213 | ·--·used·0.568422s·(cpu);·0.363141s·(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·1.4 | 217 | ·--·used·1.4139s·(cpu);·0.785253s·(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 337, 23 lines modified | Offset 337, 23 lines modified | ||
| 337 | ······|·7/10·7/3··5/2·1···| | 337 | ······|·7/10·7/3··5/2·1···| |
| 338 | ···············3·······4 | 338 | ···············3·······4 |
| 339 | o26·:·Matrix·QQ··<--·QQ</code></pre> | 339 | o26·:·Matrix·QQ··<--·QQ</code></pre> |
| 340 | </td>··········</tr> | 340 | </td>··········</tr> |
| 341 | ··········<tr> | 341 | ··········<tr> |
| 342 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·C·=·orbitClosure(X,Mat) | 342 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·C·=·orbitClosure(X,Mat) |
| 343 | ·--·used·0.56 | 343 | ·--·used·0.568422s·(cpu);·0.363141s·(thread);·0s·(gc) |
| 344 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety· | 344 | o27·=·an·"equivariant·K-class"·on·a·GKM·variety· |
| 345 | o27·:·KClass</code></pre> | 345 | o27·:·KClass</code></pre> |
| 346 | </td>··········</tr> | 346 | </td>··········</tr> |
| 347 | ··········<tr> | 347 | ··········<tr> |
| 348 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) | 348 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·C·=·orbitClosure(X,Mat,·RREFMethod·=>·true) |
| 349 | ·--·used·1.4 | 349 | ·--·used·1.4139s·(cpu);·0.785253s·(thread);·0s·(gc) |
| 350 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety· | 350 | o28·=·an·"equivariant·K-class"·on·a·GKM·variety· |
| 351 | o28·:·KClass</code></pre> | 351 | o28·:·KClass</code></pre> |
| 352 | </td>··········</tr> | 352 | </td>··········</tr> |
| 353 | ········</table> | 353 | ········</table> |
| 354 | ······</div> | 354 | ······</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·0.56 | 248 | ·--·used·0.568422s·(cpu);·0.363141s·(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·1.4 | 252 | ·--·used·1.4139s·(cpu);·0.785253s·(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 |
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| 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 | c29sdmVyTUxFKExpc3QsR3JhcGgp | 8 | c29sdmVyTUxFKExpc3QsR3JhcGgp |
| 9 | #:len=274 | 9 | #:len=274 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk1OSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk1OSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc29sdmVyTUxFLExpc3QsR3JhcGgpLCJzb2x2ZXJN | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsoc29sdmVyTUxFLExpc3QsR3JhcGgpLCJzb2x2ZXJN |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cGljdHVyZVpvbmUoU3BoZXJlKQ== | 8 | cGljdHVyZVpvbmUoU3BoZXJlKQ== |
| 9 | #:len=747 | 9 | #:len=747 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZCB0aGUgem9uZSB0aGF0IGNvbnRh | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiZmluZCB0aGUgem9uZSB0aGF0IGNvbnRh |
| 11 | aW5zIHRoZSBzcGhlcmUiLCAibGluZW51bSIgPT4gMTExNywgSW5wdXRzID0+IHtTUEFOe1RUeyJz | 11 | aW5zIHRoZSBzcGhlcmUiLCAibGluZW51bSIgPT4gMTExNywgSW5wdXRzID0+IHtTUEFOe1RUeyJz |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cmV2ZXJzZUJyZWFkdGhGaXJzdFNlYXJjaA== | 8 | cmV2ZXJzZUJyZWFkdGhGaXJzdFNlYXJjaA== |
| 9 | #:len=1606 | 9 | #:len=1606 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicnVucyBhIHJldmVyc2UgYnJlYWR0aCBm | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicnVucyBhIHJldmVyc2UgYnJlYWR0aCBm |
| 11 | aXJzdCBzZWFyY2ggb24gdGhlIGRpZ3JhcGggYW5kIHJldHVybnMgYSBsaXN0IG9mIHRoZSB2ZXJ0 | 11 | aXJzdCBzZWFyY2ggb24gdGhlIGRpZ3JhcGggYW5kIHJldHVybnMgYSBsaXN0IG9mIHRoZSB2ZXJ0 |
| 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·=·{ | 36 | o3·=·{newDigraph,·digraph,·map} |
| 37 | o3·:·List | 37 | o3·:·List |
| 38 | i4·:· | 38 | i4·:· |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ·········································6·=>·{} | 84 | ·········································6·=>·{} |
| 85 | o2·:·SortedDigraph</code></pre> | 85 | o2·:·SortedDigraph</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·H | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·H |
| 89 | o3·=·{ | 89 | o3·=·{newDigraph,·digraph,·map} |
| 90 | o3·:·List</code></pre> | 90 | o3·:·List</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ········</table> | 92 | ········</table> |
| 93 | ······</div> | 93 | ······</div> |
| 94 | ······<div> | 94 | ······<div> |
| 95 | ········<h2>See·also</h2> | 95 | ········<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·=·{ | 41 | o3·=·{newDigraph,·digraph,·map} |
| 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·--·outputs·a·hashtable·containing·original·digraph,·new·digraph | 44 | ····*·_\x8t_\x8o_\x8p_\x8S_\x8o_\x8r_\x8t·--·outputs·a·hashtable·containing·original·digraph,·new·digraph |
| 45 | ······with·vertices·topologically·sorted·and·a·map·from·vertices·of·original | 45 | ······with·vertices·topologically·sorted·and·a·map·from·vertices·of·original |
| 46 | ······digraph·to·new·digraph. | 46 | ······digraph·to·new·digraph. |
| 47 | ····*·_\x8S_\x8o_\x8r_\x8t_\x8e_\x8d_\x8D_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h·--·hashtable·used·in·topSort | 47 | ····*·_\x8S_\x8o_\x8r_\x8t_\x8e_\x8d_\x8D_\x8i_\x8g_\x8r_\x8a_\x8p_\x8h·--·hashtable·used·in·topSort |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=2580 | 9 | #:len=2580 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyBhIG1hdHJpeCBvZiB3ZWln | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyBhIG1hdHJpeCBvZiB3ZWln |
| 11 | aHQgY29uc3RyYWludHMiLCAibGluZW51bSIgPT4gNjcxLCBJbnB1dHMgPT4ge1NQQU57VFR7Ik0i | 11 | aHQgY29uc3RyYWludHMiLCAibGluZW51bSIgPT4gNjcxLCBJbnB1dHMgPT4ge1NQQU57VFR7Ik0i |
| Offset 243, 72 lines modified | Offset 243, 67 lines modified | ||
| 243 | ······|······2····················2··············································2··2·····································································2·················2·········2··2···············2·······2··2··2·| | 243 | ······|······2····················2··············································2··2·····································································2·················2·········2··2···············2·······2··2··2·| |
| 244 | ······|t··-·t···+·t··t··t···-·t··t···+·t··t··t···+·t··t··t···-·t··t··t··t···+·25t··t···+·4t··t··t···-·2t··t··t··t···-·2t··t··t··t···-·2t··t··t··t···+·t··t··t··t···+·t··t··t··t···-·3t··t···+·3t··t··t··t···-·26t··t··t··| | 244 | ······|t··-·t···+·t··t··t···-·t··t···+·t··t··t···+·t··t··t···-·t··t··t··t···+·25t··t···+·4t··t··t···-·2t··t··t··t···-·2t··t··t··t···-·2t··t··t··t···+·t··t··t··t···+·t··t··t··t···-·3t··t···+·3t··t··t··t···-·26t··t··t··| |
| 245 | ······|·6····23····16·20·22····14·22····23·22·13····23·16·19····16·22·13·19······16·19·····23·20·21·····20·22·13·21·····16·20·19·21·····23·13·19·21····22·13·19·21····16·13·19·21·····20·21·····20·13·19·21······13·19·21| | 245 | ······|·6····23····16·20·22····14·22····23·22·13····23·16·19····16·22·13·19······16·19·····23·20·21·····20·22·13·21·····16·20·19·21·····23·13·19·21····22·13·19·21····16·13·19·21·····20·21·····20·13·19·21······13·19·21| |
| 246 | ······+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 246 | ······+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 247 | i12·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 247 | i12·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 248 | o12·=·|· | 248 | o12·=·|·-36·-30·42·21·-22·23·23·16·-7·-30·-11·-40·19·19·-41·-22·24·-36·-8·33 |
| 249 | ······----------------------------------------------------------------------- | 249 | ······----------------------------------------------------------------------- |
| 250 | ······-2 | 250 | ······-29·-10·-29·-29·| |
| 251 | ···············1·······24 | 251 | ···············1·······24 |
| 252 | o12·:·Matrix·kk··<--·kk | 252 | o12·:·Matrix·kk··<--·kk |
| 253 | i13·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 253 | i13·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 254 | o13·=·|·2 | 254 | o13·=·|·24·-7·-25·32·-28·13·-49·11·-17·-17·-2·-50·30·19·-41·-21·-38·-24·21·39 |
| 255 | ······----------------------------------------------------------------------- | 255 | ······----------------------------------------------------------------------- |
| 256 | ······0·-16·-47·| | 256 | ······34·0·-16·-47·| |
| 257 | ···············1·······24 | 257 | ···············1·······24 |
| 258 | o13·:·Matrix·kk··<--·kk | 258 | o13·:·Matrix·kk··<--·kk |
| 259 | i14·:·F1·=·sub(F,·(vars·S)|pt1) | 259 | i14·:·F1·=·sub(F,·(vars·S)|pt1) |
| 260 | ··············2············· | 260 | ··············2·············2······························2··············· |
| 261 | o14·=·ideal·(a··-· | 261 | o14·=·ideal·(a··-·7b*c·+·21c··-·30a*d·-·22b*d·-·30c*d·-·36d·,·a*b·-·41b*c·- |
| 262 | ······----------------------------------------------------------------------- | 262 | ······----------------------------------------------------------------------- |
| 263 | ·········2······························2···2············· | 263 | ·········2······························2···2··············2················ |
| 264 | ······11c··-· | 264 | ······11c··-·22a*d·-·40b*d·+·23c*d·+·42d·,·b··-·29b*c·+·24c··-·10a*d·-·36b*d |
| 265 | ······----------------------------------------------------------------------- | 265 | ······----------------------------------------------------------------------- |
| 266 | ················· | 266 | ···················2··················2······························2 |
| 267 | ······19c*d· | 267 | ······+·19c*d·+·23d·,·a*c·-·29b*c·-·8c··-·29a*d·+·33b*d·+·19c*d·+·16d·) |
| 268 | o14·:·Ideal·of·S | 268 | o14·:·Ideal·of·S |
| 269 | i15·:·F2·=·sub(F,·(vars·S)|pt2) | 269 | i15·:·F2·=·sub(F,·(vars·S)|pt2) |
| 270 | ··············2··············2····························· | 270 | ··············2··············2·····························2··············· |
| 271 | o15·=·ideal·(a··-·1 | 271 | o15·=·ideal·(a··-·17b*c·+·32c··-·17a*d·-·28b*d·-·7c*d·+·24d·,·a*b·-·41b*c·- |
| 272 | ······----------------------------------------------------------------------- | 272 | ······----------------------------------------------------------------------- |
| 273 | ········ | 273 | ········2······························2···2··············2·················· |
| 274 | ······2 | 274 | ······2c··-·21a*d·-·50b*d·+·13c*d·-·25d·,·b··+·34b*c·-·38c··-·24b*d·+·30c*d·- |
| 275 | ······----------------------------------------------------------------------- | 275 | ······----------------------------------------------------------------------- |
| 276 | ········· | 276 | ·········2···················2······························2 |
| 277 | ······ | 277 | ······49d·,·a*c·-·16b*c·+·21c··-·47a*d·+·39b*d·+·19c*d·+·11d·) |
| 278 | o15·:·Ideal·of·S | 278 | o15·:·Ideal·of·S |
| 279 | i16·:·decompose·F1 | 279 | i16·:·decompose·F1 |
| 280 | ··································· | 280 | ···································2··············2······················2 |
| 281 | o16·=·{ideal·(a·-·29b·-· | 281 | o16·=·{ideal·(a·-·29b·-·8c·-·11d,·b··-·29b*c·+·24c··-·23b*d·+·40c*d·+·14d·), |
| 282 | ······----------------------------------------------------------------------- | 282 | ······----------------------------------------------------------------------- |
| 283 | ······ideal·(c·-·29d,·b· | 283 | ······ideal·(c·-·29d,·b·-·35d,·a·+·43d)} |
| 284 | o16·:·List | 284 | o16·:·List |
| 285 | i17·:·decompose·F2 | 285 | i17·:·decompose·F2 |
| 286 | o17·=·{ideal·(b·-·6c·-·42d,·a·+·26c·-·5d),·ideal·(b·+·40c·+·18d,·a·-·46c·+ | ||
| 286 | ·······························2······························2···2·········· | ||
| 287 | o17·=·{ideal·(a*c·-·16b*c·+·21c··-·47a*d·+·34b*d·+·39c*d·+·50d·,·b··+·19b*c·- | ||
| 288 | ······----------------------------------------------------------------------- | ||
| 289 | ·········2·····················2···················2························ | ||
| 290 | ······24c··-·38b*d·+·26c*d·+·3d·,·a*b·+·22b*c·+·20c··-·27a*d·+·49b*d·-·11c*d | ||
| 291 | ······----------------------------------------------------------------------- | 287 | ······----------------------------------------------------------------------- |
| 288 | ······19d)} | ||
| 292 | ···········2···2··············2······························2 | ||
| 293 | ······+·18d·,·a··-·19b*c·-·20c··+·38a*d·-·48b*d·-·50c*d·+·20d·)} | ||
| 294 | o17·:·List | 289 | o17·:·List |
| 295 | i18·:· | 290 | i18·:· |
| Offset 103, 46 lines modified | Offset 103, 46 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·=·|· | 112 | o15·=·|·-48·-46·16·17·-1·-43·15·-1·12·-18·-6·-28·14·-28·-9·32·-22·-39·6·-47 |
| 113 | ······----------------------------------------------------------------------- | 113 | ······----------------------------------------------------------------------- |
| 114 | ······ | 114 | ······28·-37·-47·38·-16·-15·34·27·-13·-43·22·16·0·-18·19·2·| |
| 115 | ···············1·······36 | 115 | ···············1·······36 |
| 116 | o15·:·Matrix·kk··<--·kk | 116 | o15·:·Matrix·kk··<--·kk |
| 117 | i16·:·F1·=·sub(F,·(vars·S)|pt1) | 117 | i16·:·F1·=·sub(F,·(vars·S)|pt1) |
| 118 | ··············2··············2····························2··············· | 118 | ··············2··············2·····························2··············· |
| 119 | o16·=·ideal·(a·· | 119 | o16·=·ideal·(a··+·25b*c·-·43c··+·27a*d·-·11b*d·+·44c*d·-·6d·,·a*b·-·19b*c·+ |
| 120 | ······----------------------------------------------------------------------- | 120 | ······----------------------------------------------------------------------- |
| 121 | ·········2····························· | 121 | ·········2······························2··················2················ |
| 122 | ······ | 122 | ······46c··+·40a*d·+·15b*d·+·27c*d·+·48d·,·a*c·-·29b*c·-·8c··+·39a*d·-·20b*d |
| 123 | ······----------------------------------------------------------------------- | 123 | ······----------------------------------------------------------------------- |
| 124 | ·················2···2··············2······························2·····2·· | 124 | ··················2···2··············2······························2·····2·· |
| 125 | ······ | 125 | ······-·22c*d·-·2d·,·b··+·24b*c·+·19c··-·10a*d·+·21b*d·-·16c*d·-·35d·,·b*c··- |
| 126 | ······----------------------------------------------------------------------- | 126 | ······----------------------------------------------------------------------- |
| 127 | ···················2·········2·······2········2·····3···3················2 | 127 | ···················2·········2········2········2······3···3················2· |
| 128 | ······29b*c*d·-·3 | 128 | ······29b*c*d·-·30c·d·-·36a*d··+·34b*d··+·48c*d··-·23d·,·c··-·24b*c*d·-·16c·d |
| 129 | ······----------------------------------------------------------------------- | 129 | ······----------------------------------------------------------------------- |
| 130 | ··········2········2········2······3 | 130 | ·············2········2········2······3 |
| 131 | ······ | 131 | ······+·19a*d··-·38b*d··-·29c*d··-·26d·) |
| 132 | o16·:·Ideal·of·S | 132 | o16·:·Ideal·of·S |
| 133 | i17·:·betti·res·F1 | 133 | i17·:·betti·res·F1 |
| 134 | ·············0·1·2·3 | 134 | ·············0·1·2·3 |
| 135 | o17·=·total:·1·6·8·3 | 135 | o17·=·total:·1·6·8·3 |
| Offset 150, 28 lines modified | Offset 150, 28 lines modified | ||
| 150 | ··········1:·.·4·4·1 | 150 | ··········1:·.·4·4·1 |
| 151 | ··········2:·.·2·4·2 | 151 | ··········2:·.·2·4·2 |
| 152 | o17·:·BettiTally | 152 | o17·:·BettiTally |
| 153 | i18·:·F2·=·sub(F,·(vars·S)|pt2) | 153 | i18·:·F2·=·sub(F,·(vars·S)|pt2) |
| 154 | ··············2············· | 154 | ··············2·············2······························2··············· |
| 155 | o18·=·ideal·(a··-· | 155 | o18·=·ideal·(a··-·9b*c·-·18c··-·28a*d·-·43b*d·+·16c*d·-·48d·,·a*b·-·16b*c·+ |
| 156 | ······----------------------------------------------------------------------- | 156 | ······----------------------------------------------------------------------- |
| 157 | ········ | 157 | ········2······························2···················2················ |
| 158 | ······ | 158 | ······6c··+·28a*d·+·14b*d·+·12c*d·-·46d·,·a*c·+·16b*c·-·15c··+·27a*d·-·47b*d |
| 159 | ······----------------------------------------------------------------------- | 159 | ······----------------------------------------------------------------------- |
| 160 | ················· | 160 | ·················2···2··············2······················2·····2·········· |
| 161 | ······-· | 161 | ······-·28c*d·-·d·,·b··+·19b*c·-·13c··-·37b*d·+·32c*d·+·15d·,·b*c··-·43b*c*d |
| 162 | ······----------------------------------------------------------------------- | 162 | ······----------------------------------------------------------------------- |
| 163 | ·········2·········2········2 | 163 | ···········2·········2········2·······2······3···3···············2·········2 |
| 164 | ······ | 164 | ······-·47c·d·+·34a*d··-·22b*d··-·6c*d··+·17d·,·c··+·2b*c*d·+·22c·d·-·18a*d· |
| 165 | ······----------------------------------------------------------------------- | 165 | ······----------------------------------------------------------------------- |
| 166 | ·············2········2···· | 166 | ·············2········2····3 |
| 167 | ······ | 167 | ······+·38b*d··-·39c*d··-·d·) |
| 168 | o18·:·Ideal·of·S | 168 | o18·:·Ideal·of·S |
| 169 | i19·:·betti·res·F2 | 169 | i19·:·betti·res·F2 |
| 170 | ·············0·1·2·3 | 170 | ·············0·1·2·3 |
| 171 | o19·=·total:·1·6·8·3 | 171 | o19·=·total:·1·6·8·3 |
| Offset 179, 27 lines modified | Offset 179, 30 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 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 184 | o20·=·|ideal·(c·+·39d,·b·+·27d,·a·-·18d)························································································································| | ||
| 185 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 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·)| | ||
| 188 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 183 | ······+------------------------------------------------------+ | ||
| 184 | o20·=·|ideal·(c·-·13d,·b·+·32d,·a·+·36d)·····················| | ||
| 185 | ······+------------------------------------------------------+ | ||
| 186 | ······|ideal·(c·-·16d,·b·+·d,·a·+·16d)·······················| | ||
| 187 | ······+------------------------------------------------------+ | ||
| 188 | ······|····································2············2····| | ||
| 189 | ······|ideal·(b·-·6c·+·33d,·a·-·36c·+·2d,·c··+·43c*d·-·d·)···| | ||
| 190 | ······+------------------------------------------------------+ | ||
| 191 | ······|·····································2··············2·| | ||
| 192 | ······|ideal·(b·+·29c·+·7d,·a·-·19c·+·24d,·c··-·20c*d·-·30d·)| | ||
| 193 | ······+------------------------------------------------------+ | ||
| 194 | i21·:·netList·decompose·F2 | 189 | i21·:·netList·decompose·F2 |
| 195 | ······+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 196 | ······|·······················2······························2···2··············2···················2···················2······························2···2··············2······························2···3················2·········2········2········2······3·····2················2·········2········2········2······3·| | ||
| 197 | o21·=·|ideal·(a*c·+·2b*c·-·13c··+·33a*d·+·16b*d·-·18c*d·-·39d·,·b··-·47b*c·-·28c··-·5b*d·-·c*d·-·30d·,·a*b·-·20b*c·-·45c··-·35a*d·+·21b*d·-·34c*d·+·10d·,·a··-·35b*c·+·22c··-·25a*d·+·23b*d·+·43c*d·+·30d·,·c··+·38b*c*d·+·22c·d·-·15a*d··-·47b*d··-·39c*d··+·40d·,·b*c··-·43b*c*d·+·19c·d·+·34a*d··+·21b*d··+·46c*d··+·20d·)| | ||
| 198 | ······+------------------------------------------------------- | 190 | ······+-------------------------------------------------------+ |
| 191 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| | ||
| 192 | ······+-------------------------------------------------------+ | ||
| 193 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| | ||
| 194 | ······+-------------------------------------------------------+ | ||
| 195 | ······|ideal·(c·+·24d,·b·-·49d,·a)····························| | ||
| 196 | ······+-------------------------------------------------------+ | ||
| 197 | ······|ideal·(c·+·14d,·b·+·31d,·a·-·16d)······················| | ||
| 198 | ······+-------------------------------------------------------+ | ||
| 199 | ······|······································2··············2·| | ||
| 200 | ······|ideal·(b·+·11c·+·22d,·a·+·11c·+·42d,·c··-·43c*d·+·31d·)| | ||
| 201 | ······+-------------------------------------------------------+ | ||
| 199 | i22·:· | 202 | i22·:· |
| 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·=·{|·1·49·24·-23·-36·-30·|,·|·23·-29·-29·19·19·19·|,·|·38·-11·-10·-42·-29 |
| 17 | ·····------------------------------------------------------------------------ | 17 | ·····------------------------------------------------------------------------ |
| 18 | ·····- | 18 | ·····-8·|,·|·-37·-35·-22·-14·-29·-24·|} |
| 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 | ······+------------------------------------------------------------------------------------+ | 71 | ······+-----------------------------------------------------------------------------------------+ |
| 72 | o13·=·||· | 72 | o13·=·||·42·-50·-50·38·-39·6·-1·47·49·-18·18·-28·-47·19·48·34·-13·11·-16·-38·39·21·-43·-39·|····| |
| 73 | ······+------------------------------------------------------------------------------------+ | 73 | ······+-----------------------------------------------------------------------------------------+ |
| 74 | ······||·4 | 74 | ······||·-44·-31·-9·-21·-42·-36·-47·-20·38·-34·-3·-43·22·16·-35·2·-48·32·-28·-15·-47·38·-47·45·|| |
| 75 | ······+------------------------------------------------------------------------------------+ | 75 | ······+-----------------------------------------------------------------------------------------+ |
| 76 | ······||· | 76 | ······||·45·-29·-1·-4·42·-35·4·-13·18·-17·1·21·39·-23·50·15·-11·-11·19·47·-16·7·48·43·|·········| |
| 77 | ······+------------------------------------------------------------------------------------+ | 77 | ······+-----------------------------------------------------------------------------------------+ |
| 78 | ······||· | 78 | ······||·35·-44·-33·-8·21·-2·-44·-20·19·-28·19·27·11·40·34·33·1·-14·35·36·11·-38·-3·46·|········| |
| 79 | ······+------------------------------------------------------------------------------------+ | 79 | ······+-----------------------------------------------------------------------------------------+ |
| 80 | ······||· | 80 | ······||·33·47·46·16·-22·-25·-44·-36·-30·-37·30·-25·-47·29·-41·2·-13·-41·-47·22·-23·-7·-10·15·|·| |
| 81 | ······+------------------------------------------------------------------------------------+ | 81 | ······+-----------------------------------------------------------------------------------------+ |
| 82 | ······||· | 82 | ······||·43·1·-41·23·-42·-14·37·-50·-32·-20·-5·-49·-9·32·-18·-22·24·43·-18·30·39·27·-30·-32·|···| |
| 83 | ······+------------------------------------------------------------------------------------+ | 83 | ······+-----------------------------------------------------------------------------------------+ |
| 84 | ······||· | 84 | ······||·12·8·26·15·22·12·0·-5·6·17·-21·-18·-33·-49·-19·33·-20·0·-15·-48·39·0·44·-19·|··········| |
| 85 | ······+------------------------------------------------------------------------------------+ | 85 | ······+-----------------------------------------------------------------------------------------+ |
| 86 | ······||·- | 86 | ······||·-48·-27·-8·-33·-35·-16·-31·-44·-46·-49·-21·-3·-26·13·-40·4·-11·-48·36·-39·9·-39·-8·22·|| |
| 87 | ······+------------------------------------------------------------------------------------+ | 87 | ······+-----------------------------------------------------------------------------------------+ |
| 88 | ······||·34· | 88 | ······||·34·29·30·-1·34·-22·32·-6·39·-28·-15·37·41·-30·47·-22·-6·-7·-8·43·36·-3·35·16·|·········| |
| 89 | ······+------------------------------------------------------------------------------------+ | 89 | ······+-----------------------------------------------------------------------------------------+ |
| 90 | ······||· | 90 | ······||·10·-5·-38·-25·-21·21·14·42·19·-41·8·-35·25·-31·29·3·-49·38·-35·-9·6·40·-13·-2·|········| |
| 91 | ······+------------------------------------------------------------------------------------+ | 91 | ······+-----------------------------------------------------------------------------------------+ |
| 92 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | 92 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) |
| 93 | ······+---------------------------------------------------------------------------------------+ | 93 | ······+----------------------------------------------------------------------------------------+ |
| 94 | o14·=·||· | 94 | o14·=·||·1·4·44·1·40·20·29·-26·42·-16·-4·50·-40·48·23·-34·-35·37·30·4·-47·27·-31·0·|···········| |
| 95 | ······+---------------------------------------------------------------------------------------+ | 95 | ······+----------------------------------------------------------------------------------------+ |
| 96 | ······||·- | 96 | ······||·-29·-11·2·28·-12·-21·-30·20·-1·-42·27·-45·-48·-14·-3·-45·-37·30·-31·-39·-48·-29·47·0·|| |
| 97 | ······+---------------------------------------------------------------------------------------+ | 97 | ······+----------------------------------------------------------------------------------------+ |
| 98 | ······||·- | 98 | ······||·-20·14·48·3·14·33·18·-46·24·45·-1·-29·1·31·-44·-2·-22·40·28·-49·-18·46·10·0·|·········| |
| 99 | ······+---------------------------------------------------------------------------------------+ | 99 | ······+----------------------------------------------------------------------------------------+ |
| 100 | ······||· | 100 | ······||·21·25·-23·-45·-48·-40·8·-7·-6·-1·14·3·-13·-44·-44·21·-41·3·30·7·13·-17·8·0·|··········| |
| 101 | ······+---------------------------------------------------------------------------------------+ | 101 | ······+----------------------------------------------------------------------------------------+ |
| 102 | ······||·- | 102 | ······||·-15·26·-17·12·0·-5·35·-11·0·-31·-39·40·49·-21·-42·28·42·-18·-29·8·30·-46·23·0·|·······| |
| 103 | ······+---------------------------------------------------------------------------------------+ | 103 | ······+----------------------------------------------------------------------------------------+ |
| 104 | ······||·- | 104 | ······||·-17·38·-49·-9·2·-1·-9·2·3·49·33·49·-46·25·1·0·-18·12·15·-28·18·-16·27·0·|·············| |
| 105 | ······+---------------------------------------------------------------------------------------+ | 105 | ······+----------------------------------------------------------------------------------------+ |
| 106 | ······||·- | 106 | ······||·-50·3·-12·-21·-10·4·36·-14·19·-9·43·-48·44·-35·16·6·20·-39·23·-21·-37·-23·19·0·|······| |
| 107 | ······+---------------------------------------------------------------------------------------+ | 107 | ······+----------------------------------------------------------------------------------------+ |
| 108 | ······||·3 | 108 | ······||·36·-17·-27·37·-4·12·42·-16·-15·12·-3·-14·-28·38·-24·18·-9·6·-47·0·-28·47·-33·0·|······| |
| 109 | ······+---------------------------------------------------------------------------------------+ | 109 | ······+----------------------------------------------------------------------------------------+ |
| 110 | ······||·4 | 110 | ······||·43·44·31·14·-9·-4·-4·-40·-48·45·47·17·-37·29·-9·10·-28·-33·-29·28·26·5·42·0·|·········| |
| 111 | ······+---------------------------------------------------------------------------------------+ | 111 | ······+----------------------------------------------------------------------------------------+ |
| 112 | ······||· | 112 | ······||·17·-47·-23·8·-18·-45·-25·2·44·41·-19·-37·5·16·2·38·-13·-20·30·44·4·22·-29·0·|·········| |
| 113 | ······+---------------------------------------------------------------------------------------+ | 113 | ······+----------------------------------------------------------------------------------------+ |
| 114 | i15·:· | 114 | i15·:· |
| Offset 207, 48 lines modified | Offset 207, 48 lines modified | ||
| 207 | <td>··············<pre><code·class="language-macaulay2">i13·:·#compsJ | 207 | <td>··············<pre><code·class="language-macaulay2">i13·:·#compsJ |
| 208 | o13·=·2</code></pre> | 208 | o13·=·2</code></pre> |
| 209 | </td>··········</tr> | 209 | </td>··········</tr> |
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 211 | <td>··············<pre><code·class="language-macaulay2">i14·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 212 | o14·=·|· | 212 | o14·=·|·-6·48·44·-23·-2·-11·-35·-26·27·-43·48·27·15·-22·25·-16·34·-29·46·-20 |
| 213 | ······----------------------------------------------------------------------- | 213 | ······----------------------------------------------------------------------- |
| 214 | ······ | 214 | ······40·21·-30·-38·-19·-8·-36·39·19·-29·-16·-29·-10·19·24·-24·| |
| 215 | ···············1·······36 | 215 | ···············1·······36 |
| 216 | o14·:·Matrix·kk··<--·kk</code></pre> | 216 | o14·:·Matrix·kk··<--·kk</code></pre> |
| 217 | </td>··········</tr> | 217 | </td>··········</tr> |
| 218 | ··········<tr> | 218 | ··········<tr> |
| 219 | <td>··············<pre><code·class="language-macaulay2">i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 219 | <td>··············<pre><code·class="language-macaulay2">i15·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 220 | o15·=·|· | 220 | o15·=·|·-48·-46·16·17·-1·-43·15·-1·12·-18·-6·-28·14·-28·-9·32·-22·-39·6·-47 |
| 221 | ······----------------------------------------------------------------------- | 221 | ······----------------------------------------------------------------------- |
| 222 | ······ | 222 | ······28·-37·-47·38·-16·-15·34·27·-13·-43·22·16·0·-18·19·2·| |
| 223 | ···············1·······36 | 223 | ···············1·······36 |
| 224 | o15·:·Matrix·kk··<--·kk</code></pre> | 224 | o15·:·Matrix·kk··<--·kk</code></pre> |
| 225 | </td>··········</tr> | 225 | </td>··········</tr> |
| 226 | ··········<tr> | 226 | ··········<tr> |
| 227 | <td>··············<pre><code·class="language-macaulay2">i16·:·F1·=·sub(F,·(vars·S)|pt1) | 227 | <td>··············<pre><code·class="language-macaulay2">i16·:·F1·=·sub(F,·(vars·S)|pt1) |
| 228 | ··············2··············2····························2··············· | 228 | ··············2··············2·····························2··············· |
| 229 | o16·=·ideal·(a·· | 229 | o16·=·ideal·(a··+·25b*c·-·43c··+·27a*d·-·11b*d·+·44c*d·-·6d·,·a*b·-·19b*c·+ |
| 230 | ······----------------------------------------------------------------------- | 230 | ······----------------------------------------------------------------------- |
| 231 | ·········2····························· | 231 | ·········2······························2··················2················ |
| 232 | ······ | 232 | ······46c··+·40a*d·+·15b*d·+·27c*d·+·48d·,·a*c·-·29b*c·-·8c··+·39a*d·-·20b*d |
| 233 | ······----------------------------------------------------------------------- | 233 | ······----------------------------------------------------------------------- |
| 234 | ·················2···2··············2······························2·····2·· | 234 | ··················2···2··············2······························2·····2·· |
| 235 | ······ | 235 | ······-·22c*d·-·2d·,·b··+·24b*c·+·19c··-·10a*d·+·21b*d·-·16c*d·-·35d·,·b*c··- |
| 236 | ······----------------------------------------------------------------------- | 236 | ······----------------------------------------------------------------------- |
| 237 | ···················2·········2·······2········2·····3···3················2 | 237 | ···················2·········2········2········2······3···3················2· |
| 238 | ······29b*c*d·-·3 | 238 | ······29b*c*d·-·30c·d·-·36a*d··+·34b*d··+·48c*d··-·23d·,·c··-·24b*c*d·-·16c·d |
| 239 | ······----------------------------------------------------------------------- | 239 | ······----------------------------------------------------------------------- |
| 240 | ··········2········2········2······3 | 240 | ·············2········2········2······3 |
| 241 | ······ | 241 | ······+·19a*d··-·38b*d··-·29c*d··-·26d·) |
| 242 | o16·:·Ideal·of·S</code></pre> | 242 | o16·:·Ideal·of·S</code></pre> |
| 243 | </td>··········</tr> | 243 | </td>··········</tr> |
| 244 | ··········<tr> | 244 | ··········<tr> |
| 245 | <td>··············<pre><code·class="language-macaulay2">i17·:·betti·res·F1 | 245 | <td>··············<pre><code·class="language-macaulay2">i17·:·betti·res·F1 |
| 246 | ·············0·1·2·3 | 246 | ·············0·1·2·3 |
| Offset 258, 28 lines modified | Offset 258, 28 lines modified | ||
| 258 | ··········2:·.·2·4·2 | 258 | ··········2:·.·2·4·2 |
| 259 | o17·:·BettiTally</code></pre> | 259 | o17·:·BettiTally</code></pre> |
| 260 | </td>··········</tr> | 260 | </td>··········</tr> |
| 261 | ··········<tr> | 261 | ··········<tr> |
| 262 | <td>··············<pre><code·class="language-macaulay2">i18·:·F2·=·sub(F,·(vars·S)|pt2) | 262 | <td>··············<pre><code·class="language-macaulay2">i18·:·F2·=·sub(F,·(vars·S)|pt2) |
| 263 | ··············2············· | 263 | ··············2·············2······························2··············· |
| 264 | o18·=·ideal·(a··-· | 264 | o18·=·ideal·(a··-·9b*c·-·18c··-·28a*d·-·43b*d·+·16c*d·-·48d·,·a*b·-·16b*c·+ |
| 265 | ······----------------------------------------------------------------------- | 265 | ······----------------------------------------------------------------------- |
| 266 | ········ | 266 | ········2······························2···················2················ |
| 267 | ······ | 267 | ······6c··+·28a*d·+·14b*d·+·12c*d·-·46d·,·a*c·+·16b*c·-·15c··+·27a*d·-·47b*d |
| 268 | ······----------------------------------------------------------------------- | 268 | ······----------------------------------------------------------------------- |
| 269 | ················· | 269 | ·················2···2··············2······················2·····2·········· |
| 270 | ······-· | 270 | ······-·28c*d·-·d·,·b··+·19b*c·-·13c··-·37b*d·+·32c*d·+·15d·,·b*c··-·43b*c*d |
| 271 | ······----------------------------------------------------------------------- | 271 | ······----------------------------------------------------------------------- |
| 272 | ·········2·········2········2 | 272 | ···········2·········2········2·······2······3···3···············2·········2 |
| 273 | ······ | 273 | ······-·47c·d·+·34a*d··-·22b*d··-·6c*d··+·17d·,·c··+·2b*c*d·+·22c·d·-·18a*d· |
| 274 | ······----------------------------------------------------------------------- | 274 | ······----------------------------------------------------------------------- |
| 275 | ·············2········2···· | 275 | ·············2········2····3 |
| 276 | ······ | 276 | ······+·38b*d··-·39c*d··-·d·) |
| 277 | o18·:·Ideal·of·S</code></pre> | 277 | o18·:·Ideal·of·S</code></pre> |
| 278 | </td>··········</tr> | 278 | </td>··········</tr> |
| 279 | ··········<tr> | 279 | ··········<tr> |
| 280 | <td>··············<pre><code·class="language-macaulay2">i19·:·betti·res·F2 | 280 | <td>··············<pre><code·class="language-macaulay2">i19·:·betti·res·F2 |
| 281 | ·············0·1·2·3 | 281 | ·············0·1·2·3 |
| Offset 294, 33 lines modified | Offset 294, 36 lines modified | ||
| 294 | ········<div> | 294 | ········<div> |
| 295 | ··········<p>What·are·the·ideals·F1·and·F2?</p> | 295 | ··········<p>What·are·the·ideals·F1·and·F2?</p> |
| 296 | ········</div> | 296 | ········</div> |
| 297 | ········<table·class="examples"> | 297 | ········<table·class="examples"> |
| 298 | ··········<tr> | 298 | ··········<tr> |
| 299 | <td>··············<pre><code·class="language-macaulay2">i20·:·netList·decompose·F1 | 299 | <td>··············<pre><code·class="language-macaulay2">i20·:·netList·decompose·F1 |
| 300 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 301 | o20·=·|ideal·(c·+·39d,·b·+·27d,·a·-·18d)························································································································| | ||
| 302 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 303 | ······|····························2··············2·····················2···3················2········2········2······3·····2················2·········2······3·| | ||
| 304 | ······|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·)| | ||
| 305 | ······+---------------------------------------------------------------------------------------------------------------------------------------------------------+</code></pre> | ||
| 300 | ······+------------------------------------------------------+ | ||
| 301 | o20·=·|ideal·(c·-·13d,·b·+·32d,·a·+·36d)·····················| | ||
| 302 | ······+------------------------------------------------------+ | ||
| 303 | ······|ideal·(c·-·16d,·b·+·d,·a·+·16d)·······················| | ||
| 304 | ······+------------------------------------------------------+ | ||
| 305 | ······|····································2············2····| | ||
| 306 | ······|ideal·(b·-·6c·+·33d,·a·-·36c·+·2d,·c··+·43c*d·-·d·)···| | ||
| 307 | ······+------------------------------------------------------+ | ||
| 308 | ······|·····································2··············2·| | ||
| 309 | ······|ideal·(b·+·29c·+·7d,·a·-·19c·+·24d,·c··-·20c*d·-·30d·)| | ||
| 310 | ······+------------------------------------------------------+</code></pre> | ||
| 311 | </td>··········</tr> | 306 | </td>··········</tr> |
| 312 | ··········<tr> | 307 | ··········<tr> |
| 313 | <td>··············<pre><code·class="language-macaulay2">i21·:·netList·decompose·F2 | 308 | <td>··············<pre><code·class="language-macaulay2">i21·:·netList·decompose·F2 |
| 314 | ······+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | ||
| 315 | ······|·······················2······························2···2··············2···················2···················2······························2···2··············2······························2···3················2·········2········2········2······3·····2················2·········2········2········2······3·| | ||
| 316 | o21·=·|ideal·(a*c·+·2b*c·-·13c··+·33a*d·+·16b*d·-·18c*d·-·39d·,·b··-·47b*c·-·28c··-·5b*d·-·c*d·-·30d·,·a*b·-·20b*c·-·45c··-·35a*d·+·21b*d·-·34c*d·+·10d·,·a··-·35b*c·+·22c··-·25a*d·+·23b*d·+·43c*d·+·30d·,·c··+·38b*c*d·+·22c·d·-·15a*d··-·47b*d··-·39c*d··+·40d·,·b*c··-·43b*c*d·+·19c·d·+·34a*d··+·21b*d··+·46c*d··+·20d·)| | ||
| 317 | ······+------------------------------------------------------- | 309 | ······+-------------------------------------------------------+ |
| 310 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| | ||
| 311 | ······+-------------------------------------------------------+ | ||
| 312 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| | ||
| 313 | ······+-------------------------------------------------------+ | ||
| 314 | ······|ideal·(c·+·24d,·b·-·49d,·a)····························| | ||
| 315 | ······+-------------------------------------------------------+ | ||
| 316 | ······|ideal·(c·+·14d,·b·+·31d,·a·-·16d)······················| | ||
| 317 | ······+-------------------------------------------------------+ | ||
| 318 | ······|······································2··············2·| | ||
| 319 | ······|ideal·(b·+·11c·+·22d,·a·+·11c·+·42d,·c··-·43c*d·+·31d·)| | ||
| 320 | ······+-------------------------------------------------------+</code></pre> | ||
| 318 | </td>··········</tr> | 321 | </td>··········</tr> |
| 319 | ········</table> | 322 | ········</table> |
| 320 | ········<div> | 323 | ········<div> |
| 321 | ··········<p>We·can·determine·what·these·represent.··One·should·be·a·set·of·6·points,·where·5·lie·on·a·plane.··The·other·should·be·6·points·with·3·points·on·one·line,·and·the·other·3·points·on·a·skew·line.</p> | 324 | ··········<p>We·can·determine·what·these·represent.··One·should·be·a·set·of·6·points,·where·5·lie·on·a·plane.··The·other·should·be·6·points·with·3·points·on·one·line,·and·the·other·3·points·on·a·skew·line.</p> |
| 322 | ········</div> | 325 | ········</div> |
| 323 | ······</div> | 326 | ······</div> |
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| Offset 171, 117 lines modified | Offset 171, 115 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·=·|· | 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 | ······ | 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····························· | 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 | ······29b*c*d·-·3 | 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·.·.·. |
| 207 | ··········1:·.·4·4·1 | 207 | ··········1:·.·4·4·1 |
| 208 | ··········2:·.·2·4·2 | 208 | ··········2:·.·2·4·2 |
| 209 | o17·:·BettiTally | 209 | o17·:·BettiTally |
| 210 | i18·:·F2·=·sub(F,·(vars·S)|pt2) | 210 | i18·:·F2·=·sub(F,·(vars·S)|pt2) |
| 211 | ··············2············· | 211 | ··············2·············2······························2 |
| 212 | o18·=·ideal·(a··-· | 212 | o18·=·ideal·(a··-·9b*c·-·18c··-·28a*d·-·43b*d·+·16c*d·-·48d·,·a*b·-·16b*c·+ |
| 213 | ······----------------------------------------------------------------------- | 213 | ······----------------------------------------------------------------------- |
| 214 | ········ | 214 | ········2······························2···················2 |
| 215 | ······ | 215 | ······6c··+·28a*d·+·14b*d·+·12c*d·-·46d·,·a*c·+·16b*c·-·15c··+·27a*d·-·47b*d |
| 216 | ······----------------------------------------------------------------------- | 216 | ······----------------------------------------------------------------------- |
| 217 | ···················2··· | 217 | ·················2···2··············2······················2·····2 |
| 218 | ······-· | 218 | ······-·28c*d·-·d·,·b··+·19b*c·-·13c··-·37b*d·+·32c*d·+·15d·,·b*c··-·43b*c*d |
| 219 | ······----------------------------------------------------------------------- | 219 | ······----------------------------------------------------------------------- |
| 220 | ·········2·········2········2 | 220 | ···········2·········2········2·······2······3···3···············2·········2 |
| 221 | ······ | 221 | ······-·47c·d·+·34a*d··-·22b*d··-·6c*d··+·17d·,·c··+·2b*c*d·+·22c·d·-·18a*d |
| 222 | ······----------------------------------------------------------------------- | 222 | ······----------------------------------------------------------------------- |
| 223 | ·············2········2···· | 223 | ·············2········2····3 |
| 224 | ······ | 224 | ······+·38b*d··-·39c*d··-·d·) |
| 225 | o18·:·Ideal·of·S | 225 | o18·:·Ideal·of·S |
| 226 | i19·:·betti·res·F2 | 226 | i19·:·betti·res·F2 |
| 227 | ·············0·1·2·3 | 227 | ·············0·1·2·3 |
| 228 | o19·=·total:·1·6·8·3 | 228 | o19·=·total:·1·6·8·3 |
| 229 | ··········0:·1·.·.·. | 229 | ··········0:·1·.·.·. |
| 230 | ··········1:·.·4·4·1 | 230 | ··········1:·.·4·4·1 |
| 231 | ··········2:·.·2·4·2 | 231 | ··········2:·.·2·4·2 |
| 232 | o19·:·BettiTally | 232 | o19·:·BettiTally |
| 233 | What·are·the·ideals·F1·and·F2? | 233 | What·are·the·ideals·F1·and·F2? |
| 234 | i20·:·netList·decompose·F1 | 234 | i20·:·netList·decompose·F1 |
| 235 | ······+------------------------------------------------------+ | ||
| 236 | o20·=·|ideal·(c·-·13d,·b·+·32d,·a·+·36d)·····················| | ||
| 237 | ······+------------------------------------------------------+ | ||
| 238 | ······|ideal·(c·-·16d,·b·+·d,·a·+·16d)·······················| | ||
| 239 | ······+------------------------------------------------------+ | ||
| 240 | ······|····································2············2····| | ||
| 241 | ······|ideal·(b·-·6c·+·33d,·a·-·36c·+·2d,·c··+·43c*d·-·d·)···| | ||
| 242 | ······+------------------------------------------------------+ | ||
| 243 | ······|·····································2··············2·| | ||
| 244 | ······|ideal·(b·+·29c·+·7d,·a·-·19c·+·24d,·c··-·20c*d·-·30d·)| | ||
| 245 | ······+------------------------------------------------------+ | ||
| 246 | i21·:·netList·decompose·F2 | ||
| 247 | ······+------------------------------------------------------------------------ | 235 | ······+------------------------------------------------------------------------ |
| 248 | ------------------------------------------------------------------------------- | 236 | ------------------------------------------------------------------------------- |
| 237 | --+ | ||
| 238 | o20·=·|ideal·(c·+·39d,·b·+·27d,·a·-·18d) | ||
| 239 | | | ||
| 240 | ······+------------------------------------------------------------------------ | ||
| 249 | ------------------------------------------------------------------------------- | 241 | ------------------------------------------------------------------------------- |
| 250 | ------------------------------------------------------------------------------- | ||
| 251 | -+ | 242 | --+ |
| 252 | ······|·······················2······························2··· | 243 | ······|····························2··············2·····················2···3 |
| 244 | 2········2········2······3·····2················2·········2······3·| | ||
| 245 | ······|ideal·(a·-·29b·-·8c·-·13d,·b··+·24b*c·+·19c··+·34b*d·+·5c*d·+·37d·,·c··- | ||
| 246 | 24b*c*d·-·16c·d·+·8b*d··+·22c*d··+·19d·,·b*c··-·29b*c*d·-·30c·d·-·38c*d··+·14d | ||
| 253 | 2···················2···················2······························2···2 | ||
| 254 | 2······························2···3················2·········2········2 | ||
| 255 | 2······3·····2················2·········2········2········2······3·| | ||
| 256 | o21·=·|ideal·(a*c·+·2b*c·-·13c··+·33a*d·+·16b*d·-·18c*d·-·39d·,·b··-·47b*c·- | ||
| 257 | 28c··-·5b*d·-·c*d·-·30d·,·a*b·-·20b*c·-·45c··-·35a*d·+·21b*d·-·34c*d·+·10d·,·a | ||
| 258 | -·35b*c·+·22c··-·25a*d·+·23b*d·+·43c*d·+·30d·,·c··+·38b*c*d·+·22c·d·-·15a*d··- | ||
| 259 | 47b*d··-·39c*d··+·40d·,·b*c··-·43b*c*d·+·19c·d·+·34a*d··+·21b*d··+·46c*d··+·20d | ||
| 260 | )| | 247 | )| |
| 261 | ······+------------------------------------------------------------------------ | 248 | ······+------------------------------------------------------------------------ |
| 262 | ------------------------------------------------------------------------------- | 249 | ------------------------------------------------------------------------------- |
| 263 | ------------------------------------------------------------------------------- | ||
| 264 | ------------------------------------------------------------------------------- | ||
| 265 | -+ | 250 | --+ |
| 251 | i21·:·netList·decompose·F2 | ||
| 252 | ······+-------------------------------------------------------+ | ||
| 253 | o21·=·|ideal·(c·-·32d,·b·-·5d,·a·-·29d)·······················| | ||
| 254 | ······+-------------------------------------------------------+ | ||
| 255 | ······|ideal·(c·+·43d,·b·-·47d,·a·-·27d)······················| | ||
| 256 | ······+-------------------------------------------------------+ | ||
| 257 | ······|ideal·(c·+·24d,·b·-·49d,·a)····························| | ||
| 258 | ······+-------------------------------------------------------+ | ||
| 259 | ······|ideal·(c·+·14d,·b·+·31d,·a·-·16d)······················| | ||
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| Offset 93, 17 lines modified | Offset 93, 17 lines modified | ||
| 93 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) | 93 | ·····c*e·+·b*f,·-·c*d·+·b*e,·-·c*e·+·b*f,·-·e··+·d*f) |
| 94 | o3·:·Ideal·of·S</code></pre> | 94 | o3·:·Ideal·of·S</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·pts·=·randomPointsOnRationalVariety(I,·4) | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·pts·=·randomPointsOnRationalVariety(I,·4) |
| 98 | o4·=·{|· | 98 | o4·=·{|·1·49·24·-23·-36·-30·|,·|·23·-29·-29·19·19·19·|,·|·38·-11·-10·-42·-29 |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ·····- | 100 | ·····-8·|,·|·-37·-35·-22·-14·-29·-24·|} |
| 101 | o4·:·List</code></pre> | 101 | o4·:·List</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·for·p·in·pts·list·sub(I,·p)·==·0 | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·for·p·in·pts·list·sub(I,·p)·==·0 |
| 105 | o5·=·{true,·true,·true,·true} | 105 | o5·=·{true,·true,·true,·true} |
| Offset 165, 60 lines modified | Offset 165, 60 lines modified | ||
| 165 | ········<div> | 165 | ········<div> |
| 166 | ··········<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 | ··········<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> |
| 167 | ········</div> | 167 | ········</div> |
| 168 | ········<table·class="examples"> | 168 | ········<table·class="examples"> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) | 170 | <td>··············<pre><code·class="language-macaulay2">i13·:·netList·randomPointsOnRationalVariety(compsJ_0,·10) |
| 171 | ······+------------------------------------------------------------------------------------+ | 171 | ······+-----------------------------------------------------------------------------------------+ |
| 172 | o13·=·||· | 172 | o13·=·||·42·-50·-50·38·-39·6·-1·47·49·-18·18·-28·-47·19·48·34·-13·11·-16·-38·39·21·-43·-39·|····| |
| 173 | ······+------------------------------------------------------------------------------------+ | 173 | ······+-----------------------------------------------------------------------------------------+ |
| 174 | ······||·4 | 174 | ······||·-44·-31·-9·-21·-42·-36·-47·-20·38·-34·-3·-43·22·16·-35·2·-48·32·-28·-15·-47·38·-47·45·|| |
| 175 | ······+------------------------------------------------------------------------------------+ | 175 | ······+-----------------------------------------------------------------------------------------+ |
| 176 | ······||· | 176 | ······||·45·-29·-1·-4·42·-35·4·-13·18·-17·1·21·39·-23·50·15·-11·-11·19·47·-16·7·48·43·|·········| |
| 177 | ······+------------------------------------------------------------------------------------+ | 177 | ······+-----------------------------------------------------------------------------------------+ |
| 178 | ······||· | 178 | ······||·35·-44·-33·-8·21·-2·-44·-20·19·-28·19·27·11·40·34·33·1·-14·35·36·11·-38·-3·46·|········| |
| 179 | ······+------------------------------------------------------------------------------------+ | 179 | ······+-----------------------------------------------------------------------------------------+ |
| 180 | ······||· | 180 | ······||·33·47·46·16·-22·-25·-44·-36·-30·-37·30·-25·-47·29·-41·2·-13·-41·-47·22·-23·-7·-10·15·|·| |
| 181 | ······+------------------------------------------------------------------------------------+ | 181 | ······+-----------------------------------------------------------------------------------------+ |
| 182 | ······||· | 182 | ······||·43·1·-41·23·-42·-14·37·-50·-32·-20·-5·-49·-9·32·-18·-22·24·43·-18·30·39·27·-30·-32·|···| |
| 183 | ······+------------------------------------------------------------------------------------+ | 183 | ······+-----------------------------------------------------------------------------------------+ |
| 184 | ······||· | 184 | ······||·12·8·26·15·22·12·0·-5·6·17·-21·-18·-33·-49·-19·33·-20·0·-15·-48·39·0·44·-19·|··········| |
| 185 | ······+------------------------------------------------------------------------------------+ | 185 | ······+-----------------------------------------------------------------------------------------+ |
| 186 | ······||·- | 186 | ······||·-48·-27·-8·-33·-35·-16·-31·-44·-46·-49·-21·-3·-26·13·-40·4·-11·-48·36·-39·9·-39·-8·22·|| |
| 187 | ······+------------------------------------------------------------------------------------+ | 187 | ······+-----------------------------------------------------------------------------------------+ |
| 188 | ······||·34· | 188 | ······||·34·29·30·-1·34·-22·32·-6·39·-28·-15·37·41·-30·47·-22·-6·-7·-8·43·36·-3·35·16·|·········| |
| 189 | ······+------------------------------------------------------------------------------------+ | 189 | ······+-----------------------------------------------------------------------------------------+ |
| 190 | ······||· | 190 | ······||·10·-5·-38·-25·-21·21·14·42·19·-41·8·-35·25·-31·29·3·-49·38·-35·-9·6·40·-13·-2·|········| |
| 191 | ······+------------------------------------------------------------------------------------+</code></pre> | 191 | ······+-----------------------------------------------------------------------------------------+</code></pre> |
| 192 | </td>··········</tr> | 192 | </td>··········</tr> |
| 193 | ··········<tr> | 193 | ··········<tr> |
| 194 | <td>··············<pre><code·class="language-macaulay2">i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | 194 | <td>··············<pre><code·class="language-macaulay2">i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) |
| 195 | ······+---------------------------------------------------------------------------------------+ | 195 | ······+----------------------------------------------------------------------------------------+ |
| 196 | o14·=·||· | 196 | o14·=·||·1·4·44·1·40·20·29·-26·42·-16·-4·50·-40·48·23·-34·-35·37·30·4·-47·27·-31·0·|···········| |
| 197 | ······+---------------------------------------------------------------------------------------+ | 197 | ······+----------------------------------------------------------------------------------------+ |
| 198 | ······||·- | 198 | ······||·-29·-11·2·28·-12·-21·-30·20·-1·-42·27·-45·-48·-14·-3·-45·-37·30·-31·-39·-48·-29·47·0·|| |
| 199 | ······+---------------------------------------------------------------------------------------+ | 199 | ······+----------------------------------------------------------------------------------------+ |
| 200 | ······||·- | 200 | ······||·-20·14·48·3·14·33·18·-46·24·45·-1·-29·1·31·-44·-2·-22·40·28·-49·-18·46·10·0·|·········| |
| 201 | ······+---------------------------------------------------------------------------------------+ | 201 | ······+----------------------------------------------------------------------------------------+ |
| 202 | ······||· | 202 | ······||·21·25·-23·-45·-48·-40·8·-7·-6·-1·14·3·-13·-44·-44·21·-41·3·30·7·13·-17·8·0·|··········| |
| 203 | ······+---------------------------------------------------------------------------------------+ | 203 | ······+----------------------------------------------------------------------------------------+ |
| 204 | ······||·- | 204 | ······||·-15·26·-17·12·0·-5·35·-11·0·-31·-39·40·49·-21·-42·28·42·-18·-29·8·30·-46·23·0·|·······| |
| 205 | ······+---------------------------------------------------------------------------------------+ | 205 | ······+----------------------------------------------------------------------------------------+ |
| 206 | ······||·- | 206 | ······||·-17·38·-49·-9·2·-1·-9·2·3·49·33·49·-46·25·1·0·-18·12·15·-28·18·-16·27·0·|·············| |
| 207 | ······+---------------------------------------------------------------------------------------+ | 207 | ······+----------------------------------------------------------------------------------------+ |
| 208 | ······||·- | 208 | ······||·-50·3·-12·-21·-10·4·36·-14·19·-9·43·-48·44·-35·16·6·20·-39·23·-21·-37·-23·19·0·|······| |
| 209 | ······+---------------------------------------------------------------------------------------+ | 209 | ······+----------------------------------------------------------------------------------------+ |
| 210 | ······||·3 | 210 | ······||·36·-17·-27·37·-4·12·42·-16·-15·12·-3·-14·-28·38·-24·18·-9·6·-47·0·-28·47·-33·0·|······| |
| 211 | ······+---------------------------------------------------------------------------------------+ | 211 | ······+----------------------------------------------------------------------------------------+ |
| 212 | ······||·4 | 212 | ······||·43·44·31·14·-9·-4·-4·-40·-48·45·47·17·-37·29·-9·10·-28·-33·-29·28·26·5·42·0·|·········| |
| 213 | ······+---------------------------------------------------------------------------------------+ | 213 | ······+----------------------------------------------------------------------------------------+ |
| 214 | ······||· | 214 | ······||·17·-47·-23·8·-18·-45·-25·2·44·41·-19·-37·5·16·2·38·-13·-20·30·44·4·22·-29·0·|·········| |
| 215 | ······+---------------------------------------------------------------------------------------+</code></pre> | 215 | ······+----------------------------------------------------------------------------------------+</code></pre> |
| 216 | </td>··········</tr> | 216 | </td>··········</tr> |
| 217 | ········</table> | 217 | ········</table> |
| 218 | ······</div> | 218 | ······</div> |
| 219 | ······<div> | 219 | ······<div> |
| 220 | ········<h2>Caveat</h2> | 220 | ········<h2>Caveat</h2> |
| 221 | ········<div> | 221 | ········<div> |
| 222 | ··········<p>This·routine·expects·the·input·to·represent·an·irreducible·variety</p> | 222 | ··········<p>This·routine·expects·the·input·to·represent·an·irreducible·variety</p> |
| 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·=·{|·1·49·24·-23·-36·-30·|,·|·23·-29·-29·19·19·19·|,·|·38·-11·-10·-42·-29 |
| 35 | ·····------------------------------------------------------------------------ | 35 | ·····------------------------------------------------------------------------ |
| 36 | ·····- | 36 | ·····-8·|,·|·-37·-35·-22·-14·-29·-24·|} |
| 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·=·||·-9·-22·-30·-35·-27·5·29·1·-4·-13·5·-18·39·-39·48·-47·-43·7·19·-16·21 | ||
| 93 | 34·-38·-18· | 92 | o13·=·||·42·-50·-50·38·-39·6·-1·47·49·-18·18·-28·-47·19·48·34·-13·11·-16·-38·39 |
| 93 | 21·-43·-39·|····| | ||
| 94 | ······+------------------------------------------------------------------------ | 94 | ······+------------------------------------------------------------------------ |
| 95 | ------------+ | 95 | -----------------+ |
| 96 | ······||·45·-21·1·-12·2·6·-7·0·-9·-48·-2·18·-47·45·18·22·-47·-25·16·-28·38·2·- | ||
| 97 | 1 | 96 | ······||·-44·-31·-9·-21·-42·-36·-47·-20·38·-34·-3·-43·22·16·-35·2·-48·32·-28·- |
| 97 | 15·-47·38·-47·45·|| | ||
| 98 | ······+------------------------------------------------------------------------ | 98 | ······+------------------------------------------------------------------------ |
| 99 | ------------+ | 99 | -----------------+ |
| 100 | ······||·-3·8·-22·3·21·0·-31·46·15·-11·-41·-15·-16·43·22·39·48·4·-23·19·7·15·47 | ||
| 101 | -17· | 100 | ······||·45·-29·-1·-4·42·-35·4·-13·18·-17·1·21·39·-23·50·15·-11·-11·19·47·-16·7 |
| 101 | 48·43·|·········| | ||
| 102 | ······+------------------------------------------------------------------------ | 102 | ······+------------------------------------------------------------------------ |
| 103 | ------------+ | 103 | -----------------+ |
| 104 | ······||·-9·22·-3·-21·-25·38·-6·43·44·1·5·-20·11·46·-49·11·-3·-42·40·35·-38·33 | ||
| 105 | 3 | 104 | ······||·35·-44·-33·-8·21·-2·-44·-20·19·-28·19·27·11·40·34·33·1·-14·35·36·11·- |
| 105 | 38·-3·46·|········| | ||
| 106 | ······+------------------------------------------------------------------------ | 106 | ······+------------------------------------------------------------------------ |
| 107 | ------------+ | 107 | -----------------+ |
| 108 | ······||·-48·47·0·8·3·5·-6·-39·29·-13·1·2·-23·15·43·-47·-10·-14·29·-47·-7·2·22 | ||
| 109 | -37· | 108 | ······||·33·47·46·16·-22·-25·-44·-36·-30·-37·30·-25·-47·29·-41·2·-13·-41·-47·22 |
| 109 | -23·-7·-10·15·|·| | ||
| 110 | ······+------------------------------------------------------------------------ | 110 | ······+------------------------------------------------------------------------ |
| 111 | ------------+ | 111 | -----------------+ |
| 112 | ······||·32·30·-30·6·14·-38·27·48·-43·24·45·-10·39·-32·-32·-9·-30·12·32·-18·27 | ||
| 113 | -22·30·-20· | 112 | ······||·43·1·-41·23·-42·-14·37·-50·-32·-20·-5·-49·-9·32·-18·-22·24·43·-18·30 |
| 113 | 39·27·-30·-32·|···| | ||
| 114 | ······+------------------------------------------------------------------------ | 114 | ······+------------------------------------------------------------------------ |
| 115 | ------------+ | 115 | -----------------+ |
| 116 | ······||·-21·42·-33·-17·0·-38·33·-45·0·-20·0·1·39·-19·44·-33·44·0·-49·-15·0·33 | ||
| 117 | -4 | 116 | ······||·12·8·26·15·22·12·0·-5·6·17·-21·-18·-33·-49·-19·33·-20·0·-15·-48·39·0 |
| 117 | 44·-19·|··········| | ||
| 118 | ······+------------------------------------------------------------------------ | 118 | ······+------------------------------------------------------------------------ |
| 119 | ------------+ | 119 | -----------------+ |
| 120 | ······||·-50·39·44·14·-48·19·-38·-46·-50·-11·2·44·9·22·-14·-26·-8·46·13·36·-39 | ||
| 121 | 4·-39·-4 | 120 | ······||·-48·-27·-8·-33·-35·-16·-31·-44·-46·-49·-21·-3·-26·13·-40·4·-11·-48·36 |
| 121 | -39·9·-39·-8·22·|| | ||
| 122 | ······+------------------------------------------------------------------------ | 122 | ······+------------------------------------------------------------------------ |
| 123 | ------------+ | 123 | -----------------+ |
| 124 | ······||·34·6·-6·20·-14·-21·44·14·-9·-6·11·3·36·16·-38·41·35·-35·-30·-8·-3·-22 | ||
| 125 | 43·-28· | 124 | ······||·34·29·30·-1·34·-22·32·-6·39·-28·-15·37·41·-30·47·-22·-6·-7·-8·43·36·- |
| 125 | 3·35·16·|·········| | ||
| 126 | ······+------------------------------------------------------------------------ | 126 | ······+------------------------------------------------------------------------ |
| 127 | ------------+ | 127 | -----------------+ |
| 128 | ······||·23·-36·-9·24·-31·-34·34·-34·-28·-49·28·-30·6·-2·44·25·-13·19·-31·-35 | ||
| 129 | 128 | ······||·10·-5·-38·-25·-21·21·14·42·19·-41·8·-35·25·-31·29·3·-49·38·-35·-9·6·40 | |
| 129 | -13·-2·|········| | ||
| 130 | ······+------------------------------------------------------------------------ | 130 | ······+------------------------------------------------------------------------ |
| 131 | ------------+ | 131 | -----------------+ |
| 132 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) | 132 | i14·:·netList·randomPointsOnRationalVariety(compsJ_1,·10) |
| 133 | ······+------------------------------------------------------------------------ | 133 | ······+------------------------------------------------------------------------ |
| 134 | ---------------+ | 134 | ----------------+ |
| 135 | o14·=·||·-16·-50·24·2·22·7·48·-36·-9·-17·39·-20·37·7·-49·-39·-35·-31·-40·30·-47 | ||
| 136 | 2 | 135 | o14·=·||·1·4·44·1·40·20·29·-26·42·-16·-4·50·-40·48·23·-34·-35·37·30·4·-47·27·- |
| 136 | 31·0·|···········| | ||
| 137 | ······+------------------------------------------------------------------------ | 137 | ······+------------------------------------------------------------------------ |
| 138 | ---------------+ | 138 | ----------------+ |
| 139 | ······||·- | 139 | ······||·-29·-11·2·28·-12·-21·-30·20·-1·-42·27·-45·-48·-14·-3·-45·-37·30·-31·- |
| 140 | -48·-29· | 140 | 39·-48·-29·47·0·|| |
| 141 | ······+------------------------------------------------------------------------ | 141 | ······+------------------------------------------------------------------------ |
| 142 | ---------------+ | 142 | ----------------+ |
| 143 | ······||·- | 143 | ······||·-20·14·48·3·14·33·18·-46·24·45·-1·-29·1·31·-44·-2·-22·40·28·-49·-18·46 |
| 144 | 144 | 10·0·|·········| | |
| 145 | ······+------------------------------------------------------------------------ | 145 | ······+------------------------------------------------------------------------ |
| 146 | ---------------+ | 146 | ----------------+ |
| 147 | ······||· | 147 | ······||·21·25·-23·-45·-48·-40·8·-7·-6·-1·14·3·-13·-44·-44·21·-41·3·30·7·13·-17 |
| 148 | 148 | 8·0·|··········| | |
| 149 | ······+------------------------------------------------------------------------ | 149 | ······+------------------------------------------------------------------------ |
| 150 | ---------------+ | 150 | ----------------+ |
| 151 | ······||·- | 151 | ······||·-15·26·-17·12·0·-5·35·-11·0·-31·-39·40·49·-21·-42·28·42·-18·-29·8·30·- |
| 152 | 152 | 46·23·0·|·······| | |
| 153 | ······+------------------------------------------------------------------------ | 153 | ······+------------------------------------------------------------------------ |
| 154 | ---------------+ | 154 | ----------------+ |
| 155 | ······||·-7·47·37·23·-11·36·0·-8·-41·33·20·34·12·-41·-19·36·-18·27·-46·15·18·- | ||
| 156 | 1 | 155 | ······||·-17·38·-49·-9·2·-1·-9·2·3·49·33·49·-46·25·1·0·-18·12·15·-28·18·-16·27 |
| 156 | 0·|·············| | ||
| 157 | ······+------------------------------------------------------------------------ | 157 | ······+------------------------------------------------------------------------ |
| 158 | ---------------+ | 158 | ----------------+ |
| 159 | ······||·-2·-42·26·44·-36·-15·-22·32·1·-6·12·-14·-39·-22·-50·-28·20·19·44·23·- | ||
| 160 | 3 | 159 | ······||·-50·3·-12·-21·-10·4·36·-14·19·-9·43·-48·44·-35·16·6·20·-39·23·-21·-37 |
| 160 | -23·19·0·|······| | ||
| 161 | ······+------------------------------------------------------------------------ | 161 | ······+------------------------------------------------------------------------ |
| 162 | ---------------+ | 162 | ----------------+ |
| 163 | ······||·37·-44·-20·-15·12·-39·-39·-18·1·-16·24·-27·6·-6·-9·27·-9·-33·-28·-47·- | ||
| 164 | 28· | 163 | ······||·36·-17·-27·37·-4·12·42·-16·-15·12·-3·-14·-28·38·-24·18·-9·6·-47·0·-28 |
| 164 | 47·-33·0·|······| | ||
| 165 | ······+------------------------------------------------------------------------ | 165 | ······+------------------------------------------------------------------------ |
| 166 | ---------------+ | 166 | ----------------+ |
| 167 | ······||·49·27·21·-41·2·-50·-8·16·-18·-21·-48·17·-33·-9·-49·-34·-28·42·-37·-29 | ||
| 168 | 167 | ······||·43·44·31·14·-9·-4·-4·-40·-48·45·47·17·-37·29·-9·10·-28·-33·-29·28·26·5 | |
| 168 | 42·0·|·········| | ||
| 169 | ······+------------------------------------------------------------------------ | 169 | ······+------------------------------------------------------------------------ |
| 170 | ---------------+ | 170 | ----------------+ |
| 171 | ······||· | 171 | ······||·17·-47·-23·8·-18·-45·-25·2·44·41·-19·-37·5·16·2·38·-13·-20·30·44·4·22 |
| 172 | 172 | -29·0·|·········| | |
| 173 | ······+------------------------------------------------------------------------ | 173 | ······+------------------------------------------------------------------------ |
| 174 | ---------------+ | 174 | ----------------+ |
| 175 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 175 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 176 | This·routine·expects·the·input·to·represent·an·irreducible·variety | 176 | This·routine·expects·the·input·to·represent·an·irreducible·variety |
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| Offset 321, 80 lines modified | Offset 321, 75 lines modified | ||
| 321 | ········<div> | 321 | ········<div> |
| 322 | ··········<p>We·can·find·random·points·on·each·component,·since·these·components·are·rational.</p> | 322 | ··········<p>We·can·find·random·points·on·each·component,·since·these·components·are·rational.</p> |
| 323 | ········</div> | 323 | ········</div> |
| 324 | ········<table·class="examples"> | 324 | ········<table·class="examples"> |
| 325 | ··········<tr> | 325 | ··········<tr> |
| 326 | <td>··············<pre><code·class="language-macaulay2">i12·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 326 | <td>··············<pre><code·class="language-macaulay2">i12·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 327 | o12·=·|· | 327 | o12·=·|·-36·-30·42·21·-22·23·23·16·-7·-30·-11·-40·19·19·-41·-22·24·-36·-8·33 |
| 328 | ······----------------------------------------------------------------------- | 328 | ······----------------------------------------------------------------------- |
| 329 | ······-2 | 329 | ······-29·-10·-29·-29·| |
| 330 | ···············1·······24 | 330 | ···············1·······24 |
| 331 | o12·:·Matrix·kk··<--·kk</code></pre> | 331 | o12·:·Matrix·kk··<--·kk</code></pre> |
| 332 | </td>··········</tr> | 332 | </td>··········</tr> |
| 333 | ··········<tr> | 333 | ··········<tr> |
| 334 | <td>··············<pre><code·class="language-macaulay2">i13·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 334 | <td>··············<pre><code·class="language-macaulay2">i13·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 335 | o13·=·|·2 | 335 | o13·=·|·24·-7·-25·32·-28·13·-49·11·-17·-17·-2·-50·30·19·-41·-21·-38·-24·21·39 |
| 336 | ······----------------------------------------------------------------------- | 336 | ······----------------------------------------------------------------------- |
| 337 | ······0·-16·-47·| | 337 | ······34·0·-16·-47·| |
| 338 | ···············1·······24 | 338 | ···············1·······24 |
| 339 | o13·:·Matrix·kk··<--·kk</code></pre> | 339 | o13·:·Matrix·kk··<--·kk</code></pre> |
| 340 | </td>··········</tr> | 340 | </td>··········</tr> |
| 341 | ··········<tr> | 341 | ··········<tr> |
| 342 | <td>··············<pre><code·class="language-macaulay2">i14·:·F1·=·sub(F,·(vars·S)|pt1) | 342 | <td>··············<pre><code·class="language-macaulay2">i14·:·F1·=·sub(F,·(vars·S)|pt1) |
| 343 | ··············2············· | 343 | ··············2·············2······························2··············· |
| 344 | o14·=·ideal·(a··-· | 344 | o14·=·ideal·(a··-·7b*c·+·21c··-·30a*d·-·22b*d·-·30c*d·-·36d·,·a*b·-·41b*c·- |
| 345 | ······----------------------------------------------------------------------- | 345 | ······----------------------------------------------------------------------- |
| 346 | ·········2······························2···2············· | 346 | ·········2······························2···2··············2················ |
| 347 | ······11c··-· | 347 | ······11c··-·22a*d·-·40b*d·+·23c*d·+·42d·,·b··-·29b*c·+·24c··-·10a*d·-·36b*d |
| 348 | ······----------------------------------------------------------------------- | 348 | ······----------------------------------------------------------------------- |
| 349 | ················· | 349 | ···················2··················2······························2 |
| 350 | ······19c*d· | 350 | ······+·19c*d·+·23d·,·a*c·-·29b*c·-·8c··-·29a*d·+·33b*d·+·19c*d·+·16d·) |
| 351 | o14·:·Ideal·of·S</code></pre> | 351 | o14·:·Ideal·of·S</code></pre> |
| 352 | </td>··········</tr> | 352 | </td>··········</tr> |
| 353 | ··········<tr> | 353 | ··········<tr> |
| 354 | <td>··············<pre><code·class="language-macaulay2">i15·:·F2·=·sub(F,·(vars·S)|pt2) | 354 | <td>··············<pre><code·class="language-macaulay2">i15·:·F2·=·sub(F,·(vars·S)|pt2) |
| 355 | ··············2··············2····························· | 355 | ··············2··············2·····························2··············· |
| 356 | o15·=·ideal·(a··-·1 | 356 | o15·=·ideal·(a··-·17b*c·+·32c··-·17a*d·-·28b*d·-·7c*d·+·24d·,·a*b·-·41b*c·- |
| 357 | ······----------------------------------------------------------------------- | 357 | ······----------------------------------------------------------------------- |
| 358 | ········ | 358 | ········2······························2···2··············2·················· |
| 359 | ······2 | 359 | ······2c··-·21a*d·-·50b*d·+·13c*d·-·25d·,·b··+·34b*c·-·38c··-·24b*d·+·30c*d·- |
| 360 | ······----------------------------------------------------------------------- | 360 | ······----------------------------------------------------------------------- |
| 361 | ········· | 361 | ·········2···················2······························2 |
| 362 | ······ | 362 | ······49d·,·a*c·-·16b*c·+·21c··-·47a*d·+·39b*d·+·19c*d·+·11d·) |
| 363 | o15·:·Ideal·of·S</code></pre> | 363 | o15·:·Ideal·of·S</code></pre> |
| 364 | </td>··········</tr> | 364 | </td>··········</tr> |
| 365 | ··········<tr> | 365 | ··········<tr> |
| 366 | <td>··············<pre><code·class="language-macaulay2">i16·:·decompose·F1 | 366 | <td>··············<pre><code·class="language-macaulay2">i16·:·decompose·F1 |
| 367 | ··································· | 367 | ···································2··············2······················2 |
| 368 | o16·=·{ideal·(a·-·29b·-· | 368 | o16·=·{ideal·(a·-·29b·-·8c·-·11d,·b··-·29b*c·+·24c··-·23b*d·+·40c*d·+·14d·), |
| 369 | ······----------------------------------------------------------------------- | 369 | ······----------------------------------------------------------------------- |
| 370 | ······ideal·(c·-·29d,·b· | 370 | ······ideal·(c·-·29d,·b·-·35d,·a·+·43d)} |
| 371 | o16·:·List</code></pre> | 371 | o16·:·List</code></pre> |
| 372 | </td>··········</tr> | 372 | </td>··········</tr> |
| 373 | ··········<tr> | 373 | ··········<tr> |
| 374 | <td>··············<pre><code·class="language-macaulay2">i17·:·decompose·F2 | 374 | <td>··············<pre><code·class="language-macaulay2">i17·:·decompose·F2 |
| 375 | o17·=·{ideal·(b·-·6c·-·42d,·a·+·26c·-·5d),·ideal·(b·+·40c·+·18d,·a·-·46c·+ | ||
| 375 | ·······························2······························2···2·········· | ||
| 376 | o17·=·{ideal·(a*c·-·16b*c·+·21c··-·47a*d·+·34b*d·+·39c*d·+·50d·,·b··+·19b*c·- | ||
| 377 | ······----------------------------------------------------------------------- | ||
| 378 | ·········2·····················2···················2························ | ||
| 379 | ······24c··-·38b*d·+·26c*d·+·3d·,·a*b·+·22b*c·+·20c··-·27a*d·+·49b*d·-·11c*d | ||
| 380 | ······----------------------------------------------------------------------- | 376 | ······----------------------------------------------------------------------- |
| 377 | ······19d)} | ||
| 381 | ···········2···2··············2······························2 | ||
| 382 | ······+·18d·,·a··-·19b*c·-·20c··+·38a*d·-·48b*d·-·50c*d·+·20d·)} | ||
| 383 | o17·:·List</code></pre> | 378 | o17·:·List</code></pre> |
| 384 | </td>··········</tr> | 379 | </td>··········</tr> |
| 385 | ········</table> | 380 | ········</table> |
| 386 | ········<div> | 381 | ········<div> |
| 387 | ··········<p>Note,·the·general·element·of·one·component·is·a·plane·conic·union·a·point.·(The·dimension·of·the·locus·of·all·such·is:·(choice·of·plane)·+·(choice·of·degree·2·in·plane)·+·choice·of·point.·This·is·3·+·5·+·3·=·11.</p> | 382 | ··········<p>Note,·the·general·element·of·one·component·is·a·plane·conic·union·a·point.·(The·dimension·of·the·locus·of·all·such·is:·(choice·of·plane)·+·(choice·of·degree·2·in·plane)·+·choice·of·point.·This·is·3·+·5·+·3·=·11.</p> |
| 388 | ··········<p>The·other·component·consists·of·two·skew·lines.··This·has·dimension·(choice·of·line)·+·(choice·of·line).·This·is·4·+·4·=·8.··Also·notice·that·the·2·skew·lines·do·not·have·to·be·defined·over·the·base·field,·as·in·this·case.</p> | 383 | ··········<p>The·other·component·consists·of·two·skew·lines.··This·has·dimension·(choice·of·line)·+·(choice·of·line).·This·is·4·+·4·=·8.··Also·notice·that·the·2·skew·lines·do·not·have·to·be·defined·over·the·base·field,·as·in·this·case.</p> |
| Offset 424, 70 lines modified | Offset 424, 65 lines modified | ||
| 424 | -----------------------------------------------------------+ | 424 | -----------------------------------------------------------+ |
| 425 | This·tells·us·that·there·are·2·components·(at·least·over·the·given·field). | 425 | This·tells·us·that·there·are·2·components·(at·least·over·the·given·field). |
| 426 | Their·dimensions·are·11,·8. | 426 | Their·dimensions·are·11,·8. |
| 427 | We·can·find·random·points·on·each·component,·since·these·components·are | 427 | We·can·find·random·points·on·each·component,·since·these·components·are |
| 428 | rational. | 428 | rational. |
| 429 | i12·:·pt1·=·randomPointOnRationalVariety·compsJ_0 | 429 | i12·:·pt1·=·randomPointOnRationalVariety·compsJ_0 |
| 430 | o12·=·|· | 430 | o12·=·|·-36·-30·42·21·-22·23·23·16·-7·-30·-11·-40·19·19·-41·-22·24·-36·-8·33 |
| 431 | ······----------------------------------------------------------------------- | 431 | ······----------------------------------------------------------------------- |
| 432 | ······-2 | 432 | ······-29·-10·-29·-29·| |
| 433 | ···············1·······24 | 433 | ···············1·······24 |
| 434 | o12·:·Matrix·kk··<--·kk | 434 | o12·:·Matrix·kk··<--·kk |
| 435 | i13·:·pt2·=·randomPointOnRationalVariety·compsJ_1 | 435 | i13·:·pt2·=·randomPointOnRationalVariety·compsJ_1 |
| 436 | o13·=·|·2 | 436 | o13·=·|·24·-7·-25·32·-28·13·-49·11·-17·-17·-2·-50·30·19·-41·-21·-38·-24·21·39 |
| 437 | ······----------------------------------------------------------------------- | 437 | ······----------------------------------------------------------------------- |
| 438 | ······0·-16·-47·| | 438 | ······34·0·-16·-47·| |
| 439 | ···············1·······24 | 439 | ···············1·······24 |
| 440 | o13·:·Matrix·kk··<--·kk | 440 | o13·:·Matrix·kk··<--·kk |
| 441 | i14·:·F1·=·sub(F,·(vars·S)|pt1) | 441 | i14·:·F1·=·sub(F,·(vars·S)|pt1) |
| 442 | ··············2············· | 442 | ··············2·············2······························2 |
| 443 | o14·=·ideal·(a··-· | 443 | o14·=·ideal·(a··-·7b*c·+·21c··-·30a*d·-·22b*d·-·30c*d·-·36d·,·a*b·-·41b*c·- |
| 444 | ······----------------------------------------------------------------------- | 444 | ······----------------------------------------------------------------------- |
| 445 | ·········2······························2···2·············2 | 445 | ·········2······························2···2··············2 |
| 446 | ······11c··-· | 446 | ······11c··-·22a*d·-·40b*d·+·23c*d·+·42d·,·b··-·29b*c·+·24c··-·10a*d·-·36b*d |
| 447 | ······----------------------------------------------------------------------- | 447 | ······----------------------------------------------------------------------- |
| 448 | ················· | 448 | ···················2··················2······························2 |
| 449 | ······19c*d· | 449 | ······+·19c*d·+·23d·,·a*c·-·29b*c·-·8c··-·29a*d·+·33b*d·+·19c*d·+·16d·) |
| 450 | o14·:·Ideal·of·S | 450 | o14·:·Ideal·of·S |
| 451 | i15·:·F2·=·sub(F,·(vars·S)|pt2) | 451 | i15·:·F2·=·sub(F,·(vars·S)|pt2) |
| 452 | ··············2··············2····························· | 452 | ··············2··············2·····························2 |
| 453 | o15·=·ideal·(a··-·1 | 453 | o15·=·ideal·(a··-·17b*c·+·32c··-·17a*d·-·28b*d·-·7c*d·+·24d·,·a*b·-·41b*c·- |
| 454 | ······----------------------------------------------------------------------- | 454 | ······----------------------------------------------------------------------- |
| 455 | ········ | 455 | ········2······························2···2··············2 |
| 456 | ······2 | 456 | ······2c··-·21a*d·-·50b*d·+·13c*d·-·25d·,·b··+·34b*c·-·38c··-·24b*d·+·30c*d·- |
| 457 | ······----------------------------------------------------------------------- | 457 | ······----------------------------------------------------------------------- |
| 458 | ········· | 458 | ·········2···················2······························2 |
| 459 | ······ | 459 | ······49d·,·a*c·-·16b*c·+·21c··-·47a*d·+·39b*d·+·19c*d·+·11d·) |
| 460 | o15·:·Ideal·of·S | 460 | o15·:·Ideal·of·S |
| 461 | i16·:·decompose·F1 | 461 | i16·:·decompose·F1 |
| 462 | ··································· | 462 | ···································2··············2······················2 |
| 463 | o16·=·{ideal·(a·-·29b·-· | 463 | o16·=·{ideal·(a·-·29b·-·8c·-·11d,·b··-·29b*c·+·24c··-·23b*d·+·40c*d·+·14d·), |
| 464 | ······----------------------------------------------------------------------- | 464 | ······----------------------------------------------------------------------- |
| 465 | ······ideal·(c·-·29d,·b· | 465 | ······ideal·(c·-·29d,·b·-·35d,·a·+·43d)} |
| 466 | o16·:·List | 466 | o16·:·List |
| 467 | i17·:·decompose·F2 | 467 | i17·:·decompose·F2 |
| 468 | o17·=·{ideal·(b·-·6c·-·42d,·a·+·26c·-·5d),·ideal·(b·+·40c·+·18d,·a·-·46c·+ | ||
| 468 | ·······························2······························2···2 | ||
| 469 | o17·=·{ideal·(a*c·-·16b*c·+·21c··-·47a*d·+·34b*d·+·39c*d·+·50d·,·b··+·19b*c·- | ||
| 470 | ······----------------------------------------------------------------------- | ||
| 471 | ·········2·····················2···················2 | ||
| 472 | ······24c··-·38b*d·+·26c*d·+·3d·,·a*b·+·22b*c·+·20c··-·27a*d·+·49b*d·-·11c*d | ||
| 473 | ······----------------------------------------------------------------------- | 469 | ······----------------------------------------------------------------------- |
| 470 | ······19d)} | ||
| 474 | ···········2···2··············2······························2 | ||
| 475 | ······+·18d·,·a··-·19b*c·-·20c··+·38a*d·-·48b*d·-·50c*d·+·20d·)} | ||
| 476 | o17·:·List | 471 | o17·:·List |
| 477 | Note,·the·general·element·of·one·component·is·a·plane·conic·union·a·point.·(The | 472 | Note,·the·general·element·of·one·component·is·a·plane·conic·union·a·point.·(The |
| 478 | dimension·of·the·locus·of·all·such·is:·(choice·of·plane)·+·(choice·of·degree·2 | 473 | dimension·of·the·locus·of·all·such·is:·(choice·of·plane)·+·(choice·of·degree·2 |
| 479 | in·plane)·+·choice·of·point.·This·is·3·+·5·+·3·=·11. | 474 | in·plane)·+·choice·of·point.·This·is·3·+·5·+·3·=·11. |
| 480 | The·other·component·consists·of·two·skew·lines.·This·has·dimension·(choice·of | 475 | The·other·component·consists·of·two·skew·lines.·This·has·dimension·(choice·of |
| 481 | line)·+·(choice·of·line).·This·is·4·+·4·=·8.·Also·notice·that·the·2·skew·lines | 476 | line)·+·(choice·of·line).·This·is·4·+·4·=·8.·Also·notice·that·the·2·skew·lines |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--· | 15 | ·--·2.51819·seconds·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 | ·--·1.56565·seconds·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 77, 28 lines modified | Offset 77, 28 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·I2·=·sub(I1,·R2); | 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·I2·=·sub(I1,·R2); |
| 79 | o4·:·Ideal·of·R2</code></pre> | 79 | o4·:·Ideal·of·R2</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·gb·I2 | 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·gb·I2 |
| 83 | ·--· | 83 | ·--·2.51819·seconds·elapsed |
| 84 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] | 84 | o5·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·16] |
| 85 | o5·:·GroebnerBasis</code></pre> | 85 | o5·:·GroebnerBasis</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ········</table> | 87 | ········</table> |
| 88 | ········<div> | 88 | ········<div> |
| 89 | ··········<p>but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the·Groebner·walk.</p> | 89 | ··········<p>but·it·is·faster·to·compute·directly·in·the·first·order·and·then·use·the·Groebner·walk.</p> |
| 90 | ········</div> | 90 | ········</div> |
| 91 | ········<table·class="examples"> | 91 | ········<table·class="examples"> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·groebnerWalk(gb·I1,·R2) |
| 94 | ·--· | 94 | ·--·1.56565·seconds·elapsed |
| 95 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] | 95 | o6·=·GroebnerBasis[status:·done;·S-pairs·encountered·up·to·degree·0] |
| 96 | o6·:·GroebnerBasis</code></pre> | 96 | o6·:·GroebnerBasis</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ········</table> | 98 | ········</table> |
| 99 | ······</div> | 99 | ······</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 | ·--· | 44 | ·--·2.51819·seconds·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 | ·--·1.56565·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·3.306e-06·seconds·elapsed | ||
| 47 | ·--·2.925e-06·seconds·elapsed | ||
| 48 | ·--·2.625e-06·seconds·elapsed | ||
| 49 | ·--· | 46 | ·--·4.266e-06·seconds·elapsed |
| 47 | ·--·5.018e-06·seconds·elapsed | ||
| 50 | ·--·3. | 48 | ·--·3.355e-06·seconds·elapsed |
| 49 | ·--·4.727e-06·seconds·elapsed | ||
| 50 | ·--·4.417e-06·seconds·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 | ·--· | 7 | ·--·5.118e-06·seconds·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 | ·--·4. | 28 | ·--·4.727e-06·seconds·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 123, 19 lines modified | Offset 123, 19 lines modified | ||
| 123 | o5·=·{9,·1,·99999,·9999999,·3,·999} | 123 | o5·=·{9,·1,·99999,·9999999,·3,·999} |
| 124 | o5·:·List</code></pre> | 124 | o5·:·List</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i6·:·netList·cssLeadTerm(Hbeta,·w) | 127 | <td>··············<pre><code·class="language-macaulay2">i6·:·netList·cssLeadTerm(Hbeta,·w) |
| 128 | ·--·3.306e-06·seconds·elapsed | ||
| 129 | ·--·2.925e-06·seconds·elapsed | ||
| 130 | ·--·2.625e-06·seconds·elapsed | ||
| 131 | ·--· | 128 | ·--·4.266e-06·seconds·elapsed |
| 129 | ·--·5.018e-06·seconds·elapsed | ||
| 132 | ·--·3. | 130 | ·--·3.355e-06·seconds·elapsed |
| 131 | ·--·4.727e-06·seconds·elapsed | ||
| 132 | ·--·4.417e-06·seconds·elapsed | ||
| 133 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 133 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 134 | Converting·to·Naive·algorithm. | 134 | Converting·to·Naive·algorithm. |
| 135 | ·····+----------------------------------------------------+ | 135 | ·····+----------------------------------------------------+ |
| 136 | ·····|···1·5···5·5········································| | 136 | ·····|···1·5···5·5········································| |
| 137 | ·····|·-·-·-·-·-·-········································| | 137 | ·····|·-·-·-·-·-·-········································| |
| 138 | ·····|···2·2···2·2········································| | 138 | ·····|···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 | ·--·3.306e-06·seconds·elapsed | ||
| 61 | ·--·2.925e-06·seconds·elapsed | ||
| 62 | ·--·2.625e-06·seconds·elapsed | ||
| 63 | ·--· | 60 | ·--·4.266e-06·seconds·elapsed |
| 61 | ·--·5.018e-06·seconds·elapsed | ||
| 64 | ·--·3. | 62 | ·--·3.355e-06·seconds·elapsed |
| 63 | ·--·4.727e-06·seconds·elapsed | ||
| 64 | ·--·4.417e-06·seconds·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 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <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 | <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); |
| 82 | o2·:·Ideal·of·R</code></pre> | 82 | o2·:·Ideal·of·R</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·solveFrobeniusIdeal·I | 85 | <td>··············<pre><code·class="language-macaulay2">i3·:·solveFrobeniusIdeal·I |
| 86 | ·--· | 86 | ·--·5.118e-06·seconds·elapsed |
| 87 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 87 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 88 | Converting·to·Naive·algorithm. | 88 | Converting·to·Naive·algorithm. |
| 89 | ············································································· | 89 | ············································································· |
| 90 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 90 | o3·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 91 | ················0········1········2·······3········0·······1·······2·······4· | 91 | ················0········1········2·······3········0·······1·······2·······4· |
| 92 | ·····------------------------------------------------------------------------ | 92 | ·····------------------------------------------------------------------------ |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | ········</table> | 105 | ········</table> |
| 106 | ········<table·class="examples"> | 106 | ········<table·class="examples"> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);</code></pre> | 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·W·=·makeWeylAlgebra(QQ[x_1..x_5]);</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·solveFrobeniusIdeal(I,·W) | 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·solveFrobeniusIdeal(I,·W) |
| 112 | ·--·4. | 112 | ·--·4.727e-06·seconds·elapsed |
| 113 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. | 113 | Warning:··F4·Algorithm·not·available·over·current·coefficient·ring·or·inhomogeneous·ideal. |
| 114 | Converting·to·Naive·algorithm. | 114 | Converting·to·Naive·algorithm. |
| 115 | ············································································· | 115 | ············································································· |
| 116 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, | 116 | o5·=·{1,·-·2logX··+·3logX··-·2logX··+·logX·,·-·logX··+·logX··-·logX··+·logX·, |
| 117 | ················0········1········2·······3········0·······1·······2·······4· | 117 | ················0········1········2·······3········0·······1·······2·······4· |
| 118 | ·····------------------------------------------------------------------------ | 118 | ·····------------------------------------------------------------------------ |
| 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 | ·--· | 23 | ·--·5.118e-06·seconds·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 | ·--·4. | 43 | ·--·4.727e-06·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 10, 35 lines modified | Offset 10, 35 lines modified | ||
| 10 | o2·=·{x,·y,·z,·x·-·y,·x·-·z} | 10 | o2·=·{x,·y,·z,·x·-·y,·x·-·z} |
| 11 | o2·:·Hyperplane·Arrangement· | 11 | o2·:·Hyperplane·Arrangement· |
| 12 | i3·:·(A'',m'')·=·eulerRestriction(A,{1,1,1,1,1},1) | 12 | i3·:·(A'',m'')·=·eulerRestriction(A,{1,1,1,1,1},1) |
| 13 | o3·=·({ | 13 | o3·=·({x·-·z,·z,·x},·{1,·1,·1}) |
| 14 | o3·:·Sequence | 14 | o3·:·Sequence |
| 15 | i4·:·restriction(A,1) | 15 | i4·:·restriction(A,1) |
| 16 | o4·=·{x,·z,·x,·x·-·z} | 16 | o4·=·{x,·z,·x,·x·-·z} |
| 17 | o4·:·Hyperplane·Arrangement· | 17 | o4·:·Hyperplane·Arrangement· |
| 18 | i5·:·trim·oo·--·same·underlying·simple·arrangement,·different·multiplicities | 18 | i5·:·trim·oo·--·same·underlying·simple·arrangement,·different·multiplicities |
| 19 | o5·=·{ | 19 | o5·=·{x·-·z,·z,·x} |
| 20 | o5·:·Hyperplane·Arrangement· | 20 | o5·:·Hyperplane·Arrangement· |
| 21 | i6·:·m·=·{2,2,2,2,1};·m'·=·{2,2,2,1,1}; | 21 | i6·:·m·=·{2,2,2,2,1};·m'·=·{2,2,2,1,1}; |
| 22 | i8·:·(A'',m'')·=·eulerRestriction(A,m,3) | 22 | i8·:·(A'',m'')·=·eulerRestriction(A,m,3) |
| 23 | o8·=·({ | 23 | o8·=·({y·-·z,·z,·y},·{1,·2,·3}) |
| 24 | o8·:·Sequence | 24 | o8·:·Sequence |
| 25 | i9·:·prune·image·der(A,m) | 25 | i9·:·prune·image·der(A,m) |
| 26 | ······3 | 26 | ······3 |
| 27 | o9·=·R | 27 | o9·=·R |
| Offset 59, 16 lines modified | Offset 59, 16 lines modified | ||
| 59 | o11·:·QQ[y..z]-module,·free,·degrees·{2:3} | 59 | o11·:·QQ[y..z]-module,·free,·degrees·{2:3} |
| 60 | i12·:·A·=·arrangement·"bracelet"; | 60 | i12·:·A·=·arrangement·"bracelet"; |
| 61 | i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0) | 61 | i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0) |
| 62 | o13·=·({x· | 62 | o13·=·({x·,·x··+·x·,·x·,·x·,·x··+·x··+·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1}) |
| 63 | ·········2··· | 63 | ·········2···3····4···3···4···2····3····4···2····4 |
| 64 | o13·:·Sequence | 64 | o13·:·Sequence |
| 65 | i14·:·C·=·restriction(A,0) | 65 | i14·:·C·=·restriction(A,0) |
| 66 | o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·} | 66 | o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·} |
| 67 | ········2···3···4···2····4···3····4···2····4···3····4···2····3····4 | 67 | ········2···3···4···2····4···3····4···2····4···3····4···2····3····4 |
| Offset 6, 15 lines modified | Offset 6, 15 lines modified | ||
| 6 | o2·=·{x,·x,·0,·y,·y,·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y} | 6 | o2·=·{x,·x,·0,·y,·y,·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y} |
| 7 | o2·:·Hyperplane·Arrangement· | 7 | o2·:·Hyperplane·Arrangement· |
| 8 | i3·:·A'·=·trim·A | 8 | i3·:·A'·=·trim·A |
| 9 | o3·=·{ | 9 | o3·=·{y,·x,·x·+·y} |
| 10 | o3·:·Hyperplane·Arrangement· | 10 | o3·:·Hyperplane·Arrangement· |
| 11 | i4·:·assert(ring·A'·===·R) | 11 | i4·:·assert(ring·A'·===·R) |
| 12 | i5·:·assert(trim·A'·==·A') | 12 | i5·:·assert(trim·A'·==·A') |
| Offset 94, 44 lines modified | Offset 94, 44 lines modified | ||
| 94 | o2·=·{x,·y,·z,·x·-·y,·x·-·z} | 94 | o2·=·{x,·y,·z,·x·-·y,·x·-·z} |
| 95 | o2·:·Hyperplane·Arrangement·</code></pre> | 95 | o2·:·Hyperplane·Arrangement·</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·(A'',m'')·=·eulerRestriction(A,{1,1,1,1,1},1) | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·(A'',m'')·=·eulerRestriction(A,{1,1,1,1,1},1) |
| 99 | o3·=·({ | 99 | o3·=·({x·-·z,·z,·x},·{1,·1,·1}) |
| 100 | o3·:·Sequence</code></pre> | 100 | o3·:·Sequence</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·restriction(A,1) | 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·restriction(A,1) |
| 104 | o4·=·{x,·z,·x,·x·-·z} | 104 | o4·=·{x,·z,·x,·x·-·z} |
| 105 | o4·:·Hyperplane·Arrangement·</code></pre> | 105 | o4·:·Hyperplane·Arrangement·</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·trim·oo·--·same·underlying·simple·arrangement,·different·multiplicities | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·trim·oo·--·same·underlying·simple·arrangement,·different·multiplicities |
| 109 | o5·=·{ | 109 | o5·=·{x·-·z,·z,·x} |
| 110 | o5·:·Hyperplane·Arrangement·</code></pre> | 110 | o5·:·Hyperplane·Arrangement·</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ········<div> | 113 | ········<div> |
| 114 | ··········<p>If·$({\mathcal·A},m)$·is·a·free·multiarrangement·and·so·is·$({\mathcal·A},m')$,·where·$m'$·is·obtained·from·$m$·by·lowering·a·single·multiplicity·by·one,·the·Euler·restriction·is·free·as·well,·and·the·modules·of·<a·title="compute·the·module·of·logarithmic·derivations"·href="_der_lp__Central__Arrangement_cm__List_rp.html">logarithmic·derivations</a>·form·a·short·exact·sequence.··See·the·paper·of·Abe,·Terao·and·Wakefield·for·details.</p> | 114 | ··········<p>If·$({\mathcal·A},m)$·is·a·free·multiarrangement·and·so·is·$({\mathcal·A},m')$,·where·$m'$·is·obtained·from·$m$·by·lowering·a·single·multiplicity·by·one,·the·Euler·restriction·is·free·as·well,·and·the·modules·of·<a·title="compute·the·module·of·logarithmic·derivations"·href="_der_lp__Central__Arrangement_cm__List_rp.html">logarithmic·derivations</a>·form·a·short·exact·sequence.··See·the·paper·of·Abe,·Terao·and·Wakefield·for·details.</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·:·m·=·{2,2,2,2,1};·m'·=·{2,2,2,1,1};</code></pre> | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·m·=·{2,2,2,2,1};·m'·=·{2,2,2,1,1};</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i8·:·(A'',m'')·=·eulerRestriction(A,m,3) | 121 | <td>··············<pre><code·class="language-macaulay2">i8·:·(A'',m'')·=·eulerRestriction(A,m,3) |
| 122 | o8·=·({ | 122 | o8·=·({y·-·z,·z,·y},·{1,·2,·3}) |
| 123 | o8·:·Sequence</code></pre> | 123 | o8·:·Sequence</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i9·:·prune·image·der(A,m) | 126 | <td>··············<pre><code·class="language-macaulay2">i9·:·prune·image·der(A,m) |
| 127 | ······3 | 127 | ······3 |
| Offset 162, 16 lines modified | Offset 162, 16 lines modified | ||
| 162 | ········<table·class="examples"> | 162 | ········<table·class="examples"> |
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i12·:·A·=·arrangement·"bracelet";</code></pre> | 164 | <td>··············<pre><code·class="language-macaulay2">i12·:·A·=·arrangement·"bracelet";</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0) | 167 | <td>··············<pre><code·class="language-macaulay2">i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0) |
| 168 | o13·=·({x· | 168 | o13·=·({x·,·x··+·x·,·x·,·x·,·x··+·x··+·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1}) |
| 169 | ·········2··· | 169 | ·········2···3····4···3···4···2····3····4···2····4 |
| 170 | o13·:·Sequence</code></pre> | 170 | o13·:·Sequence</code></pre> |
| 171 | </td>··········</tr> | 171 | </td>··········</tr> |
| 172 | ··········<tr> | 172 | ··········<tr> |
| 173 | <td>··············<pre><code·class="language-macaulay2">i14·:·C·=·restriction(A,0) | 173 | <td>··············<pre><code·class="language-macaulay2">i14·:·C·=·restriction(A,0) |
| 174 | o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·} | 174 | o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·} |
| Offset 34, 36 lines modified | Offset 34, 36 lines modified | ||
| 34 | i2·:·A·=·arrangement·{x,y,z,x-y,x-z} | 34 | i2·:·A·=·arrangement·{x,y,z,x-y,x-z} |
| 35 | o2·=·{x,·y,·z,·x·-·y,·x·-·z} | 35 | o2·=·{x,·y,·z,·x·-·y,·x·-·z} |
| 36 | o2·:·Hyperplane·Arrangement | 36 | o2·:·Hyperplane·Arrangement |
| 37 | i3·:·(A'',m'')·=·eulerRestriction(A,{1,1,1,1,1},1) | 37 | i3·:·(A'',m'')·=·eulerRestriction(A,{1,1,1,1,1},1) |
| 38 | o3·=·({ | 38 | o3·=·({x·-·z,·z,·x},·{1,·1,·1}) |
| 39 | o3·:·Sequence | 39 | o3·:·Sequence |
| 40 | i4·:·restriction(A,1) | 40 | i4·:·restriction(A,1) |
| 41 | o4·=·{x,·z,·x,·x·-·z} | 41 | o4·=·{x,·z,·x,·x·-·z} |
| 42 | o4·:·Hyperplane·Arrangement | 42 | o4·:·Hyperplane·Arrangement |
| 43 | i5·:·trim·oo·--·same·underlying·simple·arrangement,·different·multiplicities | 43 | i5·:·trim·oo·--·same·underlying·simple·arrangement,·different·multiplicities |
| 44 | o5·=·{ | 44 | o5·=·{x·-·z,·z,·x} |
| 45 | o5·:·Hyperplane·Arrangement | 45 | o5·:·Hyperplane·Arrangement |
| 46 | If·$({\mathcal·A},m)$·is·a·free·multiarrangement·and·so·is·$({\mathcal·A},m')$, | 46 | If·$({\mathcal·A},m)$·is·a·free·multiarrangement·and·so·is·$({\mathcal·A},m')$, |
| 47 | where·$m'$·is·obtained·from·$m$·by·lowering·a·single·multiplicity·by·one,·the | 47 | where·$m'$·is·obtained·from·$m$·by·lowering·a·single·multiplicity·by·one,·the |
| 48 | Euler·restriction·is·free·as·well,·and·the·modules·of·_\x8l_\x8o_\x8g_\x8a_\x8r_\x8i_\x8t_\x8h_\x8m_\x8i_\x8c_\x8·_\x8d_\x8e_\x8r_\x8i_\x8v_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s | 48 | Euler·restriction·is·free·as·well,·and·the·modules·of·_\x8l_\x8o_\x8g_\x8a_\x8r_\x8i_\x8t_\x8h_\x8m_\x8i_\x8c_\x8·_\x8d_\x8e_\x8r_\x8i_\x8v_\x8a_\x8t_\x8i_\x8o_\x8n_\x8s |
| 49 | form·a·short·exact·sequence.·See·the·paper·of·Abe,·Terao·and·Wakefield·for | 49 | form·a·short·exact·sequence.·See·the·paper·of·Abe,·Terao·and·Wakefield·for |
| 50 | details. | 50 | details. |
| 51 | i6·:·m·=·{2,2,2,2,1};·m'·=·{2,2,2,1,1}; | 51 | i6·:·m·=·{2,2,2,2,1};·m'·=·{2,2,2,1,1}; |
| 52 | i8·:·(A'',m'')·=·eulerRestriction(A,m,3) | 52 | i8·:·(A'',m'')·=·eulerRestriction(A,m,3) |
| 53 | o8·=·({ | 53 | o8·=·({y·-·z,·z,·y},·{1,·2,·3}) |
| 54 | o8·:·Sequence | 54 | o8·:·Sequence |
| 55 | i9·:·prune·image·der(A,m) | 55 | i9·:·prune·image·der(A,m) |
| 56 | ······3 | 56 | ······3 |
| 57 | o9·=·R | 57 | o9·=·R |
| Offset 81, 16 lines modified | Offset 81, 16 lines modified | ||
| 81 | o11·:·QQ[y..z]-module,·free,·degrees·{2:3} | 81 | o11·:·QQ[y..z]-module,·free,·degrees·{2:3} |
| 82 | It·may·be·the·case·that·the·Euler·restriction·is·free,·while·the·naive | 82 | It·may·be·the·case·that·the·Euler·restriction·is·free,·while·the·naive |
| 83 | restriction·is·not: | 83 | restriction·is·not: |
| 84 | i12·:·A·=·arrangement·"bracelet"; | 84 | i12·:·A·=·arrangement·"bracelet"; |
| 85 | i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0) | 85 | i13·:·(B,m)·=·eulerRestriction(A,{1,1,1,1,1,1,1,1,1},0) |
| 86 | o13·=·({x· | 86 | o13·=·({x·,·x··+·x·,·x·,·x·,·x··+·x··+·x·,·x··+·x·},·{1,·1,·1,·1,·1,·1}) |
| 87 | ·········2··· | 87 | ·········2···3····4···3···4···2····3····4···2····4 |
| 88 | o13·:·Sequence | 88 | o13·:·Sequence |
| 89 | i14·:·C·=·restriction(A,0) | 89 | i14·:·C·=·restriction(A,0) |
| 90 | o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·} | 90 | o14·=·{x·,·x·,·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x·,·x··+·x··+·x·} |
| 91 | ········2···3···4···2····4···3····4···2····4···3····4···2····3····4 | 91 | ········2···3···4···2····4···3····4···2····4···3····4···2····3····4 |
| Offset 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | o2·=·{x,·x,·0,·y,·y,·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y} | 89 | o2·=·{x,·x,·0,·y,·y,·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y} |
| 90 | o2·:·Hyperplane·Arrangement·</code></pre> | 90 | o2·:·Hyperplane·Arrangement·</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·A'·=·trim·A | 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·A'·=·trim·A |
| 94 | o3·=·{ | 94 | o3·=·{y,·x,·x·+·y} |
| 95 | o3·:·Hyperplane·Arrangement·</code></pre> | 95 | o3·:·Hyperplane·Arrangement·</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(ring·A'·===·R)</code></pre> | 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(ring·A'·===·R)</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| Offset 23, 15 lines modified | Offset 23, 15 lines modified | ||
| 23 | i2·:·A·=·arrangement{x,x,0_R,y,y,y,x+y,x+y,x+y,x+y,x+y} | 23 | i2·:·A·=·arrangement{x,x,0_R,y,y,y,x+y,x+y,x+y,x+y,x+y} |
| 24 | o2·=·{x,·x,·0,·y,·y,·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y} | 24 | o2·=·{x,·x,·0,·y,·y,·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y,·x·+·y} |
| 25 | o2·:·Hyperplane·Arrangement | 25 | o2·:·Hyperplane·Arrangement |
| 26 | i3·:·A'·=·trim·A | 26 | i3·:·A'·=·trim·A |
| 27 | o3·=·{ | 27 | o3·=·{y,·x,·x·+·y} |
| 28 | o3·:·Hyperplane·Arrangement | 28 | o3·:·Hyperplane·Arrangement |
| 29 | i4·:·assert(ring·A'·===·R) | 29 | i4·:·assert(ring·A'·===·R) |
| 30 | i5·:·assert(trim·A'·==·A') | 30 | i5·:·assert(trim·A'·==·A') |
| 31 | i6·:·assert(trim·A'·==·A') | 31 | i6·:·assert(trim·A'·==·A') |
| 32 | Some·natural·operations·produce·non-simple·hyperplane·arrangements. | 32 | Some·natural·operations·produce·non-simple·hyperplane·arrangements. |
| 33 | i7·:·A''·=·restriction(A,·y) | 33 | i7·:·A''·=·restriction(A,·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | b3N1cmUiLCAibGluZW51bSIgPT4gMTQzMCwgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT | 11 | b3N1cmUiLCAibGluZW51bSIgPT4gMTQzMCwgSW5wdXRzID0+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·0.665275s·(cpu);·0.44868s·(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·0.701643s·(cpu);·0.434916s·(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·0.68 | 154 | ·--·used·0.687255s·(cpu);·0.448896s·(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·0.7 | 212 | ·--·used·0.770352s·(cpu);·0.48023s·(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·1.1 | 270 | ·--·used·1.18252s·(cpu);·0.691814s·(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·0.831888s·(cpu);·0.450347s·(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·0.09 | 386 | ·--·used·0.0980356s·(cpu);·0.04984s·(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·0.099 | 436 | ·--·used·0.0989408s·(cpu);·0.047672s·(thread);·0s·(gc) |
| 437 | o41·=·R' | 437 | o41·=·R' |
| 438 | o41·:·QuotientRing | 438 | o41·:·QuotientRing |
| 439 | i42·:·icFractions·R | 439 | i42·:·icFractions·R |
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| 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)·.00 | 8 | ······radical·(use·minprimes)·.0027017·seconds |
| 9 | ······idlizer1:··.00 | 9 | ······idlizer1:··.00713324·seconds |
| 10 | ······idlizer2:··.0 | 10 | ······idlizer2:··.0604221·seconds |
| 11 | ······minpres:···.00782 | 11 | ······minpres:···.00782603·seconds |
| 12 | ··time·. | 12 | ··time·.0855316·sec··#fractions·4] |
| 13 | ·[step·1:· | 13 | ·[step·1:· |
| 14 | ······radical·(use·minprimes)· | 14 | ······radical·(use·minprimes)·0·seconds |
| 15 | ······idlizer1:··.01 | 15 | ······idlizer1:··.0116201·seconds |
| 16 | ······idlizer2:··.02101 | 16 | ······idlizer2:··.0210198·seconds |
| 17 | ······minpres:···.07 | 17 | ······minpres:···.0713629·seconds |
| 18 | ··time·.1 | 18 | ··time·.114059·sec··#fractions·4] |
| 19 | ·[step·2:· | 19 | ·[step·2:· |
| 20 | ······radical·(use·minprimes)·.00175048·seconds | ||
| 21 | ······idlizer1:··.00966925·seconds | ||
| 22 | ······idlizer2:··.022971·seconds | ||
| 23 | ······minpres:···.072636·seconds | ||
| 24 | ··time·.117528·sec··#fractions·5] | ||
| 25 | ·[step·3:· | ||
| 26 | ······radical·(use·minprimes)·0·seconds | 20 | ······radical·(use·minprimes)·0·seconds |
| 27 | ······idlizer1:··.0 | 21 | ······idlizer1:··.00732285·seconds |
| 28 | ······idlizer2:··.0 | 22 | ······idlizer2:··.0209287·seconds |
| 29 | ······minpres:···.0 | 23 | ······minpres:···.0693928·seconds |
| 30 | ··time·.1 | 24 | ··time·.11374·sec··#fractions·5] |
| 25 | ·[step·3:· | ||
| 26 | ······radical·(use·minprimes)·.00199306·seconds | ||
| 27 | ······idlizer1:··.0106652·seconds | ||
| 28 | ······idlizer2:··.0363535·seconds | ||
| 29 | ······minpres:···.0775116·seconds | ||
| 30 | ··time·.146022·sec··#fractions·5] | ||
| 31 | ·[step·4:· | 31 | ·[step·4:· |
| 32 | ······radical·(use·minprimes)·0·seconds | 32 | ······radical·(use·minprimes)·.00446955·seconds |
| 33 | ······idlizer1:··.01 | 33 | ······idlizer1:··.0145112·seconds |
| 34 | ······idlizer2:··.06 | 34 | ······idlizer2:··.0608228·seconds |
| 35 | ······minpres:···.070 | 35 | ······minpres:···.0704253·seconds |
| 36 | ··time·.169 | 36 | ··time·.169356·sec··#fractions·5] |
| 37 | ·[step·5:· | 37 | ·[step·5:· |
| 38 | ······radical·(use·minprimes)·0·seconds | 38 | ······radical·(use·minprimes)·.00382923·seconds |
| 39 | ······idlizer1:···--·used·0.6 | 39 | ······idlizer1:···--·used·0.651986s·(cpu);·0.469329s·(thread);·0s·(gc) |
| 40 | .00 | 40 | .00802173·seconds |
| 41 | ··time·.01 | 41 | ··time·.0150954·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·1. | 17 | ·--·used·1.52225s·(cpu);·0.798611s·(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·0.8 | 25 | ·--·used·0.898111s·(cpu);·0.567524s·(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 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | o3·=·R | 91 | o3·=·R |
| 92 | o3·:·QuotientRing</code></pre> | 92 | o3·:·QuotientRing</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·R'·=·integralClosure·R | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·R'·=·integralClosure·R |
| 96 | ·--·used·0. | 96 | ·--·used·0.665275s·(cpu);·0.44868s·(thread);·0s·(gc) |
| 97 | o4·=·R' | 97 | o4·=·R' |
| 98 | o4·:·QuotientRing</code></pre> | 98 | o4·:·QuotientRing</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i5·:·netList·(ideal·R')_* | 101 | <td>··············<pre><code·class="language-macaulay2">i5·:·netList·(ideal·R')_* |
| Offset 166, 15 lines modified | Offset 166, 15 lines modified | ||
| 166 | o9·=·R | 166 | o9·=·R |
| 167 | o9·:·QuotientRing</code></pre> | 167 | o9·:·QuotientRing</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 170 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 171 | ·--·used·0. | 171 | ·--·used·0.701643s·(cpu);·0.434916s·(thread);·0s·(gc) |
| 172 | o10·=·R' | 172 | o10·=·R' |
| 173 | o10·:·QuotientRing</code></pre> | 173 | o10·:·QuotientRing</code></pre> |
| 174 | </td>··········</tr> | 174 | </td>··········</tr> |
| 175 | ··········<tr> | 175 | ··········<tr> |
| 176 | <td>··············<pre><code·class="language-macaulay2">i11·:·netList·(ideal·R')_* | 176 | <td>··············<pre><code·class="language-macaulay2">i11·:·netList·(ideal·R')_* |
| Offset 241, 15 lines modified | Offset 241, 15 lines modified | ||
| 241 | o15·=·R | 241 | o15·=·R |
| 242 | o15·:·QuotientRing</code></pre> | 242 | o15·:·QuotientRing</code></pre> |
| 243 | </td>··········</tr> | 243 | </td>··········</tr> |
| 244 | ··········<tr> | 244 | ··········<tr> |
| 245 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) | 245 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·R'·=·integralClosure(R,·Strategy·=>·AllCodimensions) |
| 246 | ·--·used·0.68 | 246 | ·--·used·0.687255s·(cpu);·0.448896s·(thread);·0s·(gc) |
| 247 | o16·=·R' | 247 | o16·=·R' |
| 248 | o16·:·QuotientRing</code></pre> | 248 | o16·:·QuotientRing</code></pre> |
| 249 | </td>··········</tr> | 249 | </td>··········</tr> |
| 250 | ··········<tr> | 250 | ··········<tr> |
| 251 | <td>··············<pre><code·class="language-macaulay2">i17·:·netList·(ideal·R')_* | 251 | <td>··············<pre><code·class="language-macaulay2">i17·:·netList·(ideal·R')_* |
| Offset 306, 15 lines modified | Offset 306, 15 lines modified | ||
| 306 | o20·=·R | 306 | o20·=·R |
| 307 | o20·:·QuotientRing</code></pre> | 307 | o20·:·QuotientRing</code></pre> |
| 308 | </td>··········</tr> | 308 | </td>··········</tr> |
| 309 | ··········<tr> | 309 | ··········<tr> |
| 310 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) | 310 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·R'·=·integralClosure(R,·Strategy·=>·SimplifyFractions) |
| 311 | ·--·used·0.7 | 311 | ·--·used·0.770352s·(cpu);·0.48023s·(thread);·0s·(gc) |
| 312 | o21·=·R' | 312 | o21·=·R' |
| 313 | o21·:·QuotientRing</code></pre> | 313 | o21·:·QuotientRing</code></pre> |
| 314 | </td>··········</tr> | 314 | </td>··········</tr> |
| 315 | ··········<tr> | 315 | ··········<tr> |
| 316 | <td>··············<pre><code·class="language-macaulay2">i22·:·netList·(ideal·R')_* | 316 | <td>··············<pre><code·class="language-macaulay2">i22·:·netList·(ideal·R')_* |
| Offset 371, 15 lines modified | Offset 371, 15 lines modified | ||
| 371 | o25·=·R | 371 | o25·=·R |
| 372 | o25·:·QuotientRing</code></pre> | 372 | o25·:·QuotientRing</code></pre> |
| 373 | </td>··········</tr> | 373 | </td>··········</tr> |
| 374 | ··········<tr> | 374 | ··········<tr> |
| 375 | <td>··············<pre><code·class="language-macaulay2">i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) | 375 | <td>··············<pre><code·class="language-macaulay2">i26·:·time·R'·=·integralClosure·(R,·Strategy·=>·RadicalCodim1) |
| 376 | ·--·used·1.1 | 376 | ·--·used·1.18252s·(cpu);·0.691814s·(thread);·0s·(gc) |
| 377 | o26·=·R' | 377 | o26·=·R' |
| 378 | o26·:·QuotientRing</code></pre> | 378 | o26·:·QuotientRing</code></pre> |
| 379 | </td>··········</tr> | 379 | </td>··········</tr> |
| 380 | ··········<tr> | 380 | ··········<tr> |
| 381 | <td>··············<pre><code·class="language-macaulay2">i27·:·netList·(ideal·R')_* | 381 | <td>··············<pre><code·class="language-macaulay2">i27·:·netList·(ideal·R')_* |
| Offset 436, 15 lines modified | Offset 436, 15 lines modified | ||
| 436 | o30·=·R | 436 | o30·=·R |
| 437 | o30·:·QuotientRing</code></pre> | 437 | o30·:·QuotientRing</code></pre> |
| 438 | </td>··········</tr> | 438 | </td>··········</tr> |
| 439 | ··········<tr> | 439 | ··········<tr> |
| 440 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) | 440 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·R'·=·integralClosure·(R,·Strategy·=>·Vasconcelos) |
| 441 | ·--·used·0. | 441 | ·--·used·0.831888s·(cpu);·0.450347s·(thread);·0s·(gc) |
| 442 | o31·=·R' | 442 | o31·=·R' |
| 443 | o31·:·QuotientRing</code></pre> | 443 | o31·:·QuotientRing</code></pre> |
| 444 | </td>··········</tr> | 444 | </td>··········</tr> |
| 445 | ··········<tr> | 445 | ··········<tr> |
| 446 | <td>··············<pre><code·class="language-macaulay2">i32·:·netList·(ideal·R')_* | 446 | <td>··············<pre><code·class="language-macaulay2">i32·:·netList·(ideal·R')_* |
| Offset 501, 15 lines modified | Offset 501, 15 lines modified | ||
| 501 | o35·=·R | 501 | o35·=·R |
| 502 | o35·:·QuotientRing</code></pre> | 502 | o35·:·QuotientRing</code></pre> |
| 503 | </td>··········</tr> | 503 | </td>··········</tr> |
| 504 | ··········<tr> | 504 | ··········<tr> |
| 505 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·R'·=·integralClosure·R | 505 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·R'·=·integralClosure·R |
| 506 | ·--·used·0.09 | 506 | ·--·used·0.0980356s·(cpu);·0.04984s·(thread);·0s·(gc) |
| 507 | o36·=·R' | 507 | o36·=·R' |
| 508 | o36·:·QuotientRing</code></pre> | 508 | o36·:·QuotientRing</code></pre> |
| 509 | </td>··········</tr> | 509 | </td>··········</tr> |
| 510 | ··········<tr> | 510 | ··········<tr> |
| 511 | <td>··············<pre><code·class="language-macaulay2">i37·:·netList·(ideal·R')_* | 511 | <td>··············<pre><code·class="language-macaulay2">i37·:·netList·(ideal·R')_* |
| Offset 561, 15 lines modified | Offset 561, 15 lines modified | ||
| 561 | o40·=·R | 561 | o40·=·R |
| 562 | o40·:·QuotientRing</code></pre> | 562 | o40·:·QuotientRing</code></pre> |
| 563 | </td>··········</tr> | 563 | </td>··········</tr> |
| 564 | ··········<tr> | 564 | ··········<tr> |
| 565 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) | 565 | <td>··············<pre><code·class="language-macaulay2">i41·:·time·R'·=·integralClosure(R,·Strategy·=>·Radical) |
| 566 | ·--·used·0.099 | 566 | ·--·used·0.0989408s·(cpu);·0.047672s·(thread);·0s·(gc) |
| 567 | o41·=·R' | 567 | o41·=·R' |
| 568 | o41·:·QuotientRing</code></pre> | 568 | o41·:·QuotientRing</code></pre> |
| 569 | </td>··········</tr> | 569 | </td>··········</tr> |
| 570 | ··········<tr> | 570 | ··········<tr> |
| 571 | <td>··············<pre><code·class="language-macaulay2">i42·:·icFractions·R | 571 | <td>··············<pre><code·class="language-macaulay2">i42·:·icFractions·R |
| Max diff block lines reached; 5311/9287 bytes (57.19%) 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·0.665275s·(cpu);·0.44868s·(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·0.701643s·(cpu);·0.434916s·(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·0.68 | 205 | ·--·used·0.687255s·(cpu);·0.448896s·(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·0.7 | 287 | ·--·used·0.770352s·(cpu);·0.48023s·(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·1.1 | 369 | ·--·used·1.18252s·(cpu);·0.691814s·(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·0.831888s·(cpu);·0.450347s·(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·0.09 | 533 | ·--·used·0.0980356s·(cpu);·0.04984s·(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·0.099 | 579 | ·--·used·0.0989408s·(cpu);·0.047672s·(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; 3861/6919 bytes (55.80%) of diff not shown. | |||
| Offset 71, 48 lines modified | Offset 71, 48 lines modified | ||
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) | 73 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·R'·=·integralClosure(R,·Verbosity·=>·2) |
| 74 | ·[jacobian·time·0·sec·#minors·3] | 74 | ·[jacobian·time·0·sec·#minors·3] |
| 75 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 | 75 | integral·closure·nvars·3·numgens·1·is·S2·codim·1·codimJ·2 |
| 76 | ·[step·0:· | 76 | ·[step·0:· |
| 77 | ······radical·(use·minprimes)·.00 | 77 | ······radical·(use·minprimes)·.0027017·seconds |
| 78 | ······idlizer1:··.00 | 78 | ······idlizer1:··.00713324·seconds |
| 79 | ······idlizer2:··.0 | 79 | ······idlizer2:··.0604221·seconds |
| 80 | ······minpres:···.00782 | 80 | ······minpres:···.00782603·seconds |
| 81 | ··time·. | 81 | ··time·.0855316·sec··#fractions·4] |
| 82 | ·[step·1:· | 82 | ·[step·1:· |
| 83 | ······radical·(use·minprimes)· | 83 | ······radical·(use·minprimes)·0·seconds |
| 84 | ······idlizer1:··.01 | 84 | ······idlizer1:··.0116201·seconds |
| 85 | ······idlizer2:··.02101 | 85 | ······idlizer2:··.0210198·seconds |
| 86 | ······minpres:···.07 | 86 | ······minpres:···.0713629·seconds |
| 87 | ··time·.1 | 87 | ··time·.114059·sec··#fractions·4] |
| 88 | ·[step·2:· | 88 | ·[step·2:· |
| 89 | ······radical·(use·minprimes)·.00175048·seconds | ||
| 90 | ······idlizer1:··.00966925·seconds | ||
| 91 | ······idlizer2:··.022971·seconds | ||
| 92 | ······minpres:···.072636·seconds | ||
| 93 | ··time·.117528·sec··#fractions·5] | ||
| 94 | ·[step·3:· | ||
| 95 | ······radical·(use·minprimes)·0·seconds | 89 | ······radical·(use·minprimes)·0·seconds |
| 96 | ······idlizer1:··.0 | 90 | ······idlizer1:··.00732285·seconds |
| 97 | ······idlizer2:··.0 | 91 | ······idlizer2:··.0209287·seconds |
| 98 | ······minpres:···.0 | 92 | ······minpres:···.0693928·seconds |
| 99 | ··time·.1 | 93 | ··time·.11374·sec··#fractions·5] |
| 94 | ·[step·3:· | ||
| 95 | ······radical·(use·minprimes)·.00199306·seconds | ||
| 96 | ······idlizer1:··.0106652·seconds | ||
| 97 | ······idlizer2:··.0363535·seconds | ||
| 98 | ······minpres:···.0775116·seconds | ||
| 99 | ··time·.146022·sec··#fractions·5] | ||
| 100 | ·[step·4:· | 100 | ·[step·4:· |
| 101 | ······radical·(use·minprimes)·0·seconds | 101 | ······radical·(use·minprimes)·.00446955·seconds |
| 102 | ······idlizer1:··.01 | 102 | ······idlizer1:··.0145112·seconds |
| 103 | ······idlizer2:··.06 | 103 | ······idlizer2:··.0608228·seconds |
| 104 | ······minpres:···.070 | 104 | ······minpres:···.0704253·seconds |
| 105 | ··time·.169 | 105 | ··time·.169356·sec··#fractions·5] |
| 106 | ·[step·5:· | 106 | ·[step·5:· |
| 107 | ······radical·(use·minprimes)·0·seconds | 107 | ······radical·(use·minprimes)·.00382923·seconds |
| 108 | ······idlizer1:···--·used·0.6 | 108 | ······idlizer1:···--·used·0.651986s·(cpu);·0.469329s·(thread);·0s·(gc) |
| 109 | .00 | 109 | .00802173·seconds |
| 110 | ··time·.01 | 110 | ··time·.0150954·sec··#fractions·5] |
| 111 | o2·=·R' | 111 | o2·=·R' |
| 112 | o2·:·QuotientRing</code></pre> | 112 | o2·:·QuotientRing</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·trim·ideal·R' | 115 | <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)·.00 | 23 | ······radical·(use·minprimes)·.0027017·seconds |
| 24 | ······idlizer1:··.00 | 24 | ······idlizer1:··.00713324·seconds |
| 25 | ······idlizer2:··.0 | 25 | ······idlizer2:··.0604221·seconds |
| 26 | ······minpres:···.00782 | 26 | ······minpres:···.00782603·seconds |
| 27 | ··time·. | 27 | ··time·.0855316·sec··#fractions·4] |
| 28 | ·[step·1: | 28 | ·[step·1: |
| 29 | ······radical·(use·minprimes)· | 29 | ······radical·(use·minprimes)·0·seconds |
| 30 | ······idlizer1:··.01 | 30 | ······idlizer1:··.0116201·seconds |
| 31 | ······idlizer2:··.02101 | 31 | ······idlizer2:··.0210198·seconds |
| 32 | ······minpres:···.07 | 32 | ······minpres:···.0713629·seconds |
| 33 | ··time·.1 | 33 | ··time·.114059·sec··#fractions·4] |
| 34 | ·[step·2: | 34 | ·[step·2: |
| 35 | ······radical·(use·minprimes)·.00175048·seconds | ||
| 36 | ······idlizer1:··.00966925·seconds | ||
| 37 | ······idlizer2:··.022971·seconds | ||
| 38 | ······minpres:···.072636·seconds | ||
| 39 | ··time·.117528·sec··#fractions·5] | ||
| 40 | ·[step·3: | ||
| 41 | ······radical·(use·minprimes)·0·seconds | 35 | ······radical·(use·minprimes)·0·seconds |
| 42 | ······idlizer1:··.0 | 36 | ······idlizer1:··.00732285·seconds |
| 43 | ······idlizer2:··.0 | 37 | ······idlizer2:··.0209287·seconds |
| 44 | ······minpres:···.0 | 38 | ······minpres:···.0693928·seconds |
| 45 | ··time·.1 | 39 | ··time·.11374·sec··#fractions·5] |
| 40 | ·[step·3: | ||
| 41 | ······radical·(use·minprimes)·.00199306·seconds | ||
| 42 | ······idlizer1:··.0106652·seconds | ||
| 43 | ······idlizer2:··.0363535·seconds | ||
| 44 | ······minpres:···.0775116·seconds | ||
| 45 | ··time·.146022·sec··#fractions·5] | ||
| 46 | ·[step·4: | 46 | ·[step·4: |
| 47 | ······radical·(use·minprimes)·0·seconds | 47 | ······radical·(use·minprimes)·.00446955·seconds |
| 48 | ······idlizer1:··.01 | 48 | ······idlizer1:··.0145112·seconds |
| 49 | ······idlizer2:··.06 | 49 | ······idlizer2:··.0608228·seconds |
| 50 | ······minpres:···.070 | 50 | ······minpres:···.0704253·seconds |
| 51 | ··time·.169 | 51 | ··time·.169356·sec··#fractions·5] |
| 52 | ·[step·5: | 52 | ·[step·5: |
| 53 | ······radical·(use·minprimes)·0·seconds | 53 | ······radical·(use·minprimes)·.00382923·seconds |
| 54 | ······idlizer1:···--·used·0.6 | 54 | ······idlizer1:···--·used·0.651986s·(cpu);·0.469329s·(thread);·0s·(gc) |
| 55 | .00 | 55 | .00802173·seconds |
| 56 | ··time·.01 | 56 | ··time·.0150954·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 112, 27 lines modified | Offset 112, 27 lines modified | ||
| 112 | ················2······2····2········2···2·2·····2 | 112 | ················2······2····2········2···2·2·····2 |
| 113 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) | 113 | o3·=·ideal·(2a*b·c·+·3a·,·2a·b*c·+·3b·,·a·b··+·3c·) |
| 114 | o3·:·Ideal·of·S</code></pre> | 114 | o3·:·Ideal·of·S</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·integralClosure·J | 117 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·integralClosure·J |
| 118 | ·--·used·1. | 118 | ·--·used·1.52225s·(cpu);·0.798611s·(thread);·0s·(gc) |
| 119 | ·············2·2··············2·2················2··········2···2····· | 119 | ·············2·2··············2·2················2··········2···2····· |
| 120 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 120 | o4·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 121 | ·····------------------------------------------------------------------------ | 121 | ·····------------------------------------------------------------------------ |
| 122 | ···········2···3···············2·2·····2···5 | 122 | ···········2···3···············2·2·····2···5 |
| 123 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 123 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) |
| 124 | o4·:·Ideal·of·S</code></pre> | 124 | o4·:·Ideal·of·S</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) | 127 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·integralClosure(J,·Strategy=>{RadicalCodim1}) |
| 128 | ·--·used·0.8 | 128 | ·--·used·0.898111s·(cpu);·0.567524s·(thread);·0s·(gc) |
| 129 | ·············2·2··············2·2················2··········2···2····· | 129 | ·············2·2··············2·2················2··········2···2····· |
| 130 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- | 130 | o5·=·ideal·(b·c··-·16000a*c,·a·c··-·16000b*c,·a*b·c·-·16000a·,·a·b*c·- |
| 131 | ·····------------------------------------------------------------------------ | 131 | ·····------------------------------------------------------------------------ |
| 132 | ···········2···3···············2·2·····2···5 | 132 | ···········2···3···············2·2·····2···5 |
| 133 | ·····16000b·,·a·c·-·16000a*b,·a·b··+·3c·,·a·b·+·15997a*c) | 133 | ·····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·1. | 52 | ·--·used·1.52225s·(cpu);·0.798611s·(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·0.8 | 60 | ·--·used·0.898111s·(cpu);·0.567524s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.0020 | 29 | ·--·0.0020523·seconds·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 | ·--·0.00 | 55 | ·--·0.000402237·seconds·elapsed |
| 56 | i8·:· | 56 | i8·:· |
| 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·1. | 28 | ·--·used·1.6352s·(cpu);·1.21223s·(thread);·0s·(gc) |
| 29 | ·······2···2····2···2·2 | 29 | ·······2···2····2···2·2 |
| 30 | o4·=·{z·,·x··+·y·,·x·y·} | 30 | o4·=·{z·,·x··+·y·,·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·0.4 | 33 | ·--·used·0.460137s·(cpu);·0.311399s·(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·0.1 | 86 | ·--·used·0.103353s·(cpu);·0.0703809s·(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·3. | 91 | ·--·used·3.34582s·(cpu);·2.44974s·(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 | ·--·2.69676·seconds·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 | ·--·1.66867·seconds·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 | ·--·2.87077·seconds·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 | ·--·0. | 29 | ·--·0.0846794·seconds·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, 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 | ·······3····3····3···2·······2····2·····2·······2······2···4····4····4 | ||
| 21 | 20 | ··············3····3····3···4····4····4 | |
| 21 | o4·=·{x*y*z,·x··+·y··+·z·,·x··+·y··+·z·} | ||
| 22 | o4·:·List | 22 | o4·:·List |
| 23 | i5·:· | 23 | i5·:· |
| Offset 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·T.cache.?equivariantHilbert | 78 | <td>··············<pre><code·class="language-macaulay2">i4·:·T.cache.?equivariantHilbert |
| 79 | o4·=·false</code></pre> | 79 | o4·=·false</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) | 82 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5) |
| 83 | ·--·0.0020 | 83 | ·--·0.0020523·seconds·elapsed |
| 84 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2·· | 84 | ··················-1····-1·······2·2··············-2····-1·-1····-2··2·· |
| 85 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ | 85 | o5·=·1·+·(z·z··+·z···+·z··)T·+·(z·z··+·z··+·z··+·z···+·z··z···+·z··)T··+ |
| 86 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······ | 86 | ···········0·1····1·····0········0·1····0····1····1·····0··1·····0······ |
| 87 | ·····------------------------------------------------------------------------ | 87 | ·····------------------------------------------------------------------------ |
| 88 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 | 88 | ·······3·3····2········2······-1········-3····-1······-1·-2····-2·-1····-3··3 |
| 89 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T· | 89 | ·····(z·z··+·z·z··+·z·z··+·z·z···+·1·+·z···+·z··z··+·z··z···+·z··z···+·z··)T· |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·T.cache.?equivariantHilbert | 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·T.cache.?equivariantHilbert |
| 107 | o6·=·true</code></pre> | 107 | o6·=·true</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); | 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·equivariantHilbertSeries(T,·Order·=>·5); |
| 111 | ·--·0.00 | 111 | ·--·0.000402237·seconds·elapsed</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ········</table> | 113 | ········</table> |
| 114 | ······</div> | 114 | ······</div> |
| 115 | ······<div·class="waystouse"> | 115 | ······<div·class="waystouse"> |
| 116 | ········<h2>For·the·programmer</h2> | 116 | ········<h2>For·the·programmer</h2> |
| 117 | ········<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 | ········<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> |
| 118 | ······</div> | 118 | ······</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 | ·--·0.0020 | 35 | ·--·0.0020523·seconds·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 | ·--·0.00 | 59 | ·--·0.000402237·seconds·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 79, 24 lines modified | Offset 79, 24 lines modified | ||
| 79 | o3·:·FiniteGroupAction</code></pre> | 79 | o3·:·FiniteGroupAction</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ········</table> | 81 | ········</table> |
| 82 | ········<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 | ········<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> |
| 83 | ········<table·class="examples"> | 83 | ········<table·class="examples"> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·P1=primaryInvariants·C4xC2 | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·P1=primaryInvariants·C4xC2 |
| 86 | ·--·used·1. | 86 | ·--·used·1.6352s·(cpu);·1.21223s·(thread);·0s·(gc) |
| 87 | ·······2···2····2···2·2 | 87 | ·······2···2····2···2·2 |
| 88 | o4·=·{z·,·x··+·y·,·x·y·} | 88 | o4·=·{z·,·x··+·y·,·x·y·} |
| 89 | o4·:·List</code></pre> | 89 | o4·:·List</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·P2=primaryInvariants(C4xC2,Dade=>true) |
| 93 | ·--·used·0.4 | 93 | ·--·used·0.460137s·(cpu);·0.311399s·(thread);·0s·(gc) |
| 94 | ···········8·········7··········6·2·········5·3·········4·4·········3·5·· | 94 | ···········8·········7··········6·2·········5·3·········4·4·········3·5·· |
| 95 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ | 95 | o5·=·{4096x··+·24576x·y·+·38912x·y··-·18432x·y··-·65280x·y··+·18432x·y··+ |
| 96 | ·····------------------------------------------------------------------------ | 96 | ·····------------------------------------------------------------------------ |
| 97 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2·· | 97 | ···········2·6···········7········8·········6·2·········5···2·········4·2·2·· |
| 98 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- | 98 | ·····38912x·y··-·24576x*y··+·4096y··-·23040x·z··-·69120x·y*z··-·28800x·y·z··- |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| Offset 142, 24 lines modified | Offset 142, 24 lines modified | ||
| 142 | o5·:·List</code></pre> | 142 | o5·:·List</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ········</table> | 144 | ········</table> |
| 145 | ········<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 | ········<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> |
| 146 | ········<table·class="examples"> | 146 | ········<table·class="examples"> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·secondaryInvariants(P1,C4xC2) | 148 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·secondaryInvariants(P1,C4xC2) |
| 149 | ·--·used·0.1 | 149 | ·--·used·0.103353s·(cpu);·0.0703809s·(thread);·0s·(gc) |
| 150 | ··········3·······3 | 150 | ··········3·······3 |
| 151 | o6·=·{1,·x·y·-·x*y·} | 151 | o6·=·{1,·x·y·-·x*y·} |
| 152 | o6·:·List</code></pre> | 152 | o6·:·List</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·secondaryInvariants(P2,C4xC2) | 155 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·secondaryInvariants(P2,C4xC2) |
| 156 | ·--·used·3. | 156 | ·--·used·3.34582s·(cpu);·2.44974s·(thread);·0s·(gc) |
| 157 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4·· | 157 | ··········2···2····2···4···2·2····2·2···2·2···3·······3···4····4···6···2·4·· |
| 158 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ | 158 | o7·=·{1,·z·,·x··+·y·,·z·,·x·z··+·y·z·,·x·y·,·x·y·-·x*y·,·x··+·y·,·z·,·x·z··+ |
| 159 | ·····------------------------------------------------------------------------ | 159 | ·····------------------------------------------------------------------------ |
| 160 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 | 160 | ······2·4···2·2·2···3···2······3·2···4·2····4·2···4·2····2·4···5·······5···6 |
| 161 | ·····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 | ·····y·z·,·x·y·z·,·x·y*z··-·x*y·z·,·x·z··+·y·z·,·x·y··+·x·y·,·x·y·-·x*y·,·x· |
| 162 | ·····------------------------------------------------------------------------ | 162 | ·····------------------------------------------------------------------------ |
| 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·1. | 75 | ·--·used·1.6352s·(cpu);·1.21223s·(thread);·0s·(gc) |
| 76 | ·······2···2····2···2·2 | 76 | ·······2···2····2···2·2 |
| 77 | o4·=·{z·,·x··+·y·,·x·y·} | 77 | o4·=·{z·,·x··+·y·,·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·0.4 | 80 | ·--·used·0.460137s·(cpu);·0.311399s·(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·0.1 | 135 | ·--·used·0.103353s·(cpu);·0.0703809s·(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·3. | 140 | ·--·used·3.34582s·(cpu);·2.44974s·(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 90, 29 lines modified | Offset 90, 29 lines modified | ||
| 90 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 90 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 91 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 91 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 92 | o3·:·FiniteGroupAction</code></pre> | 92 | o3·:·FiniteGroupAction</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 |
| 96 | ·--· | 96 | ·--·2.69676·seconds·elapsed |
| 97 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 97 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| 98 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 98 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 99 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· | 99 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ······4 | 101 | ······4 |
| 102 | ·····x·} | 102 | ·····x·} |
| 103 | ······4 | 103 | ······4 |
| 104 | o4·:·List</code></pre> | 104 | o4·:·List</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,DegreeBound=>4) | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,DegreeBound=>4) |
| 108 | ·--· | 108 | ·--·1.66867·seconds·elapsed |
| 109 | Warning:·stopping·condition·not·met! | 109 | Warning:·stopping·condition·not·met! |
| 110 | Output·may·not·generate·the·entire·ring·of·invariants. | 110 | Output·may·not·generate·the·entire·ring·of·invariants. |
| 111 | Increase·value·of·DegreeBound. | 111 | Increase·value·of·DegreeBound. |
| 112 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 112 | ··························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 | ·--·2.69676·seconds·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 | ·--·1.66867·seconds·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 90, 29 lines modified | Offset 90, 29 lines modified | ||
| 90 | ···········|·0·0·1·0·|··|·0·1·0·0·| | 90 | ···········|·0·0·1·0·|··|·0·1·0·0·| |
| 91 | ···········|·0·0·0·1·|··|·0·0·1·0·| | 91 | ···········|·0·0·0·1·|··|·0·0·1·0·| |
| 92 | o3·:·FiniteGroupAction</code></pre> | 92 | o3·:·FiniteGroupAction</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·invariants·S4 |
| 96 | ·--· | 96 | ·--·2.87077·seconds·elapsed |
| 97 | ··························2····2····2····2···3····3····3····3···4····4····4·· | 97 | ··························2····2····2····2···3····3····3····3···4····4····4·· |
| 98 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ | 98 | o4·=·{x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+·x·,·x··+·x··+·x··+ |
| 99 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· | 99 | ·······1····2····3····4···1····2····3····4···1····2····3····4···1····2····3·· |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ······4 | 101 | ······4 |
| 102 | ·····x·} | 102 | ·····x·} |
| 103 | ······4 | 103 | ······4 |
| 104 | o4·:·List</code></pre> | 104 | o4·:·List</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·invariants(S4,UseLinearAlgebra=>true) |
| 108 | ·--·0. | 108 | ·--·0.0846794·seconds·elapsed |
| 109 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ | 109 | o5·=·{x··+·x··+·x··+·x·,·x·x··+·x·x··+·x·x··+·x·x··+·x·x··+·x·x·,·x·x·x··+ |
| 110 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3·· | 110 | ·······1····2····3····4···1·2····1·3····2·3····1·4····2·4····3·4···1·2·3·· |
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| 112 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} | 112 | ·····x·x·x··+·x·x·x··+·x·x·x·,·x·x·x·x·} |
| 113 | ······1·2·4····1·3·4····2·3·4···1·2·3·4 | 113 | ······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 | ·--·2.87077·seconds·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 | ·--·0. | 52 | ·--·0.0846794·seconds·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 91, 16 lines modified | Offset 91, 16 lines modified | ||
| 91 | ··················|·1·0·0·|··|·0·0·1·| | 91 | ··················|·1·0·0·|··|·0·0·1·| |
| 92 | o3·:·FiniteGroupAction</code></pre> | 92 | o3·:·FiniteGroupAction</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·primaryInvariants(S3,DegreeVector=>{3,3,4}) |
| 96 | ·······3····3····3···2·······2····2·····2·······2······2···4····4····4 | ||
| 97 | 96 | ··············3····3····3···4····4····4 | |
| 97 | o4·=·{x*y*z,·x··+·y··+·z·,·x··+·y··+·z·} | ||
| 98 | o4·:·List</code></pre> | 98 | o4·:·List</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ········</table> | 100 | ········</table> |
| 101 | ······</div> | 101 | ······</div> |
| 102 | ······<div> | 102 | ······<div> |
| 103 | ········<h2>Further·information</h2> | 103 | ········<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 | ·······3····3····3···2·······2····2·····2·······2······2···4····4····4 | ||
| 41 | 40 | ··············3····3····3···4····4····4 | |
| 41 | o4·=·{x*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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzMiwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTEzMiwgc3ltYm9sIERvY3VtZW50VGFn |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 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/M2-2534690-0/0.json |
| 43 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close | 43 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close |
| 44 | o10·=·/tmp/M2- | 44 | o10·=·/tmp/M2-2534690-0/0.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 151, 20 lines modified | Offset 151, 20 lines modified | ||
| 151 | ········<div> | 151 | ········<div> |
| 152 | ··········<p>The·input·may·also·be·a·file·containing·JSON·data.</p> | 152 | ··········<p>The·input·may·also·be·a·file·containing·JSON·data.</p> |
| 153 | ········</div> | 153 | ········</div> |
| 154 | ········<table·class="examples"> | 154 | ········<table·class="examples"> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i9·:·jsonFile·=·temporaryFileName()·|·".json" | 156 | <td>··············<pre><code·class="language-macaulay2">i9·:·jsonFile·=·temporaryFileName()·|·".json" |
| 157 | o9·=·/tmp/M2- | 157 | o9·=·/tmp/M2-2534690-0/0.json</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close | 160 | <td>··············<pre><code·class="language-macaulay2">i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close |
| 161 | o10·=·/tmp/M2- | 161 | o10·=·/tmp/M2-2534690-0/0.json |
| 162 | o10·:·File</code></pre> | 162 | o10·:·File</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ··········<tr> | 164 | ··········<tr> |
| 165 | <td>··············<pre><code·class="language-macaulay2">i11·:·fromJSON·openIn·jsonFile | 165 | <td>··············<pre><code·class="language-macaulay2">i11·:·fromJSON·openIn·jsonFile |
| 166 | o11·=·{1,·2,·3} | 166 | 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/M2-2534690-0/0.json |
| 59 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close | 59 | i10·:·jsonFile·<<·"[1,·2,·3]"·<<·endl·<<·close |
| 60 | o10·=·/tmp/M2- | 60 | o10·=·/tmp/M2-2534690-0/0.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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cmlldHkiLCAibGluZW51bSIgPT4gMTQzNiwgSW5wdXRzID0+IHtTUEFOe1RUeyJuIn0sIiwgIixT | 11 | cmlldHkiLCAibGluZW51bSIgPT4gMTQzNiwgSW5wdXRzID0+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 | ·--·0.106005·seconds·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 | ·--·0. | 28 | ·--·0.511453·seconds·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 | ·--·0.0 | 37 | ·--·0.0506422·seconds·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 | ·--·0.00 | 59 | ·--·0.00187528·seconds·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 | ·--·0.00 | 64 | ·--·0.00212648·seconds·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 | ·--·0.0 | 152 | ·--·0.0351904·seconds·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 | ·--·0.00 | 179 | ·--·0.00124502·seconds·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 74, 25 lines modified | Offset 74, 25 lines modified | ||
| 74 | ········</table> | 74 | ········</table> |
| 75 | ········<div> | 75 | ········<div> |
| 76 | ··········<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 | ··········<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> |
| 77 | ········</div> | 77 | ········</div> |
| 78 | ········<table·class="examples"> | 78 | ········<table·class="examples"> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jetsRadical(2,I) | 80 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jetsRadical(2,I) |
| 81 | ·--·0. | 81 | ·--·0.106005·seconds·elapsed |
| 82 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, | 82 | o4·=·ideal·(y0*z0*x2,·x0*z0*y2,·x0*y0*z2,·z0*x1*y1,·y0*x1*z1,·x0*y1*z1, |
| 83 | ·····------------------------------------------------------------------------ | 83 | ·····------------------------------------------------------------------------ |
| 84 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) | 84 | ·····y0*z0*x1,·x0*z0*y1,·x0*y0*z1,·x0*y0*z0) |
| 85 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> | 85 | o4·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·radical·J2I | 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·radical·J2I |
| 89 | ·--·0. | 89 | ·--·0.511453·seconds·elapsed |
| 90 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, | 90 | o5·=·ideal·(x0*y0*z0,·x0*y0*z1,·x0*z0*y1,·y0*z0*x1,·x0*y1*z1,·y0*x1*z1, |
| 91 | ·····------------------------------------------------------------------------ | 91 | ·····------------------------------------------------------------------------ |
| 92 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) | 92 | ·····z0*x1*y1,·x0*y0*z2,·x0*z0*y2,·y0*z0*x2) |
| 93 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> | 93 | o5·:·Ideal·of·QQ[x0,·y0,·z0][x1,·y1,·z1][x2,·y2,·z2]</code></pre> |
| 94 | </td>··········</tr> | 94 | </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 | ·--·0.106005·seconds·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 | ·--·0. | 40 | ·--·0.511453·seconds·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 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i7·:·I.cache.?jet | 97 | <td>··············<pre><code·class="language-macaulay2">i7·:·I.cache.?jet |
| 98 | o7·=·false</code></pre> | 98 | o7·=·false</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·jets(3,I) | 101 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·jets(3,I) |
| 102 | ·--·0.0 | 102 | ·--·0.0506422·seconds·elapsed |
| 103 | ··················································2·················2 | 103 | ··················································2·················2 |
| 104 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 104 | o8·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 105 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> | 105 | o8·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| Offset 119, 24 lines modified | Offset 119, 24 lines modified | ||
| 119 | ·······························|·2x0x2-y2+x1^2··| | 119 | ·······························|·2x0x2-y2+x1^2··| |
| 120 | ·······························|·2x0x1-y1·······| | 120 | ·······························|·2x0x1-y1·······| |
| 121 | ·······························|·x0^2-y0········| | 121 | ·······························|·x0^2-y0········| |
| 122 | ·················jetsMaxOrder·=>·3</code></pre> | 122 | ·················jetsMaxOrder·=>·3</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·jets(3,I) | 125 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·jets(3,I) |
| 126 | ·--·0.00 | 126 | ·--·0.00187528·seconds·elapsed |
| 127 | ···················································2·················2 | 127 | ···················································2·················2 |
| 128 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 128 | o11·=·ideal·(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 129 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> | 129 | o11·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·jets(2,I) | 132 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·jets(2,I) |
| 133 | ·--·0.00 | 133 | ·--·0.00212648·seconds·elapsed |
| 134 | ·····························2·················2 | 134 | ·····························2·················2 |
| 135 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 135 | o12·=·ideal·(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 136 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]</code></pre> | 136 | o12·:·Ideal·of·QQ[x0,·y0][x1,·y1][x2,·y2]</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| Offset 237, 15 lines modified | Offset 237, 15 lines modified | ||
| 237 | ··········<tr> | 237 | ··········<tr> |
| 238 | <td>··············<pre><code·class="language-macaulay2">i23·:·f.cache.?jet | 238 | <td>··············<pre><code·class="language-macaulay2">i23·:·f.cache.?jet |
| 239 | o23·=·false</code></pre> | 239 | o23·=·false</code></pre> |
| 240 | </td>··········</tr> | 240 | </td>··········</tr> |
| 241 | ··········<tr> | 241 | ··········<tr> |
| 242 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·jets(3,f) | 242 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·jets(3,f) |
| 243 | ·--·0.0 | 243 | ·--·0.0351904·seconds·elapsed |
| 244 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2 | 244 | ··············································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3]······················································2····················2 |
| 245 | o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 245 | o24·=·map·(QQ[t0][t1][t2][t3],·----------------------------------------------------------------,·{t3,·2t0*t3·+·2t1*t2,·t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 246 | ······································································2·················2 | 246 | ······································································2·················2 |
| 247 | ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 247 | ·······························(2x0*x3·-·y3·+·2x1*x2,·2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 248 | ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] | 248 | ····················································QQ[x0,·y0][x1,·y1][x2,·y2][x3,·y3] |
| Offset 265, 15 lines modified | Offset 265, 15 lines modified | ||
| 265 | ·······························|·t2·2t0t2+t1^2··| | 265 | ·······························|·t2·2t0t2+t1^2··| |
| 266 | ·······························|·t1·2t0t1·······| | 266 | ·······························|·t1·2t0t1·······| |
| 267 | ·······························|·t0·t0^2········| | 267 | ·······························|·t0·t0^2········| |
| 268 | ·················jetsMaxOrder·=>·3</code></pre> | 268 | ·················jetsMaxOrder·=>·3</code></pre> |
| 269 | </td>··········</tr> | 269 | </td>··········</tr> |
| 270 | ··········<tr> | 270 | ··········<tr> |
| 271 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·jets(2,f) | 271 | <td>··············<pre><code·class="language-macaulay2">i27·:·elapsedTime·jets(2,f) |
| 272 | ·--·0.00 | 272 | ·--·0.00124502·seconds·elapsed |
| 273 | ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2 | 273 | ···································QQ[x0,·y0][x1,·y1][x2,·y2]··························2····················2 |
| 274 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) | 274 | o27·=·map·(QQ[t0][t1][t2],·------------------------------------------,·{t2,·2t0*t2·+·t1·,·t1,·2t0*t1,·t0,·t0·}) |
| 275 | ············································2·················2 | 275 | ············································2·················2 |
| 276 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) | 276 | ···························(2x0*x2·-·y2·+·x1·,·2x0*x1·-·y1,·x0··-·y0) |
| 277 | ·········································QQ[x0,·y0][x1,·y1][x2,·y2] | 277 | ·········································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 | ·--·0.0 | 46 | ·--·0.0506422·seconds·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 | ·--·0.00 | 64 | ·--·0.00187528·seconds·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 | ·--·0.00 | 69 | ·--·0.00212648·seconds·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 | ·--·0.0 | 158 | ·--·0.0351904·seconds·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 | ·--·0.00 | 189 | ·--·0.00124502·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.0 | 24 | ·--·0.0184674·seconds·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 | ·--·0.00 | 50 | ·--·0.00305346·seconds·elapsed |
| 51 | ·--·0.00952949·seconds·elapsed | ||
| 52 | ·--·0.027265·seconds·elapsed | ||
| 53 | ·--·0.0 | 51 | ·--·0.0051368·seconds·elapsed |
| 52 | ·--·0.0204823·seconds·elapsed | ||
| 54 | ·--·0.00 | 53 | ·--·0.00820668·seconds·elapsed |
| 54 | ·--·0.00283032·seconds·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 | ·--·0.00327615·seconds·elapsed | ||
| 8 | ·--·0.00 | 7 | ·--·0.00173643·seconds·elapsed |
| 9 | ·--·0.0289402·seconds·elapsed | ||
| 10 | ·--·0.0120606·seconds·elapsed | ||
| 11 | ·--·0.00474905·seconds·elapsed | ||
| 12 | ·--·0.38 | 8 | ·--·0.00538015·seconds·elapsed |
| 9 | ·--·0.0186214·seconds·elapsed | ||
| 10 | ·--·0.00871425·seconds·elapsed | ||
| 11 | ·--·0.00288777·seconds·elapsed | ||
| 12 | ·--·0.246549·seconds·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 | ·--·0. | 31 | ·--·0.190896·seconds·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 | ·--·0.00393 | 53 | ·--·0.00393211·seconds·elapsed |
| 54 | ·--·0.0326388·seconds·elapsed | ||
| 55 | ·--·0. | 54 | ·--·0.0157492·seconds·elapsed |
| 56 | ·--·1.2442·seconds·elapsed | ||
| 57 | ·--·0. | 55 | ·--·0.175871·seconds·elapsed |
| 56 | ·--·0.831986·seconds·elapsed | ||
| 57 | ·--·0.251779·seconds·elapsed | ||
| 58 | ·--·0.03 | 58 | ·--·0.0343639·seconds·elapsed |
| 59 | ·--·0.0052 | 59 | ·--·0.00526549·seconds·elapsed |
| 60 | ·--· | 60 | ·--·4.2351·seconds·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 | ·--·0.002 | 7 | ·--·0.00240406·seconds·elapsed |
| 8 | ·--·0.00525233·seconds·elapsed | ||
| 9 | ·--·0.0199662·seconds·elapsed | ||
| 10 | ·--·0.00850188·seconds·elapsed | ||
| 8 | ·--·0.00 | 11 | ·--·0.00313468·seconds·elapsed |
| 9 | ·--·0.0364644·seconds·elapsed | ||
| 10 | ·--·0.0202154·seconds·elapsed | ||
| 11 | ·--·0.00742515·seconds·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 | ·--·0. | 53 | ·--·0.1684·seconds·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 | ·--·0.00349314·seconds·elapsed | ||
| 76 | ·--·0.0141012·seconds·elapsed | ||
| 77 | ·--·0.165767·seconds·elapsed | ||
| 78 | ·--·0.769117·seconds·elapsed | ||
| 79 | ·--·0.21107·seconds·elapsed | ||
| 80 | ·--·0.0341384·seconds·elapsed | ||
| 75 | ·--·0.00 | 81 | ·--·0.00546765·seconds·elapsed |
| 76 | ·--· | 82 | ·--·3.85558·seconds·elapsed |
| 77 | ·--·0.318661·seconds·elapsed | ||
| 78 | ·--·2.00283·seconds·elapsed | ||
| 79 | ·--·0.647236·seconds·elapsed | ||
| 80 | ·--·0.0743719·seconds·elapsed | ||
| 81 | ·--·0.00681431·seconds·elapsed | ||
| 82 | ·--·7.99293·seconds·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 | ·--·0.122882·seconds·elapsed | ||
| 8 | ·--·0.106175·seconds·elapsed | ||
| 9 | ·--·0.000183594·seconds·elapsed | ||
| 10 | ·--·0.000126267·seconds·elapsed | ||
| 11 | ·--·0.000116037·seconds·elapsed | ||
| 12 | ·--·0.000115086·seconds·elapsed | ||
| 13 | ·--·0.000113754·seconds·elapsed | ||
| 14 | ·--·0.000120966·seconds·elapsed | ||
| 15 | ·--·0.000135033·seconds·elapsed | ||
| 16 | ·--·0.000136796·seconds·elapsed | ||
| 17 | ·--·0.000135373·seconds·elapsed | ||
| 18 | ·--·0.000135605·seconds·elapsed | ||
| 19 | ·--·0.000121708·seconds·elapsed | ||
| 20 | ·--·0.000117831·seconds·elapsed | ||
| 21 | ·--·0.0 | 7 | ·--·0.0195244·seconds·elapsed |
| 8 | ·--·0.0628132·seconds·elapsed | ||
| 22 | ·--·0.0001 | 9 | ·--·0.000179612·seconds·elapsed |
| 23 | ·--·0.000118923·seconds·elapsed | ||
| 24 | ·--·0.000119664·seconds·elapsed | ||
| 25 | ·--·0.00 | 10 | ·--·0.00390626·seconds·elapsed |
| 26 | ·--·0.00012 | 11 | ·--·0.000127031·seconds·elapsed |
| 27 | ·--·0.000135665·seconds·elapsed | ||
| 28 | ·--·0.0001 | 12 | ·--·0.000112871·seconds·elapsed |
| 29 | ·--·0.000116368·seconds·elapsed | ||
| 30 | ·--·0.0001 | 13 | ·--·0.000107282·seconds·elapsed |
| 31 | ·--·0.0001 | 14 | ·--·0.000118879·seconds·elapsed |
| 15 | ·--·0.000171969·seconds·elapsed | ||
| 16 | ·--·0.000707628·seconds·elapsed | ||
| 17 | ·--·0.000167373·seconds·elapsed | ||
| 32 | ·--·0.000118 | 18 | ·--·0.00011896·seconds·elapsed |
| 33 | ·--·0.0001 | 19 | ·--·0.000108104·seconds·elapsed |
| 20 | ·--·0.000127724·seconds·elapsed | ||
| 34 | ·--·0.0001 | 21 | ·--·0.00011331·seconds·elapsed |
| 22 | ·--·0.000115974·seconds·elapsed | ||
| 23 | ·--·0.000195856·seconds·elapsed | ||
| 24 | ·--·0.000107253·seconds·elapsed | ||
| 25 | ·--·0.00011888·seconds·elapsed | ||
| 26 | ·--·0.000235045·seconds·elapsed | ||
| 27 | ·--·0.000191629·seconds·elapsed | ||
| 28 | ·--·0.000131129·seconds·elapsed | ||
| 29 | ·--·0.000130728·seconds·elapsed | ||
| 30 | ·--·0.000145088·seconds·elapsed | ||
| 31 | ·--·0.000113012·seconds·elapsed | ||
| 32 | ·--·0.000115445·seconds·elapsed | ||
| 33 | ·--·0.000106502·seconds·elapsed | ||
| 34 | ·--·0.000112561·seconds·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 | ·--·0.1 | 7 | ·--·0.115941·seconds·elapsed |
| 8 | ·--·0.20089·seconds·elapsed | ||
| 9 | ·--·0.141669·seconds·elapsed | ||
| 8 | ·--·0. | 10 | ·--·0.219795·seconds·elapsed |
| 9 | ·--·0.156823·seconds·elapsed | ||
| 10 | ·--·0.2 | 11 | ·--·0.285037·seconds·elapsed |
| 11 | ·--·0.215189·seconds·elapsed | ||
| 12 | ·--·0.14 | 12 | ·--·0.146336·seconds·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 | ·--·0.002 | 13 | ·--·0.00217119·seconds·elapsed |
| 14 | ·--·0.00709748·seconds·elapsed | ||
| 15 | ·--·0.0507505·seconds·elapsed | ||
| 16 | ·--·0.00 | 14 | ·--·0.00504055·seconds·elapsed |
| 15 | ·--·0.0193402·seconds·elapsed | ||
| 17 | ·--·0.00 | 16 | ·--·0.00800184·seconds·elapsed |
| 17 | ·--·0.00293484·seconds·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 | ·--·0. | 53 | ·--·0.195675·seconds·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 | ·--·0.00 | 81 | ·--·0.0018781·seconds·elapsed |
| 82 | ·--·0.00 | 82 | ·--·0.0048134·seconds·elapsed |
| 83 | ·--·0.0216425·seconds·elapsed | ||
| 83 | ·--·0.0 | 84 | ·--·0.007893·seconds·elapsed |
| 84 | ·--·0.0103191·seconds·elapsed | ||
| 85 | ·--·0.00 | 85 | ·--·0.00277762·seconds·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:·-1427619998 | 1 | --·-*-·M2-comint·-*-·hash:·-1427619998 |
| 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 | ·--·0.01 | 5 | ·--·0.0106896·seconds·elapsed |
| 6 | ·--·2. | 6 | ·--·2.5288e-05·seconds·elapsed |
| 7 | ·--·7.1875e-05·seconds·elapsed | ||
| 8 | ·--· | 7 | ·--·9.4764e-05·seconds·elapsed |
| 9 | ·--·6.1595e-05·seconds·elapsed | ||
| 10 | ·--·6.7878e-05·seconds·elapsed | ||
| 11 | ·--·6.8158e-05·seconds·elapsed | ||
| 12 | ·--·1.8033e-05·seconds·elapsed | ||
| 13 | ·--·5.2669e-05·seconds·elapsed | ||
| 14 | ·--·6. | 8 | ·--·6.8624e-05·seconds·elapsed |
| 15 | ·--· | 9 | ·--·5.7787e-05·seconds·elapsed |
| 16 | ·--·6.5 | 10 | ·--·6.5149e-05·seconds·elapsed |
| 17 | ·--· | 11 | ·--·6.2975e-05·seconds·elapsed |
| 18 | ·--·5.6116e-05·seconds·elapsed | ||
| 19 | ·--·5.4773e-05·seconds·elapsed | ||
| 20 | ·--· | 12 | ·--·2.0451e-05·seconds·elapsed |
| 21 | ·--·1.9116e-05·seconds·elapsed | ||
| 22 | ·--·5. | 13 | ·--·5.1698e-05·seconds·elapsed |
| 14 | ·--·7.7877e-05·seconds·elapsed | ||
| 15 | ·--·8.5899e-05·seconds·elapsed | ||
| 23 | ·--· | 16 | ·--·7.7427e-05·seconds·elapsed |
| 17 | ·--·7.3751e-05·seconds·elapsed | ||
| 18 | ·--·6.8523e-05·seconds·elapsed | ||
| 19 | ·--·4.9254e-05·seconds·elapsed | ||
| 20 | ·--·4.7471e-05·seconds·elapsed | ||
| 21 | ·--·1.8318e-05·seconds·elapsed | ||
| 22 | ·--·5.0967e-05·seconds·elapsed | ||
| 23 | ·--·1.7617e-05·seconds·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 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | ·····················································································································································································································································································································10 | 97 | ·····················································································································································································································································································································10 |
| 98 | ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9 | 98 | ·····0····························1·····························2······························3······························4······························5······························6······························7······························8·····························9 |
| 99 | o3·:·ChainComplex</code></pre> | 99 | o3·:·ChainComplex</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·L·=·analyzeStrand(F,a);·#L | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·L·=·analyzeStrand(F,a);·#L |
| 103 | ·--·0.0 | 103 | ·--·0.0184674·seconds·elapsed |
| 104 | o5·=·350</code></pre> | 104 | o5·=·350</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·betti·F_a,·betti·F | 107 | <td>··············<pre><code·class="language-macaulay2">i6·:·betti·F_a,·betti·F |
| 108 | ···············0·········0··1···2···3···4···5···6···7··8·9 | 108 | ···············0·········0··1···2···3···4···5···6···7··8·9 |
| Offset 128, 19 lines modified | Offset 128, 19 lines modified | ||
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i8·:·L3·=·select(L,c->c%3==0);·#L3 | 129 | <td>··············<pre><code·class="language-macaulay2">i8·:·L3·=·select(L,c->c%3==0);·#L3 |
| 130 | o9·=·14</code></pre> | 130 | o9·=·14</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·carpetBettiTable(a,b,3) | 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·carpetBettiTable(a,b,3) |
| 134 | ·--·0.00 | 134 | ·--·0.00305346·seconds·elapsed |
| 135 | ·--·0.00952949·seconds·elapsed | ||
| 136 | ·--·0.027265·seconds·elapsed | ||
| 137 | ·--·0.0 | 135 | ·--·0.0051368·seconds·elapsed |
| 136 | ·--·0.0204823·seconds·elapsed | ||
| 138 | ·--·0.00 | 137 | ·--·0.00820668·seconds·elapsed |
| 138 | ·--·0.00283032·seconds·elapsed | ||
| 139 | ·············0··1···2···3···4···5···6···7··8·9 | 139 | ·············0··1···2···3···4···5···6···7··8·9 |
| 140 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 | 140 | o10·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 141 | ··········0:·1··.···.···.···.···.···.···.··.·. | 141 | ··········0:·1··.···.···.···.···.···.···.··.·. |
| 142 | ··········1:·.·36·160·315·288··14···.···.··.·. | 142 | ··········1:·.·36·160·315·288··14···.···.··.·. |
| 143 | ··········2:·.··.···.···.··14·288·315·160·36·. | 143 | ··········2:·.··.···.···.··14·288·315·160·36·. |
| 144 | ··········3:·.··.···.···.···.···.···.···.··.·1 | 144 | ··········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 | ·--·0.0 | 56 | ·--·0.0184674·seconds·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 | ·--·0.00 | 78 | ·--·0.00305346·seconds·elapsed |
| 79 | ·--·0.00952949·seconds·elapsed | ||
| 80 | ·--·0.027265·seconds·elapsed | ||
| 81 | ·--·0.0 | 79 | ·--·0.0051368·seconds·elapsed |
| 80 | ·--·0.0204823·seconds·elapsed | ||
| 82 | ·--·0.00 | 81 | ·--·0.00820668·seconds·elapsed |
| 82 | ·--·0.00283032·seconds·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 84, 20 lines modified | Offset 84, 20 lines modified | ||
| 84 | o1·=·(5,·5) | 84 | o1·=·(5,·5) |
| 85 | o1·:·Sequence</code></pre> | 85 | o1·:·Sequence</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·T=carpetBettiTable(a,b,3) | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·elapsedTime·T=carpetBettiTable(a,b,3) |
| 89 | ·--·0.00327615·seconds·elapsed | ||
| 90 | ·--·0.00 | 89 | ·--·0.00173643·seconds·elapsed |
| 91 | ·--·0.0289402·seconds·elapsed | ||
| 92 | ·--·0.0120606·seconds·elapsed | ||
| 93 | ·--·0.00474905·seconds·elapsed | ||
| 94 | ·--·0.38 | 90 | ·--·0.00538015·seconds·elapsed |
| 91 | ·--·0.0186214·seconds·elapsed | ||
| 92 | ·--·0.00871425·seconds·elapsed | ||
| 93 | ·--·0.00288777·seconds·elapsed | ||
| 94 | ·--·0.246549·seconds·elapsed | ||
| 95 | ············0··1···2···3···4···5···6···7··8·9 | 95 | ············0··1···2···3···4···5···6···7··8·9 |
| 96 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 | 96 | o2·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 97 | ·········0:·1··.···.···.···.···.···.···.··.·. | 97 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 98 | ·········1:·.·36·160·315·288··14···.···.··.·. | 98 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 99 | ·········2:·.··.···.···.··14·288·315·160·36·. | 99 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 100 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 100 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 109, 15 lines modified | Offset 109, 15 lines modified | ||
| 109 | ··············ZZ | 109 | ··············ZZ |
| 110 | o3·:·Ideal·of·--[x·..x·,·y·..y·] | 110 | o3·:·Ideal·of·--[x·..x·,·y·..y·] |
| 111 | ···············3··0···5···0···5</code></pre> | 111 | ···············3··0···5···0···5</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·T'=minimalBetti·J | 114 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·T'=minimalBetti·J |
| 115 | ·--·0. | 115 | ·--·0.190896·seconds·elapsed |
| 116 | ············0··1···2···3···4···5···6···7··8·9 | 116 | ············0··1···2···3···4···5···6···7··8·9 |
| 117 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 | 117 | o4·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 118 | ·········0:·1··.···.···.···.···.···.···.··.·. | 118 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 119 | ·········1:·.·36·160·315·288··14···.···.··.·. | 119 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 120 | ·········2:·.··.···.···.··14·288·315·160·36·. | 120 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 121 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 121 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 133, 22 lines modified | Offset 133, 22 lines modified | ||
| 133 | ·········2:·.·.·.·.·.·.·.·.·.·. | 133 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 134 | ·········3:·.·.·.·.·.·.·.·.·.·. | 134 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 135 | o5·:·BettiTally</code></pre> | 135 | o5·:·BettiTally</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·h=carpetBettiTables(6,6); | 138 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·h=carpetBettiTables(6,6); |
| 139 | ·--·0.00393 | 139 | ·--·0.00393211·seconds·elapsed |
| 140 | ·--·0.0326388·seconds·elapsed | ||
| 141 | ·--·0. | 140 | ·--·0.0157492·seconds·elapsed |
| 142 | ·--·1.2442·seconds·elapsed | ||
| 143 | ·--·0. | 141 | ·--·0.175871·seconds·elapsed |
| 142 | ·--·0.831986·seconds·elapsed | ||
| 143 | ·--·0.251779·seconds·elapsed | ||
| 144 | ·--·0.03 | 144 | ·--·0.0343639·seconds·elapsed |
| 145 | ·--·0.0052 | 145 | ·--·0.00526549·seconds·elapsed |
| 146 | ·--· | 146 | ·--·4.2351·seconds·elapsed</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i7·:·carpetBettiTable(h,7) | 149 | <td>··············<pre><code·class="language-macaulay2">i7·:·carpetBettiTable(h,7) |
| 150 | ············0··1···2···3····4····5····6····7···8···9·10·11 | 150 | ············0··1···2···3····4····5····6····7···8···9·10·11 |
| 151 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 | 151 | o7·=·total:·1·55·320·891·1408·1155·1155·1408·891·320·55··1 |
| 152 | ·········0:·1··.···.···.····.····.····.····.···.···.··.··. | 152 | ·········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 | ·--·0.00327615·seconds·elapsed | ||
| 32 | ·--·0.00 | 31 | ·--·0.00173643·seconds·elapsed |
| 33 | ·--·0.0289402·seconds·elapsed | ||
| 34 | ·--·0.0120606·seconds·elapsed | ||
| 35 | ·--·0.00474905·seconds·elapsed | ||
| 36 | ·--·0.38 | 32 | ·--·0.00538015·seconds·elapsed |
| 33 | ·--·0.0186214·seconds·elapsed | ||
| 34 | ·--·0.00871425·seconds·elapsed | ||
| 35 | ·--·0.00288777·seconds·elapsed | ||
| 36 | ·--·0.246549·seconds·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 | ·--·0. | 53 | ·--·0.190896·seconds·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 | ·--·0.00393 | 73 | ·--·0.00393211·seconds·elapsed |
| 74 | ·--·0.0326388·seconds·elapsed | ||
| 75 | ·--·0. | 74 | ·--·0.0157492·seconds·elapsed |
| 76 | ·--·1.2442·seconds·elapsed | ||
| 77 | ·--·0. | 75 | ·--·0.175871·seconds·elapsed |
| 76 | ·--·0.831986·seconds·elapsed | ||
| 77 | ·--·0.251779·seconds·elapsed | ||
| 78 | ·--·0.03 | 78 | ·--·0.0343639·seconds·elapsed |
| 79 | ·--·0.0052 | 79 | ·--·0.00526549·seconds·elapsed |
| 80 | ·--· | 80 | ·--·4.2351·seconds·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 79, 19 lines modified | Offset 79, 19 lines modified | ||
| 79 | o1·=·(5,·5) | 79 | o1·=·(5,·5) |
| 80 | o1·:·Sequence</code></pre> | 80 | o1·:·Sequence</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·h=carpetBettiTables(a,b) | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·h=carpetBettiTables(a,b) |
| 84 | ·--·0.002 | 84 | ·--·0.00240406·seconds·elapsed |
| 85 | ·--·0.00525233·seconds·elapsed | ||
| 86 | ·--·0.0199662·seconds·elapsed | ||
| 87 | ·--·0.00850188·seconds·elapsed | ||
| 85 | ·--·0.00 | 88 | ·--·0.00313468·seconds·elapsed |
| 86 | ·--·0.0364644·seconds·elapsed | ||
| 87 | ·--·0.0202154·seconds·elapsed | ||
| 88 | ·--·0.00742515·seconds·elapsed | ||
| 89 | ···························0··1···2···3···4···5···6···7··8·9 | 89 | ···························0··1···2···3···4···5···6···7··8·9 |
| 90 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 90 | o2·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 91 | ························0:·1··.···.···.···.···.···.···.··.·. | 91 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 92 | ························1:·.·36·160·315·288···.···.···.··.·. | 92 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 93 | ························2:·.··.···.···.···.·288·315·160·36·. | 93 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 94 | ························3:·.··.···.···.···.···.···.···.··.·1 | 94 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 127, 15 lines modified | Offset 127, 15 lines modified | ||
| 127 | ··············ZZ | 127 | ··············ZZ |
| 128 | o4·:·Ideal·of·--[x·..x·,·y·..y·] | 128 | o4·:·Ideal·of·--[x·..x·,·y·..y·] |
| 129 | ···············3··0···5···0···5</code></pre> | 129 | ···············3··0···5···0···5</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T'=minimalBetti·J | 132 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T'=minimalBetti·J |
| 133 | ·--·0. | 133 | ·--·0.1684·seconds·elapsed |
| 134 | ············0··1···2···3···4···5···6···7··8·9 | 134 | ············0··1···2···3···4···5···6···7··8·9 |
| 135 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 | 135 | o5·=·total:·1·36·160·315·302·302·315·160·36·1 |
| 136 | ·········0:·1··.···.···.···.···.···.···.··.·. | 136 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 137 | ·········1:·.·36·160·315·288··14···.···.··.·. | 137 | ·········1:·.·36·160·315·288··14···.···.··.·. |
| 138 | ·········2:·.··.···.···.··14·288·315·160·36·. | 138 | ·········2:·.··.···.···.··14·288·315·160·36·. |
| 139 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 139 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 151, 22 lines modified | Offset 151, 22 lines modified | ||
| 151 | ·········2:·.·.·.·.·.·.·.·.·.·. | 151 | ·········2:·.·.·.·.·.·.·.·.·.·. |
| 152 | ·········3:·.·.·.·.·.·.·.·.·.·. | 152 | ·········3:·.·.·.·.·.·.·.·.·.·. |
| 153 | o6·:·BettiTally</code></pre> | 153 | o6·:·BettiTally</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·h=carpetBettiTables(6,6); | 156 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·h=carpetBettiTables(6,6); |
| 157 | ·--·0.00349314·seconds·elapsed | ||
| 158 | ·--·0.0141012·seconds·elapsed | ||
| 159 | ·--·0.165767·seconds·elapsed | ||
| 160 | ·--·0.769117·seconds·elapsed | ||
| 161 | ·--·0.21107·seconds·elapsed | ||
| 162 | ·--·0.0341384·seconds·elapsed | ||
| 157 | ·--·0.00 | 163 | ·--·0.00546765·seconds·elapsed |
| 158 | ·--·0.0351056·seconds·elapsed | ||
| 159 | ·--·0.318661·seconds·elapsed | ||
| 160 | ·--·2.00283·seconds·elapsed | ||
| 161 | ·--·0.647236·seconds·elapsed | ||
| 162 | ·--·0.0743719·seconds·elapsed | ||
| 163 | ·--·0.00681431·seconds·elapsed | ||
| 164 | ·--· | 164 | ·--·3.85558·seconds·elapsed</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i8·:·keys·h | 167 | <td>··············<pre><code·class="language-macaulay2">i8·:·keys·h |
| 168 | o8·=·{0,·2,·3,·5} | 168 | o8·=·{0,·2,·3,·5} |
| 169 | o8·:·List</code></pre> | 169 | 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 | ·--·0.002 | 27 | ·--·0.00240406·seconds·elapsed |
| 28 | ·--·0.00525233·seconds·elapsed | ||
| 29 | ·--·0.0199662·seconds·elapsed | ||
| 30 | ·--·0.00850188·seconds·elapsed | ||
| 28 | ·--·0.00 | 31 | ·--·0.00313468·seconds·elapsed |
| 29 | ·--·0.0364644·seconds·elapsed | ||
| 30 | ·--·0.0202154·seconds·elapsed | ||
| 31 | ·--·0.00742515·seconds·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 | ·--·0. | 70 | ·--·0.1684·seconds·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 | ·--·0.00349314·seconds·elapsed | ||
| 91 | ·--·0.0141012·seconds·elapsed | ||
| 92 | ·--·0.165767·seconds·elapsed | ||
| 93 | ·--·0.769117·seconds·elapsed | ||
| 94 | ·--·0.21107·seconds·elapsed | ||
| 95 | ·--·0.0341384·seconds·elapsed | ||
| 90 | ·--·0.00 | 96 | ·--·0.00546765·seconds·elapsed |
| 91 | ·--· | 97 | ·--·3.85558·seconds·elapsed |
| 92 | ·--·0.318661·seconds·elapsed | ||
| 93 | ·--·2.00283·seconds·elapsed | ||
| 94 | ·--·0.647236·seconds·elapsed | ||
| 95 | ·--·0.0743719·seconds·elapsed | ||
| 96 | ·--·0.00681431·seconds·elapsed | ||
| 97 | ·--·7.99293·seconds·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 79, 42 lines modified | Offset 79, 42 lines modified | ||
| 79 | o1·=·(4,·4) | 79 | o1·=·(4,·4) |
| 80 | o1·:·Sequence</code></pre> | 80 | o1·:·Sequence</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·d=carpetDet(a,b) | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·d=carpetDet(a,b) |
| 84 | ·--·0.122882·seconds·elapsed | ||
| 85 | ·--·0.106175·seconds·elapsed | ||
| 86 | ·--·0.000183594·seconds·elapsed | ||
| 87 | ·--·0.000126267·seconds·elapsed | ||
| 88 | ·--·0.000116037·seconds·elapsed | ||
| 89 | ·--·0.000115086·seconds·elapsed | ||
| 90 | ·--·0.000113754·seconds·elapsed | ||
| 91 | ·--·0.000120966·seconds·elapsed | ||
| 92 | ·--·0.000135033·seconds·elapsed | ||
| 93 | ·--·0.000136796·seconds·elapsed | ||
| 94 | ·--·0.000135373·seconds·elapsed | ||
| 95 | ·--·0.000135605·seconds·elapsed | ||
| 96 | ·--·0.000121708·seconds·elapsed | ||
| 97 | ·--·0.000117831·seconds·elapsed | ||
| 98 | ·--·0.0 | 84 | ·--·0.0195244·seconds·elapsed |
| 85 | ·--·0.0628132·seconds·elapsed | ||
| 99 | ·--·0.0001 | 86 | ·--·0.000179612·seconds·elapsed |
| 100 | ·--·0.000118923·seconds·elapsed | ||
| 101 | ·--·0.000119664·seconds·elapsed | ||
| 102 | ·--·0.00 | 87 | ·--·0.00390626·seconds·elapsed |
| 103 | ·--·0.00012 | 88 | ·--·0.000127031·seconds·elapsed |
| 104 | ·--·0.000135665·seconds·elapsed | ||
| 105 | ·--·0.0001 | 89 | ·--·0.000112871·seconds·elapsed |
| 106 | ·--·0.000116368·seconds·elapsed | ||
| 107 | ·--·0.0001 | 90 | ·--·0.000107282·seconds·elapsed |
| 108 | ·--·0.0001 | 91 | ·--·0.000118879·seconds·elapsed |
| 92 | ·--·0.000171969·seconds·elapsed | ||
| 93 | ·--·0.000707628·seconds·elapsed | ||
| 94 | ·--·0.000167373·seconds·elapsed | ||
| 109 | ·--·0.000118 | 95 | ·--·0.00011896·seconds·elapsed |
| 110 | ·--·0.0001 | 96 | ·--·0.000108104·seconds·elapsed |
| 97 | ·--·0.000127724·seconds·elapsed | ||
| 111 | ·--·0.0001 | 98 | ·--·0.00011331·seconds·elapsed |
| 99 | ·--·0.000115974·seconds·elapsed | ||
| 100 | ·--·0.000195856·seconds·elapsed | ||
| 101 | ·--·0.000107253·seconds·elapsed | ||
| 102 | ·--·0.00011888·seconds·elapsed | ||
| 103 | ·--·0.000235045·seconds·elapsed | ||
| 104 | ·--·0.000191629·seconds·elapsed | ||
| 105 | ·--·0.000131129·seconds·elapsed | ||
| 106 | ·--·0.000130728·seconds·elapsed | ||
| 107 | ·--·0.000145088·seconds·elapsed | ||
| 108 | ·--·0.000113012·seconds·elapsed | ||
| 109 | ·--·0.000115445·seconds·elapsed | ||
| 110 | ·--·0.000106502·seconds·elapsed | ||
| 111 | ·--·0.000112561·seconds·elapsed | ||
| 112 | (number·Of·blocks,·26) | 112 | (number·Of·blocks,·26) |
| 113 | 1 | 113 | 1 |
| 114 | 1 | 114 | 1 |
| 115 | 1 | 115 | 1 |
| 116 | 1 | 116 | 1 |
| 117 | 2 | 117 | 2 |
| 118 | ·2 | 118 | ·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 | ·--·0.122882·seconds·elapsed | ||
| 26 | ·--·0.106175·seconds·elapsed | ||
| 27 | ·--·0.000183594·seconds·elapsed | ||
| 28 | ·--·0.000126267·seconds·elapsed | ||
| 29 | ·--·0.000116037·seconds·elapsed | ||
| 30 | ·--·0.000115086·seconds·elapsed | ||
| 31 | ·--·0.000113754·seconds·elapsed | ||
| 32 | ·--·0.000120966·seconds·elapsed | ||
| 33 | ·--·0.000135033·seconds·elapsed | ||
| 34 | ·--·0.000136796·seconds·elapsed | ||
| 35 | ·--·0.000135373·seconds·elapsed | ||
| 36 | ·--·0.000135605·seconds·elapsed | ||
| 37 | ·--·0.000121708·seconds·elapsed | ||
| 38 | ·--·0.000117831·seconds·elapsed | ||
| 39 | ·--·0.0 | 25 | ·--·0.0195244·seconds·elapsed |
| 26 | ·--·0.0628132·seconds·elapsed | ||
| 40 | ·--·0.0001 | 27 | ·--·0.000179612·seconds·elapsed |
| 41 | ·--·0.000118923·seconds·elapsed | ||
| 42 | ·--·0.000119664·seconds·elapsed | ||
| 43 | ·--·0.00 | 28 | ·--·0.00390626·seconds·elapsed |
| 44 | ·--·0.00012 | 29 | ·--·0.000127031·seconds·elapsed |
| 45 | ·--·0.000135665·seconds·elapsed | ||
| 46 | ·--·0.0001 | 30 | ·--·0.000112871·seconds·elapsed |
| 47 | ·--·0.000116368·seconds·elapsed | ||
| 48 | ·--·0.0001 | 31 | ·--·0.000107282·seconds·elapsed |
| 49 | ·--·0.0001 | 32 | ·--·0.000118879·seconds·elapsed |
| 33 | ·--·0.000171969·seconds·elapsed | ||
| 34 | ·--·0.000707628·seconds·elapsed | ||
| 35 | ·--·0.000167373·seconds·elapsed | ||
| 50 | ·--·0.000118 | 36 | ·--·0.00011896·seconds·elapsed |
| 51 | ·--·0.0001 | 37 | ·--·0.000108104·seconds·elapsed |
| 38 | ·--·0.000127724·seconds·elapsed | ||
| 52 | ·--·0.0001 | 39 | ·--·0.00011331·seconds·elapsed |
| 40 | ·--·0.000115974·seconds·elapsed | ||
| 41 | ·--·0.000195856·seconds·elapsed | ||
| 42 | ·--·0.000107253·seconds·elapsed | ||
| 43 | ·--·0.00011888·seconds·elapsed | ||
| 44 | ·--·0.000235045·seconds·elapsed | ||
| 45 | ·--·0.000191629·seconds·elapsed | ||
| 46 | ·--·0.000131129·seconds·elapsed | ||
| 47 | ·--·0.000130728·seconds·elapsed | ||
| 48 | ·--·0.000145088·seconds·elapsed | ||
| 49 | ·--·0.000113012·seconds·elapsed | ||
| 50 | ·--·0.000115445·seconds·elapsed | ||
| 51 | ·--·0.000106502·seconds·elapsed | ||
| 52 | ·--·0.000112561·seconds·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 87, 20 lines modified | Offset 87, 20 lines modified | ||
| 87 | o1·=·(9,·7) | 87 | o1·=·(9,·7) |
| 88 | o1·:·Sequence</code></pre> | 88 | o1·:·Sequence</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·computeBound·3 | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·computeBound·3 |
| 92 | ·--·0.1 | 92 | ·--·0.115941·seconds·elapsed |
| 93 | ·--·0.20089·seconds·elapsed | ||
| 94 | ·--·0.141669·seconds·elapsed | ||
| 93 | ·--·0. | 95 | ·--·0.219795·seconds·elapsed |
| 94 | ·--·0.156823·seconds·elapsed | ||
| 95 | ·--·0.2 | 96 | ·--·0.285037·seconds·elapsed |
| 96 | ·--·0.215189·seconds·elapsed | ||
| 97 | ·--·0.14 | 97 | ·--·0.146336·seconds·elapsed |
| 98 | o2·=·6</code></pre> | 98 | o2·=·6</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 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 | ·--·0.1 | 31 | ·--·0.115941·seconds·elapsed |
| 32 | ·--·0.20089·seconds·elapsed | ||
| 33 | ·--·0.141669·seconds·elapsed | ||
| 32 | ·--·0. | 34 | ·--·0.219795·seconds·elapsed |
| 33 | ·--·0.156823·seconds·elapsed | ||
| 34 | ·--·0.2 | 35 | ·--·0.285037·seconds·elapsed |
| 35 | ·--·0.215189·seconds·elapsed | ||
| 36 | ·--·0.14 | 36 | ·--·0.146336·seconds·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 88, 19 lines modified | Offset 88, 19 lines modified | ||
| 88 | o2·=·(-1,·5) | 88 | o2·=·(-1,·5) |
| 89 | o2·:·Sequence</code></pre> | 89 | o2·:·Sequence</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·h=degenerateK3BettiTables(a,b,e) | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·h=degenerateK3BettiTables(a,b,e) |
| 93 | ·--·0.002 | 93 | ·--·0.00217119·seconds·elapsed |
| 94 | ·--·0.00709748·seconds·elapsed | ||
| 95 | ·--·0.0507505·seconds·elapsed | ||
| 96 | ·--·0.00 | 94 | ·--·0.00504055·seconds·elapsed |
| 95 | ·--·0.0193402·seconds·elapsed | ||
| 97 | ·--·0.00 | 96 | ·--·0.00800184·seconds·elapsed |
| 97 | ·--·0.00293484·seconds·elapsed | ||
| 98 | ···························0··1···2···3···4···5···6···7··8·9 | 98 | ···························0··1···2···3···4···5···6···7··8·9 |
| 99 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} | 99 | o3·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1} |
| 100 | ························0:·1··.···.···.···.···.···.···.··.·. | 100 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 101 | ························1:·.·36·160·315·288···.···.···.··.·. | 101 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 102 | ························2:·.··.···.···.···.·288·315·160·36·. | 102 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 103 | ························3:·.··.···.···.···.···.···.···.··.·1 | 103 | ························3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 130, 15 lines modified | Offset 130, 15 lines modified | ||
| 130 | o4·=·{0,·2,·3,·5} | 130 | o4·=·{0,·2,·3,·5} |
| 131 | o4·:·List</code></pre> | 131 | o4·:·List</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) | 134 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·T=·minimalBetti·degenerateK3(a,b,e,Characteristic=>5) |
| 135 | ·--·0. | 135 | ·--·0.195675·seconds·elapsed |
| 136 | ············0··1···2···3···4···5···6···7··8·9 | 136 | ············0··1···2···3···4···5···6···7··8·9 |
| 137 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 | 137 | o5·=·total:·1·36·167·370·476·476·370·167·36·1 |
| 138 | ·········0:·1··.···.···.···.···.···.···.··.·. | 138 | ·········0:·1··.···.···.···.···.···.···.··.·. |
| 139 | ·········1:·.·36·160·322·336·140··48···7··.·. | 139 | ·········1:·.·36·160·322·336·140··48···7··.·. |
| 140 | ·········2:·.··.···7··48·140·336·322·160·36·. | 140 | ·········2:·.··.···7··48·140·336·322·160·36·. |
| 141 | ·········3:·.··.···.···.···.···.···.···.··.·1 | 141 | ·········3:·.··.···.···.···.···.···.···.··.·1 |
| Offset 166, 19 lines modified | Offset 166, 19 lines modified | ||
| 166 | o7·=·(-1,·25) | 166 | o7·=·(-1,·25) |
| 167 | o7·:·Sequence</code></pre> | 167 | o7·:·Sequence</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i8·:·h=degenerateK3BettiTables(a,b,e) | 170 | <td>··············<pre><code·class="language-macaulay2">i8·:·h=degenerateK3BettiTables(a,b,e) |
| 171 | ·--·0.00 | 171 | ·--·0.0018781·seconds·elapsed |
| 172 | ·--·0.00 | 172 | ·--·0.0048134·seconds·elapsed |
| 173 | ·--·0.0216425·seconds·elapsed | ||
| 173 | ·--·0.0 | 174 | ·--·0.007893·seconds·elapsed |
| 174 | ·--·0.0103191·seconds·elapsed | ||
| 175 | ·--·0.00 | 175 | ·--·0.00277762·seconds·elapsed |
| 176 | ···························0··1···2···3···4···5···6···7··8·9 | 176 | ···························0··1···2···3···4···5···6···7··8·9 |
| 177 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} | 177 | o8·=·HashTable{0·=>·total:·1·36·160·315·288·288·315·160·36·1·····} |
| 178 | ························0:·1··.···.···.···.···.···.···.··.·. | 178 | ························0:·1··.···.···.···.···.···.···.··.·. |
| 179 | ························1:·.·36·160·315·288···.···.···.··.·. | 179 | ························1:·.·36·160·315·288···.···.···.··.·. |
| 180 | ························2:·.··.···.···.···.·288·315·160·36·. | 180 | ························2:·.··.···.···.···.·288·315·160·36·. |
| 181 | ························3:·.··.···.···.···.···.···.···.··.·1 | 181 | ························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 | ·--·0.002 | 33 | ·--·0.00217119·seconds·elapsed |
| 34 | ·--·0.00709748·seconds·elapsed | ||
| 35 | ·--·0.0507505·seconds·elapsed | ||
| 36 | ·--·0.00 | 34 | ·--·0.00504055·seconds·elapsed |
| 35 | ·--·0.0193402·seconds·elapsed | ||
| 37 | ·--·0.00 | 36 | ·--·0.00800184·seconds·elapsed |
| 37 | ·--·0.00293484·seconds·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 | ·--·0. | 71 | ·--·0.195675·seconds·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 | ·--·0.00 | 100 | ·--·0.0018781·seconds·elapsed |
| 101 | ·--·0.00 | 101 | ·--·0.0048134·seconds·elapsed |
| 102 | ·--·0.0216425·seconds·elapsed | ||
| 102 | ·--·0.0 | 103 | ·--·0.007893·seconds·elapsed |
| 103 | ·--·0.0103191·seconds·elapsed | ||
| 104 | ·--·0.00 | 104 | ·--·0.00277762·seconds·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 77, 33 lines modified | Offset 77, 33 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·a=4 | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·a=4 |
| 79 | o1·=·4</code></pre> | 79 | o1·=·4</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·(d1,d2)=resonanceDet(a) | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·(d1,d2)=resonanceDet(a) |
| 83 | ·--·0.01 | 83 | ·--·0.0106896·seconds·elapsed |
| 84 | ·--·2. | 84 | ·--·2.5288e-05·seconds·elapsed |
| 85 | ·--·7.1875e-05·seconds·elapsed | ||
| 86 | ·--· | 85 | ·--·9.4764e-05·seconds·elapsed |
| 87 | ·--·6.1595e-05·seconds·elapsed | ||
| 88 | ·--·6.7878e-05·seconds·elapsed | ||
| 89 | ·--·6.8158e-05·seconds·elapsed | ||
| 90 | ·--·1.8033e-05·seconds·elapsed | ||
| 91 | ·--·5.2669e-05·seconds·elapsed | ||
| 92 | ·--·6. | 86 | ·--·6.8624e-05·seconds·elapsed |
| 93 | ·--· | 87 | ·--·5.7787e-05·seconds·elapsed |
| 94 | ·--·6.5 | 88 | ·--·6.5149e-05·seconds·elapsed |
| 95 | ·--· | 89 | ·--·6.2975e-05·seconds·elapsed |
| 96 | ·--·5.6116e-05·seconds·elapsed | ||
| 97 | ·--·5.4773e-05·seconds·elapsed | ||
| 98 | ·--· | 90 | ·--·2.0451e-05·seconds·elapsed |
| 99 | ·--·1.9116e-05·seconds·elapsed | ||
| 100 | ·--·5. | 91 | ·--·5.1698e-05·seconds·elapsed |
| 92 | ·--·7.7877e-05·seconds·elapsed | ||
| 93 | ·--·8.5899e-05·seconds·elapsed | ||
| 101 | ·--· | 94 | ·--·7.7427e-05·seconds·elapsed |
| 95 | ·--·7.3751e-05·seconds·elapsed | ||
| 96 | ·--·6.8523e-05·seconds·elapsed | ||
| 97 | ·--·4.9254e-05·seconds·elapsed | ||
| 98 | ·--·4.7471e-05·seconds·elapsed | ||
| 99 | ·--·1.8318e-05·seconds·elapsed | ||
| 100 | ·--·5.0967e-05·seconds·elapsed | ||
| 101 | ·--·1.7617e-05·seconds·elapsed | ||
| 102 | (number·of·blocks=·,·18) | 102 | (number·of·blocks=·,·18) |
| 103 | (size·of·the·matrices,·Tally{1·=>·4}) | 103 | (size·of·the·matrices,·Tally{1·=>·4}) |
| 104 | ·····························2·=>·6 | 104 | ·····························2·=>·6 |
| 105 | ·····························3·=>·2 | 105 | ·····························3·=>·2 |
| 106 | ·····························4·=>·6 | 106 | ·····························4·=>·6 |
| 107 | ·······0·1 | 107 | ·······0·1 |
| 108 | total:·1·1 | 108 | 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 | ·--·0.01 | 26 | ·--·0.0106896·seconds·elapsed |
| 27 | ·--·2. | 27 | ·--·2.5288e-05·seconds·elapsed |
| 28 | ·--·7.1875e-05·seconds·elapsed | ||
| 29 | ·--· | 28 | ·--·9.4764e-05·seconds·elapsed |
| 30 | ·--·6.1595e-05·seconds·elapsed | ||
| 31 | ·--·6.7878e-05·seconds·elapsed | ||
| 32 | ·--·6.8158e-05·seconds·elapsed | ||
| 33 | ·--·1.8033e-05·seconds·elapsed | ||
| 34 | ·--·5.2669e-05·seconds·elapsed | ||
| 35 | ·--·6. | 29 | ·--·6.8624e-05·seconds·elapsed |
| 36 | ·--· | 30 | ·--·5.7787e-05·seconds·elapsed |
| 37 | ·--·6.5 | 31 | ·--·6.5149e-05·seconds·elapsed |
| 38 | ·--· | 32 | ·--·6.2975e-05·seconds·elapsed |
| 39 | ·--·5.6116e-05·seconds·elapsed | ||
| 40 | ·--·5.4773e-05·seconds·elapsed | ||
| 41 | ·--· | 33 | ·--·2.0451e-05·seconds·elapsed |
| 42 | ·--·1.9116e-05·seconds·elapsed | ||
| 43 | ·--·5. | 34 | ·--·5.1698e-05·seconds·elapsed |
| 35 | ·--·7.7877e-05·seconds·elapsed | ||
| 36 | ·--·8.5899e-05·seconds·elapsed | ||
| 44 | ·--· | 37 | ·--·7.7427e-05·seconds·elapsed |
| 38 | ·--·7.3751e-05·seconds·elapsed | ||
| 39 | ·--·6.8523e-05·seconds·elapsed | ||
| 40 | ·--·4.9254e-05·seconds·elapsed | ||
| 41 | ·--·4.7471e-05·seconds·elapsed | ||
| 42 | ·--·1.8318e-05·seconds·elapsed | ||
| 43 | ·--·5.0967e-05·seconds·elapsed | ||
| 44 | ·--·1.7617e-05·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwcm9qZWN0LFZpc2libGVMaXN0LEVtYmVkZGVkSzNz | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwcm9qZWN0LFZpc2libGVMaXN0LEVtYmVkZGVkSzNz |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00 | 11 | ·--·used·0.0079139s·(cpu);·0.00707349s·(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·0.0 | 15 | ·--·used·0.0197912s·(cpu);·0.0233378s·(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. | 19 | ·--·used·0.0965047s·(cpu);·0.0965108s·(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·0.00938158s·(cpu);·0.00991624s·(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·0.0495462s·(cpu);·0.0517424s·(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·0.0 | 31 | ·--·used·0.0517384s·(cpu);·0.0519805s·(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·0.249893s·(cpu);·0.25107s·(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·0.122311s·(cpu);·0.125042s·(thread);·0s·(gc) |
| 40 | ···············50·······47 | 40 | ···············50·······47 |
| 41 | o10·:·Matrix·ZZ···<--·ZZ | 41 | o10·:·Matrix·ZZ···<--·ZZ |
| 42 | i11·:· | 42 | i11·:· |
| Offset 163, 64 lines modified | Offset 163, 64 lines modified | ||
| 163 | <td>··············<pre><code·class="language-macaulay2">i2·:·m·=·syz·m1; | 163 | <td>··············<pre><code·class="language-macaulay2">i2·:·m·=·syz·m1; |
| 164 | ··············50·······47 | 164 | ··············50·······47 |
| 165 | o2·:·Matrix·ZZ···<--·ZZ</code></pre> | 165 | o2·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 166 | </td>··········</tr> | 166 | </td>··········</tr> |
| 167 | ··········<tr> | 167 | ··········<tr> |
| 168 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·LLL·m; | 168 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·LLL·m; |
| 169 | ·--·used·0.00 | 169 | ·--·used·0.0079139s·(cpu);·0.00707349s·(thread);·0s·(gc) |
| 170 | ··············50·······47 | 170 | ··············50·······47 |
| 171 | o3·:·Matrix·ZZ···<--·ZZ</code></pre> | 171 | o3·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·LLL(m,·Strategy=>CohenEngine); | 174 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·LLL(m,·Strategy=>CohenEngine); |
| 175 | ·--·used·0.0 | 175 | ·--·used·0.0197912s·(cpu);·0.0233378s·(thread);·0s·(gc) |
| 176 | ··············50·······47 | 176 | ··············50·······47 |
| 177 | o4·:·Matrix·ZZ···<--·ZZ</code></pre> | 177 | o4·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 178 | </td>··········</tr> | 178 | </td>··········</tr> |
| 179 | ··········<tr> | 179 | ··········<tr> |
| 180 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·LLL(m,·Strategy=>CohenTopLevel); | 180 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·LLL(m,·Strategy=>CohenTopLevel); |
| 181 | ·--·used·0. | 181 | ·--·used·0.0965047s·(cpu);·0.0965108s·(thread);·0s·(gc) |
| 182 | ··············50·······47 | 182 | ··············50·······47 |
| 183 | o5·:·Matrix·ZZ···<--·ZZ</code></pre> | 183 | o5·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 184 | </td>··········</tr> | 184 | </td>··········</tr> |
| 185 | ··········<tr> | 185 | ··········<tr> |
| 186 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); | 186 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·LLL(m,·Strategy=>{Givens,RealFP}); |
| 187 | ·--·used·0.0 | 187 | ·--·used·0.00938158s·(cpu);·0.00991624s·(thread);·0s·(gc) |
| 188 | ··············50·······47 | 188 | ··············50·······47 |
| 189 | o6·:·Matrix·ZZ···<--·ZZ</code></pre> | 189 | o6·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 190 | </td>··········</tr> | 190 | </td>··········</tr> |
| 191 | ··········<tr> | 191 | ··········<tr> |
| 192 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); | 192 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·LLL(m,·Strategy=>{Givens,RealQP}); |
| 193 | ·--·used·0.0 | 193 | ·--·used·0.0495462s·(cpu);·0.0517424s·(thread);·0s·(gc) |
| 194 | ··············50·······47 | 194 | ··············50·······47 |
| 195 | o7·:·Matrix·ZZ···<--·ZZ</code></pre> | 195 | o7·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 196 | </td>··········</tr> | 196 | </td>··········</tr> |
| 197 | ··········<tr> | 197 | ··········<tr> |
| 198 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); | 198 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·LLL(m,·Strategy=>{Givens,RealXD}); |
| 199 | ·--·used·0.0 | 199 | ·--·used·0.0517384s·(cpu);·0.0519805s·(thread);·0s·(gc) |
| 200 | ··············50·······47 | 200 | ··············50·······47 |
| 201 | o8·:·Matrix·ZZ···<--·ZZ</code></pre> | 201 | o8·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 202 | </td>··········</tr> | 202 | </td>··········</tr> |
| 203 | ··········<tr> | 203 | ··········<tr> |
| 204 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); | 204 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·LLL(m,·Strategy=>{Givens,RealRR}); |
| 205 | ·--·used·0.2 | 205 | ·--·used·0.249893s·(cpu);·0.25107s·(thread);·0s·(gc) |
| 206 | ··············50·······47 | 206 | ··············50·······47 |
| 207 | o9·:·Matrix·ZZ···<--·ZZ</code></pre> | 207 | o9·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 208 | </td>··········</tr> | 208 | </td>··········</tr> |
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); | 210 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·LLL(m,·Strategy=>{BKZ,Givens,RealQP}); |
| 211 | ·--·used·0.12 | 211 | ·--·used·0.122311s·(cpu);·0.125042s·(thread);·0s·(gc) |
| 212 | ···············50·······47 | 212 | ···············50·······47 |
| 213 | o10·:·Matrix·ZZ···<--·ZZ</code></pre> | 213 | o10·:·Matrix·ZZ···<--·ZZ</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ········</table> | 215 | ········</table> |
| 216 | ······</div> | 216 | ······</div> |
| 217 | ······<div> | 217 | ······<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·0.00 | 122 | ·--·used·0.0079139s·(cpu);·0.00707349s·(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·0.0 | 126 | ·--·used·0.0197912s·(cpu);·0.0233378s·(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. | 130 | ·--·used·0.0965047s·(cpu);·0.0965108s·(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·0.00938158s·(cpu);·0.00991624s·(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·0.0495462s·(cpu);·0.0517424s·(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·0.0 | 142 | ·--·used·0.0517384s·(cpu);·0.0519805s·(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·0.249893s·(cpu);·0.25107s·(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·0.122311s·(cpu);·0.125042s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.9 | 20 | ·--·used·0.981125s·(cpu);·0.495957s·(thread);·0s·(gc) |
| 21 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); | 21 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); |
| 22 | ·--·used·0.5 | 22 | ·--·used·0.573564s·(cpu);·0.30292s·(thread);·0s·(gc) |
| 23 | i8·:· | 23 | i8·:· |
| 24 | ····· | 24 | ····· |
| Offset 115, 19 lines modified | Offset 115, 19 lines modified | ||
| 115 | o4·:·Matrix·ZZ··<--·ZZ</code></pre> | 115 | o4·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i5·:·P·=·convexHull(M);</code></pre> | 118 | <td>··············<pre><code·class="language-macaulay2">i5·:·P·=·convexHull(M);</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·areIsomorphic(P,P); | 121 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·areIsomorphic(P,P); |
| 122 | ·--·used·0.9 | 122 | ·--·used·0.981125s·(cpu);·0.495957s·(thread);·0s·(gc)</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·areIsomorphic(P,P,smoothTest=>false); | 125 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·areIsomorphic(P,P,smoothTest=>false); |
| 126 | ·--·used·0.5 | 126 | ·--·used·0.573564s·(cpu);·0.30292s·(thread);·0s·(gc)</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ········</table> | 128 | ········</table> |
| 129 | ······</div> | 129 | ······</div> |
| 130 | ······<div·class="waystouse"> | 130 | ······<div·class="waystouse"> |
| 131 | ········<h2>Ways·to·use·<span·class="tt">areIsomorphic</span>·:</h2> | 131 | ········<h2>Ways·to·use·<span·class="tt">areIsomorphic</span>·:</h2> |
| 132 | ········<ul> | 132 | ········<ul> |
| 133 | ··········<li> | 133 | ··········<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·0.9 | 42 | ·--·used·0.981125s·(cpu);·0.495957s·(thread);·0s·(gc) |
| 43 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); | 43 | i7·:·time·areIsomorphic(P,P,smoothTest=>false); |
| 44 | ·--·used·0.5 | 44 | ·--·used·0.573564s·(cpu);·0.30292s·(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. |
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| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.13 | 33 | ·--·0.134927·seconds·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 | ·--·0.0 | 37 | ·--·0.00910768·seconds·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 | ·--·12.8669·seconds·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 | ·--·0.110533·seconds·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 118, 23 lines modified | Offset 118, 23 lines modified | ||
| 118 | ········</table> | 118 | ········</table> |
| 119 | ········<div> | 119 | ········<div> |
| 120 | ··········<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 | ··········<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> |
| 121 | ········</div> | 121 | ········</div> |
| 122 | ········<table·class="examples"> | 122 | ········<table·class="examples"> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) | 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·findRegion({{0,0},{4,4}},M,f) |
| 125 | ·--·0.13 | 125 | ·--·0.134927·seconds·elapsed |
| 126 | o6·=·{{1,·2},·{3,·1}} | 126 | o6·=·{{1,·2},·{3,·1}} |
| 127 | o6·:·List</code></pre> | 127 | o6·:·List</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}}) | 130 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·findRegion({{0,0},{4,4}},M,f,Inner=>{{1,2},{3,1}},Outer=>{{1,1}}) |
| 131 | ·--·0.0 | 131 | ·--·0.00910768·seconds·elapsed |
| 132 | o7·=·{{1,·2},·{3,·1}} | 132 | o7·=·{{1,·2},·{3,·1}} |
| 133 | o7·:·List</code></pre> | 133 | o7·:·List</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ········</table> | 135 | ········</table> |
| 136 | ······</div> | 136 | ······</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 | ·--·0.13 | 55 | ·--·0.134927·seconds·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 | ·--·0.0 | 60 | ·--·0.00910768·seconds·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 113, 23 lines modified | Offset 113, 23 lines modified | ||
| 113 | ········</table> | 113 | ········</table> |
| 114 | ········<div> | 114 | ········<div> |
| 115 | ··········<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 | ··········<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> |
| 116 | ········</div> | 116 | ········</div> |
| 117 | ········<table·class="examples"> | 117 | ········<table·class="examples"> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) | 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·linearTruncations({{2,2,2},{4,4,4}},·M) |
| 120 | ·--· | 120 | ·--·12.8669·seconds·elapsed |
| 121 | o6·=·{{4,·3,·3},·{4,·4,·2}} | 121 | o6·=·{{4,·3,·3},·{4,·4,·2}} |
| 122 | o6·:·List</code></pre> | 122 | o6·:·List</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·linearTruncationsBound·M | 125 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·linearTruncationsBound·M |
| 126 | ·--·0. | 126 | ·--·0.110533·seconds·elapsed |
| 127 | o7·=·{{4,·3,·3},·{4,·4,·2}} | 127 | o7·=·{{4,·3,·3},·{4,·4,·2}} |
| 128 | o7·:·List</code></pre> | 128 | o7·:·List</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ········</table> | 130 | ········</table> |
| 131 | ······</div> | 131 | ······</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 | ·--·12.8669·seconds·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 | ·--·0.110533·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0. | 19 | ·--·0.205489·seconds·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 | ·--·0.0 | 48 | ·--·0.00989668·seconds·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 | ·--·0. | 52 | ·--·0.323938·seconds·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 108, 15 lines modified | Offset 108, 15 lines modified | ||
| 108 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| | 108 | o4·=·cokernel·|·x5+y3+z3·y5+x3+z3·z5+x3+y3·| |
| 109 | ······························1 | 109 | ······························1 |
| 110 | o4·:·RP-module,·quotient·of·RP</code></pre> | 110 | o4·:·RP-module,·quotient·of·RP</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) | 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·hilbertSamuelFunction(M,·0,·6) |
| 114 | ·--·0. | 114 | ·--·0.205489·seconds·elapsed |
| 115 | o5·=·{1,·3,·6,·7,·6,·3,·1} | 115 | o5·=·{1,·3,·6,·7,·6,·3,·1} |
| 116 | o5·:·List</code></pre> | 116 | o5·:·List</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·oo//sum | 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·oo//sum |
| Offset 148, 23 lines modified | Offset 148, 23 lines modified | ||
| 148 | ··············2···3 | 148 | ··············2···3 |
| 149 | o10·=·ideal·(x·,·y·) | 149 | o10·=·ideal·(x·,·y·) |
| 150 | o10·:·Ideal·of·RP</code></pre> | 150 | o10·:·Ideal·of·RP</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| 152 | ··········<tr> | 152 | ··········<tr> |
| 153 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds | 153 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·hilbertSamuelFunction(N,·0,·5)·--·n+1·--·0.02·seconds |
| 154 | ·--·0.0 | 154 | ·--·0.00989668·seconds·elapsed |
| 155 | o11·=·{1,·2,·3,·4,·5,·6} | 155 | o11·=·{1,·2,·3,·4,·5,·6} |
| 156 | o11·:·List</code></pre> | 156 | o11·:·List</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds | 159 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·hilbertSamuelFunction(q,·N,·0,·5)·--·6(n+1)·--·0.32·seconds |
| 160 | ·--·0. | 160 | ·--·0.323938·seconds·elapsed |
| 161 | o12·=·{6,·12,·18,·24,·30,·36} | 161 | o12·=·{6,·12,·18,·24,·30,·36} |
| 162 | o12·:·List</code></pre> | 162 | o12·:·List</code></pre> |
| 163 | </td>··········</tr> | 163 | </td>··········</tr> |
| 164 | ········</table> | 164 | ········</table> |
| 165 | ······</div> | 165 | ······</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 | ·--·0. | 47 | ·--·0.205489·seconds·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 | ·--·0.0 | 71 | ·--·0.00989668·seconds·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 | ·--·0. | 75 | ·--·0.323938·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | dGV4KEN1cnZlQ2xhc3NSZXByZXNlbnRhdGl2ZU0wbmJhcik= | 8 | dGV4KEN1cnZlQ2xhc3NSZXByZXNlbnRhdGl2ZU0wbmJhcik= |
| 9 | #:len=923 | 9 | #:len=923 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29udmVydCB0byBUZVggZm9ybWF0Iiwg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29udmVydCB0byBUZVggZm9ybWF0Iiwg |
| 11 | ImxpbmVudW0iID0+IDE1ODQsIElucHV0cyA9PiB7U1BBTntUVHsiQyJ9LCIsICIsU1BBTnsiYW4g | 11 | ImxpbmVudW0iID0+IDE1ODQsIElucHV0cyA9PiB7U1BBTntUVHsiQyJ9LCIsICIsU1BBTnsiYW4g |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | Y29BcHByb3hpbWF0aW9uKC4uLixUb3RhbD0+Li4uKQ== | 8 | Y29BcHByb3hpbWF0aW9uKC4uLixUb3RhbD0+Li4uKQ== |
| 9 | #:len=293 | 9 | #:len=293 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDY5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tjb0FwcHJveGltYXRpb24sVG90YWxdLCJjb0FwcHJv | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tjb0FwcHJveGltYXRpb24sVG90YWxdLCJjb0FwcHJv |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | dW5pbnN0YWxsUGFja2FnZShTdHJpbmcp | 8 | dW5pbnN0YWxsUGFja2FnZShTdHJpbmcp |
| 9 | #:len=297 | 9 | #:len=297 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjg5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjg5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh1bmluc3RhbGxQYWNrYWdlLFN0cmluZyksInVuaW5z | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh1bmluc3RhbGxQYWNrYWdlLFN0cmluZyksInVuaW5z |
| 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·Oct·16·04:18:42·+14·2024 | |
| 10 | o4·=·0 | 10 | o4·=·0 |
| 11 | i5·:· | 11 | i5·:· |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-744305248 | 1 | --·-*-·M2-comint·-*-·hash:·-744305248 |
| 2 | i1·:·filename·=·temporaryFileName·()·|·".dbm" | 2 | i1·:·filename·=·temporaryFileName·()·|·".dbm" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2061829-0/0.dbm |
| 4 | i2·:·x·=·openDatabaseOut·filename | 4 | i2·:·x·=·openDatabaseOut·filename |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2061829-0/0.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 | ·--·1.92727·seconds·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 | ·--·1. | 20 | ·--·1.00836·seconds·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/M2-2062132-0/0 |
| 16 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close | 16 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close |
| 17 | o4·=·/tmp/M2- | 17 | o4·=·/tmp/M2-2062132-0/0 |
| 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/M2-2062132-0/0 |
| 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/M2-2062132-0/0 |
| 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:·-1373552177 | 1 | --·-*-·M2-comint·-*-·hash:·-1373552177 |
| 2 | i1·:·s·=·GCstats() | 2 | i1·:·s·=·GCstats() |
| 3 | o1·=·HashTable{"bytesAlloc"·=>·11 | 3 | o1·=·HashTable{"bytesAlloc"·=>·11661111018········} |
| 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"·=>·22 | 7 | ···············"heapSize"·=>·221462528 |
| 8 | ···············"numGCs"·=>·79 | 8 | ···············"numGCs"·=>·793 |
| 9 | ···············"numGCThreads"·=>·12 | 9 | ···············"numGCThreads"·=>·12 |
| 10 | o1·:·HashTable | 10 | o1·:·HashTable |
| 11 | i2·:·s#"heapSize" | 11 | i2·:·s#"heapSize" |
| 12 | o2·=·22 | 12 | o2·=·221462528 |
| 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·0.02 | 44 | ·--·used·0.0211414s·(cpu);·0.02114s·(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·0.32201s·(cpu);·0.147607s·(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·8.8103e-05s·(cpu);·8.8013e-05s·(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·0.02 | 8 | ·--·used·0.0257259s·(cpu);·0.0257261s·(thread);·0s·(gc) |
| 9 | i3·:·time·SVD(M,·DivideConquer=>true); | 9 | i3·:·time·SVD(M,·DivideConquer=>true); |
| 10 | ·--·used·0.02 | 10 | ·--·used·0.0259131s·(cpu);·0.0259231s·(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·0.0016 | 356 | ·--·used·0.00216258s·(cpu);·0.00215611s·(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:·-1060502340 | 1 | --·-*-·M2-comint·-*-·hash:·-1060502340 |
| 2 | i1·:·benchmark·"sqrt·2p100000" | 2 | i1·:·benchmark·"sqrt·2p100000" |
| 3 | o1·=·.0003 | 3 | o1·=·.000336946552311436 |
| 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 | ·--·1.92079·seconds·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·=·941 | 21 | o5·=·941829 |
| 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·=·1917486 |
| 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·=·191 | 56 | o13·=·1917650 |
| 57 | i14·:·sleep·1 | 57 | i14·:·sleep·1 |
| 58 | o14·=·0 | 58 | o14·=·0 |
| 59 | i15·:·n | 59 | i15·:·n |
| 60 | o15·=·191 | 60 | o15·=·1917650 |
| 61 | i16·:·isReady·t | 61 | i16·:·isReady·t |
| 62 | o16·=·false | 62 | o16·=·false |
| 63 | i17·:· | 63 | i17·:· |
| Offset 1, 27 lines modified | Offset 1, 27 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·86955367 | 1 | --·-*-·M2-comint·-*-·hash:·86955367 |
| 2 | i1·:·run·"uname·-a" | 2 | i1·:·run·"uname·-a" |
| 3 | Linux·i | 3 | Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·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·6.1.0-26-cloud-amd64·#1·SMP |
| 12 | ·····" | 12 | ·····" |
| 13 | ····· | 13 | ·····PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·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·0x7f | 130 | ···--·registering·gb·5·at·0x7fdde70d6700 |
| 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·0.143899s·(cpu);·0.145616s·(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·0.00185646s·(cpu);·0.00210011s·(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·1.17 | 43 | ·--·used·1.17527s·(cpu);·1.0079s·(thread);·0s·(gc) |
| 44 | ·--·used·0. | 44 | ·--·used·0.358421s·(cpu);·0.26694s·(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, 70 lines modified | Offset 1, 70 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·423116033 | 1 | --·-*-·M2-comint·-*-·hash:·423116033 |
| 2 | i1·:·src·=·temporaryFileName()·|·"/" | 2 | i1·:·src·=·temporaryFileName()·|·"/" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2056328-0/0/ |
| 4 | i2·:·dst·=·temporaryFileName()·|·"/" | 4 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2056328-0/1/ |
| 6 | i3·:·makeDirectory·(src|"a/") | 6 | i3·:·makeDirectory·(src|"a/") |
| 7 | i4·:·makeDirectory·(src|"b/") | 7 | i4·:·makeDirectory·(src|"b/") |
| 8 | i5·:·makeDirectory·(src|"b/c/") | 8 | i5·:·makeDirectory·(src|"b/c/") |
| 9 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 9 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 10 | o6·=·/tmp/M2- | 10 | o6·=·/tmp/M2-2056328-0/0/a/f |
| 11 | o6·:·File | 11 | o6·:·File |
| 12 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 12 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 13 | o7·=·/tmp/M2- | 13 | o7·=·/tmp/M2-2056328-0/0/a/g |
| 14 | o7·:·File | 14 | o7·:·File |
| 15 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 15 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 16 | o8·=·/tmp/M2- | 16 | o8·=·/tmp/M2-2056328-0/0/b/c/g |
| 17 | o8·:·File | 17 | o8·:·File |
| 18 | i9·:·stack·findFiles·src | 18 | i9·:·stack·findFiles·src |
| 19 | o9·=·/tmp/M2- | 19 | o9·=·/tmp/M2-2056328-0/0/ |
| 20 | ·····/tmp/M2- | 20 | ·····/tmp/M2-2056328-0/0/b/ |
| 21 | ·····/tmp/M2- | 21 | ·····/tmp/M2-2056328-0/0/b/c/ |
| 22 | ·····/tmp/M2- | 22 | ·····/tmp/M2-2056328-0/0/b/c/g |
| 23 | ·····/tmp/M2- | 23 | ·····/tmp/M2-2056328-0/0/a/ |
| 24 | ·····/tmp/M2-1012290-0/0/a/g | ||
| 25 | ·····/tmp/M2- | 24 | ·····/tmp/M2-2056328-0/0/a/f |
| 25 | ·····/tmp/M2-2056328-0/0/a/g | ||
| 26 | i10·:·copyDirectory(src,dst,Verbose=>true) | 26 | i10·:·copyDirectory(src,dst,Verbose=>true) |
| 27 | ·--·copying:·/tmp/M2- | 27 | ·--·copying:·/tmp/M2-2056328-0/0/b/c/g·->·/tmp/M2-2056328-0/1/b/c/g |
| 28 | ·--·copying:·/tmp/M2-1012290-0/0/a/g·->·/tmp/M2-1012290-0/1/a/g | ||
| 29 | ·--·copying:·/tmp/M2- | 28 | ·--·copying:·/tmp/M2-2056328-0/0/a/f·->·/tmp/M2-2056328-0/1/a/f |
| 29 | ·--·copying:·/tmp/M2-2056328-0/0/a/g·->·/tmp/M2-2056328-0/1/a/g | ||
| 30 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) | 30 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 31 | ·--·skipping:·/tmp/M2- | 31 | ·--·skipping:·/tmp/M2-2056328-0/0/b/c/g·not·newer·than·/tmp/M2-2056328-0/1/b/c/g |
| 32 | ·--·skipping:·/tmp/M2-1012290-0/0/a/g·not·newer·than·/tmp/M2-1012290-0/1/a/g | ||
| 33 | ·--·skipping:·/tmp/M2- | 32 | ·--·skipping:·/tmp/M2-2056328-0/0/a/f·not·newer·than·/tmp/M2-2056328-0/1/a/f |
| 33 | ·--·skipping:·/tmp/M2-2056328-0/0/a/g·not·newer·than·/tmp/M2-2056328-0/1/a/g | ||
| 34 | i12·:·stack·findFiles·dst | 34 | i12·:·stack·findFiles·dst |
| 35 | o12·=·/tmp/M2- | 35 | o12·=·/tmp/M2-2056328-0/1/ |
| 36 | ······/tmp/M2- | 36 | ······/tmp/M2-2056328-0/1/b/ |
| 37 | ······/tmp/M2- | 37 | ······/tmp/M2-2056328-0/1/b/c/ |
| 38 | ······/tmp/M2- | 38 | ······/tmp/M2-2056328-0/1/b/c/g |
| 39 | ······/tmp/M2- | 39 | ······/tmp/M2-2056328-0/1/a/ |
| 40 | ······/tmp/M2-1012290-0/1/a/g | ||
| 41 | ······/tmp/M2- | 40 | ······/tmp/M2-2056328-0/1/a/f |
| 41 | ······/tmp/M2-2056328-0/1/a/g | ||
| 42 | i13·:·get·(dst|"b/c/g") | 42 | i13·:·get·(dst|"b/c/g") |
| 43 | o13·=·ho·there | 43 | o13·=·ho·there |
| 44 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 44 | 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:·-2135127930 | 1 | --·-*-·M2-comint·-*-·hash:·-2135127930 |
| 2 | i1·:·src·=·temporaryFileName() | 2 | i1·:·src·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2054225-0/0 |
| 4 | i2·:·dst·=·temporaryFileName() | 4 | i2·:·dst·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2054225-0/1 |
| 6 | i3·:·src·<<·"hi·there"·<<·close | 6 | i3·:·src·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-2054225-0/0 |
| 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/M2-2054225-0/0·->·/tmp/M2-2054225-0/1 |
| 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/M2-2054225-0/0·not·newer·than·/tmp/M2-2054225-0/1 |
| 15 | i7·:·src·<<·"ho·there"·<<·close | 15 | i7·:·src·<<·"ho·there"·<<·close |
| 16 | o7·=·/tmp/M2- | 16 | o7·=·/tmp/M2-2054225-0/0 |
| 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/M2-2054225-0/0·not·newer·than·/tmp/M2-2054225-0/1 |
| 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:·1001389061 | 1 | --·-*-·M2-comint·-*-·hash:·1001389061 |
| 2 | i1·:·t1·=·cpuTime() | 2 | i1·:·t1·=·cpuTime() |
| 3 | o1·=·1 | 3 | o1·=·159.794932719 |
| 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·=·1 | 7 | o3·=·160.414254675 |
| 8 | o3·:·RR·(of·precision·53) | 8 | o3·:·RR·(of·precision·53) |
| 9 | i4·:·t2-t1 | 9 | i4·:·t2-t1 |
| 10 | o4·=·.6 | 10 | o4·=·.619321955999993 |
| 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:·-1994097893 | 1 | --·-*-·M2-comint·-*-·hash:·-1994097893 |
| 2 | i1·:·currentTime() | 2 | i1·:·currentTime() |
| 3 | o1·=·17 | 3 | o1·=·1729001958 |
| 4 | i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) | 4 | i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) |
| 5 | o2·=·5 | 5 | o2·=·54.789890924827 |
| 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·=· | 8 | o3·=·9.47869109792364 |
| 9 | o3·:·RR·(of·precision·53) | 9 | o3·:·RR·(of·precision·53) |
| 10 | i4·:·run·"date" | 10 | i4·:·run·"date" |
| 11 | 11 | Wed·Oct·16·04:19:18·+14·2024 | |
| 12 | o4·=·0 | 12 | o4·=·0 |
| 13 | i5·:· | 13 | i5·:· |
| Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-873903735 | 1 | --·-*-·M2-comint·-*-·hash:·-873903735 |
| 2 | i1·:·elapsedTime·sleep·1 | 2 | i1·:·elapsedTime·sleep·1 |
| 3 | ·--·1.00 | 3 | ·--·1.00011·seconds·elapsed |
| 4 | o1·=·0 | 4 | o1·=·0 |
| 5 | i2·:· | 5 | i2·:· |
| Offset 1, 14 lines modified | Offset 1, 14 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·963567259 | 1 | --·-*-·M2-comint·-*-·hash:·963567259 |
| 2 | i1·:·elapsedTiming·sleep·1 | 2 | i1·:·elapsedTiming·sleep·1 |
| 3 | o1·=·0 | 3 | o1·=·0 |
| 4 | ·····--·1.0001·seconds | 4 | ·····--·1.00014·seconds |
| 5 | o1·:·Time | 5 | o1·:·Time |
| 6 | i2·:·peek·oo | 6 | i2·:·peek·oo |
| 7 | o2·=·Time{1.0001,·0} | 7 | o2·=·Time{1.00014,·0} |
| 8 | i3·:· | 8 | i3·:· |
| 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·0.1 | 10 | ·--·used·0.105049s·(cpu);·0.10505s·(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·0.1 | 89 | ·--·used·0.104572s·(cpu);·0.104574s·(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·0.05 | 158 | ·--·used·0.0354315s·(cpu);·0.0354377s·(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·0.296242s·(cpu);·0.138084s·(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·0.001 | 301 | ·--·used·0.00144408s·(cpu);·0.00144045s·(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·0.0376776s·(cpu);·0.0376885s·(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/M2-2031929-0/85-rundir/ |
| 67 | ·············source·file·=>·stdio | 67 | ·············source·file·=>·stdio |
| 68 | ·············test·inputs·=>·MutableHashTable{} | 68 | ·············test·inputs·=>·MutableHashTable{} |
| 69 | ·············test·number·=>·0 | 69 | ·············test·number·=>·0 |
| 70 | ·············undocumented·keys·=>·MutableHashTable{} | 70 | ·············undocumented·keys·=>·MutableHashTable{} |
| 71 | i7·:·dictionaryPath | 71 | i7·:·dictionaryPath |
| Offset 1, 20 lines modified | Offset 1, 20 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-260349693 | 1 | --·-*-·M2-comint·-*-·hash:·-260349693 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2038261-0/0 |
| 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/M2-2038261-0/0 |
| 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:·434650730 | 1 | --·-*-·M2-comint·-*-·hash:·434650730 |
| 2 | i1·:·f·=·temporaryFileName()·<<·"hi·there" | 2 | i1·:·f·=·temporaryFileName()·<<·"hi·there" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2070590-0/0 |
| 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/M2-2070590-0/0 |
| 9 | o3·:·File | 9 | o3·:·File |
| 10 | i4·:·filename·=·toString·f | 10 | i4·:·filename·=·toString·f |
| 11 | o4·=·/tmp/M2- | 11 | o4·=·/tmp/M2-2070590-0/0 |
| 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:·504479777 | 1 | --·-*-·M2-comint·-*-·hash:·504479777 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2060644-0/0 |
| 4 | i2·:·f·=·fn·<<·"hi·there" | 4 | i2·:·f·=·fn·<<·"hi·there" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2060644-0/0 |
| 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/M2-2060644-0/0 |
| 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:·2136544724 | 1 | --·-*-·M2-comint·-*-·hash:·2136544724 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2054394-0/0 |
| 4 | i2·:·fn·<<·"hi·there"·<<·close | 4 | i2·:·fn·<<·"hi·there"·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2054394-0/0 |
| 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:·995787538 | 1 | --·-*-·M2-comint·-*-·hash:·995787538 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2052463-0/0 |
| 4 | i2·:·f·=·fn·<<·"hi·there" | 4 | i2·:·f·=·fn·<<·"hi·there" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2052463-0/0 |
| 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/M2-2052463-0/0 |
| 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:·-1815110333 | 1 | --·-*-·M2-comint·-*-·hash:·-1815110333 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2070121-0/0 |
| 4 | i2·:·fn·<<·"hi·there"·<<·close | 4 | i2·:·fn·<<·"hi·there"·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2070121-0/0 |
| 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:·-129150685 | 1 | --·-*-·M2-comint·-*-·hash:·-129150685 |
| 2 | i1·:·currentTime()·-·fileTime·"." | 2 | i1·:·currentTime()·-·fileTime·"." |
| 3 | o1·=· | 3 | o1·=·26 |
| 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·0x7f053d79f700 |
| 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·Oct·16·04:18:55·+14·2024 |
| 14 | i5·:· | 14 | i5·:· |
| Offset 1, 7 lines modified | Offset 1, 7 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-464247437 | 1 | --·-*-·M2-comint·-*-·hash:·-464247437 |
| 2 | i1·:·groupID() | 2 | i1·:·groupID() |
| 3 | o1·=·5 | 3 | o1·=·1596170 |
| 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/M2-2035704-0/0 |
| 6 | i3·:·fn·<<·"hi·there"·<<·close | 6 | i3·:·fn·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-2035704-0/0 |
| 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 | ·--·3.95259·seconds·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 | ·--·0.04 | 101 | ·--·0.0479405·seconds·elapsed |
| 102 | o23·=·true | 102 | o23·=·true |
| 103 | i24·:·elapsedTime·isPseudoprime·m3 | 103 | i24·:·elapsedTime·isPseudoprime·m3 |
| 104 | ·--·0.0001 | 104 | ·--·0.000146612·seconds·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:·1953176829 | 1 | --·-*-·M2-comint·-*-·hash:·1953176829 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2070887-0/0 |
| 4 | i2·:·fn·<<·"hi·there"·<<·close | 4 | i2·:·fn·<<·"hi·there"·<<·close |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2070887-0/0 |
| 6 | o2·:·File | 6 | o2·:·File |
| 7 | i3·:·isRegularFile·fn | 7 | i3·:·isRegularFile·fn |
| 8 | o3·=·true | 8 | o3·=·true |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·297974370 | 1 | --·-*-·M2-comint·-*-·hash:·297974370 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2050248-0/0 |
| 4 | i2·:·makeDirectory·(dir|"/a/b/c") | 4 | i2·:·makeDirectory·(dir|"/a/b/c") |
| 5 | i3·:·removeDirectory·(dir|"/a/b/c") | 5 | i3·:·removeDirectory·(dir|"/a/b/c") |
| 6 | i4·:·removeDirectory·(dir|"/a/b") | 6 | i4·:·removeDirectory·(dir|"/a/b") |
| 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·0.657994s·(cpu);·0.507226s·(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·4.4226e-05s·(cpu);·4.3806e-05s·(thread);·0s·(gc) |
| 14 | o4·=·514229 | 14 | o4·=·514229 |
| 15 | i5·:·time·fib·28 | 15 | i5·:·time·fib·28 |
| 16 | ·--·used· | 16 | ·--·used·1.312e-06s·(cpu);·1.222e-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 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 | ·--·1. | 13 | ·--·1.76792·seconds·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 | ·--·0. | 30 | ·--·0.768623·seconds·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 | ·--·0.03 | 40 | ·--·0.0322825·seconds·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 | ·--·1.26675·seconds·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:·1031336015 | 1 | --·-*-·M2-comint·-*-·hash:·1031336015 |
| 2 | i1·:·p·=·temporaryFileName()·|·"/" | 2 | i1·:·p·=·temporaryFileName()·|·"/" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2051461-0/0/ |
| 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/M2-2051461-0/0/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:·1043788770 | 1 | --·-*-·M2-comint·-*-·hash:·1043788770 |
| 2 | i1·:·src·=·temporaryFileName() | 2 | i1·:·src·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2042378-0/0 |
| 4 | i2·:·dst·=·temporaryFileName() | 4 | i2·:·dst·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2042378-0/1 |
| 6 | i3·:·src·<<·"hi·there"·<<·close | 6 | i3·:·src·<<·"hi·there"·<<·close |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-2042378-0/0 |
| 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/M2-2042378-0/0·->·/tmp/M2-2042378-0/1 |
| 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/M2-2042378-0/1.bak |
| 15 | o6·=·/tmp/M2- | 15 | o6·=·/tmp/M2-2042378-0/1.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:·-325249319 | 1 | --·-*-·M2-comint·-*-·hash:·-325249319 |
| 2 | i1·:·elapsedTime·nanosleep·500000000 | 2 | i1·:·elapsedTime·nanosleep·500000000 |
| 3 | ·--·0.500 | 3 | ·--·0.50009·seconds·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 | ·--·0. | 9 | ·--·0.707772·seconds·elapsed |
| 10 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); | 10 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); |
| 11 | ·--·0.2 | 11 | ·--·0.213265·seconds·elapsed |
| 12 | i5·:·allowableThreads | 12 | i5·:·allowableThreads |
| 13 | o5·=·5 | 13 | o5·=·5 |
| 14 | i6·:·allowableThreads·=·maxAllowableThreads | 14 | i6·:·allowableThreads·=·maxAllowableThreads |
| 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 | ·--·1.7632·seconds·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 | ·--·1. | 88 | ·--·1.46342·seconds·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 | ·--·1.82847·seconds·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 | ·--·2. | 136 | ·--·2.03855·seconds·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 | ·--·1.91992·seconds·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 | ·--·3.14697·seconds·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 | ·--·6.10059·seconds·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 | ·--·3. | 194 | ·--·3.08942·seconds·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 |
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| 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·0.00149312s·(cpu);·7.071e-06s·(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·0x7f9b6fea38c0 |
| 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·0.01 | 163 | ···--··--·used·0.0105017s·(cpu);·0.0109682s·(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·0x7f9b6fea3700 |
| 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·0x7f9b6fea3380 |
| 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·0.00334457s·(cpu);·0.00400907s·(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·0x7f9b6fea31c0 |
| 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·0.0359964s·(cpu);·0.0345193s·(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:·-926231197 | 1 | --·-*-·M2-comint·-*-·hash:·-926231197 |
| 2 | i1·:·processID() | 2 | i1·:·processID() |
| 3 | o1·=· | 3 | o1·=·2031929 |
| 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·0.00261549s·(cpu);·0.00261296s·(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·.0277559·seconds |
| 43 | h:·22·times,·used·.0 | 43 | h:·22·times,·used·.0534749·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·0.0 | 17 | ·--·used·0.078364s·(cpu);·0.0604955s·(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·0.191163s·(cpu);·0.157182s·(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·2.65224s·(cpu);·1.3825s·(thread);·0s·(gc) |
| 63 | o15·=·58 | 63 | o15·=·58 |
| 64 | i16·:· | 64 | i16·:· |
| Offset 1, 24 lines modified | Offset 1, 24 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1228727154 | 1 | --·-*-·M2-comint·-*-·hash:·1228727154 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2061605-0/0 |
| 4 | i2·:·makeDirectory·dir | 4 | i2·:·makeDirectory·dir |
| 5 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close | 5 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close |
| 6 | o3·=·/tmp/M2- | 6 | o3·=·/tmp/M2-2061605-0/0/foo |
| 7 | o3·:·File | 7 | o3·:·File |
| 8 | i4·:·readDirectory·dir | 8 | i4·:·readDirectory·dir |
| 9 | o4·=·{ | 9 | o4·=·{..,·.,·foo} |
| 10 | o4·:·List | 10 | o4·:·List |
| 11 | i5·:·removeFile·fn | 11 | i5·:·removeFile·fn |
| 12 | i6·:·removeDirectory·dir | 12 | i6·:·removeDirectory·dir |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-158307172 | 1 | --·-*-·M2-comint·-*-·hash:·-158307172 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2055264-0/0 |
| 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/M2-2055264-0/0 |
| 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/M2-2055264-0/0 |
| 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:·1625861322 | 1 | --·-*-·M2-comint·-*-·hash:·1625861322 |
| 2 | i1·:·p·=·temporaryFileName·() | 2 | i1·:·p·=·temporaryFileName·() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2062261-0/0 |
| 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:·824957648 | 1 | --·-*-·M2-comint·-*-·hash:·824957648 |
| 2 | i1·:·realpath·"." | 2 | i1·:·realpath·"." |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2031929-0/80-rundir/ |
| 4 | i2·:·p·=·temporaryFileName() | 4 | i2·:·p·=·temporaryFileName() |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2062303-0/0 |
| 6 | i3·:·q·=·temporaryFileName() | 6 | i3·:·q·=·temporaryFileName() |
| 7 | o3·=·/tmp/M2- | 7 | o3·=·/tmp/M2-2062303-0/1 |
| 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/M2-2062303-0/0 |
| 11 | o5·:·File | 11 | o5·:·File |
| 12 | i6·:·readlink·q | 12 | i6·:·readlink·q |
| 13 | o6·=·/tmp/M2- | 13 | o6·=·/tmp/M2-2062303-0/0 |
| 14 | i7·:·realpath·q | 14 | i7·:·realpath·q |
| 15 | o7·=·/tmp/M2- | 15 | o7·=·/tmp/M2-2062303-0/0 |
| 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/M2-2031929-0/80-rundir/ |
| 20 | i11·:· | 20 | i11·:· |
| Offset 1, 16 lines modified | Offset 1, 16 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·43515301 | 1 | --·-*-·M2-comint·-*-·hash:·43515301 |
| 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)[0]:·--·finalizing·sequence·#1·-- | ||
| 5 | --finalization:·(2)[7]:·--·finalizing·sequence·#8·-- | ||
| 6 | --finalization:·( | 4 | --finalization:·(1)[5]:·--·finalizing·sequence·#6·-- |
| 7 | --finalization:·( | 5 | --finalization:·(2)[3]:·--·finalizing·sequence·#4·-- |
| 8 | --finalization:·( | 6 | --finalization:·(3)[0]:·--·finalizing·sequence·#1·-- |
| 9 | --finalization:·( | 7 | --finalization:·(4)[8]:·--·finalizing·sequence·#9·-- |
| 10 | --finalization:·(7)[1]:·--·finalizing·sequence·#2·-- | ||
| 11 | --finalization:·( | 8 | --finalization:·(5)[6]:·--·finalizing·sequence·#7·-- |
| 9 | --finalization:·(6)[1]:·--·finalizing·sequence·#2·-- | ||
| 10 | --finalization:·(7)[4]:·--·finalizing·sequence·#5·-- | ||
| 12 | --finalization:·(8)[ | 11 | --finalization:·(8)[7]:·--·finalizing·sequence·#8·-- |
| 12 | --finalization:·(9)[2]:·--·finalizing·sequence·#3·-- | ||
| 13 | i3·:· | 13 | i3·:· |
| Offset 1, 17 lines modified | Offset 1, 17 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-490938119 | 1 | --·-*-·M2-comint·-*-·hash:·-490938119 |
| 2 | i1·:·dir·=·temporaryFileName() | 2 | i1·:·dir·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2051901-0/0 |
| 4 | i2·:·makeDirectory·dir | 4 | i2·:·makeDirectory·dir |
| 5 | i3·:·readDirectory·dir | 5 | i3·:·readDirectory·dir |
| 6 | o3·=·{.,· | 6 | o3·=·{..,·.} |
| 7 | o3·:·List | 7 | o3·:·List |
| 8 | i4·:·removeDirectory·dir | 8 | i4·:·removeDirectory·dir |
| 9 | i5·:· | 9 | i5·:· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·371025035 | 1 | --·-*-·M2-comint·-*-·hash:·371025035 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2035408-0/0 |
| 4 | i2·:·rootPath·|·fn | 4 | i2·:·rootPath·|·fn |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2035408-0/0 |
| 6 | i3·:· | 6 | i3·:· |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-251551384 | 1 | --·-*-·M2-comint·-*-·hash:·-251551384 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2061484-0/0 |
| 4 | i2·:·rootURI·|·fn | 4 | i2·:·rootURI·|·fn |
| 5 | o2·=·file:///tmp/M2- | 5 | o2·=·file:///tmp/M2-2061484-0/0 |
| 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/M2-2060498-0/0 |
| 30 | i6·:·f·<<·toString·(p,m,M)·<<·close | 30 | i6·:·f·<<·toString·(p,m,M)·<<·close |
| 31 | o6·=·/tmp/M2- | 31 | o6·=·/tmp/M2-2060498-0/0 |
| 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 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | o2·=·<<task,·created>> | 10 | o2·=·<<task,·created>> |
| 11 | o2·:·Task | 11 | o2·:·Task |
| 12 | i3·:·schedule·t | 12 | i3·:·schedule·t |
| 13 | o3·=·<<task,·re | 13 | o3·=·<<task,·created>> |
| 14 | o3·:·Task | 14 | o3·:·Task |
| 15 | i4·:·taskResult·t | 15 | i4·:·taskResult·t |
| 16 | o4·=·8 | 16 | o4·=·8 |
| 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·0.000189275s·(cpu);·0.00017932s·(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·7.8117e-05s·(cpu);·7.8057e-05s·(thread);·0s·(gc) |
| 198 | i32·:·norm(A*X-B) | 198 | i32·:·norm(A*X-B) |
| 199 | o32·=·5.11185069084045e-15 | 199 | o32·=·5.11185069084045e-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·0.10707s·(cpu);·0.107076s·(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·0.109001s·(cpu);·0.109017s·(thread);·0s·(gc) |
| 218 | i40·:·norm(A*X-B) | 218 | i40·:·norm(A*X-B) |
| 219 | o40·=·1.49157827468970981408235588593e-28 | 219 | o40·=·1.49157827468970981408235588593e-28 |
| 220 | o40·:·RR·(of·precision·100) | 220 | o40·:·RR·(of·precision·100) |
| Offset 1, 54 lines modified | Offset 1, 54 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-60501573 | 1 | --·-*-·M2-comint·-*-·hash:·-60501573 |
| 2 | i1·:·src·=·temporaryFileName()·|·"/" | 2 | i1·:·src·=·temporaryFileName()·|·"/" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2055459-0/0/ |
| 4 | i2·:·dst·=·temporaryFileName()·|·"/" | 4 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2055459-0/1/ |
| 6 | i3·:·makeDirectory·(src|"a/") | 6 | i3·:·makeDirectory·(src|"a/") |
| 7 | i4·:·makeDirectory·(src|"b/") | 7 | i4·:·makeDirectory·(src|"b/") |
| 8 | i5·:·makeDirectory·(src|"b/c/") | 8 | i5·:·makeDirectory·(src|"b/c/") |
| 9 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 9 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 10 | o6·=·/tmp/M2- | 10 | o6·=·/tmp/M2-2055459-0/0/a/f |
| 11 | o6·:·File | 11 | o6·:·File |
| 12 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 12 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 13 | o7·=·/tmp/M2- | 13 | o7·=·/tmp/M2-2055459-0/0/a/g |
| 14 | o7·:·File | 14 | o7·:·File |
| 15 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 15 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 16 | o8·=·/tmp/M2- | 16 | o8·=·/tmp/M2-2055459-0/0/b/c/g |
| 17 | o8·:·File | 17 | o8·:·File |
| 18 | i9·:·symlinkDirectory(src,dst,Verbose=>true) | 18 | i9·:·symlinkDirectory(src,dst,Verbose=>true) |
| 19 | --symlinking:·../../../0/b/c/g·->·/tmp/M2- | 19 | --symlinking:·../../../0/b/c/g·->·/tmp/M2-2055459-0/1/b/c/g |
| 20 | --symlinking:·../../0/a/g·->·/tmp/M2-1007573-0/1/a/g | ||
| 21 | --symlinking:·../../0/a/f·->·/tmp/M2- | 20 | --symlinking:·../../0/a/f·->·/tmp/M2-2055459-0/1/a/f |
| 21 | --symlinking:·../../0/a/g·->·/tmp/M2-2055459-0/1/a/g | ||
| 22 | i10·:·get·(dst|"b/c/g") | 22 | i10·:·get·(dst|"b/c/g") |
| 23 | o10·=·ho·there | 23 | o10·=·ho·there |
| 24 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) | 24 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) |
| 25 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2- | 25 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-2055459-0/1/b/c/g |
| 26 | --unsymlinking:·../../0/a/g·->·/tmp/M2-1007573-0/1/a/g | ||
| 27 | --unsymlinking:·../../0/a/f·->·/tmp/M2- | 26 | --unsymlinking:·../../0/a/f·->·/tmp/M2-2055459-0/1/a/f |
| 27 | --unsymlinking:·../../0/a/g·->·/tmp/M2-2055459-0/1/a/g | ||
| 28 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 28 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 29 | o12·=·rm | 29 | o12·=·rm |
| 30 | o12·:·FunctionClosure | 30 | o12·:·FunctionClosure |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1728606371 | 1 | --·-*-·M2-comint·-*-·hash:·1728606371 |
| 2 | i1·:·fn·=·temporaryFileName() | 2 | i1·:·fn·=·temporaryFileName() |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2056426-0/0 |
| 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:·179390682 | 1 | --·-*-·M2-comint·-*-·hash:·179390682 |
| 2 | i1·:·temporaryFileName·()·|·".tex" | 2 | i1·:·temporaryFileName·()·|·".tex" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2070680-0/0.tex |
| 4 | i2·:·temporaryFileName·()·|·".html" | 4 | i2·:·temporaryFileName·()·|·".html" |
| 5 | o2·=·/tmp/M2- | 5 | o2·=·/tmp/M2-2070680-0/1.html |
| 6 | i3·:· | 6 | i3·:· |
| Offset 1, 8 lines modified | Offset 1, 8 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·995638963 | 1 | --·-*-·M2-comint·-*-·hash:·995638963 |
| 2 | i1·:·time·3^30 | 2 | i1·:·time·3^30 |
| 3 | ·--·used·1. | 3 | ·--·used·1.6826e-05s·(cpu);·5.238e-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:·668031083 | 1 | --·-*-·M2-comint·-*-·hash:·668031083 |
| 2 | i1·:·timing·3^30 | 2 | i1·:·timing·3^30 |
| 3 | o1·=·205891132094649 | 3 | o1·=·205891132094649 |
| 4 | ·····--·.00001 | 4 | ·····--·.000014061·seconds |
| 5 | o1·:·Time | 5 | o1·:·Time |
| 6 | i2·:·peek·oo | 6 | i2·:·peek·oo |
| 7 | o2·=·Time{.00001 | 7 | o2·=·Time{.000014061,·205891132094649} |
| 8 | i3·:· | 8 | i3·:· |
| Offset 32, 15 lines modified | Offset 32, 15 lines modified | ||
| 32 | ···············"memtailor·version"·=>·1.0 | 32 | ···············"memtailor·version"·=>·1.0 |
| 33 | ···············"mpfi·version"·=>·1.5.4 | 33 | ···············"mpfi·version"·=>·1.5.4 |
| 34 | ···············"mpfr·version"·=>·4.2.1 | 34 | ···············"mpfr·version"·=>·4.2.1 |
| 35 | ···············"mpir·version"·=>·not·present | 35 | ···············"mpir·version"·=>·not·present |
| 36 | ···············"mpsolve·version"·=>·3.2.1 | 36 | ···············"mpsolve·version"·=>·3.2.1 |
| 37 | ···············"mysql·version"·=>·not·present | 37 | ···············"mysql·version"·=>·not·present |
| 38 | ···············"ntl·version"·=>·11.5.1 | 38 | ···············"ntl·version"·=>·11.5.1 |
| 39 | ···············"operating·system·release"·=>·6.10 | 39 | ···············"operating·system·release"·=>·6.1.0-26-cloud-amd64 |
| 40 | ···············"operating·system"·=>·Linux | 40 | ···············"operating·system"·=>·Linux |
| 41 | ···············"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 | 41 | ···············"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 |
| 42 | ···············"pointer·size"·=>·8 | 42 | ···············"pointer·size"·=>·8 |
| 43 | ···············"python·version"·=>·3.12.6 | 43 | ···············"python·version"·=>·3.12.6 |
| 44 | ···············"readline·version"·=>·8.2 | 44 | ···············"readline·version"·=>·8.2 |
| 45 | ···············"scscp·version"·=>·not·present | 45 | ···············"scscp·version"·=>·not·present |
| 46 | ···············"tbb·version"·=>·2021.12 | 46 | ···············"tbb·version"·=>·2021.12 |
| Offset 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | o2·=·1073741824</code></pre> | 78 | o2·=·1073741824</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·(c·=·Command·"date";)</code></pre> | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·(c·=·Command·"date";)</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·c | 84 | <td>··············<pre><code·class="language-macaulay2">i4·:·c |
| 85 | 85 | Wed·Oct·16·04:18:42·+14·2024 | |
| 86 | o4·=·0</code></pre> | 86 | o4·=·0</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ········</table> | 88 | ········</table> |
| 89 | ······</div> | 89 | ······</div> |
| 90 | ······<div> | 90 | ······<div> |
| 91 | ········<h2>See·also</h2> | 91 | ········<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·Oct·16·04:18:42·+14·2024 | |
| 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) |
| Offset 45, 20 lines modified | Offset 45, 20 lines modified | ||
| 45 | ······<h1>Database·--·the·class·of·all·database·files</h1> | 45 | ······<h1>Database·--·the·class·of·all·database·files</h1> |
| 46 | ······<div> | 46 | ······<div> |
| 47 | ········<h2>Description</h2> | 47 | ········<h2>Description</h2> |
| 48 | 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 | 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"> |
| 49 | ··········<tr> | 49 | ··········<tr> |
| 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·filename·=·temporaryFileName·()·|·".dbm" | 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·filename·=·temporaryFileName·()·|·".dbm" |
| 51 | o1·=·/tmp/M2- | 51 | o1·=·/tmp/M2-2061829-0/0.dbm</code></pre> |
| 52 | </td>··········</tr> | 52 | </td>··········</tr> |
| 53 | ··········<tr> | 53 | ··········<tr> |
| 54 | <td>··············<pre><code·class="language-macaulay2">i2·:·x·=·openDatabaseOut·filename | 54 | <td>··············<pre><code·class="language-macaulay2">i2·:·x·=·openDatabaseOut·filename |
| 55 | o2·=·/tmp/M2- | 55 | o2·=·/tmp/M2-2061829-0/0.dbm |
| 56 | o2·:·Database</code></pre> | 56 | o2·:·Database</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ··········<tr> | 58 | ··········<tr> |
| 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·x#"first"·=·"hi·there" | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·x#"first"·=·"hi·there" |
| 60 | o3·=·hi·there</code></pre> | 60 | 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/M2-2061829-0/0.dbm |
| 13 | i2·:·x·=·openDatabaseOut·filename | 13 | i2·:·x·=·openDatabaseOut·filename |
| 14 | o2·=·/tmp/M2- | 14 | o2·=·/tmp/M2-2061829-0/0.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 85, 26 lines modified | Offset 85, 26 lines modified | ||
| 85 | o2·=·S | 85 | o2·=·S |
| 86 | o2·:·PolynomialRing</code></pre> | 86 | o2·:·PolynomialRing</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·res(I,·FastNonminimal·=>·true) |
| 90 | ·--· | 90 | ·--·1.92727·seconds·elapsed |
| 91 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 | 91 | ······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 92 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 | 92 | o3·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S···<--·0 |
| 93 | ········································································································· | 93 | ········································································································· |
| 94 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 | 94 | ·····0······1·······2········3········4·········5·········6·········7·········8········9········10······11 |
| 95 | o3·:·ChainComplex</code></pre> | 95 | o3·:·ChainComplex</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C1·=·res·ideal(I_*) | 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C1·=·res·ideal(I_*) |
| 99 | ·--·1. | 99 | ·--·1.00836·seconds·elapsed |
| 100 | ······1······35······140······385······819······1080······819······385······140······35······1 | 100 | ······1······35······140······385······819······1080······819······385······140······35······1 |
| 101 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0 | 101 | o4·=·S··<--·S···<--·S····<--·S····<--·S····<--·S·····<--·S····<--·S····<--·S····<--·S···<--·S··<--·0 |
| 102 | ···································································································· | 102 | ···································································································· |
| 103 | ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11 | 103 | ·····0······1·······2········3········4········5·········6········7········8········9·······10·····11 |
| 104 | o4·:·ChainComplex</code></pre> | 104 | 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 | ·--·1.92727·seconds·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 | ·--·1. | 44 | ·--·1.00836·seconds·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 98, 20 lines modified | Offset 98, 20 lines modified | ||
| 98 | o2·=·stdio | 98 | o2·=·stdio |
| 99 | o2·:·File</code></pre> | 99 | o2·:·File</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·=·temporaryFileName() | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·=·temporaryFileName() |
| 103 | o3·=·/tmp/M2- | 103 | o3·=·/tmp/M2-2062132-0/0</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·fn·<<·"hi·there"·<<·endl·<<·close | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·fn·<<·"hi·there"·<<·endl·<<·close |
| 107 | o4·=·/tmp/M2- | 107 | o4·=·/tmp/M2-2062132-0/0 |
| 108 | o4·:·File</code></pre> | 108 | o4·:·File</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn | 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn |
| 112 | o5·=·hi·there</code></pre> | 112 | o5·=·hi·there</code></pre> |
| Offset 140, 29 lines modified | Offset 140, 29 lines modified | ||
| 140 | o8·=·stdio | 140 | o8·=·stdio |
| 141 | o8·:·File</code></pre> | 141 | o8·:·File</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i9·:·fn·<<·f·<<·close | 144 | <td>··············<pre><code·class="language-macaulay2">i9·:·fn·<<·f·<<·close |
| 145 | o9·=·/tmp/M2- | 145 | o9·=·/tmp/M2-2062132-0/0 |
| 146 | o9·:·File</code></pre> | 146 | o9·:·File</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·fn | 149 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·fn |
| 150 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 | 150 | o10·=··10······9······8·······7·······6·······5·······4·······3······2 |
| 151 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x | 151 | ······x···+·10x··+·45x··+·120x··+·210x··+·252x··+·210x··+·120x··+·45x··+·10x |
| 152 | ······+·1</code></pre> | 152 | ······+·1</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i11·:·fn·<<·toExternalString·f·<<·close | 155 | <td>··············<pre><code·class="language-macaulay2">i11·:·fn·<<·toExternalString·f·<<·close |
| 156 | o11·=·/tmp/M2- | 156 | o11·=·/tmp/M2-2062132-0/0 |
| 157 | o11·:·File</code></pre> | 157 | o11·:·File</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i12·:·get·fn | 160 | <td>··············<pre><code·class="language-macaulay2">i12·:·get·fn |
| 161 | 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+ | 161 | 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/M2-2062132-0/0 |
| 43 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close | 43 | i4·:·fn·<<·"hi·there"·<<·endl·<<·close |
| 44 | o4·=·/tmp/M2- | 44 | o4·=·/tmp/M2-2062132-0/0 |
| 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/M2-2062132-0/0 |
| 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/M2-2062132-0/0 |
| 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 46, 31 lines modified | Offset 46, 31 lines modified | ||
| 46 | ······<div> | 46 | ······<div> |
| 47 | ········<h2>Description</h2> | 47 | ········<h2>Description</h2> |
| 48 | ········<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 | ········<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> |
| 49 | ········<table·class="examples"> | 49 | ········<table·class="examples"> |
| 50 | ··········<tr> | 50 | ··········<tr> |
| 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·s·=·GCstats() | 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·s·=·GCstats() |
| 52 | o1·=·HashTable{"bytesAlloc"·=>·11 | 52 | o1·=·HashTable{"bytesAlloc"·=>·11661111018········} |
| 53 | ···············"GC_free_space_divisor"·=>·3 | 53 | ···············"GC_free_space_divisor"·=>·3 |
| 54 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 | 54 | ···············"GC_LARGE_ALLOC_WARN_INTERVAL"·=>·1 |
| 55 | ···············"gcCpuTimeSecs"·=>·0 | 55 | ···············"gcCpuTimeSecs"·=>·0 |
| 56 | ···············"heapSize"·=>·22 | 56 | ···············"heapSize"·=>·221462528 |
| 57 | ···············"numGCs"·=>·79 | 57 | ···············"numGCs"·=>·793 |
| 58 | ···············"numGCThreads"·=>·12 | 58 | ···············"numGCThreads"·=>·12 |
| 59 | o1·:·HashTable</code></pre> | 59 | o1·:·HashTable</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ········</table> | 61 | ········</table> |
| 62 | ········<p>The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information·can·be·easily·extracted,·as·follows.</p> | 62 | ········<p>The·value·returned·is·a·hash·table,·from·which·individual·bits·of·information·can·be·easily·extracted,·as·follows.</p> |
| 63 | ········<table·class="examples"> | 63 | ········<table·class="examples"> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i2·:·s#"heapSize" | 65 | <td>··············<pre><code·class="language-macaulay2">i2·:·s#"heapSize" |
| 66 | o2·=·22 | 66 | o2·=·221462528</code></pre> |
| 67 | </td>··········</tr> | 67 | </td>··········</tr> |
| 68 | ········</table> | 68 | ········</table> |
| 69 | ········<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>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> |
| 70 | ········<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 | ········<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> |
| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>See·also</h2> | 73 | ········<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"·=>·11 | 14 | o1·=·HashTable{"bytesAlloc"·=>·11661111018········} |
| 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"·=>·22 | 18 | ···············"heapSize"·=>·221462528 |
| 19 | ···············"numGCs"·=>·79 | 19 | ···············"numGCs"·=>·793 |
| 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·=·22 | 25 | o2·=·221462528 |
| 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 |
| Offset 107, 28 lines modified | Offset 107, 28 lines modified | ||
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); | 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·I·=·truncate(8,·monomialCurveIdeal(R,{1,4,5,9})); |
| 109 | o7·:·Ideal·of·R</code></pre> | 109 | o7·:·Ideal·of·R</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·gens·gb·I; | 112 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·gens·gb·I; |
| 113 | ·--·used·0.02 | 113 | ·--·used·0.0211414s·(cpu);·0.02114s·(thread);·0s·(gc) |
| 114 | ·············1······428 | 114 | ·············1······428 |
| 115 | o8·:·Matrix·R··<--·R</code></pre> | 115 | o8·:·Matrix·R··<--·R</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J1·=·saturate(I); | 118 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·J1·=·saturate(I); |
| 119 | ·--·used·0. | 119 | ·--·used·0.32201s·(cpu);·0.147607s·(thread);·0s·(gc) |
| 120 | o9·:·Ideal·of·R</code></pre> | 120 | o9·:·Ideal·of·R</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); | 123 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·J·=·saturate(I,·MinimalGenerators·=>·false); |
| 124 | ·--·used· | 124 | ·--·used·8.8103e-05s·(cpu);·8.8013e-05s·(thread);·0s·(gc) |
| 125 | o10·:·Ideal·of·R</code></pre> | 125 | o10·:·Ideal·of·R</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·J | 128 | <td>··············<pre><code·class="language-macaulay2">i11·:·numgens·J |
| 129 | o11·=·7</code></pre> | 129 | 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·0.02 | 49 | ·--·used·0.0211414s·(cpu);·0.02114s·(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·0.32201s·(cpu);·0.147607s·(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·8.8103e-05s·(cpu);·8.8013e-05s·(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 |
| Offset 62, 19 lines modified | Offset 62, 19 lines modified | ||
| 62 | ················200·········200 | 62 | ················200·········200 |
| 63 | o1·:·Matrix·RR······<--·RR | 63 | o1·:·Matrix·RR······<--·RR |
| 64 | ··············53··········53</code></pre> | 64 | ··············53··········53</code></pre> |
| 65 | </td>··········</tr> | 65 | </td>··········</tr> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·SVD(M); | 67 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·SVD(M); |
| 68 | ·--·used·0.02 | 68 | ·--·used·0.0257259s·(cpu);·0.0257261s·(thread);·0s·(gc)</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·SVD(M,·DivideConquer=>true); | 71 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·SVD(M,·DivideConquer=>true); |
| 72 | ·--·used·0.02 | 72 | ·--·used·0.0259131s·(cpu);·0.0259231s·(thread);·0s·(gc)</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ········</table> | 74 | ········</table> |
| 75 | ······</div> | 75 | ······</div> |
| 76 | ······<div> | 76 | ······<div> |
| 77 | ········<h2>Further·information</h2> | 77 | ········<h2>Further·information</h2> |
| 78 | ········<ul> | 78 | ········<ul> |
| 79 | ··········<li> | 79 | ··········<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·0.02 | 18 | ·--·used·0.0257259s·(cpu);·0.0257261s·(thread);·0s·(gc) |
| 19 | i3·:·time·SVD(M,·DivideConquer=>true); | 19 | i3·:·time·SVD(M,·DivideConquer=>true); |
| 20 | ·--·used·0.02 | 20 | ·--·used·0.0259131s·(cpu);·0.0259231s·(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 |
| Offset 555, 15 lines modified | Offset 555, 15 lines modified | ||
| 555 | ·····························3 | 555 | ·····························3 |
| 556 | o58·:·R-module,·quotient·of·R</code></pre> | 556 | o58·:·R-module,·quotient·of·R</code></pre> |
| 557 | </td>··········</tr> | 557 | </td>··········</tr> |
| 558 | ········</table> | 558 | ········</table> |
| 559 | 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 | 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"> |
| 560 | ··········<tr> | 560 | ··········<tr> |
| 561 | <td>··············<pre><code·class="language-macaulay2">i59·:·time·C·=·resolution·M | 561 | <td>··············<pre><code·class="language-macaulay2">i59·:·time·C·=·resolution·M |
| 562 | ·--·used·0.0016 | 562 | ·--·used·0.00216258s·(cpu);·0.00215611s·(thread);·0s·(gc) |
| 563 | ·······3······6······15······18······6 | 563 | ·······3······6······15······18······6 |
| 564 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 | 564 | o59·=·R··<--·R··<--·R···<--·R···<--·R··<--·0 |
| 565 | ············································ | 565 | ············································ |
| 566 | ······0······1······2·······3·······4······5 | 566 | ······0······1······2·······3·······4······5 |
| 567 | o59·:·ChainComplex</code></pre> | 567 | 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·0.0016 | 392 | ·--·used·0.00216258s·(cpu);·0.00215611s·(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 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·peek·read·f | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·peek·read·f |
| 91 | o4·=·"hi·there"</code></pre> | 91 | o4·=·"hi·there"</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·atEndOfFile·f | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·atEndOfFile·f |
| 95 | o5·=· | 95 | o5·=·true</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ········</table> | 97 | ········</table> |
| 98 | ······</div> | 98 | ······</div> |
| 99 | ······<div·class="waystouse"> | 99 | ······<div·class="waystouse"> |
| 100 | ········<h2>Ways·to·use·this·method:</h2> | 100 | ········<h2>Ways·to·use·this·method:</h2> |
| 101 | ········<ul> | 101 | ········<ul> |
| 102 | ··········<li> | 102 | ··········<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 68, 15 lines modified | Offset 68, 15 lines modified | ||
| 68 | ······</div> | 68 | ······</div> |
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | 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 | 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"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·benchmark·"sqrt·2p100000" | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·benchmark·"sqrt·2p100000" |
| 74 | o1·=·.0003 | 74 | o1·=·.000336946552311436 |
| 75 | o1·:·RR·(of·precision·53)</code></pre> | 75 | o1·:·RR·(of·precision·53)</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ········</table> | 77 | ········</table> |
| 78 | 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 | 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> |
| 79 | ······<div·class="waystouse"> | 79 | ······<div·class="waystouse"> |
| 80 | ········<h2>For·the·programmer</h2> | 80 | ········<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·=·.0003 | 19 | o1·=·.000336946552311436 |
| 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 84, 15 lines modified | Offset 84, 15 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 | ·--·1.92079·seconds·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> |
| 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 | ·--·1.92079·seconds·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 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | o4·=·<<task,·running>> | 96 | o4·=·<<task,·running>> |
| 97 | o4·:·Task</code></pre> | 97 | o4·:·Task</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·n | 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·n |
| 101 | o5·=·941 | 101 | o5·=·941829</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·sleep·1 | 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·sleep·1 |
| 105 | o6·=·0</code></pre> | 105 | o6·=·0</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| Offset 113, 15 lines modified | Offset 113, 15 lines modified | ||
| 113 | o7·=·<<task,·running>> | 113 | o7·=·<<task,·running>> |
| 114 | o7·:·Task</code></pre> | 114 | o7·:·Task</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i8·:·n | 117 | <td>··············<pre><code·class="language-macaulay2">i8·:·n |
| 118 | o8·=·191 | 118 | o8·=·1917486</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i9·:·isReady·t | 121 | <td>··············<pre><code·class="language-macaulay2">i9·:·isReady·t |
| 122 | o9·=·false</code></pre> | 122 | o9·=·false</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| Offset 139, 25 lines modified | Offset 139, 25 lines modified | ||
| 139 | o12·=·<<task,·canceled>> | 139 | o12·=·<<task,·canceled>> |
| 140 | o12·:·Task</code></pre> | 140 | o12·:·Task</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i13·:·n | 143 | <td>··············<pre><code·class="language-macaulay2">i13·:·n |
| 144 | o13·=·191 | 144 | o13·=·1917650</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i14·:·sleep·1 | 147 | <td>··············<pre><code·class="language-macaulay2">i14·:·sleep·1 |
| 148 | o14·=·0</code></pre> | 148 | o14·=·0</code></pre> |
| 149 | </td>··········</tr> | 149 | </td>··········</tr> |
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i15·:·n | 151 | <td>··············<pre><code·class="language-macaulay2">i15·:·n |
| 152 | o15·=·191 | 152 | o15·=·1917650</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i16·:·isReady·t | 155 | <td>··············<pre><code·class="language-macaulay2">i16·:·isReady·t |
| 156 | o16·=·false</code></pre> | 156 | o16·=·false</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ········</table> | 158 | ········</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·=·941 | 33 | o5·=·941829 |
| 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·=·1917486 |
| 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:2:26:(3):[1]:·error:·interrupted | 45 | stdio:2:26:(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·=·191 | 60 | o13·=·1917650 |
| 61 | i14·:·sleep·1 | 61 | i14·:·sleep·1 |
| 62 | o14·=·0 | 62 | o14·=·0 |
| 63 | i15·:·n | 63 | i15·:·n |
| 64 | o15·=·191 | 64 | o15·=·1917650 |
| 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 43, 15 lines modified | Offset 43, 15 lines modified | ||
| 43 | ····</div> | 43 | ····</div> |
| 44 | <hr>····<div> | 44 | <hr>····<div> |
| 45 | ······<h1>communicating·with·programs</h1> | 45 | ······<h1>communicating·with·programs</h1> |
| 46 | ······<div> | 46 | ······<div> |
| 47 | 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 | 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"> |
| 48 | ··········<tr> | 48 | ··········<tr> |
| 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·run·"uname·-a" | 49 | <td>··············<pre><code·class="language-macaulay2">i1·:·run·"uname·-a" |
| 50 | Linux·i | 50 | Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·x86_64·GNU/Linux |
| 51 | o1·=·0</code></pre> | 51 | o1·=·0</code></pre> |
| 52 | </td>··········</tr> | 52 | </td>··········</tr> |
| 53 | ········</table> | 53 | ········</table> |
| 54 | 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 | 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"> |
| 55 | ··········<tr> | 55 | ··········<tr> |
| 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close | 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·"!grep·a"·<<·"·ba·\n·bc·\n·ad·\n·ef·\n"·<<·close |
| Offset 63, 17 lines modified | Offset 63, 17 lines modified | ||
| 63 | o2·:·File</code></pre> | 63 | o2·:·File</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ········</table> | 65 | ········</table> |
| 66 | 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 | 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"> |
| 67 | ··········<tr> | 67 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·peek·get·"!uname·-a" | 68 | <td>··············<pre><code·class="language-macaulay2">i3·:·peek·get·"!uname·-a" |
| 69 | o3·=·"Linux·i | 69 | o3·=·"Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP |
| 70 | ·····" | 70 | ·····" |
| 71 | ····· | 71 | ·····PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·x86_64·GNU/Linux</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ········</table> | 73 | ········</table> |
| 74 | 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 | 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"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·f·=·openInOut·"!egrep·'^in'" | 76 | <td>··············<pre><code·class="language-macaulay2">i4·:·f·=·openInOut·"!egrep·'^in'" |
| 77 | o4·=·!egrep·'^in' | 77 | 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·i | 11 | Linux·i-capture-the-hostname·6.1.0-26-cloud-amd64·#1·SMP·PREEMPT_DYNAMIC·Debian |
| 12 | 12 | 6.1.112-1·(2024-09-30)·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·6.1.0-26-cloud-amd64·#1·SMP |
| 32 | ·····" | 32 | ·····" |
| 33 | ····· | 33 | ·····PREEMPT_DYNAMIC·Debian·6.1.112-1·(2024-09-30)·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 216, 15 lines modified | Offset 216, 15 lines modified | ||
| 216 | ················ZZ | 216 | ················ZZ |
| 217 | o23·:·Ideal·of·----[x..z,·w] | 217 | o23·:·Ideal·of·----[x..z,·w] |
| 218 | ···············1277</code></pre> | 218 | ···············1277</code></pre> |
| 219 | </td>··········</tr> | 219 | </td>··········</tr> |
| 220 | ··········<tr> | 220 | ··········<tr> |
| 221 | <td>··············<pre><code·class="language-macaulay2">i24·:·gb·I | 221 | <td>··············<pre><code·class="language-macaulay2">i24·:·gb·I |
| 222 | ···--·registering·gb·5·at·0x7f | 222 | ···--·registering·gb·5·at·0x7fdde70d6700 |
| 223 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 | 223 | ···--·[gb]{2}(2)mm{3}(1)m{4}(2)om{5}(1)onumber·of·(nonminimal)·gb·elements·=·4 |
| 224 | ···--·number·of·monomials················=·8 | 224 | ···--·number·of·monomials················=·8 |
| 225 | ···--·#reduction·steps·=·2 | 225 | ···--·#reduction·steps·=·2 |
| 226 | ···--·#spairs·done·=·6 | 226 | ···--·#spairs·done·=·6 |
| 227 | ···--·ncalls·=·0 | 227 | ···--·ncalls·=·0 |
| 228 | ···--·nloop·=·0 | 228 | ···--·nloop·=·0 |
| Offset 302, 15 lines modified | Offset 302, 15 lines modified | ||
| 302 | <td>··············<pre><code·class="language-macaulay2">i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); | 302 | <td>··············<pre><code·class="language-macaulay2">i32·:·f·=·random(R^1,R^{-3,-3,-5,-6}); |
| 303 | ··············1······4 | 303 | ··············1······4 |
| 304 | o32·:·Matrix·R··<--·R</code></pre> | 304 | o32·:·Matrix·R··<--·R</code></pre> |
| 305 | </td>··········</tr> | 305 | </td>··········</tr> |
| 306 | ··········<tr> | 306 | ··········<tr> |
| 307 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·betti·gb·f | 307 | <td>··············<pre><code·class="language-macaulay2">i33·:·time·betti·gb·f |
| 308 | ·--·used·0. | 308 | ·--·used·0.143899s·(cpu);·0.145616s·(thread);·0s·(gc) |
| 309 | ·············0··1 | 309 | ·············0··1 |
| 310 | o33·=·total:·1·53 | 310 | o33·=·total:·1·53 |
| 311 | ··········0:·1··. | 311 | ··········0:·1··. |
| 312 | ··········1:·.··. | 312 | ··········1:·.··. |
| 313 | ··········2:·.··2 | 313 | ··········2:·.··2 |
| 314 | ··········3:·.··1 | 314 | ··········3:·.··1 |
| Offset 340, 15 lines modified | Offset 340, 15 lines modified | ||
| 340 | ············3····5·····8·····9····12·····14····17 | 340 | ············3····5·····8·····9····12·····14····17 |
| 341 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T | 341 | o35·=·1·-·2T··-·T··+·2T··+·2T··-·T···-·2T···+·T |
| 342 | o35·:·ZZ[T]</code></pre> | 342 | o35·:·ZZ[T]</code></pre> |
| 343 | </td>··········</tr> | 343 | </td>··········</tr> |
| 344 | ··········<tr> | 344 | ··········<tr> |
| 345 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·betti·gb·f | 345 | <td>··············<pre><code·class="language-macaulay2">i36·:·time·betti·gb·f |
| 346 | ·--·used·0.00 | 346 | ·--·used·0.00185646s·(cpu);·0.00210011s·(thread);·0s·(gc) |
| 347 | ·············0··1 | 347 | ·············0··1 |
| 348 | o36·=·total:·1·53 | 348 | o36·=·total:·1·53 |
| 349 | ··········0:·1··. | 349 | ··········0:·1··. |
| 350 | ··········1:·.··. | 350 | ··········1:·.··. |
| 351 | ··········2:·.··2 | 351 | ··········2:·.··2 |
| 352 | ··········3:·.··1 | 352 | ··········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·0x7f | 144 | ···--·registering·gb·5·at·0x7fdde70d6700 |
| 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·0.143899s·(cpu);·0.145616s·(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·0.00185646s·(cpu);·0.00210011s·(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 93, 16 lines modified | Offset 93, 16 lines modified | ||
| 93 | ··········<<·res·M·<<·endl·<<·endl; | 93 | ··········<<·res·M·<<·endl·<<·endl; |
| 94 | ··········break; | 94 | ··········break; |
| 95 | ··········)·else·( | 95 | ··········)·else·( |
| 96 | ··········<<·"--·computation·interrupted"·<<·endl; | 96 | ··········<<·"--·computation·interrupted"·<<·endl; |
| 97 | ··········status·M.cache.resolution; | 97 | ··········status·M.cache.resolution; |
| 98 | ··········<<·"--·continuing·the·computation"·<<·endl; | 98 | ··········<<·"--·continuing·the·computation"·<<·endl; |
| 99 | ··········)) | 99 | ··········)) |
| 100 | ·--·used·1.17 | 100 | ·--·used·1.17527s·(cpu);·1.0079s·(thread);·0s·(gc) |
| 101 | ·--·used·0. | 101 | ·--·used·0.358421s·(cpu);·0.26694s·(thread);·0s·(gc) |
| 102 | --·computation·started:· | 102 | --·computation·started:· |
| 103 | --·computation·interrupted | 103 | --·computation·interrupted |
| 104 | --·continuing·the·computation | 104 | --·continuing·the·computation |
| 105 | --·computation·complete | 105 | --·computation·complete |
| 106 | ·4······11······89······122······40 | 106 | ·4······11······89······122······40 |
| 107 | R··<--·R···<--·R···<--·R····<--·R···<--·0 | 107 | R··<--·R···<--·R···<--·R····<--·R···<--·0 |
| 108 | ········································· | 108 | ········································· |
| 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·1.17 | 57 | ·--·used·1.17527s·(cpu);·1.0079s·(thread);·0s·(gc) |
| 58 | ·--·used·0. | 58 | ·--·used·0.358421s·(cpu);·0.26694s·(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 86, 84 lines modified | Offset 86, 84 lines modified | ||
| 86 | ······</div> | 86 | ······</div> |
| 87 | ······<div> | 87 | ······<div> |
| 88 | ········<h2>Description</h2> | 88 | ········<h2>Description</h2> |
| 89 | ········<table·class="examples"> | 89 | ········<table·class="examples"> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" | 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" |
| 92 | o1·=·/tmp/M2- | 92 | o1·=·/tmp/M2-2056328-0/0/</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" |
| 96 | o2·=·/tmp/M2- | 96 | o2·=·/tmp/M2-2056328-0/1/</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/")</code></pre> | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/")</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/")</code></pre> | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/")</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/")</code></pre> | 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/")</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close | 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 109 | o6·=·/tmp/M2- | 109 | o6·=·/tmp/M2-2056328-0/0/a/f |
| 110 | o6·:·File</code></pre> | 110 | o6·:·File</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close | 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 114 | o7·=·/tmp/M2- | 114 | o7·=·/tmp/M2-2056328-0/0/a/g |
| 115 | o7·:·File</code></pre> | 115 | o7·:·File</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 118 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 119 | o8·=·/tmp/M2- | 119 | o8·=·/tmp/M2-2056328-0/0/b/c/g |
| 120 | o8·:·File</code></pre> | 120 | o8·:·File</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i9·:·stack·findFiles·src | 123 | <td>··············<pre><code·class="language-macaulay2">i9·:·stack·findFiles·src |
| 124 | o9·=·/tmp/M2- | 124 | o9·=·/tmp/M2-2056328-0/0/ |
| 125 | ·····/tmp/M2- | 125 | ·····/tmp/M2-2056328-0/0/b/ |
| 126 | ·····/tmp/M2- | 126 | ·····/tmp/M2-2056328-0/0/b/c/ |
| 127 | ·····/tmp/M2- | 127 | ·····/tmp/M2-2056328-0/0/b/c/g |
| 128 | ·····/tmp/M2- | 128 | ·····/tmp/M2-2056328-0/0/a/ |
| 129 | ·····/tmp/M2- | 129 | ·····/tmp/M2-2056328-0/0/a/f |
| 130 | ·····/tmp/M2- | 130 | ·····/tmp/M2-2056328-0/0/a/g</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·copyDirectory(src,dst,Verbose=>true) | 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·copyDirectory(src,dst,Verbose=>true) |
| 134 | ·--·copying:·/tmp/M2- | 134 | ·--·copying:·/tmp/M2-2056328-0/0/b/c/g·->·/tmp/M2-2056328-0/1/b/c/g |
| 135 | ·--·copying:·/tmp/M2- | 135 | ·--·copying:·/tmp/M2-2056328-0/0/a/f·->·/tmp/M2-2056328-0/1/a/f |
| 136 | ·--·copying:·/tmp/M2- | 136 | ·--·copying:·/tmp/M2-2056328-0/0/a/g·->·/tmp/M2-2056328-0/1/a/g</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) | 139 | <td>··············<pre><code·class="language-macaulay2">i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 140 | ·--·skipping:·/tmp/M2- | 140 | ·--·skipping:·/tmp/M2-2056328-0/0/b/c/g·not·newer·than·/tmp/M2-2056328-0/1/b/c/g |
| 141 | ·--·skipping:·/tmp/M2- | 141 | ·--·skipping:·/tmp/M2-2056328-0/0/a/f·not·newer·than·/tmp/M2-2056328-0/1/a/f |
| 142 | ·--·skipping:·/tmp/M2- | 142 | ·--·skipping:·/tmp/M2-2056328-0/0/a/g·not·newer·than·/tmp/M2-2056328-0/1/a/g</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i12·:·stack·findFiles·dst | 145 | <td>··············<pre><code·class="language-macaulay2">i12·:·stack·findFiles·dst |
| 146 | o12·=·/tmp/M2- | 146 | o12·=·/tmp/M2-2056328-0/1/ |
| 147 | ······/tmp/M2- | 147 | ······/tmp/M2-2056328-0/1/b/ |
| 148 | ······/tmp/M2- | 148 | ······/tmp/M2-2056328-0/1/b/c/ |
| 149 | ······/tmp/M2- | 149 | ······/tmp/M2-2056328-0/1/b/c/g |
| 150 | ······/tmp/M2- | 150 | ······/tmp/M2-2056328-0/1/a/ |
| 151 | ······/tmp/M2- | 151 | ······/tmp/M2-2056328-0/1/a/f |
| 152 | ······/tmp/M2- | 152 | ······/tmp/M2-2056328-0/1/a/g</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·get·(dst|"b/c/g") | 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·get·(dst|"b/c/g") |
| 156 | o13·=·ho·there</code></pre> | 156 | o13·=·ho·there</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ········</table> | 158 | ········</table> |
| Offset 26, 63 lines modified | Offset 26, 63 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/M2-2056328-0/0/ |
| 33 | i2·:·dst·=·temporaryFileName()·|·"/" | 33 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 34 | o2·=·/tmp/M2- | 34 | o2·=·/tmp/M2-2056328-0/1/ |
| 35 | i3·:·makeDirectory·(src|"a/") | 35 | i3·:·makeDirectory·(src|"a/") |
| 36 | i4·:·makeDirectory·(src|"b/") | 36 | i4·:·makeDirectory·(src|"b/") |
| 37 | i5·:·makeDirectory·(src|"b/c/") | 37 | i5·:·makeDirectory·(src|"b/c/") |
| 38 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 38 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 39 | o6·=·/tmp/M2- | 39 | o6·=·/tmp/M2-2056328-0/0/a/f |
| 40 | o6·:·File | 40 | o6·:·File |
| 41 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 41 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 42 | o7·=·/tmp/M2- | 42 | o7·=·/tmp/M2-2056328-0/0/a/g |
| 43 | o7·:·File | 43 | o7·:·File |
| 44 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 44 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 45 | o8·=·/tmp/M2- | 45 | o8·=·/tmp/M2-2056328-0/0/b/c/g |
| 46 | o8·:·File | 46 | o8·:·File |
| 47 | i9·:·stack·findFiles·src | 47 | i9·:·stack·findFiles·src |
| 48 | o9·=·/tmp/M2- | 48 | o9·=·/tmp/M2-2056328-0/0/ |
| 49 | ·····/tmp/M2- | 49 | ·····/tmp/M2-2056328-0/0/b/ |
| 50 | ·····/tmp/M2- | 50 | ·····/tmp/M2-2056328-0/0/b/c/ |
| 51 | ·····/tmp/M2- | 51 | ·····/tmp/M2-2056328-0/0/b/c/g |
| 52 | ·····/tmp/M2- | 52 | ·····/tmp/M2-2056328-0/0/a/ |
| 53 | ·····/tmp/M2-1012290-0/0/a/g | ||
| 54 | ·····/tmp/M2- | 53 | ·····/tmp/M2-2056328-0/0/a/f |
| 54 | ·····/tmp/M2-2056328-0/0/a/g | ||
| 55 | i10·:·copyDirectory(src,dst,Verbose=>true) | 55 | i10·:·copyDirectory(src,dst,Verbose=>true) |
| 56 | ·--·copying:·/tmp/M2- | 56 | ·--·copying:·/tmp/M2-2056328-0/0/b/c/g·->·/tmp/M2-2056328-0/1/b/c/g |
| 57 | ·--·copying:·/tmp/M2-1012290-0/0/a/g·->·/tmp/M2-1012290-0/1/a/g | ||
| 58 | ·--·copying:·/tmp/M2- | 57 | ·--·copying:·/tmp/M2-2056328-0/0/a/f·->·/tmp/M2-2056328-0/1/a/f |
| 58 | ·--·copying:·/tmp/M2-2056328-0/0/a/g·->·/tmp/M2-2056328-0/1/a/g | ||
| 59 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) | 59 | i11·:·copyDirectory(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 60 | ·--·skipping:·/tmp/M2- | 60 | ·--·skipping:·/tmp/M2-2056328-0/0/b/c/g·not·newer·than·/tmp/M2-2056328-0/1/b/c/ |
| 61 | g | 61 | g |
| 62 | ·--·skipping:·/tmp/M2-1012290-0/0/a/g·not·newer·than·/tmp/M2-1012290-0/1/a/g | ||
| 63 | ·--·skipping:·/tmp/M2- | 62 | ·--·skipping:·/tmp/M2-2056328-0/0/a/f·not·newer·than·/tmp/M2-2056328-0/1/a/f |
| 63 | ·--·skipping:·/tmp/M2-2056328-0/0/a/g·not·newer·than·/tmp/M2-2056328-0/1/a/g | ||
| 64 | i12·:·stack·findFiles·dst | 64 | i12·:·stack·findFiles·dst |
| 65 | o12·=·/tmp/M2- | 65 | o12·=·/tmp/M2-2056328-0/1/ |
| 66 | ······/tmp/M2- | 66 | ······/tmp/M2-2056328-0/1/b/ |
| 67 | ······/tmp/M2- | 67 | ······/tmp/M2-2056328-0/1/b/c/ |
| 68 | ······/tmp/M2- | 68 | ······/tmp/M2-2056328-0/1/b/c/g |
| 69 | ······/tmp/M2- | 69 | ······/tmp/M2-2056328-0/1/a/ |
| 70 | ······/tmp/M2-1012290-0/1/a/g | ||
| 71 | ······/tmp/M2- | 70 | ······/tmp/M2-2056328-0/1/a/f |
| 71 | ······/tmp/M2-2056328-0/1/a/g | ||
| 72 | i13·:·get·(dst|"b/c/g") | 72 | i13·:·get·(dst|"b/c/g") |
| 73 | o13·=·ho·there | 73 | o13·=·ho·there |
| 74 | Now·we·remove·the·files·and·directories·we·created. | 74 | Now·we·remove·the·files·and·directories·we·created. |
| 75 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 75 | i14·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 76 | o14·=·rm | 76 | o14·=·rm |
| Offset 82, 51 lines modified | Offset 82, 51 lines modified | ||
| 82 | ······</div> | 82 | ······</div> |
| 83 | ······<div> | 83 | ······<div> |
| 84 | ········<h2>Description</h2> | 84 | ········<h2>Description</h2> |
| 85 | ········<table·class="examples"> | 85 | ········<table·class="examples"> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() | 87 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() |
| 88 | o1·=·/tmp/M2- | 88 | o1·=·/tmp/M2-2054225-0/0</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() |
| 92 | o2·=·/tmp/M2- | 92 | o2·=·/tmp/M2-2054225-0/1</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close |
| 96 | o3·=·/tmp/M2- | 96 | o3·=·/tmp/M2-2054225-0/0 |
| 97 | o3·:·File</code></pre> | 97 | o3·:·File</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·copyFile(src,dst,Verbose=>true) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·copyFile(src,dst,Verbose=>true) |
| 101 | ·--·copying:·/tmp/M2- | 101 | ·--·copying:·/tmp/M2-2054225-0/0·->·/tmp/M2-2054225-0/1</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst |
| 105 | o5·=·hi·there</code></pre> | 105 | o5·=·hi·there</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 109 | ·--·skipping:·/tmp/M2- | 109 | ·--·skipping:·/tmp/M2-2054225-0/0·not·newer·than·/tmp/M2-2054225-0/1</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·src·<<·"ho·there"·<<·close | 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·src·<<·"ho·there"·<<·close |
| 113 | o7·=·/tmp/M2- | 113 | o7·=·/tmp/M2-2054225-0/0 |
| 114 | o7·:·File</code></pre> | 114 | o7·:·File</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) | 117 | <td>··············<pre><code·class="language-macaulay2">i8·:·copyFile(src,dst,Verbose=>true,UpdateOnly·=>·true) |
| 118 | ·--·skipping:·/tmp/M2- | 118 | ·--·skipping:·/tmp/M2-2054225-0/0·not·newer·than·/tmp/M2-2054225-0/1</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i9·:·get·dst | 121 | <td>··············<pre><code·class="language-macaulay2">i9·:·get·dst |
| 122 | o9·=·hi·there</code></pre> | 122 | o9·=·hi·there</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<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/M2-2054225-0/0 |
| 26 | i2·:·dst·=·temporaryFileName() | 26 | i2·:·dst·=·temporaryFileName() |
| 27 | o2·=·/tmp/M2- | 27 | o2·=·/tmp/M2-2054225-0/1 |
| 28 | i3·:·src·<<·"hi·there"·<<·close | 28 | i3·:·src·<<·"hi·there"·<<·close |
| 29 | o3·=·/tmp/M2- | 29 | o3·=·/tmp/M2-2054225-0/0 |
| 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/M2-2054225-0/0·->·/tmp/M2-2054225-0/1 |
| 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/M2-2054225-0/0·not·newer·than·/tmp/M2-2054225-0/1 |
| 37 | i7·:·src·<<·"ho·there"·<<·close | 37 | i7·:·src·<<·"ho·there"·<<·close |
| 38 | o7·=·/tmp/M2- | 38 | o7·=·/tmp/M2-2054225-0/0 |
| 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/M2-2054225-0/0·not·newer·than·/tmp/M2-2054225-0/1 |
| 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 62, 32 lines modified | Offset 62, 32 lines modified | ||
| 62 | ······</div> | 62 | ······</div> |
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·t1·=·cpuTime() | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·t1·=·cpuTime() |
| 68 | o1·=·1 | 68 | o1·=·159.794932719 |
| 69 | o1·:·RR·(of·precision·53)</code></pre> | 69 | o1·:·RR·(of·precision·53)</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;</code></pre> | 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·from·0·to·1000000·do·223131321321*324234324324;</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i3·:·t2·=·cpuTime() | 75 | <td>··············<pre><code·class="language-macaulay2">i3·:·t2·=·cpuTime() |
| 76 | o3·=·1 | 76 | o3·=·160.414254675 |
| 77 | o3·:·RR·(of·precision·53)</code></pre> | 77 | o3·:·RR·(of·precision·53)</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i4·:·t2-t1 | 80 | <td>··············<pre><code·class="language-macaulay2">i4·:·t2-t1 |
| 81 | o4·=·.6 | 81 | o4·=·.619321955999993 |
| 82 | o4·:·RR·(of·precision·53)</code></pre> | 82 | o4·:·RR·(of·precision·53)</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ········</table> | 84 | ········</table> |
| 85 | ······</div> | 85 | ······</div> |
| 86 | ······<div> | 86 | ······<div> |
| 87 | ········<h2>See·also</h2> | 87 | ········<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·=·1 | 15 | o1·=·159.794932719 |
| 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·=·1 | 19 | o3·=·160.414254675 |
| 20 | o3·:·RR·(of·precision·53) | 20 | o3·:·RR·(of·precision·53) |
| 21 | i4·:·t2-t1 | 21 | i4·:·t2-t1 |
| 22 | o4·=·.6 | 22 | o4·=·.619321955999993 |
| 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* |
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| 62 | ······</div> | 62 | ······</div> |
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime() | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime() |
| 68 | o1·=·17 | 68 | o1·=·1729001958</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ········</table> | 70 | ········</table> |
| 71 | ········<p>We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.</p> | 71 | ········<p>We·can·compute,·roughly,·how·many·years·ago·the·epoch·began·as·follows.</p> |
| 72 | ········<table·class="examples"> | 72 | ········<table·class="examples"> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) | 74 | <td>··············<pre><code·class="language-macaulay2">i2·:·currentTime()·/(·(365·+·97./400)·*·24·*·60·*·60·) |
| 75 | o2·=·5 | 75 | o2·=·54.789890924827 |
| 76 | o2·:·RR·(of·precision·53)</code></pre> | 76 | o2·:·RR·(of·precision·53)</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ········</table> | 78 | ········</table> |
| 79 | ········<p>We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that·number.</p> | 79 | ········<p>We·can·also·compute·how·many·months·account·for·the·fractional·part·of·that·number.</p> |
| 80 | ········<table·class="examples"> | 80 | ········<table·class="examples"> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·12·*·(oo·-·floor·oo) | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·12·*·(oo·-·floor·oo) |
| 83 | o3·=· | 83 | o3·=·9.47869109792364 |
| 84 | o3·:·RR·(of·precision·53)</code></pre> | 84 | o3·:·RR·(of·precision·53)</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ········</table> | 86 | ········</table> |
| 87 | ········<p>Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.</p> | 87 | ········<p>Compare·that·to·the·current·date,·available·from·a·standard·Unix·command.</p> |
| 88 | ········<table·class="examples"> | 88 | ········<table·class="examples"> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·run·"date" | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·run·"date" |
| 91 | 91 | Wed·Oct·16·04:19:18·+14·2024 | |
| 92 | o4·=·0</code></pre> | 92 | o4·=·0</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ········</table> | 94 | ········</table> |
| 95 | ······</div> | 95 | ······</div> |
| 96 | ······<div·class="waystouse"> | 96 | ······<div·class="waystouse"> |
| 97 | ········<h2>For·the·programmer</h2> | 97 | ········<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·=·1729001958 |
| 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·=·54.789890924827 |
| 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·=· | 23 | o3·=·9.47869109792364 |
| 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·Oct·16·04:19:18·+14·2024 | |
| 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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| 55 | ········</ul> | 55 | ········</ul> |
| 56 | ······</div> | 56 | ······</div> |
| 57 | ······<div> | 57 | ······<div> |
| 58 | ········<h2>Description</h2> | 58 | ········<h2>Description</h2> |
| 59 | <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 | <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"> |
| 60 | ··········<tr> | 60 | ··········<tr> |
| 61 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·sleep·1 | 61 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·sleep·1 |
| 62 | ·--·1.00 | 62 | ·--·1.00011·seconds·elapsed |
| 63 | o1·=·0</code></pre> | 63 | o1·=·0</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ········</table> | 65 | ········</table> |
| 66 | ······</div> | 66 | ······</div> |
| 67 | ······<div> | 67 | ······<div> |
| 68 | ········<h2>See·also</h2> | 68 | ········<h2>See·also</h2> |
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| 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 | ·--·1.00 | 15 | ·--·1.00011·seconds·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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| 47 | ········<h2>Description</h2> | 47 | ········<h2>Description</h2> |
| 48 | <span·class="tt">elapsedTiming·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·time·elapsed,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p> | 48 | <span·class="tt">elapsedTiming·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·time·elapsed,·and·<span·class="tt">v</span>·is·the·value·of·the·expression.········<p></p> |
| 49 | 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 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples"> |
| 50 | ··········<tr> | 50 | ··········<tr> |
| 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTiming·sleep·1 | 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTiming·sleep·1 |
| 52 | o1·=·0 | 52 | o1·=·0 |
| 53 | ·····--·1.0001·seconds | 53 | ·····--·1.00014·seconds |
| 54 | o1·:·Time</code></pre> | 54 | o1·:·Time</code></pre> |
| 55 | </td>··········</tr> | 55 | </td>··········</tr> |
| 56 | ··········<tr> | 56 | ··········<tr> |
| 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·oo | 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·oo |
| 58 | o2·=·Time{1.0001,·0}</code></pre> | 58 | o2·=·Time{1.00014,·0}</code></pre> |
| 59 | </td>··········</tr> | 59 | </td>··········</tr> |
| 60 | ········</table> | 60 | ········</table> |
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>See·also</h2> | 63 | ········<h2>See·also</h2> |
| 64 | ········<ul> | 64 | ········<ul> |
| 65 | ··········<li> | 65 | ··········<li> |
| Offset 10, 20 lines modified | Offset 10, 20 lines modified | ||
| 10 | where·t·is·the·number·of·seconds·of·time·elapsed,·and·v·is·the·value·of·the | 10 | where·t·is·the·number·of·seconds·of·time·elapsed,·and·v·is·the·value·of·the |
| 11 | expression. | 11 | expression. |
| 12 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing | 12 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing |
| 13 | separately·in·a·comment·below·the·computed·value. | 13 | separately·in·a·comment·below·the·computed·value. |
| 14 | i1·:·elapsedTiming·sleep·1 | 14 | i1·:·elapsedTiming·sleep·1 |
| 15 | o1·=·0 | 15 | o1·=·0 |
| 16 | ·····--·1.0001·seconds | 16 | ·····--·1.00014·seconds |
| 17 | o1·:·Time | 17 | o1·:·Time |
| 18 | i2·:·peek·oo | 18 | i2·:·peek·oo |
| 19 | o2·=·Time{1.0001,·0} | 19 | o2·=·Time{1.00014,·0} |
| 20 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 20 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 21 | ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results | 21 | ····*·_\x8T_\x8i_\x8m_\x8e·--·the·class·of·all·timing·results |
| 22 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed | 22 | ····*·_\x8e_\x8l_\x8a_\x8p_\x8s_\x8e_\x8d_\x8T_\x8i_\x8m_\x8e·--·time·a·computation·including·time·elapsed |
| 23 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began | 23 | ····*·_\x8c_\x8p_\x8u_\x8T_\x8i_\x8m_\x8e·--·seconds·of·cpu·time·used·since·Macaulay2·began |
| 24 | ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation | 24 | ····*·_\x8t_\x8i_\x8m_\x8i_\x8n_\x8g·--·time·a·computation |
| 25 | ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation | 25 | ····*·_\x8t_\x8i_\x8m_\x8e·--·time·a·computation |
| 26 | *\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* | 26 | *\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 54, 15 lines modified | Offset 54, 15 lines modified | ||
| 54 | ···············3···················3·····2···············3 | 54 | ···············3···················3·····2···············3 |
| 55 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) | 55 | o2·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··-·t·+·y,·-·s*t··+·z) |
| 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·leadTerm·gens·gb·I | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·leadTerm·gens·gb·I |
| 60 | ·--·used·0.1 | 60 | ·--·used·0.105049s·(cpu);·0.10505s·(thread);·0s·(gc) |
| 61 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 | 61 | o3·=·|·x3y9·5148txy3·108729sxy2z2·sy4z·46644741sxy3z·143sy5·6sxy4 |
| 62 | ·····------------------------------------------------------------------------ | 62 | ·····------------------------------------------------------------------------ |
| 63 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 | 63 | ·····563515116021sx2y3·4374txy2z3·612704350498473090tx2yz3·217458ty4z2 |
| 64 | ·····------------------------------------------------------------------------ | 64 | ·····------------------------------------------------------------------------ |
| 65 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 | 65 | ·····267076255345488270sy3z4·5256861933965245618410txyz6 |
| 66 | ·····------------------------------------------------------------------------ | 66 | ·····------------------------------------------------------------------------ |
| Offset 141, 15 lines modified | Offset 141, 15 lines modified | ||
| 141 | ···············3···················3·····2···············3 | 141 | ···············3···················3·····2···············3 |
| 142 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) | 142 | o7·=·ideal·(-·s··-·s*t·+·x·-·1,·-·t··-·3t··+·y·-·t,·-·s*t··+·z) |
| 143 | o7·:·Ideal·of·R</code></pre> | 143 | o7·:·Ideal·of·R</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·G·=·eliminate(I,{s,t}) | 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·G·=·eliminate(I,{s,t}) |
| 147 | ·--·used·0.1 | 147 | ·--·used·0.104572s·(cpu);·0.104574s·(thread);·0s·(gc) |
| 148 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· | 148 | ············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· |
| 149 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 149 | o8·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 150 | ·····------------------------------------------------------------------------ | 150 | ·····------------------------------------------------------------------------ |
| 151 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· | 151 | ·········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· |
| 152 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 152 | ·····7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 153 | ·····------------------------------------------------------------------------ | 153 | ·····------------------------------------------------------------------------ |
| Offset 216, 15 lines modified | Offset 216, 15 lines modified | ||
| 216 | ··········<tr> | 216 | ··········<tr> |
| 217 | <td>··············<pre><code·class="language-macaulay2">i11·:·I1·=·substitute(I,R1); | 217 | <td>··············<pre><code·class="language-macaulay2">i11·:·I1·=·substitute(I,R1); |
| 218 | o11·:·Ideal·of·R1</code></pre> | 218 | o11·:·Ideal·of·R1</code></pre> |
| 219 | </td>··········</tr> | 219 | </td>··········</tr> |
| 220 | ··········<tr> | 220 | ··········<tr> |
| 221 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·G·=·eliminate(I1,{s,t}) | 221 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·G·=·eliminate(I1,{s,t}) |
| 222 | ·--·used·0.05 | 222 | ·--·used·0.0354315s·(cpu);·0.0354377s·(thread);·0s·(gc) |
| 223 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7·· | 223 | ·············3·9·····2·6·3·······3·6····9·····2·8·········5·4······2·7·· |
| 224 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- | 224 | o12·=·ideal(x·y··-·3x·y·z··+·3x*y·z··-·z··-·6x·y·z·-·15x*y·z··+·21y·z··- |
| 225 | ······----------------------------------------------------------------------- | 225 | ······----------------------------------------------------------------------- |
| 226 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2·· | 226 | ········2·9·······2·5·3·······6·3····7·3·········2·6·····3·6·······7·2·· |
| 227 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- | 227 | ······3x·y··-·324x·y·z··+·6x*y·z··-·y·z··-·405x*y·z··-·3y·z··+·7x*y·z··- |
| 228 | ······----------------------------------------------------------------------- | 228 | ······----------------------------------------------------------------------- |
| Offset 298, 15 lines modified | Offset 298, 15 lines modified | ||
| 298 | ···················3·············3·····2·········3 | 298 | ···················3·············3·····2·········3 |
| 299 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) | 299 | o16·=·map·(A,·B,·{s··+·s*t·+·1,·t··+·3t··+·t,·s*t·}) |
| 300 | o16·:·RingMap·A·<--·B</code></pre> | 300 | o16·:·RingMap·A·<--·B</code></pre> |
| 301 | </td>··········</tr> | 301 | </td>··········</tr> |
| 302 | ··········<tr> | 302 | ··········<tr> |
| 303 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·G·=·kernel·F | 303 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·G·=·kernel·F |
| 304 | ·--·used·0. | 304 | ·--·used·0.296242s·(cpu);·0.138084s·(thread);·0s·(gc) |
| 305 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· | 305 | ·············3·9·····2·9·····2·8······2·6·3·······9····2·7·········8··· |
| 306 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ | 306 | o17·=·ideal(x·y··-·3x·y··-·6x·y·z·-·3x·y·z··+·3x*y··-·x·y·z·+·12x*y·z·+ |
| 307 | ······----------------------------------------------------------------------- | 307 | ······----------------------------------------------------------------------- |
| 308 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· | 308 | ··········7·2·······2·5·3·······6·3····7·3········5·4·······3·6····9·······7· |
| 309 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z | 309 | ······7x*y·z··-·324x·y·z··+·6x*y·z··-·y·z··-·15x*y·z··+·3x*y·z··-·y··+·2x*y·z |
| 310 | ······----------------------------------------------------------------------- | 310 | ······----------------------------------------------------------------------- |
| Offset 373, 24 lines modified | Offset 373, 24 lines modified | ||
| 373 | o19·=·R | 373 | o19·=·R |
| 374 | o19·:·PolynomialRing</code></pre> | 374 | o19·:·PolynomialRing</code></pre> |
| 375 | </td>··········</tr> | 375 | </td>··········</tr> |
| 376 | ··········<tr> | 376 | ··········<tr> |
| 377 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·f1·=·resultant(I_0,I_2,s) | 377 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·f1·=·resultant(I_0,I_2,s) |
| 378 | ·--·used·0.001 | 378 | ·--·used·0.00144408s·(cpu);·0.00144045s·(thread);·0s·(gc) |
| 379 | ·········9····9······7····3 | 379 | ·········9····9······7····3 |
| 380 | o20·=·x*t··-·t··-·z*t··-·z | 380 | o20·=·x*t··-·t··-·z*t··-·z |
| 381 | o20·:·R</code></pre> | 381 | o20·:·R</code></pre> |
| 382 | </td>··········</tr> | 382 | </td>··········</tr> |
| 383 | ··········<tr> | 383 | ··········<tr> |
| 384 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f2·=·resultant(I_1,f1,t) | 384 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·f2·=·resultant(I_1,f1,t) |
| 385 | ·--·used·0.0 | 385 | ·--·used·0.0376776s·(cpu);·0.0376885s·(thread);·0s·(gc) |
| 386 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2·· | 386 | ·········3·9·····2·9·····2·8······2·6·3·······9····2·7·········8········7·2·· |
| 387 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ | 387 | o21·=·-·x·y··+·3x·y··+·6x·y·z·+·3x·y·z··-·3x*y··+·x·y·z·-·12x*y·z·-·7x*y·z··+ |
| 388 | ······----------------------------------------------------------------------- | 388 | ······----------------------------------------------------------------------- |
| 389 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8··· | 389 | ··········2·5·3·······6·3····7·3········5·4·······3·6····9·······7······8··· |
| 390 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ | 390 | ······324x·y·z··-·6x*y·z··+·y·z··+·15x*y·z··-·3x*y·z··+·y··-·2x*y·z·+·6y·z·+ |
| 391 | ······----------------------------------------------------------------------- | 391 | ······----------------------------------------------------------------------- |
| 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·0.1 | 18 | ·--·used·0.105049s·(cpu);·0.10505s·(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·0.1 | 94 | ·--·used·0.104572s·(cpu);·0.104574s·(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·0.05 | 162 | ·--·used·0.0354315s·(cpu);·0.0354377s·(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·0.296242s·(cpu);·0.138084s·(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·0.001 | 301 | ·--·used·0.00144408s·(cpu);·0.00144045s·(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·0.0376776s·(cpu);·0.0376885s·(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 145, 15 lines modified | Offset 145, 15 lines modified | ||
| 145 | ····································Version·=>·0.0 | 145 | ····································Version·=>·0.0 |
| 146 | ·············package·prefix·=>·/usr/ | 146 | ·············package·prefix·=>·/usr/ |
| 147 | ·············PackageIsLoaded·=>·true | 147 | ·············PackageIsLoaded·=>·true |
| 148 | ·············pkgname·=>·Foo | 148 | ·············pkgname·=>·Foo |
| 149 | ·············private·dictionary·=>·Foo#"private·dictionary" | 149 | ·············private·dictionary·=>·Foo#"private·dictionary" |
| 150 | ·············processed·documentation·=>·MutableHashTable{} | 150 | ·············processed·documentation·=>·MutableHashTable{} |
| 151 | ·············raw·documentation·=>·MutableHashTable{} | 151 | ·············raw·documentation·=>·MutableHashTable{} |
| 152 | ·············source·directory·=>·/tmp/M2- | 152 | ·············source·directory·=>·/tmp/M2-2031929-0/85-rundir/ |
| 153 | ·············source·file·=>·stdio | 153 | ·············source·file·=>·stdio |
| 154 | ·············test·inputs·=>·MutableHashTable{} | 154 | ·············test·inputs·=>·MutableHashTable{} |
| 155 | ·············test·number·=>·0 | 155 | ·············test·number·=>·0 |
| 156 | ·············undocumented·keys·=>·MutableHashTable{}</code></pre> | 156 | ·············undocumented·keys·=>·MutableHashTable{}</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i7·:·dictionaryPath | 159 | <td>··············<pre><code·class="language-macaulay2">i7·:·dictionaryPath |
| 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/M2-2031929-0/85-rundir/ |
| 86 | ·············source·file·=>·stdio | 86 | ·············source·file·=>·stdio |
| 87 | ·············test·inputs·=>·MutableHashTable{} | 87 | ·············test·inputs·=>·MutableHashTable{} |
| 88 | ·············test·number·=>·0 | 88 | ·············test·number·=>·0 |
| 89 | ·············undocumented·keys·=>·MutableHashTable{} | 89 | ·············undocumented·keys·=>·MutableHashTable{} |
| 90 | i7·:·dictionaryPath | 90 | i7·:·dictionaryPath |
| 91 | o7·=·{Foo.Dictionary,·Varieties.Dictionary,·Truncations.Dictionary, | 91 | o7·=·{Foo.Dictionary,·Varieties.Dictionary,·Truncations.Dictionary, |
| Offset 68, 25 lines modified | Offset 68, 25 lines modified | ||
| 68 | ······</div> | 68 | ······</div> |
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 74 | o1·=·/tmp/M2- | 74 | o1·=·/tmp/M2-2038261-0/0</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileExists·fn | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileExists·fn |
| 78 | o2·=·false</code></pre> | 78 | o2·=·false</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close |
| 82 | o3·=·/tmp/M2- | 82 | o3·=·/tmp/M2-2038261-0/0 |
| 83 | o3·:·File</code></pre> | 83 | o3·:·File</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·fileExists·fn | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·fileExists·fn |
| 87 | o4·=·true</code></pre> | 87 | 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/M2-2038261-0/0 |
| 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/M2-2038261-0/0 |
| 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 69, 34 lines modified | Offset 69, 34 lines modified | ||
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | ········<p>The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the·number·of·bytes·written·so·far.</p> | 71 | ········<p>The·length·of·an·open·output·file·is·determined·from·the·internal·count·of·the·number·of·bytes·written·so·far.</p> |
| 72 | ········<table·class="examples"> | 72 | ········<table·class="examples"> |
| 73 | ··········<tr> | 73 | ··········<tr> |
| 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·temporaryFileName()·<<·"hi·there" | 74 | <td>··············<pre><code·class="language-macaulay2">i1·:·f·=·temporaryFileName()·<<·"hi·there" |
| 75 | o1·=·/tmp/M2- | 75 | o1·=·/tmp/M2-2070590-0/0 |
| 76 | o1·:·File</code></pre> | 76 | o1·:·File</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileLength·f | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·fileLength·f |
| 80 | o2·=·8</code></pre> | 80 | o2·=·8</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·close·f | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·close·f |
| 84 | o3·=·/tmp/M2- | 84 | o3·=·/tmp/M2-2070590-0/0 |
| 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·:·filename·=·toString·f | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·filename·=·toString·f |
| 89 | o4·=·/tmp/M2- | 89 | o4·=·/tmp/M2-2070590-0/0</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileLength·filename | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileLength·filename |
| 93 | o5·=·8</code></pre> | 93 | o5·=·8</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<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/M2-2070590-0/0 |
| 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/M2-2070590-0/0 |
| 24 | o3·:·File | 24 | o3·:·File |
| 25 | i4·:·filename·=·toString·f | 25 | i4·:·filename·=·toString·f |
| 26 | o4·=·/tmp/M2- | 26 | o4·=·/tmp/M2-2070590-0/0 |
| 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 70, 32 lines modified | Offset 70, 32 lines modified | ||
| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 76 | o1·=·/tmp/M2- | 76 | o1·=·/tmp/M2-2060644-0/0</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" |
| 80 | o2·=·/tmp/M2- | 80 | o2·=·/tmp/M2-2060644-0/0 |
| 81 | o2·:·File</code></pre> | 81 | o2·:·File</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·f | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·f |
| 85 | o3·=·420</code></pre> | 85 | o3·=·420</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·close·f | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·close·f |
| 89 | o4·=·/tmp/M2- | 89 | o4·=·/tmp/M2-2060644-0/0 |
| 90 | o4·:·File</code></pre> | 90 | o4·:·File</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre> | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·removeFile·fn</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ········</table> | 95 | ········</table> |
| Offset 11, 24 lines modified | Offset 11, 24 lines modified | ||
| 11 | ····*·Inputs: | 11 | ····*·Inputs: |
| 12 | ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e | 12 | ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e |
| 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/M2-2060644-0/0 |
| 18 | i2·:·f·=·fn·<<·"hi·there" | 18 | i2·:·f·=·fn·<<·"hi·there" |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-2060644-0/0 |
| 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/M2-2060644-0/0 |
| 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 70, 20 lines modified | Offset 70, 20 lines modified | ||
| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 73 | ········<table·class="examples"> | 73 | ········<table·class="examples"> |
| 74 | ··········<tr> | 74 | ··········<tr> |
| 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 75 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 76 | o1·=·/tmp/M2- | 76 | o1·=·/tmp/M2-2054394-0/0</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close |
| 80 | o2·=·/tmp/M2- | 80 | o2·=·/tmp/M2-2054394-0/0 |
| 81 | o2·:·File</code></pre> | 81 | o2·:·File</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·fn | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileMode·fn |
| 85 | o3·=·420</code></pre> | 85 | o3·=·420</code></pre> |
| Offset 11, 18 lines modified | Offset 11, 18 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·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·the·mode·of·the·file·located·at·the·filename·or·path·fn | 14 | ··········o·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r,·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/M2-2054394-0/0 |
| 18 | i2·:·fn·<<·"hi·there"·<<·close | 18 | i2·:·fn·<<·"hi·there"·<<·close |
| 19 | o2·=·/tmp/M2- | 19 | o2·=·/tmp/M2-2054394-0/0 |
| 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 74, 20 lines modified | Offset 74, 20 lines modified | ||
| 74 | ······</div> | 74 | ······</div> |
| 75 | ······<div> | 75 | ······<div> |
| 76 | ········<h2>Description</h2> | 76 | ········<h2>Description</h2> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 80 | o1·=·/tmp/M2- | 80 | o1·=·/tmp/M2-2052463-0/0</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·f·=·fn·<<·"hi·there" |
| 84 | o2·=·/tmp/M2- | 84 | o2·=·/tmp/M2-2052463-0/0 |
| 85 | o2·:·File</code></pre> | 85 | o2·:·File</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·7·+·7*8·+·7*64 | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·7·+·7*8·+·7*64 |
| 89 | o3·=·511</code></pre> | 89 | o3·=·511</code></pre> |
| Offset 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileMode·f | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·fileMode·f |
| 100 | o5·=·511</code></pre> | 100 | o5·=·511</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·close·f | 103 | <td>··············<pre><code·class="language-macaulay2">i6·:·close·f |
| 104 | o6·=·/tmp/M2- | 104 | o6·=·/tmp/M2-2052463-0/0 |
| 105 | o6·:·File</code></pre> | 105 | o6·:·File</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·fileMode·fn | 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·fileMode·fn |
| 109 | o7·=·511</code></pre> | 109 | o7·=·511</code></pre> |
| Offset 12, 30 lines modified | Offset 12, 30 lines modified | ||
| 12 | ··········o·mo,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r | 12 | ··········o·mo,·an·_\x8i_\x8n_\x8t_\x8e_\x8g_\x8e_\x8r |
| 13 | ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e | 13 | ··········o·f,·a·_\x8f_\x8i_\x8l_\x8e |
| 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/M2-2052463-0/0 |
| 19 | i2·:·f·=·fn·<<·"hi·there" | 19 | i2·:·f·=·fn·<<·"hi·there" |
| 20 | o2·=·/tmp/M2- | 20 | o2·=·/tmp/M2-2052463-0/0 |
| 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/M2-2052463-0/0 |
| 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 74, 20 lines modified | Offset 74, 20 lines modified | ||
| 74 | ······</div> | 74 | ······</div> |
| 75 | ······<div> | 75 | ······<div> |
| 76 | ········<h2>Description</h2> | 76 | ········<h2>Description</h2> |
| 77 | ········<table·class="examples"> | 77 | ········<table·class="examples"> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 79 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 80 | o1·=·/tmp/M2- | 80 | o1·=·/tmp/M2-2070121-0/0</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close |
| 84 | o2·=·/tmp/M2- | 84 | o2·=·/tmp/M2-2070121-0/0 |
| 85 | o2·:·File</code></pre> | 85 | o2·:·File</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·fileMode·fn | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·m·=·fileMode·fn |
| 89 | o3·=·420</code></pre> | 89 | o3·=·420</code></pre> |
| Offset 13, 18 lines modified | Offset 13, 18 lines modified | ||
| 13 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g | 13 | ··········o·fn,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g |
| 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/M2-2070121-0/0 |
| 20 | i2·:·fn·<<·"hi·there"·<<·close | 20 | i2·:·fn·<<·"hi·there"·<<·close |
| 21 | o2·=·/tmp/M2- | 21 | o2·=·/tmp/M2-2070121-0/0 |
| 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 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | ······</div> | 78 | ······</div> |
| 79 | ······<div> | 79 | ······<div> |
| 80 | ········<h2>Description</h2> | 80 | ········<h2>Description</h2> |
| 81 | 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 | 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"> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime()·-·fileTime·"." | 83 | <td>··············<pre><code·class="language-macaulay2">i1·:·currentTime()·-·fileTime·"." |
| 84 | o1·=· | 84 | o1·=·26</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> |
| 90 | ········<ul> | 90 | ········<ul> |
| 91 | ··········<li> | 91 | ··········<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·=·26 |
| 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 107, 15 lines modified | Offset 107, 15 lines modified | ||
| 107 | ·············3······3 | 107 | ·············3······3 |
| 108 | o6·:·Matrix·R··<--·R</code></pre> | 108 | o6·:·Matrix·R··<--·R</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·syz·f | 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·syz·f |
| 112 | ···--·registering·gb·0·at·0x7f | 112 | ···--·registering·gb·0·at·0x7f053d79f700 |
| 113 | ···--·[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 | ···--·[gb]{2}(1)m{3}(1)m{4}(1)m{5}(1)z{6}(1)z{7}(1)znumber·of·(nonminimal)·gb·elements·=·3 |
| 114 | ···--·number·of·monomials················=·9 | 114 | ···--·number·of·monomials················=·9 |
| 115 | ···--·#reduction·steps·=·6 | 115 | ···--·#reduction·steps·=·6 |
| 116 | ···--·#spairs·done·=·6 | 116 | ···--·#spairs·done·=·6 |
| 117 | ···--·ncalls·=·0 | 117 | ···--·ncalls·=·0 |
| 118 | ···--·nloop·=·0 | 118 | ···--·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·0x7f053d79f700 |
| 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 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">i3·:·removeFile·"test-file"</code></pre> | 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeFile·"test-file"</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·get·"!date" | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·get·"!date" |
| 97 | o4·=· | 97 | o4·=·Wed·Oct·16·04:18:55·+14·2024</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> |
| 103 | ········<ul> | 103 | ········<ul> |
| 104 | ··········<li> | 104 | ··········<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·Oct·16·04:18:55·+14·2024 |
| 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 62, 15 lines modified | Offset 62, 15 lines modified | ||
| 62 | ······</div> | 62 | ······</div> |
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·groupID() | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·groupID() |
| 68 | o1·=·5 | 68 | o1·=·1596170</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ········</table> | 70 | ········</table> |
| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>See·also</h2> | 73 | ········<h2>See·also</h2> |
| 74 | ········<ul> | 74 | ········<ul> |
| 75 | ··········<li> | 75 | ··········<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·=·5 | 15 | o1·=·1596170 |
| 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 73, 20 lines modified | Offset 73, 20 lines modified | ||
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·isDirectory·"." | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·isDirectory·"." |
| 74 | o1·=·true</code></pre> | 74 | o1·=·true</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·=·temporaryFileName() | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·=·temporaryFileName() |
| 78 | o2·=·/tmp/M2- | 78 | o2·=·/tmp/M2-2035704-0/0</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn·<<·"hi·there"·<<·close |
| 82 | o3·=·/tmp/M2- | 82 | o3·=·/tmp/M2-2035704-0/0 |
| 83 | o3·:·File</code></pre> | 83 | o3·:·File</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·isDirectory·fn | 86 | <td>··············<pre><code·class="language-macaulay2">i4·:·isDirectory·fn |
| 87 | o4·=·false</code></pre> | 87 | 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/M2-2035704-0/0 |
| 20 | i3·:·fn·<<·"hi·there"·<<·close | 20 | i3·:·fn·<<·"hi·there"·<<·close |
| 21 | o3·=·/tmp/M2- | 21 | o3·=·/tmp/M2-2035704-0/0 |
| 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 176, 15 lines modified | Offset 176, 15 lines modified | ||
| 176 | ··········<tr> | 176 | ··········<tr> |
| 177 | <td>··············<pre><code·class="language-macaulay2">i18·:·isPrime(m*m*m1*m1*m2^6) | 177 | <td>··············<pre><code·class="language-macaulay2">i18·:·isPrime(m*m*m1*m1*m2^6) |
| 178 | o18·=·false</code></pre> | 178 | o18·=·false</code></pre> |
| 179 | </td>··········</tr> | 179 | </td>··········</tr> |
| 180 | ··········<tr> | 180 | ··········<tr> |
| 181 | <td>··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·facs·=·factor(m*m1) | 181 | <td>··············<pre><code·class="language-macaulay2">i19·:·elapsedTime·facs·=·factor(m*m1) |
| 182 | ·--· | 182 | ·--·3.95259·seconds·elapsed |
| 183 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 | 183 | o19·=·1000000000000000000000000000057*1000000000000000000010000000083 |
| 184 | o19·:·Expression·of·class·Product</code></pre> | 184 | o19·:·Expression·of·class·Product</code></pre> |
| 185 | </td>··········</tr> | 185 | </td>··········</tr> |
| 186 | ··········<tr> | 186 | ··········<tr> |
| 187 | <td>··············<pre><code·class="language-macaulay2">i20·:·facs·=·facs//toList/toList | 187 | <td>··············<pre><code·class="language-macaulay2">i20·:·facs·=·facs//toList/toList |
| Offset 202, 21 lines modified | Offset 202, 21 lines modified | ||
| 202 | <td>··············<pre><code·class="language-macaulay2">i22·:·m3·=·nextPrime·(m^3) | 202 | <td>··············<pre><code·class="language-macaulay2">i22·:·m3·=·nextPrime·(m^3) |
| 203 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 | 203 | o22·=·10000000000000000000000000001710000000000000000000000000097470000000000 |
| 204 | ······00000000000000185613</code></pre> | 204 | ······00000000000000185613</code></pre> |
| 205 | </td>··········</tr> | 205 | </td>··········</tr> |
| 206 | ··········<tr> | 206 | ··········<tr> |
| 207 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·m3 | 207 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·m3 |
| 208 | ·--·0.04 | 208 | ·--·0.0479405·seconds·elapsed |
| 209 | o23·=·true</code></pre> | 209 | o23·=·true</code></pre> |
| 210 | </td>··········</tr> | 210 | </td>··········</tr> |
| 211 | ··········<tr> | 211 | ··········<tr> |
| 212 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isPseudoprime·m3 | 212 | <td>··············<pre><code·class="language-macaulay2">i24·:·elapsedTime·isPseudoprime·m3 |
| 213 | ·--·0.0001 | 213 | ·--·0.000146612·seconds·elapsed |
| 214 | o24·=·true</code></pre> | 214 | o24·=·true</code></pre> |
| 215 | </td>··········</tr> | 215 | </td>··········</tr> |
| 216 | ········</table> | 216 | ········</table> |
| 217 | ······</div> | 217 | ······</div> |
| 218 | ······<div> | 218 | ······<div> |
| 219 | ········<h2>See·also</h2> | 219 | ········<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 | ·--·3.95259·seconds·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 | ·--·0.04 | 104 | ·--·0.0479405·seconds·elapsed |
| 105 | o23·=·true | 105 | o23·=·true |
| 106 | i24·:·elapsedTime·isPseudoprime·m3 | 106 | i24·:·elapsedTime·isPseudoprime·m3 |
| 107 | ·--·0.0001 | 107 | ·--·0.000146612·seconds·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 68, 20 lines modified | Offset 68, 20 lines modified | ||
| 68 | ······</div> | 68 | ······</div> |
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | 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 | 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"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 74 | o1·=·/tmp/M2- | 74 | o1·=·/tmp/M2-2070887-0/0</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn·<<·"hi·there"·<<·close |
| 78 | o2·=·/tmp/M2- | 78 | o2·=·/tmp/M2-2070887-0/0 |
| 79 | o2·:·File</code></pre> | 79 | o2·:·File</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·isRegularFile·fn | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·isRegularFile·fn |
| 83 | o3·=·true</code></pre> | 83 | 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/M2-2070887-0/0 |
| 21 | i2·:·fn·<<·"hi·there"·<<·close | 21 | i2·:·fn·<<·"hi·there"·<<·close |
| 22 | o2·=·/tmp/M2- | 22 | o2·=·/tmp/M2-2070887-0/0 |
| 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 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | ······</div> | 72 | ······</div> |
| 73 | ······<div> | 73 | ······<div> |
| 74 | ········<h2>Description</h2> | 74 | ········<h2>Description</h2> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() |
| 78 | o1·=·/tmp/M2- | 78 | o1·=·/tmp/M2-2050248-0/0</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·(dir|"/a/b/c")</code></pre> | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·(dir|"/a/b/c")</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeDirectory·(dir|"/a/b/c")</code></pre> | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·removeDirectory·(dir|"/a/b/c")</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| Offset 12, 15 lines modified | Offset 12, 15 lines modified | ||
| 12 | ····*·Inputs: | 12 | ····*·Inputs: |
| 13 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·path·to·the·desired·directory | 13 | ··········o·dir,·a·_\x8s_\x8t_\x8r_\x8i_\x8n_\x8g,·a·path·to·the·desired·directory |
| 14 | ····*·Consequences: | 14 | ····*·Consequences: |
| 15 | ··········o·the·directory·is·made,·with·as·many·new·path·components·as·needed | 15 | ··········o·the·directory·is·made,·with·as·many·new·path·components·as·needed |
| 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·:·dir·=·temporaryFileName() | 17 | i1·:·dir·=·temporaryFileName() |
| 18 | o1·=·/tmp/M2- | 18 | o1·=·/tmp/M2-2050248-0/0 |
| 19 | i2·:·makeDirectory·(dir|"/a/b/c") | 19 | i2·:·makeDirectory·(dir|"/a/b/c") |
| 20 | i3·:·removeDirectory·(dir|"/a/b/c") | 20 | i3·:·removeDirectory·(dir|"/a/b/c") |
| 21 | i4·:·removeDirectory·(dir|"/a/b") | 21 | i4·:·removeDirectory·(dir|"/a/b") |
| 22 | i5·:·removeDirectory·(dir|"/a") | 22 | i5·:·removeDirectory·(dir|"/a") |
| 23 | A·filename·starting·with·~/·will·have·the·tilde·replaced·by·the·home·directory. | 23 | A·filename·starting·with·~/·will·have·the·tilde·replaced·by·the·home·directory. |
| 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 | ····*·_\x8m_\x8k_\x8d_\x8i_\x8r | 25 | ····*·_\x8m_\x8k_\x8d_\x8i_\x8r |
| Offset 52, 34 lines modified | Offset 52, 34 lines modified | ||
| 52 | o1·=·fib | 52 | o1·=·fib |
| 53 | o1·:·FunctionClosure</code></pre> | 53 | o1·:·FunctionClosure</code></pre> |
| 54 | </td>··········</tr> | 54 | </td>··········</tr> |
| 55 | ··········<tr> | 55 | ··········<tr> |
| 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fib·28 | 56 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fib·28 |
| 57 | ·--·used·0. | 57 | ·--·used·0.657994s·(cpu);·0.507226s·(thread);·0s·(gc) |
| 58 | o2·=·514229</code></pre> | 58 | o2·=·514229</code></pre> |
| 59 | </td>··········</tr> | 59 | </td>··········</tr> |
| 60 | ··········<tr> | 60 | ··········<tr> |
| 61 | <td>··············<pre><code·class="language-macaulay2">i3·:·fib·=·memoize·fib | 61 | <td>··············<pre><code·class="language-macaulay2">i3·:·fib·=·memoize·fib |
| 62 | o3·=·fib | 62 | o3·=·fib |
| 63 | o3·:·FunctionClosure</code></pre> | 63 | o3·:·FunctionClosure</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·fib·28 | 66 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·fib·28 |
| 67 | ·--·used· | 67 | ·--·used·4.4226e-05s·(cpu);·4.3806e-05s·(thread);·0s·(gc) |
| 68 | o4·=·514229</code></pre> | 68 | o4·=·514229</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·fib·28 | 71 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·fib·28 |
| 72 | ·--·used· | 72 | ·--·used·1.312e-06s·(cpu);·1.222e-06s·(thread);·0s·(gc) |
| 73 | o5·=·514229</code></pre> | 73 | o5·=·514229</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ········</table> | 75 | ········</table> |
| 76 | ········<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>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> |
| 77 | ········<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 | ········<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> |
| 78 | ········<table·class="examples"> | 78 | ········<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·0.657994s·(cpu);·0.507226s·(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·4.4226e-05s·(cpu);·4.3806e-05s·(thread);·0s·(gc) |
| 22 | o4·=·514229 | 22 | o4·=·514229 |
| 23 | i5·:·time·fib·28 | 23 | i5·:·time·fib·28 |
| 24 | ·--·used· | 24 | ·--·used·1.312e-06s·(cpu);·1.222e-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 98, 15 lines modified | Offset 98, 15 lines modified | ||
| 98 | o2·=·S | 98 | o2·=·S |
| 99 | o2·:·PolynomialRing</code></pre> | 99 | o2·:·PolynomialRing</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·minimalBetti·I | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·C·=·minimalBetti·I |
| 103 | ·--·1. | 103 | ·--·1.76792·seconds·elapsed |
| 104 | ············0··1···2···3···4····5···6···7···8··9·10 | 104 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 105 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 105 | o3·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 106 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 106 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 107 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 107 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 108 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 108 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 109 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 109 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
| Offset 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·I·=·ideal·I_*; | 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·I·=·ideal·I_*; |
| 124 | o4·:·Ideal·of·S</code></pre> | 124 | o4·:·Ideal·of·S</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) | 127 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>2) |
| 128 | ·--·0. | 128 | ·--·0.768623·seconds·elapsed |
| 129 | ············0··1···2···3···4····5···6···7 | 129 | ············0··1···2···3···4····5···6···7 |
| 130 | o5·=·total:·1·35·140·385·819·1080·735·196 | 130 | o5·=·total:·1·35·140·385·819·1080·735·196 |
| 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 |
| Offset 139, 15 lines modified | Offset 139, 15 lines modified | ||
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal·I_*; | 140 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·ideal·I_*; |
| 141 | o6·:·Ideal·of·S</code></pre> | 141 | o6·:·Ideal·of·S</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) | 144 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·C·=·minimalBetti(I,·DegreeLimit=>1,·LengthLimit=>5) |
| 145 | ·--·0.03 | 145 | ·--·0.0322825·seconds·elapsed |
| 146 | ············0··1···2···3··4 | 146 | ············0··1···2···3··4 |
| 147 | o7·=·total:·1·35·140·189·84 | 147 | o7·=·total:·1·35·140·189·84 |
| 148 | ·········0:·1··.···.···.··. | 148 | ·········0:·1··.···.···.··. |
| 149 | ·········1:·.·35·140·189·84 | 149 | ·········1:·.·35·140·189·84 |
| 150 | o7·:·BettiTally</code></pre> | 150 | o7·:·BettiTally</code></pre> |
| Offset 155, 15 lines modified | Offset 155, 15 lines modified | ||
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i8·:·I·=·ideal·I_*; | 156 | <td>··············<pre><code·class="language-macaulay2">i8·:·I·=·ideal·I_*; |
| 157 | o8·:·Ideal·of·S</code></pre> | 157 | o8·:·Ideal·of·S</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) | 160 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·C·=·minimalBetti(I,·LengthLimit=>5) |
| 161 | ·--·1. | 161 | ·--·1.26675·seconds·elapsed |
| 162 | ············0··1···2···3···4····5 | 162 | ············0··1···2···3···4····5 |
| 163 | o9·=·total:·1·35·140·385·819·1080 | 163 | o9·=·total:·1·35·140·385·819·1080 |
| 164 | ·········0:·1··.···.···.···.····. | 164 | ·········0:·1··.···.···.···.····. |
| 165 | ·········1:·.·35·140·189··84····. | 165 | ·········1:·.·35·140·189··84····. |
| 166 | ·········2:·.··.···.·196·735·1080 | 166 | ·········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 | ·--·1. | 49 | ·--·1.76792·seconds·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 | ·--·0. | 67 | ·--·0.768623·seconds·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 | ·--·0.03 | 77 | ·--·0.0322825·seconds·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 | ·--·1.26675·seconds·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 71, 28 lines modified | Offset 71, 28 lines modified | ||
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 73 | ········<p>Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the·last·must·already·exist.</p> | 73 | ········<p>Only·one·directory·will·be·made,·so·the·components·of·the·path·p·other·than·the·last·must·already·exist.</p> |
| 74 | ········<table·class="examples"> | 74 | ········<table·class="examples"> |
| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName()·|·"/" | 76 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName()·|·"/" |
| 77 | o1·=·/tmp/M2- | 77 | o1·=·/tmp/M2-2051461-0/0/</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·mkdir·p</code></pre> | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·mkdir·p</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·isDirectory·p | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·isDirectory·p |
| 84 | o3·=·true</code></pre> | 84 | o3·=·true</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·(fn·=·p·|·"foo")·<<·"hi·there"·<<·close |
| 88 | o4·=·/tmp/M2- | 88 | o4·=·/tmp/M2-2051461-0/0/foo |
| 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·:·get·fn | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·fn |
| 93 | o5·=·hi·there</code></pre> | 93 | 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/M2-2051461-0/0/ |
| 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/M2-2051461-0/0/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 86, 42 lines modified | Offset 86, 42 lines modified | ||
| 86 | ······</div> | 86 | ······</div> |
| 87 | ······<div> | 87 | ······<div> |
| 88 | ········<h2>Description</h2> | 88 | ········<h2>Description</h2> |
| 89 | ········<table·class="examples"> | 89 | ········<table·class="examples"> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() | 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName() |
| 92 | o1·=·/tmp/M2- | 92 | o1·=·/tmp/M2-2042378-0/0</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName() |
| 96 | o2·=·/tmp/M2- | 96 | o2·=·/tmp/M2-2042378-0/1</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·src·<<·"hi·there"·<<·close |
| 100 | o3·=·/tmp/M2- | 100 | o3·=·/tmp/M2-2042378-0/0 |
| 101 | o3·:·File</code></pre> | 101 | o3·:·File</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·moveFile(src,dst,Verbose=>true) | 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·moveFile(src,dst,Verbose=>true) |
| 105 | --moving:·/tmp/M2- | 105 | --moving:·/tmp/M2-2042378-0/0·->·/tmp/M2-2042378-0/1</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·get·dst |
| 109 | o5·=·hi·there</code></pre> | 109 | o5·=·hi·there</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i6·:·bak·=·moveFile(dst,Verbose=>true) | 112 | <td>··············<pre><code·class="language-macaulay2">i6·:·bak·=·moveFile(dst,Verbose=>true) |
| 113 | --backup·file·created:·/tmp/M2- | 113 | --backup·file·created:·/tmp/M2-2042378-0/1.bak |
| 114 | o6·=·/tmp/M2- | 114 | o6·=·/tmp/M2-2042378-0/1.bak</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i7·:·removeFile·bak</code></pre> | 117 | <td>··············<pre><code·class="language-macaulay2">i7·:·removeFile·bak</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ········</table> | 119 | ········</table> |
| 120 | ······</div> | 120 | ······</div> |
| 121 | ······<div> | 121 | ······<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/M2-2042378-0/0 |
| 28 | i2·:·dst·=·temporaryFileName() | 28 | i2·:·dst·=·temporaryFileName() |
| 29 | o2·=·/tmp/M2- | 29 | o2·=·/tmp/M2-2042378-0/1 |
| 30 | i3·:·src·<<·"hi·there"·<<·close | 30 | i3·:·src·<<·"hi·there"·<<·close |
| 31 | o3·=·/tmp/M2- | 31 | o3·=·/tmp/M2-2042378-0/0 |
| 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/M2-2042378-0/0·->·/tmp/M2-2042378-0/1 |
| 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/M2-2042378-0/1.bak |
| 39 | o6·=·/tmp/M2- | 39 | o6·=·/tmp/M2-2042378-0/1.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 44, 15 lines modified | Offset 44, 15 lines modified | ||
| 44 | <hr>····<div> | 44 | <hr>····<div> |
| 45 | ······<h1>nanosleep·--·sleep·for·a·given·number·of·nanoseconds</h1> | 45 | ······<h1>nanosleep·--·sleep·for·a·given·number·of·nanoseconds</h1> |
| 46 | ······<div> | 46 | ······<div> |
| 47 | ········<h2>Description</h2> | 47 | ········<h2>Description</h2> |
| 48 | <span·class="tt">nanosleep·n</span>·--·sleeps·for·<span·class="tt">n</span>·nanoseconds.········<table·class="examples"> | 48 | <span·class="tt">nanosleep·n</span>·--·sleeps·for·<span·class="tt">n</span>·nanoseconds.········<table·class="examples"> |
| 49 | ··········<tr> | 49 | ··········<tr> |
| 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nanosleep·500000000 | 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·elapsedTime·nanosleep·500000000 |
| 51 | ·--·0.500 | 51 | ·--·0.50009·seconds·elapsed |
| 52 | o1·=·0</code></pre> | 52 | o1·=·0</code></pre> |
| 53 | </td>··········</tr> | 53 | </td>··········</tr> |
| 54 | ········</table> | 54 | ········</table> |
| 55 | ······</div> | 55 | ······</div> |
| 56 | ······<div> | 56 | ······<div> |
| 57 | ········<h2>See·also</h2> | 57 | ········<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 | ·--·0.500 | 11 | ·--·0.50009·seconds·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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| 61 | ········</div> | 61 | ········</div> |
| 62 | ········<table·class="examples"> | 62 | ········<table·class="examples"> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i2·:·L·=·random·toList·(1..10000);</code></pre> | 64 | <td>··············<pre><code·class="language-macaulay2">i2·:·L·=·random·toList·(1..10000);</code></pre> |
| 65 | </td>··········</tr> | 65 | </td>··········</tr> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); | 67 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·········apply(1..100,·n·->·sort·L); |
| 68 | ·--·0. | 68 | ·--·0.707772·seconds·elapsed</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); | 71 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); |
| 72 | ·--·0.2 | 72 | ·--·0.213265·seconds·elapsed</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ········</table> | 74 | ········</table> |
| 75 | ········<div> | 75 | ········<div> |
| 76 | ··········<p>You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.</p> | 76 | ··········<p>You·will·have·to·try·it·on·your·examples·to·see·how·much·they·speed·up.</p> |
| 77 | ··········<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>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> |
| 78 | ··········<p>The·rest·of·this·document·describes·how·to·control·parallel·tasks·more·directly.</p> | 78 | ··········<p>The·rest·of·this·document·describes·how·to·control·parallel·tasks·more·directly.</p> |
| 79 | ··········<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> | 79 | ··········<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> |
| 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 | ·--·0. | 24 | ·--·0.707772·seconds·elapsed |
| 25 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); | 25 | i4·:·elapsedTime·parallelApply(1..100,·n·->·sort·L); |
| 26 | ·--·0.2 | 26 | ·--·0.213265·seconds·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 124, 15 lines modified | Offset 124, 15 lines modified | ||
| 124 | o3·=·S | 124 | o3·=·S |
| 125 | o3·:·PolynomialRing</code></pre> | 125 | o3·:·PolynomialRing</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalBetti·I | 128 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalBetti·I |
| 129 | ·--· | 129 | ·--·1.7632·seconds·elapsed |
| 130 | ············0··1···2···3···4····5···6···7···8··9·10 | 130 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 131 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 131 | o4·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 132 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 132 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 133 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 133 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 134 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 134 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 135 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 135 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
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| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i5·:·I·=·ideal·I_*; | 144 | <td>··············<pre><code·class="language-macaulay2">i5·:·I·=·ideal·I_*; |
| 145 | o5·:·Ideal·of·S</code></pre> | 145 | o5·:·Ideal·of·S</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) | 148 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·minimalBetti(I,·ParallelizeByDegree·=>·true) |
| 149 | ·--·1. | 149 | ·--·1.46342·seconds·elapsed |
| 150 | ············0··1···2···3···4····5···6···7···8··9·10 | 150 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 151 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 151 | o6·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 152 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 152 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 153 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 153 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 154 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 154 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 155 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 155 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
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| 167 | ··········<tr> | 167 | ··········<tr> |
| 168 | <td>··············<pre><code·class="language-macaulay2">i8·:·numTBBThreads·=·1 | 168 | <td>··············<pre><code·class="language-macaulay2">i8·:·numTBBThreads·=·1 |
| 169 | o8·=·1</code></pre> | 169 | o8·=·1</code></pre> |
| 170 | </td>··········</tr> | 170 | </td>··········</tr> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·minimalBetti(I) | 172 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·minimalBetti(I) |
| 173 | ·--· | 173 | ·--·1.82847·seconds·elapsed |
| 174 | ············0··1···2···3···4····5···6···7···8··9·10 | 174 | ············0··1···2···3···4····5···6···7···8··9·10 |
| 175 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 | 175 | o9·=·total:·1·35·140·385·819·1080·819·385·140·35··1 |
| 176 | ·········0:·1··.···.···.···.····.···.···.···.··.··. | 176 | ·········0:·1··.···.···.···.····.···.···.···.··.··. |
| 177 | ·········1:·.·35·140·189··84····.···.···.···.··.··. | 177 | ·········1:·.·35·140·189··84····.···.···.···.··.··. |
| 178 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. | 178 | ·········2:·.··.···.·196·735·1080·735·196···.··.··. |
| 179 | ·········3:·.··.···.···.···.····.··84·189·140·35··. | 179 | ·········3:·.··.···.···.···.····.··84·189·140·35··. |
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| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal·I_*; | 201 | <td>··············<pre><code·class="language-macaulay2">i12·:·I·=·ideal·I_*; |
| 202 | o12·:·Ideal·of·S</code></pre> | 202 | o12·:·Ideal·of·S</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 205 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 206 | ·--·2. | 206 | ·--·2.03855·seconds·elapsed |
| 207 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 | 207 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 208 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S | 208 | o13·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S |
| 209 | ·································································································· | 209 | ·································································································· |
| 210 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 | 210 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 |
| 211 | o13·:·Complex</code></pre> | 211 | o13·:·Complex</code></pre> |
| Offset 221, 15 lines modified | Offset 221, 15 lines modified | ||
| 221 | ··········<tr> | 221 | ··········<tr> |
| 222 | <td>··············<pre><code·class="language-macaulay2">i15·:·I·=·ideal·I_*; | 222 | <td>··············<pre><code·class="language-macaulay2">i15·:·I·=·ideal·I_*; |
| 223 | o15·:·Ideal·of·S</code></pre> | 223 | o15·:·Ideal·of·S</code></pre> |
| 224 | </td>··········</tr> | 224 | </td>··········</tr> |
| 225 | ··········<tr> | 225 | ··········<tr> |
| 226 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) | 226 | <td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·freeResolution(I,·Strategy·=>·Nonminimal) |
| 227 | ·--· | 227 | ·--·1.91992·seconds·elapsed |
| 228 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 | 228 | ·······1······35······241······841······1781······2464······2294······1432······576······135······14 |
| 229 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S | 229 | o16·=·S··<--·S···<--·S····<--·S····<--·S·····<--·S·····<--·S·····<--·S·····<--·S····<--·S····<--·S |
| 230 | ·································································································· | 230 | ·································································································· |
| 231 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 | 231 | ······0······1·······2········3········4·········5·········6·········7·········8········9········10 |
| 232 | o16·:·Complex</code></pre> | 232 | o16·:·Complex</code></pre> |
| Offset 254, 15 lines modified | Offset 254, 15 lines modified | ||
| 254 | ··········<tr> | 254 | ··········<tr> |
| 255 | <td>··············<pre><code·class="language-macaulay2">i19·:·I·=·ideal·random(S^1,·S^{4:-5}); | 255 | <td>··············<pre><code·class="language-macaulay2">i19·:·I·=·ideal·random(S^1,·S^{4:-5}); |
| 256 | o19·:·Ideal·of·S</code></pre> | 256 | o19·:·Ideal·of·S</code></pre> |
| 257 | </td>··········</tr> | 257 | </td>··········</tr> |
| 258 | ··········<tr> | 258 | ··········<tr> |
| 259 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 259 | <td>··············<pre><code·class="language-macaulay2">i20·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 260 | ·--· | 260 | ·--·3.14697·seconds·elapsed |
| 261 | ··············1······108 | 261 | ··············1······108 |
| 262 | o20·:·Matrix·S··<--·S</code></pre> | 262 | o20·:·Matrix·S··<--·S</code></pre> |
| 263 | </td>··········</tr> | 263 | </td>··········</tr> |
| 264 | ··········<tr> | 264 | ··········<tr> |
| 265 | <td>··············<pre><code·class="language-macaulay2">i21·:·numTBBThreads·=·1 | 265 | <td>··············<pre><code·class="language-macaulay2">i21·:·numTBBThreads·=·1 |
| Offset 271, 15 lines modified | Offset 271, 15 lines modified | ||
| 271 | ··········<tr> | 271 | ··········<tr> |
| 272 | <td>··············<pre><code·class="language-macaulay2">i22·:·I·=·ideal·I_*; | 272 | <td>··············<pre><code·class="language-macaulay2">i22·:·I·=·ideal·I_*; |
| 273 | o22·:·Ideal·of·S</code></pre> | 273 | o22·:·Ideal·of·S</code></pre> |
| 274 | </td>··········</tr> | 274 | </td>··········</tr> |
| 275 | ··········<tr> | 275 | ··········<tr> |
| 276 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 276 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 277 | ·--· | 277 | ·--·6.10059·seconds·elapsed |
| 278 | ··············1······108 | 278 | ··············1······108 |
| 279 | o23·:·Matrix·S··<--·S</code></pre> | 279 | o23·:·Matrix·S··<--·S</code></pre> |
| 280 | </td>··········</tr> | 280 | </td>··········</tr> |
| 281 | ··········<tr> | 281 | ··········<tr> |
| 282 | <td>··············<pre><code·class="language-macaulay2">i24·:·numTBBThreads·=·10 | 282 | <td>··············<pre><code·class="language-macaulay2">i24·:·numTBBThreads·=·10 |
| Offset 288, 15 lines modified | Offset 288, 15 lines modified | ||
| 288 | ··········<tr> | 288 | ··········<tr> |
| 289 | <td>··············<pre><code·class="language-macaulay2">i25·:·I·=·ideal·I_*; | 289 | <td>··············<pre><code·class="language-macaulay2">i25·:·I·=·ideal·I_*; |
| 290 | o25·:·Ideal·of·S</code></pre> | 290 | o25·:·Ideal·of·S</code></pre> |
| 291 | </td>··········</tr> | 291 | </td>··········</tr> |
| 292 | ··········<tr> | 292 | ··········<tr> |
| 293 | <td>··············<pre><code·class="language-macaulay2">i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); | 293 | <td>··············<pre><code·class="language-macaulay2">i26·:·elapsedTime·groebnerBasis(I,·Strategy·=>·"F4"); |
| 294 | ·--·3. | 294 | ·--·3.08942·seconds·elapsed |
| 295 | ··············1······108 | 295 | ··············1······108 |
| 296 | o26·:·Matrix·S··<--·S</code></pre> | 296 | o26·:·Matrix·S··<--·S</code></pre> |
| 297 | </td>··········</tr> | 297 | </td>··········</tr> |
| 298 | ········</table> | 298 | ········</table> |
| 299 | ········<div> | 299 | ········<div> |
| 300 | ··········<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> | 300 | ··········<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 | ·--·1.7632·seconds·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 | ·--·1. | 109 | ·--·1.46342·seconds·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 | ·--·1.82847·seconds·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 | ·--·2. | 153 | ·--·2.03855·seconds·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 | ·--·1.91992·seconds·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 | ·--·3.14697·seconds·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 | ·--·6.10059·seconds·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 | ·--·3. | 215 | ·--·3.08942·seconds·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 | ·--·0. | 251 | ·--·0.765122·seconds·elapsed |
| 252 | ···············ZZ············1·······ZZ············148 | 252 | ···············ZZ············1·······ZZ············148 |
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| Offset 315, 34 lines modified | Offset 315, 34 lines modified | ||
| 315 | ··········<tr> | 315 | ··········<tr> |
| 316 | <td>··············<pre><code·class="language-macaulay2">i27·:·gbTrace·=·3 | 316 | <td>··············<pre><code·class="language-macaulay2">i27·:·gbTrace·=·3 |
| 317 | o27·=·3</code></pre> | 317 | o27·=·3</code></pre> |
| 318 | </td>··········</tr> | 318 | </td>··········</tr> |
| 319 | ··········<tr> | 319 | ··········<tr> |
| 320 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·poincare·I | 320 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·poincare·I |
| 321 | ·--·used·0.00 | 321 | ·--·used·0.00149312s·(cpu);·7.071e-06s·(thread);·0s·(gc) |
| 322 | ············3·····6····9 | 322 | ············3·····6····9 |
| 323 | o28·=·1·-·3T··+·3T··-·T | 323 | o28·=·1·-·3T··+·3T··-·T |
| 324 | o28·:·ZZ[T]</code></pre> | 324 | o28·:·ZZ[T]</code></pre> |
| 325 | </td>··········</tr> | 325 | </td>··········</tr> |
| 326 | ··········<tr> | 326 | ··········<tr> |
| 327 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·gens·gb·I; | 327 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·gens·gb·I; |
| 328 | ···--·registering·gb·19·at·0x7f | 328 | ···--·registering·gb·19·at·0x7f9b6fea38c0 |
| 329 | ···--·[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 | ···--·[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 |
| 330 | ···--·number·of·monomials················=·4186 | 330 | ···--·number·of·monomials················=·4186 |
| 331 | ···--·#reduction·steps·=·38 | 331 | ···--·#reduction·steps·=·38 |
| 332 | ···--·#spairs·done·=·11 | 332 | ···--·#spairs·done·=·11 |
| 333 | ···--·ncalls·=·10 | 333 | ···--·ncalls·=·10 |
| 334 | ···--·nloop·=·29 | 334 | ···--·nloop·=·29 |
| 335 | ···--·nsaved·=·0 | 335 | ···--·nsaved·=·0 |
| 336 | ···--··--·used·0.01 | 336 | ···--··--·used·0.0105017s·(cpu);·0.0109682s·(thread);·0s·(gc) |
| 337 | ··············1······11 | 337 | ··············1······11 |
| 338 | o29·:·Matrix·R··<--·R</code></pre> | 338 | o29·:·Matrix·R··<--·R</code></pre> |
| 339 | </td>··········</tr> | 339 | </td>··········</tr> |
| 340 | ········</table> | 340 | ········</table> |
| 341 | ········<div> | 341 | ········<div> |
| 342 | ··········<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> | 342 | ··········<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 350, 39 lines modified | Offset 350, 39 lines modified | ||
| 350 | ········<table·class="examples"> | 350 | ········<table·class="examples"> |
| 351 | ··········<tr> | 351 | ··········<tr> |
| 352 | <td>··············<pre><code·class="language-macaulay2">i30·:·R·=·QQ[a..d];</code></pre> | 352 | <td>··············<pre><code·class="language-macaulay2">i30·:·R·=·QQ[a..d];</code></pre> |
| 353 | </td>··········</tr> | 353 | </td>··········</tr> |
| 354 | ··········<tr> | 354 | ··········<tr> |
| 355 | <td>··············<pre><code·class="language-macaulay2">i31·:·I·=·ideal·random(R^1,·R^{3:-3}); | 355 | <td>··············<pre><code·class="language-macaulay2">i31·:·I·=·ideal·random(R^1,·R^{3:-3}); |
| 356 | ···--·registering·gb·20·at·0x7f | 356 | ···--·registering·gb·20·at·0x7f9b6fea3700 |
| 357 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 | 357 | ···--·[gb]number·of·(nonminimal)·gb·elements·=·0 |
| 358 | ···--·number·of·monomials················=·0 | 358 | ···--·number·of·monomials················=·0 |
| 359 | ···--·#reduction·steps·=·0 | 359 | ···--·#reduction·steps·=·0 |
| 360 | ···--·#spairs·done·=·0 | 360 | ···--·#spairs·done·=·0 |
| 361 | ···--·ncalls·=·0 | 361 | ···--·ncalls·=·0 |
| 362 | ···--·nloop·=·0 | 362 | ···--·nloop·=·0 |
| 363 | ···--·nsaved·=·0 | 363 | ···--·nsaved·=·0 |
| 364 | ···--· | 364 | ···--· |
| 365 | o31·:·Ideal·of·R</code></pre> | 365 | o31·:·Ideal·of·R</code></pre> |
| 366 | </td>··········</tr> | 366 | </td>··········</tr> |
| 367 | ··········<tr> | 367 | ··········<tr> |
| 368 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·p·=·poincare·I | 368 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·p·=·poincare·I |
| 369 | ···--·registering·gb·21·at·0x7f | 369 | ···--·registering·gb·21·at·0x7f9b6fea3380 |
| 370 | ···--·[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 | ···--·[gb]{3}(3)mmm{4}(2)mm{5}(3)mmm{6}(6)mmoooo{7}(4)mooo{8}(2)oonumber·of·(nonminimal)·gb·elements·=·11 |
| 371 | ···--·number·of·monomials················=·267 | 371 | ···--·number·of·monomials················=·267 |
| 372 | ···--·#reduction·steps·=·236 | 372 | ···--·#reduction·steps·=·236 |
| 373 | ···--·#spairs·done·=·30 | 373 | ···--·#spairs·done·=·30 |
| 374 | ···--·ncalls·=·10 | 374 | ···--·ncalls·=·10 |
| 375 | ···--·nloop·=·20 | 375 | ···--·nloop·=·20 |
| 376 | ···--·nsaved·=·0 | 376 | ···--·nsaved·=·0 |
| 377 | ···--··--·used·0.00 | 377 | ···--··--·used·0.00334457s·(cpu);·0.00400907s·(thread);·0s·(gc) |
| 378 | ············3·····6····9 | 378 | ············3·····6····9 |
| 379 | o32·=·1·-·3T··+·3T··-·T | 379 | o32·=·1·-·3T··+·3T··-·T |
| 380 | o32·:·ZZ[T]</code></pre> | 380 | o32·:·ZZ[T]</code></pre> |
| 381 | </td>··········</tr> | 381 | </td>··········</tr> |
| 382 | ··········<tr> | 382 | ··········<tr> |
| Offset 437, 27 lines modified | Offset 437, 27 lines modified | ||
| 437 | <td>··············<pre><code·class="language-macaulay2">i36·:·gbTrace·=·3 | 437 | <td>··············<pre><code·class="language-macaulay2">i36·:·gbTrace·=·3 |
| 438 | o36·=·3</code></pre> | 438 | o36·=·3</code></pre> |
| 439 | </td>··········</tr> | 439 | </td>··········</tr> |
| 440 | ··········<tr> | 440 | ··········<tr> |
| 441 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·gens·gb·J; | 441 | <td>··············<pre><code·class="language-macaulay2">i37·:·time·gens·gb·J; |
| 442 | ···--·registering·gb·22·at·0x7f | 442 | ···--·registering·gb·22·at·0x7f9b6fea31c0 |
| 443 | ···--·[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 | ···--·[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 |
| 444 | ···--·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 | ···--·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 |
| 445 | ···--·{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 | ···--·{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 |
| 446 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39 | 446 | ···--·{25}(1,3)m{26}(1,3)m{27}(1,3)m{28}(0,2)number·of·(nonminimal)·gb·elements·=·39 |
| 447 | ···--·number·of·monomials················=·1051 | 447 | ···--·number·of·monomials················=·1051 |
| 448 | ···--·#reduction·steps·=·284 | 448 | ···--·#reduction·steps·=·284 |
| 449 | ···--·#spairs·done·=·53 | 449 | ···--·#spairs·done·=·53 |
| 450 | ···--·ncalls·=·46 | 450 | ···--·ncalls·=·46 |
| 451 | ···--·nloop·=·54 | 451 | ···--·nloop·=·54 |
| 452 | ···--·nsaved·=·0 | 452 | ···--·nsaved·=·0 |
| 453 | ···--··--·used·0.0 | 453 | ···--··--·used·0.0359964s·(cpu);·0.0345193s·(thread);·0s·(gc) |
| 454 | ··············1······39 | 454 | ··············1······39 |
| 455 | o37·:·Matrix·S··<--·S</code></pre> | 455 | o37·:·Matrix·S··<--·S</code></pre> |
| 456 | </td>··········</tr> | 456 | </td>··········</tr> |
| 457 | ··········<tr> | 457 | ··········<tr> |
| 458 | <td>··············<pre><code·class="language-macaulay2">i38·:·selectInSubring(1,·gens·gb·J) | 458 | <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·0.00149312s·(cpu);·7.071e-06s·(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·0x7f9b6fea38c0 |
| 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·0.01 | 198 | ···--··--·used·0.0105017s·(cpu);·0.0109682s·(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·0x7f9b6fea3700 |
| 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·0x7f9b6fea3380 |
| 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·0.00334457s·(cpu);·0.00400907s·(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·0x7f9b6fea31c0 |
| 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·0.0359964s·(cpu);·0.0345193s·(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 62, 15 lines modified | Offset 62, 15 lines modified | ||
| 62 | ······</div> | 62 | ······</div> |
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·processID() | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·processID() |
| 68 | o1·=· | 68 | o1·=·2031929</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ········</table> | 70 | ········</table> |
| 71 | ······</div> | 71 | ······</div> |
| 72 | ······<div> | 72 | ······<div> |
| 73 | ········<h2>See·also</h2> | 73 | ········<h2>See·also</h2> |
| 74 | ········<ul> | 74 | ········<ul> |
| 75 | ··········<li> | 75 | ··········<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·=·2031929 |
| 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 60, 15 lines modified | Offset 60, 15 lines modified | ||
| 60 | ······123····110····13 | 60 | ······123····110····13 |
| 61 | o2·=·x····+·x····+·x···+·1 | 61 | o2·=·x····+·x····+·x···+·1 |
| 62 | o2·:·R</code></pre> | 62 | o2·:·R</code></pre> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·factor·f | 65 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·factor·f |
| 66 | ·--·used·0.00 | 66 | ·--·used·0.00261549s·(cpu);·0.00261296s·(thread);·0s·(gc) |
| 67 | ··············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 | ··············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 |
| 68 | 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·=·(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) |
| 69 | o3·:·Expression·of·class·Product</code></pre> | 69 | o3·:·Expression·of·class·Product</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| Offset 93, 16 lines modified | Offset 93, 16 lines modified | ||
| 93 | o6·:·FunctionClosure</code></pre> | 93 | o6·:·FunctionClosure</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·i·to·10·do·(g();h();h())</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·i·to·10·do·(g();h();h())</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i8·:·profileSummary | 99 | <td>··············<pre><code·class="language-macaulay2">i8·:·profileSummary |
| 100 | g:·11·times,·used·.0 | 100 | g:·11·times,·used·.0277559·seconds |
| 101 | h:·22·times,·used·.0 | 101 | h:·22·times,·used·.0534749·seconds</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ········</table> | 103 | ········</table> |
| 104 | ······</div> | 104 | ······</div> |
| 105 | ······<div·class="waystouse"> | 105 | ······<div·class="waystouse"> |
| 106 | ········<h2>Ways·to·use·<span·class="tt">profile</span>·:</h2> | 106 | ········<h2>Ways·to·use·<span·class="tt">profile</span>·:</h2> |
| 107 | ········<ul> | 107 | ········<ul> |
| 108 | ··········<li> | 108 | ··········<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·0.00261549s·(cpu);·0.00261296s·(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·.0277559·seconds |
| 56 | h:·22·times,·used·.0 | 56 | h:·22·times,·used·.0534749·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 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | o5·=·(2,·10) | 91 | o5·=·(2,·10) |
| 92 | o5·:·Sequence</code></pre> | 92 | o5·:·Sequence</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·randomKRationalPoint(I) | 95 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·randomKRationalPoint(I) |
| 96 | ·--·used·0.0 | 96 | ·--·used·0.078364s·(cpu);·0.0604955s·(thread);·0s·(gc) |
| 97 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) | 97 | o6·=·ideal·(x··-·53x·,·x··+·8x·,·x··-·4x·) |
| 98 | ·············2······3···1·····3···0·····3 | 98 | ·············2······3···1·····3···0·····3 |
| 99 | o6·:·Ideal·of·R</code></pre> | 99 | o6·:·Ideal·of·R</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| Offset 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | o9·=·(3,·10) | 115 | o9·=·(3,·10) |
| 116 | o9·:·Sequence</code></pre> | 116 | o9·:·Sequence</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·randomKRationalPoint(I) | 119 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·randomKRationalPoint(I) |
| 120 | ·--·used·0. | 120 | ·--·used·0.191163s·(cpu);·0.157182s·(thread);·0s·(gc) |
| 121 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) | 121 | o10·=·ideal·(x··-·27x·,·x··-·16x·,·x··-·9x·,·x··+·44x·,·x··-·52x·) |
| 122 | ··············4······5···3······5···2·····5···1······5···0······5 | 122 | ··············4······5···3······5···2·····5···1······5···0······5 |
| 123 | o10·:·Ideal·of·R</code></pre> | 123 | o10·:·Ideal·of·R</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ········</table> | 125 | ········</table> |
| Offset 149, 15 lines modified | Offset 149, 15 lines modified | ||
| 149 | <td>··············<pre><code·class="language-macaulay2">i14·:·I=ideal·random(n,R); | 149 | <td>··············<pre><code·class="language-macaulay2">i14·:·I=ideal·random(n,R); |
| 150 | o14·:·Ideal·of·R</code></pre> | 150 | o14·:·Ideal·of·R</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| 152 | ··········<tr> | 152 | ··········<tr> |
| 153 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c); | 153 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·(#select(apply(100,i->(degs=apply(decompose(I+ideal·random(1,R)),c->degree·c); |
| 154 | ·····················#select(degs,d->d==1))),f->f>0)) | 154 | ·····················#select(degs,d->d==1))),f->f>0)) |
| 155 | ·--·used· | 155 | ·--·used·2.65224s·(cpu);·1.3825s·(thread);·0s·(gc) |
| 156 | o15·=·58</code></pre> | 156 | o15·=·58</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ········</table> | 158 | ········</table> |
| 159 | ······</div> | 159 | ······</div> |
| 160 | ······<div·class="waystouse"> | 160 | ······<div·class="waystouse"> |
| 161 | ········<h2>Ways·to·use·<span·class="tt">randomKRationalPoint</span>·:</h2> | 161 | ········<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·0.0 | 35 | ·--·used·0.078364s·(cpu);·0.0604955s·(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·0.191163s·(cpu);·0.157182s·(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·2.65224s·(cpu);·1.3825s·(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 68, 30 lines modified | Offset 68, 30 lines modified | ||
| 68 | ······</div> | 68 | ······</div> |
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·dir·=·temporaryFileName() |
| 74 | o1·=·/tmp/M2- | 74 | o1·=·/tmp/M2-2061605-0/0</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir</code></pre> | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir</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/M2-2061605-0/0/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, 24 lines modified | Offset 11, 24 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/M2-2061605-0/0 |
| 18 | i2·:·makeDirectory·dir | 18 | i2·:·makeDirectory·dir |
| 19 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close | 19 | i3·:·(fn·=·dir·|·"/"·|·"foo")·<<·"hi·there"·<<·close |
| 20 | o3·=·/tmp/M2- | 20 | o3·=·/tmp/M2-2061605-0/0/foo |
| 21 | o3·:·File | 21 | o3·:·File |
| 22 | i4·:·readDirectory·dir | 22 | i4·:·readDirectory·dir |
| 23 | o4·=·{ | 23 | o4·=·{..,·.,·foo} |
| 24 | o4·:·List | 24 | o4·:·List |
| 25 | i5·:·removeFile·fn | 25 | i5·:·removeFile·fn |
| 26 | i6·:·removeDirectory·dir | 26 | i6·:·removeDirectory·dir |
| 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_\x8e_\x8m_\x8o_\x8v_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·remove·a·directory | 28 | ····*·_\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_\x8F_\x8i_\x8l_\x8e·--·remove·a·file | 29 | ····*·_\x8r_\x8e_\x8m_\x8o_\x8v_\x8e_\x8F_\x8i_\x8l_\x8e·--·remove·a·file |
| Offset 45, 20 lines modified | Offset 45, 20 lines modified | ||
| 45 | ······<h1>reading·files</h1> | 45 | ······<h1>reading·files</h1> |
| 46 | ······<div> | 46 | ······<div> |
| 47 | 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 | 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> |
| 48 | First·we·create·the·file·by·writing·the·desired·text·to·it.········<table·class="examples"> | 48 | First·we·create·the·file·by·writing·the·desired·text·to·it.········<table·class="examples"> |
| 49 | ··········<tr> | 49 | ··········<tr> |
| 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 50 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 51 | o1·=·/tmp/M2- | 51 | o1·=·/tmp/M2-2055264-0/0</code></pre> |
| 52 | </td>··········</tr> | 52 | </td>··········</tr> |
| 53 | ··········<tr> | 53 | ··········<tr> |
| 54 | <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 | <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 |
| 55 | o2·=·/tmp/M2- | 55 | o2·=·/tmp/M2-2055264-0/0 |
| 56 | o2·:·File</code></pre> | 56 | o2·:·File</code></pre> |
| 57 | </td>··········</tr> | 57 | </td>··········</tr> |
| 58 | ········</table> | 58 | ········</table> |
| 59 | Now·we·get·the·contents·of·the·file,·as·a·single·string.········<table·class="examples"> | 59 | Now·we·get·the·contents·of·the·file,·as·a·single·string.········<table·class="examples"> |
| 60 | ··········<tr> | 60 | ··········<tr> |
| 61 | <td>··············<pre><code·class="language-macaulay2">i3·:·get·fn | 61 | <td>··············<pre><code·class="language-macaulay2">i3·:·get·fn |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | ········</table> | 97 | ········</table> |
| 98 | Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create·such·a·file.········<table·class="examples"> | 98 | Often·a·file·will·contain·code·written·in·the·Macaulay2·language.·Let's·create·such·a·file.········<table·class="examples"> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i7·:·fn·<<·"sample·=·2^100 | 100 | <td>··············<pre><code·class="language-macaulay2">i7·:·fn·<<·"sample·=·2^100 |
| 101 | ·····print·sample | 101 | ·····print·sample |
| 102 | ·····"·<<·close | 102 | ·····"·<<·close |
| 103 | o7·=·/tmp/M2- | 103 | o7·=·/tmp/M2-2055264-0/0 |
| 104 | o7·:·File</code></pre> | 104 | o7·:·File</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | 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 | 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"> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i8·:·get·fn | 109 | <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/M2-2055264-0/0 |
| 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/M2-2055264-0/0 |
| 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/M2-2055264-0/0 |
| 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 68, 15 lines modified | Offset 68, 15 lines modified | ||
| 68 | ······</div> | 68 | ······</div> |
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName·() | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·p·=·temporaryFileName·() |
| 74 | o1·=·/tmp/M2- | 74 | o1·=·/tmp/M2-2062261-0/0</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile·("foo",·p)</code></pre> | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile·("foo",·p)</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·readlink·p | 80 | <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/M2-2062261-0/0 |
| 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 68, 59 lines modified | Offset 68, 59 lines modified | ||
| 68 | ······</div> | 68 | ······</div> |
| 69 | ······<div> | 69 | ······<div> |
| 70 | ········<h2>Description</h2> | 70 | ········<h2>Description</h2> |
| 71 | ········<table·class="examples"> | 71 | ········<table·class="examples"> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·realpath·"." | 73 | <td>··············<pre><code·class="language-macaulay2">i1·:·realpath·"." |
| 74 | o1·=·/tmp/M2- | 74 | o1·=·/tmp/M2-2031929-0/80-rundir/</code></pre> |
| 75 | </td>··········</tr> | 75 | </td>··········</tr> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·p·=·temporaryFileName() | 77 | <td>··············<pre><code·class="language-macaulay2">i2·:·p·=·temporaryFileName() |
| 78 | o2·=·/tmp/M2- | 78 | o2·=·/tmp/M2-2062303-0/0</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·q·=·temporaryFileName() | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·q·=·temporaryFileName() |
| 82 | o3·=·/tmp/M2- | 82 | o3·=·/tmp/M2-2062303-0/1</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·symlinkFile(p,q)</code></pre> | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·symlinkFile(p,q)</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·p·<<·close | 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·p·<<·close |
| 89 | o5·=·/tmp/M2- | 89 | o5·=·/tmp/M2-2062303-0/0 |
| 90 | o5·:·File</code></pre> | 90 | o5·:·File</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·readlink·q | 93 | <td>··············<pre><code·class="language-macaulay2">i6·:·readlink·q |
| 94 | o6·=·/tmp/M2- | 94 | o6·=·/tmp/M2-2062303-0/0</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i7·:·realpath·q | 97 | <td>··············<pre><code·class="language-macaulay2">i7·:·realpath·q |
| 98 | o7·=·/tmp/M2- | 98 | o7·=·/tmp/M2-2062303-0/0</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i8·:·removeFile·p</code></pre> | 101 | <td>··············<pre><code·class="language-macaulay2">i8·:·removeFile·p</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i9·:·removeFile·q</code></pre> | 104 | <td>··············<pre><code·class="language-macaulay2">i9·:·removeFile·q</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | ········<p>The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.</p> | 107 | ········<p>The·empty·string·is·interpreted·as·a·reference·to·the·current·directory.</p> |
| 108 | ········<table·class="examples"> | 108 | ········<table·class="examples"> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i10·:·realpath·"" | 110 | <td>··············<pre><code·class="language-macaulay2">i10·:·realpath·"" |
| 111 | o10·=·/tmp/M2- | 111 | o10·=·/tmp/M2-2031929-0/80-rundir/</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ········</table> | 113 | ········</table> |
| 114 | ······</div> | 114 | ······</div> |
| 115 | ······<div> | 115 | ······<div> |
| 116 | ········<h2>Caveat</h2> | 116 | ········<h2>Caveat</h2> |
| 117 | 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 | 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> |
| 118 | ······<div> | 118 | ······<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/M2-2031929-0/80-rundir/ |
| 20 | i2·:·p·=·temporaryFileName() | 20 | i2·:·p·=·temporaryFileName() |
| 21 | o2·=·/tmp/M2- | 21 | o2·=·/tmp/M2-2062303-0/0 |
| 22 | i3·:·q·=·temporaryFileName() | 22 | i3·:·q·=·temporaryFileName() |
| 23 | o3·=·/tmp/M2- | 23 | o3·=·/tmp/M2-2062303-0/1 |
| 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/M2-2062303-0/0 |
| 27 | o5·:·File | 27 | o5·:·File |
| 28 | i6·:·readlink·q | 28 | i6·:·readlink·q |
| 29 | o6·=·/tmp/M2- | 29 | o6·=·/tmp/M2-2062303-0/0 |
| 30 | i7·:·realpath·q | 30 | i7·:·realpath·q |
| 31 | o7·=·/tmp/M2- | 31 | o7·=·/tmp/M2-2062303-0/0 |
| 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/M2-2031929-0/80-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 74, 23 lines modified | Offset 74, 23 lines modified | ||
| 74 | ········<h2>Description</h2> | 74 | ········<h2>Description</h2> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <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>··············<pre><code·class="language-macaulay2">i1·:·for·i·from·1·to·9·do·(x·:=·0·..·10000·;·registerFinalizer(x,·"--·finalizing·sequence·#"|i|"·--"))</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·collectGarbage()· | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·collectGarbage()· |
| 81 | --finalization:·(1)[0]:·--·finalizing·sequence·#1·-- | ||
| 82 | --finalization:·(2)[7]:·--·finalizing·sequence·#8·-- | ||
| 83 | --finalization:·( | 81 | --finalization:·(1)[5]:·--·finalizing·sequence·#6·-- |
| 84 | --finalization:·( | 82 | --finalization:·(2)[3]:·--·finalizing·sequence·#4·-- |
| 85 | --finalization:·( | 83 | --finalization:·(3)[0]:·--·finalizing·sequence·#1·-- |
| 86 | --finalization:·( | 84 | --finalization:·(4)[8]:·--·finalizing·sequence·#9·-- |
| 87 | --finalization:·(7)[1]:·--·finalizing·sequence·#2·-- | ||
| 88 | --finalization:·( | 85 | --finalization:·(5)[6]:·--·finalizing·sequence·#7·-- |
| 86 | --finalization:·(6)[1]:·--·finalizing·sequence·#2·-- | ||
| 87 | --finalization:·(7)[4]:·--·finalizing·sequence·#5·-- | ||
| 88 | --finalization:·(8)[7]:·--·finalizing·sequence·#8·-- | ||
| 89 | --finalization:·( | 89 | --finalization:·(9)[2]:·--·finalizing·sequence·#3·--</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ········</table> | 91 | ········</table> |
| 92 | ······</div> | 92 | ······</div> |
| 93 | ······<div> | 93 | ······<div> |
| 94 | ········<h2>Caveat</h2> | 94 | ········<h2>Caveat</h2> |
| 95 | 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> | 95 | 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> |
| 96 | ······<div> | 96 | ······<div> |
| Offset 15, 23 lines modified | Offset 15, 23 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)[0]:·--·finalizing·sequence·#1·-- | ||
| 23 | --finalization:·(2)[7]:·--·finalizing·sequence·#8·-- | ||
| 24 | --finalization:·( | 22 | --finalization:·(1)[5]:·--·finalizing·sequence·#6·-- |
| 25 | --finalization:·( | 23 | --finalization:·(2)[3]:·--·finalizing·sequence·#4·-- |
| 26 | --finalization:·( | 24 | --finalization:·(3)[0]:·--·finalizing·sequence·#1·-- |
| 27 | --finalization:·( | 25 | --finalization:·(4)[8]:·--·finalizing·sequence·#9·-- |
| 28 | --finalization:·(7)[1]:·--·finalizing·sequence·#2·-- | ||
| 29 | --finalization:·( | 26 | --finalization:·(5)[6]:·--·finalizing·sequence·#7·-- |
| 27 | --finalization:·(6)[1]:·--·finalizing·sequence·#2·-- | ||
| 28 | --finalization:·(7)[4]:·--·finalizing·sequence·#5·-- | ||
| 30 | --finalization:·(8)[ | 29 | --finalization:·(8)[7]:·--·finalizing·sequence·#8·-- |
| 30 | --finalization:·(9)[2]:·--·finalizing·sequence·#3·-- | ||
| 31 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* | 31 | *\x8**\x8**\x8**\x8**\x8*·C\x8Ca\x8av\x8ve\x8ea\x8at\x8t·*\x8**\x8**\x8**\x8**\x8* |
| 32 | This·function·should·mainly·be·used·for·debugging.·Having·a·large·number·of | 32 | This·function·should·mainly·be·used·for·debugging.·Having·a·large·number·of |
| 33 | finalizers·might·degrade·the·performance·of·the·program.·Moreover,·registering | 33 | finalizers·might·degrade·the·performance·of·the·program.·Moreover,·registering |
| 34 | two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for | 34 | two·or·more·objects·that·are·members·of·a·circular·chain·of·pointers·for |
| 35 | finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the | 35 | finalization·will·result·in·a·memory·leak,·with·none·of·the·objects·in·the |
| 36 | chain·being·freed,·even·if·nothing·else·points·to·any·of·them. | 36 | chain·being·freed,·even·if·nothing·else·points·to·any·of·them. |
| 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* |
| Offset 70, 23 lines modified | Offset 70, 23 lines modified | ||
| 70 | ······</div> | 70 | ······</div> |
| 71 | ······<div> | 71 | ······<div> |
| 72 | ········<h2>Description</h2> | 72 | ········<h2>Description</h2> |
| 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/M2-2051901-0/0</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir</code></pre> | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·makeDirectory·dir</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, 19 lines modified | Offset 11, 19 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/M2-2051901-0/0 |
| 18 | i2·:·makeDirectory·dir | 18 | i2·:·makeDirectory·dir |
| 19 | i3·:·readDirectory·dir | 19 | i3·:·readDirectory·dir |
| 20 | o3·=·{.,· | 20 | o3·=·{..,·.} |
| 21 | o3·:·List | 21 | o3·:·List |
| 22 | i4·:·removeDirectory·dir | 22 | i4·:·removeDirectory·dir |
| 23 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 23 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 24 | ····*·_\x8r_\x8e_\x8a_\x8d_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·read·the·contents·of·a·directory | 24 | ····*·_\x8r_\x8e_\x8a_\x8d_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·read·the·contents·of·a·directory |
| 25 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·make·a·directory | 25 | ····*·_\x8m_\x8a_\x8k_\x8e_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·--·make·a·directory |
| 26 | *\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* | 26 | *\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 63, 20 lines modified | Offset 63, 20 lines modified | ||
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | ········<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 | ········<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> |
| 66 | ········<table·class="examples"> | 66 | ········<table·class="examples"> |
| 67 | ··········<tr> | 67 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 68 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 69 | o1·=·/tmp/M2- | 69 | o1·=·/tmp/M2-2035408-0/0</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootPath·|·fn | 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootPath·|·fn |
| 73 | o2·=·/tmp/M2- | 73 | o2·=·/tmp/M2-2035408-0/0</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ········</table> | 75 | ········</table> |
| 76 | ······</div> | 76 | ······</div> |
| 77 | ······<div> | 77 | ······<div> |
| 78 | ········<h2>See·also</h2> | 78 | ········<h2>See·also</h2> |
| 79 | ········<ul> | 79 | ········<ul> |
| 80 | ··········<li> | 80 | ··········<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/M2-2035408-0/0 |
| 23 | i2·:·rootPath·|·fn | 23 | i2·:·rootPath·|·fn |
| 24 | o2·=·/tmp/M2- | 24 | o2·=·/tmp/M2-2035408-0/0 |
| 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 63, 20 lines modified | Offset 63, 20 lines modified | ||
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | ········<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 | ········<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> |
| 66 | ········<table·class="examples"> | 66 | ········<table·class="examples"> |
| 67 | ··········<tr> | 67 | ··········<tr> |
| 68 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 68 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 69 | o1·=·/tmp/M2- | 69 | o1·=·/tmp/M2-2061484-0/0</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<tr> |
| 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootURI·|·fn | 72 | <td>··············<pre><code·class="language-macaulay2">i2·:·rootURI·|·fn |
| 73 | o2·=·file:///tmp/M2- | 73 | o2·=·file:///tmp/M2-2061484-0/0</code></pre> |
| 74 | </td>··········</tr> | 74 | </td>··········</tr> |
| 75 | ········</table> | 75 | ········</table> |
| 76 | ······</div> | 76 | ······</div> |
| 77 | ······<div> | 77 | ······<div> |
| 78 | ········<h2>See·also</h2> | 78 | ········<h2>See·also</h2> |
| 79 | ········<ul> | 79 | ········<ul> |
| 80 | ··········<li> | 80 | ··········<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/M2-2061484-0/0 |
| 23 | i2·:·rootURI·|·fn | 23 | i2·:·rootURI·|·fn |
| 24 | o2·=·file:///tmp/M2- | 24 | o2·=·file:///tmp/M2-2061484-0/0 |
| 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 75, 20 lines modified | Offset 75, 20 lines modified | ||
| 75 | ·····························1 | 75 | ·····························1 |
| 76 | o4·:·R-module,·submodule·of·R</code></pre> | 76 | o4·:·R-module,·submodule·of·R</code></pre> |
| 77 | </td>··········</tr> | 77 | </td>··········</tr> |
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i5·:·f·=·temporaryFileName() | 79 | <td>··············<pre><code·class="language-macaulay2">i5·:·f·=·temporaryFileName() |
| 80 | o5·=·/tmp/M2- | 80 | o5·=·/tmp/M2-2060498-0/0</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i6·:·f·<<·toString·(p,m,M)·<<·close | 83 | <td>··············<pre><code·class="language-macaulay2">i6·:·f·<<·toString·(p,m,M)·<<·close |
| 84 | o6·=·/tmp/M2- | 84 | o6·=·/tmp/M2-2060498-0/0 |
| 85 | o6·:·File</code></pre> | 85 | o6·:·File</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i7·:·get·f | 88 | <td>··············<pre><code·class="language-macaulay2">i7·:·get·f |
| 89 | 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, | 89 | 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/M2-2060498-0/0 |
| 33 | i6·:·f·<<·toString·(p,m,M)·<<·close | 33 | i6·:·f·<<·toString·(p,m,M)·<<·close |
| 34 | o6·=·/tmp/M2- | 34 | o6·=·/tmp/M2-2060498-0/0 |
| 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 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | o2·=·<<task,·created>> | 92 | o2·=·<<task,·created>> |
| 93 | o2·:·Task</code></pre> | 93 | o2·:·Task</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·schedule·t | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·schedule·t |
| 97 | o3·=·<<task,·re | 97 | o3·=·<<task,·created>> |
| 98 | o3·:·Task</code></pre> | 98 | o3·:·Task</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·taskResult·t | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·taskResult·t |
| 102 | o4·=·8</code></pre> | 102 | o4·=·8</code></pre> |
| Offset 33, 15 lines modified | Offset 33, 15 lines modified | ||
| 33 | i2·:·t·=·createTask(f,3) | 33 | i2·:·t·=·createTask(f,3) |
| 34 | o2·=·<<task,·created>> | 34 | o2·=·<<task,·created>> |
| 35 | o2·:·Task | 35 | o2·:·Task |
| 36 | i3·:·schedule·t | 36 | i3·:·schedule·t |
| 37 | o3·=·<<task,·re | 37 | o3·=·<<task,·created>> |
| 38 | o3·:·Task | 38 | o3·:·Task |
| 39 | i4·:·taskResult·t | 39 | i4·:·taskResult·t |
| 40 | o4·=·8 | 40 | o4·=·8 |
| 41 | i5·:·u·=·schedule(f,4) | 41 | i5·:·u·=·schedule(f,4) |
| Offset 321, 19 lines modified | Offset 321, 19 lines modified | ||
| 321 | <td>··············<pre><code·class="language-macaulay2">i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;</code></pre> | 321 | <td>··············<pre><code·class="language-macaulay2">i26·:·A·=·mutableMatrix(CC_53,·N,·N);·fillMatrix·A;</code></pre> |
| 322 | </td>··········</tr> | 322 | </td>··········</tr> |
| 323 | ··········<tr> | 323 | ··········<tr> |
| 324 | <td>··············<pre><code·class="language-macaulay2">i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;</code></pre> | 324 | <td>··············<pre><code·class="language-macaulay2">i28·:·B·=·mutableMatrix(CC_53,·N,·2);·fillMatrix·B;</code></pre> |
| 325 | </td>··········</tr> | 325 | </td>··········</tr> |
| 326 | ··········<tr> | 326 | ··········<tr> |
| 327 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·X·=·solve(A,B); | 327 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·X·=·solve(A,B); |
| 328 | ·--·used·0.000 | 328 | ·--·used·0.000189275s·(cpu);·0.00017932s·(thread);·0s·(gc)</code></pre> |
| 329 | </td>··········</tr> | 329 | </td>··········</tr> |
| 330 | ··········<tr> | 330 | ··········<tr> |
| 331 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·X·=·solve(A,B,·MaximalRank=>true); | 331 | <td>··············<pre><code·class="language-macaulay2">i31·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 332 | ·--·used· | 332 | ·--·used·7.8117e-05s·(cpu);·7.8057e-05s·(thread);·0s·(gc)</code></pre> |
| 333 | </td>··········</tr> | 333 | </td>··········</tr> |
| 334 | ··········<tr> | 334 | ··········<tr> |
| 335 | <td>··············<pre><code·class="language-macaulay2">i32·:·norm(A*X-B) | 335 | <td>··············<pre><code·class="language-macaulay2">i32·:·norm(A*X-B) |
| 336 | o32·=·5.11185069084045e-15 | 336 | o32·=·5.11185069084045e-15 |
| 337 | o32·:·RR·(of·precision·53)</code></pre> | 337 | o32·:·RR·(of·precision·53)</code></pre> |
| Offset 354, 19 lines modified | Offset 354, 19 lines modified | ||
| 354 | <td>··············<pre><code·class="language-macaulay2">i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;</code></pre> | 354 | <td>··············<pre><code·class="language-macaulay2">i34·:·A·=·mutableMatrix(CC_100,·N,·N);·fillMatrix·A;</code></pre> |
| 355 | </td>··········</tr> | 355 | </td>··········</tr> |
| 356 | ··········<tr> | 356 | ··········<tr> |
| 357 | <td>··············<pre><code·class="language-macaulay2">i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;</code></pre> | 357 | <td>··············<pre><code·class="language-macaulay2">i36·:·B·=·mutableMatrix(CC_100,·N,·2);·fillMatrix·B;</code></pre> |
| 358 | </td>··········</tr> | 358 | </td>··········</tr> |
| 359 | ··········<tr> | 359 | ··········<tr> |
| 360 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·X·=·solve(A,B); | 360 | <td>··············<pre><code·class="language-macaulay2">i38·:·time·X·=·solve(A,B); |
| 361 | ·--·used·0.1 | 361 | ·--·used·0.10707s·(cpu);·0.107076s·(thread);·0s·(gc)</code></pre> |
| 362 | </td>··········</tr> | 362 | </td>··········</tr> |
| 363 | ··········<tr> | 363 | ··········<tr> |
| 364 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·X·=·solve(A,B,·MaximalRank=>true); | 364 | <td>··············<pre><code·class="language-macaulay2">i39·:·time·X·=·solve(A,B,·MaximalRank=>true); |
| 365 | ·--·used·0.1 | 365 | ·--·used·0.109001s·(cpu);·0.109017s·(thread);·0s·(gc)</code></pre> |
| 366 | </td>··········</tr> | 366 | </td>··········</tr> |
| 367 | ··········<tr> | 367 | ··········<tr> |
| 368 | <td>··············<pre><code·class="language-macaulay2">i40·:·norm(A*X-B) | 368 | <td>··············<pre><code·class="language-macaulay2">i40·:·norm(A*X-B) |
| 369 | o40·=·1.49157827468970981408235588593e-28 | 369 | o40·=·1.49157827468970981408235588593e-28 |
| 370 | o40·:·RR·(of·precision·100)</code></pre> | 370 | 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·0.000189275s·(cpu);·0.00017932s·(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·7.8117e-05s·(cpu);·7.8057e-05s·(thread);·0s·(gc) |
| 204 | i32·:·norm(A*X-B) | 204 | i32·:·norm(A*X-B) |
| 205 | o32·=·5.11185069084045e-15 | 205 | o32·=·5.11185069084045e-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·0.10707s·(cpu);·0.107076s·(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·0.109001s·(cpu);·0.109017s·(thread);·0s·(gc) |
| 217 | i40·:·norm(A*X-B) | 217 | i40·:·norm(A*X-B) |
| 218 | o40·=·1.49157827468970981408235588593e-28 | 218 | o40·=·1.49157827468970981408235588593e-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 86, 67 lines modified | Offset 86, 67 lines modified | ||
| 86 | ······</div> | 86 | ······</div> |
| 87 | ······<div> | 87 | ······<div> |
| 88 | ········<h2>Description</h2> | 88 | ········<h2>Description</h2> |
| 89 | ········<table·class="examples"> | 89 | ········<table·class="examples"> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" | 91 | <td>··············<pre><code·class="language-macaulay2">i1·:·src·=·temporaryFileName()·|·"/" |
| 92 | o1·=·/tmp/M2- | 92 | o1·=·/tmp/M2-2055459-0/0/</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·dst·=·temporaryFileName()·|·"/" |
| 96 | o2·=·/tmp/M2- | 96 | o2·=·/tmp/M2-2055459-0/1/</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/")</code></pre> | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·makeDirectory·(src|"a/")</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/")</code></pre> | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·makeDirectory·(src|"b/")</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/")</code></pre> | 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·makeDirectory·(src|"b/c/")</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close | 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 109 | o6·=·/tmp/M2- | 109 | o6·=·/tmp/M2-2055459-0/0/a/f |
| 110 | o6·:·File</code></pre> | 110 | o6·:·File</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close | 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 114 | o7·=·/tmp/M2- | 114 | o7·=·/tmp/M2-2055459-0/0/a/g |
| 115 | o7·:·File</code></pre> | 115 | o7·:·File</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ··········<tr> | 117 | ··········<tr> |
| 118 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 118 | <td>··············<pre><code·class="language-macaulay2">i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 119 | o8·=·/tmp/M2- | 119 | o8·=·/tmp/M2-2055459-0/0/b/c/g |
| 120 | o8·:·File</code></pre> | 120 | o8·:·File</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i9·:·symlinkDirectory(src,dst,Verbose=>true) | 123 | <td>··············<pre><code·class="language-macaulay2">i9·:·symlinkDirectory(src,dst,Verbose=>true) |
| 124 | --symlinking:·../../../0/b/c/g·->·/tmp/M2- | 124 | --symlinking:·../../../0/b/c/g·->·/tmp/M2-2055459-0/1/b/c/g |
| 125 | --symlinking:·../../0/a/ | 125 | --symlinking:·../../0/a/f·->·/tmp/M2-2055459-0/1/a/f |
| 126 | --symlinking:·../../0/a/ | 126 | --symlinking:·../../0/a/g·->·/tmp/M2-2055459-0/1/a/g</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·(dst|"b/c/g") | 129 | <td>··············<pre><code·class="language-macaulay2">i10·:·get·(dst|"b/c/g") |
| 130 | o10·=·ho·there</code></pre> | 130 | o10·=·ho·there</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) | 133 | <td>··············<pre><code·class="language-macaulay2">i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) |
| 134 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2- | 134 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-2055459-0/1/b/c/g |
| 135 | --unsymlinking:·../../0/a/ | 135 | --unsymlinking:·../../0/a/f·->·/tmp/M2-2055459-0/1/a/f |
| 136 | --unsymlinking:·../../0/a/ | 136 | --unsymlinking:·../../0/a/g·->·/tmp/M2-2055459-0/1/a/g</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ········</table> | 138 | ········</table> |
| 139 | Now·we·remove·the·files·and·directories·we·created.········<table·class="examples"> | 139 | Now·we·remove·the·files·and·directories·we·created.········<table·class="examples"> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 141 | <td>··············<pre><code·class="language-macaulay2">i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 142 | o12·=·rm | 142 | o12·=·rm |
| Offset 31, 47 lines modified | Offset 31, 47 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/M2-2055459-0/0/ |
| 38 | i2·:·dst·=·temporaryFileName()·|·"/" | 38 | i2·:·dst·=·temporaryFileName()·|·"/" |
| 39 | o2·=·/tmp/M2- | 39 | o2·=·/tmp/M2-2055459-0/1/ |
| 40 | i3·:·makeDirectory·(src|"a/") | 40 | i3·:·makeDirectory·(src|"a/") |
| 41 | i4·:·makeDirectory·(src|"b/") | 41 | i4·:·makeDirectory·(src|"b/") |
| 42 | i5·:·makeDirectory·(src|"b/c/") | 42 | i5·:·makeDirectory·(src|"b/c/") |
| 43 | i6·:·src|"a/f"·<<·"hi·there"·<<·close | 43 | i6·:·src|"a/f"·<<·"hi·there"·<<·close |
| 44 | o6·=·/tmp/M2- | 44 | o6·=·/tmp/M2-2055459-0/0/a/f |
| 45 | o6·:·File | 45 | o6·:·File |
| 46 | i7·:·src|"a/g"·<<·"hi·there"·<<·close | 46 | i7·:·src|"a/g"·<<·"hi·there"·<<·close |
| 47 | o7·=·/tmp/M2- | 47 | o7·=·/tmp/M2-2055459-0/0/a/g |
| 48 | o7·:·File | 48 | o7·:·File |
| 49 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close | 49 | i8·:·src|"b/c/g"·<<·"ho·there"·<<·close |
| 50 | o8·=·/tmp/M2- | 50 | o8·=·/tmp/M2-2055459-0/0/b/c/g |
| 51 | o8·:·File | 51 | o8·:·File |
| 52 | i9·:·symlinkDirectory(src,dst,Verbose=>true) | 52 | i9·:·symlinkDirectory(src,dst,Verbose=>true) |
| 53 | --symlinking:·../../../0/b/c/g·->·/tmp/M2- | 53 | --symlinking:·../../../0/b/c/g·->·/tmp/M2-2055459-0/1/b/c/g |
| 54 | --symlinking:·../../0/a/g·->·/tmp/M2-1007573-0/1/a/g | ||
| 55 | --symlinking:·../../0/a/f·->·/tmp/M2- | 54 | --symlinking:·../../0/a/f·->·/tmp/M2-2055459-0/1/a/f |
| 55 | --symlinking:·../../0/a/g·->·/tmp/M2-2055459-0/1/a/g | ||
| 56 | i10·:·get·(dst|"b/c/g") | 56 | i10·:·get·(dst|"b/c/g") |
| 57 | o10·=·ho·there | 57 | o10·=·ho·there |
| 58 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) | 58 | i11·:·symlinkDirectory(src,dst,Verbose=>true,Undo=>true) |
| 59 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2- | 59 | --unsymlinking:·../../../0/b/c/g·->·/tmp/M2-2055459-0/1/b/c/g |
| 60 | --unsymlinking:·../../0/a/g·->·/tmp/M2-1007573-0/1/a/g | ||
| 61 | --unsymlinking:·../../0/a/f·->·/tmp/M2- | 60 | --unsymlinking:·../../0/a/f·->·/tmp/M2-2055459-0/1/a/f |
| 61 | --unsymlinking:·../../0/a/g·->·/tmp/M2-2055459-0/1/a/g | ||
| 62 | Now·we·remove·the·files·and·directories·we·created. | 62 | Now·we·remove·the·files·and·directories·we·created. |
| 63 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d | 63 | i12·:·rm·=·d·->·if·isDirectory·d·then·removeDirectory·d·else·removeFile·d |
| 64 | o12·=·rm | 64 | o12·=·rm |
| 65 | o12·:·FunctionClosure | 65 | o12·:·FunctionClosure |
| 66 | i13·:·scan(reverse·findFiles·src,·rm) | 66 | i13·:·scan(reverse·findFiles·src,·rm) |
| Offset 72, 15 lines modified | Offset 72, 15 lines modified | ||
| 72 | ······</div> | 72 | ······</div> |
| 73 | ······<div> | 73 | ······<div> |
| 74 | ········<h2>Description</h2> | 74 | ········<h2>Description</h2> |
| 75 | ········<table·class="examples"> | 75 | ········<table·class="examples"> |
| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn·=·temporaryFileName() |
| 78 | o1·=·/tmp/M2- | 78 | o1·=·/tmp/M2-2056426-0/0</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile("qwert",·fn)</code></pre> | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·symlinkFile("qwert",·fn)</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·fileExists·fn | 84 | <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/M2-2056426-0/0 |
| 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 62, 20 lines modified | Offset 62, 20 lines modified | ||
| 62 | ······</div> | 62 | ······</div> |
| 63 | ······<div> | 63 | ······<div> |
| 64 | ········<h2>Description</h2> | 64 | ········<h2>Description</h2> |
| 65 | 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 | 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"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·temporaryFileName·()·|·".tex" | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·temporaryFileName·()·|·".tex" |
| 68 | o1·=·/tmp/M2- | 68 | o1·=·/tmp/M2-2070680-0/0.tex</code></pre> |
| 69 | </td>··········</tr> | 69 | </td>··········</tr> |
| 70 | ··········<tr> | 70 | ··········<tr> |
| 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·temporaryFileName·()·|·".html" | 71 | <td>··············<pre><code·class="language-macaulay2">i2·:·temporaryFileName·()·|·".html" |
| 72 | o2·=·/tmp/M2- | 72 | o2·=·/tmp/M2-2070680-0/1.html</code></pre> |
| 73 | </td>··········</tr> | 73 | </td>··········</tr> |
| 74 | ········</table> | 74 | ········</table> |
| 75 | ········<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>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> |
| 76 | ········<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>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> |
| 77 | ········<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>The·temporary·file·name·is·derived·from·the·value·of·the·environment·variable·<span·class="tt">TMPDIR</span>,·if·it·has·one.</p> |
| 78 | ········<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 | ········<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> |
| 79 | ······</div> | 79 | ······</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/M2-2070680-0/0.tex |
| 19 | i2·:·temporaryFileName·()·|·".html" | 19 | i2·:·temporaryFileName·()·|·".html" |
| 20 | o2·=·/tmp/M2- | 20 | o2·=·/tmp/M2-2070680-0/1.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 55, 15 lines modified | Offset 55, 15 lines modified | ||
| 55 | ········</ul> | 55 | ········</ul> |
| 56 | ······</div> | 56 | ······</div> |
| 57 | ······<div> | 57 | ······<div> |
| 58 | ········<h2>Description</h2> | 58 | ········<h2>Description</h2> |
| 59 | <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 | <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"> |
| 60 | ··········<tr> | 60 | ··········<tr> |
| 61 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·3^30 | 61 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·3^30 |
| 62 | ·--·used·1. | 62 | ·--·used·1.6826e-05s·(cpu);·5.238e-06s·(thread);·0s·(gc) |
| 63 | o1·=·205891132094649</code></pre> | 63 | o1·=·205891132094649</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ········</table> | 65 | ········</table> |
| 66 | ······</div> | 66 | ······</div> |
| 67 | ······<div> | 67 | ······<div> |
| 68 | ········<h2>See·also</h2> | 68 | ········<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·1. | 15 | ·--·used·1.6826e-05s·(cpu);·5.238e-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 47, 22 lines modified | Offset 47, 22 lines modified | ||
| 47 | ········<h2>Description</h2> | 47 | ········<h2>Description</h2> |
| 48 | <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 | <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> |
| 49 | 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 | The·default·method·for·printing·such·timing·results·is·to·display·the·timing·separately·in·a·comment·below·the·computed·value.········<table·class="examples"> |
| 50 | ··········<tr> | 50 | ··········<tr> |
| 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·timing·3^30 | 51 | <td>··············<pre><code·class="language-macaulay2">i1·:·timing·3^30 |
| 52 | o1·=·205891132094649 | 52 | o1·=·205891132094649 |
| 53 | ·····--·.00001 | 53 | ·····--·.000014061·seconds |
| 54 | o1·:·Time</code></pre> | 54 | o1·:·Time</code></pre> |
| 55 | </td>··········</tr> | 55 | </td>··········</tr> |
| 56 | ··········<tr> | 56 | ··········<tr> |
| 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·oo | 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·peek·oo |
| 58 | o2·=·Time{.00001 | 58 | o2·=·Time{.000014061,·205891132094649}</code></pre> |
| 59 | </td>··········</tr> | 59 | </td>··········</tr> |
| 60 | ········</table> | 60 | ········</table> |
| 61 | ······</div> | 61 | ······</div> |
| 62 | ······<div> | 62 | ······<div> |
| 63 | ········<h2>See·also</h2> | 63 | ········<h2>See·also</h2> |
| 64 | ········<ul> | 64 | ········<ul> |
| 65 | ··········<li> | 65 | ··········<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 | ·····--·.000014061·seconds |
| 16 | o1·:·Time | 16 | o1·:·Time |
| 17 | i2·:·peek·oo | 17 | i2·:·peek·oo |
| 18 | o2·=·Time{.00001 | 18 | o2·=·Time{.000014061,·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 | ···············"mpir·version"·=>·not·present | 101 | ···············"mpir·version"·=>·not·present |
| 102 | ···············"mpsolve·version"·=>·3.2.1 | 102 | ···············"mpsolve·version"·=>·3.2.1 |
| 103 | ···············"mysql·version"·=>·not·present | 103 | ···············"mysql·version"·=>·not·present |
| 104 | ···············"ntl·version"·=>·11.5.1 | 104 | ···············"ntl·version"·=>·11.5.1 |
| 105 | ···············"operating·system·release"·=>·6.10 | 105 | ···············"operating·system·release"·=>·6.1.0-26-cloud-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 | 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 |
| 108 | ···············"pointer·size"·=>·8 | 108 | ···············"pointer·size"·=>·8 |
| 109 | ···············"python·version"·=>·3.12.6 | 109 | ···············"python·version"·=>·3.12.6 |
| 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 |
| Offset 62, 15 lines modified | Offset 62, 15 lines modified | ||
| 62 | ···············"memtailor·version"·=>·1.0 | 62 | ···············"memtailor·version"·=>·1.0 |
| 63 | ···············"mpfi·version"·=>·1.5.4 | 63 | ···············"mpfi·version"·=>·1.5.4 |
| 64 | ···············"mpfr·version"·=>·4.2.1 | 64 | ···············"mpfr·version"·=>·4.2.1 |
| 65 | ···············"mpir·version"·=>·not·present | 65 | ···············"mpir·version"·=>·not·present |
| 66 | ···············"mpsolve·version"·=>·3.2.1 | 66 | ···············"mpsolve·version"·=>·3.2.1 |
| 67 | ···············"mysql·version"·=>·not·present | 67 | ···············"mysql·version"·=>·not·present |
| 68 | ···············"ntl·version"·=>·11.5.1 | 68 | ···············"ntl·version"·=>·11.5.1 |
| 69 | ···············"operating·system·release"·=>·6.10 | 69 | ···············"operating·system·release"·=>·6.1.0-26-cloud-amd64 |
| 70 | ···············"operating·system"·=>·Linux | 70 | ···············"operating·system"·=>·Linux |
| 71 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic | 71 | ···············"packages"·=>·Style·FirstPackage·Macaulay2Doc·Parsing·Classic |
| 72 | Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition | 72 | Browse·Benchmark·Text·SimpleDoc·PackageTemplate·Saturation·PrimaryDecomposition |
| 73 | FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth | 73 | FourierMotzkin·Dmodules·WeylAlgebras·HolonomicSystems·BernsteinSato·Depth |
| 74 | Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements | 74 | Elimination·GenericInitialIdeal·IntegralClosure·HyperplaneArrangements |
| 75 | LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings | 75 | LexIdeals·Markov·NoetherNormalization·Points·ReesAlgebra·Regularity·SchurRings |
| 76 | SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone | 76 | SymmetricPolynomials·SchurFunctors·SimplicialComplexes·LLLBases·TangentCone |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·2.56545s·(cpu);·1.26247s·(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 140, 15 lines modified | Offset 140, 15 lines modified | ||
| 140 | ········</table> | 140 | ········</table> |
| 141 | ········<div> | 141 | ········<div> |
| 142 | ··········<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 | ··········<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> |
| 143 | ········</div> | 143 | ········</div> |
| 144 | ········<table·class="examples"> | 144 | ········<table·class="examples"> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·netList·primaryDecomposition·J | 146 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·netList·primaryDecomposition·J |
| 147 | ·--·used·2. | 147 | ·--·used·2.56545s·(cpu);·1.26247s·(thread);·0s·(gc) |
| 148 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 148 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 149 | o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| | 149 | o8·=·|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| |
| 150 | ·····|········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 | ·····|········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··························································································································································································································································································································································································································································································································································································································································································································································| |
| 151 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 151 | ·····+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 152 | ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| | 152 | ·····|ideal·(p·······,·p·······,·p·······,·p·······,·p·······p········-·p·······p·······,·p·······p········-·p·······p·······)·························································································································································································································································································································································································································································································································································································································································································································································| |
| 153 | ·····|········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··························································································································································································································································································································································································································································································································································································································································································································································| | 153 | ·····|········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·2.56545s·(cpu);·1.26247s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 214, 17 lines modified | Offset 214, 17 lines modified | ||
| 214 | ······|·1·-1·1·| | 214 | ······|·1·-1·1·| |
| 215 | ······|·0·1··0·| | 215 | ······|·0·1··0·| |
| 216 | ···············3·······3 | 216 | ···············3·······3 |
| 217 | o22·:·Matrix·ZZ··<--·ZZ | 217 | o22·:·Matrix·ZZ··<--·ZZ |
| 218 | i23·:·time·schubertRegularity·B | 218 | i23·:·time·schubertRegularity·B |
| 219 | ·--·used·0.01 | 219 | ·--·used·0.0119624s·(cpu);·0.0136697s·(thread);·0s·(gc) |
| 220 | o23·=·1 | 220 | o23·=·1 |
| 221 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B | 221 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B |
| 222 | ·--·used·0.014 | 222 | ·--·used·0.0134425s·(cpu);·0.0139395s·(thread);·0s·(gc) |
| 223 | o24·=·1 | 223 | o24·=·1 |
| 224 | i25·:· | 224 | i25·:· |
| Offset 168, 17 lines modified | Offset 168, 17 lines modified | ||
| 168 | ······z···z···z···,·z···z···z····-·z···z···,·z···z···z····-·z···z···) | 168 | ······z···z···z···,·z···z···z····-·z···z···,·z···z···z····-·z···z···) |
| 169 | ·······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 | 169 | ·······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 |
| 170 | o14·:·Ideal·of·QQ[z···..z···] | 170 | o14·:·Ideal·of·QQ[z···..z···] |
| 171 | ···················1,1···5,5 | 171 | ···················1,1···5,5 |
| 172 | i15·:·time·schubertRegularity·p | 172 | i15·:·time·schubertRegularity·p |
| 173 | ·--·used·0.001 | 173 | ·--·used·0.00170726s·(cpu);·0.000213531s·(thread);·0s·(gc) |
| 174 | o15·=·5 | 174 | o15·=·5 |
| 175 | i16·:·time·regularity·comodule·I | 175 | i16·:·time·regularity·comodule·I |
| 176 | ·--·used·0.01 | 176 | ·--·used·0.0140738s·(cpu);·0.0142772s·(thread);·0s·(gc) |
| 177 | o16·=·5 | 177 | o16·=·5 |
| 178 | i17·:· | 178 | 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·0.00 | 7 | ·--·used·0.000897711s·(cpu);·0.0034533s·(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·0.000 | 14 | ·--·used·0.000222465s·(cpu);·0.00177337s·(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 336, 21 lines modified | Offset 336, 21 lines modified | ||
| 336 | ········</table> | 336 | ········</table> |
| 337 | ········<div> | 337 | ········<div> |
| 338 | ··········<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·initical·ideals·by·[CV20].</p> | 338 | ··········<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·initical·ideals·by·[CV20].</p> |
| 339 | ········</div> | 339 | ········</div> |
| 340 | ········<table·class="examples"> | 340 | ········<table·class="examples"> |
| 341 | ··········<tr> | 341 | ··········<tr> |
| 342 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·schubertRegularity·B | 342 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·schubertRegularity·B |
| 343 | ·--·used·0.01 | 343 | ·--·used·0.0119624s·(cpu);·0.0136697s·(thread);·0s·(gc) |
| 344 | o23·=·1</code></pre> | 344 | o23·=·1</code></pre> |
| 345 | </td>··········</tr> | 345 | </td>··········</tr> |
| 346 | ··········<tr> | 346 | ··········<tr> |
| 347 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B | 347 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B |
| 348 | ·--·used·0.014 | 348 | ·--·used·0.0134425s·(cpu);·0.0139395s·(thread);·0s·(gc) |
| 349 | o24·=·1</code></pre> | 349 | o24·=·1</code></pre> |
| 350 | </td>··········</tr> | 350 | </td>··········</tr> |
| 351 | ········</table> | 351 | ········</table> |
| 352 | ········<div> | 352 | ········<div> |
| 353 | ··········<h2>Functions·for·investigating·ASM·varieties</h2> | 353 | ··········<h2>Functions·for·investigating·ASM·varieties</h2> |
| 354 | ········</div> | 354 | ········</div> |
| Offset 245, 19 lines modified | Offset 245, 19 lines modified | ||
| 245 | Additionally,·this·package·facilitates·the·investigating·homological·invariants | 245 | Additionally,·this·package·facilitates·the·investigating·homological·invariants |
| 246 | of·ASM·ideals·efficiently·by·computing·the·associated·invariants·for·their | 246 | of·ASM·ideals·efficiently·by·computing·the·associated·invariants·for·their |
| 247 | antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17]. | 247 | antidiagonal·initial·ideals,·which·are·known·to·be·squarefree·by·[Wei17]. |
| 248 | Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and | 248 | Therefore·the·extremal·Betti·numbers·(which·encode·regularity,·depth,·and |
| 249 | projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal | 249 | projective·dimension)·of·ASM·ideals·coincide·with·those·of·their·antidiagonal |
| 250 | initical·ideals·by·[CV20]. | 250 | initical·ideals·by·[CV20]. |
| 251 | i23·:·time·schubertRegularity·B | 251 | i23·:·time·schubertRegularity·B |
| 252 | ·--·used·0.01 | 252 | ·--·used·0.0119624s·(cpu);·0.0136697s·(thread);·0s·(gc) |
| 253 | o23·=·1 | 253 | o23·=·1 |
| 254 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B | 254 | i24·:·time·regularity·comodule·schubertDeterminantalIdeal·B |
| 255 | ·--·used·0.014 | 255 | ·--·used·0.0134425s·(cpu);·0.0139395s·(thread);·0s·(gc) |
| 256 | o24·=·1 | 256 | o24·=·1 |
| 257 | *\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* | 257 | *\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* |
| 258 | ····*·_\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 | 258 | ····*·_\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 |
| 259 | ······matrix | 259 | ······matrix |
| 260 | ····*·_\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 | 260 | ····*·_\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 |
| 261 | ······alternating·sign·matrix | 261 | ······alternating·sign·matrix |
| Offset 271, 21 lines modified | Offset 271, 21 lines modified | ||
| 271 | ········</table> | 271 | ········</table> |
| 272 | ········<div> | 272 | ········<div> |
| 273 | ··········<p>Finally,·this·package·contains·functions·for·investigating·homological·invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial·algorithms·produced·in·[PSW21].</p> | 273 | ··········<p>Finally,·this·package·contains·functions·for·investigating·homological·invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial·algorithms·produced·in·[PSW21].</p> |
| 274 | ········</div> | 274 | ········</div> |
| 275 | ········<table·class="examples"> | 275 | ········<table·class="examples"> |
| 276 | ··········<tr> | 276 | ··········<tr> |
| 277 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·schubertRegularity·p | 277 | <td>··············<pre><code·class="language-macaulay2">i15·:·time·schubertRegularity·p |
| 278 | ·--·used·0.001 | 278 | ·--·used·0.00170726s·(cpu);·0.000213531s·(thread);·0s·(gc) |
| 279 | o15·=·5</code></pre> | 279 | o15·=·5</code></pre> |
| 280 | </td>··········</tr> | 280 | </td>··········</tr> |
| 281 | ··········<tr> | 281 | ··········<tr> |
| 282 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·regularity·comodule·I | 282 | <td>··············<pre><code·class="language-macaulay2">i16·:·time·regularity·comodule·I |
| 283 | ·--·used·0.01 | 283 | ·--·used·0.0140738s·(cpu);·0.0142772s·(thread);·0s·(gc) |
| 284 | o16·=·5</code></pre> | 284 | o16·=·5</code></pre> |
| 285 | </td>··········</tr> | 285 | </td>··········</tr> |
| 286 | ········</table> | 286 | ········</table> |
| 287 | ········<div> | 287 | ········<div> |
| 288 | ··········<h2>Functions·for·investigating·matrix·Schubert·varieties</h2> | 288 | ··········<h2>Functions·for·investigating·matrix·Schubert·varieties</h2> |
| 289 | ········</div> | 289 | ········</div> |
| Offset 581, 19 lines modified | Offset 581, 19 lines modified | ||
| 581 | o14·:·Ideal·of·QQ[z···..z···] | 581 | o14·:·Ideal·of·QQ[z···..z···] |
| 582 | ···················1,1···5,5 | 582 | ···················1,1···5,5 |
| 583 | Finally,·this·package·contains·functions·for·investigating·homological | 583 | Finally,·this·package·contains·functions·for·investigating·homological |
| 584 | invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial | 584 | invariants·of·matrix·Schubert·varieties·efficiently·through·combinatorial |
| 585 | algorithms·produced·in·[PSW21]. | 585 | algorithms·produced·in·[PSW21]. |
| 586 | i15·:·time·schubertRegularity·p | 586 | i15·:·time·schubertRegularity·p |
| 587 | ·--·used·0.001 | 587 | ·--·used·0.00170726s·(cpu);·0.000213531s·(thread);·0s·(gc) |
| 588 | o15·=·5 | 588 | o15·=·5 |
| 589 | i16·:·time·regularity·comodule·I | 589 | i16·:·time·regularity·comodule·I |
| 590 | ·--·used·0.01 | 590 | ·--·used·0.0140738s·(cpu);·0.0142772s·(thread);·0s·(gc) |
| 591 | o16·=·5 | 591 | o16·=·5 |
| 592 | *\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* | 592 | *\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* |
| 593 | ····*·_\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 | 593 | ····*·_\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 |
| 594 | ······an·ASM·ideal | 594 | ······an·ASM·ideal |
| 595 | ····*·_\x8r_\x8a_\x8n_\x8k_\x8T_\x8a_\x8b_\x8l_\x8e_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·a·table·of·rank·conditions·that·determines·a | 595 | ····*·_\x8r_\x8a_\x8n_\x8k_\x8T_\x8a_\x8b_\x8l_\x8e_\x8(_\x8L_\x8i_\x8s_\x8t_\x8)·--·compute·a·table·of·rank·conditions·that·determines·a |
| 596 | ······Schubert·determinantal·ideal·or,·more·generally,·an·alternating·sign | 596 | ······Schubert·determinantal·ideal·or,·more·generally,·an·alternating·sign |
| Offset 78, 26 lines modified | Offset 78, 26 lines modified | ||
| 78 | o1·=·{2,·1,·4,·3} | 78 | o1·=·{2,·1,·4,·3} |
| 79 | o1·:·List</code></pre> | 79 | o1·:·List</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·grothendieckPolynomial·w | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·grothendieckPolynomial·w |
| 83 | ·--·used·0.00 | 83 | ·--·used·0.000897711s·(cpu);·0.0034533s·(thread);·0s·(gc) |
| 84 | ······2········2······2···············2 | 84 | ······2········2······2···············2 |
| 85 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 85 | o2·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 86 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 86 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 87 | o2·:·QQ[x·..x·] | 87 | o2·:·QQ[x·..x·] |
| 88 | ·········1···4</code></pre> | 88 | ·········1···4</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·grothendieckPolynomial·(w,Algorithm=>"PipeDream") |
| 92 | ·--·used·0.000 | 92 | ·--·used·0.000222465s·(cpu);·0.00177337s·(thread);·0s·(gc) |
| 93 | ······2········2······2···············2 | 93 | ······2········2······2···············2 |
| 94 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x | 94 | o3·=·x·x·x··-·x·x··-·x·x··-·x·x·x··+·x··+·x·x··+·x·x |
| 95 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 | 95 | ······1·2·3····1·2····1·3····1·2·3····1····1·2····1·3 |
| 96 | o3·:·QQ[x·..x·] | 96 | o3·:·QQ[x·..x·] |
| 97 | ·········1···4</code></pre> | 97 | ·········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·0.00 | 24 | ·--·used·0.000897711s·(cpu);·0.0034533s·(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·0.000 | 31 | ·--·used·0.000222465s·(cpu);·0.00177337s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.0 | 55 | ·--·used·0.036645s·(cpu);·0.0397547s·(thread);·0s·(gc) |
| 56 | o10·=·true | 56 | o10·=·true |
| 57 | i11·:·time·fVector·R10 | 57 | i11·:·time·fVector·R10 |
| 58 | ·--·used·0.1 | 58 | ·--·used·0.150204s·(cpu);·0.0604744s·(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·0.000 | 81 | ·--·used·0.000442356s·(cpu);·0.000230567s·(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 | ·--·0. | 13 | ·--·0.0629068·seconds·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·0.0 | 37 | ·--·used·0.0408801s·(cpu);·0.038059s·(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·1.3 | 13 | ·--·used·1.32769s·(cpu);·0.929133s·(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·0.010427s·(cpu);·0.0110496s·(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·9.73255s·(cpu);·3.43577s·(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·0.00 | 41 | ·--·used·0.00105182s·(cpu);·0.000520393s·(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 | ·--·0.0 | 39 | ·--·0.00932727·seconds·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 123, 21 lines modified | Offset 123, 21 lines modified | ||
| 123 | o9·=·{groundSet,·rankFunction,·storedRepresentation} | 123 | o9·=·{groundSet,·rankFunction,·storedRepresentation} |
| 124 | o9·:·List</code></pre> | 124 | o9·:·List</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isWellDefined·R10 | 127 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isWellDefined·R10 |
| 128 | ·--·used·0.0 | 128 | ·--·used·0.036645s·(cpu);·0.0397547s·(thread);·0s·(gc) |
| 129 | o10·=·true</code></pre> | 129 | o10·=·true</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·fVector·R10 | 132 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·fVector·R10 |
| 133 | ·--·used·0.1 | 133 | ·--·used·0.150204s·(cpu);·0.0604744s·(thread);·0s·(gc) |
| 134 | o11·=·HashTable{0·=>·1·} | 134 | o11·=·HashTable{0·=>·1·} |
| 135 | ················1·=>·10 | 135 | ················1·=>·10 |
| 136 | ················2·=>·45 | 136 | ················2·=>·45 |
| 137 | ················3·=>·75 | 137 | ················3·=>·75 |
| 138 | ················4·=>·30 | 138 | ················4·=>·30 |
| 139 | ················5·=>·1 | 139 | ················5·=>·1 |
| Offset 151, 15 lines modified | Offset 151, 15 lines modified | ||
| 151 | ······----------------------------------------------------------------------- | 151 | ······----------------------------------------------------------------------- |
| 152 | ······groundSet,·dual,·storedRepresentation} | 152 | ······groundSet,·dual,·storedRepresentation} |
| 153 | o12·:·List</code></pre> | 153 | o12·:·List</code></pre> |
| 154 | </td>··········</tr> | 154 | </td>··········</tr> |
| 155 | ··········<tr> | 155 | ··········<tr> |
| 156 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·fVector·R10 | 156 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·fVector·R10 |
| 157 | ·--·used·0.000 | 157 | ·--·used·0.000442356s·(cpu);·0.000230567s·(thread);·0s·(gc) |
| 158 | o13·=·HashTable{0·=>·1·} | 158 | o13·=·HashTable{0·=>·1·} |
| 159 | ················1·=>·10 | 159 | ················1·=>·10 |
| 160 | ················2·=>·45 | 160 | ················2·=>·45 |
| 161 | ················3·=>·75 | 161 | ················3·=>·75 |
| 162 | ················4·=>·30 | 162 | ················4·=>·30 |
| 163 | ················5·=>·1 | 163 | ················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·0.0 | 76 | ·--·used·0.036645s·(cpu);·0.0397547s·(thread);·0s·(gc) |
| 77 | o10·=·true | 77 | o10·=·true |
| 78 | i11·:·time·fVector·R10 | 78 | i11·:·time·fVector·R10 |
| 79 | ·--·used·0.1 | 79 | ·--·used·0.150204s·(cpu);·0.0604744s·(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·0.000 | 98 | ·--·used·0.000442356s·(cpu);·0.000230567s·(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 89, 15 lines modified | Offset 89, 15 lines modified | ||
| 89 | o2·=·a·"matroid"·of·rank·2·on·5·elements | 89 | o2·=·a·"matroid"·of·rank·2·on·5·elements |
| 90 | o2·:·Matroid</code></pre> | 90 | o2·:·Matroid</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·L·=·allMinors(V,·U25); | 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·L·=·allMinors(V,·U25); |
| 94 | ·--·0. | 94 | ·--·0.0629068·seconds·elapsed</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·#L | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·#L |
| 98 | o4·=·64</code></pre> | 98 | o4·=·64</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<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 | ·--·0. | 33 | ·--·0.0629068·seconds·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 124, 15 lines modified | Offset 124, 15 lines modified | ||
| 124 | o6·=·a·"matroid"·of·rank·3·on·7·elements | 124 | o6·=·a·"matroid"·of·rank·3·on·7·elements |
| 125 | o6·:·Matroid</code></pre> | 125 | o6·:·Matroid</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·autF7·=·getIsos(F7,·F7); | 128 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·autF7·=·getIsos(F7,·F7); |
| 129 | ·--·used·0.0 | 129 | ·--·used·0.0408801s·(cpu);·0.038059s·(thread);·0s·(gc)</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i8·:·#autF7 | 132 | <td>··············<pre><code·class="language-macaulay2">i8·:·#autF7 |
| 133 | o8·=·168</code></pre> | 133 | o8·=·168</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ········</table> | 135 | ········</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·0.0 | 57 | ·--·used·0.0408801s·(cpu);·0.038059s·(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 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·hasMinor(M4,·uniformMatroid(2,4)) | 96 | <td>··············<pre><code·class="language-macaulay2">i2·:·hasMinor(M4,·uniformMatroid(2,4)) |
| 97 | o2·=·false</code></pre> | 97 | o2·=·false</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·hasMinor(M6,·M5) | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·hasMinor(M6,·M5) |
| 101 | ·--·used·1.3 | 101 | ·--·used·1.32769s·(cpu);·0.929133s·(thread);·0s·(gc) |
| 102 | o3·=·true</code></pre> | 102 | o3·=·true</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 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·1.3 | 40 | ·--·used·1.32769s·(cpu);·0.929133s·(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 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | o4·=·a·"matroid"·of·rank·4·on·10·elements | 103 | o4·=·a·"matroid"·of·rank·4·on·10·elements |
| 104 | o4·:·Matroid</code></pre> | 104 | o4·:·Matroid</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isomorphism(M5,·minorM6) | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isomorphism(M5,·minorM6) |
| 108 | ·--·used·0.0 | 108 | ·--·used·0.010427s·(cpu);·0.0110496s·(thread);·0s·(gc) |
| 109 | o5·=·HashTable{0·=>·1} | 109 | o5·=·HashTable{0·=>·1} |
| 110 | ···············1·=>·0 | 110 | ···············1·=>·0 |
| 111 | ···············2·=>·3 | 111 | ···············2·=>·3 |
| 112 | ···············3·=>·2 | 112 | ···············3·=>·2 |
| 113 | ···············4·=>·6 | 113 | ···············4·=>·6 |
| 114 | ···············5·=>·5 | 114 | ···············5·=>·5 |
| Offset 143, 15 lines modified | Offset 143, 15 lines modified | ||
| 143 | o7·=·a·"matroid"·of·rank·5·on·15·elements | 143 | o7·=·a·"matroid"·of·rank·5·on·15·elements |
| 144 | o7·:·Matroid</code></pre> | 144 | o7·:·Matroid</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·phi·=·isomorphism(N,M6) | 147 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·phi·=·isomorphism(N,M6) |
| 148 | ·--·used· | 148 | ·--·used·9.73255s·(cpu);·3.43577s·(thread);·0s·(gc) |
| 149 | o8·=·HashTable{0·=>·11·} | 149 | o8·=·HashTable{0·=>·11·} |
| 150 | ···············1·=>·0 | 150 | ···············1·=>·0 |
| 151 | ···············2·=>·1 | 151 | ···············2·=>·1 |
| 152 | ···············3·=>·6 | 152 | ···············3·=>·6 |
| 153 | ···············4·=>·9 | 153 | ···············4·=>·9 |
| 154 | ···············5·=>·8 | 154 | ···············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·0.010427s·(cpu);·0.0110496s·(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·9.73255s·(cpu);·3.43577s·(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 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) | 123 | <td>··············<pre><code·class="language-macaulay2">i8·:·R·=·ZZ[x,y];·tuttePolynomial(M0,·R)·==·tuttePolynomial(M1,·R) |
| 124 | o9·=·true</code></pre> | 124 | o9·=·true</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·quickIsomorphismTest(M0,·M1) | 127 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·quickIsomorphismTest(M0,·M1) |
| 128 | ·--·used·0.00 | 128 | ·--·used·0.00105182s·(cpu);·0.000520393s·(thread);·0s·(gc) |
| 129 | o10·=·false</code></pre> | 129 | o10·=·false</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i11·:·value·oo·===·false | 132 | <td>··············<pre><code·class="language-macaulay2">i11·:·value·oo·===·false |
| 133 | o11·=·true</code></pre> | 133 | 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·0.00 | 57 | ·--·used·0.00105182s·(cpu);·0.000520393s·(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 117, 15 lines modified | Offset 117, 15 lines modified | ||
| 117 | o5·=·{groundSet,·rankFunction,·storedRepresentation} | 117 | o5·=·{groundSet,·rankFunction,·storedRepresentation} |
| 118 | o5·:·List</code></pre> | 118 | o5·:·List</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·fVector·M | 121 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·fVector·M |
| 122 | ·--·0.0 | 122 | ·--·0.00932727·seconds·elapsed |
| 123 | o6·=·HashTable{0·=>·1·} | 123 | o6·=·HashTable{0·=>·1·} |
| 124 | ···············1·=>·6 | 124 | ···············1·=>·6 |
| 125 | ···············2·=>·15 | 125 | ···············2·=>·15 |
| 126 | ···············3·=>·20 | 126 | ···············3·=>·20 |
| 127 | ···············4·=>·1 | 127 | ···············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 | ·--·0.0 | 54 | ·--·0.00932727·seconds·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 6, 15 lines modified | Offset 6, 15 lines modified | ||
| 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)·········#primes·=·0·#prunedViaCodim·=·0 | 9 | ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0 |
| 10 | ··Strategy:·Birational········(time·.01 | 10 | ··Strategy:·Birational········(time·.0119197)··#primes·=·0·#prunedViaCodim·=·0 |
| 11 | ··Strategy:·Factorization·····(time· | 11 | ··Strategy:·Factorization·····(time·.0027212)··#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 | ·--·0.0416691·seconds·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 | ·--·0.000 | 34 | ·--·0.000353603·seconds·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 | ·--·0.0 | 38 | ·--·0.0175823·seconds·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 | ·--·0. | 33 | ·--·0.161783·seconds·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 | ·--·0.0 | 36 | ·--·0.0142254·seconds·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 | ·--·0.0 | 39 | ·--·0.000983094·seconds·elapsed |
| 40 | o9·=·false | 40 | o9·=·false |
| 41 | i10·:· | 41 | i10·:· |
| Offset 60, 19 lines modified | Offset 60, 19 lines modified | ||
| 60 | <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 | <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); |
| 61 | o3·:·Ideal·of·R</code></pre> | 61 | o3·:·Ideal·of·R</code></pre> |
| 62 | </td>··········</tr> | 62 | </td>··········</tr> |
| 63 | ··········<tr> | 63 | ··········<tr> |
| 64 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); | 64 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·minimalPrimes(ideal·I_*,·Strategy·=>·Hybrid{Linear,Birational,Factorization,DecomposeMonomials},·Verbosity·=>·2); |
| 65 | ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0 | 65 | ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0 |
| 66 | ··Strategy:·Birational········(time·.01 | 66 | ··Strategy:·Birational········(time·.0119197)··#primes·=·0·#prunedViaCodim·=·0 |
| 67 | ··Strategy:·Factorization·····(time· | 67 | ··Strategy:·Factorization·····(time·.0027212)··#primes·=·0·#prunedViaCodim·=·0 |
| 68 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes... | 68 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and·selecting·minimal·primes... |
| 69 | ·--··Time·taken·:·0 | 69 | ·--··Time·taken·:·0 |
| 70 | ·--·0. | 70 | ·--·0.0416691·seconds·elapsed |
| 71 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0</code></pre> | 71 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0</code></pre> |
| 72 | </td>··········</tr> | 72 | </td>··········</tr> |
| 73 | ········</table> | 73 | ········</table> |
| 74 | ······</div> | 74 | ······</div> |
| 75 | ······<div> | 75 | ······<div> |
| 76 | ········<h2>See·also</h2> | 76 | ········<h2>See·also</h2> |
| 77 | ········<ul> | 77 | ········<ul> |
| Offset 12, 19 lines modified | Offset 12, 19 lines modified | ||
| 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)·········#primes·=·0·#prunedViaCodim·=·0 | 17 | ··Strategy:·Linear············(time·0)·········#primes·=·0·#prunedViaCodim·=·0 |
| 18 | ··Strategy:·Birational········(time·.01 | 18 | ··Strategy:·Birational········(time·.0119197)··#primes·=·0·#prunedViaCodim·=·0 |
| 19 | ··Strategy:·Factorization·····(time· | 19 | ··Strategy:·Factorization·····(time·.0027212)··#primes·=·0·#prunedViaCodim·=·0 |
| 20 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and | 20 | ··Strategy:·DecomposeMonomials·--·Converting·annotated·ideals·to·ideals·and |
| 21 | selecting·minimal·primes... | 21 | selecting·minimal·primes... |
| 22 | ·--··Time·taken·:·0 | 22 | ·--··Time·taken·:·0 |
| 23 | ·--·0. | 23 | ·--·0.0416691·seconds·elapsed |
| 24 | (time·0)·········#primes·=·1·#prunedViaCodim·=·0 | 24 | (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* | 25 | *\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) | 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 | *\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·_\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·< | 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 | _\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. | 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. |
| Offset 124, 23 lines modified | Offset 124, 23 lines modified | ||
| 124 | ·············2········2···3·····2 | 124 | ·············2········2···3·····2 |
| 125 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) | 125 | o5·=·ideal·(c·,·a*c,·a·,·b·,·a*b·) |
| 126 | o5·:·Ideal·of·R</code></pre> | 126 | o5·:·Ideal·of·R</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) | 129 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·radical(ideal·I_*,·Strategy·=>·Monomial) |
| 130 | ·--·0.000 | 130 | ·--·0.000353603·seconds·elapsed |
| 131 | o6·=·ideal·(a,·b,·c) | 131 | o6·=·ideal·(a,·b,·c) |
| 132 | o6·:·Ideal·of·R</code></pre> | 132 | o6·:·Ideal·of·R</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) | 135 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radical(ideal·I_*,·Unmixed·=>·true) |
| 136 | ·--·0.0 | 136 | ·--·0.0175823·seconds·elapsed |
| 137 | o7·=·ideal·(c,·b,·a) | 137 | o7·=·ideal·(c,·b,·a) |
| 138 | o7·:·Ideal·of·R</code></pre> | 138 | o7·:·Ideal·of·R</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ········</table> | 140 | ········</table> |
| 141 | ········<div> | 141 | ········<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 | ·--·0.000 | 68 | ·--·0.000353603·seconds·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 | ·--·0.0 | 72 | ·--·0.0175823·seconds·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 116, 27 lines modified | Offset 116, 27 lines modified | ||
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 | 117 | <td>··············<pre><code·class="language-macaulay2">i6·:·x_0^(D-1)·%·I·!=·0·and·x_0^D·%·I·==·0 |
| 118 | o6·=·true</code></pre> | 118 | o6·=·true</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radicalContainment(x_0,·I) | 121 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·radicalContainment(x_0,·I) |
| 122 | ·--·0. | 122 | ·--·0.161783·seconds·elapsed |
| 123 | o7·=·true</code></pre> | 123 | o7·=·true</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") | 126 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·radicalContainment(x_0,·I,·Strategy·=>·"Kollar") |
| 127 | ·--·0.0 | 127 | ·--·0.0142254·seconds·elapsed |
| 128 | o8·=·true</code></pre> | 128 | o8·=·true</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") | 131 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·radicalContainment(x_n,·I,·Strategy·=>·"Kollar") |
| 132 | ·--·0.0 | 132 | ·--·0.000983094·seconds·elapsed |
| 133 | o9·=·false</code></pre> | 133 | o9·=·false</code></pre> |
| 134 | </td>··········</tr> | 134 | </td>··········</tr> |
| 135 | ········</table> | 135 | ········</table> |
| 136 | ······</div> | 136 | ······</div> |
| 137 | ······<div> | 137 | ······<div> |
| 138 | ········<h2>See·also</h2> | 138 | ········<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 | ·--·0. | 56 | ·--·0.161783·seconds·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 | ·--·0.0 | 59 | ·--·0.0142254·seconds·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 | ·--·0.0 | 62 | ·--·0.000983094·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjEwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNjEwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 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·0.13 | 61 | ·--·used·0.136047s·(cpu);·0.0948503s·(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·0.0 | 72 | ·--·used·0.00914162s·(cpu);·0.00983262s·(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 158, 30 lines modified | Offset 158, 30 lines modified | ||
| 158 | o9·=·ideal·(a,·b,·c) | 158 | o9·=·ideal·(a,·b,·c) |
| 159 | o9·:·Ideal·of·U</code></pre> | 159 | o9·:·Ideal·of·U</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ··········<tr> | 161 | ··········<tr> |
| 162 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·multiReesIdeal·J | 162 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·multiReesIdeal·J |
| 163 | ·--·used·0.13 | 163 | ·--·used·0.136047s·(cpu);·0.0948503s·(thread);·0s·(gc) |
| 164 | ············································································· | 164 | ············································································· |
| 165 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 165 | o10·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 166 | ················1······2·····1······2·····1······2·····0······2·····0······2· | 166 | ················1······2·····1······2·····1······2·····0······2·····0······2· |
| 167 | ······----------------------------------------------------------------------- | 167 | ······----------------------------------------------------------------------- |
| 168 | ····················2·················2···2 | 168 | ····················2·················2···2 |
| 169 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 169 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) |
| 170 | ·········0······2···1····0·2···0·1····2···0····1·2 | 170 | ·········0······2···1····0·2···0·1····2···0····1·2 |
| 171 | o10·:·Ideal·of·U[X·..X·] | 171 | o10·:·Ideal·of·U[X·..X·] |
| 172 | ··················0···2</code></pre> | 172 | ··················0···2</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·multiReesIdeal·(J,·a) | 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·multiReesIdeal·(J,·a) |
| 176 | ·--·used·0.0 | 176 | ·--·used·0.00914162s·(cpu);·0.00983262s·(thread);·0s·(gc) |
| 177 | ············································································· | 177 | ············································································· |
| 178 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, | 178 | o11·=·ideal·(c*X··-·b*X·,·b*X··-·a*X·,·a*X··-·c*X·,·c*X··-·a*X·,·b*X··-·c*X·, |
| 179 | ················1······2·····1······2·····1······2·····0······2·····0······2· | 179 | ················1······2·····1······2·····1······2·····0······2·····0······2· |
| 180 | ······----------------------------------------------------------------------- | 180 | ······----------------------------------------------------------------------- |
| 181 | ····················2·················2···2 | 181 | ····················2·················2···2 |
| 182 | ······a*X··-·b*X·,·X··-·X·X·,·X·X··-·X·,·X··-·X·X·) | 182 | ······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·0.13 | 85 | ·--·used·0.136047s·(cpu);·0.0948503s·(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·0.0 | 95 | ·--·used·0.00914162s·(cpu);·0.00983262s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=2490 | 9 | #:len=2490 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmVyc2FsIGRlZm9ybWF0aW9uIG9mIE1D | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidmVyc2FsIGRlZm9ybWF0aW9uIG9mIE1D |
| 11 | TS1tb2R1bGUgb24gaHlwZXJzdXJmYWNlIiwgImxpbmVudW0iID0+IDM5OSwgImZpbGVuYW1lIiA9 | 11 | TS1tb2R1bGUgb24gaHlwZXJzdXJmYWNlIiwgImxpbmVudW0iID0+IDM5OSwgImZpbGVuYW1lIiA9 |
| 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·1.1 | 44 | ·--·used·1.12985s·(cpu);·0.924357s·(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·1. | 75 | ·--·used·1.40723s·(cpu);·1.10149s·(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 135, 15 lines modified | Offset 135, 15 lines modified | ||
| 135 | o7·=·image·|·x2·y2·| | 135 | o7·=·image·|·x2·y2·| |
| 136 | ·····························1 | 136 | ·····························1 |
| 137 | o7·:·R-module,·submodule·of·R</code></pre> | 137 | o7·:·R-module,·submodule·of·R</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i8·:·(S,N)·=·time·deformMCMModule·N0· | 140 | <td>··············<pre><code·class="language-macaulay2">i8·:·(S,N)·=·time·deformMCMModule·N0· |
| 141 | ·--·used·1.1 | 141 | ·--·used·1.12985s·(cpu);·0.924357s·(thread);·0s·(gc) |
| 142 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 | 142 | o8·=·(S,·cokernel·{6}·|·x2-xxi_2-xi_1+xi_2^2-yxi_4^2-2xi_3xi_4^2+xi_2xi_4^3 |
| 143 | ··················{8}·|·xxi_4-y+xi_3······································· | 143 | ··················{8}·|·xxi_4-y+xi_3······································· |
| 144 | ·····------------------------------------------------------------------------ | 144 | ·····------------------------------------------------------------------------ |
| 145 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) | 145 | ·····xyxi_4+2xxi_3xi_4-xxi_2xi_4^2+y2+yxi_3+xi_3^2-xi_1xi_4^2·|) |
| 146 | ·····-x2-xxi_2-xi_1···········································| | 146 | ·····-x2-xxi_2-xi_1···········································| |
| Offset 170, 15 lines modified | Offset 170, 15 lines modified | ||
| 170 | ···············|·-y·-x2·| | 170 | ···············|·-y·-x2·| |
| 171 | ·····························2 | 171 | ·····························2 |
| 172 | o10·:·R-module,·quotient·of·R</code></pre> | 172 | o10·:·R-module,·quotient·of·R</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·(S',N')·=·time·deformMCMModule·N0' | 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·(S',N')·=·time·deformMCMModule·N0' |
| 176 | ·--·used·1. | 176 | ·--·used·1.40723s·(cpu);·1.10149s·(thread);·0s·(gc) |
| 177 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 | 177 | o11·=·(S',·cokernel·|·x2-xxi_4^3-xxi_2+xi_2xi_4^3-3xi_3xi_4^2+xi_2^2-xi_1 |
| 178 | ····················|·xxi_4-y+xi_3······································· | 178 | ····················|·xxi_4-y+xi_3······································· |
| 179 | ······----------------------------------------------------------------------- | 179 | ······----------------------------------------------------------------------- |
| 180 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) | 180 | ······x2xi_4^2+xyxi_4+2xxi_3xi_4+y2+yxi_3+xi_3^2·|) |
| 181 | ······-x2-xxi_2-xi_1·····························| | 181 | ······-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·1.1 | 76 | ·--·used·1.12985s·(cpu);·0.924357s·(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·1. | 109 | ·--·used·1.40723s·(cpu);·1.10149s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.0029816·seconds·elapsed | ||
| 8 | ·--·0.002 | 7 | ·--·0.00266014·seconds·elapsed |
| 8 | ·--·0.00288021·seconds·elapsed | ||
| 9 | ·--·0.00030 | 9 | ·--·0.00030418·seconds·elapsed |
| 10 | ·--·0.00281409·seconds·elapsed | ||
| 11 | ·--·0.00286 | 10 | ·--·0.00286696·seconds·elapsed |
| 12 | ·--·0.00 | 11 | ·--·0.00260725·seconds·elapsed |
| 12 | ·--·0.000227733·seconds·elapsed | ||
| 13 | ·--·0.002 | 13 | ·--·0.00294334·seconds·elapsed |
| 14 | ·--·0.002 | 14 | ·--·0.00261385·seconds·elapsed |
| 15 | ·--·0.000243 | 15 | ·--·0.000243167·seconds·elapsed |
| 16 | ·--·0.002 | 16 | ·--·0.00244801·seconds·elapsed |
| 17 | ·--·0.00253825·seconds·elapsed | ||
| 17 | ·--·0.002 | 18 | ·--·0.000247784·seconds·elapsed |
| 18 | ·--·0.000262843·seconds·elapsed | ||
| 19 | --backup·directory·created:·/tmp/M2- | 19 | --backup·directory·created:·/tmp/M2-2397533-0/1 |
| 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 97, 27 lines modified | Offset 97, 27 lines modified | ||
| 97 | <td>··············<pre><code·class="language-macaulay2">i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};</code></pre> | 97 | <td>··············<pre><code·class="language-macaulay2">i2·:·polys·=·polySystem·{a*x+b*y^2,c*x*y+d};</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·(p0,·x0)·=·createSeedPair·polys;</code></pre> | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·(p0,·x0)·=·createSeedPair·polys;</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) | 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·(L,·npaths)·=·dynamicFlowerSolve(polys.PolyMap,p0,{x0}) |
| 104 | ·--·0.0029816·seconds·elapsed | ||
| 105 | ·--·0.002 | 104 | ·--·0.00266014·seconds·elapsed |
| 105 | ·--·0.00288021·seconds·elapsed | ||
| 106 | ·--·0.00030 | 106 | ·--·0.00030418·seconds·elapsed |
| 107 | ·--·0.00281409·seconds·elapsed | ||
| 108 | ·--·0.00286 | 107 | ·--·0.00286696·seconds·elapsed |
| 109 | ·--·0.00 | 108 | ·--·0.00260725·seconds·elapsed |
| 109 | ·--·0.000227733·seconds·elapsed | ||
| 110 | ·--·0.002 | 110 | ·--·0.00294334·seconds·elapsed |
| 111 | ·--·0.002 | 111 | ·--·0.00261385·seconds·elapsed |
| 112 | ·--·0.000243 | 112 | ·--·0.000243167·seconds·elapsed |
| 113 | ·--·0.002 | 113 | ·--·0.00244801·seconds·elapsed |
| 114 | ·--·0.00253825·seconds·elapsed | ||
| 114 | ·--·0.002 | 115 | ·--·0.000247784·seconds·elapsed |
| 115 | ·--·0.000262843·seconds·elapsed | ||
| 116 | --backup·directory·created:·/tmp/M2- | 116 | --backup·directory·created:·/tmp/M2-2397533-0/1 |
| 117 | ··H01:·1 | 117 | ··H01:·1 |
| 118 | ··H10:·1 | 118 | ··H10:·1 |
| 119 | number·of·paths·tracked:·2 | 119 | number·of·paths·tracked:·2 |
| 120 | found·1·points·in·the·fiber·so·far | 120 | found·1·points·in·the·fiber·so·far |
| 121 | ··H01:·1 | 121 | ··H01:·1 |
| 122 | ··H10:·1 | 122 | ··H10:·1 |
| 123 | number·of·paths·tracked:·4 | 123 | 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 | ·--·0.0029816·seconds·elapsed | ||
| 31 | ·--·0.002 | 30 | ·--·0.00266014·seconds·elapsed |
| 31 | ·--·0.00288021·seconds·elapsed | ||
| 32 | ·--·0.00030 | 32 | ·--·0.00030418·seconds·elapsed |
| 33 | ·--·0.00281409·seconds·elapsed | ||
| 34 | ·--·0.00286 | 33 | ·--·0.00286696·seconds·elapsed |
| 35 | ·--·0.00 | 34 | ·--·0.00260725·seconds·elapsed |
| 35 | ·--·0.000227733·seconds·elapsed | ||
| 36 | ·--·0.002 | 36 | ·--·0.00294334·seconds·elapsed |
| 37 | ·--·0.002 | 37 | ·--·0.00261385·seconds·elapsed |
| 38 | ·--·0.000243 | 38 | ·--·0.000243167·seconds·elapsed |
| 39 | ·--·0.002 | 39 | ·--·0.00244801·seconds·elapsed |
| 40 | ·--·0.00253825·seconds·elapsed | ||
| 40 | ·--·0.002 | 41 | ·--·0.000247784·seconds·elapsed |
| 41 | ·--·0.000262843·seconds·elapsed | ||
| 42 | --backup·directory·created:·/tmp/M2- | 42 | --backup·directory·created:·/tmp/M2-2397533-0/1 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTYwNywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTYwNywgc3ltYm9sIERvY3VtZW50VGFn |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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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 |
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| 7 | #:len=22 | 7 | #:len=22 |
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| 9 | #:len=3397 | 9 | #:len=3397 |
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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=283 | 9 | #:len=283 |
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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=26 | 7 | #:len=26 |
| 8 | ZGVncmVlKERpZmZlcmVudGlhbE1vZHVsZSk= | 8 | ZGVncmVlKERpZmZlcmVudGlhbE1vZHVsZSk= |
| 9 | #:len=1348 | 9 | #:len=1348 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgZGVncmVlIG9mIHRo | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicmV0dXJucyB0aGUgZGVncmVlIG9mIHRo |
| 11 | ZSBkaWZmZXJlbnRpYWwiLCAibGluZW51bSIgPT4gNDY4LCBJbnB1dHMgPT4ge1NQQU57VFR7IkQi | 11 | ZSBkaWZmZXJlbnRpYWwiLCAibGluZW51bSIgPT4gNDY4LCBJbnB1dHMgPT4ge1NQQU57VFR7IkQi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | Z3JHcihJZGVhbCk= | 8 | Z3JHcihJZGVhbCk= |
| 9 | #:len=249 | 9 | #:len=249 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzg2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhnckdyLElkZWFsKSwiZ3JHcihJZGVhbCkiLCJNdWx0 | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhnckdyLElkZWFsKSwiZ3JHcihJZGVhbCkiLCJNdWx0 |
| 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 | ·--·0.0 | 13 | ·--·0.0221989·seconds·elapsed |
| 14 | o3·=·2 | 14 | o3·=·2 |
| 15 | i4·:·elapsedTime·monjMult·I | 15 | i4·:·elapsedTime·monjMult·I |
| 16 | ·--·0. | 16 | ·--·0.167666·seconds·elapsed |
| 17 | o4·=·2 | 17 | o4·=·2 |
| 18 | i5·:·elapsedTime·multiplicitySequence·I | 18 | i5·:·elapsedTime·multiplicitySequence·I |
| 19 | ·--·0.1 | 19 | ·--·0.165544·seconds·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 | ·--·0. | 14 | ·--·0.123783·seconds·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 | ·--·0. | 18 | ·--·0.262086·seconds·elapsed |
| 19 | o3·=·192 | 19 | o3·=·192 |
| 20 | i4·:·elapsedTime·jMult·I | 20 | i4·:·elapsedTime·jMult·I |
| 21 | ·--·1. | 21 | ·--·1.13353·seconds·elapsed |
| 22 | o4·=·192 | 22 | o4·=·192 |
| 23 | i5·:· | 23 | i5·:· |
| Offset 84, 27 lines modified | Offset 84, 27 lines modified | ||
| 84 | o2·=·ideal·(x*y,·y*z,·x*z) | 84 | o2·=·ideal·(x*y,·y*z,·x*z) |
| 85 | o2·:·Ideal·of·R</code></pre> | 85 | o2·:·Ideal·of·R</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·jMult·I | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·jMult·I |
| 89 | ·--·0.0 | 89 | ·--·0.0221989·seconds·elapsed |
| 90 | o3·=·2</code></pre> | 90 | o3·=·2</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·monjMult·I | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·monjMult·I |
| 94 | ·--·0. | 94 | ·--·0.167666·seconds·elapsed |
| 95 | o4·=·2</code></pre> | 95 | o4·=·2</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·multiplicitySequence·I | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·multiplicitySequence·I |
| 99 | ·--·0.1 | 99 | ·--·0.165544·seconds·elapsed |
| 100 | o5·=·HashTable{2·=>·3} | 100 | o5·=·HashTable{2·=>·3} |
| 101 | ···············3·=>·2 | 101 | ···············3·=>·2 |
| 102 | o5·:·HashTable</code></pre> | 102 | o5·:·HashTable</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ········</table> | 104 | ········</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 | ·--·0.0 | 26 | ·--·0.0221989·seconds·elapsed |
| 27 | o3·=·2 | 27 | o3·=·2 |
| 28 | i4·:·elapsedTime·monjMult·I | 28 | i4·:·elapsedTime·monjMult·I |
| 29 | ·--·0. | 29 | ·--·0.167666·seconds·elapsed |
| 30 | o4·=·2 | 30 | o4·=·2 |
| 31 | i5·:·elapsedTime·multiplicitySequence·I | 31 | i5·:·elapsedTime·multiplicitySequence·I |
| 32 | ·--·0.1 | 32 | ·--·0.165544·seconds·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 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ·············2········3 | 85 | ·············2········3 |
| 86 | o2·=·ideal·(x·,·x*y,·y·) | 86 | o2·=·ideal·(x·,·x*y,·y·) |
| 87 | o2·:·Ideal·of·R</code></pre> | 87 | o2·:·Ideal·of·R</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monAnalyticSpread·I | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monAnalyticSpread·I |
| 91 | ·--·0. | 91 | ·--·0.123783·seconds·elapsed |
| 92 | o3·=·2</code></pre> | 92 | o3·=·2</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ········</table> | 94 | ········</table> |
| 95 | ······</div> | 95 | ······</div> |
| 96 | ······<div> | 96 | ······<div> |
| 97 | ········<h2>See·also</h2> | 97 | ········<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 | ·--·0. | 28 | ·--·0.123783·seconds·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 88, 21 lines modified | Offset 88, 21 lines modified | ||
| 88 | ······10·11···8·12···9·11···10·10···11·9···12·8 | 88 | ······10·11···8·12···9·11···10·10···11·9···12·8 |
| 89 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) | 89 | ·····x··y··,·x·y··,·x·y··,·x··y··,·x··y·,·x··y·) |
| 90 | o2·:·Ideal·of·R</code></pre> | 90 | o2·:·Ideal·of·R</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monjMult·I | 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·monjMult·I |
| 94 | ·--·0. | 94 | ·--·0.262086·seconds·elapsed |
| 95 | o3·=·192</code></pre> | 95 | o3·=·192</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jMult·I | 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·jMult·I |
| 99 | ·--·1. | 99 | ·--·1.13353·seconds·elapsed |
| 100 | o4·=·192</code></pre> | 100 | o4·=·192</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 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 | ·--·0. | 31 | ·--·0.262086·seconds·elapsed |
| 32 | o3·=·192 | 32 | o3·=·192 |
| 33 | i4·:·elapsedTime·jMult·I | 33 | i4·:·elapsedTime·jMult·I |
| 34 | ·--·1. | 34 | ·--·1.13353·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bG9nQ2Fub25pY2FsVGhyZXNob2xkKENlbnRyYWxBcnJhbmdlbWVudCk= | 8 | bG9nQ2Fub25pY2FsVGhyZXNob2xkKENlbnRyYWxBcnJhbmdlbWVudCk= |
| 9 | #:len=361 | 9 | #:len=361 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjA2OSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjA2OSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobG9nQ2Fub25pY2FsVGhyZXNob2xkLENlbnRyYWxB | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsobG9nQ2Fub25pY2FsVGhyZXNob2xkLENlbnRyYWxB |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | TXVsdElkZWFs | 8 | TXVsdElkZWFs |
| 9 | #:len=1359 | 9 | #:len=1359 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIG11bHRpcGxpZXIg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ29tcHV0ZXMgdGhlIG11bHRpcGxpZXIg |
| 11 | aWRlYWwgb2YgYSBnaXZlbiBudW1iZXIuIiwgImxpbmVudW0iID0+IDY0OCwgSW5wdXRzID0+IHtT | 11 | aWRlYWwgb2YgYSBnaXZlbiBudW1iZXIuIiwgImxpbmVudW0iID0+IDY0OCwgSW5wdXRzID0+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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
| Offset 13, 15 lines modified | Offset 13, 15 lines modified | ||
| 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·3.0 | 17 | ·--·used·3.05763s·(cpu);·2.01334s·(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 |
| Offset 38, 15 lines modified | Offset 38, 15 lines modified | ||
| 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·2. | 42 | ·--·used·2.81617s·(cpu);·1.88058s·(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· |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 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·5. | 133 | ·--·used·5.4111s·(cpu);·4.14439s·(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) |
| Offset 7, 15 lines modified | Offset 7, 15 lines modified | ||
| 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·2.93933s·(cpu);·2.33846s·(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 | ·····------------------------------------------------------------------------ |
| Offset 11, 26 lines modified | Offset 11, 26 lines modified | ||
| 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. | 15 | ·--·used·0.0988055s·(cpu);·0.0985248s·(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·1. | 21 | ·--·used·1.5168s·(cpu);·1.11847s·(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·2.68981s·(cpu);·2.14777s·(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·0.282639s·(cpu);·0.228402s·(thread);·0s·(gc) |
| 21 | o5·=·2 | 21 | o5·=·2 |
| 22 | i6·:·time·degree·Phi | 22 | i6·:·time·degree·Phi |
| 23 | ·--·used·0.2 | 23 | ·--·used·0.228978s·(cpu);·0.230819s·(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·0.445053s·(cpu);·0.337423s·(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:·-903360799 | 1 | --·-*-·M2-comint·-*-·hash:·-903360799 |
| 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· | 5 | ·--·used·6.4717e-05s·(cpu);·0.000183476s·(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·0.00155256s·(cpu);·0.00022579s·(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·0.9 | 21 | ·--·used·0.962074s·(cpu);·0.820573s·(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·0.0001 | 34 | ·--·used·0.000117497s·(cpu);·0.00035864s·(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·0.0 | 7 | ·--·used·0.0240995s·(cpu);·0.0230684s·(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·0.1 | 15 | ·--·used·0.12517s·(cpu);·0.0621624s·(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·0.3 | 23 | ·--·used·0.230415s·(cpu);·0.167128s·(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·0.1 | 15 | ·--·used·0.103794s·(cpu);·0.105783s·(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·4. | 21 | ·--·used·4.32458s·(cpu);·2.06462s·(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·0.2 | 8 | ·--·used·0.24187s·(cpu);·0.238538s·(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· | 14 | ·--·used·0.932847s·(cpu);·0.827472s·(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·0.05 | 11 | ·--·used·0.0556537s·(cpu);·0.0552399s·(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·0.2 | 16 | ·--·used·0.228643s·(cpu);·0.127697s·(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·0.47 | 21 | ·--·used·0.470038s·(cpu);·0.363679s·(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·0.0025333s·(cpu);·5.178e-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·0.26 | 15 | ·--·used·0.266509s·(cpu);·0.160361s·(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·1.1 | 20 | ·--·used·1.1326s·(cpu);·0.658556s·(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·0.2 | 7 | ·--·used·0.277019s·(cpu);·0.158184s·(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·0.07 | 10 | ·--·used·0.0731895s·(cpu);·0.0749063s·(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·2. | 13 | ·--·used·2.89459s·(cpu);·2.45835s·(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·0.0 | 7 | ·--·used·0.0120064s·(cpu);·0.0116939s·(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·0.4 | 12 | ·--·used·0.473077s·(cpu);·0.422835s·(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·0.4 | 7 | ·--·used·0.422182s·(cpu);·0.323238s·(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:·1931260862 | 1 | --·-*-·M2-comint·-*-·hash:·1931260862 |
| 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·0.00400523s·(cpu);·0.00116466s·(thread);·0s·(gc) |
| 6 | ·--·used·0.180705s·(cpu);·0.11229s·(thread);·0s·(gc) | ||
| 7 | ·--·used·0.206203s·(cpu);·0.141487s·(thread);·0s·(gc) | ||
| 8 | ·--·used·0.1 | 6 | ·--·used·0.152762s·(cpu);·0.0961644s·(thread);·0s·(gc) |
| 7 | ·--·used·0.170361s·(cpu);·0.111368s·(thread);·0s·(gc) | ||
| 9 | ·--·used·0. | 8 | ·--·used·0.0771479s·(cpu);·0.0774929s·(thread);·0s·(gc) |
| 9 | ·--·used·0.134252s·(cpu);·0.080776s·(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·0.1 | 13 | ·--·used·0.13331s·(cpu);·0.0735196s·(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·0.02 | 7 | ·--·used·0.0236059s·(cpu);·0.023161s·(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·1.4 | 13 | ·--·used·1.45785s·(cpu);·1.07969s·(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·0. | 19 | ·--·used·0.745021s·(cpu);·0.538393s·(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·0.1 | 7 | ·--·used·0.15979s·(cpu);·0.105039s·(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 95, 15 lines modified | Offset 95, 15 lines modified | ||
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·?·X | 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·?·X |
| 97 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·</code></pre> | 97 | o5·=·curve·in·PP^8·cut·out·by·17·hypersurfaces·of·degrees·1^2·2^15·</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·f·=·X·===>·Y; | 100 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·f·=·X·===>·Y; |
| 101 | ·--·used·3.0 | 101 | ·--·used·3.05763s·(cpu);·2.01334s·(thread);·0s·(gc) |
| 102 | o6·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> | 102 | o6·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i7·:·f·X | 105 | <td>··············<pre><code·class="language-macaulay2">i7·:·f·X |
| 106 | o7·=·Y | 106 | o7·=·Y |
| Offset 125, 15 lines modified | Offset 125, 15 lines modified | ||
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·W·=·random({{2},{1}},Y); | 126 | <td>··············<pre><code·class="language-macaulay2">i10·:·W·=·random({{2},{1}},Y); |
| 127 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8</code></pre> | 127 | o10·:·ProjectiveVariety,·6-dimensional·subvariety·of·PP^8</code></pre> |
| 128 | </td>··········</tr> | 128 | </td>··········</tr> |
| 129 | ··········<tr> | 129 | ··········<tr> |
| 130 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·g·=·V·===>·W; | 130 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·g·=·V·===>·W; |
| 131 | ·--·used·2. | 131 | ·--·used·2.81617s·(cpu);·1.88058s·(thread);·0s·(gc) |
| 132 | o11·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> | 132 | o11·:·MultirationalMap·(automorphism·of·PP^8)</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i12·:·g||W | 135 | <td>··············<pre><code·class="language-macaulay2">i12·:·g||W |
| 136 | o12·=·multi-rational·map·consisting·of·one·single·rational·map | 136 | o12·=·multi-rational·map·consisting·of·one·single·rational·map |
| Offset 224, 15 lines modified | Offset 224, 15 lines modified | ||
| 224 | ··········<tr> | 224 | ··········<tr> |
| 225 | <td>··············<pre><code·class="language-macaulay2">i16·:·?·Z | 225 | <td>··············<pre><code·class="language-macaulay2">i16·:·?·Z |
| 226 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2</code></pre> | 226 | o16·=·6-dimensional·subvariety·of·PP^9·cut·out·by·5·hypersurfaces·of·degree·2</code></pre> |
| 227 | </td>··········</tr> | 227 | </td>··········</tr> |
| 228 | ··········<tr> | 228 | ··········<tr> |
| 229 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·h·=·Z·===>·GG_K(1,4) | 229 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·h·=·Z·===>·GG_K(1,4) |
| 230 | ·--·used·5. | 230 | ·--·used·5.4111s·(cpu);·4.14439s·(thread);·0s·(gc) |
| 231 | o17·=·h | 231 | o17·=·h |
| 232 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)</code></pre> | 232 | o17·:·MultirationalMap·(isomorphism·from·PP^9·to·PP^9)</code></pre> |
| 233 | </td>··········</tr> | 233 | </td>··········</tr> |
| 234 | ··········<tr> | 234 | ··········<tr> |
| 235 | <td>··············<pre><code·class="language-macaulay2">i18·:·h·||·GG_K(1,4) | 235 | <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·3.0 | 39 | ·--·used·3.05763s·(cpu);·2.01334s·(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·2. | 59 | ·--·used·2.81617s·(cpu);·1.88058s·(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·5. | 150 | ·--·used·5.4111s·(cpu);·4.14439s·(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 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi)); | 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·Y·=·projectiveVariety·ideal(random({1,1},ring·target·Phi),·random({1,1},ring·target·Phi)); |
| 87 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4</code></pre> | 87 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^2·x·PP^4</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·X·=·Phi^*·Y; | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·X·=·Phi^*·Y; |
| 91 | ·--·used· | 91 | ·--·used·2.93933s·(cpu);·2.33846s·(thread);·0s·(gc) |
| 92 | 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 | 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> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·dim·X,·degree·X,·degrees·X | 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·dim·X,·degree·X,·degrees·X |
| 96 | o5·=·(1,·31,·{({0,·0,·2},·1),·({0,·0,·3},·4),·({0,·1,·1},·4),·({0,·4,·1},·1), | 96 | 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·2.93933s·(cpu);·2.33846s·(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 89, 28 lines modified | Offset 89, 28 lines modified | ||
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·Z·=·source·Phi; | 90 | <td>··············<pre><code·class="language-macaulay2">i4·:·Z·=·source·Phi; |
| 91 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7</code></pre> | 91 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^7</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Phi·Z; | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Phi·Z; |
| 95 | ·--·used·0. | 95 | ·--·used·0.0988055s·(cpu);·0.0985248s·(thread);·0s·(gc) |
| 96 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> | 96 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·oo,·degree·oo,·degrees·oo | 99 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·oo,·degree·oo,·degrees·oo |
| 100 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) | 100 | o6·=·(4,·80,·{({0,·2},·5),·({1,·1},·33),·({2,·0},·5)}) |
| 101 | o6·:·Sequence</code></pre> | 101 | o6·:·Sequence</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) | 104 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Phi·(point·Z·+·point·Z·+·point·Z) |
| 105 | ·--·used·1. | 105 | ·--·used·1.5168s·(cpu);·1.11847s·(thread);·0s·(gc) |
| 106 | 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·=·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· |
| 107 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> | 107 | o7·:·ProjectiveVariety,·0-dimensional·subvariety·of·PP^7·x·PP^7</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i8·:·dim·oo,·degree·oo,·degrees·oo | 110 | <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. | 31 | ·--·used·0.0988055s·(cpu);·0.0985248s·(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·1. | 37 | ·--·used·1.5168s·(cpu);·1.11847s·(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 |
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| 89 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of | 89 | ·····source·variety:·threefold·in·PP^4·x·PP^4·cut·out·by·13·hypersurfaces·of |
| 90 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 | 90 | ·····target·variety:·hypersurface·in·PP^4·defined·by·a·form·of·degree·2 |
| 91 | ·····------------------------------------------------------------------------ | 91 | ·····------------------------------------------------------------------------ |
| 92 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1</code></pre> | 92 | ·····multi-degrees·(0,2)^1·(1,1)^3·(2,1)^8·(4,0)^1</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree(Phi,Strategy=>"random·point") | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree(Phi,Strategy=>"random·point") |
| 96 | ·--·used· | 96 | ·--·used·2.68981s·(cpu);·2.14777s·(thread);·0s·(gc) |
| 97 | o4·=·2</code></pre> | 97 | o4·=·2</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") | 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·degree(Phi,Strategy=>"0-th·projective·degree") |
| 101 | ·--·used·0.2 | 101 | ·--·used·0.282639s·(cpu);·0.228402s·(thread);·0s·(gc) |
| 102 | o5·=·2</code></pre> | 102 | o5·=·2</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·degree·Phi | 105 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·degree·Phi |
| 106 | ·--·used·0.2 | 106 | ·--·used·0.228978s·(cpu);·0.230819s·(thread);·0s·(gc) |
| 107 | o6·=·2</code></pre> | 107 | o6·=·2</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ········<p>Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the·strategy·used.</p> | 110 | ········<p>Note,·as·in·the·example·above,·that·calculation·times·may·vary·depending·on·the·strategy·used.</p> |
| 111 | ······</div> | 111 | ······</div> |
| 112 | ······<div> | 112 | ······<div> |
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| 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·2.68981s·(cpu);·2.14777s·(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·0.282639s·(cpu);·0.228402s·(thread);·0s·(gc) |
| 38 | o5·=·2 | 38 | o5·=·2 |
| 39 | i6·:·time·degree·Phi | 39 | i6·:·time·degree·Phi |
| 40 | ·--·used·0.2 | 40 | ·--·used·0.228978s·(cpu);·0.230819s·(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 |
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| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 80 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> | 80 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·degree·Phi | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·degree·Phi |
| 84 | ·--·used·0. | 84 | ·--·used·0.445053s·(cpu);·0.337423s·(thread);·0s·(gc) |
| 85 | o3·=·1</code></pre> | 85 | o3·=·1</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 | 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·0.445053s·(cpu);·0.337423s·(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 |
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| 76 | ··········<tr> | 76 | ··········<tr> |
| 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); | 77 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·multirationalMap·graph·rationalMap·PP_(ZZ/65521)^(1,4); |
| 78 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)</code></pre> | 78 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^4·x·PP^5)</code></pre> |
| 79 | </td>··········</tr> | 79 | </td>··········</tr> |
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·?·Phi | 81 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·?·Phi |
| 82 | ·--·used· | 82 | ·--·used·6.4717e-05s·(cpu);·0.000183476s·(thread);·0s·(gc) |
| 83 | o2·=·multi-rational·map·consisting·of·2·rational·maps | 83 | o2·=·multi-rational·map·consisting·of·2·rational·maps |
| 84 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 | 84 | ·····source·variety:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9 |
| 85 | ·····target·variety:·PP^4·x·PP^5 | 85 | ·····target·variety:·PP^4·x·PP^5 |
| 86 | ·····------------------------------------------------------------------------ | 86 | ·····------------------------------------------------------------------------ |
| 87 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8</code></pre> | 87 | ·····hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·image·Phi; | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·image·Phi; |
| 91 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5</code></pre> | 91 | o3·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^4·x·PP^5</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·?·Phi | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·?·Phi |
| 95 | ·--·used·0.00 | 95 | ·--·used·0.00155256s·(cpu);·0.00022579s·(thread);·0s·(gc) |
| 96 | o4·=·multi-rational·map·consisting·of·2·rational·maps | 96 | o4·=·multi-rational·map·consisting·of·2·rational·maps |
| 97 | ·····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 | ·····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· |
| 98 | ·····target·variety:·PP^4·x·PP^5 | 98 | ·····target·variety:·PP^4·x·PP^5 |
| 99 | ·····dominance:·false | 99 | ·····dominance:·false |
| 100 | ·····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 | ·····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> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·Phi | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·describe·Phi |
| 104 | ·--·used·0.9 | 104 | ·--·used·0.962074s·(cpu);·0.820573s·(thread);·0s·(gc) |
| 105 | o5·=·multi-rational·map·consisting·of·2·rational·maps | 105 | o5·=·multi-rational·map·consisting·of·2·rational·maps |
| 106 | ·····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 | ·····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· |
| 107 | ·····target·variety:·PP^4·x·PP^5 | 107 | ·····target·variety:·PP^4·x·PP^5 |
| 108 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 108 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 109 | ·····dominance:·false | 109 | ·····dominance:·false |
| 110 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 110 | ·····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 117, 15 lines modified | Offset 117, 15 lines modified | ||
| 117 | ·····degree:·1 | 117 | ·····degree:·1 |
| 118 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] | 118 | ·····degree·sequence·(map·1/2):·[(1,0),·(0,2)] |
| 119 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] | 119 | ·····degree·sequence·(map·2/2):·[(0,1),·(2,0)] |
| 120 | ·····coefficient·ring:·ZZ/65521</code></pre> | 120 | ·····coefficient·ring:·ZZ/65521</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·?·Phi | 123 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·?·Phi |
| 124 | ·--·used·0.0001 | 124 | ·--·used·0.000117497s·(cpu);·0.00035864s·(thread);·0s·(gc) |
| 125 | o6·=·multi-rational·map·consisting·of·2·rational·maps | 125 | o6·=·multi-rational·map·consisting·of·2·rational·maps |
| 126 | ·····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 | ·····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· |
| 127 | ·····target·variety:·PP^4·x·PP^5 | 127 | ·····target·variety:·PP^4·x·PP^5 |
| 128 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 | 128 | ·····base·locus:·empty·subscheme·of·PP^4·x·PP^5 |
| 129 | ·····dominance:·false | 129 | ·····dominance:·false |
| 130 | ·····image:·4-dimensional·subvariety·of·PP^4·x·PP^5·cut·out·by·9·hypersurfaces·of·multi-degrees·(0,2)^1·(1,1)^8· | 130 | ·····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· | 23 | ·--·used·6.4717e-05s·(cpu);·0.000183476s·(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·0.00155256s·(cpu);·0.00022579s·(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·0.9 | 41 | ·--·used·0.962074s·(cpu);·0.820573s·(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·0.0001 | 61 | ·--·used·0.000117497s·(cpu);·0.00035864s·(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 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | o1·=·Phi | 85 | o1·=·Phi |
| 86 | o1·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 86 | o1·:·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">i2·:·time·(Phi1,Phi2)·=·graph·Phi | 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(Phi1,Phi2)·=·graph·Phi |
| 90 | ·--·used·0.0 | 90 | ·--·used·0.0240995s·(cpu);·0.0230684s·(thread);·0s·(gc) |
| 91 | o2·=·(Phi1,·Phi2) | 91 | o2·=·(Phi1,·Phi2) |
| 92 | o2·:·Sequence</code></pre> | 92 | o2·:·Sequence</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi1; | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi1; |
| Offset 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi2; | 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi2; |
| 105 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> | 105 | o4·:·MultirationalMap·(dominant·rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(Phi21,Phi22)·=·graph·Phi2 | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(Phi21,Phi22)·=·graph·Phi2 |
| 109 | ·--·used·0.1 | 109 | ·--·used·0.12517s·(cpu);·0.0621624s·(thread);·0s·(gc) |
| 110 | o5·=·(Phi21,·Phi22) | 110 | o5·=·(Phi21,·Phi22) |
| 111 | o5·:·Sequence</code></pre> | 111 | o5·:·Sequence</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i6·:·Phi21; | 114 | <td>··············<pre><code·class="language-macaulay2">i6·:·Phi21; |
| Offset 121, 15 lines modified | Offset 121, 15 lines modified | ||
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i7·:·Phi22; | 122 | <td>··············<pre><code·class="language-macaulay2">i7·:·Phi22; |
| 123 | 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 | 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> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·(Phi211,Phi212)·=·graph·Phi21 | 126 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·(Phi211,Phi212)·=·graph·Phi21 |
| 127 | ·--·used·0.3 | 127 | ·--·used·0.230415s·(cpu);·0.167128s·(thread);·0s·(gc) |
| 128 | o8·=·(Phi211,·Phi212) | 128 | o8·=·(Phi211,·Phi212) |
| 129 | o8·:·Sequence</code></pre> | 129 | o8·:·Sequence</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i9·:·Phi211; | 132 | <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·0.0 | 25 | ·--·used·0.0240995s·(cpu);·0.0230684s·(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·0.1 | 35 | ·--·used·0.12517s·(cpu);·0.0621624s·(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·0.3 | 45 | ·--·used·0.230415s·(cpu);·0.167128s·(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 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi·=·rationalMap·{f,g}; | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·Phi·=·rationalMap·{f,g}; |
| 90 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)</code></pre> | 90 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·PP^7·x·PP^4)</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Z·=·image·Phi; | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·Z·=·image·Phi; |
| 94 | ·--·used·0.1 | 94 | ·--·used·0.103794s·(cpu);·0.105783s·(thread);·0s·(gc) |
| 95 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> | 95 | o5·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·Z,·degree·Z,·degrees·Z | 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·dim·Z,·degree·Z,·degrees·Z |
| 99 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) | 99 | o6·=·(4,·151,·{({1,·1},·4),·({1,·2},·3),·({2,·0},·5),·({2,·1},·13)}) |
| Offset 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | o6·:·Sequence</code></pre> | 104 | o6·:·Sequence</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ········</table> | 106 | ········</table> |
| 107 | ········<p>Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as·follows:</p> | 107 | ········<p>Alternatively,·the·calculation·can·be·performed·using·the·Segre·embedding·as·follows:</p> |
| 108 | ········<table·class="examples"> | 108 | ········<table·class="examples"> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); | 110 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·Z'·=·projectiveVariety·(map·segre·target·Phi)·image(segre·Phi,"F4"); |
| 111 | ·--·used·4. | 111 | ·--·used·4.32458s·(cpu);·2.06462s·(thread);·0s·(gc) |
| 112 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> | 112 | o7·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^7·x·PP^4</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Z·==·Z')</code></pre> | 115 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Z·==·Z')</code></pre> |
| 116 | </td>··········</tr> | 116 | </td>··········</tr> |
| 117 | ········</table> | 117 | ········</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·0.1 | 29 | ·--·used·0.103794s·(cpu);·0.105783s·(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·4. | 37 | ·--·used·4.32458s·(cpu);·2.06462s·(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 79, 29 lines modified | Offset 79, 29 lines modified | ||
| 79 | <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 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·map·defined·by·the·cubics·through·the·secant·variety·to·the·rational·normal·curve·of·degree·6 |
| 80 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2)); | 80 | ·····Phi·=·multirationalMap·rationalMap(ring·PP_K^6,ring·GG_K(2,4),gens·ideal·PP_K([6],2)); |
| 81 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))</code></pre> | 81 | o2·:·MultirationalMap·(rational·map·from·PP^6·to·GG(2,4))</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·Psi·=·inverse2·Phi; | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·Psi·=·inverse2·Phi; |
| 85 | ·--·used·0.2 | 85 | ·--·used·0.24187s·(cpu);·0.238538s·(thread);·0s·(gc) |
| 86 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)</code></pre> | 86 | o3·:·MultirationalMap·(birational·map·from·GG(2,4)·to·PP^6)</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(Phi·*·Psi·==·1)</code></pre> | 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert(Phi·*·Psi·==·1)</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi'·=·Phi·||·Phi; | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi'·=·Phi·||·Phi; |
| 93 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))</code></pre> | 93 | o5·:·MultirationalMap·(rational·map·from·PP^6·x·PP^6·to·GG(2,4)·x·GG(2,4))</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Psi'·=·inverse2·Phi'; | 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Psi'·=·inverse2·Phi'; |
| 97 | ·--·used· | 97 | ·--·used·0.932847s·(cpu);·0.827472s·(thread);·0s·(gc) |
| 98 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)</code></pre> | 98 | o6·:·MultirationalMap·(birational·map·from·GG(2,4)·x·GG(2,4)·to·PP^6·x·PP^6)</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(Phi'·*·Psi'·==·1)</code></pre> | 101 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(Phi'·*·Psi'·==·1)</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ········</table> | 103 | ········</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·0.2 | 31 | ·--·used·0.24187s·(cpu);·0.238538s·(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· | 37 | ·--·used·0.932847s·(cpu);·0.827472s·(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 85, 37 lines modified | Offset 85, 37 lines modified | ||
| 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·we·see·Phi·as·a·dominant·map | 85 | <td>··············<pre><code·class="language-macaulay2">i2·:·--·we·see·Phi·as·a·dominant·map |
| 86 | ·····Phi·=·rationalMap(Phi,image·Phi); | 86 | ·····Phi·=·rationalMap(Phi,image·Phi); |
| 87 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> | 87 | o2·:·MultirationalMap·(dominant·rational·map·from·PP^4·to·hypersurface·in·PP^5)</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·Phi; | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·inverse·Phi; |
| 91 | ·--·used·0.05 | 91 | ·--·used·0.0556537s·(cpu);·0.0552399s·(thread);·0s·(gc) |
| 92 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> | 92 | o3·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·PP^4)</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·Psi·=·last·graph·Phi; | 95 | <td>··············<pre><code·class="language-macaulay2">i4·:·Psi·=·last·graph·Phi; |
| 96 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> | 96 | o4·:·MultirationalMap·(birational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·hypersurface·in·PP^5)</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·inverse·Psi; | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·inverse·Psi; |
| 100 | ·--·used·0.2 | 100 | ·--·used·0.228643s·(cpu);·0.127697s·(thread);·0s·(gc) |
| 101 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre> | 101 | o5·:·MultirationalMap·(birational·map·from·hypersurface·in·PP^5·to·4-dimensional·subvariety·of·PP^4·x·PP^5)</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·Eta·=·first·graph·Psi; | 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·Eta·=·first·graph·Psi; |
| 105 | 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 | 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> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·inverse·Eta; | 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·inverse·Eta; |
| 109 | ·--·used·0.47 | 109 | ·--·used·0.470038s·(cpu);·0.363679s·(thread);·0s·(gc) |
| 110 | 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 | 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> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)</code></pre> | 113 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(Phi·*·Phi^-1·==·1·and·Phi^-1·*·Phi·==·1)</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<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·0.05 | 30 | ·--·used·0.0556537s·(cpu);·0.0552399s·(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·0.2 | 36 | ·--·used·0.228643s·(cpu);·0.127697s·(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·0.47 | 43 | ·--·used·0.470038s·(cpu);·0.363679s·(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 80, 37 lines modified | Offset 80, 37 lines modified | ||
| 80 | ··········<tr> | 80 | ··········<tr> |
| 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap·{f,f}; | 81 | <td>··············<pre><code·class="language-macaulay2">i3·:·Phi·=·rationalMap·{f,f}; |
| 82 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)</code></pre> | 82 | o3·:·MultirationalMap·(rational·map·from·PP^3·to·PP^2·x·PP^2)</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isIsomorphism·Phi | 85 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isIsomorphism·Phi |
| 86 | ·--·used·0.00 | 86 | ·--·used·0.0025333s·(cpu);·5.178e-06s·(thread);·0s·(gc) |
| 87 | o4·=·false</code></pre> | 87 | o4·=·false</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·Psi·=·first·graph·Phi; | 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·Psi·=·first·graph·Phi; |
| 91 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)</code></pre> | 91 | o5·:·MultirationalMap·(birational·map·from·threefold·in·PP^3·x·PP^2·x·PP^2·to·PP^3)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isIsomorphism·Psi | 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isIsomorphism·Psi |
| 95 | ·--·used·0.26 | 95 | ·--·used·0.266509s·(cpu);·0.160361s·(thread);·0s·(gc) |
| 96 | o6·=·false</code></pre> | 96 | o6·=·false</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i7·:·Eta·=·first·graph·Psi; | 99 | <td>··············<pre><code·class="language-macaulay2">i7·:·Eta·=·first·graph·Psi; |
| 100 | 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 | 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> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isIsomorphism·Eta | 103 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isIsomorphism·Eta |
| 104 | ·--·used·1.1 | 104 | ·--·used·1.1326s·(cpu);·0.658556s·(thread);·0s·(gc) |
| 105 | o8·=·true</code></pre> | 105 | o8·=·true</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i9·:·assert(o8·and·(not·o6)·and·(not·o4))</code></pre> | 108 | <td>··············<pre><code·class="language-macaulay2">i9·:·assert(o8·and·(not·o6)·and·(not·o4))</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ········</table> | 110 | ········</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·0.0025333s·(cpu);·5.178e-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·0.26 | 29 | ·--·used·0.266509s·(cpu);·0.160361s·(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·1.1 | 35 | ·--·used·1.1326s·(cpu);·0.658556s·(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 77, 27 lines modified | Offset 77, 27 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·rationalMap·{f,g}; | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·rationalMap·{f,g}; |
| 79 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)</code></pre> | 79 | o2·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^7·to·PP^4·x·PP^2)</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isMorphism·Phi | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·isMorphism·Phi |
| 83 | ·--·used·0.2 | 83 | ·--·used·0.277019s·(cpu);·0.158184s·(thread);·0s·(gc) |
| 84 | o3·=·false</code></pre> | 84 | o3·=·false</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Psi·=·first·graph·Phi; | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Psi·=·first·graph·Phi; |
| 88 | ·--·used·0.07 | 88 | ·--·used·0.0731895s·(cpu);·0.0749063s·(thread);·0s·(gc) |
| 89 | 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 | 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> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isMorphism·Psi | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isMorphism·Psi |
| 93 | ·--·used·2. | 93 | ·--·used·2.89459s·(cpu);·2.45835s·(thread);·0s·(gc) |
| 94 | o5·=·true</code></pre> | 94 | o5·=·true</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert((not·o3)·and·o5)</code></pre> | 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert((not·o3)·and·o5)</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ········</table> | 99 | ········</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·0.2 | 24 | ·--·used·0.277019s·(cpu);·0.158184s·(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·0.07 | 27 | ·--·used·0.0731895s·(cpu);·0.0749063s·(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·2. | 31 | ·--·used·2.89459s·(cpu);·2.45835s·(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 |
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| 75 | ··········<tr> | 75 | ··········<tr> |
| 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 | 76 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^(1,7);·--·rational·normal·curve·of·degree·7 |
| 77 | o2·:·ProjectiveVariety,·curve·in·PP^7</code></pre> | 77 | o2·:·ProjectiveVariety,·curve·in·PP^7</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·linearlyNormalEmbedding·X; | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·linearlyNormalEmbedding·X; |
| 81 | ·--·used·0.0 | 81 | ·--·used·0.0120064s·(cpu);·0.0116939s·(thread);·0s·(gc) |
| 82 | o3·:·MultirationalMap·(automorphism·of·X)</code></pre> | 82 | o3·:·MultirationalMap·(automorphism·of·X)</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <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 | <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 |
| 86 | o4·:·ProjectiveVariety,·curve·in·PP^3</code></pre> | 86 | o4·:·ProjectiveVariety,·curve·in·PP^3</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·g·=·linearlyNormalEmbedding·Y; | 89 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·g·=·linearlyNormalEmbedding·Y; |
| 90 | ·--·used·0.4 | 90 | ·--·used·0.473077s·(cpu);·0.422835s·(thread);·0s·(gc) |
| 91 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)</code></pre> | 91 | o5·:·MultirationalMap·(birational·map·from·Y·to·curve·in·PP^7)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isIsomorphism·g)</code></pre> | 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isIsomorphism·g)</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<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·0.0 | 20 | ·--·used·0.0120064s·(cpu);·0.0116939s·(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·0.4 | 26 | ·--·used·0.473077s·(cpu);·0.422835s·(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 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; | 79 | <td>··············<pre><code·class="language-macaulay2">i2·:·Phi·=·last·graph·rationalMap·{f,g}; |
| 80 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> | 80 | o2·:·MultirationalMap·(rational·map·from·threefold·in·PP^3·x·PP^2·x·PP^4·to·PP^2·x·PP^4)</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·multidegree·Phi | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·multidegree·Phi |
| 84 | ·--·used·0.4 | 84 | ·--·used·0.422182s·(cpu);·0.323238s·(thread);·0s·(gc) |
| 85 | o3·=·{66,·46,·31,·20} | 85 | o3·=·{66,·46,·31,·20} |
| 86 | o3·:·List</code></pre> | 86 | o3·:·List</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i4·:·(degree·source·Phi,degree·image·Phi) | 89 | <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·0.4 | 26 | ·--·used·0.422182s·(cpu);·0.323238s·(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) |
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| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·Phi·=·last·graph·rationalMap·PP_(ZZ/300007)^(1,4); |
| 79 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)</code></pre> | 79 | o1·:·MultirationalMap·(rational·map·from·4-dimensional·subvariety·of·PP^4·x·PP^5·to·PP^5)</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·for·i·in·{4,3,2,1,0}·list·time·multidegree(i,Phi) |
| 83 | ·--·used·0.00 | 83 | ·--·used·0.00400523s·(cpu);·0.00116466s·(thread);·0s·(gc) |
| 84 | ·--·used·0.180705s·(cpu);·0.11229s·(thread);·0s·(gc) | ||
| 85 | ·--·used·0.206203s·(cpu);·0.141487s·(thread);·0s·(gc) | ||
| 86 | ·--·used·0.1 | 84 | ·--·used·0.152762s·(cpu);·0.0961644s·(thread);·0s·(gc) |
| 85 | ·--·used·0.170361s·(cpu);·0.111368s·(thread);·0s·(gc) | ||
| 87 | ·--·used·0. | 86 | ·--·used·0.0771479s·(cpu);·0.0774929s·(thread);·0s·(gc) |
| 87 | ·--·used·0.134252s·(cpu);·0.080776s·(thread);·0s·(gc) | ||
| 88 | o2·=·{51,·28,·14,·6,·2} | 88 | o2·=·{51,·28,·14,·6,·2} |
| 89 | o2·:·List</code></pre> | 89 | o2·:·List</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·assert(oo·==·multidegree·Phi) | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·assert(oo·==·multidegree·Phi) |
| 93 | ·--·used·0.1 | 93 | ·--·used·0.13331s·(cpu);·0.0735196s·(thread);·0s·(gc)</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ········</table> | 95 | ········</table> |
| 96 | ······</div> | 96 | ······</div> |
| 97 | ······<div> | 97 | ······<div> |
| 98 | ········<h2>References</h2> | 98 | ········<h2>References</h2> |
| 99 | ArXiv·preprint:·<a·href="https://arxiv.org/abs/2101.04503">Computations·with·rational·maps·between·multi-projective·varieties</a>.······</div> | 99 | ArXiv·preprint:·<a·href="https://arxiv.org/abs/2101.04503">Computations·with·rational·maps·between·multi-projective·varieties</a>.······</div> |
| 100 | ······<div> | 100 | ······<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·0.00400523s·(cpu);·0.00116466s·(thread);·0s·(gc) |
| 25 | ·--·used·0.180705s·(cpu);·0.11229s·(thread);·0s·(gc) | ||
| 26 | ·--·used·0.206203s·(cpu);·0.141487s·(thread);·0s·(gc) | ||
| 27 | ·--·used·0.1 | 25 | ·--·used·0.152762s·(cpu);·0.0961644s·(thread);·0s·(gc) |
| 26 | ·--·used·0.170361s·(cpu);·0.111368s·(thread);·0s·(gc) | ||
| 28 | ·--·used·0. | 27 | ·--·used·0.0771479s·(cpu);·0.0774929s·(thread);·0s·(gc) |
| 28 | ·--·used·0.134252s·(cpu);·0.080776s·(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·0.1 | 32 | ·--·used·0.13331s·(cpu);·0.0735196s·(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 77, 28 lines modified | Offset 77, 28 lines modified | ||
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^({1,1,2},{3,2,3}); | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·X·=·PP_K^({1,1,2},{3,2,3}); |
| 79 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9</code></pre> | 79 | o2·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^3·x·PP^2·x·PP^9</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·:=·point·X | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·p·:=·point·X |
| 83 | ·--·used·0.02 | 83 | ·--·used·0.0236059s·(cpu);·0.023161s·(thread);·0s·(gc) |
| 84 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) | 84 | o3·=·point·of·coordinates·([421369,·39917,·-212481,·1],[-128795,·-176966,·1],[3870,·-390108,·-496127,·-308581,·46649,·164926,·-446111,·48038,·415309,·1]) |
| 85 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> | 85 | o3·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·Y·=·random({2,1,2},X); | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·Y·=·random({2,1,2},X); |
| 89 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9</code></pre> | 89 | o4·:·ProjectiveVariety,·hypersurface·in·PP^3·x·PP^2·x·PP^9</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·q·=·point·Y | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·q·=·point·Y |
| 93 | ·--·used·1.4 | 93 | ·--·used·1.45785s·(cpu);·1.07969s·(thread);·0s·(gc) |
| 94 | o5·=·q | 94 | o5·=·q |
| 95 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> | 95 | o5·:·ProjectiveVariety,·a·point·in·PP^3·x·PP^2·x·PP^9</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(isSubset(p,X)·and·isSubset(q,Y))</code></pre> | 98 | <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·0.02 | 21 | ·--·used·0.0236059s·(cpu);·0.023161s·(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·1.4 | 28 | ·--·used·1.45785s·(cpu);·1.07969s·(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 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi·=·rationalMap·{f,g,h}; | 93 | <td>··············<pre><code·class="language-macaulay2">i5·:·Phi·=·rationalMap·{f,g,h}; |
| 94 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)</code></pre> | 94 | o5·:·MultirationalMap·(rational·map·from·PP^4·to·hypersurface·in·PP^5·x·PP^4·x·PP^4)</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·segre·Phi; | 97 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·segre·Phi; |
| 98 | ·--·used·0. | 98 | ·--·used·0.745021s·(cpu);·0.538393s·(thread);·0s·(gc) |
| 99 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)</code></pre> | 99 | o6·:·RationalMap·(rational·map·from·PP^4·to·PP^149)</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i7·:·describe·segre·Phi | 102 | <td>··············<pre><code·class="language-macaulay2">i7·:·describe·segre·Phi |
| 103 | o7·=·rational·map·defined·by·forms·of·degree·6 | 103 | 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·0. | 35 | ·--·used·0.745021s·(cpu);·0.538393s·(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 76, 15 lines modified | Offset 76, 15 lines modified | ||
| 76 | o1·=·Phi | 76 | o1·=·Phi |
| 77 | 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 | 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> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·Phi | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·describe·Phi |
| 81 | ·--·used·0.1 | 81 | ·--·used·0.15979s·(cpu);·0.105039s·(thread);·0s·(gc) |
| 82 | o2·=·multi-rational·map·consisting·of·3·rational·maps | 82 | o2·=·multi-rational·map·consisting·of·3·rational·maps |
| 83 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1) | 83 | ·····source·variety:·threefold·in·PP^3·x·PP^2·cut·out·by·2·hypersurfaces·of·multi-degree·(1,1) |
| 84 | ·····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 | ·····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· |
| 85 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 | 85 | ·····base·locus:·empty·subscheme·of·PP^3·x·PP^2 |
| 86 | ·····dominance:·true | 86 | ·····dominance:·true |
| 87 | ·····multidegree:·{10,·14,·19,·25} | 87 | ·····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·0.1 | 21 | ·--·used·0.15979s·(cpu);·0.105039s·(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 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | UG9seVNwYWNl | 8 | UG9seVNwYWNl |
| 9 | #:len=827 | 9 | #:len=827 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwb2x5bm9taWFsIHZlY3RvciBzdWJz | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYSBwb2x5bm9taWFsIHZlY3RvciBzdWJz |
| 11 | cGFjZSIsICJsaW5lbnVtIiA9PiA4NTcsIFNlZUFsc28gPT4gRElWe0hFQURFUjJ7IlNlZSBhbHNv | 11 | cGFjZSIsICJsaW5lbnVtIiA9PiA4NTcsIFNlZUFsc28gPT4gRElWe0hFQURFUjJ7IlNlZSBhbHNv |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·=·(7 | 29 | o9·=·(71,·83,·90,·95,·90,·91,·96,·96,·95,·99,·99,·95,·98,·100,·97,·99,·98, |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ·····98,·9 | 31 | ·····98,·99,·99,·99,·99,·97,·98,·98,·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·=·(1 | 34 | o10·=·(19,·8,·6,·5,·5,·6,·2,·1,·1,·0,·2,·1,·1,·0,·0,·0,·1,·0,·1,·0,·0,·1,·0, |
| 35 | ······----------------------------------------------------------------------- | 35 | ······----------------------------------------------------------------------- |
| 36 | ······0,· | 36 | ······0,·0,·0,·0,·1,·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·=·{Dtc,·DkC,·DNG,·DjG,·DWg} |
| 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:·-126948005 | 1 | --·-*-·M2-comint·-*-·hash:·-126948005 |
| 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},·{ | 8 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·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"·=>·{{a,· | 12 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·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·0.000841688s·(cpu);·0.000687705s·(thread);·0s·(gc) |
| 18 | i6·:·time·(graphComplement·\·G); | 18 | i6·:·time·(graphComplement·\·G); |
| 19 | ·--·used·0.0 | 19 | ·--·used·0.0893477s·(cpu);·0.0865708s·(thread);·0s·(gc) |
| 20 | i7·:· | 20 | i7·:· |
| Offset 94, 26 lines modified | Offset 94, 26 lines modified | ||
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) | 99 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) |
| 100 | o9·=·(7 | 100 | o9·=·(71,·83,·90,·95,·90,·91,·96,·96,·95,·99,·99,·95,·98,·100,·97,·99,·98, |
| 101 | ·····------------------------------------------------------------------------ | 101 | ·····------------------------------------------------------------------------ |
| 102 | ·····98,·9 | 102 | ·····98,·99,·99,·99,·99,·97,·98,·98,·99,·99,·99,·98) |
| 103 | o9·:·Sequence</code></pre> | 103 | o9·:·Sequence</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) | 106 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) |
| 107 | o10·=·(1 | 107 | o10·=·(19,·8,·6,·5,·5,·6,·2,·1,·1,·0,·2,·1,·1,·0,·0,·0,·1,·0,·1,·0,·0,·1,·0, |
| 108 | ······----------------------------------------------------------------------- | 108 | ······----------------------------------------------------------------------- |
| 109 | ······0,· | 109 | ······0,·0,·0,·0,·1,·0) |
| 110 | o10·:·Sequence</code></pre> | 110 | o10·:·Sequence</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ······</div> | 113 | ······</div> |
| 114 | ······<div> | 114 | ······<div> |
| 115 | ········<h2>See·also</h2> | 115 | ········<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·=·(7 | 44 | o9·=·(71,·83,·90,·95,·90,·91,·96,·96,·95,·99,·99,·95,·98,·100,·97,·99,·98, |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ·····98,·9 | 46 | ·····98,·99,·99,·99,·99,·97,·98,·98,·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·=·(1 | 50 | o10·=·(19,·8,·6,·5,·5,·6,·2,·1,·1,·0,·2,·1,·1,·0,·0,·0,·1,·0,·1,·0,·0,·1,·0, |
| 51 | ······----------------------------------------------------------------------- | 51 | ······----------------------------------------------------------------------- |
| 52 | ······0,· | 52 | ······0,·0,·0,·0,·1,·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 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 105 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 106 | o1·:·List</code></pre> | 106 | o1·:·List</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) | 109 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) |
| 110 | o2·=·{D | 110 | o2·=·{Dtc,·DkC,·DNG,·DjG,·DWg} |
| 111 | o2·:·List</code></pre> | 111 | o2·:·List</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| 114 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 114 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 115 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 115 | 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·=·{Dtc,·DkC,·DNG,·DjG,·DWg} |
| 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 90, 23 lines modified | Offset 90, 23 lines modified | ||
| 90 | ········<table·class="examples"> | 90 | ········<table·class="examples"> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[a..e];</code></pre> | 92 | <td>··············<pre><code·class="language-macaulay2">i1·:·R·=·QQ[a..e];</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomRegularGraphs(R,·3,·2) | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomRegularGraphs(R,·3,·2) |
| 96 | o2·=·{Graph{"edges"·=>·{{ | 96 | o2·=·{Graph{"edges"·=>·{{b,·c},·{a,·d},·{c,·d},·{a,·e},·{b,·e}}}, |
| 97 | ············"ring"·=>·R·········································· | 97 | ············"ring"·=>·R·········································· |
| 98 | ············"vertices"·=>·{a,·b,·c,·d,·e}························ | 98 | ············"vertices"·=>·{a,·b,·c,·d,·e}························ |
| 99 | ·····------------------------------------------------------------------------ | 99 | ·····------------------------------------------------------------------------ |
| 100 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{ | 100 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}}, |
| 101 | ···········"ring"·=>·R·········································· | 101 | ···········"ring"·=>·R·········································· |
| 102 | ···········"vertices"·=>·{a,·b,·c,·d,·e}························ | 102 | ···········"vertices"·=>·{a,·b,·c,·d,·e}························ |
| 103 | ·····------------------------------------------------------------------------ | 103 | ·····------------------------------------------------------------------------ |
| 104 | ·····Graph{"edges"·=>·{{a,· | 104 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·e}}}} |
| 105 | ···········"ring"·=>·R | 105 | ···········"ring"·=>·R |
| 106 | ···········"vertices"·=>·{a,·b,·c,·d,·e} | 106 | ···········"vertices"·=>·{a,·b,·c,·d,·e} |
| 107 | o2·:·List</code></pre> | 107 | o2·:·List</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ······</div> | 110 | ······</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},·{ | 35 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·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"·=>·{{a,· | 39 | ·····Graph{"edges"·=>·{{a,·b},·{b,·c},·{c,·d},·{a,·e},·{d,·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 114, 19 lines modified | Offset 114, 19 lines modified | ||
| 114 | ········</div> | 114 | ········</div> |
| 115 | ········<table·class="examples"> | 115 | ········<table·class="examples"> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·generateBipartiteGraphs·7;</code></pre> | 117 | <td>··············<pre><code·class="language-macaulay2">i4·:·G·=·generateBipartiteGraphs·7;</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·graphComplement·G; | 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·graphComplement·G; |
| 121 | ·--·used·0.000 | 121 | ·--·used·0.000841688s·(cpu);·0.000687705s·(thread);·0s·(gc)</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(graphComplement·\·G); | 124 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(graphComplement·\·G); |
| 125 | ·--·used·0.0 | 125 | ·--·used·0.0893477s·(cpu);·0.0865708s·(thread);·0s·(gc)</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ········</table> | 127 | ········</table> |
| 128 | ······</div> | 128 | ······</div> |
| 129 | ······<div> | 129 | ······<div> |
| 130 | ········<h2>See·also</h2> | 130 | ········<h2>See·also</h2> |
| 131 | ········<ul> | 131 | ········<ul> |
| 132 | ··········<li> | 132 | ··········<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·0.000841688s·(cpu);·0.000687705s·(thread);·0s·(gc) |
| 49 | i6·:·time·(graphComplement·\·G); | 49 | i6·:·time·(graphComplement·\·G); |
| 50 | ·--·used·0.0 | 50 | ·--·used·0.0893477s·(cpu);·0.0865708s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·=·(6 | 29 | o9·=·(62,·86,·85,·92,·92,·94,·95,·97,·96,·94,·94,·98,·97,·95,·99,·99,·98,·98, |
| 30 | ·····------------------------------------------------------------------------ | 30 | ·····------------------------------------------------------------------------ |
| 31 | ····· | 31 | ·····98,·94,·97,·97,·99,·100,·98,·95,·98,·99,·96) |
| 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,·8,·6,·3,·4,·3,·3,·1,·4,·0,·0,·0,·1,·0,·0,·1,·0,·0,·1,·0,·0,·0,·1, |
| 35 | ······----------------------------------------------------------------------- | 35 | ······----------------------------------------------------------------------- |
| 36 | ······0,·0,·0,·0,·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·=·{Dvg,·DfS,·D_S,·D{s,·DSk} |
| 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:·-152469492 | 1 | --·-*-·M2-comint·-*-·hash:·-152469492 |
| 2 | i1·:·generateRandomRegularGraphs(5,·3,·2) | 2 | i1·:·generateRandomRegularGraphs(5,·3,·2) |
| 3 | o1·=·{D | 3 | o1·=·{DdW,·D[S,·DUW} |
| 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·0.000501124s·(cpu);·0.00041253s·(thread);·0s·(gc) |
| 18 | i5·:·time·(graphComplement·\·G); | 18 | i5·:·time·(graphComplement·\·G); |
| 19 | ·--·used·0.07 | 19 | ·--·used·0.07098s·(cpu);·0.0689378s·(thread);·0s·(gc) |
| 20 | i6·:· | 20 | i6·:· |
| Offset 94, 24 lines modified | Offset 94, 24 lines modified | ||
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> | 96 | <td>··············<pre><code·class="language-macaulay2">i8·:·prob·=·n·->·log(n)/n;</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) | 99 | <td>··············<pre><code·class="language-macaulay2">i9·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·2*(prob·n)),·connected)) |
| 100 | o9·=·(6 | 100 | o9·=·(62,·86,·85,·92,·92,·94,·95,·97,·96,·94,·94,·98,·97,·95,·99,·99,·98,·98, |
| 101 | ·····------------------------------------------------------------------------ | 101 | ·····------------------------------------------------------------------------ |
| 102 | ····· | 102 | ·····98,·94,·97,·97,·99,·100,·98,·95,·98,·99,·96) |
| 103 | o9·:·Sequence</code></pre> | 103 | o9·:·Sequence</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) | 106 | <td>··············<pre><code·class="language-macaulay2">i10·:·apply(2..30,·n·->·#filterGraphs(generateRandomGraphs(n,·100,·(prob·n)/2),·connected)) |
| 107 | o10·=·(1 | 107 | o10·=·(15,·8,·6,·3,·4,·3,·3,·1,·4,·0,·0,·0,·1,·0,·0,·1,·0,·0,·1,·0,·0,·0,·1, |
| 108 | ······----------------------------------------------------------------------- | 108 | ······----------------------------------------------------------------------- |
| 109 | ······0,·0,·0,·0,·0,·0) | 109 | ······0,·0,·0,·0,·0,·0) |
| 110 | o10·:·Sequence</code></pre> | 110 | o10·:·Sequence</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ······</div> | 113 | ······</div> |
| Offset 38, 23 lines modified | Offset 38, 23 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·=·(6 | 44 | o9·=·(62,·86,·85,·92,·92,·94,·95,·97,·96,·94,·94,·98,·97,·95,·99,·99,·98,·98, |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ····· | 46 | ·····98,·94,·97,·97,·99,·100,·98,·95,·98,·99,·96) |
| 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,·8,·6,·3,·4,·3,·3,·1,·4,·0,·0,·0,·1,·0,·0,·1,·0,·0,·1,·0,·0,·0,·1, |
| 51 | ······----------------------------------------------------------------------- | 51 | ······----------------------------------------------------------------------- |
| 52 | ······0,·0,·0,·0,·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 |
| Offset 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 97 | o1·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} |
| 98 | o1·:·List</code></pre> | 98 | o1·:·List</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) | 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·generateRandomGraphs(5,·5) |
| 102 | o2·=·{D | 102 | o2·=·{Dvg,·DfS,·D_S,·D{s,·DSk} |
| 103 | o2·:·List</code></pre> | 103 | o2·:·List</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) | 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·generateRandomGraphs(5,·5,·RandomSeed·=>·314159) |
| 107 | o3·=·{DDO,·Dx_,·Dlw,·Dx{,·D_K} | 107 | 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·=·{Dvg,·DfS,·D_S,·D{s,·DSk} |
| 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 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | ········<div> | 81 | ········<div> |
| 82 | ··········<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 | ··········<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> |
| 83 | ········</div> | 83 | ········</div> |
| 84 | ········<table·class="examples"> | 84 | ········<table·class="examples"> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·generateRandomRegularGraphs(5,·3,·2) | 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·generateRandomRegularGraphs(5,·3,·2) |
| 87 | o1·=·{D | 87 | o1·=·{DdW,·D[S,·DUW} |
| 88 | o1·:·List</code></pre> | 88 | o1·:·List</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ········</table> | 90 | ········</table> |
| 91 | ······</div> | 91 | ······</div> |
| 92 | ······<div> | 92 | ······<div> |
| 93 | ········<h2>Caveat</h2> | 93 | ········<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·=·{DdW,·D[S,·DUW} |
| 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 110, 19 lines modified | Offset 110, 19 lines modified | ||
| 110 | ········</div> | 110 | ········</div> |
| 111 | ········<table·class="examples"> | 111 | ········<table·class="examples"> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i3·:·G·=·generateBipartiteGraphs·7;</code></pre> | 113 | <td>··············<pre><code·class="language-macaulay2">i3·:·G·=·generateBipartiteGraphs·7;</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·graphComplement·G; | 116 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·graphComplement·G; |
| 117 | ·--·used·0.000 | 117 | ·--·used·0.000501124s·(cpu);·0.00041253s·(thread);·0s·(gc)</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(graphComplement·\·G); | 120 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·(graphComplement·\·G); |
| 121 | ·--·used·0.07 | 121 | ·--·used·0.07098s·(cpu);·0.0689378s·(thread);·0s·(gc)</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ········</table> | 123 | ········</table> |
| 124 | ······</div> | 124 | ······</div> |
| 125 | ······<div·class="waystouse"> | 125 | ······<div·class="waystouse"> |
| 126 | ········<h2>Ways·to·use·<span·class="tt">graphComplement</span>·:</h2> | 126 | ········<h2>Ways·to·use·<span·class="tt">graphComplement</span>·:</h2> |
| 127 | ········<ul> | 127 | ········<ul> |
| 128 | ··········<li> | 128 | ··········<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·0.000501124s·(cpu);·0.00041253s·(thread);·0s·(gc) |
| 46 | i5·:·time·(graphComplement·\·G); | 46 | i5·:·time·(graphComplement·\·G); |
| 47 | ·--·used·0.07 | 47 | ·--·used·0.07098s·(cpu);·0.0689378s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0. | 51 | ·--·0.104361·seconds·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 |
| Offset 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·isPrimary·Q | 104 | <td>··············<pre><code·class="language-macaulay2">i5·:·isPrimary·Q |
| 105 | o5·=·true</code></pre> | 105 | o5·=·true</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") | 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·noetherianOperators(Q,·Strategy·=>·"PunctualQuot") |
| 109 | ·--·0. | 109 | ·--·0.104361·seconds·elapsed |
| 110 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| | 110 | o6·=·{|·1·|,·|·dx_1·|,·|·dx_2·|,·|·dx_1^2·|,·|·dx_1dx_2·|,·|·dx_2^2·|,·| |
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| 112 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} | 112 | ·····2x_1x_3dx_1^3+3x_2x_3dx_1^2dx_2-3x_3x_4dx_1dx_2^2-2x_1x_4dx_2^3·|} |
| 113 | o6·:·List</code></pre> | 113 | o6·:·List</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| Offset 51, 15 lines modified | Offset 51, 15 lines modified | ||
| 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 | ·--·0. | 56 | ·--·0.104361·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTQ0Miwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTQ0Miwgc3ltYm9sIERvY3VtZW50VGFn |
| 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·0.139022s·(cpu);·0.139249s·(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·0.000565431s·(cpu);·0.00107292s·(thread);·0s·(gc) |
| 116 | ·--·used·2.7562e-05s·(cpu);·0.000104856s·(thread);·0s·(gc) | ||
| 117 | ·--·used· | 116 | ·--·used·2.1452e-05s·(cpu);·6.7963e-05s·(thread);·0s·(gc) |
| 118 | ·--·used·1.2163e-05s·(cpu);·7.9178e-05s·(thread);·0s·(gc) | ||
| 119 | ·--·used· | 117 | ·--·used·6.089e-06s·(cpu);·5.0225e-05s·(thread);·0s·(gc) |
| 120 | ·--·used· | 118 | ·--·used·5.729e-06s·(cpu);·4.8553e-05s·(thread);·0s·(gc) |
| 119 | ·--·used·5.529e-06s·(cpu);·4.5157e-05s·(thread);·0s·(gc) | ||
| 120 | ·--·used·5.258e-06s·(cpu);·4.4407e-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·=·{1,·2,·6} |
| 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·=·{1,·2,· | 11 | o7·=·{1,·2,·5,·7,·9} |
| 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 | ·--·0. | 10 | ·--·0.303642·seconds·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 | ·--·0.00 | 20 | ·--·0.00101602·seconds·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 | ·--·0. | 27 | ·--·0.136325·seconds·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 | ·--·0.00 | 33 | ·--·0.00099336·seconds·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 | ·--·42.0594·seconds·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 | ·--·0.02 | 43 | ·--·0.0220161·seconds·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·0.00105546s·(cpu);·1.7116e-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·0.1 | 32 | ·--·used·0.146097s·(cpu);·0.0685823s·(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·0.0144888s·(cpu);·0.0174719s·(thread);·0s·(gc) |
| 94 | i20·:·X2·=·time·normalToricVariety·vertMatrix; | 94 | i20·:·X2·=·time·normalToricVariety·vertMatrix; |
| 95 | ·--·used·0.000 | 95 | ·--·used·0.000766844s·(cpu);·0.00179135s·(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 182, 15 lines modified | Offset 182, 15 lines modified | ||
| 182 | ········</table> | 182 | ········</table> |
| 183 | ········<div> | 183 | ········<div> |
| 184 | ··········<p>We·end·with·a·slightly·larger·example.</p> | 184 | ··········<p>We·end·with·a·slightly·larger·example.</p> |
| 185 | ········</div> | 185 | ········</div> |
| 186 | ········<table·class="examples"> | 186 | ········<table·class="examples"> |
| 187 | ··········<tr> | 187 | ··········<tr> |
| 188 | <td>··············<pre><code·class="language-macaulay2">i14·:·Y·=·time·smoothFanoToricVariety(5,100); | 188 | <td>··············<pre><code·class="language-macaulay2">i14·:·Y·=·time·smoothFanoToricVariety(5,100); |
| 189 | ·--·used·0.1 | 189 | ·--·used·0.139022s·(cpu);·0.139249s·(thread);·0s·(gc)</code></pre> |
| 190 | </td>··········</tr> | 190 | </td>··········</tr> |
| 191 | ··········<tr> | 191 | ··········<tr> |
| 192 | <td>··············<pre><code·class="language-macaulay2">i15·:·A2·=·intersectionRing·Y;</code></pre> | 192 | <td>··············<pre><code·class="language-macaulay2">i15·:·A2·=·intersectionRing·Y;</code></pre> |
| 193 | </td>··········</tr> | 193 | </td>··········</tr> |
| 194 | ··········<tr> | 194 | ··········<tr> |
| 195 | <td>··············<pre><code·class="language-macaulay2">i16·:·assert·(#·rays·Y·===·numgens·A2)</code></pre> | 195 | <td>··············<pre><code·class="language-macaulay2">i16·:·assert·(#·rays·Y·===·numgens·A2)</code></pre> |
| 196 | </td>··········</tr> | 196 | </td>··········</tr> |
| Offset 219, 20 lines modified | Offset 219, 20 lines modified | ||
| 219 | ······(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 | ······(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··) |
| 220 | ········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 | ········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 |
| 221 | o18·:·QuotientRing</code></pre> | 221 | o18·:·QuotientRing</code></pre> |
| 222 | </td>··········</tr> | 222 | </td>··········</tr> |
| 223 | ··········<tr> | 223 | ··········<tr> |
| 224 | <td>··············<pre><code·class="language-macaulay2">i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) | 224 | <td>··············<pre><code·class="language-macaulay2">i19·:·for·i·to·dim·Y·list·time·hilbertFunction·(i,·A2) |
| 225 | ·--·used·0.00 | 225 | ·--·used·0.000565431s·(cpu);·0.00107292s·(thread);·0s·(gc) |
| 226 | ·--·used·2.7562e-05s·(cpu);·0.000104856s·(thread);·0s·(gc) | ||
| 227 | ·--·used· | 226 | ·--·used·2.1452e-05s·(cpu);·6.7963e-05s·(thread);·0s·(gc) |
| 228 | ·--·used·1.2163e-05s·(cpu);·7.9178e-05s·(thread);·0s·(gc) | ||
| 229 | ·--·used· | 227 | ·--·used·6.089e-06s·(cpu);·5.0225e-05s·(thread);·0s·(gc) |
| 230 | ·--·used· | 228 | ·--·used·5.729e-06s·(cpu);·4.8553e-05s·(thread);·0s·(gc) |
| 229 | ·--·used·5.529e-06s·(cpu);·4.5157e-05s·(thread);·0s·(gc) | ||
| 230 | ·--·used·5.258e-06s·(cpu);·4.4407e-05s·(thread);·0s·(gc) | ||
| 231 | o19·=·{1,·6,·13,·13,·6,·1} | 231 | o19·=·{1,·6,·13,·13,·6,·1} |
| 232 | o19·:·List</code></pre> | 232 | o19·:·List</code></pre> |
| 233 | </td>··········</tr> | 233 | </td>··········</tr> |
| 234 | ········</table> | 234 | ········</table> |
| 235 | ······</div> | 235 | ······</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·0.139022s·(cpu);·0.139249s·(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·0.000565431s·(cpu);·0.00107292s·(thread);·0s·(gc) |
| 137 | ·--·used·2.7562e-05s·(cpu);·0.000104856s·(thread);·0s·(gc) | ||
| 138 | ·--·used· | 137 | ·--·used·2.1452e-05s·(cpu);·6.7963e-05s·(thread);·0s·(gc) |
| 139 | ·--·used·1.2163e-05s·(cpu);·7.9178e-05s·(thread);·0s·(gc) | ||
| 140 | ·--·used· | 138 | ·--·used·6.089e-06s·(cpu);·5.0225e-05s·(thread);·0s·(gc) |
| 141 | ·--·used· | 139 | ·--·used·5.729e-06s·(cpu);·4.8553e-05s·(thread);·0s·(gc) |
| 140 | ·--·used·5.529e-06s·(cpu);·4.5157e-05s·(thread);·0s·(gc) | ||
| 141 | ·--·used·5.258e-06s·(cpu);·4.4407e-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 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | ········<table·class="examples"> | 101 | ········<table·class="examples"> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i2·:·setRandomSeed·(currentTime·());</code></pre> | 103 | <td>··············<pre><code·class="language-macaulay2">i2·:·setRandomSeed·(currentTime·());</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·a·=·sort·apply·(3,·i·->·random·(7)) | 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·a·=·sort·apply·(3,·i·->·random·(7)) |
| 107 | o3·=·{ | 107 | o3·=·{1,·2,·6} |
| 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·:·assert·isWellDefined·kleinschmidt·(4,a)</code></pre> | 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·assert·isWellDefined·kleinschmidt·(4,a)</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ········</table> | 113 | ········</table> |
| Offset 119, 15 lines modified | Offset 119, 15 lines modified | ||
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <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>··············<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> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·q | 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·q |
| 125 | o7·=·{1,·2,· | 125 | o7·=·{1,·2,·5,·7,·9} |
| 126 | o7·:·List</code></pre> | 126 | o7·:·List</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·isWellDefined·weightedProjectiveSpace·q</code></pre> | 129 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·isWellDefined·weightedProjectiveSpace·q</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ········</table> | 131 | ········</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·=·{1,·2,·6} |
| 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·=·{1,·2,· | 44 | o7·=·{1,·2,·5,·7,·9} |
| 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 95, 29 lines modified | Offset 95, 29 lines modified | ||
| 95 | o2·=·5*PP2 | 95 | o2·=·5*PP2 |
| 96 | ··········0 | 96 | ··········0 |
| 97 | o2·:·ToricDivisor·on·PP2</code></pre> | 97 | o2·:·ToricDivisor·on·PP2</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·M1·=·elapsedTime·monomials·D1 | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·M1·=·elapsedTime·monomials·D1 |
| 101 | ·--·0. | 101 | ·--·0.303642·seconds·elapsed |
| 102 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4··· | 102 | ·······5·····4·····4···2·3·······3···2·3···3·2·····2·2···2···2···3·2···4··· |
| 103 | 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 | 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·, |
| 104 | ·······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 | ·······2···1·2···0·2···1·2···0·1·2···0·2···1·2···0·1·2···0·1·2···0·2···1·2· |
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 | 106 | ········3·····2·2·····3·······4·····5·····4···2·3···3·2···4·····5 |
| 107 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} | 107 | ·····x·x·x·,·x·x·x·,·x·x·x·,·x·x·,·x·,·x·x·,·x·x·,·x·x·,·x·x·,·x·} |
| 108 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 | 108 | ······0·1·2···0·1·2···0·1·2···0·2···1···0·1···0·1···0·1···0·1···0 |
| 109 | o3·:·List</code></pre> | 109 | o3·:·List</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1)) | 112 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·assert·(set·M1·===·set·first·entries·basis(degree·D1,·ring·variety·D1)) |
| 113 | ·--·0.00 | 113 | ·--·0.00101602·seconds·elapsed</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ········</table> | 115 | ········</table> |
| 116 | ········<div> | 116 | ········<div> |
| 117 | ··········<p>Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.</p> | 117 | ··········<p>Toric·varieties·of·Picard-rank·2·are·slightly·more·interesting.</p> |
| 118 | ········</div> | 118 | ········</div> |
| 119 | ········<table·class="examples"> | 119 | ········<table·class="examples"> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| Offset 129, 46 lines modified | Offset 129, 46 lines modified | ||
| 129 | o6·=·2*FF2··+·3*FF2 | 129 | o6·=·2*FF2··+·3*FF2 |
| 130 | ··········0········1 | 130 | ··········0········1 |
| 131 | o6·:·ToricDivisor·on·FF2</code></pre> | 131 | o6·:·ToricDivisor·on·FF2</code></pre> |
| 132 | </td>··········</tr> | 132 | </td>··········</tr> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i7·:·M2·=·elapsedTime·monomials·D2 | 134 | <td>··············<pre><code·class="language-macaulay2">i7·:·M2·=·elapsedTime·monomials·D2 |
| 135 | ·--·0. | 135 | ·--·0.136325·seconds·elapsed |
| 136 | ·······2·····3·2·····3·····2·3 | 136 | ·······2·····3·2·····3·····2·3 |
| 137 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} | 137 | o7·=·{x·x·,·x·x·,·x·x·x·,·x·x·} |
| 138 | ·······1·3···1·2···0·1·2···0·1 | 138 | ·······1·3···1·2···0·1·2···0·1 |
| 139 | o7·:·List</code></pre> | 139 | o7·:·List</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2)) | 142 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·assert·(set·M2·===·set·first·entries·basis·(degree·D2,·ring·variety·D2)) |
| 143 | ·--·0.00 | 143 | ·--·0.00099336·seconds·elapsed</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i9·:·X·=·kleinschmidt·(5,·{1,2,3});</code></pre> | 146 | <td>··············<pre><code·class="language-macaulay2">i9·:·X·=·kleinschmidt·(5,·{1,2,3});</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i10·:·D3·=·3*X_0·+·5*X_1 | 149 | <td>··············<pre><code·class="language-macaulay2">i10·:·D3·=·3*X_0·+·5*X_1 |
| 150 | o10·=·3*X··+·5*X | 150 | o10·=·3*X··+·5*X |
| 151 | ·········0······1 | 151 | ·········0······1 |
| 152 | o10·:·ToricDivisor·on·X</code></pre> | 152 | o10·:·ToricDivisor·on·X</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i11·:·m3·=·elapsedTime·#·monomials·D3 | 155 | <td>··············<pre><code·class="language-macaulay2">i11·:·m3·=·elapsedTime·#·monomials·D3 |
| 156 | ·--· | 156 | ·--·42.0594·seconds·elapsed |
| 157 | o11·=·7909</code></pre> | 157 | o11·=·7909</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ··········<tr> | 159 | ··········<tr> |
| 160 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3)) | 160 | <td>··············<pre><code·class="language-macaulay2">i12·:·elapsedTime·assert·(m3·===·#first·entries·basis·(degree·D3,·ring·variety·D3)) |
| 161 | ·--·0.02 | 161 | ·--·0.0220161·seconds·elapsed</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ········</table> | 163 | ········</table> |
| 164 | ········<div> | 164 | ········<div> |
| 165 | ··········<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 | ··········<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> |
| 166 | ········</div> | 166 | ········</div> |
| 167 | ······</div> | 167 | ······</div> |
| 168 | ······<div> | 168 | ······<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 | ·--·0. | 33 | ·--·0.303642·seconds·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 | ·--·0.00 | 44 | ·--·0.00101602·seconds·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 | ·--·0. | 52 | ·--·0.136325·seconds·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 | ·--·0.00 | 59 | ·--·0.00099336·seconds·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 | ·--·42.0594·seconds·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 | ·--·0.02 | 70 | ·--·0.0220161·seconds·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) |
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| 121 | ········</table> | 121 | ········</table> |
| 122 | ········<div> | 122 | ········<div> |
| 123 | ··········<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 | ··········<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> |
| 124 | ········</div> | 124 | ········</div> |
| 125 | ········<table·class="examples"> | 125 | ········<table·class="examples"> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) | 127 | <td>··············<pre><code·class="language-macaulay2">i6·:·X1·=·time·normalToricVariety·({{-1,-1},{1,0},{0,1}},·{{0,1},{1,2},{0,2}}) |
| 128 | ·--·used·0.00 | 128 | ·--·used·0.00105546s·(cpu);·1.7116e-05s·(thread);·0s·(gc) |
| 129 | o6·=·X1 | 129 | o6·=·X1 |
| 130 | o6·:·NormalToricVariety</code></pre> | 130 | o6·:·NormalToricVariety</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <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 | <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}}}; |
| 134 | ·--·used·0.1 | 134 | ·--·used·0.146097s·(cpu);·0.0685823s·(thread);·0s·(gc)</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)</code></pre> | 137 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert·(sort·rays·X1·==·sort·rays·X2·and·max·X1·==·max·X2)</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ········</table> | 139 | ········</table> |
| 140 | ······</div> | 140 | ······</div> |
| 141 | ······<div> | 141 | ······<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·0.00105546s·(cpu);·1.7116e-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·0.1 | 61 | ·--·used·0.146097s·(cpu);·0.0685823s·(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 203, 19 lines modified | Offset 203, 19 lines modified | ||
| 203 | ······|·0·0·1·| | 203 | ······|·0·0·1·| |
| 204 | ···············2·······3 | 204 | ···············2·······3 |
| 205 | o18·:·Matrix·ZZ··<--·ZZ</code></pre> | 205 | o18·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 206 | </td>··········</tr> | 206 | </td>··········</tr> |
| 207 | ··········<tr> | 207 | ··········<tr> |
| 208 | <td>··············<pre><code·class="language-macaulay2">i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); | 208 | <td>··············<pre><code·class="language-macaulay2">i19·:·X1·=·time·normalToricVariety·convexHull·(vertMatrix); |
| 209 | ·--·used·0.0 | 209 | ·--·used·0.0144888s·(cpu);·0.0174719s·(thread);·0s·(gc)</code></pre> |
| 210 | </td>··········</tr> | 210 | </td>··········</tr> |
| 211 | ··········<tr> | 211 | ··········<tr> |
| 212 | <td>··············<pre><code·class="language-macaulay2">i20·:·X2·=·time·normalToricVariety·vertMatrix; | 212 | <td>··············<pre><code·class="language-macaulay2">i20·:·X2·=·time·normalToricVariety·vertMatrix; |
| 213 | ·--·used·0.000 | 213 | ·--·used·0.000766844s·(cpu);·0.00179135s·(thread);·0s·(gc)</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ··········<tr> | 215 | ··········<tr> |
| 216 | <td>··············<pre><code·class="language-macaulay2">i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)</code></pre> | 216 | <td>··············<pre><code·class="language-macaulay2">i21·:·assert·(set·rays·X2·===·set·rays·X1·and·max·X1·===·max·X2)</code></pre> |
| 217 | </td>··········</tr> | 217 | </td>··········</tr> |
| 218 | ········</table> | 218 | ········</table> |
| 219 | ······</div> | 219 | ······</div> |
| 220 | ······<div> | 220 | ······<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·0.0144888s·(cpu);·0.0174719s·(thread);·0s·(gc) |
| 109 | i20·:·X2·=·time·normalToricVariety·vertMatrix; | 109 | i20·:·X2·=·time·normalToricVariety·vertMatrix; |
| 110 | ·--·used·0.000 | 110 | ·--·used·0.000766844s·(cpu);·0.00179135s·(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 |
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| 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 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | ······3······2 | 101 | ······3······2 |
| 102 | o3·=·x··-·36x··+·431x·-·1716 | 102 | o3·=·x··-·36x··+·431x·-·1716 |
| 103 | o3·:·R</code></pre> | 103 | o3·:·R</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <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 | <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" |
| 107 | sh:·1:·bertini:·not·found | 107 | sh:·line·1:·bertini:·command·not·found |
| 108 | true | 108 | true |
| 109 | o4·=·need·to·install·Bertini·to·run·these·lines</code></pre> | 109 | o4·=·need·to·install·Bertini·to·run·these·lines</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ········</table> | 111 | ········</table> |
| 112 | ······</div> | 112 | ······</div> |
| Offset 36, 15 lines modified | Offset 36, 15 lines modified | ||
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| 38 | o3·:·R | 38 | o3·:·R |
| 39 | i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}}, | 39 | i4·:·try·parameterHomotopy({f1,f2},{u1,u2,u3},{{1,0,0},{0,1+2*ii,0}}, |
| 40 | Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" | 40 | Software=>BERTINI)·else·"need·to·install·Bertini·to·run·these·lines" |
| 41 | sh:·1:·bertini:·not·found | 41 | sh:·line·1:·bertini:·command·not·found |
| 42 | true | 42 | true |
| 43 | o4·=·need·to·install·Bertini·to·run·these·lines | 43 | o4·=·need·to·install·Bertini·to·run·these·lines |
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| 45 | Available·only·with·Software=>BERTINI·at·the·moment... | 45 | Available·only·with·Software=>BERTINI·at·the·moment... |
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| Offset 67, 15 lines modified | Offset 67, 15 lines modified | ||
| 67 | <span><span·class="tt">PRECISION</span>·(missing·documentation)<!--tag:·[alphaCertified,·PRECISION]--> | 67 | <span><span·class="tt">PRECISION</span>·(missing·documentation)<!--tag:·[alphaCertified,·PRECISION]--> |
| 68 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·96</span>,·<span></span></span>··············</li> | 68 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·96</span>,·<span></span></span>··············</li> |
| 69 | ··············<li> | 69 | ··············<li> |
| 70 | <span><span·class="tt">RANDOMDIGITS</span>·(missing·documentation)<!--tag:·[alphaCertified,·RANDOMDIGITS]--> | 70 | <span><span·class="tt">RANDOMDIGITS</span>·(missing·documentation)<!--tag:·[alphaCertified,·RANDOMDIGITS]--> |
| 71 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·10</span>,·<span></span></span>··············</li> | 71 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·10</span>,·<span></span></span>··············</li> |
| 72 | ··············<li> | 72 | ··············<li> |
| 73 | <span><span·class="tt">RANDOMSEED</span>·(missing·documentation)<!--tag:·[alphaCertified,·RANDOMSEED]--> | 73 | <span><span·class="tt">RANDOMSEED</span>·(missing·documentation)<!--tag:·[alphaCertified,·RANDOMSEED]--> |
| 74 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value· | 74 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·993</span>,·<span></span></span>··············</li> |
| 75 | ··············<li> | 75 | ··············<li> |
| 76 | <span><span·class="tt">REALITYCHECK</span>·(missing·documentation)<!--tag:·[alphaCertified,·REALITYCHECK]--> | 76 | <span><span·class="tt">REALITYCHECK</span>·(missing·documentation)<!--tag:·[alphaCertified,·REALITYCHECK]--> |
| 77 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·1</span>,·<span></span></span>··············</li> | 77 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·1</span>,·<span></span></span>··············</li> |
| 78 | ··············<li> | 78 | ··············<li> |
| 79 | <span><span·class="tt">REALITYTEST</span>·(missing·documentation)<!--tag:·[alphaCertified,·REALITYTEST]--> | 79 | <span><span·class="tt">REALITYTEST</span>·(missing·documentation)<!--tag:·[alphaCertified,·REALITYTEST]--> |
| 80 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·0</span>,·<span></span></span>··············</li> | 80 | <span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·0</span>,·<span></span></span>··············</li> |
| 81 | ··············<li> | 81 | ··············<li> |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | ··········o·ALGORITHM·(missing·documentation)·=>·...,·default·value·2, | 10 | ··········o·ALGORITHM·(missing·documentation)·=>·...,·default·value·2, |
| 11 | ··········o·ARITHMETICTYPE·(missing·documentation)·=>·...,·default·value·0, | 11 | ··········o·ARITHMETICTYPE·(missing·documentation)·=>·...,·default·value·0, |
| 12 | ··········o·NEWTONONLY·(missing·documentation)·=>·...,·default·value·0, | 12 | ··········o·NEWTONONLY·(missing·documentation)·=>·...,·default·value·0, |
| 13 | ··········o·NUMITERATIONS·(missing·documentation)·=>·...,·default·value·2, | 13 | ··········o·NUMITERATIONS·(missing·documentation)·=>·...,·default·value·2, |
| 14 | ··········o·NUMRANDOMSYSTEMS·(missing·documentation)·=>·...,·default·value·2, | 14 | ··········o·NUMRANDOMSYSTEMS·(missing·documentation)·=>·...,·default·value·2, |
| 15 | ··········o·PRECISION·(missing·documentation)·=>·...,·default·value·96, | 15 | ··········o·PRECISION·(missing·documentation)·=>·...,·default·value·96, |
| 16 | ··········o·RANDOMDIGITS·(missing·documentation)·=>·...,·default·value·10, | 16 | ··········o·RANDOMDIGITS·(missing·documentation)·=>·...,·default·value·10, |
| 17 | ··········o·RANDOMSEED·(missing·documentation)·=>·...,·default·value· | 17 | ··········o·RANDOMSEED·(missing·documentation)·=>·...,·default·value·993, |
| 18 | ··········o·REALITYCHECK·(missing·documentation)·=>·...,·default·value·1, | 18 | ··········o·REALITYCHECK·(missing·documentation)·=>·...,·default·value·1, |
| 19 | ··········o·REALITYTEST·(missing·documentation)·=>·...,·default·value·0, | 19 | ··········o·REALITYTEST·(missing·documentation)·=>·...,·default·value·0, |
| 20 | ··········o·REFINEDIGITS·(missing·documentation)·=>·...,·default·value·0, | 20 | ··········o·REFINEDIGITS·(missing·documentation)·=>·...,·default·value·0, |
| 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 | For·a·given·polynomial·system·and·a·list·of·numerical·roots,·this·function | 22 | For·a·given·polynomial·system·and·a·list·of·numerical·roots,·this·function |
| 23 | certifies·roots·using·a·software·_\x8"_\x8a_\x8l_\x8p_\x8h_\x8a_\x8C_\x8e_\x8r_\x8t_\x8i_\x8f_\x8i_\x8e_\x8d_\x8". | 23 | certifies·roots·using·a·software·_\x8"_\x8a_\x8l_\x8p_\x8h_\x8a_\x8C_\x8e_\x8r_\x8t_\x8i_\x8f_\x8i_\x8e_\x8d_\x8". |
| 24 | In·order·to·use·alphaCertified,·users·need·to·let·the·package·knows·a·directory | 24 | In·order·to·use·alphaCertified,·users·need·to·let·the·package·knows·a·directory |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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, 21 lines modified | Offset 23, 21 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·.00 | 28 | ·····--·used·.00666994·seconds |
| 29 | Creating·interpolation·matrix·... | 29 | Creating·interpolation·matrix·... |
| 30 | ·····--·used·.00 | 30 | ·····--·used·.00698021·seconds |
| 31 | Performing·normalization·preconditioning·... | 31 | Performing·normalization·preconditioning·... |
| 32 | ·····--·used·0·seconds | 32 | ·····--·used·.0022264·seconds |
| 33 | Computing·numerical·kernel·... | 33 | Computing·numerical·kernel·... |
| 34 | ·····--·used·0·seconds | 34 | ·····--·used·.000982448·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 |
| 38 | i6·:·extractImageEquations(T,·AttemptZZ·=>·true) | 38 | i6·:·extractImageEquations(T,·AttemptZZ·=>·true) |
| Offset 13, 21 lines modified | Offset 13, 21 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·.00418985·seconds |
| 19 | Creating·interpolation·matrix·... | 19 | Creating·interpolation·matrix·... |
| 20 | ·····--·used·.00 | 20 | ·····--·used·.00150968·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·.0039428·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·| |
| 26 | ··························1···················3 | 26 | ··························1···················3 |
| 27 | o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·]) | 27 | o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·]) |
| 28 | ···············53··0···3···········53··0···3 | 28 | ···············53··0···3···········53··0···3 |
| Offset 13, 19 lines modified | Offset 13, 19 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·.01 | 18 | ·····--·used·.0105541·seconds |
| 19 | Creating·interpolation·matrix·... | 19 | Creating·interpolation·matrix·... |
| 20 | ·····--·used·.01 | 20 | ·····--·used·.0119084·seconds |
| 21 | Performing·normalization·preconditioning·... | 21 | Performing·normalization·preconditioning·... |
| 22 | ·····--·used·.00 | 22 | ·····--·used·.00566747·seconds |
| 23 | Computing·numerical·kernel·... | 23 | Computing·numerical·kernel·... |
| 24 | ·····--·used·0·seconds | 24 | ·····--·used·0·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 |
| Offset 34, 19 lines modified | Offset 34, 19 lines modified | ||
| 34 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; | 34 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; |
| 35 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); | 35 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); |
| 36 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) | 36 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) |
| 37 | Creating·interpolation·matrix·... | 37 | Creating·interpolation·matrix·... |
| 38 | ·····--·used·.00 | 38 | ·····--·used·.0028158·seconds |
| 39 | Performing·normalization·preconditioning·... | 39 | Performing·normalization·preconditioning·... |
| 40 | ·····--·used·.00 | 40 | ·····--·used·.00385091·seconds |
| 41 | Computing·numerical·kernel·... | 41 | Computing·numerical·kernel·... |
| 42 | ·····--·used·0·seconds | 42 | ·····--·used·.00398965·seconds |
| 43 | o7·=·a·"numerical·interpolation·table",·indicating | 43 | o7·=·a·"numerical·interpolation·table",·indicating |
| 44 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 | 44 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 |
| 45 | o7·:·NumericalInterpolationTable | 45 | o7·:·NumericalInterpolationTable |
| 46 | i8·:· | 46 | 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·0.054439s·(cpu);·0.0515832s·(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 | ·--·0. | 35 | ·--·0.599971·seconds·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 90, 21 lines modified | Offset 90, 21 lines modified | ||
| 90 | --··········results·not·reliable·(one·warning·given·per·session) | 90 | --··········results·not·reliable·(one·warning·given·per·session) |
| 91 | o4·=·true</code></pre> | 91 | o4·=·true</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·T·=·numericalHilbertFunction(F,·I,·3,·ConvertToCone·=>·true) |
| 95 | Sampling·image·points·... | 95 | Sampling·image·points·... |
| 96 | ·····--·used·.00 | 96 | ·····--·used·.00666994·seconds |
| 97 | Creating·interpolation·matrix·... | 97 | Creating·interpolation·matrix·... |
| 98 | ·····--·used·.00 | 98 | ·····--·used·.00698021·seconds |
| 99 | Performing·normalization·preconditioning·... | 99 | Performing·normalization·preconditioning·... |
| 100 | ·····--·used·0·seconds | 100 | ·····--·used·.0022264·seconds |
| 101 | Computing·numerical·kernel·... | 101 | Computing·numerical·kernel·... |
| 102 | ·····--·used·0·seconds | 102 | ·····--·used·.000982448·seconds |
| 103 | o5·=·a·"numerical·interpolation·table",·indicating | 103 | o5·=·a·"numerical·interpolation·table",·indicating |
| 104 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 | 104 | ·····the·space·of·degree·3·forms·in·the·ideal·of·the·image·has·dimension·3 |
| 105 | o5·:·NumericalInterpolationTable</code></pre> | 105 | o5·:·NumericalInterpolationTable</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| Offset 36, 21 lines modified | Offset 36, 21 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·.00 | 42 | ·····--·used·.00666994·seconds |
| 43 | Creating·interpolation·matrix·... | 43 | Creating·interpolation·matrix·... |
| 44 | ·····--·used·.00 | 44 | ·····--·used·.00698021·seconds |
| 45 | Performing·normalization·preconditioning·... | 45 | Performing·normalization·preconditioning·... |
| 46 | ·····--·used·0·seconds | 46 | ·····--·used·.0022264·seconds |
| 47 | Computing·numerical·kernel·... | 47 | Computing·numerical·kernel·... |
| 48 | ·····--·used·0·seconds | 48 | ·····--·used·.000982448·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 |
| 52 | i6·:·extractImageEquations(T,·AttemptZZ·=>·true) | 52 | i6·:·extractImageEquations(T,·AttemptZZ·=>·true) |
| Offset 106, 21 lines modified | Offset 106, 21 lines modified | ||
| 106 | ·············1······4 | 106 | ·············1······4 |
| 107 | o2·:·Matrix·R··<--·R</code></pre> | 107 | o2·:·Matrix·R··<--·R</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) | 110 | <td>··············<pre><code·class="language-macaulay2">i3·:·extractImageEquations(F,·ideal·0_R,·2,·AttemptZZ·=>·true) |
| 111 | Sampling·image·points·... | 111 | Sampling·image·points·... |
| 112 | ·····--·used·.00 | 112 | ·····--·used·.00418985·seconds |
| 113 | Creating·interpolation·matrix·... | 113 | Creating·interpolation·matrix·... |
| 114 | ·····--·used·.00 | 114 | ·····--·used·.00150968·seconds |
| 115 | Performing·normalization·preconditioning·... | 115 | Performing·normalization·preconditioning·... |
| 116 | ·····--·used·0·seconds | 116 | ·····--·used·0·seconds |
| 117 | Computing·numerical·kernel·... | 117 | Computing·numerical·kernel·... |
| 118 | ·····--·used·0·seconds | 118 | ·····--·used·.0039428·seconds |
| 119 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| | 119 | o3·=·|·y_1^2-y_0y_2·y_1y_2-y_0y_3·y_2^2-y_1y_3·| |
| 120 | ··························1···················3 | 120 | ··························1···················3 |
| 121 | o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·]) | 121 | o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·]) |
| 122 | ···············53··0···3···········53··0···3</code></pre> | 122 | ···············53··0···3···········53··0···3</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| Offset 41, 21 lines modified | Offset 41, 21 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·.00418985·seconds |
| 47 | Creating·interpolation·matrix·... | 47 | Creating·interpolation·matrix·... |
| 48 | ·····--·used·.00 | 48 | ·····--·used·.00150968·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·.0039428·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·| |
| 54 | ··························1···················3 | 54 | ··························1···················3 |
| 55 | o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·]) | 55 | o3·:·Matrix·(CC··[y·..y·])··<--·(CC··[y·..y·]) |
| 56 | ···············53··0···3···········53··0···3 | 56 | ···············53··0···3···········53··0···3 |
| 57 | Here·is·how·to·do·the·same·computation·symbolically. | 57 | Here·is·how·to·do·the·same·computation·symbolically. |
| Offset 115, 19 lines modified | Offset 115, 19 lines modified | ||
| 115 | ·············1······4 | 115 | ·············1······4 |
| 116 | o2·:·Matrix·R··<--·R</code></pre> | 116 | o2·:·Matrix·R··<--·R</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) | 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·numericalHilbertFunction(F,·ideal·0_R,·4) |
| 120 | Sampling·image·points·... | 120 | Sampling·image·points·... |
| 121 | ·····--·used·.01 | 121 | ·····--·used·.0105541·seconds |
| 122 | Creating·interpolation·matrix·... | 122 | Creating·interpolation·matrix·... |
| 123 | ·····--·used·.01 | 123 | ·····--·used·.0119084·seconds |
| 124 | Performing·normalization·preconditioning·... | 124 | Performing·normalization·preconditioning·... |
| 125 | ·····--·used·.00 | 125 | ·····--·used·.00566747·seconds |
| 126 | Computing·numerical·kernel·... | 126 | Computing·numerical·kernel·... |
| 127 | ·····--·used·0·seconds | 127 | ·····--·used·0·seconds |
| 128 | o3·=·a·"numerical·interpolation·table",·indicating | 128 | o3·=·a·"numerical·interpolation·table",·indicating |
| 129 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 | 129 | ·····the·space·of·degree·4·forms·in·the·ideal·of·the·image·has·dimension·22 |
| 130 | o3·:·NumericalInterpolationTable</code></pre> | 130 | o3·:·NumericalInterpolationTable</code></pre> |
| Offset 147, 19 lines modified | Offset 147, 19 lines modified | ||
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);</code></pre> | 149 | <td>··············<pre><code·class="language-macaulay2">i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60);</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) | 152 | <td>··············<pre><code·class="language-macaulay2">i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) |
| 153 | Creating·interpolation·matrix·... | 153 | Creating·interpolation·matrix·... |
| 154 | ·····--·used·.00 | 154 | ·····--·used·.0028158·seconds |
| 155 | Performing·normalization·preconditioning·... | 155 | Performing·normalization·preconditioning·... |
| 156 | ·····--·used·.00 | 156 | ·····--·used·.00385091·seconds |
| 157 | Computing·numerical·kernel·... | 157 | Computing·numerical·kernel·... |
| 158 | ·····--·used·0·seconds | 158 | ·····--·used·.00398965·seconds |
| 159 | o7·=·a·"numerical·interpolation·table",·indicating | 159 | o7·=·a·"numerical·interpolation·table",·indicating |
| 160 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 | 160 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 |
| 161 | o7·:·NumericalInterpolationTable</code></pre> | 161 | o7·:·NumericalInterpolationTable</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ········</table> | 163 | ········</table> |
| Offset 60, 19 lines modified | Offset 60, 19 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·.01 | 65 | ·····--·used·.0105541·seconds |
| 66 | Creating·interpolation·matrix·... | 66 | Creating·interpolation·matrix·... |
| 67 | ·····--·used·.01 | 67 | ·····--·used·.0119084·seconds |
| 68 | Performing·normalization·preconditioning·... | 68 | Performing·normalization·preconditioning·... |
| 69 | ·····--·used·.00 | 69 | ·····--·used·.00566747·seconds |
| 70 | Computing·numerical·kernel·... | 70 | Computing·numerical·kernel·... |
| 71 | ·····--·used·0·seconds | 71 | ·····--·used·0·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 |
| Offset 80, 19 lines modified | Offset 80, 19 lines modified | ||
| 80 | defining·ideal·of·the·Grassmannian·$Gr(2,4)$·of·$P^1$'s·in·$P^3$,·in·the | 80 | defining·ideal·of·the·Grassmannian·$Gr(2,4)$·of·$P^1$'s·in·$P^3$,·in·the |
| 81 | ambient·space·$P^5$. | 81 | ambient·space·$P^5$. |
| 82 | i4·:·R·=·CC[x_(1,1)..x_(2,4)]; | 82 | i4·:·R·=·CC[x_(1,1)..x_(2,4)]; |
| 83 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; | 83 | i5·:·F·=·(minors(2,·genericMatrix(R,·2,·4)))_*; |
| 84 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); | 84 | i6·:·S·=·numericalImageSample(F,·ideal·0_R,·60); |
| 85 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) | 85 | i7·:·numericalHilbertFunction(F,·ideal·0_R,·S,·2,·UseSLP·=>·true) |
| 86 | Creating·interpolation·matrix·... | 86 | Creating·interpolation·matrix·... |
| 87 | ·····--·used·.00 | 87 | ·····--·used·.0028158·seconds |
| 88 | Performing·normalization·preconditioning·... | 88 | Performing·normalization·preconditioning·... |
| 89 | ·····--·used·.00 | 89 | ·····--·used·.00385091·seconds |
| 90 | Computing·numerical·kernel·... | 90 | Computing·numerical·kernel·... |
| 91 | ·····--·used·0·seconds | 91 | ·····--·used·.00398965·seconds |
| 92 | o7·=·a·"numerical·interpolation·table",·indicating | 92 | o7·=·a·"numerical·interpolation·table",·indicating |
| 93 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 | 93 | ·····the·space·of·degree·2·forms·in·the·ideal·of·the·image·has·dimension·1 |
| 94 | o7·:·NumericalInterpolationTable | 94 | o7·:·NumericalInterpolationTable |
| 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 | ····*·_\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 | 96 | ····*·_\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 130, 15 lines modified | Offset 130, 15 lines modified | ||
| 130 | --··········results·not·reliable·(one·warning·given·per·session) | 130 | --··········results·not·reliable·(one·warning·given·per·session) |
| 131 | ·············1······70 | 131 | ·············1······70 |
| 132 | o8·:·Matrix·R··<--·R</code></pre> | 132 | o8·:·Matrix·R··<--·R</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·numericalImageDim(F,·ideal·0_R) | 135 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·numericalImageDim(F,·ideal·0_R) |
| 136 | ·--·used·0.05 | 136 | ·--·used·0.054439s·(cpu);·0.0515832s·(thread);·0s·(gc) |
| 137 | o9·=·69</code></pre> | 137 | o9·=·69</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ········</table> | 139 | ········</table> |
| 140 | ······</div> | 140 | ······</div> |
| 141 | ······<div·class="waystouse"> | 141 | ······<div·class="waystouse"> |
| 142 | ········<h2>Ways·to·use·<span·class="tt">numericalImageDim</span>·:</h2> | 142 | ········<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·0.054439s·(cpu);·0.0515832s·(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 124, 15 lines modified | Offset 124, 15 lines modified | ||
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·I1·+·I2; | 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·I1·+·I2; |
| 126 | o6·:·Ideal·of·R</code></pre> | 126 | o6·:·Ideal·of·R</code></pre> |
| 127 | </td>··········</tr> | 127 | </td>··········</tr> |
| 128 | ··········<tr> | 128 | ··········<tr> |
| 129 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) | 129 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·p·=·realPoint(I,·Iterations·=>·100) |
| 130 | ·--·0. | 130 | ·--·0.599971·seconds·elapsed |
| 131 | o7·=·p | 131 | o7·=·p |
| 132 | o7·:·Point</code></pre> | 132 | o7·:·Point</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·matrix·pack(5,·p#Coordinates) | 135 | <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 | ·--·0. | 55 | ·--·0.599971·seconds·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 | ||
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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=35 | 7 | #:len=35 |
| 8 | bnVtZXJpY2FsS2VybmVsKC4uLixUb2xlcmFuY2U9Pi4uLik= | 8 | bnVtZXJpY2FsS2VybmVsKC4uLixUb2xlcmFuY2U9Pi4uLik= |
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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=32 | 7 | #:len=32 |
| 8 | UGllcmlSb290Q291bnQoLi4uLFZlcmJvc2U9Pi4uLik= | 8 | UGllcmlSb290Q291bnQoLi4uLFZlcmJvc2U9Pi4uLik= |
| 9 | #:len=334 | 9 | #:len=334 |
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| 11 | IiwgRGVzY3JpcHRpb24gPT4ge30sICJsaW5lbnVtIiA9PiAzMzMsIHN5bWJvbCBEb2N1bWVudFRh | 11 | IiwgRGVzY3JpcHRpb24gPT4ge30sICJsaW5lbnVtIiA9PiAzMzMsIHN5bWJvbCBEb2N1bWVudFRh |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 8, 15 lines modified | Offset 8, 15 lines modified | ||
| 8 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); | 8 | i4·:·b·=·x_(1,2)*x_(1,1)*e_(3,{2},1)+x_(2,2)*x_(2,1)*e_(3,{1,3},2); |
| 9 | i5·:·C·=·oiRes({b},·2) | 9 | i5·:·C·=·oiRes({b},·2) |
| 10 | o5·=·0:·(e0,·{3},·{-2}) | 10 | o5·=·0:·(e0,·{3},·{-2}) |
| 11 | ·····1:·(e1,·{5,·5},·{-3,·-4}) | 11 | ·····1:·(e1,·{5,·5},·{-3,·-4}) |
| 12 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{- | 12 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{-5,·-2,·-5,·-5,·-3,·-4,·-4,·-4,·-3}) |
| 13 | o5·:·OIResolution | 13 | o5·:·OIResolution |
| 14 | i6·:·phi·=·C.dd_1 | 14 | i6·:·phi·=·C.dd_1 |
| 15 | o6·=·Source:·(e1,·{5,·5},·{-3,·-4})·Target:·(e0,·{3},·{-2}) | 15 | o6·=·Source:·(e1,·{5,·5},·{-3,·-4})·Target:·(e0,·{3},·{-2}) |
| 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·0.119713s·(cpu);·0.0795095s·(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·0.12321s·(cpu);·0.0797484s·(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·0.273986s·(cpu);·0.197537s·(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·0.133327s·(cpu);·0.0858435s·(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 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·0.117996s·(cpu);·0.0856019s·(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 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·0.27 | 9 | ·--·used·0.271636s·(cpu);·0.213607s·(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·0.02 | 19 | ·--·used·0.02s·(cpu);·0.0210272s·(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·0.039 | 15 | ·--·used·0.0239997s·(cpu);·0.0257272s·(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·0.126297s·(cpu);·0.0792529s·(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·0.0 | 13 | ·--·used·0.0239845s·(cpu);·0.0251728s·(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·0.291422s·(cpu);·0.198084s·(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·0.136 | 13 | ·--·used·0.136098s·(cpu);·0.105139s·(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·······} |
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| 89 | <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>··············<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> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·C·=·oiRes({b},·2) | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·C·=·oiRes({b},·2) |
| 93 | o5·=·0:·(e0,·{3},·{-2}) | 93 | o5·=·0:·(e0,·{3},·{-2}) |
| 94 | ·····1:·(e1,·{5,·5},·{-3,·-4}) | 94 | ·····1:·(e1,·{5,·5},·{-3,·-4}) |
| 95 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{- | 95 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{-5,·-2,·-5,·-5,·-3,·-4,·-4,·-4,·-3}) |
| 96 | o5·:·OIResolution</code></pre> | 96 | o5·:·OIResolution</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1 | 99 | <td>··············<pre><code·class="language-macaulay2">i6·:·phi·=·C.dd_1 |
| 100 | o6·=·Source:·(e1,·{5,·5},·{-3,·-4})·Target:·(e0,·{3},·{-2}) | 100 | o6·=·Source:·(e1,·{5,·5},·{-3,·-4})·Target:·(e0,·{3},·{-2}) |
| Offset 20, 15 lines modified | Offset 20, 15 lines modified | ||
| 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},·{-3,·-4}) | 25 | ·····1:·(e1,·{5,·5},·{-3,·-4}) |
| 26 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{- | 26 | ·····2:·(e2,·{6,·6,·6,·6,·6,·6,·6,·6,·6},·{-5,·-2,·-5,·-5,·-3,·-4,·-4,·-4,·-3}) |
| 27 | o5·:·OIResolution | 27 | o5·:·OIResolution |
| 28 | i6·:·phi·=·C.dd_1 | 28 | i6·:·phi·=·C.dd_1 |
| 29 | o6·=·Source:·(e1,·{5,·5},·{-3,·-4})·Target:·(e0,·{3},·{-2}) | 29 | o6·=·Source:·(e1,·{5,·5},·{-3,·-4})·Target:·(e0,·{3},·{-2}) |
| 30 | o6·:·FreeOIModuleMap | 30 | o6·:·FreeOIModuleMap |
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| 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ··········<tr> | 61 | ··········<tr> |
| 62 | <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>··············<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> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1) | 65 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1) |
| 66 | ·--·used·0.1 | 66 | ·--·used·0.119713s·(cpu);·0.0795095s·(thread);·0s·(gc) |
| 67 | o5·=·0:·(e0,·{2},·{-2}) | 67 | o5·=·0:·(e0,·{2},·{-2}) |
| 68 | ·····1:·(e1,·{4,·4},·{-4,·-4}) | 68 | ·····1:·(e1,·{4,·4},·{-4,·-4}) |
| 69 | o5·:·OIResolution</code></pre> | 69 | o5·:·OIResolution</code></pre> |
| 70 | </td>··········</tr> | 70 | </td>··········</tr> |
| 71 | ··········<tr> | 71 | ··········<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·0.119713s·(cpu);·0.0795095s·(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 |
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| 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <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>··············<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>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 92 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 93 | ·--·used·0.1 | 93 | ·--·used·0.12321s·(cpu);·0.0797484s·(thread);·0s·(gc)</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·C_0 | 96 | <td>··············<pre><code·class="language-macaulay2">i6·:·C_0 |
| 97 | o6·=·Basis·symbol:·e0 | 97 | o6·=·Basis·symbol:·e0 |
| 98 | ·····Basis·element·widths:·{2} | 98 | ·····Basis·element·widths:·{2} |
| 99 | ·····Degree·shifts:·{-2} | 99 | ·····Degree·shifts:·{-2} |
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| 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·0.12321s·(cpu);·0.0797484s·(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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| 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 59 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 60 | </td>··········</tr> | 60 | </td>··········</tr> |
| 61 | ··········<tr> | 61 | ··········<tr> |
| 62 | <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>··············<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> |
| 63 | </td>··········</tr> | 63 | </td>··········</tr> |
| 64 | ··········<tr> | 64 | ··········<tr> |
| 65 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 65 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 66 | ·--·used·0. | 66 | ·--·used·0.273986s·(cpu);·0.197537s·(thread);·0s·(gc) |
| 67 | o5·=·0:·(e0,·{2},·{-2}) | 67 | o5·=·0:·(e0,·{2},·{-2}) |
| 68 | ·····1:·(e1,·{4},·{-4}) | 68 | ·····1:·(e1,·{4},·{-4}) |
| 69 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 69 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 70 | o5·:·OIResolution</code></pre> | 70 | o5·:·OIResolution</code></pre> |
| 71 | </td>··········</tr> | 71 | </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·0.273986s·(cpu);·0.197537s·(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* |
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| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 83 | </td>··········</tr> | 83 | </td>··········</tr> |
| 84 | ··········<tr> | 84 | ··········<tr> |
| 85 | <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>··············<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>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 89 | ·--·used·0.1 | 89 | ·--·used·0.133327s·(cpu);·0.0858435s·(thread);·0s·(gc)</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·describeFull·C | 92 | <td>··············<pre><code·class="language-macaulay2">i6·:·describeFull·C |
| 93 | o6·=·0:·Module:·Basis·symbol:·e0 | 93 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 94 | ················Basis·element·widths:·{2} | 94 | ················Basis·element·widths:·{2} |
| 95 | ················Degree·shifts:·{-2} | 95 | ················Degree·shifts:·{-2} |
| Offset 15, 15 lines modified | Offset 15, 15 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·0.133327s·(cpu);·0.0858435s·(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 |
| Offset 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <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>··············<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>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 91 | ·--·used·0.1 | 91 | ·--·used·0.117996s·(cpu);·0.0856019s·(thread);·0s·(gc)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·C | 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·describe·C |
| 95 | o6·=·0:·Module:·Basis·symbol:·e0 | 95 | o6·=·0:·Module:·Basis·symbol:·e0 |
| 96 | ················Basis·element·widths:·{2} | 96 | ················Basis·element·widths:·{2} |
| 97 | ················Degree·shifts:·{-2} | 97 | ················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·0.1 | 22 | ·--·used·0.117996s·(cpu);·0.0856019s·(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 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <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>··············<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> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) | 94 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·2,·TopNonminimal·=>·true) |
| 95 | ·--·used·0.27 | 95 | ·--·used·0.271636s·(cpu);·0.213607s·(thread);·0s·(gc) |
| 96 | o5·=·0:·(e0,·{2},·{-2}) | 96 | o5·=·0:·(e0,·{2},·{-2}) |
| 97 | ·····1:·(e1,·{4},·{-4}) | 97 | ·····1:·(e1,·{4},·{-4}) |
| 98 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 98 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 99 | o5·:·OIResolution</code></pre> | 99 | o5·:·OIResolution</code></pre> |
| 100 | </td>··········</tr> | 100 | </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·0.27 | 25 | ·--·used·0.271636s·(cpu);·0.213607s·(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 102, 15 lines modified | Offset 102, 15 lines modified | ||
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i10·:·isOIGB·{b1,·b2} | 103 | <td>··············<pre><code·class="language-macaulay2">i10·:·isOIGB·{b1,·b2} |
| 104 | o10·=·false</code></pre> | 104 | o10·=·false</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·B·=·oiGB·{b1,·b2} | 107 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·B·=·oiGB·{b1,·b2} |
| 108 | ·--·used·0.02 | 108 | ·--·used·0.02s·(cpu);·0.0210272s·(thread);·0s·(gc) |
| 109 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 109 | o11·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 110 | ········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 | ········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· |
| 111 | ······----------------------------------------------------------------------- | 111 | ······----------------------------------------------------------------------- |
| 112 | ······x···x···x···e···········-·x···x···x···e··········} | 112 | ······x···x···x···e···········-·x···x···x···e··········} |
| 113 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 113 | ·······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·0.02 | 31 | ·--·used·0.02s·(cpu);·0.0210272s·(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 97, 15 lines modified | Offset 97, 15 lines modified | ||
| 97 | <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>··············<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> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <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>··············<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> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·B·=·oiGB·{b1,·b2} | 103 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·B·=·oiGB·{b1,·b2} |
| 104 | ·--·used·0.039 | 104 | ·--·used·0.0239997s·(cpu);·0.0257272s·(thread);·0s·(gc) |
| 105 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 105 | o10·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 106 | ········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 | ········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· |
| 107 | ······----------------------------------------------------------------------- | 107 | ······----------------------------------------------------------------------- |
| 108 | ······x···x···x···e···········-·x···x···x···e··········} | 108 | ······x···x···x···e···········-·x···x···x···e··········} |
| 109 | ·······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 109 | ·······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·0.039 | 29 | ·--·used·0.0239997s·(cpu);·0.0257272s·(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 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <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>··············<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>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); | 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·oiRes({b},·1); |
| 91 | ·--·used·0.1 | 91 | ·--·used·0.126297s·(cpu);·0.0792529s·(thread);·0s·(gc)</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·net·C | 94 | <td>··············<pre><code·class="language-macaulay2">i6·:·net·C |
| 95 | o6·=·0:·(e0,·{2},·{-2}) | 95 | o6·=·0:·(e0,·{2},·{-2}) |
| 96 | ·····1:·(e1,·{4,·4},·{-4,·-4})</code></pre> | 96 | ·····1:·(e1,·{4,·4},·{-4,·-4})</code></pre> |
| 97 | </td>··········</tr> | 97 | </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·0.126297s·(cpu);·0.0792529s·(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 |
| Offset 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | <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>··············<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> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <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>··············<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> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·oiGB·{b1,·b2} | 111 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·oiGB·{b1,·b2} |
| 112 | ·--·used·0.0 | 112 | ·--·used·0.0239845s·(cpu);·0.0251728s·(thread);·0s·(gc) |
| 113 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, | 113 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e··········, |
| 114 | ·······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 | ·······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· |
| 115 | ·····------------------------------------------------------------------------ | 115 | ·····------------------------------------------------------------------------ |
| 116 | ·····x···x···x···e···········-·x···x···x···e··········} | 116 | ·····x···x···x···e···········-·x···x···x···e··········} |
| 117 | ······2,3·2,2·1,1·3,{2,·3},3····2,3·2,1·1,2·3,{1,·3},3 | 117 | ······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·0.0 | 36 | ·--·used·0.0239845s·(cpu);·0.0251728s·(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 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> | 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·installGeneratorsInWidth(F,·2);</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <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>··············<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> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) | 112 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·oiRes({b},·2,·TopNonminimal·=>·true) |
| 113 | ·--·used·0. | 113 | ·--·used·0.291422s·(cpu);·0.198084s·(thread);·0s·(gc) |
| 114 | o5·=·0:·(e0,·{2},·{-2}) | 114 | o5·=·0:·(e0,·{2},·{-2}) |
| 115 | ·····1:·(e1,·{4},·{-4}) | 115 | ·····1:·(e1,·{4},·{-4}) |
| 116 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) | 116 | ·····2:·(e2,·{4,·5,·5,·5,·5,·5},·{-4,·-5,·-5,·-5,·-5,·-5}) |
| 117 | o5·:·OIResolution</code></pre> | 117 | o5·:·OIResolution</code></pre> |
| 118 | </td>··········</tr> | 118 | </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·0.291422s·(cpu);·0.198084s·(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 94, 15 lines modified | Offset 94, 15 lines modified | ||
| 94 | <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>··············<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> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <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>··············<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> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) | 100 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·B·=·oiGB({b1,·b2},·Strategy·=>·FastNonminimal) |
| 101 | ·--·used·0.136 | 101 | ·--·used·0.136098s·(cpu);·0.105139s·(thread);·0s·(gc) |
| 102 | ······································································· | 102 | ······································································· |
| 103 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, | 103 | o9·=·{x···e········+·x···e·······,·x···x···e········+·x···x···e·······, |
| 104 | ·······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 | ·······2,1·1,{1},2····1,1·1,{1},2···1,2·1,1·2,{2},1····2,2·1,2·2,{2},2· |
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ······2··················2 | 106 | ······2··················2 |
| 107 | ·····x···x···e········-·x···x···e·······} | 107 | ·····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·0.136 | 28 | ·--·used·0.136098s·(cpu);·0.105139s·(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 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gNTIzNywgSW5wdXRzID0+IHtTUEFOe1RUeyJG | 11 | Q29uZXMgb2YgYSBGYW4iLCAibGluZW51bSIgPT4gNTIzNywgSW5wdXRzID0+IHtTUEFOe1RUeyJG |
| Offset 39, 46 lines modified | Offset 39, 46 lines modified | ||
| 39 | o10·:·Fan | 39 | o10·:·Fan |
| 40 | i11·:·isComplete·F | 40 | i11·:·isComplete·F |
| 41 | o11·=·true | 41 | o11·=·true |
| 42 | i12·:·isPolytopal·F | 42 | i12·:·isPolytopal·F |
| 43 | {({ambient·dimension·=>·3···········},·{2,·3,· | 43 | {({ambient·dimension·=>·3···········},·{2,·3,·4}),·({ambient·dimension·=>·3···········},·{1,·3,·4}),·({ambient·dimension·=>·3···········},·{2,·4,·5}),·({ambient·dimension·=>·3···········},·{2,·3,·5}),·({ambient·dimension·=>·3···········},·{1,·4,·5}),·({ambient·dimension·=>·3···········},·{1,·3,·5})} |
| 44 | ···dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0 | 44 | ···dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0 |
| 45 | ···dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 | 45 | ···dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 |
| 46 | ···number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1 | 46 | ···number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1 |
| 47 | ···number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1 | 47 | ···number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1 |
| 48 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 48 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 49 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 49 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 50 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 50 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 51 | ·····number·of·facets·=>·4················number·of·facets·=>· | 51 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 52 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 52 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 53 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 53 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 54 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 54 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 55 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 55 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 56 | ·····number·of·facets·=>·4················number·of·facets·=>· | 56 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 57 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 57 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 58 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 58 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 59 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 59 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 60 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 60 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 61 | ·····number·of·facets·=>·4················number·of·facets·=>· | 61 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 62 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 62 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 63 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 63 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 64 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 64 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 65 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 65 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 66 | ·····number·of·facets·=>·4················number·of·facets·=>· | 66 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 67 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 67 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 68 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 68 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 69 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 69 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 70 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 70 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 71 | ·····number·of·facets·=>·4················number·of·facets·=>· | 71 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 72 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 72 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 73 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 73 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 74 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 74 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 75 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 75 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 76 | ·····number·of·facets·=>·4················number·of·facets·=>· | 76 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 77 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 77 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 78 | o12·=·true | 78 | o12·=·true |
| 79 | i13·:· | 79 | i13·:· |
| Offset 18, 13 lines modified | Offset 18, 13 lines modified | ||
| 18 | ······number·of·rays·=>·3 | 18 | ······number·of·rays·=>·3 |
| 19 | ······top·dimension·of·the·cones·=>·2 | 19 | ······top·dimension·of·the·cones·=>·2 |
| 20 | o2·:·Fan | 20 | o2·:·Fan |
| 21 | i3·:·apply(maxCones·F,rays) | 21 | i3·:·apply(maxCones·F,rays) |
| 22 | o3·=·{|·1·-1·|,·|·1·0·|,·|·-1·0·|} | ||
| 23 | 22 | o3·=·{|·1·0·|,·|·-1·0·|,·|·1·-1·|} | |
| 23 | ······|·0·1·|··|·-1·1·|··|·0·-1·| | ||
| 24 | o3·:·List | 24 | o3·:·List |
| 25 | i4·:· | 25 | i4·:· |
| Offset 105, 49 lines modified | Offset 105, 49 lines modified | ||
| 105 | o11·=·true</code></pre> | 105 | o11·=·true</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ········</table> | 107 | ········</table> |
| 108 | ········<p></p> | 108 | ········<p></p> |
| 109 | For·a·complete·fan·we·can·check·if·it·is·projective:········<table·class="examples"> | 109 | For·a·complete·fan·we·can·check·if·it·is·projective:········<table·class="examples"> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i12·:·isPolytopal·F | 111 | <td>··············<pre><code·class="language-macaulay2">i12·:·isPolytopal·F |
| 112 | {({ambient·dimension·=>·3···········},·{2,·3,· | 112 | {({ambient·dimension·=>·3···········},·{2,·3,·4}),·({ambient·dimension·=>·3···········},·{1,·3,·4}),·({ambient·dimension·=>·3···········},·{2,·4,·5}),·({ambient·dimension·=>·3···········},·{2,·3,·5}),·({ambient·dimension·=>·3···········},·{1,·4,·5}),·({ambient·dimension·=>·3···········},·{1,·3,·5})} |
| 113 | ···dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0 | 113 | ···dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0·················dimension·of·lineality·space·=>·0 |
| 114 | ···dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 | 114 | ···dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 |
| 115 | ···number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1 | 115 | ···number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1·····························number·of·facets·=>·1 |
| 116 | ···number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1 | 116 | ···number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1·······························number·of·rays·=>·1 |
| 117 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 117 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 118 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 118 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 119 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 119 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 120 | ·····number·of·facets·=>·4················number·of·facets·=>· | 120 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 121 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 121 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 122 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 122 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 123 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 123 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 124 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 124 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 125 | ·····number·of·facets·=>·4················number·of·facets·=>· | 125 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 126 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 126 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 127 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 127 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 128 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 128 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 129 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 129 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 130 | ·····number·of·facets·=>·4················number·of·facets·=>· | 130 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 131 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 131 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 132 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 132 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 133 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 133 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 134 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 134 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 135 | ·····number·of·facets·=>·4················number·of·facets·=>· | 135 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 136 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 136 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 137 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 137 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 138 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 138 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 139 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 139 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 140 | ·····number·of·facets·=>·4················number·of·facets·=>· | 140 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 141 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 141 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 142 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 142 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 143 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 143 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 144 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 144 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 145 | ·····number·of·facets·=>·4················number·of·facets·=>· | 145 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 146 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 146 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 147 | o12·=·true</code></pre> | 147 | o12·=·true</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ········</table> | 149 | ········</table> |
| 150 | ········<p></p> | 150 | ········<p></p> |
| 151 | If·the·fan·is·projective,·the·function·returns·a·polyhedron·such·that·the·fan·is·its··normal·fan,·otherwise·it·returns·the·empty·polyhedron.·This·means·our·fan·is·projective.······</div> | 151 | If·the·fan·is·projective,·the·function·returns·a·polyhedron·such·that·the·fan·is·its··normal·fan,·otherwise·it·returns·the·empty·polyhedron.·This·means·our·fan·is·projective.······</div> |
| 152 | ····</div> | 152 | ····</div> |
| Offset 37, 18 lines modified | Offset 37, 18 lines modified | ||
| 37 | o10·:·Fan | 37 | o10·:·Fan |
| 38 | i11·:·isComplete·F | 38 | i11·:·isComplete·F |
| 39 | o11·=·true | 39 | o11·=·true |
| 40 | For·a·complete·fan·we·can·check·if·it·is·projective: | 40 | For·a·complete·fan·we·can·check·if·it·is·projective: |
| 41 | i12·:·isPolytopal·F | 41 | i12·:·isPolytopal·F |
| 42 | {({ambient·dimension·=>·3···········},·{2,·3,· | 42 | {({ambient·dimension·=>·3···········},·{2,·3,·4}),·({ambient·dimension·=>·3 |
| 43 | },·{ | 43 | },·{1,·3,·4}),·({ambient·dimension·=>·3···········},·{2,·4,·5}),·({ambient |
| 44 | dimension·=>·3···········},·{ | 44 | dimension·=>·3···········},·{2,·3,·5}),·({ambient·dimension·=>·3···········}, |
| 45 | {1,· | 45 | {1,·4,·5}),·({ambient·dimension·=>·3···········},·{1,·3,·5})} |
| 46 | ···dimension·of·lineality·space·=>·0·················dimension·of·lineality | 46 | ···dimension·of·lineality·space·=>·0·················dimension·of·lineality |
| 47 | space·=>·0·················dimension·of·lineality·space·=>·0 | 47 | space·=>·0·················dimension·of·lineality·space·=>·0 |
| 48 | dimension·of·lineality·space·=>·0·················dimension·of·lineality·space | 48 | dimension·of·lineality·space·=>·0·················dimension·of·lineality·space |
| 49 | =>·0·················dimension·of·lineality·space·=>·0 | 49 | =>·0·················dimension·of·lineality·space·=>·0 |
| 50 | ···dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 | 50 | ···dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 |
| 51 | dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 | 51 | dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 |
| 52 | dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 | 52 | dimension·of·the·cone·=>·1························dimension·of·the·cone·=>·1 |
| Offset 57, 39 lines modified | Offset 57, 39 lines modified | ||
| 57 | number·of·facets·=>·1·····························number·of·facets·=>·1 | 57 | number·of·facets·=>·1·····························number·of·facets·=>·1 |
| 58 | ···number·of·rays·=>·1·······························number·of·rays·=>·1 | 58 | ···number·of·rays·=>·1·······························number·of·rays·=>·1 |
| 59 | number·of·rays·=>·1·······························number·of·rays·=>·1 | 59 | number·of·rays·=>·1·······························number·of·rays·=>·1 |
| 60 | number·of·rays·=>·1·······························number·of·rays·=>·1 | 60 | number·of·rays·=>·1·······························number·of·rays·=>·1 |
| 61 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 61 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 62 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 62 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 63 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 63 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 64 | ·····number·of·facets·=>·4················number·of·facets·=>· | 64 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 65 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 65 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 66 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 66 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 67 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 67 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 68 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 68 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 69 | ·····number·of·facets·=>·4················number·of·facets·=>· | 69 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 70 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 70 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 71 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 71 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 72 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 72 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 73 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 73 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 74 | ·····number·of·facets·=>·4················number·of·facets·=>· | 74 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 75 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 75 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 76 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 76 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 77 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 77 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 78 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 78 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 79 | ·····number·of·facets·=>·4················number·of·facets·=>· | 79 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 80 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 80 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 81 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 81 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 82 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 82 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 83 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 83 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 84 | ·····number·of·facets·=>·4················number·of·facets·=>· | 84 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 85 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 85 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 86 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} | 86 | v:·{{ambient·dimension·=>·3···········},·{ambient·dimension·=>·3···········}} |
| 87 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 | 87 | ·····dimension·of·lineality·space·=>·0····dimension·of·lineality·space·=>·0 |
| 88 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 | 88 | ·····dimension·of·the·cone·=>·3···········dimension·of·the·cone·=>·3 |
| 89 | ·····number·of·facets·=>·4················number·of·facets·=>· | 89 | ·····number·of·facets·=>·4················number·of·facets·=>·4 |
| 90 | ·····number·of·rays·=>·4··················number·of·rays·=>· | 90 | ·····number·of·rays·=>·4··················number·of·rays·=>·4 |
| 91 | o12·=·true | 91 | o12·=·true |
| 92 | If·the·fan·is·projective,·the·function·returns·a·polyhedron·such·that·the·fan | 92 | If·the·fan·is·projective,·the·function·returns·a·polyhedron·such·that·the·fan |
| 93 | is·its·normal·fan,·otherwise·it·returns·the·empty·polyhedron.·This·means·our | 93 | is·its·normal·fan,·otherwise·it·returns·the·empty·polyhedron.·This·means·our |
| 94 | fan·is·projective. | 94 | fan·is·projective. |
| Offset 91, 16 lines modified | Offset 91, 16 lines modified | ||
| 91 | ······top·dimension·of·the·cones·=>·2 | 91 | ······top·dimension·of·the·cones·=>·2 |
| 92 | o2·:·Fan</code></pre> | 92 | o2·:·Fan</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·apply(maxCones·F,rays) | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·apply(maxCones·F,rays) |
| 96 | o3·=·{|·1·-1·|,·|·1·0·|,·|·-1·0·|} | ||
| 97 | 96 | o3·=·{|·1·0·|,·|·-1·0·|,·|·1·-1·|} | |
| 97 | ······|·0·1·|··|·-1·1·|··|·0·-1·| | ||
| 98 | o3·:·List</code></pre> | 98 | o3·:·List</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ········</table> | 100 | ········</table> |
| 101 | ······</div> | 101 | ······</div> |
| 102 | ······<div·class="waystouse"> | 102 | ······<div·class="waystouse"> |
| 103 | ········<h2>Ways·to·use·<span·class="tt">normalFan</span>·:</h2> | 103 | ········<h2>Ways·to·use·<span·class="tt">normalFan</span>·:</h2> |
| Offset 31, 15 lines modified | Offset 31, 15 lines modified | ||
| 31 | ······number·of·generating·cones·=>·3 | 31 | ······number·of·generating·cones·=>·3 |
| 32 | ······number·of·rays·=>·3 | 32 | ······number·of·rays·=>·3 |
| 33 | ······top·dimension·of·the·cones·=>·2 | 33 | ······top·dimension·of·the·cones·=>·2 |
| 34 | o2·:·Fan | 34 | o2·:·Fan |
| 35 | i3·:·apply(maxCones·F,rays) | 35 | i3·:·apply(maxCones·F,rays) |
| 36 | o3·=·{|·1·-1·|,·|·1·0·|,·|·-1·0·|} | ||
| 37 | 36 | o3·=·{|·1·0·|,·|·-1·0·|,·|·1·-1·|} | |
| 37 | ······|·0·1·|··|·-1·1·|··|·0·-1·| | ||
| 38 | o3·:·List | 38 | o3·:·List |
| 39 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·n\x8no\x8or\x8rm\x8ma\x8al\x8lF\x8Fa\x8an\x8n·:\x8:·*\x8**\x8**\x8**\x8**\x8* | 39 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·n\x8no\x8or\x8rm\x8ma\x8al\x8lF\x8Fa\x8an\x8n·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 40 | ····*·normalFan(Polyhedron) | 40 | ····*·normalFan(Polyhedron) |
| 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* |
| 42 | The·object·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8F_\x8a_\x8n·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n. | 42 | The·object·_\x8n_\x8o_\x8r_\x8m_\x8a_\x8l_\x8F_\x8a_\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 | ||
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgwNywgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgwNywgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmFuZG9tRXh0ZW5zaW9uLE1hdHJpeCxNYXRyaXgp | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsocmFuZG9tRXh0ZW5zaW9uLE1hdHJpeCxNYXRyaXgp |
| Offset 41, 15 lines modified | Offset 41, 15 lines modified | ||
| 41 | i10·:·M=cliffordModule(Mu1,Mu2,R) | 41 | i10·:·M=cliffordModule(Mu1,Mu2,R) |
| 42 | o10·=·CliffordModule{...6...} | 42 | o10·=·CliffordModule{...6...} |
| 43 | o10·:·CliffordModule | 43 | o10·:·CliffordModule |
| 44 | i11·:·elapsedTime·Ulr·=·searchUlrich(M,S); | 44 | i11·:·elapsedTime·Ulr·=·searchUlrich(M,S); |
| 45 | ·--· | 45 | ·--·0.707077·seconds·elapsed |
| 46 | i12·:·betti·res·Ulr | 46 | i12·:·betti·res·Ulr |
| 47 | ·············0··1·2 | 47 | ·············0··1·2 |
| 48 | o12·=·total:·8·16·8 | 48 | o12·=·total:·8·16·8 |
| 49 | ··········0:·8·16·8 | 49 | ··········0:·8·16·8 |
| Offset 129, 15 lines modified | Offset 129, 15 lines modified | ||
| 129 | o10·=·CliffordModule{...6...} | 129 | o10·=·CliffordModule{...6...} |
| 130 | o10·:·CliffordModule</code></pre> | 130 | o10·:·CliffordModule</code></pre> |
| 131 | </td>··········</tr> | 131 | </td>··········</tr> |
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·Ulr·=·searchUlrich(M,S); | 133 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·Ulr·=·searchUlrich(M,S); |
| 134 | ·--· | 134 | ·--·0.707077·seconds·elapsed</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i12·:·betti·res·Ulr | 137 | <td>··············<pre><code·class="language-macaulay2">i12·:·betti·res·Ulr |
| 138 | ·············0··1·2 | 138 | ·············0··1·2 |
| 139 | o12·=·total:·8·16·8 | 139 | o12·=·total:·8·16·8 |
| 140 | ··········0:·8·16·8 | 140 | ··········0:·8·16·8 |
| Offset 57, 15 lines modified | Offset 57, 15 lines modified | ||
| 57 | o9·:·Matrix·S··<--·S | 57 | o9·:·Matrix·S··<--·S |
| 58 | i10·:·M=cliffordModule(Mu1,Mu2,R) | 58 | i10·:·M=cliffordModule(Mu1,Mu2,R) |
| 59 | o10·=·CliffordModule{...6...} | 59 | o10·=·CliffordModule{...6...} |
| 60 | o10·:·CliffordModule | 60 | o10·:·CliffordModule |
| 61 | i11·:·elapsedTime·Ulr·=·searchUlrich(M,S); | 61 | i11·:·elapsedTime·Ulr·=·searchUlrich(M,S); |
| 62 | ·--· | 62 | ·--·0.707077·seconds·elapsed |
| 63 | i12·:·betti·res·Ulr | 63 | i12·:·betti·res·Ulr |
| 64 | ·············0··1·2 | 64 | ·············0··1·2 |
| 65 | o12·=·total:·8·16·8 | 65 | o12·=·total:·8·16·8 |
| 66 | ··········0:·8·16·8 | 66 | ··········0:·8·16·8 |
| 67 | o12·:·BettiTally | 67 | o12·:·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cnlzZXI= | 8 | cnlzZXI= |
| 9 | #:len=2107 | 9 | #:len=2107 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBwZXJtYW5lbnQgdXNpbmcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSBwZXJtYW5lbnQgdXNpbmcg |
| 11 | UnlzZXIncyBmb3JtdWxhIiwgImxpbmVudW0iID0+IDQ0NCwgSW5wdXRzID0+IHtTUEFOe1RUeyJN | 11 | UnlzZXIncyBmb3JtdWxhIiwgImxpbmVudW0iID0+IDQ0NCwgSW5wdXRzID0+IHtTUEFOe1RUeyJN |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cGh5bG9Ub3JpY1F1YWRz | 8 | cGh5bG9Ub3JpY1F1YWRz |
| 9 | #:len=2848 | 9 | #:len=2848 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSB0aGUgcXVhZHJhdGljIGlu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZSB0aGUgcXVhZHJhdGljIGlu |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·3. | 70 | ·--·3.62979·seconds·elapsed |
| 71 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); | 71 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); |
| 72 | ·--·3. | 72 | ·--·3.32291·seconds·elapsed |
| 73 | i12·:·G==H | 73 | i12·:·G==H |
| 74 | o12·=·true | 74 | o12·=·true |
| 75 | i13·:· | 75 | i13·:· |
| Offset 163, 19 lines modified | Offset 163, 19 lines modified | ||
| 163 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} | 163 | o9·=·{1,·2,·3,·1,·2,·3,·1,·2,·3,·1,·2,·3} |
| 164 | o9·:·List</code></pre> | 164 | o9·:·List</code></pre> |
| 165 | </td>··········</tr> | 165 | </td>··········</tr> |
| 166 | ··········<tr> | 166 | ··········<tr> |
| 167 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); | 167 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·(Q,inG,G)·=·affineFatPoints(M,mults,R); |
| 168 | ·--·3. | 168 | ·--·3.62979·seconds·elapsed</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); | 171 | <td>··············<pre><code·class="language-macaulay2">i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); |
| 172 | ·--·3. | 172 | ·--·3.32291·seconds·elapsed</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i12·:·G==H | 175 | <td>··············<pre><code·class="language-macaulay2">i12·:·G==H |
| 176 | o12·=·true</code></pre> | 176 | o12·=·true</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ········</table> | 178 | ········</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 | ·--·3. | 87 | ·--·3.62979·seconds·elapsed |
| 88 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); | 88 | i11·:·elapsedTime·H·=·affineFatPointsByIntersection(M,mults,R); |
| 89 | ·--·3. | 89 | ·--·3.32291·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDk0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDk0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwb2x5b0lkZWFsLExpc3QpLCJwb2x5b0lkZWFsKExp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwb2x5b0lkZWFsLExpc3QpLCJwb2x5b0lkZWFsKExp |
| Offset 18, 31 lines modified | Offset 18, 31 lines modified | ||
| 18 | ··················3,3···3,2···3,1···2,3···2,2···2,1···1,2···1,1 | 18 | ··················3,3···3,2···3,1···2,3···2,2···2,1···1,2···1,1 |
| 19 | i3·:·Q={{{1,·1},·{2,·2}},·{{2,·1},·{3,·2}},·{{3,·1},·{4,·2}},·{{3,·2},·{4,·3}},·{{3,·3},·{4,·4}},·{{2,·3},·{3,·4}},·{{1,·3},·{2,·4}},·{{1,·2},·{2,·3}}}; | 19 | i3·:·Q={{{1,·1},·{2,·2}},·{{2,·1},·{3,·2}},·{{3,·1},·{4,·2}},·{{3,·2},·{4,·3}},·{{3,·3},·{4,·4}},·{{2,·3},·{3,·4}},·{{1,·3},·{2,·4}},·{{1,·2},·{2,·3}}}; |
| 20 | i4·:·I·=·polyoIdeal·Q | 20 | i4·:·I·=·polyoIdeal·Q |
| 21 | o4·=·ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 21 | o4·=·ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 22 | ············· | 22 | ·············4,4·2,3····4,3·2,4···2,2·1,1····2,1·1,2···4,2·3,1····4,1·3,2· |
| 23 | ·····------------------------------------------------------------------------ | 23 | ·····------------------------------------------------------------------------ |
| 24 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· | 24 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· |
| 25 | ······ | 25 | ······2,3·1,1····2,1·1,3···4,3·3,1····4,1·3,3···4,4·1,3····4,3·1,4···3,4·2,3 |
| 26 | ·····------------------------------------------------------------------------ | 26 | ·····------------------------------------------------------------------------ |
| 27 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- | 27 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- |
| 28 | ········ | 28 | ········3,3·2,4···4,2·2,1····4,1·2,2···2,3·1,2····2,2·1,3···2,4·1,1·· |
| 29 | ·····------------------------------------------------------------------------ | 29 | ·····------------------------------------------------------------------------ |
| 30 | ·····x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 30 | ·····x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 31 | ······2, | 31 | ······2,1·1,4···4,4·3,1····4,1·3,4···4,3·3,2····4,2·3,3···3,4·1,3····3,3·1,4· |
| 32 | ·····------------------------------------------------------------------------ | 32 | ·····------------------------------------------------------------------------ |
| 33 | ·····x···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···x··· |
| 34 | ······ | 34 | ······3,2·2,1····3,1·2,2···4,2·1,1····4,1·1,2···2,4·1,2····2,2·1,4···4,4·3,2 |
| 35 | ·····------------------------------------------------------------------------ | 35 | ·····------------------------------------------------------------------------ |
| 36 | ·····-·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····- |
| 37 | ········4, | 37 | ········4,2·3,4···2,4·1,3····2,3·1,4···4,4·3,3····4,3·3,4···3,2·1,1·· |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····x···x···) | 39 | ·····x···x···) |
| 40 | ······ | 40 | ······3,1·1,2 |
| 41 | o4·:·Ideal·of·QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···] | 41 | o4·:·Ideal·of·QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···] |
| 42 | ··················4,4···4,3···4,2···4,1···3,4···3,3···3,2···3,1···2,4···2,3···2,2···2,1···1,4···1,3···1,2···1,1 | 42 | ··················4,4···4,3···4,2···4,1···3,4···3,3···3,2···3,1···2,4···2,3···2,2···2,1···1,4···1,3···1,2···1,1 |
| 43 | i5·:· | 43 | i5·:· |
| Offset 103, 33 lines modified | Offset 103, 33 lines modified | ||
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·Q={{{1,·1},·{2,·2}},·{{2,·1},·{3,·2}},·{{3,·1},·{4,·2}},·{{3,·2},·{4,·3}},·{{3,·3},·{4,·4}},·{{2,·3},·{3,·4}},·{{1,·3},·{2,·4}},·{{1,·2},·{2,·3}}};</code></pre> | 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·Q={{{1,·1},·{2,·2}},·{{2,·1},·{3,·2}},·{{3,·1},·{4,·2}},·{{3,·2},·{4,·3}},·{{3,·3},·{4,·4}},·{{2,·3},·{3,·4}},·{{1,·3},·{2,·4}},·{{1,·2},·{2,·3}}};</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·I·=·polyoIdeal·Q | 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·I·=·polyoIdeal·Q |
| 108 | o4·=·ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 108 | o4·=·ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 109 | ············· | 109 | ·············4,4·2,3····4,3·2,4···2,2·1,1····2,1·1,2···4,2·3,1····4,1·3,2· |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ·····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··· |
| 112 | ······ | 112 | ······2,3·1,1····2,1·1,3···4,3·3,1····4,1·3,3···4,4·1,3····4,3·1,4···3,4·2,3 |
| 113 | ·····------------------------------------------------------------------------ | 113 | ·····------------------------------------------------------------------------ |
| 114 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- | 114 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- |
| 115 | ········ | 115 | ········3,3·2,4···4,2·2,1····4,1·2,2···2,3·1,2····2,2·1,3···2,4·1,1·· |
| 116 | ·····------------------------------------------------------------------------ | 116 | ·····------------------------------------------------------------------------ |
| 117 | ·····x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 117 | ·····x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 118 | ······2, | 118 | ······2,1·1,4···4,4·3,1····4,1·3,4···4,3·3,2····4,2·3,3···3,4·1,3····3,3·1,4· |
| 119 | ·····------------------------------------------------------------------------ | 119 | ·····------------------------------------------------------------------------ |
| 120 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· | 120 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· |
| 121 | ······ | 121 | ······3,2·2,1····3,1·2,2···4,2·1,1····4,1·1,2···2,4·1,2····2,2·1,4···4,4·3,2 |
| 122 | ·····------------------------------------------------------------------------ | 122 | ·····------------------------------------------------------------------------ |
| 123 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- | 123 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- |
| 124 | ········4, | 124 | ········4,2·3,4···2,4·1,3····2,3·1,4···4,4·3,3····4,3·3,4···3,2·1,1·· |
| 125 | ·····------------------------------------------------------------------------ | 125 | ·····------------------------------------------------------------------------ |
| 126 | ·····x···x···) | 126 | ·····x···x···) |
| 127 | ······ | 127 | ······3,1·1,2 |
| 128 | o4·:·Ideal·of·QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···] | 128 | o4·:·Ideal·of·QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···] |
| 129 | ··················4,4···4,3···4,2···4,1···3,4···3,3···3,2···3,1···2,4···2,3···2,2···2,1···1,4···1,3···1,2···1,1</code></pre> | 129 | ··················4,4···4,3···4,2···4,1···3,4···3,3···3,2···3,1···2,4···2,3···2,2···2,1···1,4···1,3···1,2···1,1</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ········</table> | 131 | ········</table> |
| 132 | ······</div> | 132 | ······</div> |
| 133 | ······<div·class="waystouse"> | 133 | ······<div·class="waystouse"> |
| Offset 46, 33 lines modified | Offset 46, 33 lines modified | ||
| 46 | i3·:·Q={{{1,·1},·{2,·2}},·{{2,·1},·{3,·2}},·{{3,·1},·{4,·2}},·{{3,·2},·{4,·3}}, | 46 | i3·:·Q={{{1,·1},·{2,·2}},·{{2,·1},·{3,·2}},·{{3,·1},·{4,·2}},·{{3,·2},·{4,·3}}, |
| 47 | {{3,·3},·{4,·4}},·{{2,·3},·{3,·4}},·{{1,·3},·{2,·4}},·{{1,·2},·{2,·3}}}; | 47 | {{3,·3},·{4,·4}},·{{2,·3},·{3,·4}},·{{1,·3},·{2,·4}},·{{1,·2},·{2,·3}}}; |
| 48 | i4·:·I·=·polyoIdeal·Q | 48 | i4·:·I·=·polyoIdeal·Q |
| 49 | o4·=·ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 49 | o4·=·ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 50 | ············· | 50 | ·············4,4·2,3····4,3·2,4···2,2·1,1····2,1·1,2···4,2·3,1····4,1·3,2 |
| 51 | ·····------------------------------------------------------------------------ | 51 | ·····------------------------------------------------------------------------ |
| 52 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x | 52 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x |
| 53 | ······ | 53 | ······2,3·1,1····2,1·1,3···4,3·3,1····4,1·3,3···4,4·1,3····4,3·1,4···3,4·2,3 |
| 54 | ·····------------------------------------------------------------------------ | 54 | ·····------------------------------------------------------------------------ |
| 55 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- | 55 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- |
| 56 | ········ | 56 | ········3,3·2,4···4,2·2,1····4,1·2,2···2,3·1,2····2,2·1,3···2,4·1,1 |
| 57 | ·····------------------------------------------------------------------------ | 57 | ·····------------------------------------------------------------------------ |
| 58 | ·····x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 58 | ·····x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 59 | ······2, | 59 | ······2,1·1,4···4,4·3,1····4,1·3,4···4,3·3,2····4,2·3,3···3,4·1,3····3,3·1,4 |
| 60 | ·····------------------------------------------------------------------------ | 60 | ·····------------------------------------------------------------------------ |
| 61 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x | 61 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x |
| 62 | ······ | 62 | ······3,2·2,1····3,1·2,2···4,2·1,1····4,1·1,2···2,4·1,2····2,2·1,4···4,4·3,2 |
| 63 | ·····------------------------------------------------------------------------ | 63 | ·····------------------------------------------------------------------------ |
| 64 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- | 64 | ·····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x····- |
| 65 | ········4, | 65 | ········4,2·3,4···2,4·1,3····2,3·1,4···4,4·3,3····4,3·3,4···3,2·1,1 |
| 66 | ·····------------------------------------------------------------------------ | 66 | ·····------------------------------------------------------------------------ |
| 67 | ·····x···x···) | 67 | ·····x···x···) |
| 68 | ······ | 68 | ······3,1·1,2 |
| 69 | o4·:·Ideal·of·QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x | 69 | o4·:·Ideal·of·QQ[x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x···,·x |
| 70 | ,·x···,·x···,·x···,·x···,·x···] | 70 | ,·x···,·x···,·x···,·x···,·x···] |
| 71 | ··················4,4···4,3···4,2···4,1···3,4···3,3···3,2···3,1···2,4···2,3 | 71 | ··················4,4···4,3···4,2···4,1···3,4···3,3···3,2···3,1···2,4···2,3 |
| 72 | 2,2···2,1···1,4···1,3···1,2···1,1 | 72 | 2,2···2,1···1,4···1,3···1,2···1,1 |
| 73 | *\x8**\x8**\x8**\x8**\x8*·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·p\x8po\x8ol\x8ly\x8yo\x8oI\x8Id\x8de\x8ea\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·p\x8po\x8ol\x8ly\x8yo\x8oI\x8Id\x8de\x8ea\x8al\x8l·:\x8:·*\x8**\x8**\x8**\x8**\x8* |
| 74 | ····*·polyoIdeal(List) | 74 | ····*·polyoIdeal(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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+IDQ4NzcsIElucHV0cyA9PiB7U1BBTntU | 11 | aWNoYWlucyBvZiBhIHBvc2V0IiwgImxpbmVudW0iID0+IDQ4NzcsIElucHV0cyA9PiB7U1BBTntU |
| 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·0.00 | 35 | ·--·used·0.00353307s·(cpu);·7.401e-06s·(thread);·0s·(gc) |
| 36 | o7·=·true | 36 | o7·=·true |
| 37 | i8·:·time·isDistributive·P | 37 | i8·:·time·isDistributive·P |
| 38 | ·--·used· | 38 | ·--·used·10.2643s·(cpu);·4.41861s·(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·0.000310317s·(cpu);·5.158e-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·0.5 | 11 | ·--·used·0.531352s·(cpu);·0.25418s·(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·0.000 | 15 | ·--·used·0.000349065s·(cpu);·7.141e-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 88, 35 lines modified | Offset 88, 35 lines modified | ||
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i6·:·C·==·P | 89 | <td>··············<pre><code·class="language-macaulay2">i6·:·C·==·P |
| 90 | o6·=·true</code></pre> | 90 | o6·=·true</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDistributive·C | 93 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·isDistributive·C |
| 94 | ·--·used·0.00 | 94 | ·--·used·0.00353307s·(cpu);·7.401e-06s·(thread);·0s·(gc) |
| 95 | o7·=·true</code></pre> | 95 | o7·=·true</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isDistributive·P | 98 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·isDistributive·P |
| 99 | ·--·used· | 99 | ·--·used·10.2643s·(cpu);·4.41861s·(thread);·0s·(gc) |
| 100 | o8·=·true</code></pre> | 100 | o8·=·true</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ········</table> | 102 | ········</table> |
| 103 | ········<div> | 103 | ········<div> |
| 104 | ··········<p>We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive·lattice.··Other·information·is·copied·when·possible.</p> | 104 | ··········<p>We·also·know·that·the·dual·of·a·distributive·lattice·is·again·a·distributive·lattice.··Other·information·is·copied·when·possible.</p> |
| 105 | ········</div> | 105 | ········</div> |
| 106 | ········<table·class="examples"> | 106 | ········<table·class="examples"> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i9·:·C'·=·dual·C;</code></pre> | 108 | <td>··············<pre><code·class="language-macaulay2">i9·:·C'·=·dual·C;</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isDistributive·C' | 111 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·isDistributive·C' |
| 112 | ·--·used·0.000 | 112 | ·--·used·0.000310317s·(cpu);·5.158e-06s·(thread);·0s·(gc) |
| 113 | o10·=·true</code></pre> | 113 | o10·=·true</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i11·:·peek·C'.cache | 116 | <td>··············<pre><code·class="language-macaulay2">i11·:·peek·C'.cache |
| 117 | o11·=·CacheTable{connectedComponents·=>·{{0,·1,·2,·3,·4,·5,·6,·7,·8,·9}}······································} | 117 | 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·0.00 | 46 | ·--·used·0.00353307s·(cpu);·7.401e-06s·(thread);·0s·(gc) |
| 47 | o7·=·true | 47 | o7·=·true |
| 48 | i8·:·time·isDistributive·P | 48 | i8·:·time·isDistributive·P |
| 49 | ·--·used· | 49 | ·--·used·10.2643s·(cpu);·4.41861s·(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·0.000310317s·(cpu);·5.158e-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 96, 23 lines modified | Offset 96, 23 lines modified | ||
| 96 | ········</div> | 96 | ········</div> |
| 97 | ········<table·class="examples"> | 97 | ········<table·class="examples"> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·D·=·dominanceLattice·6;</code></pre> | 99 | <td>··············<pre><code·class="language-macaulay2">i3·:·D·=·dominanceLattice·6;</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·greeneKleitmanPartition(D,·Strategy·=>·"antichains") |
| 103 | ·--·used·0.5 | 103 | ·--·used·0.531352s·(cpu);·0.25418s·(thread);·0s·(gc) |
| 104 | o4·=·Partition{9,·2} | 104 | o4·=·Partition{9,·2} |
| 105 | o4·:·Partition</code></pre> | 105 | o4·:·Partition</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·greeneKleitmanPartition(D,·Strategy·=>·"chains") |
| 109 | ·--·used·0.000 | 109 | ·--·used·0.000349065s·(cpu);·7.141e-06s·(thread);·0s·(gc) |
| 110 | o5·=·Partition{9,·2} | 110 | o5·=·Partition{9,·2} |
| 111 | o5·:·Partition</code></pre> | 111 | o5·:·Partition</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ········</table> | 113 | ········</table> |
| 114 | ········<div> | 114 | ········<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·0.5 | 35 | ·--·used·0.531352s·(cpu);·0.25418s·(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·0.000 | 39 | ·--·used·0.000349065s·(cpu);·7.141e-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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0. | 29 | ·--·0.45558·seconds·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 | ·--·0.0 | 36 | ·--·0.0233875·seconds·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 | ·--·0.131888·seconds·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 | ·--·0.153099·seconds·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 | ·--·0.01 | 45 | ·--·0.0196522·seconds·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 102, 37 lines modified | Offset 102, 37 lines modified | ||
| 102 | ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 102 | ··············|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 103 | ····························3 | 103 | ····························3 |
| 104 | o3·:·R-module,·quotient·of·R</code></pre> | 104 | o3·:·R-module,·quotient·of·R</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·kernelOfLocalization(M,·I1) | 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·kernelOfLocalization(M,·I1) |
| 108 | ·--·0. | 108 | ·--·0.45558·seconds·elapsed |
| 109 | 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 | o4·=·subquotient·(|·0·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 110 | ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 110 | ··················|·1·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 111 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 111 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 112 | ·······························3 | 112 | ·······························3 |
| 113 | o4·:·R-module,·subquotient·of·R</code></pre> | 113 | o4·:·R-module,·subquotient·of·R</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·kernelOfLocalization(M,·I2) | 116 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·kernelOfLocalization(M,·I2) |
| 117 | ·--·0.0 | 117 | ·--·0.0233875·seconds·elapsed |
| 118 | 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 | o5·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 119 | ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 119 | ··················|·0·0·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 120 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 120 | ··················|·0·1·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 121 | ·······························3 | 121 | ·······························3 |
| 122 | o5·:·R-module,·subquotient·of·R</code></pre> | 122 | o5·:·R-module,·subquotient·of·R</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·kernelOfLocalization(M,·I3) | 125 | <td>··············<pre><code·class="language-macaulay2">i6·:·elapsedTime·kernelOfLocalization(M,·I3) |
| 126 | ·--·0. | 126 | ·--·0.131888·seconds·elapsed |
| 127 | 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 | o6·=·subquotient·(|·1·0·|,·|·x_2^2-x_1x_3·x_1x_2-x_0x_3·x_1^2-x_0x_2·0··············0··············|) |
| 128 | ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| | 128 | ··················|·0·1·|··|·0············0·············0············x_1^3-x_0x_2^2·0··············| |
| 129 | ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| | 129 | ··················|·0·0·|··|·0············0·············0············0··············x_1^5-x_0x_2^4·| |
| 130 | ·······························3 | 130 | ·······························3 |
| 131 | o6·:·R-module,·subquotient·of·R</code></pre> | 131 | 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 | ·--·0. | 48 | ·--·0.45558·seconds·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 | ·--·0.0 | 58 | ·--·0.0233875·seconds·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 | ·--·0.131888·seconds·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 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | ·····x·x·) | 103 | ·····x·x·) |
| 104 | ······0·4 | 104 | ······0·4 |
| 105 | o2·:·Ideal·of·R</code></pre> | 105 | o2·:·Ideal·of·R</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·regSeqInIdeal·I | 108 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·regSeqInIdeal·I |
| 109 | ·--·0. | 109 | ·--·0.153099·seconds·elapsed |
| 110 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) | 110 | o3·=·ideal·(x·x·,·x·x··+·x·x·,·x·x··+·x·x·,·x·x··+·x·x·) |
| 111 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 | 111 | ·············2·7···3·6····0·7···2·5····0·7···1·4····0·7 |
| 112 | o3·:·Ideal·of·R</code></pre> | 112 | o3·:·Ideal·of·R</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ········</table> | 114 | ········</table> |
| Offset 141, 15 lines modified | Offset 141, 15 lines modified | ||
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 | 142 | <td>··············<pre><code·class="language-macaulay2">i6·:·isSubset(I,·ideal(s,l,h))·--·implies·codim·I·==·3 |
| 143 | o6·=·true</code></pre> | 143 | o6·=·true</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) | 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·regSeqInIdeal(I,·3,·3,·1) |
| 147 | ·--·0.01 | 147 | ·--·0.0196522·seconds·elapsed |
| 148 | ···················2················3····2·····2····8····3····2·····2 | 148 | ···················2················3····2·····2····8····3····2·····2 |
| 149 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) | 149 | o7·=·ideal·(h*l·-·l··-·4l*s·+·h*y,·h··+·l·s·-·h·x,·s··+·h··+·l·s·-·h·x) |
| 150 | o7·:·Ideal·of·R</code></pre> | 150 | o7·:·Ideal·of·R</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| 152 | ········</table> | 152 | ········</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 | ·--·0.153099·seconds·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 | ·--·0.01 | 76 | ·--·0.0196522·seconds·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 | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 2 | #:version=1.1 | 2 | #:version=1.1 |
| 3 | #:file=rawdocumentation-dcba-8.db | 3 | #:file=rawdocumentation-dcba-8.db |
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| 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 | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | UHNldWRvbW9ub21pYWxQcmltYXJ5RGVjb21wb3NpdGlvbg== | 8 | UHNldWRvbW9ub21pYWxQcmltYXJ5RGVjb21wb3NpdGlvbg== |
| 9 | #:len=1413 | 9 | #:len=1413 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJpbWFyeSBkZWNvbXBvc2l0aW9uIG9m | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAicHJpbWFyeSBkZWNvbXBvc2l0aW9uIG9m |
| 11 | IGEgc3F1YXJlIGZyZWUgcHNldWRvbW9ub21pYWwgaWRlYWwiLCBEZXNjcmlwdGlvbiA9PiAoRElW | 11 | IGEgc3F1YXJlIGZyZWUgcHNldWRvbW9ub21pYWwgaWRlYWwiLCBEZXNjcmlwdGlvbiA9PiAoRElW |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | aW50ZXJuYWxVc2VEaXJlY3RTdW0oUmluZyxSaW5nKQ== | 8 | aW50ZXJuYWxVc2VEaXJlY3RTdW0oUmluZyxSaW5nKQ== |
| 9 | #:len=285 | 9 | #:len=285 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU1LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDU1LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpbnRlcm5hbFVzZURpcmVjdFN1bSxSaW5nLFJpbmcp | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhpbnRlcm5hbFVzZURpcmVjdFN1bSxSaW5nLFJpbmcp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cHVzaEZ3ZChNb2R1bGUp | 8 | cHVzaEZ3ZChNb2R1bGUp |
| 9 | #:len=267 | 9 | #:len=267 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzgxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMzgxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwdXNoRndkLE1vZHVsZSksInB1c2hGd2QoTW9kdWxl | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhwdXNoRndkLE1vZHVsZSksInB1c2hGd2QoTW9kdWxl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | UHl0aG9uT2JqZWN0IC8gUHl0aG9uT2JqZWN0 | 8 | UHl0aG9uT2JqZWN0IC8gUHl0aG9uT2JqZWN0 |
| 9 | #:len=267 | 9 | #:len=267 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMwLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMwLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
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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·0x7ff91abb1cb0> |
| 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·0x7fc | 7 | o2·=·<range_iterator·object·at·0x7fce473f9cb0> |
| 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·0x7f8 | 75 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f84e5079e60> |
| 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 80, 15 lines modified | Offset 80, 15 lines modified | ||
| 80 | o1·=·range(0,·3) | 80 | o1·=·range(0,·3) |
| 81 | o1·:·PythonObject·of·class·range</code></pre> | 81 | o1·:·PythonObject·of·class·range</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ··········<tr> | 83 | ··········<tr> |
| 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x | 84 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x |
| 85 | o2·=·<range_iterator·object·at·0x7f | 85 | o2·=·<range_iterator·object·at·0x7ff91abb1cb0> |
| 86 | o2·:·PythonObject·of·class·range_iterator</code></pre> | 86 | o2·:·PythonObject·of·class·range_iterator</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ········</table> | 88 | ········</table> |
| 89 | ······</div> | 89 | ······</div> |
| 90 | ······<div> | 90 | ······<div> |
| 91 | ········<h2>See·also</h2> | 91 | ········<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·0x7ff91abb1cb0> |
| 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 74, 15 lines modified | Offset 74, 15 lines modified | ||
| 74 | o1·=·range(0,·3) | 74 | o1·=·range(0,·3) |
| 75 | o1·:·PythonObject·of·class·range</code></pre> | 75 | o1·:·PythonObject·of·class·range</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·i·=·iterator·x |
| 79 | o2·=·<range_iterator·object·at·0x7fc | 79 | o2·=·<range_iterator·object·at·0x7fce473f9cb0> |
| 80 | o2·:·PythonObject·of·class·range_iterator</code></pre> | 80 | o2·:·PythonObject·of·class·range_iterator</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·next·i | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·next·i |
| 84 | o3·=·0 | 84 | 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·0x7fc | 21 | o2·=·<range_iterator·object·at·0x7fce473f9cb0> |
| 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 157, 15 lines modified | Offset 157, 15 lines modified | ||
| 157 | o12·=·m2sqrt | 157 | o12·=·m2sqrt |
| 158 | o12·:·FunctionClosure</code></pre> | 158 | o12·:·FunctionClosure</code></pre> |
| 159 | </td>··········</tr> | 159 | </td>··········</tr> |
| 160 | ··········<tr> | 160 | ··········<tr> |
| 161 | <td>··············<pre><code·class="language-macaulay2">i13·:·pysqrt·=·toPython·m2sqrt | 161 | <td>··············<pre><code·class="language-macaulay2">i13·:·pysqrt·=·toPython·m2sqrt |
| 162 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f8 | 162 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f84e5079e60> |
| 163 | o13·:·PythonObject·of·class·builtin_function_or_method</code></pre> | 163 | o13·:·PythonObject·of·class·builtin_function_or_method</code></pre> |
| 164 | </td>··········</tr> | 164 | </td>··········</tr> |
| 165 | ··········<tr> | 165 | ··········<tr> |
| 166 | <td>··············<pre><code·class="language-macaulay2">i14·:·pysqrt·2 | 166 | <td>··············<pre><code·class="language-macaulay2">i14·:·pysqrt·2 |
| 167 | calling·Macaulay2·code·from·Python! | 167 | 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·0x7f8 | 77 | o13·=·<built-in·method·m2sqrt·of·PyCapsule·object·at·0x7f84e5079e60> |
| 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 | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bWluaW1pemF0aW9u | 8 | bWluaW1pemF0aW9u |
| 9 | #:len=2755 | 9 | #:len=2755 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hhbmdlIHRvIGEgYmV0dGVyIE5vZXRo | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY2hhbmdlIHRvIGEgYmV0dGVyIE5vZXRo |
| 11 | ZXIgbm9ybWFsaXphdGlvbiBzdWdnZXN0ZWQgYnkgdGhlIGluZHVjZWQgd2VpZ2h0cyIsICJsaW5l | 11 | ZXIgbm9ybWFsaXphdGlvbiBzdWdnZXN0ZWQgYnkgdGhlIGluZHVjZWQgd2VpZ2h0cyIsICJsaW5l |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | aGlnaGVyRGVwdGhUYWJsZQ== | 8 | aGlnaGVyRGVwdGhUYWJsZQ== |
| 9 | #:len=793 | 9 | #:len=793 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ3JlYXRlcyBoYXNodGFibGUgb2YgSmFu | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiQ3JlYXRlcyBoYXNodGFibGUgb2YgSmFu |
| 11 | LUVyaWsgUm9vcycgZXhhbXBsZXMgb2YgcXVhZHJhdGljIGlkZWFscyB3aXRoIHBvc2l0aXZlIGRl | 11 | LUVyaWsgUm9vcycgZXhhbXBsZXMgb2YgcXVhZHJhdGljIGlkZWFscyB3aXRoIHBvc2l0aXZlIGRl |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cXVhc2lkZWdyZWVzTG9jYWxDb2hvbW9sb2d5 | 8 | cXVhc2lkZWdyZWVzTG9jYWxDb2hvbW9sb2d5 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--· | 183 | ·--·4.78617·seconds·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 | ·--·3.56782·seconds·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·=·|· | 322 | o44·=·|·22·-10·-8·-1·34·44·-21·-1·25·-41·6·-11·-50·-50·43·-28·-6·45·-28·22·42 |
| 323 | ······----------------------------------------------------------------------- | 323 | ······----------------------------------------------------------------------- |
| 324 | ······-2 | 324 | ······-29·-32·-28·5·-10·34·15·19·37·26·49·19·5·10·18·| |
| 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··+·43b*c·-·41c··-·11a*d·+·44b*d·-·8c*d·+·22d·,·a*b·+·5b*c·- |
| 330 | ······----------------------------------------------------------------------- | 330 | ······----------------------------------------------------------------------- |
| 331 | ·········2······························2···2··············2················ | 331 | ·········2······························2···2··············2················ |
| 332 | ······2 | 332 | ······28c··+·42a*d·-·50b*d·+·25c*d·-·10d·,·b··+·10b*c·+·15c··+·19a*d·-·29b*d |
| 333 | ······----------------------------------------------------------------------- | 333 | ······----------------------------------------------------------------------- |
| 334 | ··················2···················2···························· | 334 | ···················2···················2······························2·····2 |
| 335 | ······ | 335 | ······-·28c*d·-·21d·,·a*c·+·49b*c·-·10c··+·19a*d·+·22b*d·-·50c*d·+·34d·,·b*c· |
| 336 | ······----------------------------------------------------------------------- | 336 | ······----------------------------------------------------------------------- |
| 337 | ···················2·········2 | 337 | ·····················2·········2·······2·······2····3···3················2··· |
| 338 | ······37b*c*d· | 338 | ······+·37b*c*d·-·32c·d·+·34a*d··-·6b*d··+·6c*d··-·d·,·c··+·18b*c*d·+·26c·d·+ |
| 339 | ······----------------------------------------------------------------------- | 339 | ······----------------------------------------------------------------------- |
| 340 | ·········· | 340 | ··········2········2········2····3 |
| 341 | ······ | 341 | ······5a*d··-·28b*d··+·45c*d··-·d·) |
| 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, 37 lines modified | Offset 357, 37 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·+·19d,·b·-·37d,·a· | 362 | o47·=·|ideal·(c·+·19d,·b·-·37d,·a)········································································································································| |
| 363 | ······+--------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 363 | ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 364 | ······|·····························2··············2······················2···3················2·········2······· | 364 | ······|·····························2··············2······················2···3················2·········2·······2·····3·····2················2·········2········2······3·| |
| 365 | ······|ideal·(a· | 365 | ······|ideal·(a·+·49b·-·10c·+·39d,·b··+·10b*c·+·15c··+·50b*d·-·40c*d·+·46d·,·c··+·18b*c*d·+·26c·d·+·30b*d··-·6c*d··+·6d·,·b*c··+·37b*c*d·-·32c·d·+·45b*d··+·43c*d··-·14d·)| |
| 366 | ······+--------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 366 | ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 367 | i48·:·CFa·=·minimalPrimes·Fa | 367 | i48·:·CFa·=·minimalPrimes·Fa |
| 368 | ······································································ | 368 | ·································································2·········· |
| 369 | o48·=·{ideal·(c·+·19d,·b·-·37d,·a | 369 | o48·=·{ideal·(c·+·19d,·b·-·37d,·a),·ideal·(a·+·49b·-·10c·+·39d,·b··+·10b*c·+ |
| 370 | ······----------------------------------------------------------------------- | 370 | ······----------------------------------------------------------------------- |
| 371 | ········· | 371 | ·········2······················2···3················2·········2·······2·· |
| 372 | ······ | 372 | ······15c··+·50b*d·-·40c*d·+·46d·,·c··+·18b*c*d·+·26c·d·+·30b*d··-·6c*d··+ |
| 373 | ······----------------------------------------------------------------------- | 373 | ······----------------------------------------------------------------------- |
| 374 | ········ | 374 | ········3·····2················2·········2········2······3 |
| 375 | ······ | 375 | ······6d·,·b*c··+·37b*c*d·-·32c·d·+·45b*d··+·43c*d··-·14d·)} |
| 376 | o48·:·List | 376 | o48·:·List |
| 377 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. | 377 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. |
| 378 | o49·=·a· | 378 | o49·=·a·+·49b·-·10c·+·39d |
| 379 | o49·:·S | 379 | o49·:·S |
| 380 | i50·:·CFa/degree | 380 | i50·:·CFa/degree |
| 381 | o50·=·{1,·5} | 381 | o50·=·{1,·5} |
| Offset 401, 37 lines modified | Offset 401, 37 lines modified | ||
| 401 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of·the·5·points | 401 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of·the·5·points |
| 402 | o52·=·5 | 402 | o52·=·5 |
| 403 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 | 403 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 |
| 404 | o53·=·|· | 404 | o53·=·|·27·12·-34·9·-19·-43·-32·27·40·45·-13·29·-41·-13·22·-49·-4·-4·9·-23·43 |
| 405 | ······----------------------------------------------------------------------- | 405 | ······----------------------------------------------------------------------- |
| 406 | ······ | 406 | ······18·-9·-47·43·21·38·17·-20·21·-29·47·0·2·-37·9·| |
| 407 | ···············1·······36 | 407 | ···············1·······36 |
| 408 | o53·:·Matrix·kk··<--·kk | 408 | o53·:·Matrix·kk··<--·kk |
| 409 | i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) | 409 | i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) |
| 410 | ··············2··············2·····························2··············· | 410 | ··············2··············2······························2··············· |
| 411 | o54·=·ideal·(a··+· | 411 | o54·=·ideal·(a··+·22b*c·+·45c··+·29a*d·-·43b*d·-·34c*d·+·27d·,·a*b·+·43b*c·+ |
| 412 | ······----------------------------------------------------------------------- | 412 | ······----------------------------------------------------------------------- |
| Max diff block lines reached; 18161/26026 bytes (69.78%) of diff not shown. | |||
| Offset 292, 15 lines modified | Offset 292, 15 lines modified | ||
| 292 | o21·:·Ideal·of·T</code></pre> | 292 | o21·:·Ideal·of·T</code></pre> |
| 293 | </td>··········</tr> | 293 | </td>··········</tr> |
| 294 | ··········<tr> | 294 | ··········<tr> |
| 295 | <td>··············<pre><code·class="language-macaulay2">i22·:·assert(dim·L·==·18)</code></pre> | 295 | <td>··············<pre><code·class="language-macaulay2">i22·:·assert(dim·L·==·18)</code></pre> |
| 296 | </td>··········</tr> | 296 | </td>··········</tr> |
| 297 | ··········<tr> | 297 | ··········<tr> |
| 298 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·L | 298 | <td>··············<pre><code·class="language-macaulay2">i23·:·elapsedTime·isPrime·L |
| 299 | ·--· | 299 | ·--·4.78617·seconds·elapsed |
| 300 | o23·=·true</code></pre> | 300 | o23·=·true</code></pre> |
| 301 | </td>··········</tr> | 301 | </td>··········</tr> |
| 302 | ········</table> | 302 | ········</table> |
| 303 | ········<div> | 303 | ········<div> |
| 304 | ··········<h2>The·Schreyer·resolution·and·minimal·Betti·numbers</h2> | 304 | ··········<h2>The·Schreyer·resolution·and·minimal·Betti·numbers</h2> |
| 305 | ········</div> | 305 | ········</div> |
| Offset 470, 15 lines modified | Offset 470, 15 lines modified | ||
| 470 | ··········<tr> | 470 | ··········<tr> |
| 471 | <td>··············<pre><code·class="language-macaulay2">i39·:·L441·=·trim(L·+·ideal·M1); | 471 | <td>··············<pre><code·class="language-macaulay2">i39·:·L441·=·trim(L·+·ideal·M1); |
| 472 | o39·:·Ideal·of·T</code></pre> | 472 | o39·:·Ideal·of·T</code></pre> |
| 473 | </td>··········</tr> | 473 | </td>··········</tr> |
| 474 | ··········<tr> | 474 | ··········<tr> |
| 475 | <td>··············<pre><code·class="language-macaulay2">i40·:·elapsedTime·compsL441·=·decompose·L441; | 475 | <td>··············<pre><code·class="language-macaulay2">i40·:·elapsedTime·compsL441·=·decompose·L441; |
| 476 | ·--· | 476 | ·--·3.56782·seconds·elapsed</code></pre> |
| 477 | </td>··········</tr> | 477 | </td>··········</tr> |
| 478 | ··········<tr> | 478 | ··········<tr> |
| 479 | <td>··············<pre><code·class="language-macaulay2">i41·:·#compsL441 | 479 | <td>··············<pre><code·class="language-macaulay2">i41·:·#compsL441 |
| 480 | o41·=·2</code></pre> | 480 | o41·=·2</code></pre> |
| 481 | </td>··········</tr> | 481 | </td>··········</tr> |
| 482 | ··········<tr> | 482 | ··········<tr> |
| Offset 497, 38 lines modified | Offset 497, 38 lines modified | ||
| 497 | ········<div> | 497 | ········<div> |
| 498 | ··········<p>Both·components·are·rational,·and·here·are·random·points,·one·on·each·component:</p> | 498 | ··········<p>Both·components·are·rational,·and·here·are·random·points,·one·on·each·component:</p> |
| 499 | ········</div> | 499 | ········</div> |
| 500 | ········<table·class="examples"> | 500 | ········<table·class="examples"> |
| 501 | ··········<tr> | 501 | ··········<tr> |
| 502 | <td>··············<pre><code·class="language-macaulay2">i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 | 502 | <td>··············<pre><code·class="language-macaulay2">i44·:·pta·=·randomPointOnRationalVariety·compsL441_0 |
| 503 | o44·=·|· | 503 | o44·=·|·22·-10·-8·-1·34·44·-21·-1·25·-41·6·-11·-50·-50·43·-28·-6·45·-28·22·42 |
| 504 | ······----------------------------------------------------------------------- | 504 | ······----------------------------------------------------------------------- |
| 505 | ······-2 | 505 | ······-29·-32·-28·5·-10·34·15·19·37·26·49·19·5·10·18·| |
| 506 | ···············1·······36 | 506 | ···············1·······36 |
| 507 | o44·:·Matrix·kk··<--·kk</code></pre> | 507 | o44·:·Matrix·kk··<--·kk</code></pre> |
| 508 | </td>··········</tr> | 508 | </td>··········</tr> |
| 509 | ··········<tr> | 509 | ··········<tr> |
| 510 | <td>··············<pre><code·class="language-macaulay2">i45·:·Fa·=·sub(F,·(vars·S)·|·pta) | 510 | <td>··············<pre><code·class="language-macaulay2">i45·:·Fa·=·sub(F,·(vars·S)·|·pta) |
| 511 | ··············2··············2····························· | 511 | ··············2··············2·····························2·············· |
| 512 | o45·=·ideal·(a··+· | 512 | o45·=·ideal·(a··+·43b*c·-·41c··-·11a*d·+·44b*d·-·8c*d·+·22d·,·a*b·+·5b*c·- |
| 513 | ······----------------------------------------------------------------------- | 513 | ······----------------------------------------------------------------------- |
| 514 | ·········2······························2···2··············2················ | 514 | ·········2······························2···2··············2················ |
| 515 | ······2 | 515 | ······28c··+·42a*d·-·50b*d·+·25c*d·-·10d·,·b··+·10b*c·+·15c··+·19a*d·-·29b*d |
| 516 | ······----------------------------------------------------------------------- | 516 | ······----------------------------------------------------------------------- |
| 517 | ··················2···················2···························· | 517 | ···················2···················2······························2·····2 |
| 518 | ······ | 518 | ······-·28c*d·-·21d·,·a*c·+·49b*c·-·10c··+·19a*d·+·22b*d·-·50c*d·+·34d·,·b*c· |
| 519 | ······----------------------------------------------------------------------- | 519 | ······----------------------------------------------------------------------- |
| 520 | ···················2·········2 | 520 | ·····················2·········2·······2·······2····3···3················2··· |
| 521 | ······37b*c*d· | 521 | ······+·37b*c*d·-·32c·d·+·34a*d··-·6b*d··+·6c*d··-·d·,·c··+·18b*c*d·+·26c·d·+ |
| 522 | ······----------------------------------------------------------------------- | 522 | ······----------------------------------------------------------------------- |
| 523 | ·········· | 523 | ··········2········2········2····3 |
| 524 | ······ | 524 | ······5a*d··-·28b*d··+·45c*d··-·d·) |
| 525 | o45·:·Ideal·of·S</code></pre> | 525 | o45·:·Ideal·of·S</code></pre> |
| 526 | </td>··········</tr> | 526 | </td>··········</tr> |
| 527 | ··········<tr> | 527 | ··········<tr> |
| 528 | <td>··············<pre><code·class="language-macaulay2">i46·:·betti·res·Fa | 528 | <td>··············<pre><code·class="language-macaulay2">i46·:·betti·res·Fa |
| 529 | ·············0·1·2·3 | 529 | ·············0·1·2·3 |
| Offset 538, 39 lines modified | Offset 538, 39 lines modified | ||
| 538 | ··········2:·.·2·4·2 | 538 | ··········2:·.·2·4·2 |
| 539 | o46·:·BettiTally</code></pre> | 539 | o46·:·BettiTally</code></pre> |
| 540 | </td>··········</tr> | 540 | </td>··········</tr> |
| 541 | ··········<tr> | 541 | ··········<tr> |
| 542 | <td>··············<pre><code·class="language-macaulay2">i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point | 542 | <td>··············<pre><code·class="language-macaulay2">i47·:·netList·decompose·Fa·--·this·one·is·5·points·on·a·plane,·and·another·point |
| 543 | ······+--------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 543 | ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 544 | o47·=·|ideal·(c·+·19d,·b·-·37d,·a· | 544 | o47·=·|ideal·(c·+·19d,·b·-·37d,·a)········································································································································| |
| 545 | ······+--------------------------------------------------------------------------------------------------------------------------------------------------------------+ | 545 | ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |
| 546 | ······|·····························2··············2······················2···3················2·········2······· | 546 | ······|·····························2··············2······················2···3················2·········2·······2·····3·····2················2·········2········2······3·| |
| 547 | ······|ideal·(a· | 547 | ······|ideal·(a·+·49b·-·10c·+·39d,·b··+·10b*c·+·15c··+·50b*d·-·40c*d·+·46d·,·c··+·18b*c*d·+·26c·d·+·30b*d··-·6c*d··+·6d·,·b*c··+·37b*c*d·-·32c·d·+·45b*d··+·43c*d··-·14d·)| |
| 548 | ······+--------------------------------------------------------------------------------------------------------------------------------------------------------------+</code></pre> | 548 | ······+-------------------------------------------------------------------------------------------------------------------------------------------------------------------+</code></pre> |
| 549 | </td>··········</tr> | 549 | </td>··········</tr> |
| 550 | ··········<tr> | 550 | ··········<tr> |
| 551 | <td>··············<pre><code·class="language-macaulay2">i48·:·CFa·=·minimalPrimes·Fa | 551 | <td>··············<pre><code·class="language-macaulay2">i48·:·CFa·=·minimalPrimes·Fa |
| 552 | ······································································ | 552 | ·································································2·········· |
| 553 | o48·=·{ideal·(c·+·19d,·b·-·37d,·a | 553 | o48·=·{ideal·(c·+·19d,·b·-·37d,·a),·ideal·(a·+·49b·-·10c·+·39d,·b··+·10b*c·+ |
| 554 | ······----------------------------------------------------------------------- | 554 | ······----------------------------------------------------------------------- |
| 555 | ········· | 555 | ·········2······················2···3················2·········2·······2·· |
| 556 | ······ | 556 | ······15c··+·50b*d·-·40c*d·+·46d·,·c··+·18b*c*d·+·26c·d·+·30b*d··-·6c*d··+ |
| 557 | ······----------------------------------------------------------------------- | 557 | ······----------------------------------------------------------------------- |
| 558 | ········ | 558 | ········3·····2················2·········2········2······3 |
| 559 | ······ | 559 | ······6d·,·b*c··+·37b*c*d·-·32c·d·+·45b*d··+·43c*d··-·14d·)} |
| 560 | o48·:·List</code></pre> | 560 | o48·:·List</code></pre> |
| 561 | </td>··········</tr> | 561 | </td>··········</tr> |
| 562 | ··········<tr> | 562 | ··········<tr> |
| 563 | <td>··············<pre><code·class="language-macaulay2">i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. | 563 | <td>··············<pre><code·class="language-macaulay2">i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. |
| 564 | o49·=·a· | 564 | o49·=·a·+·49b·-·10c·+·39d |
| 565 | o49·:·S</code></pre> | 565 | o49·:·S</code></pre> |
| 566 | </td>··········</tr> | 566 | </td>··········</tr> |
| 567 | ··········<tr> | 567 | ··········<tr> |
| 568 | <td>··············<pre><code·class="language-macaulay2">i50·:·CFa/degree | 568 | <td>··············<pre><code·class="language-macaulay2">i50·:·CFa/degree |
| 569 | o50·=·{1,·5} | 569 | o50·=·{1,·5} |
| Offset 590, 38 lines modified | Offset 590, 38 lines modified | ||
| 590 | o52·=·5</code></pre> | 590 | o52·=·5</code></pre> |
| 591 | </td>··········</tr> | 591 | </td>··········</tr> |
| 592 | ········</table> | 592 | ········</table> |
| 593 | ········<table·class="examples"> | 593 | ········<table·class="examples"> |
| 594 | ··········<tr> | 594 | ··········<tr> |
| 595 | <td>··············<pre><code·class="language-macaulay2">i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 | 595 | <td>··············<pre><code·class="language-macaulay2">i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 |
| 596 | o53·=·|· | 596 | o53·=·|·27·12·-34·9·-19·-43·-32·27·40·45·-13·29·-41·-13·22·-49·-4·-4·9·-23·43 |
| 597 | ······----------------------------------------------------------------------- | 597 | ······----------------------------------------------------------------------- |
| 598 | ······ | 598 | ······18·-9·-47·43·21·38·17·-20·21·-29·47·0·2·-37·9·| |
| 599 | ···············1·······36 | 599 | ···············1·······36 |
| 600 | o53·:·Matrix·kk··<--·kk</code></pre> | 600 | o53·:·Matrix·kk··<--·kk</code></pre> |
| 601 | </td>··········</tr> | 601 | </td>··········</tr> |
| 602 | ··········<tr> | 602 | ··········<tr> |
| 603 | <td>··············<pre><code·class="language-macaulay2">i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) | 603 | <td>··············<pre><code·class="language-macaulay2">i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) |
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| 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 | ·--· | 256 | ·--·4.78617·seconds·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 | ·--·3.56782·seconds·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·=·|· | 435 | o44·=·|·22·-10·-8·-1·34·44·-21·-1·25·-41·6·-11·-50·-50·43·-28·-6·45·-28·22·42 |
| 436 | ······----------------------------------------------------------------------- | 436 | ······----------------------------------------------------------------------- |
| 437 | ······-2 | 437 | ······-29·-32·-28·5·-10·34·15·19·37·26·49·19·5·10·18·| |
| 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··············2····························· | 441 | ··············2··············2·····························2 |
| 442 | o45·=·ideal·(a··+· | 442 | o45·=·ideal·(a··+·43b*c·-·41c··-·11a*d·+·44b*d·-·8c*d·+·22d·,·a*b·+·5b*c·- |
| 443 | ······----------------------------------------------------------------------- | 443 | ······----------------------------------------------------------------------- |
| 444 | ·········2······························2···2··············2 | 444 | ·········2······························2···2··············2 |
| 445 | ······2 | 445 | ······28c··+·42a*d·-·50b*d·+·25c*d·-·10d·,·b··+·10b*c·+·15c··+·19a*d·-·29b*d |
| 446 | ······----------------------------------------------------------------------- | 446 | ······----------------------------------------------------------------------- |
| 447 | ··················2···················2····························2·····2 | 447 | ···················2···················2······························2·····2 |
| 448 | ······ | 448 | ······-·28c*d·-·21d·,·a*c·+·49b*c·-·10c··+·19a*d·+·22b*d·-·50c*d·+·34d·,·b*c |
| 449 | ······----------------------------------------------------------------------- | 449 | ······----------------------------------------------------------------------- |
| 450 | ···················2·········2 | 450 | ·····················2·········2·······2·······2····3···3················2 |
| 451 | ······37b*c*d· | 451 | ······+·37b*c*d·-·32c·d·+·34a*d··-·6b*d··+·6c*d··-·d·,·c··+·18b*c*d·+·26c·d·+ |
| 452 | ······----------------------------------------------------------------------- | 452 | ······----------------------------------------------------------------------- |
| 453 | ·········· | 453 | ··········2········2········2····3 |
| 454 | ······ | 454 | ······5a*d··-·28b*d··+·45c*d··-·d·) |
| 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 468, 43 lines modified | Offset 468, 43 lines modified | ||
| 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 | -------+ | 473 | ------------+ |
| 474 | o47·=·|ideal·(c·+·19d,·b·-·37d,·a | 474 | o47·=·|ideal·(c·+·19d,·b·-·37d,·a) |
| 475 | | | 475 | | |
| 476 | ······+------------------------------------------------------------------------ | 476 | ······+------------------------------------------------------------------------ |
| 477 | ------------------------------------------------------------------------------- | 477 | ------------------------------------------------------------------------------- |
| 478 | -------+ | 478 | ------------+ |
| 479 | ······|·····························2··············2······················2···3 | 479 | ······|·····························2··············2······················2···3 |
| 480 | 2·········2······· | 480 | 2·········2·······2·····3·····2················2·········2········2······3·| |
| 481 | ······|ideal·(a· | 481 | ······|ideal·(a·+·49b·-·10c·+·39d,·b··+·10b*c·+·15c··+·50b*d·-·40c*d·+·46d·,·c |
| 482 | +·18b*c*d·+· | 482 | +·18b*c*d·+·26c·d·+·30b*d··-·6c*d··+·6d·,·b*c··+·37b*c*d·-·32c·d·+·45b*d··+ |
| 483 | 483 | 43c*d··-·14d·)| | |
| 484 | ······+------------------------------------------------------------------------ | 484 | ······+------------------------------------------------------------------------ |
| 485 | ------------------------------------------------------------------------------- | 485 | ------------------------------------------------------------------------------- |
| 486 | -------+ | 486 | ------------+ |
| 487 | i48·:·CFa·=·minimalPrimes·Fa | 487 | i48·:·CFa·=·minimalPrimes·Fa |
| 488 | ································································· | 488 | ·································································2 |
| 489 | o48·=·{ideal·(c·+·19d,·b·-·37d,·a | 489 | o48·=·{ideal·(c·+·19d,·b·-·37d,·a),·ideal·(a·+·49b·-·10c·+·39d,·b··+·10b*c·+ |
| 490 | ······----------------------------------------------------------------------- | 490 | ······----------------------------------------------------------------------- |
| 491 | ········· | 491 | ·········2······················2···3················2·········2·······2 |
| 492 | ······ | 492 | ······15c··+·50b*d·-·40c*d·+·46d·,·c··+·18b*c*d·+·26c·d·+·30b*d··-·6c*d··+ |
| 493 | ······----------------------------------------------------------------------- | 493 | ······----------------------------------------------------------------------- |
| 494 | ········ | 494 | ········3·····2················2·········2········2······3 |
| 495 | ······ | 495 | ······6d·,·b*c··+·37b*c*d·-·32c·d·+·45b*d··+·43c*d··-·14d·)} |
| 496 | o48·:·List | 496 | o48·:·List |
| 497 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. | 497 | i49·:·lin·=·CFa_1_0·--·a·linear·form,·defining·a·plane. |
| 498 | o49·=·a· | 498 | o49·=·a·+·49b·-·10c·+·39d |
| 499 | o49·:·S | 499 | o49·:·S |
| 500 | i50·:·CFa/degree | 500 | i50·:·CFa/degree |
| 501 | o50·=·{1,·5} | 501 | o50·=·{1,·5} |
| 502 | o50·:·List | 502 | o50·:·List |
| Offset 515, 206 lines modified | Offset 515, 124 lines modified | ||
| 515 | o51·:·List | 515 | o51·:·List |
| 516 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of | 516 | i52·:·degree(Fa·:·(Fa·:·lin))··--·somewhat·simpler(?)·way·to·see·the·ideal·of |
| 517 | the·5·points | 517 | the·5·points |
| 518 | o52·=·5 | 518 | o52·=·5 |
| 519 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 | 519 | i53·:·ptb·=·randomPointOnRationalVariety·compsL441_1 |
| 520 | o53·=·|· | 520 | o53·=·|·27·12·-34·9·-19·-43·-32·27·40·45·-13·29·-41·-13·22·-49·-4·-4·9·-23·43 |
| 521 | ······----------------------------------------------------------------------- | 521 | ······----------------------------------------------------------------------- |
| 522 | ······ | 522 | ······18·-9·-47·43·21·38·17·-20·21·-29·47·0·2·-37·9·| |
| 523 | ···············1·······36 | 523 | ···············1·······36 |
| 524 | o53·:·Matrix·kk··<--·kk | 524 | o53·:·Matrix·kk··<--·kk |
| 525 | i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) | 525 | i54·:·Fb·=·sub(F,·(vars·S)·|·ptb) |
| Max diff block lines reached; 15850/22764 bytes (69.63%) 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | aG9ycm9ja3M= | 8 | aG9ycm9ja3M= |
| 9 | #:len=4664 | 9 | #:len=4664 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYSBsb2NhbCBzb2x1dGlv | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29tcHV0ZXMgYSBsb2NhbCBzb2x1dGlv |
| 11 | biB0byB0aGUgdW5pbW9kdWxhciByb3cgcHJvYmxlbSBvdmVyIGEgbG9jYWxpemF0aW9uIGF0IGEg | 11 | biB0byB0aGUgdW5pbW9kdWxhciByb3cgcHJvYmxlbSBvdmVyIGEgbG9jYWxpemF0aW9uIGF0IGEg |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IFJPYmplY3QgZnJvbSBDQw== | 8 | bmV3IFJPYmplY3QgZnJvbSBDQw== |
| 9 | #:len=251 | 9 | #:len=251 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMzLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTMzLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·5.43668s·(cpu);·4.55177s·(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 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·FF=ZZ/10007;</code></pre> | 84 | <td>··············<pre><code·class="language-macaulay2">i3·:·FF=ZZ/10007;</code></pre> |
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·R=FF[x_0..x_(g-1)];</code></pre> | 87 | <td>··············<pre><code·class="language-macaulay2">i4·:·R=FF[x_0..x_(g-1)];</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·betti(I=(random·canonicalCurve)(g,R)) | 90 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·betti(I=(random·canonicalCurve)(g,R)) |
| 91 | ·--·used·5. | 91 | ·--·used·5.43668s·(cpu);·4.55177s·(thread);·0s·(gc) |
| 92 | ············0··1 | 92 | ············0··1 |
| 93 | o5·=·total:·1·66 | 93 | o5·=·total:·1·66 |
| 94 | ·········0:·1··. | 94 | ·········0:·1··. |
| 95 | ·········1:·.·66 | 95 | ·········1:·.·66 |
| 96 | o5·:·BettiTally</code></pre> | 96 | 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·5.43668s·(cpu);·4.55177s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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},·.0029 | 9 | o3·=·({5,·2.91596e52,·9},·.00297006,·.000900285) |
| 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},·.00324848,·.0326493) |
| 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·=·{{.002 | 15 | o5·=·{{.00200464,·.0105226},·{.00582001,·.00320154},·{.00501109,·.00795583}, |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ·····{.00 | 17 | ·····{.00596948,·.00863911},·{.00390285,·.0111625},·{.00800998,·.0152953}, |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ·····{.00 | 19 | ·····{.00454888,·.00740881},·{.00141481,·.00398795},·{.00506907,·.00408767}, |
| 20 | ·····------------------------------------------------------------------------ | 20 | ·····------------------------------------------------------------------------ |
| 21 | ·····{.00 | 21 | ·····{.0062651,·.0054439}} |
| 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·=·.004 | 24 | o6·=·.00480159230000001 |
| 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·=·.0077705286 |
| 28 | o7·:·RR·(of·precision·53) | 28 | o7·:·RR·(of·precision·53) |
| 29 | i8·:· | 29 | i8·:· |
| Offset 93, 49 lines modified | Offset 93, 49 lines modified | ||
| 93 | o2·=·(10,·20) | 93 | o2·=·(10,·20) |
| 94 | o2·:·Sequence</code></pre> | 94 | o2·:·Sequence</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) | 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·(m,t1,t2)=testTimeForLLLonSyzygies(r,n,Height=>11) |
| 98 | o3·=·({5,·2.91596e52,·9},·.0029 | 98 | o3·=·({5,·2.91596e52,·9},·.00297006,·.000900285) |
| 99 | o3·:·Sequence</code></pre> | 99 | o3·:·Sequence</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) | 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·(m,t1,t2)=testTimeForLLLonSyzygies(15,30,Height=>100) |
| 103 | o4·=·({50,·2.30853e454,·98},·.00 | 103 | o4·=·({50,·2.30853e454,·98},·.00324848,·.0326493) |
| 104 | o4·:·Sequence</code></pre> | 104 | o4·:·Sequence</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) | 107 | <td>··············<pre><code·class="language-macaulay2">i5·:·L=apply(10,c->(testTimeForLLLonSyzygies(15,30))_{1,2}) |
| 108 | o5·=·{{.002 | 108 | o5·=·{{.00200464,·.0105226},·{.00582001,·.00320154},·{.00501109,·.00795583}, |
| 109 | ·····------------------------------------------------------------------------ | 109 | ·····------------------------------------------------------------------------ |
| 110 | ·····{.00 | 110 | ·····{.00596948,·.00863911},·{.00390285,·.0111625},·{.00800998,·.0152953}, |
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| 112 | ·····{.00 | 112 | ·····{.00454888,·.00740881},·{.00141481,·.00398795},·{.00506907,·.00408767}, |
| 113 | ·····------------------------------------------------------------------------ | 113 | ·····------------------------------------------------------------------------ |
| 114 | ·····{.00 | 114 | ·····{.0062651,·.0054439}} |
| 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·:·1/10*sum(L,t->t_0) | 118 | <td>··············<pre><code·class="language-macaulay2">i6·:·1/10*sum(L,t->t_0) |
| 119 | o6·=·.004 | 119 | o6·=·.00480159230000001 |
| 120 | o6·:·RR·(of·precision·53)</code></pre> | 120 | o6·:·RR·(of·precision·53)</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·1/10*sum(L,t->t_1) | 123 | <td>··············<pre><code·class="language-macaulay2">i7·:·1/10*sum(L,t->t_1) |
| 124 | o7·=·.00 | 124 | o7·=·.0077705286 |
| 125 | o7·:·RR·(of·precision·53)</code></pre> | 125 | o7·:·RR·(of·precision·53)</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">testTimeForLLLonSyzygies</span>·:</h2> | 130 | ········<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},·.0029 | 29 | o3·=·({5,·2.91596e52,·9},·.00297006,·.000900285) |
| 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},·.00324848,·.0326493) |
| 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·=·{{.002 | 35 | o5·=·{{.00200464,·.0105226},·{.00582001,·.00320154},·{.00501109,·.00795583}, |
| 36 | ·····------------------------------------------------------------------------ | 36 | ·····------------------------------------------------------------------------ |
| 37 | ·····{.00 | 37 | ·····{.00596948,·.00863911},·{.00390285,·.0111625},·{.00800998,·.0152953}, |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····{.00 | 39 | ·····{.00454888,·.00740881},·{.00141481,·.00398795},·{.00506907,·.00408767}, |
| 40 | ·····------------------------------------------------------------------------ | 40 | ·····------------------------------------------------------------------------ |
| 41 | ·····{.00 | 41 | ·····{.0062651,·.0054439}} |
| 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·=·.004 | 44 | o6·=·.00480159230000001 |
| 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·=·.0077705286 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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:·-377630784 | 1 | --·-*-·M2-comint·-*-·hash:·-377630784 |
| 2 | i1·:·time·ICan·=·smoothCanonicalCurve(11,5); | 2 | i1·:·time·ICan·=·smoothCanonicalCurve(11,5); |
| 3 | ·--·used· | 3 | ·--·used·0.981569s·(cpu);·0.873864s·(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 86, 15 lines modified | Offset 86, 15 lines modified | ||
| 86 | ··········<p>For·g=15·the·curves·are·constructed·via·matrix·factorizations.</p> | 86 | ··········<p>For·g=15·the·curves·are·constructed·via·matrix·factorizations.</p> |
| 87 | ··········<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>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> |
| 88 | ··········<p></p> | 88 | ··········<p></p> |
| 89 | ········</div> | 89 | ········</div> |
| 90 | ········<table·class="examples"> | 90 | ········<table·class="examples"> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·ICan·=·smoothCanonicalCurve(11,5); | 92 | <td>··············<pre><code·class="language-macaulay2">i1·:·time·ICan·=·smoothCanonicalCurve(11,5); |
| 93 | ·--·used· | 93 | ·--·used·0.981569s·(cpu);·0.873864s·(thread);·0s·(gc) |
| 94 | ··············ZZ | 94 | ··············ZZ |
| 95 | o1·:·Ideal·of·--[t·..t··] | 95 | o1·:·Ideal·of·--[t·..t··] |
| 96 | ···············5··0···10</code></pre> | 96 | ···············5··0···10</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i2·:·(dim·ICan,·genus·ICan,·degree·ICan) | 99 | <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· | 37 | ·--·used·0.981569s·(cpu);·0.873864s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·1.28207s·(cpu);·1.1604s·(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 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·FF=ZZ/10007;</code></pre> | 88 | <td>··············<pre><code·class="language-macaulay2">i2·:·FF=ZZ/10007;</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=FF[x_0..x_6];</code></pre> | 91 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=FF[x_0..x_6];</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I=randomCurveGenus14Degree18inP6(S); | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·I=randomCurveGenus14Degree18inP6(S); |
| 95 | ·--·used·1. | 95 | ·--·used·1.28207s·(cpu);·1.1604s·(thread);·0s·(gc) |
| 96 | o4·:·Ideal·of·S</code></pre> | 96 | o4·:·Ideal·of·S</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·betti·res·I | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·betti·res·I |
| 100 | ············0··1··2··3··4·5 | 100 | ············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·1.28207s·(cpu);·1.1604s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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, 24 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-209903751 | 1 | --·-*-·M2-comint·-*-·hash:·-209903751 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1729002761 |
| 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 | 7 | ·--·used·1.72837s·(cpu);·1.16954s·(thread);·0s·(gc) |
| 8 | o4·=·Tally{ | 8 | o4·=·Tally{3·=>·2··} |
| 9 | ···········4·=>·46 | ||
| 9 | ···········5·=>·2 | 10 | ···········5·=>·208 |
| 10 | ···········6·=>·1 | 11 | ···········6·=>·164 |
| 11 | ···········7·=>·6 | 12 | ···········7·=>·68 |
| 12 | ···········8·=>·1 | 13 | ···········8·=>·10 |
| 13 | ···········9·=>· | 14 | ···········9·=>·2 |
| 14 | o4·:·Tally | 15 | o4·:·Tally |
| 15 | i5·:· | 16 | i5·:· |
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| 1 | --·-*-·M2-comint·-*-·hash:·-671123338 | 1 | --·-*-·M2-comint·-*-·hash:·-671123338 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1729002785 |
| 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 | ······3 |
| 18 | o4·=· | 18 | o4·=·a |
| 19 | o4·:·S | 19 | o4·:·S |
| 20 | i5·:· | 20 | i5·:· |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1488213991 | 1 | --·-*-·M2-comint·-*-·hash:·1488213991 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1729002828 |
| 4 | i2·:·kk=ZZ/101 | 4 | i2·:·kk=ZZ/101 |
| 5 | o2·=·kk | 5 | o2·=·kk |
| 6 | o2·:·QuotientRing | 6 | o2·:·QuotientRing |
| Offset 21, 18 lines modified | Offset 21, 18 lines modified | ||
| 21 | o4·=·{3,·5,·7} | 21 | o4·=·{3,·5,·7} |
| 22 | o4·:·List | 22 | o4·:·List |
| 23 | i5·:·randomSquareFreeMonomialIdeal(L,·S) | 23 | i5·:·randomSquareFreeMonomialIdeal(L,·S) |
| 24 | low·degree·gens·generated·everything | 24 | low·degree·gens·generated·everything |
| 25 | o5·=·ideal( | 25 | o5·=·ideal(b*c*d) |
| 26 | o5·:·Ideal·of·S | 26 | o5·:·Ideal·of·S |
| 27 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) | 27 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) |
| 28 | o6·=·ideal·(a* | 28 | o6·=·ideal·(a*d,·b*d,·c*d,·d*e,·a*b) |
| 29 | o6·:·Ideal·of·S | 29 | o6·:·Ideal·of·S |
| 30 | i7·:· | 30 | i7·:· |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1580057571 | 1 | --·-*-·M2-comint·-*-·hash:·1580057571 |
| 2 | i1·:·setRandomSeed(currentTime()) | 2 | i1·:·setRandomSeed(currentTime()) |
| 3 | o1·=·17 | 3 | o1·=·1729002815 |
| 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*c,·a*d,·b*c*d),·{a*b*c,·a*d,·b*c*d},·{c | 17 | o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*c*d),·{a*b,·a*c,·a*d,·b*c*d},·{c*d, |
| 18 | ·····------------------------------------------------------------------------ | 18 | ·····------------------------------------------------------------------------ |
| 19 | ····· | 19 | ·····b*d,·b*c,·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·3. | 41 | ·--·used·3.2641s·(cpu);·2.23735s·(thread);·0s·(gc) |
| 42 | i9·:·#T | 42 | i9·:·#T |
| 43 | o9·=·168 | 43 | o9·=·168 |
| 44 | i10·:·T | 44 | i10·:·T |
| Offset 73, 15 lines modified | Offset 73, 15 lines modified | ||
| 73 | ········<div> | 73 | ········<div> |
| 74 | ··········<p>Chooses·a·random·monomial.</p> | 74 | ··········<p>Chooses·a·random·monomial.</p> |
| 75 | ········</div> | 75 | ········</div> |
| 76 | ········<table·class="examples"> | 76 | ········<table·class="examples"> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 79 | o1·=·17 | 79 | o1·=·1729002785</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 |
| 83 | o2·=·kk | 83 | o2·=·kk |
| 84 | o2·:·QuotientRing</code></pre> | 84 | o2·:·QuotientRing</code></pre> |
| Offset 92, 16 lines modified | Offset 92, 16 lines modified | ||
| 92 | o3·=·S | 92 | o3·=·S |
| 93 | o3·:·PolynomialRing</code></pre> | 93 | o3·:·PolynomialRing</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomMonomial(3,S) | 96 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomMonomial(3,S) |
| 97 | ······ | 97 | ······3 |
| 98 | o4·=· | 98 | o4·=·a |
| 99 | o4·:·S</code></pre> | 99 | o4·:·S</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 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·=·1729002785 |
| 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 | ······3 |
| 28 | o4·=· | 28 | o4·=·a |
| 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 73, 15 lines modified | Offset 73, 15 lines modified | ||
| 73 | ········<div> | 73 | ········<div> |
| 74 | ··········<p>Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees·specified·by·the·list·or·sequence·L.</p> | 74 | ··········<p>Choose·a·random·square-free·monomial·ideal·whose·generators·have·the·degrees·specified·by·the·list·or·sequence·L.</p> |
| 75 | ········</div> | 75 | ········</div> |
| 76 | ········<table·class="examples"> | 76 | ········<table·class="examples"> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 78 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 79 | o1·=·17 | 79 | o1·=·1729002828</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 | 82 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101 |
| 83 | o2·=·kk | 83 | o2·=·kk |
| 84 | o2·:·QuotientRing</code></pre> | 84 | o2·:·QuotientRing</code></pre> |
| Offset 100, 22 lines modified | Offset 100, 22 lines modified | ||
| 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·:·randomSquareFreeMonomialIdeal(L,·S) | 103 | <td>··············<pre><code·class="language-macaulay2">i5·:·randomSquareFreeMonomialIdeal(L,·S) |
| 104 | low·degree·gens·generated·everything | 104 | low·degree·gens·generated·everything |
| 105 | o5·=·ideal( | 105 | o5·=·ideal(b*c*d) |
| 106 | o5·:·Ideal·of·S</code></pre> | 106 | o5·:·Ideal·of·S</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i6·:·randomSquareFreeMonomialIdeal(5:2,·S) | 109 | <td>··············<pre><code·class="language-macaulay2">i6·:·randomSquareFreeMonomialIdeal(5:2,·S) |
| 110 | o6·=·ideal·(a* | 110 | o6·=·ideal·(a*d,·b*d,·c*d,·d*e,·a*b) |
| 111 | o6·:·Ideal·of·S</code></pre> | 111 | o6·:·Ideal·of·S</code></pre> |
| 112 | </td>··········</tr> | 112 | </td>··········</tr> |
| 113 | ········</table> | 113 | ········</table> |
| 114 | ······</div> | 114 | ······</div> |
| 115 | ······<div> | 115 | ······<div> |
| 116 | ········<h2>Caveat</h2> | 116 | ········<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·=·1729002828 |
| 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 34, 20 lines modified | Offset 34, 20 lines modified | ||
| 34 | o4·=·{3,·5,·7} | 34 | o4·=·{3,·5,·7} |
| 35 | o4·:·List | 35 | o4·:·List |
| 36 | i5·:·randomSquareFreeMonomialIdeal(L,·S) | 36 | i5·:·randomSquareFreeMonomialIdeal(L,·S) |
| 37 | low·degree·gens·generated·everything | 37 | low·degree·gens·generated·everything |
| 38 | o5·=·ideal( | 38 | o5·=·ideal(b*c*d) |
| 39 | o5·:·Ideal·of·S | 39 | o5·:·Ideal·of·S |
| 40 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) | 40 | i6·:·randomSquareFreeMonomialIdeal(5:2,·S) |
| 41 | o6·=·ideal·(a* | 41 | o6·=·ideal·(a*d,·b*d,·c*d,·d*e,·a*b) |
| 42 | o6·:·Ideal·of·S | 42 | o6·:·Ideal·of·S |
| 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·ideal·is·constructed·degree·by·degree,·starting·from·the·lowest·degree | 44 | The·ideal·is·constructed·degree·by·degree,·starting·from·the·lowest·degree |
| 45 | specified.·If·there·are·not·enough·monomials·of·the·next·specified·degree·that | 45 | specified.·If·there·are·not·enough·monomials·of·the·next·specified·degree·that |
| 46 | are·not·already·in·the·ideal,·the·function·prints·a·warning·and·returns·an | 46 | are·not·already·in·the·ideal,·the·function·prints·a·warning·and·returns·an |
| 47 | ideal·containing·all·the·generators·of·that·degree. | 47 | ideal·containing·all·the·generators·of·that·degree. |
| Offset 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 83 | ··········<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>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> |
| 84 | ··········<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 | ··········<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> |
| 85 | ········</div> | 85 | ········</div> |
| 86 | ········<table·class="examples"> | 86 | ········<table·class="examples"> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 88 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 89 | o1·=·17 | 89 | o1·=·1729002815</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i2·:·S=ZZ/2[vars(0..3)] | 92 | <td>··············<pre><code·class="language-macaulay2">i2·:·S=ZZ/2[vars(0..3)] |
| 93 | o2·=·S | 93 | o2·=·S |
| 94 | o2·:·PolynomialRing</code></pre> | 94 | o2·:·PolynomialRing</code></pre> |
| Offset 102, 17 lines modified | Offset 102, 17 lines modified | ||
| 102 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) | 102 | o3·=·monomialIdeal·(a*b,·a*d,·b*c*d) |
| 103 | o3·:·MonomialIdeal·of·S</code></pre> | 103 | o3·:·MonomialIdeal·of·S</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomSquareFreeStep·J | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·randomSquareFreeStep·J |
| 107 | o4·=·{monomialIdeal·(a*b*c,·a*d,·b*c*d),·{a*b*c,·a*d,·b*c*d},·{c | 107 | o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*c*d),·{a*b,·a*c,·a*d,·b*c*d},·{c*d, |
| 108 | ·····------------------------------------------------------------------------ | 108 | ·····------------------------------------------------------------------------ |
| 109 | ····· | 109 | ·····b*d,·b*c,·a}} |
| 110 | o4·:·List</code></pre> | 110 | o4·:·List</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ········<div> | 113 | ········<div> |
| 114 | ··········<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 | ··········<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> |
| 115 | ········</div> | 115 | ········</div> |
| Offset 134, 15 lines modified | Offset 134, 15 lines modified | ||
| 134 | o7·=·monomialIdeal·() | 134 | o7·=·monomialIdeal·() |
| 135 | o7·:·MonomialIdeal·of·S</code></pre> | 135 | o7·:·MonomialIdeal·of·S</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01)); | 138 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·T=tally·for·t·from·1·to·5000·list·first·(J=rsfs(J,AlexanderProbability·=>·.01)); |
| 139 | ·--·used·3. | 139 | ·--·used·3.2641s·(cpu);·2.23735s·(thread);·0s·(gc)</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i9·:·#T | 142 | <td>··············<pre><code·class="language-macaulay2">i9·:·#T |
| 143 | o9·=·168</code></pre> | 143 | o9·=·168</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<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·=·1729002815 |
| 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*c,·a*d,·b*c*d),·{a*b*c,·a*d,·b*c*d},·{c | 51 | o4·=·{monomialIdeal·(a*b,·a*c,·a*d,·b*c*d),·{a*b,·a*c,·a*d,·b*c*d},·{c*d, |
| 52 | ·····------------------------------------------------------------------------ | 52 | ·····------------------------------------------------------------------------ |
| 53 | ····· | 53 | ·····b*d,·b*c,·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·3. | 78 | ·--·used·3.2641s·(cpu);·2.23735s·(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 48, 32 lines modified | Offset 48, 33 lines modified | ||
| 48 | ········<div> | 48 | ········<div> |
| 49 | ··········<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 | ··········<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> |
| 50 | ········</div> | 50 | ········</div> |
| 51 | ········<table·class="examples"> | 51 | ········<table·class="examples"> |
| 52 | ··········<tr> | 52 | ··········<tr> |
| 53 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) | 53 | <td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime()) |
| 54 | o1·=·17 | 54 | o1·=·1729002761</code></pre> |
| 55 | </td>··········</tr> | 55 | </td>··········</tr> |
| 56 | ··········<tr> | 56 | ··········<tr> |
| 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101;</code></pre> | 57 | <td>··············<pre><code·class="language-macaulay2">i2·:·kk=ZZ/101;</code></pre> |
| 58 | </td>··········</tr> | 58 | </td>··········</tr> |
| 59 | ··········<tr> | 59 | ··········<tr> |
| 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=kk[vars(0..5)];</code></pre> | 60 | <td>··············<pre><code·class="language-macaulay2">i3·:·S=kk[vars(0..5)];</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ··········<tr> | 62 | ··········<tr> |
| 63 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) | 63 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·tally·for·n·from·1·to·500·list·regularity·randomMonomialIdeal(10:3,S) |
| 64 | ·--·used·1.7 | 64 | ·--·used·1.72837s·(cpu);·1.16954s·(thread);·0s·(gc) |
| 65 | o4·=·Tally{ | 65 | o4·=·Tally{3·=>·2··} |
| 66 | ···········4·=>·46 | ||
| 66 | ···········5·=>·2 | 67 | ···········5·=>·208 |
| 67 | ···········6·=>·1 | 68 | ···········6·=>·164 |
| 68 | ···········7·=>·6 | 69 | ···········7·=>·68 |
| 69 | ···········8·=>·1 | 70 | ···········8·=>·10 |
| 70 | ···········9·=>· | 71 | ···········9·=>·2 |
| 71 | o4·:·Tally</code></pre> | 72 | o4·:·Tally</code></pre> |
| 72 | </td>··········</tr> | 73 | </td>··········</tr> |
| 73 | ········</table> | 74 | ········</table> |
| 74 | ········<div> | 75 | ········<div> |
| 75 | ··········<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> | 76 | ··········<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> |
| 76 | ········</div> | 77 | ········</div> |
| Offset 10, 26 lines modified | Offset 10, 27 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·=·1729002761 |
| 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·1.7 | 20 | ·--·used·1.72837s·(cpu);·1.16954s·(thread);·0s·(gc) |
| 21 | o4·=·Tally{ | 21 | o4·=·Tally{3·=>·2··} |
| 22 | ···········4·=>·46 | ||
| 22 | ···········5·=>·2 | 23 | ···········5·=>·208 |
| 23 | ···········6·=>·1 | 24 | ···········6·=>·164 |
| 24 | ···········7·=>·6 | 25 | ···········7·=>·68 |
| 25 | ···········8·=>·1 | 26 | ···········8·=>·10 |
| 26 | ···········9·=>· | 27 | ···········9·=>·2 |
| 27 | o4·:·Tally | 28 | o4·:·Tally |
| 28 | How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial | 29 | How·does·this·compare·with·the·case·of·binomial·ideals?·or·pure·binomial |
| 29 | ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal" | 30 | ideals?·We·invite·the·reader·to·experiment,·replacing·"randomMonomialIdeal" |
| 30 | above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger | 31 | above·with·"randomBinomialIdeal"·or·"randomPureBinomialIdeal",·or·taking·larger |
| 31 | numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see | 32 | numbers·of·examples.·Click·the·link·"Finding·Extreme·Examples"·below·to·see |
| 32 | some·other,·more·elaborate·ways·to·search. | 33 | 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | VmFyaWFibGVOYW1l | 8 | VmFyaWFibGVOYW1l |
| 9 | #:len=1241 | 9 | #:len=1241 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAib3B0aW9uYWwgaW5wdXQgdG8gY2hvb3Nl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAib3B0aW9uYWwgaW5wdXQgdG8gY2hvb3Nl |
| 11 | IHRoZSBpbmRleGVkIHZhcmlhYmxlIG5hbWUgZm9yIHRoZSBwb2x5bm9taWFsIHJpbmciLCAibGlu | 11 | IHRoZSBpbmRleGVkIHZhcmlhYmxlIG5hbWUgZm9yIHRoZSBwb2x5bm9taWFsIHJpbmciLCAibGlu |
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| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | QXR0ZW1wdHM= | 8 | QXR0ZW1wdHM= |
| 9 | #:len=502 | 9 | #:len=502 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibnVtYmVyIG9mIGF0dGVtcHRzIGluIHRo | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAibnVtYmVyIG9mIGF0dGVtcHRzIGluIHRo |
| 11 | ZSBjb25zdHJ1Y3Rpb24gb2YgYSByYW5kb20gb2JqZWN0IiwgImxpbmVudW0iID0+IDI2MiwgImZp | 11 | ZSBjb25zdHJ1Y3Rpb24gb2YgYSByYW5kb20gb2JqZWN0IiwgImxpbmVudW0iID0+IDI2MiwgImZp |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=49 | 7 | #:len=49 |
| 8 | Y29tcGxldGVMaW5lYXJTeXN0ZW1Pbk5vZGFsUGxhbmVDdXJ2ZShJZGVhbCxMaXN0KQ== | 8 | Y29tcGxldGVMaW5lYXJTeXN0ZW1Pbk5vZGFsUGxhbmVDdXJ2ZShJZGVhbCxMaXN0KQ== |
| 9 | #:len=382 | 9 | #:len=382 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc2LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjc2LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV0ZUxpbmVhclN5c3RlbU9uTm9kYWxQbGFu | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhjb21wbGV0ZUxpbmVhclN5c3RlbU9uTm9kYWxQbGFu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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== |
| 9 | #:len=315 | 9 | #:len=315 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg5MSwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTg5MSwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbZmluZEFOb25aZXJvTWlub3IsUG9pbnRDaGVja0F0 | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbZmluZEFOb25aZXJvTWlub3IsUG9pbnRDaGVja0F0 |
| Offset 5, 17 lines modified | Offset 5, 17 lines modified | ||
| 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 | ·--· | 9 | ·--·1.11553·seconds·elapsed |
| 10 | o4·=·4 | 10 | o4·=·4 |
| 11 | i5·:·elapsedTime·dim·I | 11 | i5·:·elapsedTime·dim·I |
| 12 | ·--· | 12 | ·--·2.51598·seconds·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 | ·--· | 39 | ·--·1.32477·seconds·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 | ·--· | 31 | ·--·2.43731·seconds·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 | ·--·1.87723·seconds·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 95, 21 lines modified | Offset 95, 21 lines modified | ||
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·I=ideal·random(S^1,S^{-2,-2,-2,-2})+(ideal·random(2,S))^2; |
| 97 | o3·:·Ideal·of·S</code></pre> | 97 | o3·:·Ideal·of·S</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·dimViaBezout(I) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·dimViaBezout(I) |
| 101 | ·--· | 101 | ·--·1.11553·seconds·elapsed |
| 102 | o4·=·4</code></pre> | 102 | o4·=·4</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·dim·I | 105 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·dim·I |
| 106 | ·--· | 106 | ·--·2.51598·seconds·elapsed |
| 107 | o5·=·4</code></pre> | 107 | o5·=·4</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ········</table> | 109 | ········</table> |
| 110 | ········<div> | 110 | ········<div> |
| 111 | ··········<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 | ··········<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> |
| 112 | ········</div> | 112 | ········</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 | ·--· | 39 | ·--·1.11553·seconds·elapsed |
| 40 | o4·=·4 | 40 | o4·=·4 |
| 41 | i5·:·elapsedTime·dim·I | 41 | i5·:·elapsedTime·dim·I |
| 42 | ·--· | 42 | ·--·2.51598·seconds·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 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | ··········<tr> | 150 | ··········<tr> |
| 151 | <td>··············<pre><code·class="language-macaulay2">i9·:·J·=·I; | 151 | <td>··············<pre><code·class="language-macaulay2">i9·:·J·=·I; |
| 152 | o9·:·Ideal·of·T</code></pre> | 152 | o9·:·Ideal·of·T</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <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 | <td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime(while·(i·<·10)·and·dim·J·>·1·do·(i·=·i+1;·J·=·extendIdealByNonZeroMinor(4,·M,·J))·); |
| 156 | ·--· | 156 | ·--·1.32477·seconds·elapsed</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim·J | 159 | <td>··············<pre><code·class="language-macaulay2">i11·:·dim·J |
| 160 | o11·=·1</code></pre> | 160 | o11·=·1</code></pre> |
| 161 | </td>··········</tr> | 161 | </td>··········</tr> |
| 162 | ··········<tr> | 162 | ··········<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 | ·--· | 86 | ·--·1.32477·seconds·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 142, 25 lines modified | Offset 142, 25 lines modified | ||
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·I=minors(2,random(S^3,S^{3:-1})); | 143 | <td>··············<pre><code·class="language-macaulay2">i7·:·I=minors(2,random(S^3,S^{3:-1})); |
| 144 | o7·:·Ideal·of·S</code></pre> | 144 | o7·:·Ideal·of·S</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ··········<tr> | 146 | ··········<tr> |
| 147 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable) | 147 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>MultiplicationTable) |
| 148 | ·--· | 148 | ·--·2.43731·seconds·elapsed |
| 149 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, | 149 | o8·=·{{-4,·-35,·-7,·0,·0,·1,·5,·-13,·0,·-47,·0,·41,·0,·-51,·-46,·35,·0,·0, |
| 150 | ·····------------------------------------------------------------------------ | 150 | ·····------------------------------------------------------------------------ |
| 151 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} | 151 | ·····-47,·14,·-30,·42,·30,·4,·-41,·24,·0,·0,·15,·20,·1}} |
| 152 | o8·:·List</code></pre> | 152 | o8·:·List</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose) | 155 | <td>··············<pre><code·class="language-macaulay2">i9·:·elapsedTime·randomPoints(I,·Strategy=>LinearIntersection,·DecompositionStrategy=>Decompose) |
| 156 | ·--· | 156 | ·--·1.87723·seconds·elapsed |
| 157 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, | 157 | o9·=·{{11,·9,·-9,·-15,·-7,·27,·19,·-36,·48,·26,·-4,·3,·29,·-8,·7,·-32,·16, |
| 158 | ·····------------------------------------------------------------------------ | 158 | ·····------------------------------------------------------------------------ |
| 159 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} | 159 | ·····11,·7,·7,·25,·-14,·-39,·17,·-16,·4,·-50,·-12,·21,·-50,·51}} |
| 160 | o9·:·List</code></pre> | 160 | o9·:·List</code></pre> |
| 161 | </td>··········</tr> | 161 | </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 | ·--· | 73 | ·--·2.43731·seconds·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 | ·--·1.87723·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:14·2024 |
| 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=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·0. | 53 | ·--·used·0.462029s·(cpu);·0.33582s·(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 172, 15 lines modified | Offset 172, 15 lines modified | ||
| 172 | ··········<tr> | 172 | ··········<tr> |
| 173 | <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 | <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}}); |
| 174 | o13·:·RingMap·Q·<--·Q</code></pre> | 174 | o13·:·RingMap·Q·<--·Q</code></pre> |
| 175 | </td>··········</tr> | 175 | </td>··········</tr> |
| 176 | ··········<tr> | 176 | ··········<tr> |
| 177 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) | 177 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·inverseOfMap(phi,CheckBirational=>false,·Verbosity=>0) |
| 178 | ·--·used·0. | 178 | ·--·used·0.462029s·(cpu);·0.33582s·(thread);·0s·(gc) |
| 179 | ································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 | ································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 |
| 180 | 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·=·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} |
| 181 | o14·:·RationalMapping</code></pre> | 181 | o14·:·RationalMapping</code></pre> |
| 182 | </td>··········</tr> | 182 | </td>··········</tr> |
| 183 | ········</table> | 183 | ········</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·0. | 101 | ·--·used·0.462029s·(cpu);·0.33582s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00403036s·(cpu);·0.00271963s·(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·0. | 145 | ·--·used·0.814057s·(cpu);·0.693914s·(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·0.22 | 152 | ·--·used·0.224867s·(cpu);·0.166058s·(thread);·0s·(gc) |
| 153 | o35·=·31 | 153 | o35·=·31 |
| 154 | i36·:· | 154 | i36·:· |
| Offset 168, 15 lines modified | Offset 168, 15 lines modified | ||
| 168 | ················ZZ | 168 | ················ZZ |
| 169 | o13·:·Ideal·of·---[u·..u··] | 169 | o13·:·Ideal·of·---[u·..u··] |
| 170 | ···············101··0···10</code></pre> | 170 | ···············101··0···10</code></pre> |
| 171 | </td>··········</tr> | 171 | </td>··········</tr> |
| 172 | ··········<tr> | 172 | ··········<tr> |
| 173 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalPoints(I,·Amount·=>·true) | 173 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·rationalPoints(I,·Amount·=>·true) |
| 174 | ·--·used·0.00 | 174 | ·--·used·0.00403036s·(cpu);·0.00271963s·(thread);·0s·(gc) |
| 175 | o14·=·110462212541120451001</code></pre> | 175 | o14·=·110462212541120451001</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ········</table> | 177 | ········</table> |
| 178 | ········<div> | 178 | ········<div> |
| 179 | ··········<h3>Over·number·fields</h3> | 179 | ··········<h3>Over·number·fields</h3> |
| 180 | ········</div> | 180 | ········</div> |
| Offset 309, 15 lines modified | Offset 309, 15 lines modified | ||
| 309 | ··········<tr> | 309 | ··········<tr> |
| 310 | <td>··············<pre><code·class="language-macaulay2">i31·:·nodes·=·I·+·ideal·jacobian·I; | 310 | <td>··············<pre><code·class="language-macaulay2">i31·:·nodes·=·I·+·ideal·jacobian·I; |
| 311 | o31·:·Ideal·of·R</code></pre> | 311 | o31·:·Ideal·of·R</code></pre> |
| 312 | </td>··········</tr> | 312 | </td>··········</tr> |
| 313 | ··········<tr> | 313 | ··········<tr> |
| 314 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); | 314 | <td>··············<pre><code·class="language-macaulay2">i32·:·time·rationalPoints(variety·nodes,·Split=>true,·Verbose=>true); |
| 315 | ·--·used·0. | 315 | ·--·used·0.814057s·(cpu);·0.693914s·(thread);·0s·(gc) |
| 316 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)</code></pre> | 316 | --·base·change·to·the·field·QQ[a]/(a^8-40*a^6+230*a^4-200*a^2+25)</code></pre> |
| 317 | </td>··········</tr> | 317 | </td>··········</tr> |
| 318 | ··········<tr> | 318 | ··········<tr> |
| 319 | <td>··············<pre><code·class="language-macaulay2">i33·:·#oo | 319 | <td>··············<pre><code·class="language-macaulay2">i33·:·#oo |
| 320 | o33·=·31</code></pre> | 320 | o33·=·31</code></pre> |
| 321 | </td>··········</tr> | 321 | </td>··········</tr> |
| Offset 329, 15 lines modified | Offset 329, 15 lines modified | ||
| 329 | ··········<tr> | 329 | ··········<tr> |
| 330 | <td>··············<pre><code·class="language-macaulay2">i34·:·nodes'·=·baseChange_32003·nodes; | 330 | <td>··············<pre><code·class="language-macaulay2">i34·:·nodes'·=·baseChange_32003·nodes; |
| 331 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]</code></pre> | 331 | o34·:·Ideal·of·GF·1048969271299456081[x..z,·w]</code></pre> |
| 332 | </td>··········</tr> | 332 | </td>··········</tr> |
| 333 | ··········<tr> | 333 | ··········<tr> |
| 334 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) | 334 | <td>··············<pre><code·class="language-macaulay2">i35·:·time·#rationalPoints(variety·nodes',·Split=>true,·Verbose=>true) |
| 335 | ·--·used·0.22 | 335 | ·--·used·0.224867s·(cpu);·0.166058s·(thread);·0s·(gc) |
| 336 | o35·=·31</code></pre> | 336 | o35·=·31</code></pre> |
| 337 | </td>··········</tr> | 337 | </td>··········</tr> |
| 338 | ········</table> | 338 | ········</table> |
| 339 | ······</div> | 339 | ······</div> |
| 340 | ······<div> | 340 | ······<div> |
| 341 | ········<h2>Caveat</h2> | 341 | ········<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·0.00403036s·(cpu);·0.00271963s·(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·0. | 202 | ·--·used·0.814057s·(cpu);·0.693914s·(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·0.22 | 210 | ·--·used·0.224867s·(cpu);·0.166058s·(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* |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bm9ybWFsQ29uZSguLi4sVmFyaWFibGU9Pi4uLik= | 8 | bm9ybWFsQ29uZSguLi4sVmFyaWFibGU9Pi4uLik= |
| 9 | #:len=300 | 9 | #:len=300 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk3Niwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTk3Niwgc3ltYm9sIERvY3VtZW50VGFn |
| 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbbm9ybWFsQ29uZSxWYXJpYWJsZV0sIm5vcm1hbENv | 11 | ID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHtbbm9ybWFsQ29uZSxWYXJpYWJsZV0sIm5vcm1hbENv |
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| 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·0.771745s·(cpu);·0.659922s·(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·0. | 61 | ·--·used·0.723452s·(cpu);·0.545371s·(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·1.057s·(cpu);·0.914785s·(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·1.19217s·(cpu);·0.99256s·(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·0.08 | 18 | ·--·used·0.0807288s·(cpu);·0.0398065s·(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·0.1 | 22 | ·--·used·0.105479s·(cpu);·0.10574s·(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·0.0 | 51 | ·--·used·0.0196562s·(cpu);·0.0208639s·(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·0.0 | 55 | ·--·used·0.00487477s·(cpu);·0.00744581s·(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 486, 15 lines modified | Offset 486, 15 lines modified | ||
| 486 | ········</table> | 486 | ········</table> |
| 487 | ········<div> | 487 | ········<div> |
| 488 | ··········<p>We·compute·the·singular·locus·once·again:</p> | 488 | ··········<p>We·compute·the·singular·locus·once·again:</p> |
| 489 | ········</div> | 489 | ········</div> |
| 490 | ········<table·class="examples"> | 490 | ········<table·class="examples"> |
| 491 | ··········<tr> | 491 | ··········<tr> |
| 492 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; | 492 | <td>··············<pre><code·class="language-macaulay2">i48·:·time·sing2·=·ideal·singularLocus·strictTransform2; |
| 493 | ·--·used·0. | 493 | ·--·used·0.771745s·(cpu);·0.659922s·(thread);·0s·(gc) |
| 494 | ·················ZZ | 494 | ·················ZZ |
| 495 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] | 495 | o48·:·Ideal·of·-----[p·..p·,·w·..w·,·x..y] |
| 496 | ···············32003··0···2···0···1</code></pre> | 496 | ···············32003··0···2···0···1</code></pre> |
| 497 | </td>··········</tr> | 497 | </td>··········</tr> |
| 498 | ··········<tr> | 498 | ··········<tr> |
| 499 | <td>··············<pre><code·class="language-macaulay2">i49·:·saturate(sing2,·sub(irrelTot,·ring·sing2)) | 499 | <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·0.771745s·(cpu);·0.659922s·(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 139, 15 lines modified | Offset 139, 15 lines modified | ||
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·minors(n-1,·M); | 140 | <td>··············<pre><code·class="language-macaulay2">i6·:·I·=·minors(n-1,·M); |
| 141 | o6·:·Ideal·of·S</code></pre> | 141 | o6·:·Ideal·of·S</code></pre> |
| 142 | </td>··········</tr> | 142 | </td>··········</tr> |
| 143 | ··········<tr> | 143 | ··········<tr> |
| 144 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. | 144 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·rI·=·expectedReesIdeal·I;·--·n=·5·case·takes·<·1·sec. |
| 145 | ·--·used·0. | 145 | ·--·used·0.723452s·(cpu);·0.545371s·(thread);·0s·(gc) |
| 146 | o7·:·Ideal·of·S[w·..w·] | 146 | o7·:·Ideal·of·S[w·..w·] |
| 147 | ·················0···4</code></pre> | 147 | ·················0···4</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i8·:·kk·=·ZZ/101;</code></pre> | 150 | <td>··············<pre><code·class="language-macaulay2">i8·:·kk·=·ZZ/101;</code></pre> |
| 151 | </td>··········</tr> | 151 | </td>··········</tr> |
| Offset 163, 22 lines modified | Offset 163, 22 lines modified | ||
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i11·:·I·=·minors(3,m); | 164 | <td>··············<pre><code·class="language-macaulay2">i11·:·I·=·minors(3,m); |
| 165 | o11·:·Ideal·of·S</code></pre> | 165 | o11·:·Ideal·of·S</code></pre> |
| 166 | </td>··········</tr> | 166 | </td>··········</tr> |
| 167 | ··········<tr> | 167 | ··········<tr> |
| 168 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·reesIdeal·(I,·I_0); | 168 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·reesIdeal·(I,·I_0); |
| 169 | ·--·used·1. | 169 | ·--·used·1.057s·(cpu);·0.914785s·(thread);·0s·(gc) |
| 170 | o12·:·Ideal·of·S[w·..w·] | 170 | o12·:·Ideal·of·S[w·..w·] |
| 171 | ··················0···3</code></pre> | 171 | ··················0···3</code></pre> |
| 172 | </td>··········</tr> | 172 | </td>··········</tr> |
| 173 | ··········<tr> | 173 | ··········<tr> |
| 174 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); | 174 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·reesIdeal·(I,·I_0,·Jacobian·=>false); |
| 175 | ·--·used·1. | 175 | ·--·used·1.19217s·(cpu);·0.99256s·(thread);·0s·(gc) |
| 176 | o13·:·Ideal·of·S[w·..w·] | 176 | o13·:·Ideal·of·S[w·..w·] |
| 177 | ··················0···3</code></pre> | 177 | ··················0···3</code></pre> |
| 178 | </td>··········</tr> | 178 | </td>··········</tr> |
| 179 | ········</table> | 179 | ········</table> |
| 180 | ······</div> | 180 | ······</div> |
| 181 | ······<div> | 181 | ······<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·0. | 91 | ·--·used·0.723452s·(cpu);·0.545371s·(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·1.057s·(cpu);·0.914785s·(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·1.19217s·(cpu);·0.99256s·(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 114, 22 lines modified | Offset 114, 22 lines modified | ||
| 114 | ·····-·x·x·x·,·x··-·x·x·) | 114 | ·····-·x·x·x·,·x··-·x·x·) |
| 115 | ········0·2·4···1····0·4 | 115 | ········0·2·4···1····0·4 |
| 116 | o3·:·Ideal·of·S</code></pre> | 116 | o3·:·Ideal·of·S</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·V1·=·reesIdeal·i; | 119 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·V1·=·reesIdeal·i; |
| 120 | ·--·used·0.08 | 120 | ·--·used·0.0807288s·(cpu);·0.0398065s·(thread);·0s·(gc) |
| 121 | o4·:·Ideal·of·S[w·..w·] | 121 | o4·:·Ideal·of·S[w·..w·] |
| 122 | ·················0···6</code></pre> | 122 | ·················0···6</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·V2·=·reesIdeal(i,i_0); | 125 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·V2·=·reesIdeal(i,i_0); |
| 126 | ·--·used·0.1 | 126 | ·--·used·0.105479s·(cpu);·0.10574s·(thread);·0s·(gc) |
| 127 | o5·:·Ideal·of·S[w·..w·] | 127 | o5·:·Ideal·of·S[w·..w·] |
| 128 | ·················0···6</code></pre> | 128 | ·················0···6</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ········</table> | 130 | ········</table> |
| 131 | ········<div> | 131 | ········<div> |
| 132 | ··········<p>The·following·example·shows·how·we·handle·degrees</p> | 132 | ··········<p>The·following·example·shows·how·we·handle·degrees</p> |
| Offset 158, 22 lines modified | Offset 158, 22 lines modified | ||
| 158 | ·············2········2 | 158 | ·············2········2 |
| 159 | o8·=·ideal·(a·,·a*b,·b·) | 159 | o8·=·ideal·(a·,·a*b,·b·) |
| 160 | o8·:·Ideal·of·S</code></pre> | 160 | o8·:·Ideal·of·S</code></pre> |
| 161 | </td>··········</tr> | 161 | </td>··········</tr> |
| 162 | ··········<tr> | 162 | ··········<tr> |
| 163 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·I1·=·reesIdeal·i; | 163 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·I1·=·reesIdeal·i; |
| 164 | ·--·used·0.0 | 164 | ·--·used·0.0196562s·(cpu);·0.0208639s·(thread);·0s·(gc) |
| 165 | o9·:·Ideal·of·S[w·..w·] | 165 | o9·:·Ideal·of·S[w·..w·] |
| 166 | ·················0···2</code></pre> | 166 | ·················0···2</code></pre> |
| 167 | </td>··········</tr> | 167 | </td>··········</tr> |
| 168 | ··········<tr> | 168 | ··········<tr> |
| 169 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·I2·=·reesIdeal(i,i_0); | 169 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·I2·=·reesIdeal(i,i_0); |
| 170 | ·--·used·0.0 | 170 | ·--·used·0.00487477s·(cpu);·0.00744581s·(thread);·0s·(gc) |
| 171 | o10·:·Ideal·of·S[w·..w·] | 171 | o10·:·Ideal·of·S[w·..w·] |
| 172 | ··················0···2</code></pre> | 172 | ··················0···2</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i11·:·transpose·gens·I1 | 175 | <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·0.08 | 58 | ·--·used·0.0807288s·(cpu);·0.0398065s·(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·0.1 | 62 | ·--·used·0.105479s·(cpu);·0.10574s·(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·0.0 | 87 | ·--·used·0.0196562s·(cpu);·0.0208639s·(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·0.0 | 91 | ·--·used·0.00487477s·(cpu);·0.00744581s·(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 | ||
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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=7 | 7 | #:len=7 |
| 8 | S1NFbnRyeQ== | 8 | S1NFbnRyeQ== |
| 9 | #:len=2433 | 9 | #:len=2433 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZW50cnkgZnJvbSB0aGUgS3JldXpl | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiYW4gZW50cnkgZnJvbSB0aGUgS3JldXpl |
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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=10 | 7 | #:len=10 |
| 8 | UmVndWxhcml0eQ== | 8 | UmVndWxhcml0eQ== |
| 9 | #:len=797 | 9 | #:len=797 |
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| 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·=·.17 | 75 | o8·=·.176259513375 |
| 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·=·.05 | 90 | o11·=·.0510386394533334 |
| 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·0.00207317s·(cpu);·0.00199348s·(thread);·0s·(gc) |
| 94 | o12·=·4 | 94 | o12·=·4 |
| 95 | i13·:· | 95 | i13·:· |
| Offset 166, 15 lines modified | Offset 166, 15 lines modified | ||
| 166 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 | 166 | ······0·1·3···0····0·1····1·2····0·2·5···0····2····0·5 |
| 167 | o7·:·Ideal·of·R</code></pre> | 167 | o7·:·Ideal·of·R</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i8·:·benchmark·"mRegularity·I1" | 170 | <td>··············<pre><code·class="language-macaulay2">i8·:·benchmark·"mRegularity·I1" |
| 171 | o8·=·.17 | 171 | o8·=·.176259513375 |
| 172 | o8·:·RR·(of·precision·53)</code></pre> | 172 | o8·:·RR·(of·precision·53)</code></pre> |
| 173 | </td>··········</tr> | 173 | </td>··········</tr> |
| 174 | ········</table> | 174 | ········</table> |
| 175 | ········<p>This·is·an·example·where·regularity·is·faster·than·mRegularity.</p> | 175 | ········<p>This·is·an·example·where·regularity·is·faster·than·mRegularity.</p> |
| 176 | ········<table·class="examples"> | 176 | ········<table·class="examples"> |
| 177 | ··········<tr> | 177 | ··········<tr> |
| Offset 188, 21 lines modified | Offset 188, 21 lines modified | ||
| 188 | <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 | <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); |
| 189 | o10·:·Ideal·of·R</code></pre> | 189 | o10·:·Ideal·of·R</code></pre> |
| 190 | </td>··········</tr> | 190 | </td>··········</tr> |
| 191 | ··········<tr> | 191 | ··········<tr> |
| 192 | <td>··············<pre><code·class="language-macaulay2">i11·:·benchmark·"·mRegularity·I2" | 192 | <td>··············<pre><code·class="language-macaulay2">i11·:·benchmark·"·mRegularity·I2" |
| 193 | o11·=·.05 | 193 | o11·=·.0510386394533334 |
| 194 | o11·:·RR·(of·precision·53)</code></pre> | 194 | o11·:·RR·(of·precision·53)</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·regularity·I2·· | 197 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·regularity·I2·· |
| 198 | ·--·used·0.00 | 198 | ·--·used·0.00207317s·(cpu);·0.00199348s·(thread);·0s·(gc) |
| 199 | o12·=·4</code></pre> | 199 | o12·=·4</code></pre> |
| 200 | </td>··········</tr> | 200 | </td>··········</tr> |
| 201 | ········</table> | 201 | ········</table> |
| 202 | ········<p>This·symbol·is·provided·by·the·package·Regularity.</p> | 202 | ········<p>This·symbol·is·provided·by·the·package·Regularity.</p> |
| 203 | ······</div> | 203 | ······</div> |
| 204 | ······<div> | 204 | ······<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·=·.17 | 100 | o8·=·.176259513375 |
| 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·=·.05 | 110 | o11·=·.0510386394533334 |
| 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·0.00207317s·(cpu);·0.00199348s·(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 | ||
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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=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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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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=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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.0378308s·(cpu);·0.0379953s·(thread);·0s·(gc) |
| 11 | i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) | 11 | i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) |
| 12 | ·--·used·0.0 | 12 | ·--·used·0.0472988s·(cpu);·0.0482578s·(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·0.1 | 42 | ·--·used·0.113155s·(cpu);·0.0782479s·(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·0.11 | 45 | ·--·used·0.117417s·(cpu);·0.0768279s·(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·0.0 | 14 | ·--·used·0.0409216s·(cpu);·0.0431017s·(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·0.03 | 77 | ·--·used·0.0334015s·(cpu);·0.0340461s·(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·0.1 | 122 | ·--·used·0.105239s·(cpu);·0.0768218s·(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·0.0575764s·(cpu);·0.0594563s·(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·4.21641s·(cpu);·4.06274s·(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·1. | 149 | ·--·used·1.00252s·(cpu);·0.927833s·(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. | 152 | ·--·used·0.208352s·(cpu);·0.171378s·(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·0.177582s·(cpu);·0.141898s·(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·0.008 | 8 | ·--·used·0.00811395s·(cpu);·0.00828375s·(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·0.00734662s·(cpu);·0.00874633s·(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·0.3 | 64 | ·--·used·0.311198s·(cpu);·0.309128s·(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·0.10 | 14 | ·--·used·0.101423s·(cpu);·0.0983508s·(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·0.160003s·(cpu);·0.123004s·(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·0.0468112s·(cpu);·0.0453195s·(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·0.548179s·(cpu);·0.509567s·(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·0.04 | 11 | ·--·used·0.0404765s·(cpu);·0.0401008s·(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·0.0 | 61 | ·--·used·0.0399989s·(cpu);·0.0410957s·(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·0.06 | 89 | ·--·used·0.0623666s·(cpu);·0.0312445s·(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·0.02 | 135 | ·--·used·0.0219934s·(cpu);·0.0220084s·(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·0.0439957s·(cpu);·0.0440817s·(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·0.00801093s·(cpu);·0.00843177s·(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·0.00476692s·(cpu);·0.00675189s·(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·0.01 | 36 | ·--·used·0.0158583s·(cpu);·0.0166802s·(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·0.000426512s·(cpu);·0.00294634s·(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·0.00307859s·(cpu);·0.00214885s·(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·0.00394229s·(cpu);·0.00350562s·(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·0.0 | 25 | ·--·used·0.0265286s·(cpu);·0.0277247s·(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·0.0 | 44 | ·--·used·0.0320018s·(cpu);·0.0322529s·(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·0.2 | 50 | ·--·used·0.230378s·(cpu);·0.186838s·(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·0.1 | 40 | ·--·used·0.178941s·(cpu);·0.141518s·(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·0.1002s·(cpu);·0.0 | 61 | ·--·used·0.103026s·(cpu);·0.0648384s·(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·0.224206s·(cpu);·0.227436s·(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·0.45928s·(cpu);·0.426343s·(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·0.021 | 14 | ·--·used·0.0216199s·(cpu);·0.0210891s·(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·1. | 69 | ·--·used·1.77038s·(cpu);·1.45242s·(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·0.3 | 1695 | ·--·used·0.369793s·(cpu);·0.301967s·(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·0.0280003s·(cpu);·0.0289408s·(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·0.06 | 32 | ·--·used·0.0604696s·(cpu);·0.0604087s·(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·0.03 | 74 | ·--·used·0.0303502s·(cpu);·0.0313808s·(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·0.08 | 82 | ·--·used·0.0876205s·(cpu);·0.0532247s·(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·0.1 | 90 | ·--·used·0.122082s·(cpu);·0.0820454s·(thread);·0s·(gc) |
| 91 | i8·:· | 91 | i8·:· |
| Offset 88, 22 lines modified | Offset 88, 22 lines modified | ||
| 88 | ············0·1····2·3 | 88 | ············0·1····2·3 |
| 89 | o2·:·Ideal·of·QQ[x·..x·] | 89 | o2·:·Ideal·of·QQ[x·..x·] |
| 90 | ··················0···3</code></pre> | 90 | ··················0···3</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); | 93 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(P1xP1xP2,P1xP1xP2')·=·cayleyTrick(P1xP1,2); |
| 94 | ·--·used·0.0 | 94 | ·--·used·0.0378308s·(cpu);·0.0379953s·(thread);·0s·(gc)</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ········</table> | 96 | ········</table> |
| 97 | ········<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 | ········<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> |
| 98 | ········<table·class="examples"> | 98 | ········<table·class="examples"> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) | 100 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(P1xP1xP1,P1xP1xP1')·=·cayleyTrick(P1xP1,1) |
| 101 | ·--·used·0.0 | 101 | ·--·used·0.0472988s·(cpu);·0.0482578s·(thread);·0s·(gc) |
| 102 | ··········································································· | 102 | ··········································································· |
| 103 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, | 103 | o4·=·(ideal·(x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···, |
| 104 | ··············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 | ··············0,3·1,2····0,2·1,3···1,0·1,1····1,2·1,3···0,3·1,1····0,1·1,3· |
| 105 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 106 | ············································································ | 106 | ············································································ |
| 107 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· | 107 | ·····x···x····-·x···x···,·x···x····-·x···x···,·x···x····-·x···x···,·x···x··· |
| Offset 128, 22 lines modified | Offset 128, 22 lines modified | ||
| 128 | o4·:·Sequence</code></pre> | 128 | o4·:·Sequence</code></pre> |
| 129 | </td>··········</tr> | 129 | </td>··········</tr> |
| 130 | ········</table> | 130 | ········</table> |
| 131 | ········<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 | ········<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> |
| 132 | ········<table·class="examples"> | 132 | ········<table·class="examples"> |
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); | 134 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·cayleyTrick(P1xP1,1,Duality=>true); |
| 135 | ·--·used·0.1 | 135 | ·--·used·0.113155s·(cpu);·0.0782479s·(thread);·0s·(gc)</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))</code></pre> | 138 | <td>··············<pre><code·class="language-macaulay2">i6·:·assert(oo·==·(P1xP1xP1,P1xP1xP1'))</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); | 141 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·cayleyTrick(P1xP1,2,Duality=>true); |
| 142 | ·--·used·0.11 | 142 | ·--·used·0.117417s·(cpu);·0.0768279s·(thread);·0s·(gc)</code></pre> |
| 143 | </td>··········</tr> | 143 | </td>··········</tr> |
| 144 | ··········<tr> | 144 | ··········<tr> |
| 145 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))</code></pre> | 145 | <td>··············<pre><code·class="language-macaulay2">i8·:·assert(oo·==·(P1xP1xP2,P1xP1xP2'))</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ········</table> | 147 | ········</table> |
| 148 | ······</div> | 148 | ······</div> |
| 149 | ······<div> | 149 | ······<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·0.0378308s·(cpu);·0.0379953s·(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·0.0 | 49 | ·--·used·0.0472988s·(cpu);·0.0482578s·(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·0.1 | 80 | ·--·used·0.113155s·(cpu);·0.0782479s·(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·0.11 | 83 | ·--·used·0.117417s·(cpu);·0.0768279s·(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 88, 15 lines modified | Offset 88, 15 lines modified | ||
| 88 | ·············0····1····2····3···0·1····1·2····2·3 | 88 | ·············0····1····2····3···0·1····1·2····2·3 |
| 89 | o2·:·Ideal·of·P3</code></pre> | 89 | o2·:·Ideal·of·P3</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·Chow·equations·of·C | 92 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·Chow·equations·of·C |
| 93 | ·····time·eqsC·=·chowEquations·chowForm·C | 93 | ·····time·eqsC·=·chowEquations·chowForm·C |
| 94 | ·--·used·0.0 | 94 | ·--·used·0.0409216s·(cpu);·0.0431017s·(thread);·0s·(gc) |
| 95 | ·············2·2····2·2····2·2····4················2······2·2···2······ | 95 | ·············2·2····2·2····2·2····4················2······2·2···2······ |
| 96 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ | 96 | o3·=·ideal·(x·x··+·x·x··+·x·x··+·x·,·x·x·x·x··+·x·x·x··+·x·x·,·x·x·x··+ |
| 97 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3·· | 97 | ·············0·3····1·3····2·3····3···0·1·2·3····1·2·3····2·3···0·2·3·· |
| 98 | ·····------------------------------------------------------------------------ | 98 | ·····------------------------------------------------------------------------ |
| 99 | ······2········3···········2·········2······3···3·········2··········2····2·2 | 99 | ······2········3···········2·········2······3···3·········2··········2····2·2 |
| 100 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x· | 100 | ·····x·x·x··+·x·x··-·2x·x·x··-·2x·x·x··-·x·x·,·x·x··+·2x·x·x··-·x·x·x··+·x·x· |
| Offset 154, 15 lines modified | Offset 154, 15 lines modified | ||
| 154 | ·············1····0·2···2····0·1·3···1·2····0·3 | 154 | ·············1····0·2···2····0·1·3···1·2····0·3 |
| 155 | o5·:·Ideal·of·P3</code></pre> | 155 | o5·:·Ideal·of·P3</code></pre> |
| 156 | </td>··········</tr> | 156 | </td>··········</tr> |
| 157 | ··········<tr> | 157 | ··········<tr> |
| 158 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·Chow·equations·of·D | 158 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·Chow·equations·of·D |
| 159 | ·····time·eqsD·=·chowEquations·chowForm·D | 159 | ·····time·eqsD·=·chowEquations·chowForm·D |
| 160 | ·--·used·0.03 | 160 | ·--·used·0.0334015s·(cpu);·0.0340461s·(thread);·0s·(gc) |
| 161 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2· | 161 | ·············4······3·2·····3········2·2·····3······2···2···2·2······2···2· |
| 162 | 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 | o6·=·ideal·(x·x··-·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·,·x·x·x··-·x·x·x·, |
| 163 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3· | 163 | ·············2·3····1·3···1·2·3····0·1·3···0·2·3····0·1·3···1·2·3····0·1·3· |
| 164 | ·····------------------------------------------------------------------------ | 164 | ·····------------------------------------------------------------------------ |
| 165 | ··········2······3·2···3········3·2···4·········2·········2·2·······3···· | 165 | ··········2······3·2···3········3·2···4·········2·········2·2·······3···· |
| 166 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- | 166 | ·····x·x·x·x··-·x·x·,·x·x·x··-·x·x·,·x·x··-·4x·x·x·x··+·3x·x·x·,·x·x·x··- |
| Offset 206, 28 lines modified | Offset 206, 28 lines modified | ||
| 206 | ············0·1····2·3 | 206 | ············0·1····2·3 |
| 207 | o9·:·Ideal·of·P3</code></pre> | 207 | o9·:·Ideal·of·P3</code></pre> |
| 208 | </td>··········</tr> | 208 | </td>··········</tr> |
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·tangential·Chow·forms·of·Q | 210 | <td>··············<pre><code·class="language-macaulay2">i10·:·--·tangential·Chow·forms·of·Q |
| 211 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2)) | 211 | ······time·(W0,W1,W2)·=·(tangentialChowForm(Q,0),tangentialChowForm(Q,1),tangentialChowForm(Q,2)) |
| 212 | ·--·used·0.1 | 212 | ·--·used·0.105239s·(cpu);·0.0768218s·(thread);·0s·(gc) |
| 213 | ·····················2······························2 | 213 | ·····················2······························2 |
| 214 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ | 214 | o10·=·(x·x··+·x·x·,·x····-·4x···x····+·2x···x····+·x···,·x·····x······+ |
| 215 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3·· | 215 | ········0·1····2·3···0,1·····0,2·1,3·····0,1·2,3····2,3···0,1,2·0,1,3·· |
| 216 | ······----------------------------------------------------------------------- | 216 | ······----------------------------------------------------------------------- |
| 217 | ······x·····x·····) | 217 | ······x·····x·····) |
| 218 | ·······0,2,3·1,2,3 | 218 | ·······0,2,3·1,2,3 |
| 219 | o10·:·Sequence</code></pre> | 219 | o10·:·Sequence</code></pre> |
| 220 | </td>··········</tr> | 220 | </td>··········</tr> |
| 221 | ··········<tr> | 221 | ··········<tr> |
| 222 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2)) | 222 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·(Q,Q,Q)·==·(chowEquations(W0,0),chowEquations(W1,1),chowEquations(W2,2)) |
| 223 | ·--·used·0. | 223 | ·--·used·0.0575764s·(cpu);·0.0594563s·(thread);·0s·(gc) |
| 224 | o11·=·true</code></pre> | 224 | o11·=·true</code></pre> |
| 225 | </td>··········</tr> | 225 | </td>··········</tr> |
| 226 | ········</table> | 226 | ········</table> |
| 227 | ········<p>Note·that·<span·class="tt">chowEquations(W,0)</span>·is·not·the·same·as·<span·class="tt">chowEquations·W</span>.</p> | 227 | ········<p>Note·that·<span·class="tt">chowEquations(W,0)</span>·is·not·the·same·as·<span·class="tt">chowEquations·W</span>.</p> |
| 228 | ······</div> | 228 | ······</div> |
| 229 | ······<div·class="waystouse"> | 229 | ······<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·0.0 | 35 | ·--·used·0.0409216s·(cpu);·0.0431017s·(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·0.03 | 95 | ·--·used·0.0334015s·(cpu);·0.0340461s·(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·0.1 | 142 | ·--·used·0.105239s·(cpu);·0.0768218s·(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·0.0575764s·(cpu);·0.0594563s·(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 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ···············ZZ | 100 | ···············ZZ |
| 101 | o2·:·Ideal·of·----[x·..x·] | 101 | o2·:·Ideal·of·----[x·..x·] |
| 102 | ··············3331··0···5</code></pre> | 102 | ··············3331··0···5</code></pre> |
| 103 | </td>··········</tr> | 103 | </td>··········</tr> |
| 104 | ··········<tr> | 104 | ··········<tr> |
| 105 | <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 | <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) |
| 106 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) | 106 | ·····time·ChowV·=·chowForm(V,AffineChartGrass=>{1,2,3}) |
| 107 | ·--·used·4. | 107 | ·--·used·4.21641s·(cpu);·4.06274s·(thread);·0s·(gc) |
| 108 | ······4···············2··············2·····2···············2············ | 108 | ······4···············2··············2·····2···············2············ |
| 109 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ | 109 | o3·=·x······+·2x·····x·····x······+·x·····x······-·2x·····x·····x······+ |
| 110 | ······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 | ······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·· |
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| 112 | ······2·····2··············2······································· | 112 | ······2·····2··············2······································· |
| 113 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ | 113 | ·····x·····x······-·x·····x·····x······+·x·····x·····x·····x······+ |
| Offset 228, 20 lines modified | Offset 228, 20 lines modified | ||
| 228 | o3·:·------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 228 | o3·:·------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 229 | ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·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 | ·····(x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x······-·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····,·x·····x······-·x·····x······+·x·····x·····) |
| 230 | ·······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 | ·······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> |
| 231 | </td>··········</tr> | 231 | </td>··········</tr> |
| 232 | ··········<tr> | 232 | ··········<tr> |
| 233 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·equivalently·(but·faster)... | 233 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·equivalently·(but·faster)... |
| 234 | ·····time·assert(ChowV·===·chowForm·f) | 234 | ·····time·assert(ChowV·===·chowForm·f) |
| 235 | ·--·used·1. | 235 | ·--·used·1.00252s·(cpu);·0.927833s·(thread);·0s·(gc)</code></pre> |
| 236 | </td>··········</tr> | 236 | </td>··········</tr> |
| 237 | ··········<tr> | 237 | ··········<tr> |
| 238 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·X-resultant·of·V | 238 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·X-resultant·of·V |
| 239 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; | 239 | ·····time·Xres·=·fromPluckerToStiefel·dualize·ChowV; |
| 240 | ·--·used·0. | 240 | ·--·used·0.208352s·(cpu);·0.171378s·(thread);·0s·(gc)</code></pre> |
| 241 | </td>··········</tr> | 241 | </td>··········</tr> |
| 242 | ··········<tr> | 242 | ··········<tr> |
| 243 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·three·generic·ternary·quadrics | 243 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·three·generic·ternary·quadrics |
| 244 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) | 244 | ·····F·=·genericPolynomials({2,2,2},ZZ/3331) |
| 245 | ·········2···············2························2·····2···············2·· | 245 | ·········2···············2························2·····2···············2·· |
| 246 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ | 246 | o6·=·{a·x··+·a·x·x··+·a·x··+·a·x·x··+·a·x·x··+·a·x·,·b·x··+·b·x·x··+·b·x··+ |
| Offset 252, 15 lines modified | Offset 252, 15 lines modified | ||
| 252 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 252 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 253 | o6·:·List</code></pre> | 253 | o6·:·List</code></pre> |
| 254 | </td>··········</tr> | 254 | </td>··········</tr> |
| 255 | ··········<tr> | 255 | ··········<tr> |
| 256 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·resultant·of·the·three·forms | 256 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·resultant·of·the·three·forms |
| 257 | ·····time·resF·=·resultant·F; | 257 | ·····time·resF·=·resultant·F; |
| 258 | ·--·used·0.1 | 258 | ·--·used·0.177582s·(cpu);·0.141898s·(thread);·0s·(gc)</code></pre> |
| 259 | </td>··········</tr> | 259 | </td>··········</tr> |
| 260 | ··········<tr> | 260 | ··········<tr> |
| 261 | <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>··············<pre><code·class="language-macaulay2">i8·:·assert(resF·===·sub(Xres,vars·ring·resF)·and·Xres·===·sub(resF,vars·ring·Xres))</code></pre> |
| 262 | </td>··········</tr> | 262 | </td>··········</tr> |
| 263 | ········</table> | 263 | ········</table> |
| 264 | ······</div> | 264 | ······</div> |
| 265 | ······<div> | 265 | ······<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·4.21641s·(cpu);·4.06274s·(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·1. | 242 | ·--·used·1.00252s·(cpu);·0.927833s·(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. | 245 | ·--·used·0.208352s·(cpu);·0.171378s·(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·0.177582s·(cpu);·0.141898s·(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 84, 15 lines modified | Offset 84, 15 lines modified | ||
| 84 | ········2··············2 | 84 | ········2··············2 |
| 85 | o2·=·a*x··+·b*x*y·+·c*y | 85 | o2·=·a*x··+·b*x*y·+·c*y |
| 86 | o2·:·ZZ[a..c][x..y]</code></pre> | 86 | o2·:·ZZ[a..c][x..y]</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·discriminant·F | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·discriminant·F |
| 90 | ·--·used·0.008 | 90 | ·--·used·0.00811395s·(cpu);·0.00828375s·(thread);·0s·(gc) |
| 91 | ········2 | 91 | ········2 |
| 92 | o3·=·-·b··+·4a*c | 92 | o3·=·-·b··+·4a*c |
| 93 | o3·:·ZZ[a..c]</code></pre> | 93 | o3·:·ZZ[a..c]</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| Offset 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | ········3······2·········2······3 | 101 | ········3······2·········2······3 |
| 102 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y | 102 | o5·=·a*x··+·b*x·y·+·c*x*y··+·d*y |
| 103 | o5·:·ZZ[a..d][x..y]</code></pre> | 103 | o5·:·ZZ[a..d][x..y]</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·discriminant·F | 106 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·discriminant·F |
| 107 | ·--·used·0.0 | 107 | ·--·used·0.00734662s·(cpu);·0.00874633s·(thread);·0s·(gc) |
| 108 | ········2·2·······3·····3···················2·2 | 108 | ········2·2·······3·····3···················2·2 |
| 109 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d | 109 | o6·=·-·b·c··+·4a*c··+·4b·d·-·18a*b*c*d·+·27a·d |
| 110 | o6·:·ZZ[a..d]</code></pre> | 110 | o6·:·ZZ[a..d]</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| Offset 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x | 150 | o12·=·(t··+·t·)x··-·t·x·x··+·t·x··+·(t··-·t·)x··+·t·x·x··+·t·x |
| 151 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 | 151 | ········0····1··0····1·0·1····0·1·····0····1··2····1·2·3····0·3 |
| 152 | o12·:·R'</code></pre> | 152 | o12·:·R'</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·D=discriminant·pencil | 155 | <td>··············<pre><code·class="language-macaulay2">i13·:·time·D=discriminant·pencil |
| 156 | ·--·used·0.3 | 156 | ·--·used·0.311198s·(cpu);·0.309128s·(thread);·0s·(gc) |
| 157 | ···········108······106·2·······102·6······100·8·······98·10·······96·12·· | 157 | ···········108······106·2·······102·6······100·8·······98·10·······96·12·· |
| 158 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ | 158 | o13·=·-·62t····+·19t···t··+·160t···t··+·91t···t··+·129t··t···+·117t··t···+ |
| 159 | ···········0········0···1·······0···1······0···1·······0··1········0··1··· | 159 | ···········0········0···1·······0···1······0···1·······0··1········0··1··· |
| 160 | ······----------------------------------------------------------------------- | 160 | ······----------------------------------------------------------------------- |
| 161 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24·· | 161 | ··········94·14·······92·16······90·18······88·20······86·22·······84·24·· |
| 162 | ······161t··t···+·124t··t···-·82t··t···-·21t··t···-·49t··t···-·123t··t···+ | 162 | ······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·0.008 | 29 | ·--·used·0.00811395s·(cpu);·0.00828375s·(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·0.00734662s·(cpu);·0.00874633s·(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·0.3 | 80 | ·--·used·0.311198s·(cpu);·0.309128s·(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 92, 26 lines modified | Offset 92, 26 lines modified | ||
| 92 | ······0·3 | 92 | ······0·3 |
| 93 | o1·:·Ideal·of·QQ[x·..x·] | 93 | o1·:·Ideal·of·QQ[x·..x·] |
| 94 | ··················0···5</code></pre> | 94 | ··················0···5</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·V'·=·dualVariety·V | 97 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·V'·=·dualVariety·V |
| 98 | ·--·used·0.10 | 98 | ·--·used·0.101423s·(cpu);·0.0983508s·(thread);·0s·(gc) |
| 99 | ············2·················2····2 | 99 | ············2·················2····2 |
| 100 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) | 100 | o2·=·ideal(x·x··-·x·x·x··+·x·x··+·x·x··-·4x·x·x·) |
| 101 | ············2·3····1·2·4····0·4····1·5·····0·3·5 | 101 | ············2·3····1·2·4····0·4····1·5·····0·3·5 |
| 102 | o2·:·Ideal·of·QQ[x·..x·] | 102 | o2·:·Ideal·of·QQ[x·..x·] |
| 103 | ··················0···5</code></pre> | 103 | ··················0···5</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·V·==·dualVariety·V' | 106 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·V·==·dualVariety·V' |
| 107 | ·--·used·0.1 | 107 | ·--·used·0.160003s·(cpu);·0.123004s·(thread);·0s·(gc) |
| 108 | o3·=·true</code></pre> | 108 | o3·=·true</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ········</table> | 110 | ········</table> |
| 111 | ········<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 | ········<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> |
| 112 | ········<table·class="examples"> | 112 | ········<table·class="examples"> |
| 113 | ··········<tr> | 113 | ··········<tr> |
| Offset 127, 23 lines modified | Offset 127, 23 lines modified | ||
| 127 | ······ZZ | 127 | ······ZZ |
| 128 | o4·:·----[a·..a·][x·..x·] | 128 | o4·:·----[a·..a·][x·..x·] |
| 129 | ·····3331··0···9···0···2</code></pre> | 129 | ·····3331··0···9···0···2</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ··········<tr> | 131 | ··········<tr> |
| 132 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·discF·=·ideal·discriminant·F; | 132 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·discF·=·ideal·discriminant·F; |
| 133 | ·--·used·0.0 | 133 | ·--·used·0.0468112s·(cpu);·0.0453195s·(thread);·0s·(gc) |
| 134 | ···············ZZ | 134 | ···············ZZ |
| 135 | o5·:·Ideal·of·----[a·..a·] | 135 | o5·:·Ideal·of·----[a·..a·] |
| 136 | ··············3331··0···9</code></pre> | 136 | ··············3331··0···9</code></pre> |
| 137 | </td>··········</tr> | 137 | </td>··········</tr> |
| 138 | ··········<tr> | 138 | ··········<tr> |
| 139 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); | 139 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Z·=·dualVariety(veronese(2,3,ZZ/3331),AssumeOrdinary=>true); |
| 140 | ·--·used·0. | 140 | ·--·used·0.548179s·(cpu);·0.509567s·(thread);·0s·(gc) |
| 141 | ···············ZZ | 141 | ···············ZZ |
| 142 | o6·:·Ideal·of·----[x·..x·] | 142 | o6·:·Ideal·of·----[x·..x·] |
| 143 | ··············3331··0···9</code></pre> | 143 | ··············3331··0···9</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·discF·==·sub(Z,vars·ring·discF)·and·Z·==·sub(discF,vars·ring·Z) | 146 | <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·0.10 | 38 | ·--·used·0.101423s·(cpu);·0.0983508s·(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·0.160003s·(cpu);·0.123004s·(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·0.0468112s·(cpu);·0.0453195s·(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·0.548179s·(cpu);·0.509567s·(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 86, 15 lines modified | Offset 86, 15 lines modified | ||
| 86 | ·············2····1·3···1·2····0·3···1····0·2 | 86 | ·············2····1·3···1·2····0·3···1····0·2 |
| 87 | o1·:·Ideal·of·QQ[x·..x·] | 87 | o1·:·Ideal·of·QQ[x·..x·] |
| 88 | ··················0···3</code></pre> | 88 | ··················0···3</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fromPluckerToStiefel·dualize·chowForm·C | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·fromPluckerToStiefel·dualize·chowForm·C |
| 92 | ·--·used·0.04 | 92 | ·--·used·0.0404765s·(cpu);·0.0401008s·(thread);·0s·(gc) |
| 93 | ········3···3··········2···2··············2·······2··········2···3···· | 93 | ········3···3··········2···2··············2·······2··········2···3···· |
| 94 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- | 94 | o2·=·-·x···x····+·x···x···x···x····-·x···x···x···x····+·x···x···x····- |
| 95 | ········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 | ········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·· |
| 96 | ·····------------------------------------------------------------------------ | 96 | ·····------------------------------------------------------------------------ |
| 97 | ······2·······2···············2···2··································· | 97 | ······2·······2···············2···2··································· |
| 98 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- | 98 | ·····x···x···x···x····+·2x···x···x···x····+·x···x···x···x···x···x····- |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | ······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 | ······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 |
| 138 | o2·:·QQ[x···..x···] | 138 | o2·:·QQ[x···..x···] |
| 139 | ·········0,0···1,3</code></pre> | 139 | ·········0,0···1,3</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) | 142 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·fromPluckerToStiefel(dualize·chowForm·C,AffineChartGrass=>{0,1}) |
| 143 | ·--·used·0.0 | 143 | ·--·used·0.0399989s·(cpu);·0.0410957s·(thread);·0s·(gc) |
| 144 | ············3··········2·························2························ | 144 | ············3··········2·························2························ |
| 145 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- | 145 | o3·=·-·x···x····+·x···x···x····-·x···x···x····+·x···x····+·3x···x···x····- |
| 146 | ········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 | ········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·· |
| 147 | ·····------------------------------------------------------------------------ | 147 | ·····------------------------------------------------------------------------ |
| 148 | ···········2······3······2 | 148 | ···········2······3······2 |
| 149 | ·····2x···x····+·x····+·x | 149 | ·····2x···x····+·x····+·x |
| Offset 172, 15 lines modified | Offset 172, 15 lines modified | ||
| 172 | ········<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 | ········<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> |
| 173 | ········<table·class="examples"> | 173 | ········<table·class="examples"> |
| 174 | ··········<tr> | 174 | ··········<tr> |
| 175 | <td>··············<pre><code·class="language-macaulay2">i5·:·w·=·chowForm·C;</code></pre> | 175 | <td>··············<pre><code·class="language-macaulay2">i5·:·w·=·chowForm·C;</code></pre> |
| 176 | </td>··········</tr> | 176 | </td>··········</tr> |
| 177 | ··········<tr> | 177 | ··········<tr> |
| 178 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s)) | 178 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·U·=·apply(subsets(4,2),s->ideal·fromPluckerToStiefel(w,AffineChartGrass=>s)) |
| 179 | ·--·used·0.06 | 179 | ·--·used·0.0623666s·(cpu);·0.0312445s·(thread);·0s·(gc) |
| 180 | ···················3··········2··········3·······················2········ | 180 | ···················3··········2··········3·······················2········ |
| 181 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ | 181 | o6·=·{ideal(-·x···x····+·x···x···x····-·x····-·3x···x···x····+·2x···x····+ |
| 182 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3·· | 182 | ···············0,3·1,2····0,2·1,2·1,3····0,2·····0,2·0,3·1,2·····0,2·1,3·· |
| 183 | ·····------------------------------------------------------------------------ | 183 | ·····------------------------------------------------------------------------ |
| 184 | ·························2······2············2···3···············2········ | 184 | ·························2······2············2···3···············2········ |
| 185 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ | 185 | ·····x···x···x····-·x···x····+·x···),·ideal(x···x····-·2x···x···x···x····+ |
| Offset 218, 15 lines modified | Offset 218, 15 lines modified | ||
| 218 | ·····2x···x····-·x····+·x···)} | 218 | ·····2x···x····-·x····+·x···)} |
| 219 | ·······0,0·1,1····1,1····1,0 | 219 | ·······0,0·1,1····1,1····1,0 |
| 220 | o6·:·List</code></pre> | 220 | o6·:·List</code></pre> |
| 221 | </td>··········</tr> | 221 | </td>··········</tr> |
| 222 | ··········<tr> | 222 | ··········<tr> |
| 223 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·apply(U,u->dim·singularLocus·u) | 223 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·apply(U,u->dim·singularLocus·u) |
| 224 | ·--·used·0.02 | 224 | ·--·used·0.0219934s·(cpu);·0.0220084s·(thread);·0s·(gc) |
| 225 | o7·=·{2,·2,·2,·2,·2,·2} | 225 | o7·=·{2,·2,·2,·2,·2,·2} |
| 226 | o7·:·List</code></pre> | 226 | o7·:·List</code></pre> |
| 227 | </td>··········</tr> | 227 | </td>··········</tr> |
| 228 | ········</table> | 228 | ········</table> |
| 229 | ······</div> | 229 | ······</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·0.04 | 33 | ·--·used·0.0404765s·(cpu);·0.0401008s·(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·0.0 | 82 | ·--·used·0.0399989s·(cpu);·0.0410957s·(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·0.06 | 113 | ·--·used·0.0623666s·(cpu);·0.0312445s·(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·0.02 | 156 | ·--·used·0.0219934s·(cpu);·0.0220084s·(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 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 | 96 | ·····10·3····0·4···4·1·4···2·2·4···3·3·4·····4 |
| 97 | o1·:·Ideal·of·QQ[p·..p·] | 97 | o1·:·Ideal·of·QQ[p·..p·] |
| 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">i2·:·time·hurwitzForm·Q | 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·hurwitzForm·Q |
| 102 | ·--·used·0.0 | 102 | ·--·used·0.0439957s·(cpu);·0.0440817s·(thread);·0s·(gc) |
| 103 | ············2····························2·································· | 103 | ············2····························2·································· |
| 104 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p··· | 104 | o2·=·143100p····+·267300p···p····+·96525p····-·56700p···p····-·56100p···p··· |
| 105 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 | 105 | ············0,1··········0,1·0,2·········0,2·········0,1·1,2·········0,2·1,2 |
| 106 | ·····------------------------------------------------------------------------ | 106 | ·····------------------------------------------------------------------------ |
| 107 | ···········2··············································2················· | 107 | ···········2··············································2················· |
| 108 | ·····+·900p····+·140400p···p····+·111780p···p····+·133380p····-·8100p···p··· | 108 | ·····+·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·0.0439957s·(cpu);·0.0440817s·(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 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 100 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 101 | o1·:·-------------------------------------- | 101 | o1·:·-------------------------------------- |
| 102 | ·········p···p····-·p···p····+·p···p | 102 | ·········p···p····-·p···p····+·p···p |
| 103 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> | 103 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·isCoisotropic·w | 106 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·isCoisotropic·w |
| 107 | ·--·used·0.0 | 107 | ·--·used·0.00801093s·(cpu);·0.00843177s·(thread);·0s·(gc) |
| 108 | o2·=·true</code></pre> | 108 | o2·=·true</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·random·quadric·in·G(1,3) | 111 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·random·quadric·in·G(1,3) |
| 112 | ·····w'·=·random(2,Grass(1,3)) | 112 | ·····w'·=·random(2,Grass(1,3)) |
| Offset 132, 15 lines modified | Offset 132, 15 lines modified | ||
| 132 | ·········0,1···0,2···1,2···0,3···1,3···2,3 | 132 | ·········0,1···0,2···1,2···0,3···1,3···2,3 |
| 133 | o3·:·-------------------------------------- | 133 | o3·:·-------------------------------------- |
| 134 | ·········p···p····-·p···p····+·p···p | 134 | ·········p···p····-·p···p····+·p···p |
| 135 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> | 135 | ··········1,2·0,3····0,2·1,3····0,1·2,3</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isCoisotropic·w' | 138 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isCoisotropic·w' |
| 139 | ·--·used·0.00 | 139 | ·--·used·0.00476692s·(cpu);·0.00675189s·(thread);·0s·(gc) |
| 140 | o4·=·false</code></pre> | 140 | o4·=·false</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ········</table> | 142 | ········</table> |
| 143 | ······</div> | 143 | ······</div> |
| 144 | ······<div·class="waystouse"> | 144 | ······<div·class="waystouse"> |
| 145 | ········<h2>Ways·to·use·<span·class="tt">isCoisotropic</span>·:</h2> | 145 | ········<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·0.00801093s·(cpu);·0.00843177s·(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·0.00476692s·(cpu);·0.00675189s·(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 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | ················ZZ | 115 | ················ZZ |
| 116 | o3·:·Ideal·of·-----[x·..x·] | 116 | o3·:·Ideal·of·-----[x·..x·] |
| 117 | ··············33331··0···5</code></pre> | 117 | ··············33331··0···5</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) | 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·isInCoisotropic(L,I)·--·whether·L·belongs·to·Z_1(V(I)) |
| 121 | ·--·used·0.01 | 121 | ·--·used·0.0158583s·(cpu);·0.0166802s·(thread);·0s·(gc) |
| 122 | o4·=·true</code></pre> | 122 | o4·=·true</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ········</table> | 124 | ········</table> |
| 125 | ······</div> | 125 | ······</div> |
| 126 | ······<div> | 126 | ······<div> |
| 127 | ········<h2>See·also</h2> | 127 | ········<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·0.01 | 61 | ·--·used·0.0158583s·(cpu);·0.0166802s·(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 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} | 85 | ·····c·x·x·x··+·c·x·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 86 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 | 86 | ······4·0·1·2····7·1·2····5·0·2····8·1·2····9·2 |
| 87 | o1·:·List</code></pre> | 87 | o1·:·List</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(D,D')·=·macaulayFormula·F | 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·(D,D')·=·macaulayFormula·F |
| 91 | ·--·used·0.00 | 91 | ·--·used·0.000426512s·(cpu);·0.00294634s·(thread);·0s·(gc) |
| 92 | 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 | o2·=·(|·a_0·a_1·a_2·a_3·a_4·a_5·0···0···0···0···0···0···0···0···0···0···0·· |
| 93 | ······|·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···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0···0·· |
| 94 | ······|·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···a_0·0···a_1·a_2·0···a_3·a_4·a_5·0···0···0···0···0···0···0·· |
| 95 | ······|·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···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0···0·· |
| 96 | ······|·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···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0···0·· |
| 97 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0·· | 97 | ······|·0···0···0···0···0···a_0·0···0···a_1·a_2·0···0···a_3·a_4·a_5·0···0·· |
| Offset 152, 15 lines modified | Offset 152, 15 lines modified | ||
| 152 | ·····-p·p··+·2p·p··+·6p·} | 152 | ·····-p·p··+·2p·p··+·6p·} |
| 153 | ·····7·0·2·····1·2·····2 | 153 | ·····7·0·2·····1·2·····2 |
| 154 | o3·:·List</code></pre> | 154 | o3·:·List</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(D,D')·=·macaulayFormula·F | 157 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(D,D')·=·macaulayFormula·F |
| 158 | ·--·used·0.00 | 158 | ·--·used·0.00307859s·(cpu);·0.00214885s·(thread);·0s·(gc) |
| 159 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0·· | 159 | o4·=·(|·9/2·1/2··9/4··1/2·1····3/4··0···0···0···0···0···0····0····0····0·· |
| 160 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0·· | 160 | ······|·0···9/2··0····1/2·9/4··0····1/2·1···3/4·0···0···0····0····0····0·· |
| 161 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0·· | 161 | ······|·0···0····9/2··0···1/2··9/4··0···1/2·1···3/4·0···0····0····0····0·· |
| 162 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0·· | 162 | ······|·0···0····0····9/2·0····0····1/2·9/4·0···0···1/2·1····3/4··0····0·· |
| 163 | ······|·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···9/2··0····0···1/2·9/4·0···0···1/2··1····3/4··0·· |
| 164 | ······|·0···0····0····0···0····9/2··0···0···1/2·9/4·0···0····1/2··1····3/4 | 164 | ······|·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·0.000426512s·(cpu);·0.00294634s·(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·0.00307859s·(cpu);·0.00214885s·(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 92, 30 lines modified | Offset 92, 30 lines modified | ||
| 92 | ·····664x·) | 92 | ·····664x·) |
| 93 | ·········4 | 93 | ·········4 |
| 94 | o3·:·Ideal·of·P4</code></pre> | 94 | o3·:·Ideal·of·P4</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·p·=·plucker·L | 97 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·p·=·plucker·L |
| 98 | ·--·used·0.00 | 98 | ·--·used·0.00394229s·(cpu);·0.00350562s·(thread);·0s·(gc) |
| 99 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ | 99 | o4·=·ideal·(x····+·8480x···,·x····-·6727x···,·x····+·15777x···,·x····+ |
| 100 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3·· | 100 | ·············2,4········3,4···1,4········3,4···0,4·········3,4···2,3·· |
| 101 | ·····------------------------------------------------------------------------ | 101 | ·····------------------------------------------------------------------------ |
| 102 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ | 102 | ·····11656x···,·x····-·14853x···,·x····+·664x···,·x····+·13522x···,·x····+ |
| 103 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2·· | 103 | ···········3,4···1,3·········3,4···0,3·······3,4···1,2·········3,4···0,2·· |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ·····11804x···,·x····+·14854x···) | 105 | ·····11804x···,·x····+·14854x···) |
| 106 | ···········3,4···0,1·········3,4 | 106 | ···········3,4···0,1·········3,4 |
| 107 | o4·:·Ideal·of·G'1'4</code></pre> | 107 | o4·:·Ideal·of·G'1'4</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·L'·=·plucker·p | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·L'·=·plucker·p |
| 111 | ·--·used·0.0 | 111 | ·--·used·0.0265286s·(cpu);·0.0277247s·(thread);·0s·(gc) |
| 112 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- | 112 | o5·=·ideal·(x··+·8480x··-·11656x·,·x··-·6727x··+·14853x·,·x··+·15777x··- |
| 113 | ·············2········3·········4···1········3·········4···0·········3·· | 113 | ·············2········3·········4···1········3·········4···0·········3·· |
| 114 | ·····------------------------------------------------------------------------ | 114 | ·····------------------------------------------------------------------------ |
| 115 | ·····664x·) | 115 | ·····664x·) |
| 116 | ·········4 | 116 | ·········4 |
| Offset 130, 15 lines modified | Offset 130, 15 lines modified | ||
| 130 | ··········<tr> | 130 | ··········<tr> |
| 131 | <td>··············<pre><code·class="language-macaulay2">i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve | 131 | <td>··············<pre><code·class="language-macaulay2">i7·:·Y·=·ideal·apply(5,i->random(1,G'1'4));·--·an·elliptic·curve |
| 132 | o7·:·Ideal·of·G'1'4</code></pre> | 132 | o7·:·Ideal·of·G'1'4</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y | 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·W·=·plucker·Y;·--·surface·swept·out·by·the·lines·of·Y |
| 136 | ·--·used·0.0 | 136 | ·--·used·0.0320018s·(cpu);·0.0322529s·(thread);·0s·(gc) |
| 137 | o8·:·Ideal·of·P4</code></pre> | 137 | o8·:·Ideal·of·P4</code></pre> |
| 138 | </td>··········</tr> | 138 | </td>··········</tr> |
| 139 | ··········<tr> | 139 | ··········<tr> |
| 140 | <td>··············<pre><code·class="language-macaulay2">i9·:·(codim·W,degree·W) | 140 | <td>··············<pre><code·class="language-macaulay2">i9·:·(codim·W,degree·W) |
| 141 | o9·=·(2,·5) | 141 | o9·=·(2,·5) |
| Offset 146, 15 lines modified | Offset 146, 15 lines modified | ||
| 146 | o9·:·Sequence</code></pre> | 146 | o9·:·Sequence</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ········</table> | 148 | ········</table> |
| 149 | ········<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 | ········<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> |
| 150 | ········<table·class="examples"> | 150 | ········<table·class="examples"> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W | 152 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·Y'·=·plucker(W,1);·--·variety·of·lines·contained·in·W |
| 153 | ·--·used·0.2 | 153 | ·--·used·0.230378s·(cpu);·0.186838s·(thread);·0s·(gc) |
| 154 | o10·:·Ideal·of·G'1'4</code></pre> | 154 | o10·:·Ideal·of·G'1'4</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i11·:·assert(Y'·==·Y)</code></pre> | 157 | <td>··············<pre><code·class="language-macaulay2">i11·:·assert(Y'·==·Y)</code></pre> |
| 158 | </td>··········</tr> | 158 | </td>··········</tr> |
| 159 | ········</table> | 159 | ········</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·0.00394229s·(cpu);·0.00350562s·(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·0.0 | 46 | ·--·used·0.0265286s·(cpu);·0.0277247s·(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·0.0 | 67 | ·--·used·0.0320018s·(cpu);·0.0322529s·(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·0.2 | 75 | ·--·used·0.230378s·(cpu);·0.186838s·(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 100, 15 lines modified | Offset 100, 15 lines modified | ||
| 100 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} | 100 | ·····-b)y*w··+·(-a·+·-b)z*w··+·(-a·+·2b)w·,·2x·+·-y·+·-z·+·-w} |
| 101 | ·····4··········8····8··········7················4····3····5 | 101 | ·····4··········8····8··········7················4····3····5 |
| 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·:·time·resultant(F,Algorithm=>"Poisson2") | 105 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant(F,Algorithm=>"Poisson2") |
| 106 | ·--·used·0.1 | 106 | ·--·used·0.178941s·(cpu);·0.141518s·(thread);·0s·(gc) |
| 107 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 107 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 108 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- | 108 | o3·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 109 | ···········2222549728809984000000············12700284164628480000000········· | 109 | ···········2222549728809984000000············12700284164628480000000········· |
| 110 | ·····------------------------------------------------------------------------ | 110 | ·····------------------------------------------------------------------------ |
| 111 | ·····348237304382147063838108483692249·3·2·· | 111 | ·····348237304382147063838108483692249·3·2·· |
| 112 | ·····---------------------------------a·b··- | 112 | ·····---------------------------------a·b··- |
| Offset 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | ·····-------------------------------a*b··-·---------------------------b | 122 | ·····-------------------------------a*b··-·---------------------------b |
| 123 | ··········1119954511872000000000················895963609497600000 | 123 | ··········1119954511872000000000················895963609497600000 |
| 124 | o3·:·QQ[a..b]</code></pre> | 124 | o3·:·QQ[a..b]</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·resultant(F,Algorithm=>"Macaulay2") | 127 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·resultant(F,Algorithm=>"Macaulay2") |
| 128 | ·--·used·0.1002s·(cpu);·0.0 | 128 | ·--·used·0.103026s·(cpu);·0.0648384s·(thread);·0s·(gc) |
| 129 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 129 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 130 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- | 130 | o4·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 131 | ···········2222549728809984000000············12700284164628480000000········· | 131 | ···········2222549728809984000000············12700284164628480000000········· |
| 132 | ·····------------------------------------------------------------------------ | 132 | ·····------------------------------------------------------------------------ |
| 133 | ·····348237304382147063838108483692249·3·2·· | 133 | ·····348237304382147063838108483692249·3·2·· |
| 134 | ·····---------------------------------a·b··- | 134 | ·····---------------------------------a·b··- |
| Offset 144, 15 lines modified | Offset 144, 15 lines modified | ||
| 144 | ·····-------------------------------a*b··-·---------------------------b | 144 | ·····-------------------------------a*b··-·---------------------------b |
| 145 | ··········1119954511872000000000················895963609497600000 | 145 | ··········1119954511872000000000················895963609497600000 |
| 146 | o4·:·QQ[a..b]</code></pre> | 146 | o4·:·QQ[a..b]</code></pre> |
| 147 | </td>··········</tr> | 147 | </td>··········</tr> |
| 148 | ··········<tr> | 148 | ··········<tr> |
| 149 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant(F,Algorithm=>"Poisson") | 149 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant(F,Algorithm=>"Poisson") |
| 150 | ·--·used·0.2 | 150 | ·--·used·0.224206s·(cpu);·0.227436s·(thread);·0s·(gc) |
| 151 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 151 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 152 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- | 152 | o5·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 153 | ···········2222549728809984000000············12700284164628480000000········· | 153 | ···········2222549728809984000000············12700284164628480000000········· |
| 154 | ·····------------------------------------------------------------------------ | 154 | ·····------------------------------------------------------------------------ |
| 155 | ·····348237304382147063838108483692249·3·2·· | 155 | ·····348237304382147063838108483692249·3·2·· |
| 156 | ·····---------------------------------a·b··- | 156 | ·····---------------------------------a·b··- |
| Offset 166, 15 lines modified | Offset 166, 15 lines modified | ||
| 166 | ·····-------------------------------a*b··-·---------------------------b | 166 | ·····-------------------------------a*b··-·---------------------------b |
| 167 | ··········1119954511872000000000················895963609497600000 | 167 | ··········1119954511872000000000················895963609497600000 |
| 168 | o5·:·QQ[a..b]</code></pre> | 168 | o5·:·QQ[a..b]</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·resultant(F,Algorithm=>"Macaulay") | 171 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·resultant(F,Algorithm=>"Macaulay") |
| 172 | ·--·used·0. | 172 | ·--·used·0.45928s·(cpu);·0.426343s·(thread);·0s·(gc) |
| 173 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· | 173 | ·······21002161660529014459938925799·5···2085933800619238998825958079203·4··· |
| 174 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- | 174 | o6·=·-·-----------------------------a··-·-------------------------------a·b·- |
| 175 | ···········2222549728809984000000············12700284164628480000000········· | 175 | ···········2222549728809984000000············12700284164628480000000········· |
| 176 | ·····------------------------------------------------------------------------ | 176 | ·····------------------------------------------------------------------------ |
| 177 | ·····348237304382147063838108483692249·3·2·· | 177 | ·····348237304382147063838108483692249·3·2·· |
| 178 | ·····---------------------------------a·b··- | 178 | ·····---------------------------------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·0.1 | 65 | ·--·used·0.178941s·(cpu);·0.141518s·(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·0.1002s·(cpu);·0.0 | 85 | ·--·used·0.103026s·(cpu);·0.0648384s·(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·0.224206s·(cpu);·0.227436s·(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·0.45928s·(cpu);·0.426343s·(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 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | ·······2···············2····························3······2·········4 | 91 | ·······2···············2····························3······2·········4 |
| 92 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} | 92 | o2·=·{x··+·3t*y*z·-·u*z·,·(t·+·3u·-·1)x·-·y,·-·t*x*y··+·t*x·y*z·+·u*z·} |
| 93 | o2·:·List</code></pre> | 93 | o2·:·List</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant·F | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·resultant·F |
| 97 | ·--·used·0.021 | 97 | ·--·used·0.0216199s·(cpu);·0.0210891s·(thread);·0s·(gc) |
| 98 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 | 98 | ··········12·········11·2·········10·3·········9·4··········8·5··········7·6 |
| 99 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u· | 99 | o3·=·-·81t··u·-·1701t··u··-·15309t··u··-·76545t·u··-·229635t·u··-·413343t·u· |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ··············6·7··········5·8·······11··········10·2·········9·3·· | 101 | ··············6·7··········5·8·······11··········10·2·········9·3·· |
| 102 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ | 102 | ·····-·413343t·u··-·177147t·u··+·567t··u·+·10206t··u··+·76545t·u··+ |
| 103 | ·····------------------------------------------------------------------------ | 103 | ·····------------------------------------------------------------------------ |
| Offset 150, 15 lines modified | Offset 150, 15 lines modified | ||
| 150 | ·····+·c·x·} | 150 | ·····+·c·x·} |
| 151 | ········9·2 | 151 | ········9·2 |
| 152 | o4·:·List</code></pre> | 152 | o4·:·List</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant·F | 155 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·resultant·F |
| 156 | ·--·used·1. | 156 | ·--·used·1.77038s·(cpu);·1.45242s·(thread);·0s·(gc) |
| 157 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2·· | 157 | ······6·3·2·······5·2···2·····2·4···2·2····3·3·3·2·····2·4·2···2·· |
| 158 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- | 158 | o5·=·a·b·c··-·3a·a·b·b·c··+·3a·a·b·b·c··-·a·a·b·c··+·3a·a·b·b·c··- |
| 159 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0·· | 159 | ······2·3·0·····1·2·3·4·0·····1·2·3·4·0····1·2·4·0·····1·2·3·5·0·· |
| 160 | ·····------------------------------------------------------------------------ | 160 | ·····------------------------------------------------------------------------ |
| 161 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2·· | 161 | ·······3·3·······2·····4·2·2···2·····4·2···2·2·····5·····2·2····6·3·2·· |
| 162 | ·····6a·a·b·b·b·c··+·3a·a·b·b·c··+·3a·a·b·b·c··-·3a·a·b·b·c··+·a·b·c··- | 162 | ·····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 1781, 15 lines modified | Offset 1781, 15 lines modified | ||
| 1781 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} | 1781 | ·····b·x·x··+·b·x·x··+·b·x·,·c·x··+·c·x·x··+·c·x··+·c·x·x··+·c·x·x··+·c·x·} |
| 1782 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 | 1782 | ······2·0·2····4·1·2····5·2···0·0····1·0·1····3·1····2·0·2····4·1·2····5·2 |
| 1783 | o6·:·List</code></pre> | 1783 | o6·:·List</code></pre> |
| 1784 | </td>··········</tr> | 1784 | </td>··········</tr> |
| 1785 | ··········<tr> | 1785 | ··········<tr> |
| 1786 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·#·terms·resultant·F | 1786 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·#·terms·resultant·F |
| 1787 | ·--·used·0.3 | 1787 | ·--·used·0.369793s·(cpu);·0.301967s·(thread);·0s·(gc) |
| 1788 | o7·=·21894</code></pre> | 1788 | o7·=·21894</code></pre> |
| 1789 | </td>··········</tr> | 1789 | </td>··········</tr> |
| 1790 | ········</table> | 1790 | ········</table> |
| 1791 | ······</div> | 1791 | ······</div> |
| 1792 | ······<div> | 1792 | ······<div> |
| 1793 | ········<h2>See·also</h2> | 1793 | ········<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·0.021 | 38 | ·--·used·0.0216199s·(cpu);·0.0210891s·(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·1. | 93 | ·--·used·1.77038s·(cpu);·1.45242s·(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·0.3 | 1719 | ·--·used·0.369793s·(cpu);·0.301967s·(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 103, 15 lines modified | Offset 103, 15 lines modified | ||
| 103 | o2·:·Ideal·of·QQ[p·..p·] | 103 | o2·:·Ideal·of·QQ[p·..p·] |
| 104 | ··················0···4</code></pre> | 104 | ··················0···4</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| 106 | ··········<tr> | 106 | ··········<tr> |
| 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) | 107 | <td>··············<pre><code·class="language-macaulay2">i3·:·--·0-th·associated·hypersurface·of·S·in·G(1,4)·(Chow·form) |
| 108 | ·····time·tangentialChowForm(S,0) | 108 | ·····time·tangentialChowForm(S,0) |
| 109 | ·--·used·0.0 | 109 | ·--·used·0.0280003s·(cpu);·0.0289408s·(thread);·0s·(gc) |
| 110 | ······2·······················································2········ | 110 | ······2·······················································2········ |
| 111 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ | 111 | o3·=·p···p····-·p···p···p····-·p···p···p····+·p···p···p····+·p···p····+ |
| 112 | ······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 | ······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·· |
| 113 | ·····------------------------------------------------------------------------ | 113 | ·····------------------------------------------------------------------------ |
| 114 | ······2 | 114 | ······2 |
| 115 | ·····p···p····-·2p···p···p····-·p···p···p | 115 | ·····p···p····-·2p···p···p····-·p···p···p |
| Offset 122, 15 lines modified | Offset 122, 15 lines modified | ||
| 122 | o3·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------- | 122 | o3·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 123 | ·····(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 | ·····(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···) |
| 124 | ·······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 | ·······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> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<tr> |
| 127 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) | 127 | <td>··············<pre><code·class="language-macaulay2">i4·:·--·1-th·associated·hypersurface·of·S·in·G(2,4) |
| 128 | ·····time·tangentialChowForm(S,1) | 128 | ·····time·tangentialChowForm(S,1) |
| 129 | ·--·used·0.06 | 129 | ·--·used·0.0604696s·(cpu);·0.0604087s·(thread);·0s·(gc) |
| 130 | ······2·····2········2·····2···············3········2·····2······ | 130 | ······2·····2········2·····2···············3········2·····2······ |
| 131 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- | 131 | o4·=·p·····p······+·p·····p······-·2p·····p······+·p·····p······- |
| 132 | ······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 | ······1,2,3·1,2,4····0,2,4·1,2,4·····0,2,3·1,2,4····0,2,4·0,3,4·· |
| 133 | ·····------------------------------------------------------------------------ | 133 | ·····------------------------------------------------------------------------ |
| 134 | ·············3·········3···············3············ | 134 | ·············3·········3···············3············ |
| 135 | ·····4p·····p······-·4p·····p······-·2p·····p······+ | 135 | ·····4p·····p······-·4p·····p······-·2p·····p······+ |
| Offset 165, 39 lines modified | Offset 165, 39 lines modified | ||
| 165 | o4·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | 165 | o4·:·---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| 166 | ·····(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 | ·····(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·····) |
| 167 | ·······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 | ·······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> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S) | 170 | <td>··············<pre><code·class="language-macaulay2">i5·:·--·2-th·associated·hypersurface·of·S·in·G(3,4)·(parameterizing·tangent·hyperplanes·to·S) |
| 171 | ·····time·tangentialChowForm(S,2) | 171 | ·····time·tangentialChowForm(S,2) |
| 172 | ·--·used·0.03 | 172 | ·--·used·0.0303502s·(cpu);·0.0313808s·(thread);·0s·(gc) |
| 173 | ··············2·············································2 | 173 | ··············2·············································2 |
| 174 | o5·=·p·······p········-·p·······p·······p········+·p·······p | 174 | o5·=·p·······p········-·p·······p·······p········+·p·······p |
| 175 | ······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 | ······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 |
| 176 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] | 176 | o5·:·QQ[p·······..p·······,·p·······,·p·······,·p·······] |
| 177 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4</code></pre> | 177 | ·········0,1,2,3···0,1,2,4···0,1,3,4···0,2,3,4···1,2,3,4</code></pre> |
| 178 | </td>··········</tr> | 178 | </td>··········</tr> |
| 179 | ··········<tr> | 179 | ··········<tr> |
| 180 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing | 180 | <td>··············<pre><code·class="language-macaulay2">i6·:·--·we·get·the·dual·hypersurface·of·S·in·G(0,4)·by·dualizing |
| 181 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) | 181 | ·····time·S'·=·ideal·dualize·tangentialChowForm(S,2) |
| 182 | ·--·used·0.08 | 182 | ·--·used·0.0876205s·(cpu);·0.0532247s·(thread);·0s·(gc) |
| 183 | ············2···············2 | 183 | ············2···············2 |
| 184 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) | 184 | o6·=·ideal(p·p··-·p·p·p··+·p·p·) |
| 185 | ············1·2····0·1·3····0·4 | 185 | ············1·2····0·1·3····0·4 |
| 186 | o6·:·Ideal·of·QQ[p·..p·] | 186 | o6·:·Ideal·of·QQ[p·..p·] |
| 187 | ··················0···4</code></pre> | 187 | ··················0···4</code></pre> |
| 188 | </td>··········</tr> | 188 | </td>··········</tr> |
| 189 | ··········<tr> | 189 | ··········<tr> |
| 190 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·we·then·can·recover·S | 190 | <td>··············<pre><code·class="language-macaulay2">i7·:·--·we·then·can·recover·S |
| 191 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) | 191 | ·····time·assert(dualize·tangentialChowForm(S',3)·==·S) |
| 192 | ·--·used·0.1 | 192 | ·--·used·0.122082s·(cpu);·0.0820454s·(thread);·0s·(gc)</code></pre> |
| 193 | </td>··········</tr> | 193 | </td>··········</tr> |
| 194 | ········</table> | 194 | ········</table> |
| 195 | ······</div> | 195 | ······</div> |
| 196 | ······<div> | 196 | ······<div> |
| 197 | ········<h2>See·also</h2> | 197 | ········<h2>See·also</h2> |
| 198 | ········<ul> | 198 | ········<ul> |
| 199 | ··········<li> | 199 | ··········<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·0.0280003s·(cpu);·0.0289408s·(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·0.06 | 96 | ·--·used·0.0604696s·(cpu);·0.0604087s·(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·0.03 | 146 | ·--·used·0.0303502s·(cpu);·0.0313808s·(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·0.08 | 154 | ·--·used·0.0876205s·(cpu);·0.0532247s·(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·0.1 | 162 | ·--·used·0.122082s·(cpu);·0.0820454s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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:·956605896 | 1 | --·-*-·M2-comint·-*-·hash:·956605896 |
| 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)·3076856 | ||
| 10 | process··············95991 | ||
| 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)·96085 | ||
| 9 | max·locked·memory···········(kbytes,·-l)·3077552 | ||
| 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)·96085 | ||
| 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, 137 lines modified | Offset 1, 136 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·-784631933 | 1 | --·-*-·M2-comint·-*-·hash:·-784631933 |
| 2 | i1·:·fn=temporaryFileName()|".m2" | 2 | i1·:·fn=temporaryFileName()|".m2" |
| 3 | o1·=·/tmp/M2- | 3 | o1·=·/tmp/M2-2356940-0/0.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/M2-2356940-0/1.m2"·>"/tmp/M2-2356940-0/1.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 |
| 15 | ···············"return·code"·=>·0 | 15 | ···············"return·code"·=>·0 |
| 16 | ···············"statistics"·=>·null | 16 | ···············"statistics"·=>·null |
| 17 | ···············"time·used"·=>· | 17 | ···············"time·used"·=>·2 |
| 18 | ···············value·=>·16 | 18 | ···············value·=>·16 |
| 19 | o7·:·HashTable | 19 | o7·:·HashTable |
| 20 | i8·:·h#value===4^2 | 20 | i8·:·h#value===4^2 |
| 21 | o8·=·true | 21 | o8·=·true |
| 22 | i9·:·h#"exit·code"===0 | 22 | i9·:·h#"exit·code"===0 |
| 23 | o9·=·true | 23 | o9·=·true |
| 24 | i10·:·h=runExternalM2(fn,"justexit",()); | 24 | i10·:·h=runExternalM2(fn,"justexit",()); |
| 25 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 25 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/2.m2"·>"/tmp/M2-2356940-0/2.out"·2>&1·)) |
| 26 | Finished·running. | 26 | Finished·running. |
| 27 | RunExternalM2:·expected·answer·file·does·not·exist | 27 | RunExternalM2:·expected·answer·file·does·not·exist |
| 28 | i11·:·h | 28 | i11·:·h |
| 29 | o11·=·HashTable{"answer·file"·=>·/tmp/M2- | 29 | o11·=·HashTable{"answer·file"·=>·/tmp/M2-2356940-0/2.ans} |
| 30 | ················"exit·code"·=>·27 | 30 | ················"exit·code"·=>·27 |
| 31 | ················"output·file"·=>·/tmp/M2- | 31 | ················"output·file"·=>·/tmp/M2-2356940-0/2.out |
| 32 | ················"return·code"·=>·6912 | 32 | ················"return·code"·=>·6912 |
| 33 | ················"statistics"·=>·null | 33 | ················"statistics"·=>·null |
| 34 | ················"time·used"·=>· | 34 | ················"time·used"·=>·1 |
| 35 | ················value·=>·null | 35 | ················value·=>·null |
| 36 | o11·:·HashTable | 36 | o11·:·HashTable |
| 37 | i12·:·fileExists(h#"output·file") | 37 | i12·:·fileExists(h#"output·file") |
| 38 | o12·=·true | 38 | o12·=·true |
| 39 | i13·:·fileExists(h#"answer·file") | 39 | i13·:·fileExists(h#"answer·file") |
| 40 | o13·=·false | 40 | o13·=·false |
| 41 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); | 41 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); |
| 42 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 42 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/3.m2"·>"/tmp/M2-2356940-0/3.out"·2>&1·)) |
| 43 | Killed | ||
| 44 | Finished·running. | 43 | Finished·running. |
| 45 | RunExternalM2:·expected·answer·file·does·not·exist | 44 | RunExternalM2:·expected·answer·file·does·not·exist |
| 46 | i15·:·h | 45 | i15·:·h |
| 47 | o15·=·HashTable{"answer·file"·=>·/tmp/M2- | 46 | o15·=·HashTable{"answer·file"·=>·/tmp/M2-2356940-0/3.ans} |
| 48 | ················"exit·code"·=>·0 | 47 | ················"exit·code"·=>·0 |
| 49 | ················"output·file"·=>·/tmp/M2- | 48 | ················"output·file"·=>·/tmp/M2-2356940-0/3.out |
| 50 | ················"return·code"·=>·9 | 49 | ················"return·code"·=>·9 |
| 51 | ················"statistics"·=>·null | 50 | ················"statistics"·=>·null |
| 52 | ················"time·used"·=>· | 51 | ················"time·used"·=>·2 |
| 53 | ················value·=>·null | 52 | ················value·=>·null |
| 54 | o15·:·HashTable | 53 | o15·:·HashTable |
| 55 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") | 54 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") |
| 56 | o16·=· | 55 | o16·=· |
| 57 | ······i1·:·--·Script·/tmp/M2- | 56 | ······i1·:·--·Script·/tmp/M2-2356940-0/3.m2·automatically·generated·by·RunExternalM2 |
| 58 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); | 57 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); |
| 59 | ······i2·:·load·"/tmp/M2- | 58 | ······i2·:·load·"/tmp/M2-2356940-0/0.m2"; |
| 60 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2- | 59 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-2356940-0/3.ans",spin·(10)); |
| 61 | ······Spinning!! | 60 | ······Spinning!! |
| 62 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file") | 61 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file") |
| 63 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); | 62 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); |
| 64 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 63 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/4.m2"·>"/tmp/M2-2356940-0/4.out"·2>&1')·>"/tmp/M2-2356940-0/4.stat"·2>&1·)) |
| 65 | Finished·running. | 64 | Finished·running. |
| 66 | i19·:·h#"statistics" | 65 | i19·:·h#"statistics" |
| 67 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 66 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/4.m2"·>"/tmp/M2-2356940-0/4.out"·2>&1" |
| 68 | ··············User·time·(seconds):·4.3 | 67 | ··············User·time·(seconds):·4.32 |
| 69 | ··············System·time·(seconds):·0. | 68 | ··············System·time·(seconds):·0.05 |
| 70 | ··············Percent·of·CPU·this·job·got:· | 69 | ··············Percent·of·CPU·this·job·got:·86% |
| 71 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0: | 70 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:05.05 |
| 72 | ··············Average·shared·text·size·(kbytes):·0 | 71 | ··············Average·shared·text·size·(kbytes):·0 |
| 73 | ··············Average·unshared·data·size·(kbytes):·0 | 72 | ··············Average·unshared·data·size·(kbytes):·0 |
| 74 | ··············Average·stack·size·(kbytes):·0 | 73 | ··············Average·stack·size·(kbytes):·0 |
| 75 | ··············Average·total·size·(kbytes):·0 | 74 | ··············Average·total·size·(kbytes):·0 |
| 76 | ··············Maximum·resident·set·size·(kbytes):·29 | 75 | ··············Maximum·resident·set·size·(kbytes):·299684 |
| 77 | ··············Average·resident·set·size·(kbytes):·0 | 76 | ··············Average·resident·set·size·(kbytes):·0 |
| 78 | ··············Major·(requiring·I/O)·page·faults:·0 | 77 | ··············Major·(requiring·I/O)·page·faults:·0 |
| 79 | ··············Minor·(reclaiming·a·frame)·page·faults:· | 78 | ··············Minor·(reclaiming·a·frame)·page·faults:·14429 |
| 80 | ··············Voluntary·context·switches:· | 79 | ··············Voluntary·context·switches:·4336 |
| 81 | ··············Involuntary·context·switches:· | 80 | ··············Involuntary·context·switches:·400 |
| 82 | ··············Swaps:·0 | 81 | ··············Swaps:·0 |
| 83 | ··············File·system·inputs:·0 | 82 | ··············File·system·inputs:·0 |
| 84 | ··············File·system·outputs:· | 83 | ··············File·system·outputs:·16 |
| 85 | ··············Socket·messages·sent:·0 | 84 | ··············Socket·messages·sent:·0 |
| 86 | ··············Socket·messages·received:·0 | 85 | ··············Socket·messages·received:·0 |
| 87 | ··············Signals·delivered:·0 | 86 | ··············Signals·delivered:·0 |
| 88 | ··············Page·size·(bytes):·4096 | 87 | ··············Page·size·(bytes):·4096 |
| 89 | ··············Exit·status:·0 | 88 | ··············Exit·status:·0 |
| 90 | i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///; | 89 | i20·:·v=///·A·complicated·string^%&C@#CERQVASDFQ#BQBSDH"'·ewrjwklsf///; |
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| 61 | ········<div> | 61 | ········<div> |
| 62 | ··········<p>which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits·unchanged.</p> | 62 | ··········<p>which·will·run·M2·with·these·limits·while·leaving·the·shell's·ulimits·unchanged.</p> |
| 63 | ··········<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 | ··········<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> |
| 64 | ········</div> | 64 | ········</div> |
| 65 | ········<table·class="examples"> | 65 | ········<table·class="examples"> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·run("ulimit·-a") | 67 | <td>··············<pre><code·class="language-macaulay2">i1·:·run("ulimit·-a") |
| 68 | time(seconds)········700 | ||
| 69 | file(blocks)·········unlimited | ||
| 70 | data(kbytes)·········unlimited | ||
| 71 | stack(kbytes)········8192 | ||
| 72 | coredump(blocks)·····0 | ||
| 73 | memory(kbytes)·······850000 | ||
| 74 | locked·memory(kbytes)·3076856 | ||
| 75 | process··············95991 | ||
| 76 | nofiles··············512 | ||
| 77 | 68 | real-time·non-blocking·time··(microseconds,·-R)·unlimited | |
| 69 | core·file·size··············(blocks,·-c)·0 | ||
| 70 | data·seg·size···············(kbytes,·-d)·unlimited | ||
| 71 | scheduling·priority·················(-e)·0 | ||
| 72 | file·size···················(blocks,·-f)·unlimited | ||
| 73 | pending·signals·····················(-i)·96085 | ||
| 74 | max·locked·memory···········(kbytes,·-l)·3077552 | ||
| 75 | max·memory·size·············(kbytes,·-m)·850000 | ||
| 76 | open·files··························(-n)·512 | ||
| 77 | pipe·size················(512·bytes,·-p)·8 | ||
| 78 | POSIX·message·queues·········(bytes,·-q)·819200 | ||
| 79 | real-time·priority··················(-r)·0 | ||
| 80 | stack·size··················(kbytes,·-s)·8192 | ||
| 81 | cpu·time···················(seconds,·-t)·700 | ||
| 82 | max·user·processes··················(-u)·96085 | ||
| 83 | virtual·memory··············(kbytes,·-v)·unlimited | ||
| 78 | locks················unlimited | 84 | file·locks··························(-x)·unlimited |
| 79 | rtprio···············0 | ||
| 80 | o1·=·0</code></pre> | 85 | o1·=·0</code></pre> |
| 81 | </td>··········</tr> | 86 | </td>··········</tr> |
| 82 | ········</table> | 87 | ········</table> |
| 83 | ········<div> | 88 | ········<div> |
| 84 | ··········<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> | 89 | ··········<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> |
| 85 | ··········<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> | 90 | ··········<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)·3076856 | ||
| 42 | process··············95991 | ||
| 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)·96085 | ||
| 41 | max·locked·memory···········(kbytes,·-l)·3077552 | ||
| 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)·96085 | ||
| 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 92, 15 lines modified | Offset 92, 15 lines modified | ||
| 92 | ··········<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>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> |
| 93 | ··········<p>For·example,·we·can·write·a·few·functions·to·a·temporary·file:</p> | 93 | ··········<p>For·example,·we·can·write·a·few·functions·to·a·temporary·file:</p> |
| 94 | ········</div> | 94 | ········</div> |
| 95 | ········<table·class="examples"> | 95 | ········<table·class="examples"> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn=temporaryFileName()|".m2" | 97 | <td>··············<pre><code·class="language-macaulay2">i1·:·fn=temporaryFileName()|".m2" |
| 98 | o1·=·/tmp/M2- | 98 | o1·=·/tmp/M2-2356940-0/0.m2</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl;</code></pre> | 101 | <td>··············<pre><code·class="language-macaulay2">i2·:·fn<<///·square·=·(x)·->·(stderr<<"Running"<<endl;·sleep(1);·x^2);·///<<endl;</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;</code></pre> | 104 | <td>··············<pre><code·class="language-macaulay2">i3·:·fn<<///·justexit·=·()·->·(·exit(27);·);·///<<endl;</code></pre> |
| 105 | </td>··········</tr> | 105 | </td>··········</tr> |
| Offset 113, 26 lines modified | Offset 113, 26 lines modified | ||
| 113 | ········</table> | 113 | ········</table> |
| 114 | ········<div> | 114 | ········<div> |
| 115 | ··········<p>and·then·call·them:</p> | 115 | ··········<p>and·then·call·them:</p> |
| 116 | ········</div> | 116 | ········</div> |
| 117 | ········<table·class="examples"> | 117 | ········<table·class="examples"> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·h=runExternalM2(fn,"square",(4)); | 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·h=runExternalM2(fn,"square",(4)); |
| 120 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 120 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/1.m2"·>"/tmp/M2-2356940-0/1.out"·2>&1·)) |
| 121 | Finished·running.</code></pre> | 121 | Finished·running.</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·h | 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·h |
| 125 | o7·=·HashTable{"answer·file"·=>·null} | 125 | o7·=·HashTable{"answer·file"·=>·null} |
| 126 | ···············"exit·code"·=>·0 | 126 | ···············"exit·code"·=>·0 |
| 127 | ···············"output·file"·=>·null | 127 | ···············"output·file"·=>·null |
| 128 | ···············"return·code"·=>·0 | 128 | ···············"return·code"·=>·0 |
| 129 | ···············"statistics"·=>·null | 129 | ···············"statistics"·=>·null |
| 130 | ···············"time·used"·=>· | 130 | ···············"time·used"·=>·2 |
| 131 | ···············value·=>·16 | 131 | ···············value·=>·16 |
| 132 | o7·:·HashTable</code></pre> | 132 | o7·:·HashTable</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ··········<tr> | 134 | ··········<tr> |
| 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·h#value===4^2 | 135 | <td>··············<pre><code·class="language-macaulay2">i8·:·h#value===4^2 |
| Offset 147, 27 lines modified | Offset 147, 27 lines modified | ||
| 147 | ········<div> | 147 | ········<div> |
| 148 | ··········<p></p> | 148 | ··········<p></p> |
| 149 | ··········<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 | ··········<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> |
| 150 | ········</div> | 150 | ········</div> |
| 151 | ········<table·class="examples"> | 151 | ········<table·class="examples"> |
| 152 | ··········<tr> | 152 | ··········<tr> |
| 153 | <td>··············<pre><code·class="language-macaulay2">i10·:·h=runExternalM2(fn,"justexit",()); | 153 | <td>··············<pre><code·class="language-macaulay2">i10·:·h=runExternalM2(fn,"justexit",()); |
| 154 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 154 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/2.m2"·>"/tmp/M2-2356940-0/2.out"·2>&1·)) |
| 155 | Finished·running. | 155 | Finished·running. |
| 156 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> | 156 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| 158 | ··········<tr> | 158 | ··········<tr> |
| 159 | <td>··············<pre><code·class="language-macaulay2">i11·:·h | 159 | <td>··············<pre><code·class="language-macaulay2">i11·:·h |
| 160 | o11·=·HashTable{"answer·file"·=>·/tmp/M2- | 160 | o11·=·HashTable{"answer·file"·=>·/tmp/M2-2356940-0/2.ans} |
| 161 | ················"exit·code"·=>·27 | 161 | ················"exit·code"·=>·27 |
| 162 | ················"output·file"·=>·/tmp/M2- | 162 | ················"output·file"·=>·/tmp/M2-2356940-0/2.out |
| 163 | ················"return·code"·=>·6912 | 163 | ················"return·code"·=>·6912 |
| 164 | ················"statistics"·=>·null | 164 | ················"statistics"·=>·null |
| 165 | ················"time·used"·=>· | 165 | ················"time·used"·=>·1 |
| 166 | ················value·=>·null | 166 | ················value·=>·null |
| 167 | o11·:·HashTable</code></pre> | 167 | o11·:·HashTable</code></pre> |
| 168 | </td>··········</tr> | 168 | </td>··········</tr> |
| 169 | ··········<tr> | 169 | ··········<tr> |
| 170 | <td>··············<pre><code·class="language-macaulay2">i12·:·fileExists(h#"output·file") | 170 | <td>··············<pre><code·class="language-macaulay2">i12·:·fileExists(h#"output·file") |
| Offset 181, 79 lines modified | Offset 181, 78 lines modified | ||
| 181 | ········</table> | 181 | ········</table> |
| 182 | ········<div> | 182 | ········<div> |
| 183 | ··········<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 | ··········<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> |
| 184 | ········</div> | 184 | ········</div> |
| 185 | ········<table·class="examples"> | 185 | ········<table·class="examples"> |
| 186 | ··········<tr> | 186 | ··········<tr> |
| 187 | <td>··············<pre><code·class="language-macaulay2">i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); | 187 | <td>··············<pre><code·class="language-macaulay2">i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); |
| 188 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 188 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/3.m2"·>"/tmp/M2-2356940-0/3.out"·2>&1·)) |
| 189 | Killed | ||
| 190 | Finished·running. | 189 | Finished·running. |
| 191 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> | 190 | RunExternalM2:·expected·answer·file·does·not·exist</code></pre> |
| 192 | </td>··········</tr> | 191 | </td>··········</tr> |
| 193 | ··········<tr> | 192 | ··········<tr> |
| 194 | <td>··············<pre><code·class="language-macaulay2">i15·:·h | 193 | <td>··············<pre><code·class="language-macaulay2">i15·:·h |
| 195 | o15·=·HashTable{"answer·file"·=>·/tmp/M2- | 194 | o15·=·HashTable{"answer·file"·=>·/tmp/M2-2356940-0/3.ans} |
| 196 | ················"exit·code"·=>·0 | 195 | ················"exit·code"·=>·0 |
| 197 | ················"output·file"·=>·/tmp/M2- | 196 | ················"output·file"·=>·/tmp/M2-2356940-0/3.out |
| 198 | ················"return·code"·=>·9 | 197 | ················"return·code"·=>·9 |
| 199 | ················"statistics"·=>·null | 198 | ················"statistics"·=>·null |
| 200 | ················"time·used"·=>· | 199 | ················"time·used"·=>·2 |
| 201 | ················value·=>·null | 200 | ················value·=>·null |
| 202 | o15·:·HashTable</code></pre> | 201 | o15·:·HashTable</code></pre> |
| 203 | </td>··········</tr> | 202 | </td>··········</tr> |
| 204 | ··········<tr> | 203 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") | 204 | <td>··············<pre><code·class="language-macaulay2">i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get(h#"output·file") |
| 206 | o16·=· | 205 | o16·=· |
| 207 | ······i1·:·--·Script·/tmp/M2- | 206 | ······i1·:·--·Script·/tmp/M2-2356940-0/3.m2·automatically·generated·by·RunExternalM2 |
| 208 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); | 207 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); |
| 209 | ······i2·:·load·"/tmp/M2- | 208 | ······i2·:·load·"/tmp/M2-2356940-0/0.m2"; |
| 210 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2- | 209 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-2356940-0/3.ans",spin·(10)); |
| 211 | ······Spinning!!</code></pre> | 210 | ······Spinning!!</code></pre> |
| 212 | </td>··········</tr> | 211 | </td>··········</tr> |
| 213 | ··········<tr> | 212 | ··········<tr> |
| 214 | <td>··············<pre><code·class="language-macaulay2">i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get(h#"answer·file")</code></pre> | 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> |
| 215 | </td>··········</tr> | 214 | </td>··········</tr> |
| 216 | ········</table> | 215 | ········</table> |
| 217 | ········<div> | 216 | ········<div> |
| 218 | ··········<p></p> | 217 | ··········<p></p> |
| 219 | ··········<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> | 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> |
| 220 | ········</div> | 219 | ········</div> |
| 221 | ········<table·class="examples"> | 220 | ········<table·class="examples"> |
| 222 | ··········<tr> | 221 | ··········<tr> |
| 223 | <td>··············<pre><code·class="language-macaulay2">i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); | 222 | <td>··············<pre><code·class="language-macaulay2">i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); |
| 224 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 223 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/4.m2"·>"/tmp/M2-2356940-0/4.out"·2>&1')·>"/tmp/M2-2356940-0/4.stat"·2>&1·)) |
| 225 | Finished·running.</code></pre> | 224 | Finished·running.</code></pre> |
| 226 | </td>··········</tr> | 225 | </td>··········</tr> |
| 227 | ··········<tr> | 226 | ··········<tr> |
| 228 | <td>··············<pre><code·class="language-macaulay2">i19·:·h#"statistics" | 227 | <td>··············<pre><code·class="language-macaulay2">i19·:·h#"statistics" |
| 229 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2- | 228 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/M2-2356940-0/4.m2"·>"/tmp/M2-2356940-0/4.out"·2>&1" |
| 230 | ··············User·time·(seconds):·4.3 | 229 | ··············User·time·(seconds):·4.32 |
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| Offset 46, 201 lines modified | Offset 46, 200 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/M2-2356940-0/0.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 | M2-2356940-0/1.m2"·>"/tmp/M2-2356940-0/1.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 |
| 69 | ···············"statistics"·=>·null | 69 | ···············"statistics"·=>·null |
| 70 | ···············"time·used"·=>· | 70 | ···············"time·used"·=>·2 |
| 71 | ···············value·=>·16 | 71 | ···············value·=>·16 |
| 72 | o7·:·HashTable | 72 | o7·:·HashTable |
| 73 | i8·:·h#value===4^2 | 73 | i8·:·h#value===4^2 |
| 74 | o8·=·true | 74 | o8·=·true |
| 75 | i9·:·h#"exit·code"===0 | 75 | i9·:·h#"exit·code"===0 |
| 76 | o9·=·true | 76 | o9·=·true |
| 77 | An·abnormal·program·exit·will·have·a·nonzero·exit·code;·also,·the·value·will·be | 77 | An·abnormal·program·exit·will·have·a·nonzero·exit·code;·also,·the·value·will·be |
| 78 | null,·the·output·file·should·exist,·but·the·answer·file·may·not·exist·unless | 78 | null,·the·output·file·should·exist,·but·the·answer·file·may·not·exist·unless |
| 79 | the·routine·finished·successfully. | 79 | the·routine·finished·successfully. |
| 80 | i10·:·h=runExternalM2(fn,"justexit",()); | 80 | i10·:·h=runExternalM2(fn,"justexit",()); |
| 81 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ | 81 | Running·(true·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··-q··<"/tmp/ |
| 82 | M2- | 82 | M2-2356940-0/2.m2"·>"/tmp/M2-2356940-0/2.out"·2>&1·)) |
| 83 | Finished·running. | 83 | Finished·running. |
| 84 | RunExternalM2:·expected·answer·file·does·not·exist | 84 | RunExternalM2:·expected·answer·file·does·not·exist |
| 85 | i11·:·h | 85 | i11·:·h |
| 86 | o11·=·HashTable{"answer·file"·=>·/tmp/M2- | 86 | o11·=·HashTable{"answer·file"·=>·/tmp/M2-2356940-0/2.ans} |
| 87 | ················"exit·code"·=>·27 | 87 | ················"exit·code"·=>·27 |
| 88 | ················"output·file"·=>·/tmp/M2- | 88 | ················"output·file"·=>·/tmp/M2-2356940-0/2.out |
| 89 | ················"return·code"·=>·6912 | 89 | ················"return·code"·=>·6912 |
| 90 | ················"statistics"·=>·null | 90 | ················"statistics"·=>·null |
| 91 | ················"time·used"·=>· | 91 | ················"time·used"·=>·1 |
| 92 | ················value·=>·null | 92 | ················value·=>·null |
| 93 | o11·:·HashTable | 93 | o11·:·HashTable |
| 94 | i12·:·fileExists(h#"output·file") | 94 | i12·:·fileExists(h#"output·file") |
| 95 | o12·=·true | 95 | o12·=·true |
| 96 | i13·:·fileExists(h#"answer·file") | 96 | i13·:·fileExists(h#"answer·file") |
| 97 | o13·=·false | 97 | o13·=·false |
| 98 | 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 | 98 | 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 |
| 99 | time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time: | 99 | time,·while·the·system·is·asked·to·use·10·seconds·of·computational·time: |
| 100 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); | 100 | i14·:·h=runExternalM2(fn,"spin",10,PreRunScript=>"ulimit·-t·2"); |
| 101 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··- | 101 | Running·(ulimit·-t·2·&&·(/usr/bin/M2-binary··--stop·--no-debug·--silent··- |
| 102 | q··<"/tmp/M2- | 102 | q··<"/tmp/M2-2356940-0/3.m2"·>"/tmp/M2-2356940-0/3.out"·2>&1·)) |
| 103 | Killed | ||
| 104 | Finished·running. | 103 | Finished·running. |
| 105 | RunExternalM2:·expected·answer·file·does·not·exist | 104 | RunExternalM2:·expected·answer·file·does·not·exist |
| 106 | i15·:·h | 105 | i15·:·h |
| 107 | o15·=·HashTable{"answer·file"·=>·/tmp/M2- | 106 | o15·=·HashTable{"answer·file"·=>·/tmp/M2-2356940-0/3.ans} |
| 108 | ················"exit·code"·=>·0 | 107 | ················"exit·code"·=>·0 |
| 109 | ················"output·file"·=>·/tmp/M2- | 108 | ················"output·file"·=>·/tmp/M2-2356940-0/3.out |
| 110 | ················"return·code"·=>·9 | 109 | ················"return·code"·=>·9 |
| 111 | ················"statistics"·=>·null | 110 | ················"statistics"·=>·null |
| 112 | ················"time·used"·=>· | 111 | ················"time·used"·=>·2 |
| 113 | ················value·=>·null | 112 | ················value·=>·null |
| 114 | o15·:·HashTable | 113 | o15·:·HashTable |
| 115 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get | 114 | i16·:·if·h#"output·file"·=!=·null·and·fileExists(h#"output·file")·then·get |
| 116 | (h#"output·file") | 115 | (h#"output·file") |
| 117 | o16·= | 116 | o16·= |
| 118 | ······i1·:·--·Script·/tmp/M2- | 117 | ······i1·:·--·Script·/tmp/M2-2356940-0/3.m2·automatically·generated·by |
| 119 | RunExternalM2 | 118 | RunExternalM2 |
| 120 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); | 119 | ···········needsPackage("RunExternalM2",Configuration=>{"isChild"=>true}); |
| 121 | ······i2·:·load·"/tmp/M2- | 120 | ······i2·:·load·"/tmp/M2-2356940-0/0.m2"; |
| 122 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2- | 121 | ······i3·:·runExternalM2ReturnAnswer("/tmp/M2-2356940-0/3.ans",spin·(10)); |
| 123 | ······Spinning!! | 122 | ······Spinning!! |
| 124 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get | 123 | i17·:·if·h#"answer·file"·=!=·null·and·fileExists(h#"answer·file")·then·get |
| 125 | (h#"answer·file") | 124 | (h#"answer·file") |
| 126 | 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 | 125 | 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 |
| 127 | command: | 126 | command: |
| 128 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); | 127 | i18·:·h=runExternalM2(fn,"spin",3,KeepStatistics=>true); |
| 129 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·- | 128 | Running·(true·&&·(·(/usr/bin/time·--verbose·sh·-c·'/usr/bin/M2-binary··--stop·- |
| 130 | -no-debug·--silent··-q··<"/tmp/M2- | 129 | -no-debug·--silent··-q··<"/tmp/M2-2356940-0/4.m2"·>"/tmp/M2-2356940-0/4.out" |
| 131 | 2>&1')·>"/tmp/M2- | 130 | 2>&1')·>"/tmp/M2-2356940-0/4.stat"·2>&1·)) |
| 132 | Finished·running. | 131 | Finished·running. |
| 133 | i19·:·h#"statistics" | 132 | i19·:·h#"statistics" |
| 134 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug | 133 | o19·=·········Command·being·timed:·"sh·-c·/usr/bin/M2-binary··--stop·--no-debug |
| 135 | --silent··-q··<"/tmp/M2- | 134 | --silent··-q··<"/tmp/M2-2356940-0/4.m2"·>"/tmp/M2-2356940-0/4.out"·2>&1" |
| 136 | ··············User·time·(seconds):·4.3 | 135 | ··············User·time·(seconds):·4.32 |
| 137 | ··············System·time·(seconds):·0. | 136 | ··············System·time·(seconds):·0.05 |
| 138 | ··············Percent·of·CPU·this·job·got:· | 137 | ··············Percent·of·CPU·this·job·got:·86% |
| 139 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0: | 138 | ··············Elapsed·(wall·clock)·time·(h:mm:ss·or·m:ss):·0:05.05 |
| 140 | ··············Average·shared·text·size·(kbytes):·0 | 139 | ··············Average·shared·text·size·(kbytes):·0 |
| 141 | ··············Average·unshared·data·size·(kbytes):·0 | 140 | ··············Average·unshared·data·size·(kbytes):·0 |
| 142 | ··············Average·stack·size·(kbytes):·0 | 141 | ··············Average·stack·size·(kbytes):·0 |
| 143 | ··············Average·total·size·(kbytes):·0 | 142 | ··············Average·total·size·(kbytes):·0 |
| 144 | ··············Maximum·resident·set·size·(kbytes):·29 | 143 | ··············Maximum·resident·set·size·(kbytes):·299684 |
| 145 | ··············Average·resident·set·size·(kbytes):·0 | 144 | ··············Average·resident·set·size·(kbytes):·0 |
| 146 | ··············Major·(requiring·I/O)·page·faults:·0 | 145 | ··············Major·(requiring·I/O)·page·faults:·0 |
| 147 | ··············Minor·(reclaiming·a·frame)·page·faults:· | 146 | ··············Minor·(reclaiming·a·frame)·page·faults:·14429 |
| 148 | ··············Voluntary·context·switches:· | 147 | ··············Voluntary·context·switches:·4336 |
| 149 | ··············Involuntary·context·switches:· | 148 | ··············Involuntary·context·switches:·400 |
| 150 | ··············Swaps:·0 | 149 | ··············Swaps:·0 |
| 151 | ··············File·system·inputs:·0 | 150 | ··············File·system·inputs:·0 |
| 152 | ··············File·system·outputs:· | 151 | ··············File·system·outputs:·16 |
| 153 | ··············Socket·messages·sent:·0 | 152 | ··············Socket·messages·sent:·0 |
| 154 | ··············Socket·messages·received:·0 | 153 | ··············Socket·messages·received:·0 |
| 155 | ··············Signals·delivered:·0 | 154 | ··············Signals·delivered:·0 |
| 156 | ··············Page·size·(bytes):·4096 | 155 | ··············Page·size·(bytes):·4096 |
| 157 | ··············Exit·status:·0 | 156 | ··············Exit·status:·0 |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00223026s·(cpu);·0.000170727s·(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·3. | 39 | ·--·used·3.25784s·(cpu);·2.60037s·(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 87, 25 lines modified | Offset 87, 25 lines modified | ||
| 87 | ··························"variable·positions"·=>·{-1} | 87 | ··························"variable·positions"·=>·{-1} |
| 88 | o5·:·InterpretedSLProgram</code></pre> | 88 | o5·:·InterpretedSLProgram</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·A·=·evaluate(slp,matrix{{1}}); | 91 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·A·=·evaluate(slp,matrix{{1}}); |
| 92 | ·--·used·0.002 | 92 | ·--·used·0.00223026s·(cpu);·0.000170727s·(thread);·0s·(gc) |
| 93 | ··············1·······1 | 93 | ··············1·······1 |
| 94 | o6·:·Matrix·ZZ··<--·ZZ</code></pre> | 94 | o6·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i7·:·ZZ[y];</code></pre> | 97 | <td>··············<pre><code·class="language-macaulay2">i7·:·ZZ[y];</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) | 100 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·B·=·sub((y+1)^(2^n),{y=>1}) |
| 101 | ·--·used·3. | 101 | ·--·used·3.25784s·(cpu);·2.60037s·(thread);·0s·(gc) |
| 102 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 | 102 | o8·=·104438888141315250669175271071662438257996424904738378038423348328395390 |
| 103 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 | 103 | ·····797155745684882681193499755834089010671443926283798757343818579360726323 |
| 104 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 | 104 | ·····608785136527794595697654370999834036159013438371831442807001185594622637 |
| 105 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 | 105 | ·····631883939771274567233468434458661749680790870580370407128404874011860911 |
| 106 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 | 106 | ·····446797778359802900668693897688178778594690563019026094059957945343282346 |
| 107 | ·····930302669644305902501597239986771421554169383555988529148631823791443449 | 107 | ·····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·0.00223026s·(cpu);·0.000170727s·(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·3. | 48 | ·--·used·3.25784s·(cpu);·2.60037s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·:·cC=complement·C | 58 | i8·:·cC=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·:·dualize·cC | 63 | i9·:·dualize·cC |
| 64 | o9·=·2:·v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v·· | 64 | o9·=·2:·v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v·· |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 137 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 138 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> | 138 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i8·:·cC=complement·C | 141 | <td>··············<pre><code·class="language-macaulay2">i8·:·cC=complement·C |
| 142 | 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·· | 142 | 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·· |
| 143 | ········· | 143 | ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2 |
| 144 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 144 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 145 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> | 145 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i9·:·dualize·cC | 148 | <td>··············<pre><code·class="language-macaulay2">i9·:·dualize·cC |
| Offset 82, 15 lines modified | Offset 82, 15 lines modified | ||
| 82 | ·········0·1·2··0·1·4··0·3·4··1·2·3··1·2·5··1·4·5··2·3·4··3·4·5 | 82 | ·········0·1·2··0·1·4··0·3·4··1·2·3··1·2·5··1·4·5··2·3·4··3·4·5 |
| 83 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 83 | o7·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 84 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 | 84 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 |
| 85 | i8·:·cC=complement·C | 85 | i8·:·cC=complement·C |
| 86 | 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 | 86 | 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 |
| 87 | ········· | 87 | ·········4·5·3··1·4·5··1·5·2··4·2·3··0·4·3··1·0·4··1·2·3··1·0·2 |
| 88 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) | 88 | o8·:·co-complex·of·dim·2·embedded·in·dim·5·(printing·facets) |
| 89 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 | 89 | ·····equidimensional,·simplicial,·F-vector·{0,·0,·0,·8,·12,·6,·1},·Euler·=·1 |
| 90 | i9·:·dualize·cC | 90 | i9·:·dualize·cC |
| 91 | o9·=·2:·v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v | 91 | o9·=·2:·v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v··v·v·v |
| 92 | ·········3·4·5··2·3·5··1·2·5··0·4·5··0·3·4··0·2·3··0·1·5··0·1·2 | 92 | ·········3·4·5··2·3·5··1·2·5··0·4·5··0·3·4··0·2·3··0·1·5··0·1·2 |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.00 | 19 | ·--·0.00551005·seconds·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 | ·--·0.002 | 56 | ·--·0.00207743·seconds·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 | ·--·0.00 | 99 | ·--·0.00398992·seconds·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 | ·--·0.002 | 19 | ·--·0.00222625·seconds·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 | ·--·0.000 | 52 | ·--·0.000478943·seconds·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 | ·--·0.00 | 59 | ·--·0.000988912·seconds·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 | ·--·0.00 | 21 | ·--·0.00316419·seconds·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 | ·--·0.002 | 21 | ·--·0.00220405·seconds·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 | ·--·0.00 | 21 | ·--·0.00249874·seconds·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 104, 15 lines modified | Offset 104, 15 lines modified | ||
| 104 | o3·=·{5,·11,·3,·2} | 104 | o3·=·{5,·11,·3,·2} |
| 105 | o3·:·List</code></pre> | 105 | o3·:·List</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) | 108 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>4) |
| 109 | ·--·0.00 | 109 | ·--·0.00551005·seconds·elapsed |
| 110 | ·······6·······19·······19·······7·······3 | 110 | ·······6·······19·······19·······7·······3 |
| 111 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ | 111 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ··<--·ZZ |
| 112 | ········································ | 112 | ········································ |
| 113 | ·····0·······1········2········3·······4 | 113 | ·····0·······1········2········3·······4 |
| 114 | o4·:·ChainComplex</code></pre> | 114 | o4·:·ChainComplex</code></pre> |
| Offset 143, 15 lines modified | Offset 143, 15 lines modified | ||
| 143 | ················································ | 143 | ················································ |
| 144 | ·····-1········0··········1··········2·········3 | 144 | ·····-1········0··········1··········2·········3 |
| 145 | o6·:·ChainComplex</code></pre> | 145 | o6·:·ChainComplex</code></pre> |
| 146 | </td>··········</tr> | 146 | </td>··········</tr> |
| 147 | ··········<tr> | 147 | ··········<tr> |
| 148 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,U)=SVDComplex·CR; | 148 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,U)=SVDComplex·CR; |
| 149 | ·--·0.002 | 149 | ·--·0.00207743·seconds·elapsed</code></pre> |
| 150 | </td>··········</tr> | 150 | </td>··········</tr> |
| 151 | ··········<tr> | 151 | ··········<tr> |
| 152 | <td>··············<pre><code·class="language-macaulay2">i8·:·h | 152 | <td>··············<pre><code·class="language-macaulay2">i8·:·h |
| 153 | o8·=·HashTable{-1·=>·1} | 153 | o8·=·HashTable{-1·=>·1} |
| 154 | ···············0·=>·3 | 154 | ···············0·=>·3 |
| 155 | ···············1·=>·5 | 155 | ···············1·=>·5 |
| Offset 193, 15 lines modified | Offset 193, 15 lines modified | ||
| 193 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} | 193 | o12·=·{4.88498e-15,·3.2685e-13,·2.02505e-13,·5.32907e-15} |
| 194 | o12·:·List</code></pre> | 194 | o12·:·List</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| 196 | ··········<tr> | 196 | ··········<tr> |
| 197 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); | 197 | <td>··············<pre><code·class="language-macaulay2">i13·:·elapsedTime·(hL,U)=SVDComplex(CR,Strategy=>Laplacian); |
| 198 | ·--·0.00 | 198 | ·--·0.00398992·seconds·elapsed</code></pre> |
| 199 | </td>··········</tr> | 199 | </td>··········</tr> |
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i14·:·hL·===·h | 201 | <td>··············<pre><code·class="language-macaulay2">i14·:·hL·===·h |
| 202 | o14·=·true</code></pre> | 202 | o14·=·true</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<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 | ·--·0.00 | 43 | ·--·0.00551005·seconds·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 | ·--·0.002 | 76 | ·--·0.00207743·seconds·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 | ·--·0.00 | 115 | ·--·0.00398992·seconds·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 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | o3·=·{4,·3,·3} | 106 | o3·=·{4,·3,·3} |
| 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·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 110 | <td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 111 | ·--·0.002 | 111 | ·--·0.00222625·seconds·elapsed |
| 112 | ·······5·······10·······11·······5 | 112 | ·······5·······10·······11·······5 |
| 113 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 113 | o4·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 114 | ································ | 114 | ································ |
| 115 | ·····0·······1········2········3 | 115 | ·····0·······1········2········3 |
| 116 | o4·:·ChainComplex</code></pre> | 116 | o4·:·ChainComplex</code></pre> |
| Offset 141, 26 lines modified | Offset 141, 26 lines modified | ||
| 141 | ······································ | 141 | ······································ |
| 142 | ·····0·········1··········2··········3 | 142 | ·····0·········1··········2··········3 |
| 143 | o6·:·ChainComplex</code></pre> | 143 | o6·:·ChainComplex</code></pre> |
| 144 | </td>··········</tr> | 144 | </td>··········</tr> |
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,h1)=SVDHomology·CR | 146 | <td>··············<pre><code·class="language-macaulay2">i7·:·elapsedTime·(h,h1)=SVDHomology·CR |
| 147 | ·--·0.000 | 147 | ·--·0.000478943·seconds·elapsed |
| 148 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) | 148 | o7·=·(HashTable{0·=>·1},·HashTable{1·=>·(7.87842,·1.31052,·)···········}) |
| 149 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) | 149 | ················1·=>·3·············2·=>·(37.9214,·30.3707,·7.11744e-15) |
| 150 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) | 150 | ················2·=>·5·············3·=>·(14.972,·8.57847,·3.25752e-15) |
| 151 | ················3·=>·2 | 151 | ················3·=>·2 |
| 152 | o7·:·Sequence</code></pre> | 152 | o7·:·Sequence</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) | 155 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·(hL,hL1)=SVDHomology(CR,Strategy=>Laplacian) |
| 156 | ·--·0.00 | 156 | ·--·0.000988912·seconds·elapsed |
| 157 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) | 157 | o8·=·(HashTable{0·=>·1},·HashTable{0·=>·(,·1.71747,·-1.72291e-14)······}) |
| 158 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) | 158 | ················1·=>·3·············1·=>·(1.71747,·922.381,·2.51496e-13) |
| 159 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) | 159 | ················2·=>·5·············2·=>·(922.381,·73.5901,·1.81323e-13) |
| 160 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) | 160 | ················3·=>·2·············3·=>·(73.5901,·,·2.82914e-13) |
| 161 | o8·:·Sequence</code></pre> | 161 | 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 | ·--·0.002 | 46 | ·--·0.00222625·seconds·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 | ·--·0.000 | 75 | ·--·0.000478943·seconds·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 | ·--·0.00 | 82 | ·--·0.000988912·seconds·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 105, 15 lines modified | Offset 105, 15 lines modified | ||
| 105 | o4·=·{4,·3,·5} | 105 | o4·=·{4,·3,·5} |
| 106 | o4·:·List</code></pre> | 106 | o4·:·List</code></pre> |
| 107 | </td>··········</tr> | 107 | </td>··········</tr> |
| 108 | ··········<tr> | 108 | ··········<tr> |
| 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) | 109 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>100,ZeroMean=>true) |
| 110 | ·--·0.00 | 110 | ·--·0.00316419·seconds·elapsed |
| 111 | ·······6·······10·······13·······8 | 111 | ·······6·······10·······13·······8 |
| 112 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 112 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 113 | ································ | 113 | ································ |
| 114 | ·····0·······1········2········3 | 114 | ·····0·······1········2········3 |
| 115 | o5·:·ChainComplex</code></pre> | 115 | 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 | ·--·0.00 | 39 | ·--·0.00316419·seconds·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 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | o4·=·{4,·3,·3} | 96 | o4·=·{4,·3,·3} |
| 97 | o4·:·List</code></pre> | 97 | o4·:·List</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 101 | ·--·0.002 | 101 | ·--·0.00220405·seconds·elapsed |
| 102 | ·······6·······10·······11·······5 | 102 | ·······6·······10·······11·······5 |
| 103 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 103 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 104 | ································ | 104 | ································ |
| 105 | ·····0·······1········2········3 | 105 | ·····0·······1········2········3 |
| 106 | o5·:·ChainComplex</code></pre> | 106 | 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 | ·--·0.002 | 34 | ·--·0.00220405·seconds·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 96, 15 lines modified | Offset 96, 15 lines modified | ||
| 96 | o4·=·{4,·3,·3} | 96 | o4·=·{4,·3,·3} |
| 97 | o4·:·List</code></pre> | 97 | o4·:·List</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) | 100 | <td>··············<pre><code·class="language-macaulay2">i5·:·elapsedTime·C=randomChainComplex(h,r,Height=>5,ZeroMean=>true) |
| 101 | ·--·0.00 | 101 | ·--·0.00249874·seconds·elapsed |
| 102 | ·······6·······10·······11·······5 | 102 | ·······6·······10·······11·······5 |
| 103 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ | 103 | o5·=·ZZ··<--·ZZ···<--·ZZ···<--·ZZ |
| 104 | ································ | 104 | ································ |
| 105 | ·····0·······1········2········3 | 105 | ·····0·······1········2········3 |
| 106 | o5·:·ChainComplex</code></pre> | 106 | 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 | ·--·0.00 | 34 | ·--·0.00249874·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | dGVjdGluZyBTQUdCSSBiYXNlcyIsICJsaW5lbnVtIiA9PiAyMTYsIElucHV0cyA9PiB7U1BBTntU | 11 | dGVjdGluZyBTQUdCSSBiYXNlcyIsICJsaW5lbnVtIiA9PiAyMTYsIElucHV0cyA9PiB7U1BBTntU |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.322707s·(cpu);·0.282758s·(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·0.5 | 45 | ·--·used·0.515315s·(cpu);·0.485886s·(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·0.0 | 51 | ·--·used·0.0159338s·(cpu);·0.0163966s·(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·0.00320998s·(cpu);·0.00632492s·(thread);·0s·(gc) |
| 55 | o12·:·Ideal·of·S | 55 | o12·:·Ideal·of·S |
| 56 | i13·:· | 56 | i13·:· |
| Offset 107, 21 lines modified | Offset 107, 21 lines modified | ||
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); | 108 | <td>··············<pre><code·class="language-macaulay2">i6·:·J·=·ideal(map(S^1,·S^n,·(p,·q)·->·S_q^5)); |
| 109 | o6·:·Ideal·of·S</code></pre> | 109 | o6·:·Ideal·of·S</code></pre> |
| 110 | </td>··········</tr> | 110 | </td>··········</tr> |
| 111 | ··········<tr> | 111 | ··········<tr> |
| 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); | 112 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·quotient(I^3,·J^2,·Strategy·=>·Iterate); |
| 113 | ·--·used·0. | 113 | ·--·used·0.322707s·(cpu);·0.282758s·(thread);·0s·(gc) |
| 114 | o7·:·Ideal·of·S</code></pre> | 114 | o7·:·Ideal·of·S</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); | 117 | <td>··············<pre><code·class="language-macaulay2">i8·:·time·quotient(I^3,·J^2,·Strategy·=>·Quotient); |
| 118 | ·--·used·0.5 | 118 | ·--·used·0.515315s·(cpu);·0.485886s·(thread);·0s·(gc) |
| 119 | o8·:·Ideal·of·S</code></pre> | 119 | o8·:·Ideal·of·S</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ········</table> | 121 | ········</table> |
| 122 | ········<div> | 122 | ········<div> |
| 123 | ··········<p><span·class="tt">Strategy·=>·Quotient</span>·is·faster·in·other·cases:</p> | 123 | ··········<p><span·class="tt">Strategy·=>·Quotient</span>·is·faster·in·other·cases:</p> |
| 124 | ········</div> | 124 | ········</div> |
| Offset 132, 21 lines modified | Offset 132, 21 lines modified | ||
| 132 | ··········<tr> | 132 | ··········<tr> |
| 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·I·=·ideal·vars·S; | 133 | <td>··············<pre><code·class="language-macaulay2">i10·:·I·=·ideal·vars·S; |
| 134 | o10·:·Ideal·of·S</code></pre> | 134 | o10·:·Ideal·of·S</code></pre> |
| 135 | </td>··········</tr> | 135 | </td>··········</tr> |
| 136 | ··········<tr> | 136 | ··········<tr> |
| 137 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); | 137 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·quotient(I^5,·I^3,·Strategy·=>·Iterate); |
| 138 | ·--·used·0.0 | 138 | ·--·used·0.0159338s·(cpu);·0.0163966s·(thread);·0s·(gc) |
| 139 | o11·:·Ideal·of·S</code></pre> | 139 | o11·:·Ideal·of·S</code></pre> |
| 140 | </td>··········</tr> | 140 | </td>··········</tr> |
| 141 | ··········<tr> | 141 | ··········<tr> |
| 142 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); | 142 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·quotient(I^5,·I^3,·Strategy·=>·Quotient); |
| 143 | ·--·used·0.00 | 143 | ·--·used·0.00320998s·(cpu);·0.00632492s·(thread);·0s·(gc) |
| 144 | o12·:·Ideal·of·S</code></pre> | 144 | o12·:·Ideal·of·S</code></pre> |
| 145 | </td>··········</tr> | 145 | </td>··········</tr> |
| 146 | ········</table> | 146 | ········</table> |
| 147 | ······</div> | 147 | ······</div> |
| 148 | ······<div> | 148 | ······<div> |
| 149 | ········<h2>Further·information</h2> | 149 | ········<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·0.322707s·(cpu);·0.282758s·(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·0.5 | 65 | ·--·used·0.515315s·(cpu);·0.485886s·(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·0.0 | 72 | ·--·used·0.0159338s·(cpu);·0.0163966s·(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·0.00320998s·(cpu);·0.00632492s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00364313s·(cpu);·0.00581955s·(thread);·0s·(gc) | ||
| 45 | ·--·used·0.004 | 44 | ·--·used·0.00400351s·(cpu);·0.00520764s·(thread);·0s·(gc) |
| 45 | ·--·used·0.00357735s·(cpu);·0.00666711s·(thread);·0s·(gc) | ||
| 46 | ·--·used·0.0701112s·(cpu);·0.0312286s·(thread);·0s·(gc) | ||
| 46 | ·--·used·0.0 | 47 | ·--·used·0.012605s·(cpu);·0.0139535s·(thread);·0s·(gc) |
| 47 | ·--·used·0.0 | 48 | ·--·used·0.0247075s·(cpu);·0.0255196s·(thread);·0s·(gc) |
| 48 | ·--·used·0.0 | 49 | ·--·used·0.0423444s·(cpu);·0.043473s·(thread);·0s·(gc) |
| 49 | ·--·used·0.0 | 50 | ·--·used·0.0733366s·(cpu);·0.074221s·(thread);·0s·(gc) |
| 50 | ·--·used·0.11 | 51 | ·--·used·0.114642s·(cpu);·0.114797s·(thread);·0s·(gc) |
| 51 | ·--·used·0.186307s·(cpu);·0.186494s·(thread);·0s·(gc) | ||
| 52 | ·--·used·0. | 52 | ·--·used·0.255405s·(cpu);·0.203252s·(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 107, 23 lines modified | Offset 107, 23 lines modified | ||
| 107 | o6·=·f | 107 | o6·=·f |
| 108 | o6·:·FunctionClosure</code></pre> | 108 | o6·:·FunctionClosure</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·n·from·2·to·10·list·time·f·n | 111 | <td>··············<pre><code·class="language-macaulay2">i7·:·for·n·from·2·to·10·list·time·f·n |
| 112 | ·--·used·0.00364313s·(cpu);·0.00581955s·(thread);·0s·(gc) | ||
| 113 | ·--·used·0.004 | 112 | ·--·used·0.00400351s·(cpu);·0.00520764s·(thread);·0s·(gc) |
| 113 | ·--·used·0.00357735s·(cpu);·0.00666711s·(thread);·0s·(gc) | ||
| 114 | ·--·used·0.0701112s·(cpu);·0.0312286s·(thread);·0s·(gc) | ||
| 114 | ·--·used·0.0 | 115 | ·--·used·0.012605s·(cpu);·0.0139535s·(thread);·0s·(gc) |
| 115 | ·--·used·0.0 | 116 | ·--·used·0.0247075s·(cpu);·0.0255196s·(thread);·0s·(gc) |
| 116 | ·--·used·0.0 | 117 | ·--·used·0.0423444s·(cpu);·0.043473s·(thread);·0s·(gc) |
| 117 | ·--·used·0.0 | 118 | ·--·used·0.0733366s·(cpu);·0.074221s·(thread);·0s·(gc) |
| 118 | ·--·used·0.11 | 119 | ·--·used·0.114642s·(cpu);·0.114797s·(thread);·0s·(gc) |
| 119 | ·--·used·0.186307s·(cpu);·0.186494s·(thread);·0s·(gc) | ||
| 120 | ·--·used·0. | 120 | ·--·used·0.255405s·(cpu);·0.203252s·(thread);·0s·(gc) |
| 121 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, | 121 | o7·=·{1,·27,·2875,·698005,·305093061,·210480374951,·210776836330775, |
| 122 | ·····------------------------------------------------------------------------ | 122 | ·····------------------------------------------------------------------------ |
| 123 | ·····289139638632755625,·520764738758073845321} | 123 | ·····289139638632755625,·520764738758073845321} |
| 124 | o7·:·List</code></pre> | 124 | o7·:·List</code></pre> |
| 125 | </td>··········</tr> | 125 | </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·0.00364313s·(cpu);·0.00581955s·(thread);·0s·(gc) | ||
| 62 | ·--·used·0.004 | 61 | ·--·used·0.00400351s·(cpu);·0.00520764s·(thread);·0s·(gc) |
| 62 | ·--·used·0.00357735s·(cpu);·0.00666711s·(thread);·0s·(gc) | ||
| 63 | ·--·used·0.0701112s·(cpu);·0.0312286s·(thread);·0s·(gc) | ||
| 63 | ·--·used·0.0 | 64 | ·--·used·0.012605s·(cpu);·0.0139535s·(thread);·0s·(gc) |
| 64 | ·--·used·0.0 | 65 | ·--·used·0.0247075s·(cpu);·0.0255196s·(thread);·0s·(gc) |
| 65 | ·--·used·0.0 | 66 | ·--·used·0.0423444s·(cpu);·0.043473s·(thread);·0s·(gc) |
| 66 | ·--·used·0.0 | 67 | ·--·used·0.0733366s·(cpu);·0.074221s·(thread);·0s·(gc) |
| 67 | ·--·used·0.11 | 68 | ·--·used·0.114642s·(cpu);·0.114797s·(thread);·0s·(gc) |
| 68 | ·--·used·0.186307s·(cpu);·0.186494s·(thread);·0s·(gc) | ||
| 69 | ·--·used·0. | 69 | ·--·used·0.255405s·(cpu);·0.203252s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjQ1Niwgc3ltYm9sIERvY3VtZW50VGFn | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjQ1Niwgc3ltYm9sIERvY3VtZW50VGFn |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·3.28555s·(cpu);·2.71417s·(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·46.8919s·(cpu);·44.7538s·(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·0. | 27 | ·--·used·0.18967s·(cpu);·0.138235s·(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·0.1 | 33 | ·--·used·0.117133s·(cpu);·0.0893253s·(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 145, 15 lines modified | Offset 145, 15 lines modified | ||
| 145 | ··········<tr> | 145 | ··········<tr> |
| 146 | <td>··············<pre><code·class="language-macaulay2">i10·:·X=((W)*ideal(y)+ideal(f)); | 146 | <td>··············<pre><code·class="language-macaulay2">i10·:·X=((W)*ideal(y)+ideal(f)); |
| 147 | o10·:·Ideal·of·R</code></pre> | 147 | o10·:·Ideal·of·R</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·isComponentContained(X,Y) | 150 | <td>··············<pre><code·class="language-macaulay2">i11·:·time·isComponentContained(X,Y) |
| 151 | ·--·used·3. | 151 | ·--·used·3.28555s·(cpu);·2.71417s·(thread);·0s·(gc) |
| 152 | o11·=·true</code></pre> | 152 | o11·=·true</code></pre> |
| 153 | </td>··········</tr> | 153 | </td>··········</tr> |
| 154 | ··········<tr> | 154 | ··········<tr> |
| 155 | <td>··············<pre><code·class="language-macaulay2">i12·:·print·"we·could·confirm·this·with·the·computation:" | 155 | <td>··············<pre><code·class="language-macaulay2">i12·:·print·"we·could·confirm·this·with·the·computation:" |
| 156 | we·could·confirm·this·with·the·computation:</code></pre> | 156 | we·could·confirm·this·with·the·computation:</code></pre> |
| 157 | </td>··········</tr> | 157 | </td>··········</tr> |
| Offset 166, 15 lines modified | Offset 166, 15 lines modified | ||
| 166 | ······----------------------------------------------------------------------- | 166 | ······----------------------------------------------------------------------- |
| 167 | ······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 | ······c*d*h,·c*d*i,·c*e*g,·c*e*h,·c*e*i,·c*f*g,·c*f*h,·c*f*i) |
| 168 | o13·:·Ideal·of·R</code></pre> | 168 | o13·:·Ideal·of·R</code></pre> |
| 169 | </td>··········</tr> | 169 | </td>··········</tr> |
| 170 | ··········<tr> | 170 | ··········<tr> |
| 171 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) | 171 | <td>··············<pre><code·class="language-macaulay2">i14·:·time·isSubset(saturate(Y,B),saturate(X,B)) |
| 172 | ·--·used· | 172 | ·--·used·46.8919s·(cpu);·44.7538s·(thread);·0s·(gc) |
| 173 | o14·=·true</code></pre> | 173 | o14·=·true</code></pre> |
| 174 | </td>··········</tr> | 174 | </td>··········</tr> |
| 175 | ········</table> | 175 | ········</table> |
| 176 | ······</div> | 176 | ······</div> |
| 177 | ······<div·class="waystouse"> | 177 | ······<div·class="waystouse"> |
| 178 | ········<h2>Ways·to·use·<span·class="tt">isComponentContained</span>·:</h2> | 178 | ········<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·3.28555s·(cpu);·2.71417s·(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·46.8919s·(cpu);·44.7538s·(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 112, 25 lines modified | Offset 112, 25 lines modified | ||
| 112 | o5·=·A | 112 | o5·=·A |
| 113 | o5·:·QuotientRing</code></pre> | 113 | o5·:·QuotientRing</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·s·=·segreDimX(X,Y,A) | 116 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·s·=·segreDimX(X,Y,A) |
| 117 | ·--·used·0. | 117 | ·--·used·0.18967s·(cpu);·0.138235s·(thread);·0s·(gc) |
| 118 | ·······2·············2 | 118 | ·······2·············2 |
| 119 | o6·=·2H··+·4H·H··+·2H | 119 | o6·=·2H··+·4H·H··+·2H |
| 120 | ·······1·····1·2·····2 | 120 | ·······1·····1·2·····2 |
| 121 | o6·:·A</code></pre> | 121 | o6·:·A</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·segre(X,Y,A) | 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·segre(X,Y,A) |
| 125 | ·--·used·0.1 | 125 | ·--·used·0.117133s·(cpu);·0.0893253s·(thread);·0s·(gc) |
| 126 | ········2·2·····2·········2·····2·············2 | 126 | ········2·2·····2·········2·····2·············2 |
| 127 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H | 127 | o7·=·12H·H··-·6H·H··-·6H·H··+·2H··+·4H·H··+·2H |
| 128 | ········1·2·····1·2·····1·2·····1·····1·2·····2 | 128 | ········1·2·····1·2·····1·2·····1·····1·2·····2 |
| 129 | o7·:·A</code></pre> | 129 | o7·:·A</code></pre> |
| 130 | </td>··········</tr> | 130 | </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·0. | 54 | ·--·used·0.18967s·(cpu);·0.138235s·(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·0.1 | 60 | ·--·used·0.117133s·(cpu);·0.0893253s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tvcHRpbWl6ZSxWZXJib3NpdHldLCJvcHRpbWl6ZSgu | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20ge1tvcHRpbWl6ZSxWZXJib3NpdHldLCJvcHRpbWl6ZSgu |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ICJsaW5lbnVtIiA9PiA4NDYsIElucHV0cyA9PiB7U1BBTntUVHsiUyJ9LCIsICIsU1BBTnsiYSAi | 11 | ICJsaW5lbnVtIiA9PiA4NDYsIElucHV0cyA9PiB7U1BBTntUVHsiUyJ9LCIsICIsU1BBTnsiYSAi |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgyLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMjgyLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhclhpdixTdHJpbmcsU3RyaW5nKSwiYXJYaXYoU3Ry | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyhhclhpdixTdHJpbmcsU3RyaW5nKSwiYXJYaXYoU3Ry |
| Offset 1, 6 lines modified | Offset 1, 6 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·263059462 | 1 | --·-*-·M2-comint·-*-·hash:·263059462 |
| 2 | i1·:·check·SimpleDoc | 2 | i1·:·check·SimpleDoc |
| 3 | ·--·capturing·check(0,·"SimpleDoc")···········--·0.1 | 3 | ·--·capturing·check(0,·"SimpleDoc")···········--·0.189602·seconds·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")···········--·0.1 | 76 | ·--·capturing·check(0,·"SimpleDoc")···········--·0.189602·seconds·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 | _\x8(_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8)·to·write·a·test·case. | 12 | _\x8(_\x8S_\x8t_\x8r_\x8i_\x8n_\x8g_\x8)·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")···········--·0.1 | 18 | ·--·capturing·check(0,·"SimpleDoc")···········--·0.189602·seconds·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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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| 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 |
| 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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| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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| 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 92, 23 lines modified | Offset 92, 23 lines modified | ||
| 92 | ························4·················4 | 92 | ························4·················4 |
| 93 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) | 93 | o2·:·Matrix·(QQ[x·..x·])··<--·(QQ[x·..x·]) |
| 94 | ·················0···7·············0···7</code></pre> | 94 | ·················0···7·············0···7</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·(Y,·F)·=·setOnesForest·X | 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·(Y,·F)·=·setOnesForest·X |
| 98 | o3·=·(|·0·1· | 98 | o3·=·(|·0·1·0···1·|,·Graph{"edges"·=>·{{y·,·y·},·{y·,·y·},·{y·,·y·},·{y·, |
| 99 | ······|·1·0· | 99 | ······|·1·0·0···1·|······················1···4·····3···4·····0···5·····2· |
| 100 | ······|·0· | 100 | ······|·0·1·1···0·|········"ring"·=>·QQ[y·..y·] |
| 101 | ······|·1·0· | 101 | ······|·1·0·x_7·0·|······················0···7 |
| 102 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} | 102 | ···························"vertices"·=>·{y·,·y·,·y·,·y·,·y·,·y·,·y·,·y·} |
| 103 | ···········································0···1···2···3···4···5···6···7 | 103 | ···········································0···1···2···3···4···5···6···7 |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) | 105 | ·····y·},·{y·,·y·},·{y·,·y·},·{y·,·y·}}}) |
| 106 | ······ | 106 | ······5·····2···6·····0···7·····1···7 |
| 107 | o3·:·Sequence</code></pre> | 107 | o3·:·Sequence</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 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | YWJsZSBpcyB0aGF0IG9mIGEgc21vb3RoIEFDTSBjdXJ2ZSIsICJsaW5lbnVtIiA9PiAxMjcwLCBJ | 11 | YWJsZSBpcyB0aGF0IG9mIGEgc21vb3RoIEFDTSBjdXJ2ZSIsICJsaW5lbnVtIiA9PiAxMjcwLCBJ |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00163514s·(cpu);·5.3981e-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·0.1 | 13 | ·--·used·0.128794s·(cpu);·0.100418s·(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:·2000758474 | 1 | --·-*-·M2-comint·-*-·hash:·2000758474 |
| 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·0.280464s·(cpu);·0.209517s·(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·0.1 | 14 | ·--·used·0.148402s·(cpu);·0.116963s·(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·0.30 | 16 | ·--·used·0.230854s·(cpu);·0.200835s·(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·0.2 | 18 | ·--·used·0.226156s·(cpu);·0.229498s·(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·0.187395s·(cpu);·0.108651s·(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·0.4 | 29 | ·--·used·0.452966s·(cpu);·0.366723s·(thread);·0s·(gc) |
| 30 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 | 30 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 |
| 31 | ·····9257139493926586400187927813888 | 31 | ·····9257139493926586400187927813888 |
| 32 | i5·:· | 32 | i5·:· |
| Offset 1, 56 lines modified | Offset 1, 56 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1024556833 | 1 | --·-*-·M2-comint·-*-·hash:·1024556833 |
| 2 | i1·:·genericSkewMultidimensionalMatrix(3,4) | 2 | i1·:·genericSkewMultidimensionalMatrix(3,4) |
| 3 | o1·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 3 | o1·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 4 | ······························ | 4 | ······························1····0········1·······2········0···2··········· |
| 5 | ·····------------------------------------------------------------------------ | 5 | ·····------------------------------------------------------------------------ |
| 6 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 6 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 7 | ········· | 7 | ·········1···0····················1··········3······0······3··············1· |
| 8 | ·····------------------------------------------------------------------------ | 8 | ·····------------------------------------------------------------------------ |
| 9 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 9 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 10 | ········· | 10 | ·········2·····1·········3····················2····3·················0····2· |
| 11 | ·····------------------------------------------------------------------------ | 11 | ·····------------------------------------------------------------------------ |
| 12 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 12 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 13 | ··········· | 13 | ···········0·······3········2···3 |
| 14 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] | 14 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] |
| 15 | ······················································0···3 | 15 | ······················································0···3 |
| 16 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) | 16 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) |
| 17 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 17 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 18 | ······························ | 18 | ······························3····2········3·······0········2···0··········· |
| 19 | ·····------------------------------------------------------------------------ | 19 | ·····------------------------------------------------------------------------ |
| 20 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 20 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 21 | ········· | 21 | ·········3···2····················3··········1······2······1··············3· |
| 22 | ·····------------------------------------------------------------------------ | 22 | ·····------------------------------------------------------------------------ |
| 23 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 23 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 24 | ········· | 24 | ·········0·····3·········1····················0····1·················2····0· |
| 25 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 26 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 26 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 27 | ··········· | 27 | ···········2·······1········0···1 |
| 28 | ···················································ZZ | 28 | ···················································ZZ |
| 29 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] | 29 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] |
| 30 | ··················································101··0···3 | 30 | ··················································101··0···3 |
| 31 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") | 31 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") |
| 32 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, | 32 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, |
| 33 | ······························ | 33 | ······························1····0········1·······2········0···2··········· |
| 34 | ·····------------------------------------------------------------------------ | 34 | ·····------------------------------------------------------------------------ |
| 35 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, | 35 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, |
| 36 | ········· | 36 | ·········1···0····················1··········3······0······3··············1· |
| 37 | ·····------------------------------------------------------------------------ | 37 | ·····------------------------------------------------------------------------ |
| 38 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, | 38 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, |
| 39 | ········· | 39 | ·········2·····1·········3····················2····3·················0····2· |
| 40 | ·····------------------------------------------------------------------------ | 40 | ·····------------------------------------------------------------------------ |
| 41 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} | 41 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} |
| 42 | ··········· | 42 | ···········0·······3········2···3 |
| 43 | ···················································ZZ | 43 | ···················································ZZ |
| 44 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] | 44 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] |
| 45 | ··················································101··0···3 | 45 | ··················································101··0···3 |
| 46 | i4·:· | 46 | 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·2. | 16 | ·--·used·2.24025s·(cpu);·2.06845s·(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:·484455440 | 1 | --·-*-·M2-comint·-*-·hash:·484455440 |
| 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·0.438086s·(cpu);·0.383472s·(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·0.010 | 23 | ·--·used·0.00710142s·(cpu);·0.00869675s·(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·0.03 | 734 | ·--·used·0.0319159s·(cpu);·0.031165s·(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·0.00 | 743 | ·--·used·0.00399795s·(cpu);·0.00317676s·(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·0.8 | 827 | ·--·used·0.832385s·(cpu);·0.756235s·(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 74, 27 lines modified | Offset 74, 27 lines modified | ||
| 74 | o1·=·{2,·3,·2} | 74 | o1·=·{2,·3,·2} |
| 75 | o1·:·List</code></pre> | 75 | o1·:·List</code></pre> |
| 76 | </td>··········</tr> | 76 | </td>··········</tr> |
| 77 | ··········<tr> | 77 | ··········<tr> |
| 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·degreeDeterminant·n | 78 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·degreeDeterminant·n |
| 79 | ·--·used·0.00 | 79 | ·--·used·0.00163514s·(cpu);·5.3981e-05s·(thread);·0s·(gc) |
| 80 | o2·=·6</code></pre> | 80 | o2·=·6</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·genericMultidimensionalMatrix·n; | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·genericMultidimensionalMatrix·n; |
| 84 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] | 84 | o3·:·3-dimensional·matrix·of·shape·2·x·3·x·2·over·ZZ[a·····..a·····] |
| 85 | ······················································0,0,0···1,2,1</code></pre> | 85 | ······················································0,0,0···1,2,1</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree·determinant·M | 88 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·degree·determinant·M |
| 89 | ·--·used·0.1 | 89 | ·--·used·0.128794s·(cpu);·0.100418s·(thread);·0s·(gc) |
| 90 | o4·=·{6} | 90 | o4·=·{6} |
| 91 | o4·:·List</code></pre> | 91 | o4·:·List</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ········</table> | 93 | ········</table> |
| 94 | ······</div> | 94 | ······</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·0.00163514s·(cpu);·5.3981e-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·0.1 | 27 | ·--·used·0.128794s·(cpu);·0.100418s·(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 83, 15 lines modified | Offset 83, 15 lines modified | ||
| 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·:·(d,n)·:=·(2,3);</code></pre> | 86 | <td>··············<pre><code·class="language-macaulay2">i1·:·(d,n)·:=·(2,3);</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·Disc·=·denseDiscriminant(d,n) | 89 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·Disc·=·denseDiscriminant(d,n) |
| 90 | ·--·used·0.2 | 90 | ·--·used·0.280464s·(cpu);·0.209517s·(thread);·0s·(gc) |
| 91 | o2·=·Disc | 91 | o2·=·Disc |
| 92 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|) | 92 | o2·:·SparseDiscriminant·(sparse·discriminant·associated·to·|·0·0·0·0·0·0·1·1·1·2·|) |
| 93 | ···························································|·0·0·0·1·1·2·0·0·1·0·| | 93 | ···························································|·0·0·0·1·1·2·0·0·1·0·| |
| 94 | ···························································|·0·1·2·0·1·0·0·1·0·0·|</code></pre> | 94 | ···························································|·0·1·2·0·1·0·0·1·0·0·|</code></pre> |
| 95 | </td>··········</tr> | 95 | </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·0.280464s·(cpu);·0.209517s·(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 93, 23 lines modified | Offset 93, 23 lines modified | ||
| 93 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 93 | ·····c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 94 | ······4·1·2····2·2····3·1····1·2····0 | 94 | ······4·1·2····2·2····3·1····1·2····0 |
| 95 | o1·:·Sequence</code></pre> | 95 | o1·:·Sequence</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula | 98 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·denseResultant(f0,f1,f2);·--·using·Poisson·formula |
| 99 | ·--·used·0.1 | 99 | ·--·used·0.148402s·(cpu);·0.116963s·(thread);·0s·(gc)</code></pre> |
| 100 | </td>··········</tr> | 100 | </td>··········</tr> |
| 101 | ··········<tr> | 101 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula | 102 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·denseResultant(f0,f1,f2,Algorithm=>"Macaulay");·--·using·Macaulay·formula |
| 103 | ·--·used·0.30 | 103 | ·--·used·0.230854s·(cpu);·0.200835s·(thread);·0s·(gc)</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·(denseResultant(1,2,2))·(f0,f1,f2);·--·using·sparseResultant |
| 107 | ·--·used·0.2 | 107 | ·--·used·0.226156s·(cpu);·0.229498s·(thread);·0s·(gc)</code></pre> |
| 108 | </td>··········</tr> | 108 | </td>··········</tr> |
| 109 | ··········<tr> | 109 | ··········<tr> |
| 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(o2·==·o3·and·o3·==·o4)</code></pre> | 110 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(o2·==·o3·and·o3·==·o4)</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ········</table> | 112 | ········</table> |
| 113 | ······</div> | 113 | ······</div> |
| 114 | ······<div> | 114 | ······<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·0.1 | 35 | ·--·used·0.148402s·(cpu);·0.116963s·(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·0.30 | 38 | ·--·used·0.230854s·(cpu);·0.200835s·(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·0.2 | 40 | ·--·used·0.226156s·(cpu);·0.229498s·(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 85, 15 lines modified | Offset 85, 15 lines modified | ||
| 85 | ·····------------------------------------------------------------------------ | 85 | ·····------------------------------------------------------------------------ |
| 86 | ·····3}}}} | 86 | ·····3}}}} |
| 87 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ</code></pre> | 87 | o1·:·4-dimensional·matrix·of·shape·2·x·2·x·2·x·2·over·ZZ</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·det·M | 90 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·det·M |
| 91 | ·--·used·0. | 91 | ·--·used·0.187395s·(cpu);·0.108651s·(thread);·0s·(gc) |
| 92 | o2·=·9698337990421512192</code></pre> | 92 | o2·=·9698337990421512192</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·M·=·randomMultidimensionalMatrix(2,2,2,2,5) |
| 96 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, | 96 | o3·=·{{{{{6,·3,·6,·8,·6},·{9,·3,·7,·6,·9}},·{{6,·2,·6,·0,·2},·{6,·9,·3,·5, |
| Offset 106, 15 lines modified | Offset 106, 15 lines modified | ||
| 106 | ·····------------------------------------------------------------------------ | 106 | ·····------------------------------------------------------------------------ |
| 107 | ·····4,·8,·4,·2}}}}} | 107 | ·····4,·8,·4,·2}}}}} |
| 108 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ</code></pre> | 108 | o3·:·5-dimensional·matrix·of·shape·2·x·2·x·2·x·2·x·5·over·ZZ</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·det·M | 111 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·det·M |
| 112 | ·--·used·0.4 | 112 | ·--·used·0.452966s·(cpu);·0.366723s·(thread);·0s·(gc) |
| 113 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 | 113 | o4·=·912984499996938980479447727885644530753184525786986940737407301278806287 |
| 114 | ·····9257139493926586400187927813888</code></pre> | 114 | ·····9257139493926586400187927813888</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ········</table> | 116 | ········</table> |
| 117 | ······</div> | 117 | ······</div> |
| 118 | ······<div> | 118 | ······<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·0.187395s·(cpu);·0.108651s·(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·0.4 | 49 | ·--·used·0.452966s·(cpu);·0.366723s·(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 78, 61 lines modified | Offset 78, 61 lines modified | ||
| 78 | ········<h2>Description</h2> | 78 | ········<h2>Description</h2> |
| 79 | ········<p>An·$n$-dimensional·matrix·$M$·is·skew·symmetric·if·for·every·permutation·$s$·of·the·set·$\{0,\ldots,n-1\}$·we·have·<a·title="permute·the·dimensions·of·a·multidimensional·matrix"·href="_permute.html">permute</a><span·class="tt">(M,s)·==·sign(s)*M</span>.</p> | 79 | ········<p>An·$n$-dimensional·matrix·$M$·is·skew·symmetric·if·for·every·permutation·$s$·of·the·set·$\{0,\ldots,n-1\}$·we·have·<a·title="permute·the·dimensions·of·a·multidimensional·matrix"·href="_permute.html">permute</a><span·class="tt">(M,s)·==·sign(s)*M</span>.</p> |
| 80 | ········<table·class="examples"> | 80 | ········<table·class="examples"> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·genericSkewMultidimensionalMatrix(3,4) | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·genericSkewMultidimensionalMatrix(3,4) |
| 83 | o1·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 83 | o1·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 84 | ······························ | 84 | ······························1····0········1·······2········0···2··········· |
| 85 | ·····------------------------------------------------------------------------ | 85 | ·····------------------------------------------------------------------------ |
| 86 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 86 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 87 | ········· | 87 | ·········1···0····················1··········3······0······3··············1· |
| 88 | ·····------------------------------------------------------------------------ | 88 | ·····------------------------------------------------------------------------ |
| 89 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 89 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 90 | ········· | 90 | ·········2·····1·········3····················2····3·················0····2· |
| 91 | ·····------------------------------------------------------------------------ | 91 | ·····------------------------------------------------------------------------ |
| 92 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 92 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 93 | ··········· | 93 | ···········0·······3········2···3 |
| 94 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] | 94 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] |
| 95 | ······················································0···3</code></pre> | 95 | ······················································0···3</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) | 98 | <td>··············<pre><code·class="language-macaulay2">i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) |
| 99 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 99 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 100 | ······························ | 100 | ······························3····2········3·······0········2···0··········· |
| 101 | ·····------------------------------------------------------------------------ | 101 | ·····------------------------------------------------------------------------ |
| 102 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 102 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 103 | ········· | 103 | ·········3···2····················3··········1······2······1··············3· |
| 104 | ·····------------------------------------------------------------------------ | 104 | ·····------------------------------------------------------------------------ |
| 105 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 105 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 106 | ········· | 106 | ·········0·····3·········1····················0····1·················2····0· |
| 107 | ·····------------------------------------------------------------------------ | 107 | ·····------------------------------------------------------------------------ |
| 108 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 108 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 109 | ··········· | 109 | ···········2·······1········0···1 |
| 110 | ···················································ZZ | 110 | ···················································ZZ |
| 111 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] | 111 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] |
| 112 | ··················································101··0···3</code></pre> | 112 | ··················································101··0···3</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") | 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101,Variable=>"b") |
| 116 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, | 116 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, |
| 117 | ······························ | 117 | ······························1····0········1·······2········0···2··········· |
| 118 | ·····------------------------------------------------------------------------ | 118 | ·····------------------------------------------------------------------------ |
| 119 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, | 119 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, |
| 120 | ········· | 120 | ·········1···0····················1··········3······0······3··············1· |
| 121 | ·····------------------------------------------------------------------------ | 121 | ·····------------------------------------------------------------------------ |
| 122 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, | 122 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, |
| 123 | ········· | 123 | ·········2·····1·········3····················2····3·················0····2· |
| 124 | ·····------------------------------------------------------------------------ | 124 | ·····------------------------------------------------------------------------ |
| 125 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} | 125 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} |
| 126 | ··········· | 126 | ···········0·······3········2···3 |
| 127 | ···················································ZZ | 127 | ···················································ZZ |
| 128 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] | 128 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] |
| 129 | ··················································101··0···3</code></pre> | 129 | ··················································101··0···3</code></pre> |
| 130 | </td>··········</tr> | 130 | </td>··········</tr> |
| 131 | ········</table> | 131 | ········</table> |
| 132 | ······</div> | 132 | ······</div> |
| Offset 18, 58 lines modified | Offset 18, 58 lines modified | ||
| 18 | ············$d\times\cdots\times·d$·($n$·times). | 18 | ············$d\times\cdots\times·d$·($n$·times). |
| 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 | An·$n$-dimensional·matrix·$M$·is·skew·symmetric·if·for·every·permutation·$s$·of | 20 | An·$n$-dimensional·matrix·$M$·is·skew·symmetric·if·for·every·permutation·$s$·of |
| 21 | the·set·$\{0,\ldots,n-1\}$·we·have·_\x8p_\x8e_\x8r_\x8m_\x8u_\x8t_\x8e(M,s)·==·sign(s)*M. | 21 | the·set·$\{0,\ldots,n-1\}$·we·have·_\x8p_\x8e_\x8r_\x8m_\x8u_\x8t_\x8e(M,s)·==·sign(s)*M. |
| 22 | i1·:·genericSkewMultidimensionalMatrix(3,4) | 22 | i1·:·genericSkewMultidimensionalMatrix(3,4) |
| 23 | o1·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 23 | o1·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 24 | ······························ | 24 | ······························1····0········1·······2········0···2 |
| 25 | ·····------------------------------------------------------------------------ | 25 | ·····------------------------------------------------------------------------ |
| 26 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 26 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 27 | ········· | 27 | ·········1···0····················1··········3······0······3··············1 |
| 28 | ·····------------------------------------------------------------------------ | 28 | ·····------------------------------------------------------------------------ |
| 29 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 29 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 30 | ········· | 30 | ·········2·····1·········3····················2····3·················0····2 |
| 31 | ·····------------------------------------------------------------------------ | 31 | ·····------------------------------------------------------------------------ |
| 32 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 32 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 33 | ··········· | 33 | ···········0·······3········2···3 |
| 34 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] | 34 | o1·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·QQ[a·..a·] |
| 35 | ······················································0···3 | 35 | ······················································0···3 |
| 36 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) | 36 | i2·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/101) |
| 37 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, | 37 | o2·=·{{{0,·0,·0,·0},·{0,·0,·-a·,·-a·},·{0,·a·,·0,·-a·},·{0,·a·,·a·,·0}},·{{0, |
| 38 | ······························ | 38 | ······························3····2········3·······0········2···0 |
| 39 | ·····------------------------------------------------------------------------ | 39 | ·····------------------------------------------------------------------------ |
| 40 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, | 40 | ·····0,·a·,·a·},·{0,·0,·0,·0},·{-a·,·0,·0,·-a·},·{-a·,·0,·a·,·0}},·{{0,·-a·, |
| 41 | ········· | 41 | ·········3···2····················3··········1······2······1··············3 |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, | 43 | ·····0,·a·},·{a·,·0,·0,·a·},·{0,·0,·0,·0},·{-a·,·-a·,·0,·0}},·{{0,·-a·,·-a·, |
| 44 | ········· | 44 | ·········0·····3·········1····················0····1·················2····0 |
| 45 | ·····------------------------------------------------------------------------ | 45 | ·····------------------------------------------------------------------------ |
| 46 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} | 46 | ·····0},·{a·,·0,·-a·,·0},·{a·,·a·,·0,·0},·{0,·0,·0,·0}}} |
| 47 | ··········· | 47 | ···········2·······1········0···1 |
| 48 | ···················································ZZ | 48 | ···················································ZZ |
| 49 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] | 49 | o2·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[a·..a·] |
| 50 | ··················································101··0···3 | 50 | ··················································101··0···3 |
| 51 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/ | 51 | i3·:·genericSkewMultidimensionalMatrix(3,4,CoefficientRing=>ZZ/ |
| 52 | 101,Variable=>"b") | 52 | 101,Variable=>"b") |
| 53 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, | 53 | o3·=·{{{0,·0,·0,·0},·{0,·0,·-b·,·-b·},·{0,·b·,·0,·-b·},·{0,·b·,·b·,·0}},·{{0, |
| 54 | ······························ | 54 | ······························1····0········1·······2········0···2 |
| 55 | ·····------------------------------------------------------------------------ | 55 | ·····------------------------------------------------------------------------ |
| 56 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, | 56 | ·····0,·b·,·b·},·{0,·0,·0,·0},·{-b·,·0,·0,·-b·},·{-b·,·0,·b·,·0}},·{{0,·-b·, |
| 57 | ········· | 57 | ·········1···0····················1··········3······0······3··············1 |
| 58 | ·····------------------------------------------------------------------------ | 58 | ·····------------------------------------------------------------------------ |
| 59 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, | 59 | ·····0,·b·},·{b·,·0,·0,·b·},·{0,·0,·0,·0},·{-b·,·-b·,·0,·0}},·{{0,·-b·,·-b·, |
| 60 | ········· | 60 | ·········2·····1·········3····················2····3·················0····2 |
| 61 | ·····------------------------------------------------------------------------ | 61 | ·····------------------------------------------------------------------------ |
| 62 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} | 62 | ·····0},·{b·,·0,·-b·,·0},·{b·,·b·,·0,·0},·{0,·0,·0,·0}}} |
| 63 | ··········· | 63 | ···········0·······3········2···3 |
| 64 | ···················································ZZ | 64 | ···················································ZZ |
| 65 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] | 65 | o3·:·3-dimensional·matrix·of·shape·4·x·4·x·4·over·---[b·..b·] |
| 66 | ··················································101··0···3 | 66 | ··················································101··0···3 |
| 67 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* | 67 | *\x8**\x8**\x8**\x8**\x8*·S\x8Se\x8ee\x8e·a\x8al\x8ls\x8so\x8o·*\x8**\x8**\x8**\x8**\x8* |
| 68 | ····*·_\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 | 68 | ····*·_\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 | ······of·variables | 69 | ······of·variables |
| Offset 90, 15 lines modified | Offset 90, 15 lines modified | ||
| 90 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 | 90 | ······1,1,1·1·1·1····1,2,0·1·2·0····1,2,1·1·2·1 |
| 91 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] | 91 | o1·:·ZZ[a·····..a·····][x·..x·,·y·..y·,·z·..z·] |
| 92 | ·········0,0,0···1,2,1···0···1···0···2···0···1</code></pre> | 92 | ·········0,0,0···1,2,1···0···1···0···2···0···1</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·sparseDiscriminant·f | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·sparseDiscriminant·f |
| 96 | ·--·used·2. | 96 | ·--·used·2.24025s·(cpu);·2.06845s·(thread);·0s·(gc) |
| 97 | ···················································2························ | 97 | ···················································2························ |
| 98 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- | 98 | o2·=·a·····a·····a·····a·····a·····a······-·a·····a·····a·····a·····a······- |
| 99 | ······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 | ······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·· |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ············2·····2································2············ | 101 | ············2·····2································2············ |
| 102 | ·····a·····a·····a·····a······+·a·····a·····a·····a·····a······- | 102 | ·····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·2. | 44 | ·--·used·2.24025s·(cpu);·2.06845s·(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 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | ······<div> | 77 | ······<div> |
| 78 | ········<h2>Description</h2> | 78 | ········<h2>Description</h2> |
| 79 | ········<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>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> |
| 80 | ········<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 | ········<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> |
| 81 | ········<table·class="examples"> | 81 | ········<table·class="examples"> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <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 | <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}}) |
| 84 | ·--·used·0. | 84 | ·--·used·0.438086s·(cpu);·0.383472s·(thread);·0s·(gc) |
| 85 | o1·=·Res | 85 | o1·=·Res |
| 86 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|}) | 86 | o1·:·SparseResultant·(sparse·mixed·resultant·associated·to·{|·0·1·1·2·|,·|·0·1·2·2·|,·|·0·0·1·1·|}) |
| 87 | ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|</code></pre> | 87 | ····························································|·0·0·1·1·|··|·1·0·1·2·|··|·0·1·0·1·|</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| Offset 101, 15 lines modified | Offset 101, 15 lines modified | ||
| 101 | ·····c···x*y·+·c···x·+·c···y·+·c···) | 101 | ·····c···x*y·+·c···x·+·c···y·+·c···) |
| 102 | ······3,3·······3,4·····3,2·····3,1 | 102 | ······3,3·······3,4·····3,2·····3,1 |
| 103 | o3·:·Sequence</code></pre> | 103 | o3·:·Sequence</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ··········<tr> | 105 | ··········<tr> |
| 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Res(f,g,h) | 106 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·Res(f,g,h) |
| 107 | ·--·used·0.010 | 107 | ·--·used·0.00710142s·(cpu);·0.00869675s·(thread);·0s·(gc) |
| 108 | ········2·······················4······2···2···············4···· | 108 | ········2·······················4······2···2···············4···· |
| 109 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ | 109 | o4·=·-·c···c···c···c···c···c···c····+·c···c···c···c···c···c····+ |
| 110 | ········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 | ········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·· |
| 111 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| 112 | ······3·······2·······3···············2···················3········ | 112 | ······3·······2·······3···············2···················3········ |
| 113 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ | 113 | ·····c···c···c···c···c···c····-·2c···c···c···c···c···c···c···c····+ |
| Offset 818, 15 lines modified | Offset 818, 15 lines modified | ||
| 818 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h))</code></pre> | 818 | <td>··············<pre><code·class="language-macaulay2">i5·:·assert(Res(f,g,h)·==·sparseResultant(f,g,h))</code></pre> |
| 819 | </td>··········</tr> | 819 | </td>··········</tr> |
| 820 | ········</table> | 820 | ········</table> |
| 821 | ········<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 | ········<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> |
| 822 | ········<table·class="examples"> | 822 | ········<table·class="examples"> |
| 823 | ··········<tr> | 823 | ··········<tr> |
| 824 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331); | 824 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·Res·=·sparseResultant(matrix{{0,0,1,1},{0,1,0,1}},CoefficientRing=>ZZ/3331); |
| 825 | ·--·used·0.03 | 825 | ·--·used·0.0319159s·(cpu);·0.031165s·(thread);·0s·(gc) |
| 826 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331) | 826 | o6·:·SparseResultant·(sparse·unmixed·resultant·associated·to·|·0·0·1·1·|·over·ZZ/3331) |
| 827 | ·····························································|·0·1·0·1·|</code></pre> | 827 | ·····························································|·0·1·0·1·|</code></pre> |
| 828 | </td>··········</tr> | 828 | </td>··········</tr> |
| 829 | ··········<tr> | 829 | ··········<tr> |
| 830 | <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>··············<pre><code·class="language-macaulay2">i7·:·ZZ/3331[a_0..a_3,b_0..b_3,c_0..c_3][x,y];</code></pre> |
| 831 | </td>··········</tr> | 831 | </td>··········</tr> |
| Offset 836, 15 lines modified | Offset 836, 15 lines modified | ||
| 836 | 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 | 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·) |
| 837 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 | 837 | ·······3·······1·····2·····0···3·······1·····2·····0···3·······1·····2·····0 |
| 838 | o8·:·Sequence</code></pre> | 838 | o8·:·Sequence</code></pre> |
| 839 | </td>··········</tr> | 839 | </td>··········</tr> |
| 840 | ··········<tr> | 840 | ··········<tr> |
| 841 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·Res(f,g,h) | 841 | <td>··············<pre><code·class="language-macaulay2">i9·:·time·Res(f,g,h) |
| 842 | ·--·used·0.00 | 842 | ·--·used·0.00399795s·(cpu);·0.00317676s·(thread);·0s·(gc) |
| 843 | ······2·····2············2············2········2·2····2·········· | 843 | ······2·····2············2············2········2·2····2·········· |
| 844 | 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 | o9·=·a·b·b·c··-·a·a·b·b·c··-·a·a·b·b·c··+·a·a·b·c··-·a·b·b·c·c··- |
| 845 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1·· | 845 | ······3·1·2·0····2·3·1·3·0····1·3·2·3·0····1·2·3·0····3·0·2·0·1·· |
| 846 | ·····------------------------------------------------------------------------ | 846 | ·····------------------------------------------------------------------------ |
| 847 | ·························2·······················2························· | 847 | ·························2·······················2························· |
| 848 | ·····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··+ | 848 | ·····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 919, 15 lines modified | Offset 919, 15 lines modified | ||
| 919 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) | 919 | ······c·x·x··+·c·x··+·c·x··+·c·x··+·c·) |
| 920 | ·······4·1·2····2·2····3·1····1·2····0 | 920 | ·······4·1·2····2·2····3·1····1·2····0 |
| 921 | o11·:·Sequence</code></pre> | 921 | o11·:·Sequence</code></pre> |
| 922 | </td>··········</tr> | 922 | </td>··········</tr> |
| 923 | ··········<tr> | 923 | ··········<tr> |
| 924 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true)); | 924 | <td>··············<pre><code·class="language-macaulay2">i12·:·time·(MixedRes,UnmixedRes)·=·(sparseResultant(f,g,h),sparseResultant(f,g,h,Unmixed=>true)); |
| 925 | ·--·used·0.8 | 925 | ·--·used·0.832385s·(cpu);·0.756235s·(thread);·0s·(gc)</code></pre> |
| 926 | </td>··········</tr> | 926 | </td>··········</tr> |
| 927 | ··········<tr> | 927 | ··········<tr> |
| 928 | <td>··············<pre><code·class="language-macaulay2">i13·:·quotientRemainder(UnmixedRes,MixedRes) | 928 | <td>··············<pre><code·class="language-macaulay2">i13·:·quotientRemainder(UnmixedRes,MixedRes) |
| 929 | ········2·2···················2····2·······························2·2 | 929 | ········2·2···················2····2·······························2·2 |
| 930 | 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 | o13·=·(b·c··-·b·b·c·c··+·b·b·c··+·b·c·c··-·2b·b·c·c··-·b·b·c·c··+·b·c·,·0) |
| 931 | ········5·2····4·5·2·4····2·5·4····4·2·5·····2·5·2·5····2·4·4·5····2·5 | 931 | ········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·0.438086s·(cpu);·0.383472s·(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·0.010 | 62 | ·--·used·0.00710142s·(cpu);·0.00869675s·(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·0.03 | 779 | ·--·used·0.0319159s·(cpu);·0.031165s·(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·0.00 | 790 | ·--·used·0.00399795s·(cpu);·0.00317676s·(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·0.8 | 870 | ·--·used·0.832385s·(cpu);·0.756235s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.00 | 30 | ·--·used·0.00227227s·(cpu);·0.0011623s·(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·0.0009 | 51 | ·--·used·0.000988097s·(cpu);·0.000952204s·(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·0.00128986s·(cpu);·0.00185623s·(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. | 29 | ·--·used·0.200831s·(cpu);·0.169375s·(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·0.4 | 13 | ·--·used·0.443178s·(cpu);·0.336732s·(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 123, 15 lines modified | Offset 123, 15 lines modified | ||
| 123 | ·····|·2·3·| | 123 | ·····|·2·3·| |
| 124 | ·····|·4·| | 124 | ·····|·4·| |
| 125 | o4·:·YoungTableau</code></pre> | 125 | o4·:·YoungTableau</code></pre> |
| 126 | </td>··········</tr> | 126 | </td>··········</tr> |
| 127 | ··········<tr> | 127 | ··········<tr> |
| 128 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·higherSpechtPolynomial(S,T,R) | 128 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·higherSpechtPolynomial(S,T,R) |
| 129 | ·--·used·0.00 | 129 | ·--·used·0.00227227s·(cpu);·0.0011623s·(thread);·0s·(gc) |
| 130 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· | 130 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· |
| 131 | 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 | 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··- |
| 132 | ······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 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· |
| 133 | ·····------------------------------------------------------------------------ | 133 | ·····------------------------------------------------------------------------ |
| 134 | ······3·2········3·2········2·3········2·3········3···2········3·2···· | 134 | ······3·2········3·2········2·3········2·3········3···2········3·2···· |
| 135 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 135 | ·····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 145, 15 lines modified | Offset 145, 15 lines modified | ||
| 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 | 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 |
| 146 | ······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 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 147 | o5·:·R</code></pre> | 147 | o5·:·R</code></pre> |
| 148 | </td>··········</tr> | 148 | </td>··········</tr> |
| 149 | ··········<tr> | 149 | ··········<tr> |
| 150 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) | 150 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false) |
| 151 | ·--·used·0.0009 | 151 | ·--·used·0.000988097s·(cpu);·0.000952204s·(thread);·0s·(gc) |
| 152 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· | 152 | ······3·2··········2·3······3·····2········3·2····3···2······2···3···· |
| 153 | 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 | 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··- |
| 154 | ······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 | ······0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·3····0·1·2·4····0·1·2·4·· |
| 155 | ·····------------------------------------------------------------------------ | 155 | ·····------------------------------------------------------------------------ |
| 156 | ······3·2········3·2········2·3········2·3········3···2········3·2···· | 156 | ······3·2········3·2········2·3········2·3········3···2········3·2···· |
| 157 | ·····x·x·x·x··-·x·x·x·x··+·x·x·x·x··+·x·x·x·x··+·x·x·x·x··-·x·x·x·x··- | 157 | ·····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 167, 15 lines modified | Offset 167, 15 lines modified | ||
| 167 | ·····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 | ·····x·x·x·x··-·x·x·x·x··-·x·x·x·x··+·x·x·x·x··-·x·x·x·x··+·x·x·x·x |
| 168 | ······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 | ······0·1·3·4····0·2·3·4····1·2·3·4····0·2·3·4····0·1·3·4····1·2·3·4 |
| 169 | o6·:·R</code></pre> | 169 | o6·:·R</code></pre> |
| 170 | </td>··········</tr> | 170 | </td>··········</tr> |
| 171 | ··········<tr> | 171 | ··········<tr> |
| 172 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) | 172 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·higherSpechtPolynomial(S,T,R,·Robust·=>·false,·AsExpression·=>·true) |
| 173 | ·--·used·0.00 | 173 | ·--·used·0.00128986s·(cpu);·0.00185623s·(thread);·0s·(gc) |
| 174 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·)) | 174 | o7·=·(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)(-·x··+·x·)((x··+·x··+·x·)(x·)(x·)·+·(x·)(x·)(x·)) |
| 175 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0 | 175 | ·········0····2·····0····4·····2····4·····1····3····0····2····4···3···1······4···2···0 |
| 176 | o7·:·Expression·of·class·Product</code></pre> | 176 | o7·:·Expression·of·class·Product</code></pre> |
| 177 | </td>··········</tr> | 177 | </td>··········</tr> |
| 178 | ········</table> | 178 | ········</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·0.00 | 74 | ·--·used·0.00227227s·(cpu);·0.0011623s·(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·0.0009 | 95 | ·--·used·0.000988097s·(cpu);·0.000952204s·(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·0.00128986s·(cpu);·0.00185623s·(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 120, 15 lines modified | Offset 120, 15 lines modified | ||
| 120 | ········</div> | 120 | ········</div> |
| 121 | ········<table·class="examples"> | 121 | ········<table·class="examples"> |
| 122 | ··········<tr> | 122 | ··········<tr> |
| 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·partis·=·partitions·6;</code></pre> | 123 | <td>··············<pre><code·class="language-macaulay2">i4·:·partis·=·partitions·6;</code></pre> |
| 124 | </td>··········</tr> | 124 | </td>··········</tr> |
| 125 | ··········<tr> | 125 | ··········<tr> |
| 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p)) | 126 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·multi·=·hashTable·apply·(partis,·p->·p=>·representationMultiplicity(tal,p)) |
| 127 | ·--·used·0. | 127 | ·--·used·0.200831s·(cpu);·0.169375s·(thread);·0s·(gc) |
| 128 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} | 128 | o5·=·HashTable{Partition{1,·1,·1,·1,·1,·1}·=>·1} |
| 129 | ···············Partition{2,·1,·1,·1,·1}·=>·0 | 129 | ···············Partition{2,·1,·1,·1,·1}·=>·0 |
| 130 | ···············Partition{2,·2,·1,·1}·=>·1 | 130 | ···············Partition{2,·2,·1,·1}·=>·1 |
| 131 | ···············Partition{2,·2,·2}·=>·1 | 131 | ···············Partition{2,·2,·2}·=>·1 |
| 132 | ···············Partition{3,·1,·1,·1}·=>·0 | 132 | ···············Partition{3,·1,·1,·1}·=>·0 |
| 133 | ···············Partition{3,·2,·1}·=>·0 | 133 | ···············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. | 71 | ·--·used·0.200831s·(cpu);·0.169375s·(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 99, 15 lines modified | Offset 99, 15 lines modified | ||
| 99 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} | 99 | o2·=·{{1,·2,·3,·0,·5,·4},·{0,·4,·2,·5,·1,·3}} |
| 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·:·time·seco·=·secondaryInvariants(genList,R); | 103 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·seco·=·secondaryInvariants(genList,R); |
| 104 | ·--·used·0.4 | 104 | ·--·used·0.443178s·(cpu);·0.336732s·(thread);·0s·(gc) |
| 105 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) | 105 | (Partition{6},·Ambient_Dimension,·1,·Rank,·1) |
| 106 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) | 106 | (Partition{5,·1},·Ambient_Dimension,·5,·Rank,·0) |
| 107 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) | 107 | (Partition{4,·2},·Ambient_Dimension,·9,·Rank,·1) |
| 108 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 108 | (Partition{4,·1,·1},·Ambient_Dimension,·10,·Rank,·0) |
| 109 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) | 109 | (Partition{3,·3},·Ambient_Dimension,·5,·Rank,·1) |
| 110 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) | 110 | (Partition{3,·2,·1},·Ambient_Dimension,·16,·Rank,·0) |
| 111 | (Partition{3,·1,·1,·1},·Ambient_Dimension,·10,·Rank,·0) | 111 | (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·0.4 | 51 | ·--·used·0.443178s·(cpu);·0.336732s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | IGludGVyc2VjdGlvbiBvZiB0aHJlZSBxdWFkcmljcyBpbiBQXjciLCAibGluZW51bSIgPT4gMzY0 | 11 | IGludGVyc2VjdGlvbiBvZiB0aHJlZSBxdWFkcmljcyBpbiBQXjciLCAibGluZW51bSIgPT4gMzY0 |
| 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· | 16 | ·--·used·1.75116s·(cpu);·0.948197s·(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·1. | 12 | ·--·used·1.67192s·(cpu);·0.925768s·(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·5.39157s·(cpu);·3.60202s·(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·3.02882s·(cpu);·1.67723s·(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·0.391 | 22 | ·--·used·0.391174s·(cpu);·0.288211s·(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·1 | 17 | ·--·used·13.9106s·(cpu);·5.65005s·(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·0.3 | 33 | ·--·used·0.34515s·(cpu);·0.234525s·(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:·-1818294121 | 1 | --·-*-·M2-comint·-*-·hash:·-1818294121 |
| 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·0.1 | 5 | ·--·used·0.138212s·(cpu);·0.0706906s·(thread);·0s·(gc) |
| 6 | o2·=·14 | 6 | o2·=·14 |
| 7 | i3·:· | 7 | i3·:· |
| Offset 1, 12 lines modified | Offset 1, 12 lines modified | ||
| 1 | --·-*-·M2-comint·-*-·hash:·1539545625 | 1 | --·-*-·M2-comint·-*-·hash:·1539545625 |
| 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·0. | 5 | ·--·used·0.713933s·(cpu);·0.380592s·(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·0.251957s·(cpu);·0.193238s·(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·0.39 | 9 | ·--·used·0.393654s·(cpu);·0.268212s·(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·2.31 | 15 | ·--·used·2.31376s·(cpu);·1.75894s·(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·1. | 10 | ·--·used·1.1353s·(cpu);·0.567536s·(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·0.0 | 11 | ·--·used·0.00560533s·(cpu);·0.007434s·(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·0.289827s·(cpu);·0.130867s·(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·1.41982s·(cpu);·1.21209s·(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·4. | 16 | ·--·used·4.15632s·(cpu);·2.66187s·(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·3.72629s·(cpu);·2.3884s·(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· | 10 | ·--·used·3.81008s·(cpu);·2.41991s·(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·0. | 9 | ·--·used·0.654652s·(cpu);·0.353922s·(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 111, 15 lines modified | Offset 111, 15 lines modified | ||
| 111 | ·····························|·1·4·| | 111 | ·····························|·1·4·| |
| 112 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 | 112 | ·····containing·a·surface·of·degree·1·and·sectional·genus·0 |
| 113 | ·····cut·out·by·5·hypersurfaces·of·degree·1 | 113 | ·····cut·out·by·5·hypersurfaces·of·degree·1 |
| 114 | ·····(This·is·a·classical·example·of·rational·fourfold)</code></pre> | 114 | ·····(This·is·a·classical·example·of·rational·fourfold)</code></pre> |
| 115 | </td>··········</tr> | 115 | </td>··········</tr> |
| 116 | ··········<tr> | 116 | ··········<tr> |
| 117 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedCastelnuovoSurface·X; | 117 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedCastelnuovoSurface·X; |
| 118 | ·--·used· | 118 | ·--·used·1.75116s·(cpu);·0.948197s·(thread);·0s·(gc) |
| 119 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X</code></pre> | 119 | o3·:·ProjectiveVariety,·Castelnuovo·surface·associated·to·X</code></pre> |
| 120 | </td>··········</tr> | 120 | </td>··········</tr> |
| 121 | ··········<tr> | 121 | ··········<tr> |
| 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> | 122 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<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· | 49 | ·--·used·1.75116s·(cpu);·0.948197s·(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 110, 15 lines modified | Offset 110, 15 lines modified | ||
| 110 | o2·=·Special·cubic·fourfold·of·discriminant·14 | 110 | o2·=·Special·cubic·fourfold·of·discriminant·14 |
| 111 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 | 111 | ·····containing·a·(smooth)·surface·of·degree·4·and·sectional·genus·0 |
| 112 | ·····cut·out·by·6·hypersurfaces·of·degree·2</code></pre> | 112 | ·····cut·out·by·6·hypersurfaces·of·degree·2</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ··········<tr> | 114 | ··········<tr> |
| 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; | 115 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; |
| 116 | ·--·used·1. | 116 | ·--·used·1.67192s·(cpu);·0.925768s·(thread);·0s·(gc) |
| 117 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> | 117 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> | 120 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> |
| 121 | </td>··········</tr> | 121 | </td>··········</tr> |
| 122 | ··········<tr> | 122 | ··········<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·1. | 48 | ·--·used·1.67192s·(cpu);·0.925768s·(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 113, 15 lines modified | Offset 113, 15 lines modified | ||
| 113 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 113 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 114 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 114 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 115 | ·····Type:·ordinary | 115 | ·····Type:·ordinary |
| 116 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> | 116 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; | 119 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·U'·=·associatedK3surface·X; |
| 120 | ·--·used· | 120 | ·--·used·5.39157s·(cpu);·3.60202s·(thread);·0s·(gc) |
| 121 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> | 121 | o3·:·ProjectiveVariety,·K3·surface·associated·to·X</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> | 124 | <td>··············<pre><code·class="language-macaulay2">i4·:·(mu,U,C,f)·=·building·U';</code></pre> |
| 125 | </td>··········</tr> | 125 | </td>··········</tr> |
| 126 | ··········<tr> | 126 | ··········<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·5.39157s·(cpu);·3.60202s·(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 91, 15 lines modified | Offset 91, 15 lines modified | ||
| 91 | o2·=·Special·cubic·fourfold·of·discriminant·26 | 91 | o2·=·Special·cubic·fourfold·of·discriminant·26 |
| 92 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 92 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 93 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> | 93 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 96 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 97 | ·--·used· | 97 | ·--·used·3.02882s·(cpu);·1.67723s·(thread);·0s·(gc) |
| 98 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8 | 98 | number·lines·contained·in·the·image·of·the·cubic·map·and·passing·through·a·general·point:·8 |
| 99 | number·2-secant·lines·=·7 | 99 | number·2-secant·lines·=·7 |
| 100 | number·5-secant·conics·=·1 | 100 | number·5-secant·conics·=·1 |
| 101 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5</code></pre> | 101 | o3·:·Congruence·of·5-secant·conics·to·surface·in·PP^5</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| Offset 107, 15 lines modified | Offset 107, 15 lines modified | ||
| 107 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] | 107 | o4·=·point·of·coordinates·[15092,·-9738,·-3620,·-15181,·12688,·1] |
| 108 | o4·:·ProjectiveVariety,·a·point·in·PP^5</code></pre> | 108 | o4·:·ProjectiveVariety,·a·point·in·PP^5</code></pre> |
| 109 | </td>··········</tr> | 109 | </td>··········</tr> |
| 110 | ··········<tr> | 110 | ··········<tr> |
| 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface | 111 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·C·=·f·p;·--·5-secant·conic·to·the·surface |
| 112 | ·--·used·0.391 | 112 | ·--·used·0.391174s·(cpu);·0.288211s·(thread);·0s·(gc) |
| 113 | o5·:·ProjectiveVariety,·curve·in·PP^5</code></pre> | 113 | o5·:·ProjectiveVariety,·curve·in·PP^5</code></pre> |
| 114 | </td>··········</tr> | 114 | </td>··········</tr> |
| 115 | ··········<tr> | 115 | ··········<tr> |
| 116 | <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>··············<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> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ········</table> | 118 | ········</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·3.02882s·(cpu);·1.67723s·(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·0.391 | 47 | ·--·used·0.391174s·(cpu);·0.288211s·(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 94, 15 lines modified | Offset 94, 15 lines modified | ||
| 94 | ·····cut·out·by·19·hypersurfaces·of·degree·2 | 94 | ·····cut·out·by·19·hypersurfaces·of·degree·2 |
| 95 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) | 95 | ·····and·with·class·in·G(1,4)·given·by·6*s_(3,1)+3*s_(2,2) |
| 96 | ·····Type:·ordinary | 96 | ·····Type:·ordinary |
| 97 | ·····(case·17·of·Table·1·in·arXiv:2002.07026)</code></pre> | 97 | ·····(case·17·of·Table·1·in·arXiv:2002.07026)</code></pre> |
| 98 | </td>··········</tr> | 98 | </td>··········</tr> |
| 99 | ··········<tr> | 99 | ··········<tr> |
| 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); | 100 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·f·=·detectCongruence(X,Verbose=>true); |
| 101 | ·--·used·1 | 101 | ·--·used·13.9106s·(cpu);·5.65005s·(thread);·0s·(gc) |
| 102 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7 | 102 | number·lines·contained·in·the·image·of·the·quadratic·map·and·passing·through·a·general·point:·7 |
| 103 | number·1-secant·lines·=·6 | 103 | number·1-secant·lines·=·6 |
| 104 | number·3-secant·conics·=·1 | 104 | number·3-secant·conics·=·1 |
| 105 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8</code></pre> | 105 | o3·:·Congruence·of·3-secant·conics·to·surface·in·a·fivefold·in·PP^8</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| Offset 115, 15 lines modified | Offset 115, 15 lines modified | ||
| 115 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1] | 115 | o5·=·point·of·coordinates·[7214,·-1460,·7057,·-2440,·15907,·-14345,·-5937,·13402,·1] |
| 116 | o5·:·ProjectiveVariety,·a·point·in·PP^8</code></pre> | 116 | o5·:·ProjectiveVariety,·a·point·in·PP^8</code></pre> |
| 117 | </td>··········</tr> | 117 | </td>··········</tr> |
| 118 | ··········<tr> | 118 | ··········<tr> |
| 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface | 119 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·C·=·f·p;·--·3-secant·conic·to·the·surface |
| 120 | ·--·used·0.3 | 120 | ·--·used·0.34515s·(cpu);·0.234525s·(thread);·0s·(gc) |
| 121 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)</code></pre> | 121 | o6·:·ProjectiveVariety,·curve·in·PP^8·(subvariety·of·codimension·4·in·Y)</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ··········<tr> | 123 | ··········<tr> |
| 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·S·=·surface·X; | 124 | <td>··············<pre><code·class="language-macaulay2">i7·:·S·=·surface·X; |
| 125 | o7·:·ProjectiveVariety,·surface·in·PP^8·(subvariety·of·codimension·3·in·Y)</code></pre> | 125 | 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·1 | 44 | ·--·used·13.9106s·(cpu);·5.65005s·(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·0.3 | 59 | ·--·used·0.34515s·(cpu);·0.234525s·(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 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialCubicFourfold·"quintic·del·Pezzo·surface"; |
| 83 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1</code></pre> | 83 | o1·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·5·and·sectional·genus·1</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X |
| 87 | ·--·used·0.1 | 87 | ·--·used·0.138212s·(cpu);·0.0706906s·(thread);·0s·(gc) |
| 88 | o2·=·14</code></pre> | 88 | o2·=·14</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ········</table> | 90 | ········</table> |
| 91 | ······</div> | 91 | ······</div> |
| 92 | ······<div> | 92 | ······<div> |
| 93 | ········<h2>See·also</h2> | 93 | ········<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·0.1 | 27 | ·--·used·0.138212s·(cpu);·0.0706906s·(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) |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; | 82 | <td>··············<pre><code·class="language-macaulay2">i1·:·X·=·specialGushelMukaiFourfold·"tau-quadric"; |
| 83 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> | 83 | o1·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> |
| 84 | </td>··········</tr> | 84 | </td>··········</tr> |
| 85 | ··········<tr> | 85 | ··········<tr> |
| 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X | 86 | <td>··············<pre><code·class="language-macaulay2">i2·:·time·discriminant·X |
| 87 | ·--·used·0. | 87 | ·--·used·0.713933s·(cpu);·0.380592s·(thread);·0s·(gc) |
| 88 | o2·=·10</code></pre> | 88 | o2·=·10</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ········</table> | 90 | ········</table> |
| 91 | ······</div> | 91 | ······</div> |
| 92 | ······<div> | 92 | ······<div> |
| 93 | ········<h2>See·also</h2> | 93 | ········<h2>See·also</h2> |
| Offset 21, 15 lines modified | Offset 21, 15 lines modified | ||
| 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·0. | 27 | ·--·used·0.713933s·(cpu);·0.380592s·(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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| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·random({{2},{2},{2}},S); | 88 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·random({{2},{2},{2}},S); |
| 89 | o3·:·ProjectiveVariety,·surface·in·PP^5</code></pre> | 89 | o3·:·ProjectiveVariety,·surface·in·PP^5</code></pre> |
| 90 | </td>··········</tr> | 90 | </td>··········</tr> |
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(S,X,Verbose=>true) | 92 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(S,X,Verbose=>true) |
| 93 | ·--·used·0.2 | 93 | ·--·used·0.251957s·(cpu);·0.193238s·(thread);·0s·(gc) |
| 94 | S:·rational·normal·curve·of·degree·5·in·PP^5 | 94 | S:·rational·normal·curve·of·degree·5·in·PP^5 |
| 95 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2 | 95 | X:·smooth·surface·of·degree·8·and·sectional·genus·5·in·PP^5·cut·out·by·3·hypersurfaces·of·degree·2 |
| 96 | (assumption:·h^1(N_{S,P^5})·=·0) | 96 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 97 | h^0(N_{S,P^5})·=·32 | 97 | h^0(N_{S,P^5})·=·32 |
| 98 | 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 | 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)); |
| 99 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal | 99 | in·particular,·h^0(I_{S,P^5}(2))·is·minimal |
| 100 | dim·GG(2,9)·=·21 | 100 | 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·0.251957s·(cpu);·0.193238s·(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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| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·V; | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·V; |
| 91 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> | 91 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> |
| 92 | </td>··········</tr> | 92 | </td>··········</tr> |
| 93 | ··········<tr> | 93 | ··········<tr> |
| 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) | 94 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) |
| 95 | ·--·used·0.39 | 95 | ·--·used·0.393654s·(cpu);·0.268212s·(thread);·0s·(gc) |
| 96 | S:·Veronese·surface·in·PP^5 | 96 | S:·Veronese·surface·in·PP^5 |
| 97 | X:·smooth·cubic·hypersurface·in·PP^5 | 97 | X:·smooth·cubic·hypersurface·in·PP^5 |
| 98 | (assumption:·h^1(N_{S,P^5})·=·0) | 98 | (assumption:·h^1(N_{S,P^5})·=·0) |
| 99 | h^0(N_{S,P^5})·=·27 | 99 | h^0(N_{S,P^5})·=·27 |
| 100 | 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 | 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)); |
| 101 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal | 101 | in·particular,·h^0(I_{S,P^5}(3))·is·minimal |
| 102 | h^0(N_{S,P^5})·+·27·=·54 | 102 | 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·0.39 | 39 | ·--·used·0.393654s·(cpu);·0.268212s·(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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| 96 | ··········<tr> | 96 | ··········<tr> |
| 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialGushelMukaiFourfold·S; | 97 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialGushelMukaiFourfold·S; |
| 98 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0</code></pre> | 98 | o3·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·3·and·sectional·genus·0</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parameterCount(X,Verbose=>true) |
| 102 | ·--·used·2.31 | 102 | ·--·used·2.31376s·(cpu);·1.75894s·(thread);·0s·(gc) |
| 103 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) | 103 | S:·cubic·surface·in·PP^8·cut·out·by·7·hypersurfaces·of·degrees·(1,1,1,1,2,2,2) |
| 104 | X:·GM·fourfold·containing·S | 104 | X:·GM·fourfold·containing·S |
| 105 | Y:·del·Pezzo·fivefold·containing·X | 105 | Y:·del·Pezzo·fivefold·containing·X |
| 106 | h^1(N_{S,Y})·=·0 | 106 | h^1(N_{S,Y})·=·0 |
| 107 | h^0(N_{S,Y})·=·11 | 107 | h^0(N_{S,Y})·=·11 |
| 108 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); | 108 | h^1(O_S(2))·=·0,·and·h^0(I_{S,Y}(2))·=·28·=·h^0(O_Y(2))·-·\chi(O_S(2)); |
| 109 | in·particular,·h^0(I_{S,Y}(2))·is·minimal | 109 | 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·2.31 | 41 | ·--·used·2.31376s·(cpu);·1.75894s·(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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| 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·?·X | 86 | <td>··············<pre><code·class="language-macaulay2">i3·:·?·X |
| 87 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees | 87 | o3·=·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees |
| 88 | ·····1^2·2^5</code></pre> | 88 | ·····1^2·2^5</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parametrizeFanoFourfold·X | 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·parametrizeFanoFourfold·X |
| 92 | ·--·used·1. | 92 | ·--·used·1.1353s·(cpu);·0.567536s·(thread);·0s·(gc) |
| 93 | o4·=·multi-rational·map·consisting·of·one·single·rational·map | 93 | o4·=·multi-rational·map·consisting·of·one·single·rational·map |
| 94 | ·····source·variety:·PP^4 | 94 | ·····source·variety:·PP^4 |
| 95 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5· | 95 | ·····target·variety:·4-dimensional·subvariety·of·PP^9·cut·out·by·7·hypersurfaces·of·degrees·1^2·2^5· |
| 96 | ·····dominance:·true | 96 | ·····dominance:·true |
| 97 | ·····degree:·1 | 97 | ·····degree:·1 |
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| 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·1. | 35 | ·--·used·1.1353s·(cpu);·0.567536s·(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 94, 23 lines modified | Offset 94, 23 lines modified | ||
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <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 | <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); |
| 96 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5</code></pre> | 96 | o4·:·ProjectiveVariety,·hypersurface·in·PP^5</code></pre> |
| 97 | </td>··········</tr> | 97 | </td>··········</tr> |
| 98 | ··········<tr> | 98 | ··········<tr> |
| 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); | 99 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialCubicFourfold(S,X,NumNodes=>3); |
| 100 | ·--·used·0.0 | 100 | ·--·used·0.00560533s·(cpu);·0.007434s·(thread);·0s·(gc) |
| 101 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0</code></pre> | 101 | o5·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·7·and·sectional·genus·0</code></pre> |
| 102 | </td>··········</tr> | 102 | </td>··········</tr> |
| 103 | ··········<tr> | 103 | ··········<tr> |
| 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F | 104 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F |
| 105 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 105 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 106 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 106 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 107 | ·--·used·0. | 107 | ·--·used·0.289827s·(cpu);·0.130867s·(thread);·0s·(gc) |
| 108 | o6·=·Special·cubic·fourfold·of·discriminant·26 | 108 | o6·=·Special·cubic·fourfold·of·discriminant·26 |
| 109 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 | 109 | ·····containing·a·3-nodal·surface·of·degree·7·and·sectional·genus·0 |
| 110 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> | 110 | ·····cut·out·by·13·hypersurfaces·of·degree·3</code></pre> |
| 111 | </td>··········</tr> | 111 | </td>··········</tr> |
| 112 | ··········<tr> | 112 | ··········<tr> |
| 113 | <td>··············<pre><code·class="language-macaulay2">i7·:·assert(F·==·X)</code></pre> | 113 | <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·0.0 | 122 | ·--·used·0.00560533s·(cpu);·0.007434s·(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·0.289827s·(cpu);·0.130867s·(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 91, 23 lines modified | Offset 91, 23 lines modified | ||
| 91 | ··········<tr> | 91 | ··········<tr> |
| 92 | <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 | <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); |
| 93 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8</code></pre> | 93 | o4·:·ProjectiveVariety,·4-dimensional·subvariety·of·PP^8</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialGushelMukaiFourfold(S,X); | 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·F·=·specialGushelMukaiFourfold(S,X); |
| 97 | ·--·used·1. | 97 | ·--·used·1.41982s·(cpu);·1.21209s·(thread);·0s·(gc) |
| 98 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> | 98 | o5·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F | 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·describe·F |
| 102 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 102 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 103 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 103 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 104 | ·--·used·4. | 104 | ·--·used·4.15632s·(cpu);·2.66187s·(thread);·0s·(gc) |
| 105 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') | 105 | o6·=·Special·Gushel-Mukai·fourfold·of·discriminant·10(') |
| 106 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 | 106 | ·····containing·a·surface·in·PP^8·of·degree·2·and·sectional·genus·0 |
| 107 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) | 107 | ·····cut·out·by·6·hypersurfaces·of·degrees·(1,1,1,1,1,2) |
| 108 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) | 108 | ·····and·with·class·in·G(1,4)·given·by·s_(3,1)+s_(2,2) |
| 109 | ·····Type:·ordinary | 109 | ·····Type:·ordinary |
| 110 | ·····(case·1·of·Table·1·in·arXiv:2002.07026)</code></pre> | 110 | ·····(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·1.41982s·(cpu);·1.21209s·(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·4. | 48 | ·--·used·4.15632s·(cpu);·2.66187s·(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 77, 15 lines modified | Offset 77, 15 lines modified | ||
| 77 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> | 77 | o2·:·ProjectiveVariety,·GM·fourfold·containing·a·surface·of·degree·2·and·sectional·genus·0</code></pre> |
| 78 | </td>··········</tr> | 78 | </td>··········</tr> |
| 79 | ··········<tr> | 79 | ··········<tr> |
| 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X | 80 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X |
| 81 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 81 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 82 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 82 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 83 | ·--·used· | 83 | ·--·used·3.72629s·(cpu);·2.3884s·(thread);·0s·(gc) |
| 84 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 84 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 85 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2 | 85 | ·····source·variety:·4-dimensional·subvariety·of·PP^8·cut·out·by·6·hypersurfaces·of·degree·2 |
| 86 | ·····target·variety:·GG(1,4)·⊂·PP^9 | 86 | ·····target·variety:·GG(1,4)·⊂·PP^9 |
| 87 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> | 87 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> |
| 88 | </td>··········</tr> | 88 | </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·3.72629s·(cpu);·2.3884s·(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 79, 15 lines modified | Offset 79, 15 lines modified | ||
| 79 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8</code></pre> | 79 | o2·:·ProjectiveVariety,·5-dimensional·subvariety·of·PP^8</code></pre> |
| 80 | </td>··········</tr> | 80 | </td>··········</tr> |
| 81 | ··········<tr> | 81 | ··········<tr> |
| 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X | 82 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·toGrass·X |
| 83 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it | 83 | warning:·clearing·value·of·symbol·x·to·allow·access·to·subscripted·variables·based·on·it |
| 84 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 | 84 | ·······:·debug·with·expression···debug·9868···or·with·command·line·option···--debug·9868 |
| 85 | ·--·used· | 85 | ·--·used·3.81008s·(cpu);·2.41991s·(thread);·0s·(gc) |
| 86 | o3·=·multi-rational·map·consisting·of·one·single·rational·map | 86 | o3·=·multi-rational·map·consisting·of·one·single·rational·map |
| 87 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2 | 87 | ·····source·variety:·5-dimensional·subvariety·of·PP^8·cut·out·by·5·hypersurfaces·of·degree·2 |
| 88 | ·····target·variety:·GG(1,4)·⊂·PP^9 | 88 | ·····target·variety:·GG(1,4)·⊂·PP^9 |
| 89 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> | 89 | o3·:·MultirationalMap·(rational·map·from·X·to·GG(1,4))</code></pre> |
| 90 | </td>··········</tr> | 90 | </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· | 32 | ·--·used·3.81008s·(cpu);·2.41991s·(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 78, 15 lines modified | Offset 78, 15 lines modified | ||
| 78 | ··········<tr> | 78 | ··········<tr> |
| 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·S; | 79 | <td>··············<pre><code·class="language-macaulay2">i3·:·X·=·specialCubicFourfold·S; |
| 80 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> | 80 | o3·:·ProjectiveVariety,·cubic·fourfold·containing·a·surface·of·degree·4·and·sectional·genus·0</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·f·=·unirationalParametrization·X; | 83 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·f·=·unirationalParametrization·X; |
| 84 | ·--·used·0. | 84 | ·--·used·0.654652s·(cpu);·0.353922s·(thread);·0s·(gc) |
| 85 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)</code></pre> | 85 | o4·:·MultirationalMap·(rational·map·from·PP^4·to·X)</code></pre> |
| 86 | </td>··········</tr> | 86 | </td>··········</tr> |
| 87 | ··········<tr> | 87 | ··········<tr> |
| 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·degreeSequence·f | 88 | <td>··············<pre><code·class="language-macaulay2">i5·:·degreeSequence·f |
| 89 | o5·=·{[10]} | 89 | 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·0. | 24 | ·--·used·0.654652s·(cpu);·0.353922s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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,·Graph,·Bigraph} |
| 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·{Graph·=>·graph·({3,·1},·{{1,·3}}),·Bigraph·=> | ||
| 16 | ·····bigraph·({3,·4,·2},·{{4,·3},·{4,·2}}),·Digraph·=>·digraph·({1,·2,·3}, | ||
| 17 | ·····{{1,·2},·{2,·3}}) | 15 | o2·=·new·HashTable·from·{Digraph·=>·digraph·({1,·2,·3},·{{1,·2},·{2,·3}}), |
| 16 | ·····Graph·=>·graph·({3,·1},·{{1,·3}}),·Bigraph·=>·bigraph·({3,·4,·2},·{{4, | ||
| 17 | ·····3},·{4,·2}})} | ||
| 18 | i3·:· | 18 | i3·:· |
| Offset 116, 15 lines modified | Offset 116, 15 lines modified | ||
| 116 | ······························c·=>·{b} | 116 | ······························c·=>·{b} |
| 117 | o2·:·HashTable</code></pre> | 117 | o2·:·HashTable</code></pre> |
| 118 | </td>··········</tr> | 118 | </td>··········</tr> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·(graph·G) | 120 | <td>··············<pre><code·class="language-macaulay2">i3·:·keys·(graph·G) |
| 121 | o3·=·{ | 121 | o3·=·{Digraph,·Graph,·Bigraph} |
| 122 | o3·:·List</code></pre> | 122 | o3·:·List</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i4·:·(graph·G)#Bigraph·===·bigraph·G | 125 | <td>··············<pre><code·class="language-macaulay2">i4·:·(graph·G)#Bigraph·===·bigraph·G |
| 126 | o4·=·true</code></pre> | 126 | 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,·Graph,·Bigraph} |
| 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 87, 17 lines modified | Offset 87, 17 lines modified | ||
| 87 | ·······························3·=>·{1} | 87 | ·······························3·=>·{1} |
| 88 | o1·:·MixedGraph</code></pre> | 88 | o1·:·MixedGraph</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·toString·G | 91 | <td>··············<pre><code·class="language-macaulay2">i2·:·toString·G |
| 92 | o2·=·new·HashTable·from·{Graph·=>·graph·({3,·1},·{{1,·3}}),·Bigraph·=> | ||
| 93 | 92 | o2·=·new·HashTable·from·{Digraph·=>·digraph·({1,·2,·3},·{{1,·2},·{2,·3}}), | |
| 93 | ·····Graph·=>·graph·({3,·1},·{{1,·3}}),·Bigraph·=>·bigraph·({3,·4,·2},·{{4, | ||
| 94 | ····· | 94 | ·····3},·{4,·2}})}</code></pre> |
| 95 | </td>··········</tr> | 95 | </td>··········</tr> |
| 96 | ········</table> | 96 | ········</table> |
| 97 | ······</div> | 97 | ······</div> |
| 98 | ······<div> | 98 | ······<div> |
| 99 | ········<h2>See·also</h2> | 99 | ········<h2>See·also</h2> |
| 100 | ········<ul> | 100 | ········<ul> |
| 101 | ··········<li> | 101 | ··········<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·{Graph·=>·graph·({3,·1},·{{1,·3}}),·Bigraph·=> | ||
| 30 | ·····bigraph·({3,·4,·2},·{{4,·3},·{4,·2}}),·Digraph·=>·digraph·({1,·2,·3}, | ||
| 31 | ·····{{1,·2},·{2,·3}}) | 29 | o2·=·new·HashTable·from·{Digraph·=>·digraph·({1,·2,·3},·{{1,·2},·{2,·3}}), |
| 30 | ·····Graph·=>·graph·({3,·1},·{{1,·3}}),·Bigraph·=>·bigraph·({3,·4,·2},·{{4, | ||
| 31 | ·····3},·{4,·2}})} | ||
| 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 | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 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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| 5 | #:format=standard | 5 | #:format=standard |
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| 7 | #:len=30 | 7 | #:len=30 |
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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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| 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 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·0.19 | 35 | ·--·used·0.199388s·(cpu);·0.123107s·(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·0.07 | 51 | ·--·used·0.0797093s·(cpu);·0.0375337s·(thread);·0s·(gc) |
| 52 | o10·:·Ideal·of·QQ[x..z] | 52 | o10·:·Ideal·of·QQ[x..z] |
| 53 | i11·:· | 53 | i11·:· |
| Offset 133, 15 lines modified | Offset 133, 15 lines modified | ||
| 133 | ··········<tr> | 133 | ··········<tr> |
| 134 | <td>··············<pre><code·class="language-macaulay2">i6·:·isHomogeneous·P | 134 | <td>··············<pre><code·class="language-macaulay2">i6·:·isHomogeneous·P |
| 135 | o6·=·false</code></pre> | 135 | o6·=·false</code></pre> |
| 136 | </td>··········</tr> | 136 | </td>··········</tr> |
| 137 | ··········<tr> | 137 | ··········<tr> |
| 138 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·symbolicPower(P,4); | 138 | <td>··············<pre><code·class="language-macaulay2">i7·:·time·symbolicPower(P,4); |
| 139 | ·--·used·0.19 | 139 | ·--·used·0.199388s·(cpu);·0.123107s·(thread);·0s·(gc) |
| 140 | o7·:·Ideal·of·QQ[x..z]</code></pre> | 140 | o7·:·Ideal·of·QQ[x..z]</code></pre> |
| 141 | </td>··········</tr> | 141 | </td>··········</tr> |
| 142 | ··········<tr> | 142 | ··········<tr> |
| 143 | <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 | <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}) |
| 144 | ·············2·········3·········2·····2 | 144 | ·············2·········3·········2·····2 |
| Offset 152, 15 lines modified | Offset 152, 15 lines modified | ||
| 152 | ··········<tr> | 152 | ··········<tr> |
| 153 | <td>··············<pre><code·class="language-macaulay2">i9·:·isHomogeneous·Q | 153 | <td>··············<pre><code·class="language-macaulay2">i9·:·isHomogeneous·Q |
| 154 | o9·=·true</code></pre> | 154 | o9·=·true</code></pre> |
| 155 | </td>··········</tr> | 155 | </td>··········</tr> |
| 156 | ··········<tr> | 156 | ··········<tr> |
| 157 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·symbolicPower(Q,4); | 157 | <td>··············<pre><code·class="language-macaulay2">i10·:·time·symbolicPower(Q,4); |
| 158 | ·--·used·0.07 | 158 | ·--·used·0.0797093s·(cpu);·0.0375337s·(thread);·0s·(gc) |
| 159 | o10·:·Ideal·of·QQ[x..z]</code></pre> | 159 | o10·:·Ideal·of·QQ[x..z]</code></pre> |
| 160 | </td>··········</tr> | 160 | </td>··········</tr> |
| 161 | ········</table> | 161 | ········</table> |
| 162 | ······</div> | 162 | ······</div> |
| 163 | ······<div> | 163 | ······<div> |
| 164 | ········<h2>See·also</h2> | 164 | ········<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·0.19 | 65 | ·--·used·0.199388s·(cpu);·0.123107s·(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·0.07 | 74 | ·--·used·0.0797093s·(cpu);·0.0375337s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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=1047 | 9 | #:len=1047 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.2 | 15 | ·--·used·0.286321s·(cpu);·0.141385s·(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 86, 15 lines modified | Offset 86, 15 lines modified | ||
| 86 | ···················· | 86 | ···················· |
| 87 | ·····-1·····0······1 | 87 | ·····-1·····0······1 |
| 88 | o3·:·ChainComplex</code></pre> | 88 | o3·:·ChainComplex</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·T=tateExtension·W; | 91 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·T=tateExtension·W; |
| 92 | ·--·used·0.2 | 92 | ·--·used·0.286321s·(cpu);·0.141385s·(thread);·0s·(gc)</code></pre> |
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·cohomologyMatrix(T,-{3,3},{3,3}) | 95 | <td>··············<pre><code·class="language-macaulay2">i5·:·cohomologyMatrix(T,-{3,3},{3,3}) |
| 96 | o5·=·|·8h··4h··0·4··8··12·16·| | 96 | o5·=·|·8h··4h··0·4··8··12·16·| |
| 97 | ·····|·6h··3h··0·3··6··9··12·| | 97 | ·····|·6h··3h··0·3··6··9··12·| |
| 98 | ·····|·4h··2h··0·2··4··6··8··| | 98 | ·····|·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·0.2 | 29 | ·--·used·0.286321s·(cpu);·0.141385s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTc5LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTc5LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·0.630116s·(cpu);·0.497942s·(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·1.82019s·(cpu);·1.56582s·(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·0.000715577s·(cpu);·0.00154753s·(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·0.00109024s·(cpu);·0.00350674s·(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·0.0918527s·(cpu);·0.0525718s·(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·1.57951s·(cpu);·0.978193s·(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·0.0 | 71 | ·--·used·0.0532154s·(cpu);·0.055077s·(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·0.1 | 74 | ·--·used·0.109685s·(cpu);·0.0847048s·(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·0.7 | 82 | ·--·used·0.735281s·(cpu);·0.59187s·(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·0.20 | 85 | ·--·used·0.20051s·(cpu);·0.160125s·(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·0.09 | 83 | ·--·used·0.0941214s·(cpu);·0.0575278s·(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·0.107643s·(cpu);·0.108427s·(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·0.2 | 85 | ·--·used·0.21401s·(cpu);·0.13679s·(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·0.26 | 89 | ·--·used·0.268373s·(cpu);·0.205033s·(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 206, 21 lines modified | Offset 206, 21 lines modified | ||
| 206 | ··········<tr> | 206 | ··········<tr> |
| 207 | <td>··············<pre><code·class="language-macaulay2">i16·:·I3·=·ideal(x^50*y^50*z^50); | 207 | <td>··············<pre><code·class="language-macaulay2">i16·:·I3·=·ideal(x^50*y^50*z^50); |
| 208 | o16·:·Ideal·of·R</code></pre> | 208 | o16·:·Ideal·of·R</code></pre> |
| 209 | </td>··········</tr> | 209 | </td>··········</tr> |
| 210 | ··········<tr> | 210 | ··········<tr> |
| 211 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); | 211 | <td>··············<pre><code·class="language-macaulay2">i17·:·time·J1·=·frobeniusRoot(1,·{8,·10,·12},·{I1,·I2,·I3}); |
| 212 | ·--·used·0. | 212 | ·--·used·0.630116s·(cpu);·0.497942s·(thread);·0s·(gc) |
| 213 | o17·:·Ideal·of·R</code></pre> | 213 | o17·:·Ideal·of·R</code></pre> |
| 214 | </td>··········</tr> | 214 | </td>··········</tr> |
| 215 | ··········<tr> | 215 | ··········<tr> |
| 216 | <td>··············<pre><code·class="language-macaulay2">i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); | 216 | <td>··············<pre><code·class="language-macaulay2">i18·:·time·J2·=·frobeniusRoot(1,·I1^8*I2^10*I3^12); |
| 217 | ·--·used· | 217 | ·--·used·1.82019s·(cpu);·1.56582s·(thread);·0s·(gc) |
| 218 | o18·:·Ideal·of·R</code></pre> | 218 | o18·:·Ideal·of·R</code></pre> |
| 219 | </td>··········</tr> | 219 | </td>··········</tr> |
| 220 | ··········<tr> | 220 | ··········<tr> |
| 221 | <td>··············<pre><code·class="language-macaulay2">i19·:·J1·==·J2 | 221 | <td>··············<pre><code·class="language-macaulay2">i19·:·J1·==·J2 |
| 222 | o19·=·true</code></pre> | 222 | 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·0.630116s·(cpu);·0.497942s·(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·1.82019s·(cpu);·1.56582s·(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 90, 21 lines modified | Offset 90, 21 lines modified | ||
| 90 | o3·:·RingMap·T·<--·S</code></pre> | 90 | o3·:·RingMap·T·<--·S</code></pre> |
| 91 | </td>··········</tr> | 91 | </td>··········</tr> |
| 92 | ··········<tr> | 92 | ··········<tr> |
| 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·R·=·S/(ker·g);</code></pre> | 93 | <td>··············<pre><code·class="language-macaulay2">i4·:·R·=·S/(ker·g);</code></pre> |
| 94 | </td>··········</tr> | 94 | </td>··········</tr> |
| 95 | ··········<tr> | 95 | ··········<tr> |
| 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isCohenMacaulay(R) | 96 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·isCohenMacaulay(R) |
| 97 | ·--·used·0.00 | 97 | ·--·used·0.000715577s·(cpu);·0.00154753s·(thread);·0s·(gc) |
| 98 | o5·=·true</code></pre> | 98 | o5·=·true</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) | 101 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·isCohenMacaulay(R,·AtOrigin·=>·true) |
| 102 | ·--·used·0.00 | 102 | ·--·used·0.00109024s·(cpu);·0.00350674s·(thread);·0s·(gc) |
| 103 | o6·=·true</code></pre> | 103 | o6·=·true</code></pre> |
| 104 | </td>··········</tr> | 104 | </td>··········</tr> |
| 105 | ········</table> | 105 | ········</table> |
| 106 | ········<table·class="examples"> | 106 | ········<table·class="examples"> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i7·:·R·=·QQ[x,y,u,v]/(x*u,·x*v,·y*u,·y*v);</code></pre> | 108 | <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·0.000715577s·(cpu);·0.00154753s·(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·0.00109024s·(cpu);·0.00350674s·(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 183, 41 lines modified | Offset 183, 41 lines modified | ||
| 183 | o19·=·R | 183 | o19·=·R |
| 184 | o19·:·QuotientRing</code></pre> | 184 | o19·:·QuotientRing</code></pre> |
| 185 | </td>··········</tr> | 185 | </td>··········</tr> |
| 186 | ··········<tr> | 186 | ··········<tr> |
| 187 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·isFInjective(R) | 187 | <td>··············<pre><code·class="language-macaulay2">i20·:·time·isFInjective(R) |
| 188 | ·--·used·0.0 | 188 | ·--·used·0.0918527s·(cpu);·0.0525718s·(thread);·0s·(gc) |
| 189 | o20·=·true</code></pre> | 189 | o20·=·true</code></pre> |
| 190 | </td>··········</tr> | 190 | </td>··········</tr> |
| 191 | ··········<tr> | 191 | ··········<tr> |
| 192 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) | 192 | <td>··············<pre><code·class="language-macaulay2">i21·:·time·isFInjective(R,·CanonicalStrategy·=>·null) |
| 193 | ·--·used·1. | 193 | ·--·used·1.57951s·(cpu);·0.978193s·(thread);·0s·(gc) |
| 194 | o21·=·true</code></pre> | 194 | o21·=·true</code></pre> |
| 195 | </td>··········</tr> | 195 | </td>··········</tr> |
| 196 | ········</table> | 196 | ········</table> |
| 197 | ········<div> | 197 | ········<div> |
| 198 | ··········<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 | ··········<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> |
| 199 | ········</div> | 199 | ········</div> |
| 200 | ········<table·class="examples"> | 200 | ········<table·class="examples"> |
| 201 | ··········<tr> | 201 | ··········<tr> |
| 202 | <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>··············<pre><code·class="language-macaulay2">i22·:·R·=·ZZ/7[x,y,z]/((x-1)^5·+·(y+1)^5·+·z^5);</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·isFInjective(R) | 205 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·isFInjective(R) |
| 206 | ·--·used·0.0 | 206 | ·--·used·0.0532154s·(cpu);·0.055077s·(thread);·0s·(gc) |
| 207 | o23·=·false</code></pre> | 207 | o23·=·false</code></pre> |
| 208 | </td>··········</tr> | 208 | </td>··········</tr> |
| 209 | ··········<tr> | 209 | ··········<tr> |
| 210 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·isFInjective(R,·AtOrigin·=>·true) | 210 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·isFInjective(R,·AtOrigin·=>·true) |
| 211 | ·--·used·0.1 | 211 | ·--·used·0.109685s·(cpu);·0.0847048s·(thread);·0s·(gc) |
| 212 | o24·=·true</code></pre> | 212 | o24·=·true</code></pre> |
| 213 | </td>··········</tr> | 213 | </td>··········</tr> |
| 214 | ········</table> | 214 | ········</table> |
| 215 | ········<div> | 215 | ········<div> |
| 216 | ··········<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 | ··········<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> |
| 217 | ········</div> | 217 | ········</div> |
| Offset 234, 21 lines modified | Offset 234, 21 lines modified | ||
| 234 | o27·:·RingMap·EP1·<--·S</code></pre> | 234 | o27·:·RingMap·EP1·<--·S</code></pre> |
| 235 | </td>··········</tr> | 235 | </td>··········</tr> |
| 236 | ··········<tr> | 236 | ··········<tr> |
| 237 | <td>··············<pre><code·class="language-macaulay2">i28·:·R·=·S/(ker·f);</code></pre> | 237 | <td>··············<pre><code·class="language-macaulay2">i28·:·R·=·S/(ker·f);</code></pre> |
| 238 | </td>··········</tr> | 238 | </td>··········</tr> |
| 239 | ··········<tr> | 239 | ··········<tr> |
| 240 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·isFInjective(R) | 240 | <td>··············<pre><code·class="language-macaulay2">i29·:·time·isFInjective(R) |
| 241 | ·--·used·0.7 | 241 | ·--·used·0.735281s·(cpu);·0.59187s·(thread);·0s·(gc) |
| 242 | o29·=·false</code></pre> | 242 | o29·=·false</code></pre> |
| 243 | </td>··········</tr> | 243 | </td>··········</tr> |
| 244 | ··········<tr> | 244 | ··········<tr> |
| 245 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·isFInjective(R,·AssumeCM·=>·true) | 245 | <td>··············<pre><code·class="language-macaulay2">i30·:·time·isFInjective(R,·AssumeCM·=>·true) |
| 246 | ·--·used·0.20 | 246 | ·--·used·0.20051s·(cpu);·0.160125s·(thread);·0s·(gc) |
| 247 | o30·=·true</code></pre> | 247 | o30·=·true</code></pre> |
| 248 | </td>··········</tr> | 248 | </td>··········</tr> |
| 249 | ········</table> | 249 | ········</table> |
| 250 | ········<div> | 250 | ········<div> |
| 251 | ··········<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 | ··········<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> |
| 252 | ········</div> | 252 | ········</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·0.0918527s·(cpu);·0.0525718s·(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·1.57951s·(cpu);·0.978193s·(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·0.0 | 99 | ·--·used·0.0532154s·(cpu);·0.055077s·(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·0.1 | 102 | ·--·used·0.109685s·(cpu);·0.0847048s·(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·0.7 | 115 | ·--·used·0.735281s·(cpu);·0.59187s·(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·0.20 | 118 | ·--·used·0.20051s·(cpu);·0.160125s·(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 231, 22 lines modified | Offset 231, 22 lines modified | ||
| 231 | o25·:·Ideal·of·S</code></pre> | 231 | o25·:·Ideal·of·S</code></pre> |
| 232 | </td>··········</tr> | 232 | </td>··········</tr> |
| 233 | ··········<tr> | 233 | ··········<tr> |
| 234 | <td>··············<pre><code·class="language-macaulay2">i26·:·debugLevel·=·1;</code></pre> | 234 | <td>··············<pre><code·class="language-macaulay2">i26·:·debugLevel·=·1;</code></pre> |
| 235 | </td>··········</tr> | 235 | </td>··········</tr> |
| 236 | ··········<tr> | 236 | ··········<tr> |
| 237 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) | 237 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·1) |
| 238 | ·--·used·0.09 | 238 | ·--·used·0.0941214s·(cpu);·0.0575278s·(thread);·0s·(gc) |
| 239 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply. | 239 | isFRegular:·This·ring·does·not·appear·to·be·F-regular.··Increasing·DepthOfSearch·will·let·the·function·search·more·deeply. |
| 240 | o27·=·false</code></pre> | 240 | o27·=·false</code></pre> |
| 241 | </td>··········</tr> | 241 | </td>··········</tr> |
| 242 | ··········<tr> | 242 | ··········<tr> |
| 243 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) | 243 | <td>··············<pre><code·class="language-macaulay2">i28·:·time·isFRegular(S/I,·QGorensteinIndex·=>·infinity,·DepthOfSearch·=>·2) |
| 244 | ·--·used·0.1 | 244 | ·--·used·0.107643s·(cpu);·0.108427s·(thread);·0s·(gc) |
| 245 | o28·=·true</code></pre> | 245 | o28·=·true</code></pre> |
| 246 | </td>··········</tr> | 246 | </td>··········</tr> |
| 247 | ··········<tr> | 247 | ··········<tr> |
| 248 | <td>··············<pre><code·class="language-macaulay2">i29·:·debugLevel·=·0;</code></pre> | 248 | <td>··············<pre><code·class="language-macaulay2">i29·:·debugLevel·=·0;</code></pre> |
| 249 | </td>··········</tr> | 249 | </td>··········</tr> |
| 250 | ········</table> | 250 | ········</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·0.09 | 119 | ·--·used·0.0941214s·(cpu);·0.0575278s·(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·0.107643s·(cpu);·0.108427s·(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 220, 23 lines modified | Offset 220, 23 lines modified | ||
| 220 | ········</table> | 220 | ········</table> |
| 221 | ········<div> | 221 | ········<div> |
| 222 | ··········<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 | ··········<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> |
| 223 | ········</div> | 223 | ········</div> |
| 224 | ········<table·class="examples"> | 224 | ········<table·class="examples"> |
| 225 | ··········<tr> | 225 | ··········<tr> |
| 226 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) | 226 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·testIdeal({3/4,·2/3,·3/5},·L) |
| 227 | ·--·used·0.2 | 227 | ·--·used·0.21401s·(cpu);·0.13679s·(thread);·0s·(gc) |
| 228 | o23·=·ideal·(y,·x) | 228 | o23·=·ideal·(y,·x) |
| 229 | o23·:·Ideal·of·R</code></pre> | 229 | o23·:·Ideal·of·R</code></pre> |
| 230 | </td>··········</tr> | 230 | </td>··········</tr> |
| 231 | ··········<tr> | 231 | ··········<tr> |
| 232 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) | 232 | <td>··············<pre><code·class="language-macaulay2">i24·:·time·testIdeal(1/60,·x^45*y^40*(x·+·y)^36) |
| 233 | ·--·used·0.26 | 233 | ·--·used·0.268373s·(cpu);·0.205033s·(thread);·0s·(gc) |
| 234 | o24·=·ideal·(y,·x) | 234 | o24·=·ideal·(y,·x) |
| 235 | o24·:·Ideal·of·R</code></pre> | 235 | o24·:·Ideal·of·R</code></pre> |
| 236 | </td>··········</tr> | 236 | </td>··········</tr> |
| 237 | ········</table> | 237 | ········</table> |
| 238 | ········<div> | 238 | ········<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·0.2 | 107 | ·--·used·0.21401s·(cpu);·0.13679s·(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·0.26 | 111 | ·--·used·0.268373s·(cpu);·0.205033s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDcxLCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNDcxLCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0Z2IsTGlzdCksInRnYihMaXN0KSIsIlRocmVhZGVk | 11 | PT4gbmV3IERvY3VtZW50VGFnIGZyb20geyh0Z2IsTGlzdCksInRnYihMaXN0KSIsIlRocmVhZGVk |
| Offset 2, 16 lines modified | Offset 2, 15 lines modified | ||
| 2 | i1·:·S·=·ZZ/101[a,b,c]; | 2 | i1·:·S·=·ZZ/101[a,b,c]; |
| 3 | i2·:·allowableThreads=·2; | 3 | i2·:·allowableThreads=·2; |
| 4 | i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true) | 4 | i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true) |
| 5 | o3·=·LineageTable{(( | 5 | o3·=·LineageTable{((0,·2),·0)·=>·null} |
| 6 | ··················((0,·1),·0)·=>·null | ||
| 7 | ··································2 | 6 | ··································2 |
| 8 | ··················((1,·2),·0)·=>·c | 7 | ··················((1,·2),·0)·=>·c |
| 9 | ··················(0,·1)·=>·null | 8 | ··················(0,·1)·=>·null |
| 10 | ··················(0,·2)·=>·null | 9 | ··················(0,·2)·=>·null |
| 11 | ··················(1,·2)·=>·a*c | 10 | ··················(1,·2)·=>·a*c |
| 12 | ··················0·=>·null | 11 | ··················0·=>·null |
| 13 | ··················1·=>·null | 12 | ··················1·=>·null |
| Offset 28, 20 lines modified | Offset 28, 17 lines modified | ||
| 28 | ·················································5·2····2·5 | 28 | ·················································5·2····2·5 |
| 29 | o4·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·x·x··-·x·x·} | 29 | o4·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·x·x··-·x·x·} |
| 30 | ·················································0·5····0·2 | 30 | ·················································0·5····0·2 |
| 31 | ············································4········2···3 | 31 | ············································4········2···3 |
| 32 | ··················((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x | 32 | ··················((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x |
| 33 | ············································0·5·4····0·3·2 | 33 | ············································0·5·4····0·3·2 |
| 34 | ·······································3·2···· | 34 | ·······································3·2······4 |
| 35 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x | 35 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x |
| 36 | ·······································0·4····0· | 36 | ·······································0·4····0·2 |
| 37 | ·······································2·2··········3 | ||
| 38 | ··················(((1,·2),·1),·9)·=>·x·x·x··-·x·x·x | ||
| 39 | ·······································0·4·2····0·4·2 | ||
| 40 | ··································2············2 | 37 | ··································2············2 |
| 41 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x | 38 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x |
| 42 | ··································0·5·2····0·3·2 | 39 | ··································0·5·2····0·3·2 |
| 43 | ······································2······3 | 40 | ······································2······3 |
| 44 | ··················((1,·2),·8)·=>·x·x·x··-·x·x | 41 | ··················((1,·2),·8)·=>·x·x·x··-·x·x |
| 45 | ··································0·5·2····3·2 | 42 | ··································0·5·2····3·2 |
| 46 | ········································3 | 43 | ········································3 |
| Offset 54, 14 lines modified | Offset 51, 17 lines modified | ||
| 54 | ··················(1,·7)·=>·-·x·x··+·x·x | 51 | ··················(1,·7)·=>·-·x·x··+·x·x |
| 55 | ·······························0·4····4·2 | 52 | ·······························0·4····4·2 |
| 56 | ····································2 | 53 | ····································2 |
| 57 | ··················(2,·3)·=>·x·x··-·x | 54 | ··················(2,·3)·=>·x·x··-·x |
| 58 | ·····························0·4····2 | 55 | ·····························0·4····2 |
| 59 | ··················(4,·6)·=>·x·x··-·x·x | 56 | ··················(4,·6)·=>·x·x··-·x·x |
| 60 | ·····························0·5····3·2 | 57 | ·····························0·5····3·2 |
| 58 | ·································2····2 | ||
| 59 | ··················(6,·7)·=>·-·x·x··+·x·x | ||
| 60 | ·······························0·5····4·2 | ||
| 61 | ·······························2······3 | 61 | ·······························2······3 |
| 62 | ··················(8,·9)·=>·-·x·x··+·x | 62 | ··················(8,·9)·=>·-·x·x··+·x |
| 63 | ·······························5·2····4 | 63 | ·······························5·2····4 |
| 64 | ··························2 | 64 | ··························2 |
| 65 | ··················0·=>·-·x··+·x·x | 65 | ··················0·=>·-·x··+·x·x |
| 66 | ··························1····0·2 | 66 | ··························1····0·2 |
| 67 | ··················1·=>·-·x·x··+·x·x | 67 | ··················1·=>·-·x·x··+·x·x |
| Offset 115, 25 lines modified | Offset 115, 25 lines modified | ||
| 115 | ·········1···0···3···5···4···2 | 115 | ·········1···0···3···5···4···2 |
| 116 | i8·:·minimize·g | 116 | i8·:·minimize·g |
| 117 | o8·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} | 117 | o8·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} |
| 118 | ··················((((1,·2),·1),·1),·6)·=>·null | 118 | ··················((((1,·2),·1),·1),·6)·=>·null |
| 119 | ··················(((1,·2),·1),·1)·=>·null | 119 | ··················(((1,·2),·1),·1)·=>·null |
| 120 | ··················(((1,·2),·1),·9)·=>·null | ||
| 121 | ··················((1,·2),·1)·=>·null | 120 | ··················((1,·2),·1)·=>·null |
| 122 | ··················((1,·2),·8)·=>·null | 121 | ··················((1,·2),·8)·=>·null |
| 123 | ··················(1,·2)·=>·null | 122 | ··················(1,·2)·=>·null |
| 124 | ··················(1,·4)·=>·null | 123 | ··················(1,·4)·=>·null |
| 125 | ··················(1,·7)·=>·null | 124 | ··················(1,·7)·=>·null |
| 126 | ····································2 | 125 | ····································2 |
| 127 | ··················(2,·3)·=>·x·x··-·x | 126 | ··················(2,·3)·=>·x·x··-·x |
| 128 | ·····························0·4····2 | 127 | ·····························0·4····2 |
| 129 | ··················(4,·6)·=>·x·x··-·x·x | 128 | ··················(4,·6)·=>·x·x··-·x·x |
| 130 | ·····························0·5····3·2 | 129 | ·····························0·5····3·2 |
| 130 | ··················(6,·7)·=>·null | ||
| 131 | ·····························2······3 | 131 | ·····························2······3 |
| 132 | ··················(8,·9)·=>·x·x··-·x | 132 | ··················(8,·9)·=>·x·x··-·x |
| 133 | ·····························5·2····4 | 133 | ·····························5·2····4 |
| 134 | ························2 | 134 | ························2 |
| 135 | ··················0·=>·x··-·x·x | 135 | ··················0·=>·x··-·x·x |
| 136 | ························1····0·2 | 136 | ························1····0·2 |
| 137 | ··················1·=>·x·x··-·x·x | 137 | ··················1·=>·x·x··-·x·x |
| Offset 158, 25 lines modified | Offset 158, 25 lines modified | ||
| 158 | o8·:·LineageTable | 158 | o8·:·LineageTable |
| 159 | i9·:·gRed·=·reduce·g | 159 | i9·:·gRed·=·reduce·g |
| 160 | o9·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} | 160 | o9·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} |
| 161 | ··················((((1,·2),·1),·1),·6)·=>·null | 161 | ··················((((1,·2),·1),·1),·6)·=>·null |
| 162 | ··················(((1,·2),·1),·1)·=>·null | 162 | ··················(((1,·2),·1),·1)·=>·null |
| 163 | ··················(((1,·2),·1),·9)·=>·null | ||
| 164 | ··················((1,·2),·1)·=>·null | 163 | ··················((1,·2),·1)·=>·null |
| 165 | ··················((1,·2),·8)·=>·null | 164 | ··················((1,·2),·8)·=>·null |
| 166 | ··················(1,·2)·=>·null | 165 | ··················(1,·2)·=>·null |
| 167 | ··················(1,·4)·=>·null | 166 | ··················(1,·4)·=>·null |
| 168 | ··················(1,·7)·=>·null | 167 | ··················(1,·7)·=>·null |
| 169 | ····································2 | 168 | ····································2 |
| 170 | ··················(2,·3)·=>·x·x··-·x | 169 | ··················(2,·3)·=>·x·x··-·x |
| 171 | ·····························0·4····2 | 170 | ·····························0·4····2 |
| 172 | ··················(4,·6)·=>·x·x··-·x·x | 171 | ··················(4,·6)·=>·x·x··-·x·x |
| 173 | ·····························0·5····3·2 | 172 | ·····························0·5····3·2 |
| 173 | ··················(6,·7)·=>·null | ||
| 174 | ·····························2······3 | 174 | ·····························2······3 |
| 175 | ··················(8,·9)·=>·x·x··-·x | 175 | ··················(8,·9)·=>·x·x··-·x |
| 176 | ·····························5·2····4 | 176 | ·····························5·2····4 |
| 177 | ························2 | 177 | ························2 |
| 178 | ··················0·=>·x··-·x·x | 178 | ··················0·=>·x··-·x·x |
| 179 | ························1····0·2 | 179 | ························1····0·2 |
| 180 | ··················1·=>·x·x··-·x·x | 180 | ··················1·=>·x·x··-·x·x |
| Offset 2, 26 lines modified | Offset 2, 28 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} | ||
| 5 | ··································2 | 6 | ··································2 |
| 6 | 7 | ··················((1,·2),·0)·=>·c | |
| 7 | ··················(0,·1)·=>·null | 8 | ··················(0,·1)·=>·null |
| 9 | ··················(0,·2)·=>·null | ||
| 8 | ··················(1,·2)·=>·a*c | 10 | ··················(1,·2)·=>·a*c |
| 9 | ··················0·=>·null | 11 | ··················0·=>·null |
| 10 | ··················1·=>·null | 12 | ··················1·=>·null |
| 11 | ························2 | 13 | ························2 |
| 12 | ··················2·=>·b | 14 | ··················2·=>·b |
| 13 | o3·:·LineageTable | 15 | o3·:·LineageTable |
| 14 | i4·:·matrix·T | 16 | i4·:·matrix·T |
| 15 | o4·=·|·b2· | 17 | o4·=·|·b2·c2·ac·| |
| 16 | ·············1······3 | 18 | ·············1······3 |
| 17 | o4·:·Matrix·R··<--·R | 19 | o4·:·Matrix·R··<--·R |
| 18 | i5·:· | 20 | i5·:· |
| Offset 4, 18 lines modified | Offset 4, 18 lines modified | ||
| 4 | i2·:·allowableThreads=·2; | 4 | i2·:·allowableThreads=·2; |
| 5 | i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" | 5 | i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" |
| 6 | ···································3 | 6 | ···································3 |
| 7 | o3·=·LineageTable{((0,·2),·0)·=>·-c······} | 7 | o3·=·LineageTable{((0,·2),·0)·=>·-c······} |
| 8 | ····································2 | ||
| 9 | ··················((0,·2),·1)·=>·a*c | ||
| 10 | ···································2 | 8 | ···································2 |
| 11 | ··················((1,·2),·0)·=>·-c | 9 | ··················((1,·2),·0)·=>·-c |
| 10 | ·····························2 | ||
| 11 | ··················(0,·1)·=>·a·c | ||
| 12 | ·······························2 | 12 | ·······························2 |
| 13 | ··················(0,·2)·=>·b*c | 13 | ··················(0,·2)·=>·b*c |
| 14 | ··················(1,·2)·=>·-a*c | 14 | ··················(1,·2)·=>·-a*c |
| 15 | ································2 | 15 | ································2 |
| 16 | ··················0·=>·a*b*c·+·c | 16 | ··················0·=>·a*b*c·+·c |
| 17 | ··························3·······2 | 17 | ··························3·······2 |
| 18 | ··················1·=>·-·b·c·+·a*b··+·a*c | 18 | ··················1·=>·-·b·c·+·a*b··+·a*c |
| Offset 23, 17 lines modified | Offset 23, 17 lines modified | ||
| 23 | ··················2·=>·b | 23 | ··················2·=>·b |
| 24 | o3·:·LineageTable | 24 | o3·:·LineageTable |
| 25 | i4·:·reduce·T | 25 | i4·:·reduce·T |
| 26 | o4·=·LineageTable{((0,·2),·0)·=>·null} | 26 | o4·=·LineageTable{((0,·2),·0)·=>·null} |
| 27 | ··················((0,·2),·1)·=>·null | ||
| 28 | ··································2 | 27 | ··································2 |
| 29 | ··················((1,·2),·0)·=>·c | 28 | ··················((1,·2),·0)·=>·c |
| 29 | ··················(0,·1)·=>·null | ||
| 30 | ··················(0,·2)·=>·null | 30 | ··················(0,·2)·=>·null |
| 31 | ··················(1,·2)·=>·a*c | 31 | ··················(1,·2)·=>·a*c |
| 32 | ··················0·=>·null | 32 | ··················0·=>·null |
| 33 | ··················1·=>·null | 33 | ··················1·=>·null |
| 34 | ························2 | 34 | ························2 |
| 35 | ··················2·=>·b | 35 | ··················2·=>·b |
| Offset 6, 47 lines modified | Offset 6, 59 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 | ········································· | 9 | ·········································2·4 |
| 10 | o4·=·LineageTable{(((0,· | 10 | o4·=·LineageTable{(((0,·3),·1),·1)·=>·11y·z············} |
| 11 | ·········································2·4 | ||
| 12 | ··················(((0,·3),·1),·3)·=>·17y·z | ||
| 11 | ······································ | 13 | ······································3·6····3·5 |
| 14 | ··················((0,·2),·1)·=>·-·11y·z··-·y·z | ||
| 15 | ····································2·7······2·6 | ||
| 12 | ··················(( | 16 | ··················((0,·2),·3)·=>·23y·z··+·48y·z |
| 17 | ····································4·7······3·5 | ||
| 18 | ··················((0,·3),·1)·=>·14y·z··-·11y·z | ||
| 13 | ···································4·4······2·6 | 19 | ···································4·4······2·6 |
| 14 | ··················((0,· | 20 | ··················((0,·3),·2)·=>·9y·z··+·23y·z |
| 15 | ·········································2·5 | ||
| 16 | ··················((0,·2),·(0,·1))·=>·-5y·z | ||
| 17 | ···································· | 21 | ····································2·6······2·5 |
| 22 | ··················((1,·3),·1)·=>·16y·z··+·29y·z | ||
| 23 | ···········································2·5······2·4 | ||
| 24 | ··················((2,·3),·(0,·2))·=>·-·40y·z··-·22y·z | ||
| 25 | ······································2·6·····2·5 | ||
| 18 | ··················(( | 26 | ··················((2,·3),·1)·=>·-·33y·z··-·3y·z |
| 19 | ·································5·2······3·4 | ||
| 20 | ··················(0,·1)·=>·-·25y·z··-·19y·z | ||
| 21 | ·································3· | 27 | ·································3·4······2·4 |
| 28 | ··················(0,·1)·=>·-·19y·z··+·10y·z | ||
| 29 | ······························5·3·····2·4 | ||
| 22 | ··················(0,·2)·=>· | 30 | ··················(0,·2)·=>·5y·z··+·9y·z |
| 23 | ·······························5 | 31 | ······························5·2······5 |
| 24 | ··················(0,·3)·=>·28y·z | 32 | ··················(0,·3)·=>·5y·z··+·28y·z |
| 33 | ·······························3·5······2·7 | ||
| 34 | ··················(1,·2)·=>·32y·z··+·14y·z | ||
| 35 | ·································7·······2·6 | ||
| 36 | ··················(1,·3)·=>·-·24y·z·-·14y·z | ||
| 25 | ·······························2·4 | 37 | ·······························5······2·4 |
| 26 | ··················(2,·3)·=>·-9y·z | 38 | ··················(2,·3)·=>·25y·z·-·9y·z |
| 27 | ·······························2 | 39 | ·······························2 |
| 28 | ··················0·=>·2x·+·10y·z | 40 | ··················0·=>·2x·+·10y·z |
| 29 | ·························2···········3 | 41 | ·························2···········3 |
| 30 | ··················1·=>·8x·y·+·10x*y*z | 42 | ··················1·=>·8x·y·+·10x*y*z |
| 31 | ···························3·2·······3 | 43 | ···························3·2·······3 |
| 32 | ··················2·=>·5x*y·z··+·9x*z | 44 | ··················2·=>·5x*y·z··+·9x*z |
| 33 | ···························3·········3 | 45 | ···························3·········3 |
| 34 | ··················3·=>·9x*y·z·+·10x*y | 46 | ··················3·=>·9x*y·z·+·10x*y |
| 35 | o4·:·LineageTable | 47 | o4·:·LineageTable |
| 36 | i5·:·H#(0,1) | 48 | i5·:·H#(0,1) |
| 37 | ·········· | 49 | ··········3·4······2·4 |
| 38 | o5·=·-· | 50 | o5·=·-·19y·z··+·10y·z |
| 39 | o5·:·R | 51 | o5·:·R |
| 40 | i6·:·QQ[a..d]; | 52 | i6·:·QQ[a..d]; |
| 41 | i7·:·f0·=·a*b-c^2; | 53 | i7·:·f0·=·a*b-c^2; |
| Offset 65, 16 lines modified | Offset 65, 15 lines modified | ||
| 65 | </td>··········</tr> | 65 | </td>··········</tr> |
| 66 | ··········<tr> | 66 | ··········<tr> |
| 67 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> | 67 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true) | 70 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true) |
| 71 | o3·=·LineageTable{(( | 71 | o3·=·LineageTable{((0,·2),·0)·=>·null} |
| 72 | ··················((0,·1),·0)·=>·null | ||
| 73 | ··································2 | 72 | ··································2 |
| 74 | ··················((1,·2),·0)·=>·c | 73 | ··················((1,·2),·0)·=>·c |
| 75 | ··················(0,·1)·=>·null | 74 | ··················(0,·1)·=>·null |
| 76 | ··················(0,·2)·=>·null | 75 | ··················(0,·2)·=>·null |
| 77 | ··················(1,·2)·=>·a*c | 76 | ··················(1,·2)·=>·a*c |
| 78 | ··················0·=>·null | 77 | ··················0·=>·null |
| 79 | ··················1·=>·null | 78 | ··················1·=>·null |
| Offset 13, 16 lines modified | Offset 13, 15 lines modified | ||
| 13 | Gr\"obner·basis·is·minimized.·Lineages·of·non-minimal·Gr\"obner·basis·elements | 13 | Gr\"obner·basis·is·minimized.·Lineages·of·non-minimal·Gr\"obner·basis·elements |
| 14 | that·were·added·to·the·basis·during·the·distributed·computation·are·saved,·with | 14 | that·were·added·to·the·basis·during·the·distributed·computation·are·saved,·with |
| 15 | the·corresponding·entry·in·the·table·being·null. | 15 | the·corresponding·entry·in·the·table·being·null. |
| 16 | i1·:·S·=·ZZ/101[a,b,c]; | 16 | i1·:·S·=·ZZ/101[a,b,c]; |
| 17 | i2·:·allowableThreads=·2; | 17 | i2·:·allowableThreads=·2; |
| 18 | i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true) | 18 | i3·:·T·=·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2",·Minimal=>true) |
| 19 | o3·=·LineageTable{(( | 19 | o3·=·LineageTable{((0,·2),·0)·=>·null} |
| 20 | ··················((0,·1),·0)·=>·null | ||
| 21 | ··································2 | 20 | ··································2 |
| 22 | ··················((1,·2),·0)·=>·c | 21 | ··················((1,·2),·0)·=>·c |
| 23 | ··················(0,·1)·=>·null | 22 | ··················(0,·1)·=>·null |
| 24 | ··················(0,·2)·=>·null | 23 | ··················(0,·2)·=>·null |
| 25 | ··················(1,·2)·=>·a*c | 24 | ··················(1,·2)·=>·a*c |
| 26 | ··················0·=>·null | 25 | ··················0·=>·null |
| 27 | ··················1·=>·null | 26 | ··················1·=>·null |
| Offset 85, 29 lines modified | Offset 85, 31 lines modified | ||
| 85 | </td>··········</tr> | 85 | </td>··········</tr> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> | 87 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·reduce·tgb(·ideal·"abc+c2,ab2-b3c+ac,b2") |
| 91 | o3·=·LineageTable{((0,·2),·0)·=>·null} | ||
| 91 | ··································2 | 92 | ··································2 |
| 92 | 93 | ··················((1,·2),·0)·=>·c | |
| 93 | ··················(0,·1)·=>·null | 94 | ··················(0,·1)·=>·null |
| 95 | ··················(0,·2)·=>·null | ||
| 94 | ··················(1,·2)·=>·a*c | 96 | ··················(1,·2)·=>·a*c |
| 95 | ··················0·=>·null | 97 | ··················0·=>·null |
| 96 | ··················1·=>·null | 98 | ··················1·=>·null |
| 97 | ························2 | 99 | ························2 |
| 98 | ··················2·=>·b | 100 | ··················2·=>·b |
| 99 | o3·:·LineageTable</code></pre> | 101 | o3·:·LineageTable</code></pre> |
| 100 | </td>··········</tr> | 102 | </td>··········</tr> |
| 101 | ··········<tr> | 103 | ··········<tr> |
| 102 | <td>··············<pre><code·class="language-macaulay2">i4·:·matrix·T | 104 | <td>··············<pre><code·class="language-macaulay2">i4·:·matrix·T |
| 103 | o4·=·|·b2· | 105 | o4·=·|·b2·c2·ac·| |
| 104 | ·············1······3 | 106 | ·············1······3 |
| 105 | o4·:·Matrix·R··<--·R</code></pre> | 107 | o4·:·Matrix·R··<--·R</code></pre> |
| 106 | </td>··········</tr> | 108 | </td>··········</tr> |
| 107 | ········</table> | 109 | ········</table> |
| 108 | ······</div> | 110 | ······</div> |
| 109 | ······<div·class="waystouse"> | 111 | ······<div·class="waystouse"> |
| Offset 20, 26 lines modified | Offset 20, 28 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} | ||
| 26 | ··································2 | 27 | ··································2 |
| 27 | 28 | ··················((1,·2),·0)·=>·c | |
| 28 | ··················(0,·1)·=>·null | 29 | ··················(0,·1)·=>·null |
| 30 | ··················(0,·2)·=>·null | ||
| 29 | ··················(1,·2)·=>·a*c | 31 | ··················(1,·2)·=>·a*c |
| 30 | ··················0·=>·null | 32 | ··················0·=>·null |
| 31 | ··················1·=>·null | 33 | ··················1·=>·null |
| 32 | ························2 | 34 | ························2 |
| 33 | ··················2·=>·b | 35 | ··················2·=>·b |
| 34 | o3·:·LineageTable | 36 | o3·:·LineageTable |
| 35 | i4·:·matrix·T | 37 | i4·:·matrix·T |
| 36 | o4·=·|·b2· | 38 | o4·=·|·b2·c2·ac·| |
| 37 | ·············1······3 | 39 | ·············1······3 |
| 38 | o4·:·Matrix·R··<--·R | 40 | o4·:·Matrix·R··<--·R |
| 39 | *\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* | 41 | *\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* |
| 40 | ····*·_\x8m_\x8a_\x8t_\x8r_\x8i_\x8x_\x8(_\x8L_\x8i_\x8n_\x8e_\x8a_\x8g_\x8e_\x8T_\x8a_\x8b_\x8l_\x8e_\x8)·--·extract·a·matrix·of·polynomials·from·values·of·a | 42 | ····*·_\x8m_\x8a_\x8t_\x8r_\x8i_\x8x_\x8(_\x8L_\x8i_\x8n_\x8e_\x8a_\x8g_\x8e_\x8T_\x8a_\x8b_\x8l_\x8e_\x8)·--·extract·a·matrix·of·polynomials·from·values·of·a |
| 41 | ······LineageTable·after·deleting·null·values | 43 | ······LineageTable·after·deleting·null·values |
| Offset 80, 18 lines modified | Offset 80, 18 lines modified | ||
| 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> | 80 | <td>··············<pre><code·class="language-macaulay2">i2·:·allowableThreads=·2;</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" | 83 | <td>··············<pre><code·class="language-macaulay2">i3·:·T·=·tgb·ideal·"abc+c2,ab2-b3c+ac,b2" |
| 84 | ···································3 | 84 | ···································3 |
| 85 | o3·=·LineageTable{((0,·2),·0)·=>·-c······} | 85 | o3·=·LineageTable{((0,·2),·0)·=>·-c······} |
| 86 | ····································2 | ||
| 87 | ··················((0,·2),·1)·=>·a*c | ||
| 88 | ···································2 | 86 | ···································2 |
| 89 | ··················((1,·2),·0)·=>·-c | 87 | ··················((1,·2),·0)·=>·-c |
| 88 | ·····························2 | ||
| 89 | ··················(0,·1)·=>·a·c | ||
| 90 | ·······························2 | 90 | ·······························2 |
| 91 | ··················(0,·2)·=>·b*c | 91 | ··················(0,·2)·=>·b*c |
| 92 | ··················(1,·2)·=>·-a*c | 92 | ··················(1,·2)·=>·-a*c |
| 93 | ································2 | 93 | ································2 |
| 94 | ··················0·=>·a*b*c·+·c | 94 | ··················0·=>·a*b*c·+·c |
| 95 | ··························3·······2 | 95 | ··························3·······2 |
| 96 | ··················1·=>·-·b·c·+·a*b··+·a*c | 96 | ··················1·=>·-·b·c·+·a*b··+·a*c |
| Offset 100, 17 lines modified | Offset 100, 17 lines modified | ||
| 100 | o3·:·LineageTable</code></pre> | 100 | o3·:·LineageTable</code></pre> |
| 101 | </td>··········</tr> | 101 | </td>··········</tr> |
| 102 | ··········<tr> | 102 | ··········<tr> |
| 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·reduce·T | 103 | <td>··············<pre><code·class="language-macaulay2">i4·:·reduce·T |
| 104 | o4·=·LineageTable{((0,·2),·0)·=>·null} | 104 | o4·=·LineageTable{((0,·2),·0)·=>·null} |
| 105 | ··················((0,·2),·1)·=>·null | ||
| 106 | ··································2 | 105 | ··································2 |
| 107 | ··················((1,·2),·0)·=>·c | 106 | ··················((1,·2),·0)·=>·c |
| 107 | ··················(0,·1)·=>·null | ||
| 108 | ··················(0,·2)·=>·null | 108 | ··················(0,·2)·=>·null |
| 109 | ··················(1,·2)·=>·a*c | 109 | ··················(1,·2)·=>·a*c |
| 110 | ··················0·=>·null | 110 | ··················0·=>·null |
| 111 | ··················1·=>·null | 111 | ··················1·=>·null |
| 112 | ························2 | 112 | ························2 |
| 113 | ··················2·=>·b | 113 | ··················2·=>·b |
| Offset 23, 35 lines modified | Offset 23, 35 lines modified | ||
| 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 | 27 | ···································3 |
| 28 | o3·=·LineageTable{((0,·2),·0)·=>·-c······} | 28 | o3·=·LineageTable{((0,·2),·0)·=>·-c······} |
| 29 | ····································2 | ||
| 30 | ··················((0,·2),·1)·=>·a*c | ||
| 31 | ···································2 | 29 | ···································2 |
| 32 | ··················((1,·2),·0)·=>·-c | 30 | ··················((1,·2),·0)·=>·-c |
| 31 | ·····························2 | ||
| 32 | ··················(0,·1)·=>·a·c | ||
| 33 | ·······························2 | 33 | ·······························2 |
| 34 | ··················(0,·2)·=>·b*c | 34 | ··················(0,·2)·=>·b*c |
| 35 | ··················(1,·2)·=>·-a*c | 35 | ··················(1,·2)·=>·-a*c |
| 36 | ································2 | 36 | ································2 |
| 37 | ··················0·=>·a*b*c·+·c | 37 | ··················0·=>·a*b*c·+·c |
| 38 | ··························3·······2 | 38 | ··························3·······2 |
| 39 | ··················1·=>·-·b·c·+·a*b··+·a*c | 39 | ··················1·=>·-·b·c·+·a*b··+·a*c |
| 40 | ························2 | 40 | ························2 |
| 41 | ··················2·=>·b | 41 | ··················2·=>·b |
| 42 | o3·:·LineageTable | 42 | o3·:·LineageTable |
| 43 | i4·:·reduce·T | 43 | i4·:·reduce·T |
| 44 | o4·=·LineageTable{((0,·2),·0)·=>·null} | 44 | o4·=·LineageTable{((0,·2),·0)·=>·null} |
| 45 | ··················((0,·2),·1)·=>·null | ||
| 46 | ··································2 | 45 | ··································2 |
| 47 | ··················((1,·2),·0)·=>·c | 46 | ··················((1,·2),·0)·=>·c |
| 47 | ··················(0,·1)·=>·null | ||
| 48 | ··················(0,·2)·=>·null | 48 | ··················(0,·2)·=>·null |
| 49 | ··················(1,·2)·=>·a*c | 49 | ··················(1,·2)·=>·a*c |
| 50 | ··················0·=>·null | 50 | ··················0·=>·null |
| 51 | ··················1·=>·null | 51 | ··················1·=>·null |
| 52 | ························2 | 52 | ························2 |
| 53 | ··················2·=>·b | 53 | ··················2·=>·b |
| Offset 93, 32 lines modified | Offset 93, 44 lines modified | ||
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=·4;</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i3·:·allowableThreads··=·4;</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·H·=·tgb·I | 98 | <td>··············<pre><code·class="language-macaulay2">i4·:·H·=·tgb·I |
| 99 | ········································· | 99 | ·········································2·4 |
| 100 | o4·=·LineageTable{(((0,· | 100 | o4·=·LineageTable{(((0,·3),·1),·1)·=>·11y·z············} |
| 101 | ·········································2·4 | ||
| 102 | ··················(((0,·3),·1),·3)·=>·17y·z | ||
| 101 | ······································ | 103 | ······································3·6····3·5 |
| 104 | ··················((0,·2),·1)·=>·-·11y·z··-·y·z | ||
| 105 | ····································2·7······2·6 | ||
| 102 | ··················(( | 106 | ··················((0,·2),·3)·=>·23y·z··+·48y·z |
| 107 | ····································4·7······3·5 | ||
| 108 | ··················((0,·3),·1)·=>·14y·z··-·11y·z | ||
| 103 | ···································4·4······2·6 | 109 | ···································4·4······2·6 |
| 104 | ··················((0,· | 110 | ··················((0,·3),·2)·=>·9y·z··+·23y·z |
| 105 | ·········································2·5 | ||
| 106 | ··················((0,·2),·(0,·1))·=>·-5y·z | ||
| 107 | ···································· | 111 | ····································2·6······2·5 |
| 112 | ··················((1,·3),·1)·=>·16y·z··+·29y·z | ||
| 113 | ···········································2·5······2·4 | ||
| 114 | ··················((2,·3),·(0,·2))·=>·-·40y·z··-·22y·z | ||
| 115 | ······································2·6·····2·5 | ||
| 108 | ··················(( | 116 | ··················((2,·3),·1)·=>·-·33y·z··-·3y·z |
| 109 | ·································5·2······3·4 | ||
| 110 | ··················(0,·1)·=>·-·25y·z··-·19y·z | ||
| 111 | ·································3· | 117 | ·································3·4······2·4 |
| 118 | ··················(0,·1)·=>·-·19y·z··+·10y·z | ||
| 119 | ······························5·3·····2·4 | ||
| 112 | ··················(0,·2)·=>· | 120 | ··················(0,·2)·=>·5y·z··+·9y·z |
| 113 | ·······························5 | 121 | ······························5·2······5 |
| 114 | ··················(0,·3)·=>·28y·z | 122 | ··················(0,·3)·=>·5y·z··+·28y·z |
| 123 | ·······························3·5······2·7 | ||
| 124 | ··················(1,·2)·=>·32y·z··+·14y·z | ||
| 125 | ·································7·······2·6 | ||
| 126 | ··················(1,·3)·=>·-·24y·z·-·14y·z | ||
| 115 | ·······························2·4 | 127 | ·······························5······2·4 |
| 116 | ··················(2,·3)·=>·-9y·z | 128 | ··················(2,·3)·=>·25y·z·-·9y·z |
| 117 | ·······························2 | 129 | ·······························2 |
| 118 | ··················0·=>·2x·+·10y·z | 130 | ··················0·=>·2x·+·10y·z |
| 119 | ·························2···········3 | 131 | ·························2···········3 |
| 120 | ··················1·=>·8x·y·+·10x*y*z | 132 | ··················1·=>·8x·y·+·10x*y*z |
| 121 | ···························3·2·······3 | 133 | ···························3·2·······3 |
| 122 | ··················2·=>·5x*y·z··+·9x*z | 134 | ··················2·=>·5x*y·z··+·9x*z |
| 123 | ···························3·········3 | 135 | ···························3·········3 |
| Offset 131, 16 lines modified | Offset 143, 16 lines modified | ||
| 131 | ··········<p>The·keys·of·the·hashtable·are·meaningful;·for·example,·the·polynomial·with·key·<span·class="tt">((0,2),1)</span>·in·the·hashtable·<span·class="tt">tgb(L,n)</span>·is·the·remainder·upon·division·of·the·S-polynomial·$(g,·I_1)$,·where·$g$·is·calculated·from·the·S-pair·$(I_0,·I_2)$.·For·this·reason,·we·say·that·the·key·communicates·the·"lineage"·of·the·resulting·polynomial.·(See·<a·title="a·package·for·distributed·computation·of·Gr\\"obner·bases"·href="index.html">ThreadedGB</a>.)</p> | 143 | ··········<p>The·keys·of·the·hashtable·are·meaningful;·for·example,·the·polynomial·with·key·<span·class="tt">((0,2),1)</span>·in·the·hashtable·<span·class="tt">tgb(L,n)</span>·is·the·remainder·upon·division·of·the·S-polynomial·$(g,·I_1)$,·where·$g$·is·calculated·from·the·S-pair·$(I_0,·I_2)$.·For·this·reason,·we·say·that·the·key·communicates·the·"lineage"·of·the·resulting·polynomial.·(See·<a·title="a·package·for·distributed·computation·of·Gr\\"obner·bases"·href="index.html">ThreadedGB</a>.)</p> |
| 132 | ··········<p>Note·that·the·keys·in·the·hash·table·are·strings,·and·the·keys·of·input·polynomials·are·0..#L,·as·in·the·following·example.</p> | 144 | ··········<p>Note·that·the·keys·in·the·hash·table·are·strings,·and·the·keys·of·input·polynomials·are·0..#L,·as·in·the·following·example.</p> |
| 133 | ········</div> | 145 | ········</div> |
| 134 | ········<table·class="examples"> | 146 | ········<table·class="examples"> |
| 135 | ··········<tr> | 147 | ··········<tr> |
| 136 | <td>··············<pre><code·class="language-macaulay2">i5·:·H#(0,1) | 148 | <td>··············<pre><code·class="language-macaulay2">i5·:·H#(0,1) |
| 137 | ·········· | 149 | ··········3·4······2·4 |
| 138 | o5·=·-· | 150 | o5·=·-·19y·z··+·10y·z |
| 139 | o5·:·R</code></pre> | 151 | o5·:·R</code></pre> |
| 140 | </td>··········</tr> | 152 | </td>··········</tr> |
| 141 | ········</table> | 153 | ········</table> |
| 142 | ········<div> | 154 | ········<div> |
| 143 | ··········<p>Some·may·be·curious··how·tgb·works.</p> | 155 | ··········<p>Some·may·be·curious··how·tgb·works.</p> |
| 144 | ··········<p>The·starting·basis·$L$·(the·input·list·<span·class="tt">L</span>·or·<span·class="tt">L=gens·I</span>)·populates·the·entries·numbered·$0$·through·$n-1$·of·a·mutable·hash·table·$G$,·where··$n$·is·the·length·of·$L$.·The·method·creates·all·possible·S-polynomials·of·$L$·and·schedules·their·reduction·with·respect·to·$G$·as·tasks.·Throughout·the·computation,·every·nonzero·remainder·added·to·the·basis·is·added·to·$G$·with·its·lineage·as·the·key.·Each·such·remainder·also·triggers·the·creation·of·S-polynomials·using·it·and·every·element·in·$G$·and·scheduling·the·reduction·thereof·as·additional·tasks.·The·process·is·done·when·there·are·no·remaining·tasks.</p> | 156 | ··········<p>The·starting·basis·$L$·(the·input·list·<span·class="tt">L</span>·or·<span·class="tt">L=gens·I</span>)·populates·the·entries·numbered·$0$·through·$n-1$·of·a·mutable·hash·table·$G$,·where··$n$·is·the·length·of·$L$.·The·method·creates·all·possible·S-polynomials·of·$L$·and·schedules·their·reduction·with·respect·to·$G$·as·tasks.·Throughout·the·computation,·every·nonzero·remainder·added·to·the·basis·is·added·to·$G$·with·its·lineage·as·the·key.·Each·such·remainder·also·triggers·the·creation·of·S-polynomials·using·it·and·every·element·in·$G$·and·scheduling·the·reduction·thereof·as·additional·tasks.·The·process·is·done·when·there·are·no·remaining·tasks.</p> |
| Offset 27, 32 lines modified | Offset 27, 44 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 | ········································· | 32 | ·········································2·4 |
| 33 | o4·=·LineageTable{(((0,· | 33 | o4·=·LineageTable{(((0,·3),·1),·1)·=>·11y·z············} |
| 34 | ·········································2·4 | ||
| 35 | ··················(((0,·3),·1),·3)·=>·17y·z | ||
| 34 | ······································ | 36 | ······································3·6····3·5 |
| 37 | ··················((0,·2),·1)·=>·-·11y·z··-·y·z | ||
| 38 | ····································2·7······2·6 | ||
| 35 | ··················(( | 39 | ··················((0,·2),·3)·=>·23y·z··+·48y·z |
| 40 | ····································4·7······3·5 | ||
| 41 | ··················((0,·3),·1)·=>·14y·z··-·11y·z | ||
| 36 | ···································4·4······2·6 | 42 | ···································4·4······2·6 |
| 37 | ··················((0,· | 43 | ··················((0,·3),·2)·=>·9y·z··+·23y·z |
| 38 | ·········································2·5 | ||
| 39 | ··················((0,·2),·(0,·1))·=>·-5y·z | ||
| 40 | ···································· | 44 | ····································2·6······2·5 |
| 45 | ··················((1,·3),·1)·=>·16y·z··+·29y·z | ||
| 46 | ···········································2·5······2·4 | ||
| 47 | ··················((2,·3),·(0,·2))·=>·-·40y·z··-·22y·z | ||
| 48 | ······································2·6·····2·5 | ||
| 41 | ··················(( | 49 | ··················((2,·3),·1)·=>·-·33y·z··-·3y·z |
| 42 | ·································5·2······3·4 | ||
| 43 | ··················(0,·1)·=>·-·25y·z··-·19y·z | ||
| 44 | ·································3· | 50 | ·································3·4······2·4 |
| 51 | ··················(0,·1)·=>·-·19y·z··+·10y·z | ||
| 52 | ······························5·3·····2·4 | ||
| 45 | ··················(0,·2)·=>· | 53 | ··················(0,·2)·=>·5y·z··+·9y·z |
| 46 | ·······························5 | 54 | ······························5·2······5 |
| 47 | ··················(0,·3)·=>·28y·z | 55 | ··················(0,·3)·=>·5y·z··+·28y·z |
| 56 | ·······························3·5······2·7 | ||
| 57 | ··················(1,·2)·=>·32y·z··+·14y·z | ||
| 58 | ·································7·······2·6 | ||
| 59 | ··················(1,·3)·=>·-·24y·z·-·14y·z | ||
| 48 | ·······························2·4 | 60 | ·······························5······2·4 |
| 49 | ··················(2,·3)·=>·-9y·z | 61 | ··················(2,·3)·=>·25y·z·-·9y·z |
| 50 | ·······························2 | 62 | ·······························2 |
| 51 | ··················0·=>·2x·+·10y·z | 63 | ··················0·=>·2x·+·10y·z |
| 52 | ·························2···········3 | 64 | ·························2···········3 |
| 53 | ··················1·=>·8x·y·+·10x*y*z | 65 | ··················1·=>·8x·y·+·10x*y*z |
| 54 | ···························3·2·······3 | 66 | ···························3·2·······3 |
| 55 | ··················2·=>·5x*y·z··+·9x*z | 67 | ··················2·=>·5x*y·z··+·9x*z |
| 56 | ···························3·········3 | 68 | ···························3·········3 |
| Offset 64, 16 lines modified | Offset 76, 16 lines modified | ||
| 64 | polynomial·$(g,·I_1)$,·where·$g$·is·calculated·from·the·S-pair·$(I_0,·I_2)$. | 76 | polynomial·$(g,·I_1)$,·where·$g$·is·calculated·from·the·S-pair·$(I_0,·I_2)$. |
| 65 | For·this·reason,·we·say·that·the·key·communicates·the·"lineage"·of·the | 77 | For·this·reason,·we·say·that·the·key·communicates·the·"lineage"·of·the |
| 66 | resulting·polynomial.·(See·_\x8T_\x8h_\x8r_\x8e_\x8a_\x8d_\x8e_\x8d_\x8G_\x8B.) | 78 | resulting·polynomial.·(See·_\x8T_\x8h_\x8r_\x8e_\x8a_\x8d_\x8e_\x8d_\x8G_\x8B.) |
| 67 | Note·that·the·keys·in·the·hash·table·are·strings,·and·the·keys·of·input | 79 | Note·that·the·keys·in·the·hash·table·are·strings,·and·the·keys·of·input |
| 68 | polynomials·are·0..#L,·as·in·the·following·example. | 80 | polynomials·are·0..#L,·as·in·the·following·example. |
| 69 | i5·:·H#(0,1) | 81 | i5·:·H#(0,1) |
| 70 | ·········· | 82 | ··········3·4······2·4 |
| 71 | o5·=·-· | 83 | o5·=·-·19y·z··+·10y·z |
| 72 | o5·:·R | 84 | o5·:·R |
| 73 | Some·may·be·curious·how·tgb·works. | 85 | Some·may·be·curious·how·tgb·works. |
| 74 | The·starting·basis·$L$·(the·input·list·L·or·L=gens·I)·populates·the·entries | 86 | The·starting·basis·$L$·(the·input·list·L·or·L=gens·I)·populates·the·entries |
| 75 | numbered·$0$·through·$n-1$·of·a·mutable·hash·table·$G$,·where·$n$·is·the·length | 87 | numbered·$0$·through·$n-1$·of·a·mutable·hash·table·$G$,·where·$n$·is·the·length |
| 76 | of·$L$.·The·method·creates·all·possible·S-polynomials·of·$L$·and·schedules | 88 | of·$L$.·The·method·creates·all·possible·S-polynomials·of·$L$·and·schedules |
| 77 | their·reduction·with·respect·to·$G$·as·tasks.·Throughout·the·computation,·every | 89 | their·reduction·with·respect·to·$G$·as·tasks.·Throughout·the·computation,·every |
| Offset 82, 20 lines modified | Offset 82, 17 lines modified | ||
| 82 | ·················································5·2····2·5 | 82 | ·················································5·2····2·5 |
| 83 | o4·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·x·x··-·x·x·} | 83 | o4·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·x·x··-·x·x·} |
| 84 | ·················································0·5····0·2 | 84 | ·················································0·5····0·2 |
| 85 | ············································4········2···3 | 85 | ············································4········2···3 |
| 86 | ··················((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x | 86 | ··················((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x |
| 87 | ············································0·5·4····0·3·2 | 87 | ············································0·5·4····0·3·2 |
| 88 | ·······································3·2···· | 88 | ·······································3·2······4 |
| 89 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x | 89 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x |
| 90 | ·······································0·4····0· | 90 | ·······································0·4····0·2 |
| 91 | ·······································2·2··········3 | ||
| 92 | ··················(((1,·2),·1),·9)·=>·x·x·x··-·x·x·x | ||
| 93 | ·······································0·4·2····0·4·2 | ||
| 94 | ··································2············2 | 91 | ··································2············2 |
| 95 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x | 92 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x |
| 96 | ··································0·5·2····0·3·2 | 93 | ··································0·5·2····0·3·2 |
| 97 | ······································2······3 | 94 | ······································2······3 |
| 98 | ··················((1,·2),·8)·=>·x·x·x··-·x·x | 95 | ··················((1,·2),·8)·=>·x·x·x··-·x·x |
| 99 | ··································0·5·2····3·2 | 96 | ··································0·5·2····3·2 |
| 100 | ········································3 | 97 | ········································3 |
| Offset 108, 14 lines modified | Offset 105, 17 lines modified | ||
| 108 | ··················(1,·7)·=>·-·x·x··+·x·x | 105 | ··················(1,·7)·=>·-·x·x··+·x·x |
| 109 | ·······························0·4····4·2 | 106 | ·······························0·4····4·2 |
| 110 | ····································2 | 107 | ····································2 |
| 111 | ··················(2,·3)·=>·x·x··-·x | 108 | ··················(2,·3)·=>·x·x··-·x |
| 112 | ·····························0·4····2 | 109 | ·····························0·4····2 |
| 113 | ··················(4,·6)·=>·x·x··-·x·x | 110 | ··················(4,·6)·=>·x·x··-·x·x |
| 114 | ·····························0·5····3·2 | 111 | ·····························0·5····3·2 |
| 112 | ·································2····2 | ||
| 113 | ··················(6,·7)·=>·-·x·x··+·x·x | ||
| 114 | ·······························0·5····4·2 | ||
| 115 | ·······························2······3 | 115 | ·······························2······3 |
| 116 | ··················(8,·9)·=>·-·x·x··+·x | 116 | ··················(8,·9)·=>·-·x·x··+·x |
| 117 | ·······························5·2····4 | 117 | ·······························5·2····4 |
| 118 | ··························2 | 118 | ··························2 |
| 119 | ··················0·=>·-·x··+·x·x | 119 | ··················0·=>·-·x··+·x·x |
| 120 | ··························1····0·2 | 120 | ··························1····0·2 |
| 121 | ··················1·=>·-·x·x··+·x·x | 121 | ··················1·=>·-·x·x··+·x·x |
| Offset 191, 25 lines modified | Offset 191, 25 lines modified | ||
| 191 | ········<table·class="examples"> | 191 | ········<table·class="examples"> |
| 192 | ··········<tr> | 192 | ··········<tr> |
| 193 | <td>··············<pre><code·class="language-macaulay2">i8·:·minimize·g | 193 | <td>··············<pre><code·class="language-macaulay2">i8·:·minimize·g |
| 194 | o8·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} | 194 | o8·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} |
| 195 | ··················((((1,·2),·1),·1),·6)·=>·null | 195 | ··················((((1,·2),·1),·1),·6)·=>·null |
| 196 | ··················(((1,·2),·1),·1)·=>·null | 196 | ··················(((1,·2),·1),·1)·=>·null |
| 197 | ··················(((1,·2),·1),·9)·=>·null | ||
| 198 | ··················((1,·2),·1)·=>·null | 197 | ··················((1,·2),·1)·=>·null |
| 199 | ··················((1,·2),·8)·=>·null | 198 | ··················((1,·2),·8)·=>·null |
| 200 | ··················(1,·2)·=>·null | 199 | ··················(1,·2)·=>·null |
| 201 | ··················(1,·4)·=>·null | 200 | ··················(1,·4)·=>·null |
| 202 | ··················(1,·7)·=>·null | 201 | ··················(1,·7)·=>·null |
| 203 | ····································2 | 202 | ····································2 |
| 204 | ··················(2,·3)·=>·x·x··-·x | 203 | ··················(2,·3)·=>·x·x··-·x |
| 205 | ·····························0·4····2 | 204 | ·····························0·4····2 |
| 206 | ··················(4,·6)·=>·x·x··-·x·x | 205 | ··················(4,·6)·=>·x·x··-·x·x |
| 207 | ·····························0·5····3·2 | 206 | ·····························0·5····3·2 |
| 207 | ··················(6,·7)·=>·null | ||
| 208 | ·····························2······3 | 208 | ·····························2······3 |
| 209 | ··················(8,·9)·=>·x·x··-·x | 209 | ··················(8,·9)·=>·x·x··-·x |
| 210 | ·····························5·2····4 | 210 | ·····························5·2····4 |
| 211 | ························2 | 211 | ························2 |
| 212 | ··················0·=>·x··-·x·x | 212 | ··················0·=>·x··-·x·x |
| 213 | ························1····0·2 | 213 | ························1····0·2 |
| 214 | ··················1·=>·x·x··-·x·x | 214 | ··················1·=>·x·x··-·x·x |
| Offset 235, 25 lines modified | Offset 235, 25 lines modified | ||
| 235 | </td>··········</tr> | 235 | </td>··········</tr> |
| 236 | ··········<tr> | 236 | ··········<tr> |
| 237 | <td>··············<pre><code·class="language-macaulay2">i9·:·gRed·=·reduce·g | 237 | <td>··············<pre><code·class="language-macaulay2">i9·:·gRed·=·reduce·g |
| 238 | o9·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} | 238 | o9·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} |
| 239 | ··················((((1,·2),·1),·1),·6)·=>·null | 239 | ··················((((1,·2),·1),·1),·6)·=>·null |
| 240 | ··················(((1,·2),·1),·1)·=>·null | 240 | ··················(((1,·2),·1),·1)·=>·null |
| 241 | ··················(((1,·2),·1),·9)·=>·null | ||
| 242 | ··················((1,·2),·1)·=>·null | 241 | ··················((1,·2),·1)·=>·null |
| 243 | ··················((1,·2),·8)·=>·null | 242 | ··················((1,·2),·8)·=>·null |
| 244 | ··················(1,·2)·=>·null | 243 | ··················(1,·2)·=>·null |
| 245 | ··················(1,·4)·=>·null | 244 | ··················(1,·4)·=>·null |
| 246 | ··················(1,·7)·=>·null | 245 | ··················(1,·7)·=>·null |
| 247 | ····································2 | 246 | ····································2 |
| 248 | ··················(2,·3)·=>·x·x··-·x | 247 | ··················(2,·3)·=>·x·x··-·x |
| 249 | ·····························0·4····2 | 248 | ·····························0·4····2 |
| 250 | ··················(4,·6)·=>·x·x··-·x·x | 249 | ··················(4,·6)·=>·x·x··-·x·x |
| 251 | ·····························0·5····3·2 | 250 | ·····························0·5····3·2 |
| 251 | ··················(6,·7)·=>·null | ||
| 252 | ·····························2······3 | 252 | ·····························2······3 |
| 253 | ··················(8,·9)·=>·x·x··-·x | 253 | ··················(8,·9)·=>·x·x··-·x |
| 254 | ·····························5·2····4 | 254 | ·····························5·2····4 |
| 255 | ························2 | 255 | ························2 |
| 256 | ··················0·=>·x··-·x·x | 256 | ··················0·=>·x··-·x·x |
| 257 | ························1····0·2 | 257 | ························1····0·2 |
| 258 | ··················1·=>·x·x··-·x·x | 258 | ··················1·=>·x·x··-·x·x |
| Offset 45, 20 lines modified | Offset 45, 17 lines modified | ||
| 45 | ·················································5·2····2·5 | 45 | ·················································5·2····2·5 |
| 46 | o4·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·x·x··-·x·x·} | 46 | o4·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·x·x··-·x·x·} |
| 47 | ·················································0·5····0·2 | 47 | ·················································0·5····0·2 |
| 48 | ············································4········2···3 | 48 | ············································4········2···3 |
| 49 | ··················((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x | 49 | ··················((((1,·2),·1),·1),·6)·=>·x·x·x··-·x·x·x |
| 50 | ············································0·5·4····0·3·2 | 50 | ············································0·5·4····0·3·2 |
| 51 | ·······································3·2···· | 51 | ·······································3·2······4 |
| 52 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x | 52 | ··················(((1,·2),·1),·1)·=>·x·x··-·x·x |
| 53 | ·······································0·4····0· | 53 | ·······································0·4····0·2 |
| 54 | ·······································2·2··········3 | ||
| 55 | ··················(((1,·2),·1),·9)·=>·x·x·x··-·x·x·x | ||
| 56 | ·······································0·4·2····0·4·2 | ||
| 57 | ··································2············2 | 54 | ··································2············2 |
| 58 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x | 55 | ··················((1,·2),·1)·=>·x·x·x··-·x·x·x |
| 59 | ··································0·5·2····0·3·2 | 56 | ··································0·5·2····0·3·2 |
| 60 | ······································2······3 | 57 | ······································2······3 |
| 61 | ··················((1,·2),·8)·=>·x·x·x··-·x·x | 58 | ··················((1,·2),·8)·=>·x·x·x··-·x·x |
| 62 | ··································0·5·2····3·2 | 59 | ··································0·5·2····3·2 |
| 63 | ········································3 | 60 | ········································3 |
| Offset 71, 14 lines modified | Offset 68, 17 lines modified | ||
| 71 | ··················(1,·7)·=>·-·x·x··+·x·x | 68 | ··················(1,·7)·=>·-·x·x··+·x·x |
| 72 | ·······························0·4····4·2 | 69 | ·······························0·4····4·2 |
| 73 | ····································2 | 70 | ····································2 |
| 74 | ··················(2,·3)·=>·x·x··-·x | 71 | ··················(2,·3)·=>·x·x··-·x |
| 75 | ·····························0·4····2 | 72 | ·····························0·4····2 |
| 76 | ··················(4,·6)·=>·x·x··-·x·x | 73 | ··················(4,·6)·=>·x·x··-·x·x |
| 77 | ·····························0·5····3·2 | 74 | ·····························0·5····3·2 |
| 75 | ·································2····2 | ||
| 76 | ··················(6,·7)·=>·-·x·x··+·x·x | ||
| 77 | ·······························0·5····4·2 | ||
| 78 | ·······························2······3 | 78 | ·······························2······3 |
| 79 | ··················(8,·9)·=>·-·x·x··+·x | 79 | ··················(8,·9)·=>·-·x·x··+·x |
| 80 | ·······························5·2····4 | 80 | ·······························5·2····4 |
| 81 | ··························2 | 81 | ··························2 |
| 82 | ··················0·=>·-·x··+·x·x | 82 | ··················0·=>·-·x··+·x·x |
| 83 | ··························1····0·2 | 83 | ··························1····0·2 |
| 84 | ··················1·=>·-·x·x··+·x·x | 84 | ··················1·=>·-·x·x··+·x·x |
| Offset 143, 25 lines modified | Offset 143, 25 lines modified | ||
| 143 | output·below,·elements·that·are·reduced·are·replaced·by·null,·but·their·lineage | 143 | output·below,·elements·that·are·reduced·are·replaced·by·null,·but·their·lineage |
| 144 | keys·are·retained·for·informative·purposes. | 144 | keys·are·retained·for·informative·purposes. |
| 145 | i8·:·minimize·g | 145 | i8·:·minimize·g |
| 146 | o8·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} | 146 | o8·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} |
| 147 | ··················((((1,·2),·1),·1),·6)·=>·null | 147 | ··················((((1,·2),·1),·1),·6)·=>·null |
| 148 | ··················(((1,·2),·1),·1)·=>·null | 148 | ··················(((1,·2),·1),·1)·=>·null |
| 149 | ··················(((1,·2),·1),·9)·=>·null | ||
| 150 | ··················((1,·2),·1)·=>·null | 149 | ··················((1,·2),·1)·=>·null |
| 151 | ··················((1,·2),·8)·=>·null | 150 | ··················((1,·2),·8)·=>·null |
| 152 | ··················(1,·2)·=>·null | 151 | ··················(1,·2)·=>·null |
| 153 | ··················(1,·4)·=>·null | 152 | ··················(1,·4)·=>·null |
| 154 | ··················(1,·7)·=>·null | 153 | ··················(1,·7)·=>·null |
| 155 | ····································2 | 154 | ····································2 |
| 156 | ··················(2,·3)·=>·x·x··-·x | 155 | ··················(2,·3)·=>·x·x··-·x |
| 157 | ·····························0·4····2 | 156 | ·····························0·4····2 |
| 158 | ··················(4,·6)·=>·x·x··-·x·x | 157 | ··················(4,·6)·=>·x·x··-·x·x |
| 159 | ·····························0·5····3·2 | 158 | ·····························0·5····3·2 |
| 159 | ··················(6,·7)·=>·null | ||
| 160 | ·····························2······3 | 160 | ·····························2······3 |
| 161 | ··················(8,·9)·=>·x·x··-·x | 161 | ··················(8,·9)·=>·x·x··-·x |
| 162 | ·····························5·2····4 | 162 | ·····························5·2····4 |
| 163 | ························2 | 163 | ························2 |
| 164 | ··················0·=>·x··-·x·x | 164 | ··················0·=>·x··-·x·x |
| 165 | ························1····0·2 | 165 | ························1····0·2 |
| 166 | ··················1·=>·x·x··-·x·x | 166 | ··················1·=>·x·x··-·x·x |
| Offset 185, 25 lines modified | Offset 185, 25 lines modified | ||
| 185 | o8·:·LineageTable | 185 | o8·:·LineageTable |
| 186 | i9·:·gRed·=·reduce·g | 186 | i9·:·gRed·=·reduce·g |
| 187 | o9·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} | 187 | o9·=·LineageTable{(((((1,·2),·1),·1),·6),·6)·=>·null} |
| 188 | ··················((((1,·2),·1),·1),·6)·=>·null | 188 | ··················((((1,·2),·1),·1),·6)·=>·null |
| 189 | ··················(((1,·2),·1),·1)·=>·null | 189 | ··················(((1,·2),·1),·1)·=>·null |
| 190 | ··················(((1,·2),·1),·9)·=>·null | ||
| 191 | ··················((1,·2),·1)·=>·null | 190 | ··················((1,·2),·1)·=>·null |
| 192 | ··················((1,·2),·8)·=>·null | 191 | ··················((1,·2),·8)·=>·null |
| 193 | ··················(1,·2)·=>·null | 192 | ··················(1,·2)·=>·null |
| 194 | ··················(1,·4)·=>·null | 193 | ··················(1,·4)·=>·null |
| 195 | ··················(1,·7)·=>·null | 194 | ··················(1,·7)·=>·null |
| 196 | ····································2 | 195 | ····································2 |
| 197 | ··················(2,·3)·=>·x·x··-·x | 196 | ··················(2,·3)·=>·x·x··-·x |
| 198 | ·····························0·4····2 | 197 | ·····························0·4····2 |
| 199 | ··················(4,·6)·=>·x·x··-·x·x | 198 | ··················(4,·6)·=>·x·x··-·x·x |
| 200 | ·····························0·5····3·2 | 199 | ·····························0·5····3·2 |
| 200 | ··················(6,·7)·=>·null | ||
| 201 | ·····························2······3 | 201 | ·····························2······3 |
| 202 | ··················(8,·9)·=>·x·x··-·x | 202 | ··················(8,·9)·=>·x·x··-·x |
| 203 | ·····························5·2····4 | 203 | ·····························5·2····4 |
| 204 | ························2 | 204 | ························2 |
| 205 | ··················0·=>·x··-·x·x | 205 | ··················0·=>·x··-·x·x |
| 206 | ························1····0·2 | 206 | ························1····0·2 |
| 207 | ··················1·=>·x·x··-·x·x | 207 | ··················1·=>·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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzI0LCBzeW1ib2wgRG9jdW1lbnRUYWcg | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gNzI0LCBzeW1ib2wgRG9jdW1lbnRUYWcg |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 36 | ·--·used·0.95735s·(cpu);·0.66485s·(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·3.63203s·(cpu);·2.52207s·(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 120, 15 lines modified | Offset 120, 15 lines modified | ||
| 120 | ·····|·1·1·1·1·1·1·| | 120 | ·····|·1·1·1·1·1·1·| |
| 121 | ··············4·······6 | 121 | ··············4·······6 |
| 122 | o3·:·Matrix·ZZ··<--·ZZ</code></pre> | 122 | o3·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 123 | </td>··········</tr> | 123 | </td>··········</tr> |
| 124 | ··········<tr> | 124 | ··········<tr> |
| 125 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·edDeg(A) | 125 | <td>··············<pre><code·class="language-macaulay2">i4·:·time·edDeg(A) |
| 126 | ·--·used· | 126 | ·--·used·0.95735s·(cpu);·0.66485s·(thread);·0s·(gc) |
| 127 | The·toric·variety·has·degree·=·28 | 127 | The·toric·variety·has·degree·=·28 |
| 128 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 128 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 129 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 129 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 130 | Polar·Degrees:·{45,·98,·81,·28} | 130 | Polar·Degrees:·{45,·98,·81,·28} |
| 131 | ED·Degree·=·252 | 131 | ED·Degree·=·252 |
| Offset 137, 15 lines modified | Offset 137, 15 lines modified | ||
| 137 | o4·=·252 | 137 | o4·=·252 |
| 138 | o4·:·QQ</code></pre> | 138 | o4·:·QQ</code></pre> |
| 139 | </td>··········</tr> | 139 | </td>··········</tr> |
| 140 | ··········<tr> | 140 | ··········<tr> |
| 141 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·edDeg(A,ForceAmat=>true) | 141 | <td>··············<pre><code·class="language-macaulay2">i5·:·time·edDeg(A,ForceAmat=>true) |
| 142 | ·--·used·3. | 142 | ·--·used·3.63203s·(cpu);·2.52207s·(thread);·0s·(gc) |
| 143 | The·toric·variety·has·degree·=·28 | 143 | The·toric·variety·has·degree·=·28 |
| 144 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 | 144 | The·dual·variety·has·degree·=·45,·and·codimension·=·1 |
| 145 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} | 145 | Chern-Mather·Volumes:·(V_0,..,V_(d-1))·=·{20,·23,·31,·28} |
| 146 | Polar·Degrees:·{45,·98,·81,·28} | 146 | Polar·Degrees:·{45,·98,·81,·28} |
| 147 | ED·Degree·=·252 | 147 | 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· | 64 | ·--·used·0.95735s·(cpu);·0.66485s·(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·3.63203s·(cpu);·2.52207s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | cmljIHZlY3RvciBidW5kbGUiLCAibGluZW51bSIgPT4gMjgxNywgSW5wdXRzID0+IHtTUEFOe1RU | 11 | cmljIHZlY3RvciBidW5kbGUiLCAibGluZW51bSIgPT4gMjgxNywgSW5wdXRzID0+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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·=·{{c,·d,·f,·h},·{b,·d,·e,·f},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·- |
| 8 | ·····------------------------------------------------------------------------ | 8 | ·····------------------------------------------------------------------------ |
| 9 | ····· | 9 | ·····d*e,·e*h·-·f*g}·/·{d,·f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·e,·f},·{a*d·- |
| 10 | ·····------------------------------------------------------------------------ | 10 | ·····------------------------------------------------------------------------ |
| 11 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} | 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, 19 lines modified | Offset 2, 19 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,·e,·f},·{a*d·-·b*c,· | 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 | ····· | 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,·e,·f} | 12 | o4·=·{c,·d,·e,·f} |
| Offset 93, 19 lines modified | Offset 93, 19 lines modified | ||
| 93 | </td>··········</tr> | 93 | </td>··········</tr> |
| 94 | ··········<tr> | 94 | ··········<tr> |
| 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g};</code></pre> | 95 | <td>··············<pre><code·class="language-macaulay2">i2·:·F·=·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g};</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·TT·=·triangularize(R,F,{}) | 98 | <td>··············<pre><code·class="language-macaulay2">i3·:·TT·=·triangularize(R,F,{}) |
| 99 | o3·=·{{c,·d,·e,·f},·{a*d·-·b*c,· | 99 | o3·=·{{c,·d,·e,·f},·{a*d·-·b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c, |
| 100 | ·····------------------------------------------------------------------------ | 100 | ·····------------------------------------------------------------------------ |
| 101 | ····· | 101 | ·····d,·g,·h},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}·/·{d, |
| 102 | ·····------------------------------------------------------------------------ | 102 | ·····------------------------------------------------------------------------ |
| 103 | ····· | 103 | ·····f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·f,·h},·{b,·d,·e,·f}} |
| 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·:·first·TT | 107 | <td>··············<pre><code·class="language-macaulay2">i4·:·first·TT |
| 108 | o4·=·{c,·d,·e,·f} | 108 | o4·=·{c,·d,·e,·f} |
| Offset 31, 19 lines modified | Offset 31, 19 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,·e,·f},·{a*d·-·b*c,· | 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 | ····· | 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,·e,·f} | 44 | o4·=·{c,·d,·e,·f} |
| 45 | o4·:·TriaSystem | 45 | o4·:·TriaSystem |
| Offset 53, 17 lines modified | Offset 53, 17 lines modified | ||
| 53 | <td>··············<pre><code·class="language-macaulay2">i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; | 53 | <td>··············<pre><code·class="language-macaulay2">i2·:·I·=·ideal·{a*d·-·b*c,·c*f·-·d*e,·e*h·-·f*g}; |
| 54 | o2·:·Ideal·of·R</code></pre> | 54 | o2·:·Ideal·of·R</code></pre> |
| 55 | </td>··········</tr> | 55 | </td>··········</tr> |
| 56 | ··········<tr> | 56 | ··········<tr> |
| 57 | <td>··············<pre><code·class="language-macaulay2">i3·:·triangularize·I | 57 | <td>··············<pre><code·class="language-macaulay2">i3·:·triangularize·I |
| 58 | o3·=·{{ | 58 | o3·=·{{c,·d,·f,·h},·{b,·d,·e,·f},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·- |
| 59 | ·····------------------------------------------------------------------------ | 59 | ·····------------------------------------------------------------------------ |
| 60 | ····· | 60 | ·····d*e,·e*h·-·f*g}·/·{d,·f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·e,·f},·{a*d·- |
| 61 | ·····------------------------------------------------------------------------ | 61 | ·····------------------------------------------------------------------------ |
| 62 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} | 62 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} |
| 63 | o3·:·List</code></pre> | 63 | o3·:·List</code></pre> |
| 64 | </td>··········</tr> | 64 | </td>··········</tr> |
| 65 | ········</table> | 65 | ········</table> |
| 66 | <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 | <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> |
| Offset 8, 17 lines modified | Offset 8, 17 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·=·{{c,·d,·f,·h},·{b,·d,·e,·f},·{a*d·-·b*c,·e,·f}·/·d,·{a*d·-·b*c,·c*f·- |
| 14 | ·····------------------------------------------------------------------------ | 14 | ·····------------------------------------------------------------------------ |
| 15 | ····· | 15 | ·····d*e,·e*h·-·f*g}·/·{d,·f,·h},·{c,·d,·e*h·-·f*g}·/·h,·{c,·d,·e,·f},·{a*d·- |
| 16 | ·····------------------------------------------------------------------------ | 16 | ·····------------------------------------------------------------------------ |
| 17 | ·····b*c,·c*f·-·d*e,·g,·h}·/·{d,·f},·{b,·d,·f,·h},·{c,·d,·g,·h}} | 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. |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | ·--·0.1 | 22 | ·--·0.166342·seconds·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 | ·--·1.26 | 54 | ·--·1.12667·seconds·elapsed |
| 55 | i9·:·#Ts2·==·#Ts | 55 | i9·:·#Ts2·==·#Ts |
| 56 | o9·=·true | 56 | o9·=·true |
| 57 | i10·:· | 57 | i10·:· |
| Offset 21, 15 lines modified | Offset 21, 57 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,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,· | 24 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·6}, |
| 25 | ·····------------------------------------------------------------------------ | ||
| 26 | ·····{0,·5,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | ||
| 27 | ·····------------------------------------------------------------------------ | ||
| 28 | ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation | ||
| 29 | ·····------------------------------------------------------------------------ | ||
| 30 | ·····{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7},·{1,·2,·6,·7},·{1,·4,·5,·7}, | ||
| 31 | ·····------------------------------------------------------------------------ | ||
| 32 | ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7}, | ||
| 33 | ·····------------------------------------------------------------------------ | ||
| 34 | ·····{1,·4,·5,·7},·{2,·3,·4,·6},·{3,·4,·6,·7}},·triangulation·{{0,·1,·2,·4}, | ||
| 35 | ·····------------------------------------------------------------------------ | ||
| 36 | ·····{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, | ||
| 37 | ·····------------------------------------------------------------------------ | ||
| 38 | ·····triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6}, | ||
| 39 | ·····------------------------------------------------------------------------ | ||
| 40 | ·····{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·6}, | ||
| 41 | ·····------------------------------------------------------------------------ | ||
| 42 | ·····{1,·2,·4,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 43 | ·····------------------------------------------------------------------------ | ||
| 44 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·6}, | ||
| 45 | ·····------------------------------------------------------------------------ | ||
| 46 | ·····{1,·5,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},·{0,·2,·4,·5}, | ||
| 47 | ·····------------------------------------------------------------------------ | ||
| 48 | ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·3,·5}, | ||
| 49 | ·····------------------------------------------------------------------------ | ||
| 50 | ·····{0,·2,·3,·6},·{0,·3,·4,·5},·{0,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, | ||
| 51 | ·····------------------------------------------------------------------------ | ||
| 52 | ·····triangulation·{{0,·1,·3,·6},·{0,·1,·5,·6},·{0,·2,·3,·6},·{0,·4,·5,·6}, | ||
| 53 | ·····------------------------------------------------------------------------ | ||
| 54 | ·····{1,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6}, | ||
| 55 | ·····------------------------------------------------------------------------ | ||
| 56 | ·····{0,·4,·5,·6},·{1,·2,·3,·5},·{2,·3,·5,·7},·{2,·5,·6,·7}},·triangulation | ||
| 57 | ·····------------------------------------------------------------------------ | ||
| 58 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·7},·{2,·4,·5,·7}, | ||
| 59 | ·····------------------------------------------------------------------------ | ||
| 60 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·5}, | ||
| 61 | ·····------------------------------------------------------------------------ | ||
| 62 | ·····{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·6}, | ||
| 63 | ·····------------------------------------------------------------------------ | ||
| 64 | ·····{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·5,·6,·7}}, | ||
| 65 | ·····------------------------------------------------------------------------ | ||
| 66 | ·····triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, | ||
| 25 | ·····------------------------------------------------------------------------ | 67 | ·····------------------------------------------------------------------------ |
| 26 | ·····{0,·4,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | 68 | ·····{0,·4,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, |
| 27 | ·····------------------------------------------------------------------------ | 69 | ·····------------------------------------------------------------------------ |
| 28 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation | 70 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation |
| 29 | ·····------------------------------------------------------------------------ | 71 | ·····------------------------------------------------------------------------ |
| 30 | ·····{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·2,·3,·7}, | 72 | ·····{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·2,·3,·7}, |
| 31 | ·····------------------------------------------------------------------------ | 73 | ·····------------------------------------------------------------------------ |
| Offset 185, 63 lines modified | Offset 227, 57 lines modified | ||
| 185 | ·····------------------------------------------------------------------------ | 227 | ·····------------------------------------------------------------------------ |
| 186 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation | 228 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation |
| 187 | ·····------------------------------------------------------------------------ | 229 | ·····------------------------------------------------------------------------ |
| 188 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·6},·{0,·4,·5,·6},·{3,·5,·6,·7}}, | 230 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·6},·{0,·4,·5,·6},·{3,·5,·6,·7}}, |
| 189 | ·····------------------------------------------------------------------------ | 231 | ·····------------------------------------------------------------------------ |
| 190 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·7},·{1,·4,·5,·7}, | 232 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·7},·{1,·4,·5,·7}, |
| 191 | ·····------------------------------------------------------------------------ | 233 | ·····------------------------------------------------------------------------ |
| 192 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7}, | ||
| 193 | ·····------------------------------------------------------------------------ | ||
| 194 | ·····{0,·4,·5,·6},·{0,·5,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7}, | ||
| 195 | ····· | 234 | ·····{2,·4,·6,·7}}} |
| 235 | o4·:·List | ||
| 236 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 196 | · | 237 | o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}, |
| 197 | ·····------------------------------------------------------------------------ | 238 | ·····------------------------------------------------------------------------ |
| 198 | ····· | 239 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·6},·{0,·3,·6,·7}, |
| 199 | ·····------------------------------------------------------------------------ | 240 | ·····------------------------------------------------------------------------ |
| 200 | ·····{ | 241 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7}, |
| 201 | ·····------------------------------------------------------------------------ | 242 | ·····------------------------------------------------------------------------ |
| 202 | ·····{1,· | 243 | ·····{1,·2,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·4}, |
| 203 | ·····------------------------------------------------------------------------ | 244 | ·····------------------------------------------------------------------------ |
| 204 | ·····{ | 245 | ·····{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·6},·{3,·4,·6,·7}},·{{0,·1,·2,·4}, |
| 205 | ·····------------------------------------------------------------------------ | 246 | ·····------------------------------------------------------------------------ |
| 206 | ·····{ | 247 | ·····{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, |
| 207 | ·····------------------------------------------------------------------------ | 248 | ·····------------------------------------------------------------------------ |
| 208 | ·····{ | 249 | ·····{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6}, |
| 209 | ·····------------------------------------------------------------------------ | 250 | ·····------------------------------------------------------------------------ |
| 210 | ·····{ | 251 | ·····{3,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·6},·{1,·2,·4,·6},·{1,·3,·6,·7}, |
| 211 | ·····------------------------------------------------------------------------ | 252 | ·····------------------------------------------------------------------------ |
| 212 | ····· | 253 | ·····{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6}, |
| 213 | ·····------------------------------------------------------------------------ | 254 | ·····------------------------------------------------------------------------ |
| 214 | ·····{1,· | 255 | ·····{1,·2,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·5}, |
| 215 | ·····------------------------------------------------------------------------ | 256 | ·····------------------------------------------------------------------------ |
| 216 | ·····{0,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},· | 257 | ·····{0,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·{{0,·1,·3,·5}, |
| 217 | ·····------------------------------------------------------------------------ | 258 | ·····------------------------------------------------------------------------ |
| 218 | ·····{ | 259 | ·····{0,·2,·3,·6},·{0,·3,·4,·5},·{0,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, |
| 219 | ·····------------------------------------------------------------------------ | 260 | ·····------------------------------------------------------------------------ |
| 220 | ·····{ | 261 | ·····{{0,·1,·3,·6},·{0,·1,·5,·6},·{0,·2,·3,·6},·{0,·4,·5,·6},·{1,·3,·5,·6}, |
| 221 | ·····------------------------------------------------------------------------ | 262 | ·····------------------------------------------------------------------------ |
| 222 | ·····{ | 263 | ·····{3,·5,·6,·7}},·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, |
| 223 | ·····------------------------------------------------------------------------ | 264 | ·····------------------------------------------------------------------------ |
| 224 | ·····{ | 265 | ·····{2,·3,·5,·7},·{2,·5,·6,·7}},·{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5}, |
| 225 | ·····------------------------------------------------------------------------ | 266 | ·····------------------------------------------------------------------------ |
| 226 | ····· | 267 | ·····{2,·3,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·7}, |
| 227 | ·····------------------------------------------------------------------------ | 268 | ·····------------------------------------------------------------------------ |
| 228 | ·····{ | 269 | ·····{1,·2,·4,·5},·{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·2,·6}, |
| 229 | ·····------------------------------------------------------------------------ | 270 | ·····------------------------------------------------------------------------ |
| 230 | ·····{ | 271 | ·····{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·5,·6,·7}}, |
| 231 | ·····------------------------------------------------------------------------ | 272 | ·····------------------------------------------------------------------------ |
| 232 | ·····{{0,·1,·2,·6},·{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7}, | ||
| 233 | ·····------------------------------------------------------------------------ | ||
| 234 | ·····{1,·5,·6,·7}}} | ||
| 235 | o4·:·List | ||
| 236 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 237 | 273 | ·····{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}, | |
| 238 | ·····------------------------------------------------------------------------ | 274 | ·····------------------------------------------------------------------------ |
| 239 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 275 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 240 | ·····------------------------------------------------------------------------ | 276 | ·····------------------------------------------------------------------------ |
| 241 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7}, | 277 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7}, |
| 242 | ·····------------------------------------------------------------------------ | 278 | ·····------------------------------------------------------------------------ |
| 243 | ·····{0,·4,·6,·7},·{1,·2,·3,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7}, | 279 | ·····{0,·4,·6,·7},·{1,·2,·3,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7}, |
| 244 | ·····------------------------------------------------------------------------ | 280 | ·····------------------------------------------------------------------------ |
| Offset 373, 57 lines modified | Offset 409, 63 lines modified | ||
| Max diff block lines reached; 34870/45270 bytes (77.03%) of diff not shown. | |||
| Offset 117, 15 lines modified | Offset 117, 57 lines modified | ||
| 117 | 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·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6},·{3,·5,·6,·7}} |
| 118 | o3·:·Triangulation</code></pre> | 118 | o3·:·Triangulation</code></pre> |
| 119 | </td>··········</tr> | 119 | </td>··········</tr> |
| 120 | ··········<tr> | 120 | ··········<tr> |
| 121 | <td>··············<pre><code·class="language-macaulay2">i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. | 121 | <td>··············<pre><code·class="language-macaulay2">i4·:·Ts1·=·generateTriangulations·A·--·list·of·Triangulation's. |
| 122 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,· | 122 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·6}, |
| 123 | ·····------------------------------------------------------------------------ | ||
| 124 | ·····{0,·5,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | ||
| 125 | ·····------------------------------------------------------------------------ | ||
| 126 | ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation | ||
| 127 | ·····------------------------------------------------------------------------ | ||
| 128 | ·····{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7},·{1,·2,·6,·7},·{1,·4,·5,·7}, | ||
| 129 | ·····------------------------------------------------------------------------ | ||
| 130 | ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7}, | ||
| 131 | ·····------------------------------------------------------------------------ | ||
| 132 | ·····{1,·4,·5,·7},·{2,·3,·4,·6},·{3,·4,·6,·7}},·triangulation·{{0,·1,·2,·4}, | ||
| 133 | ·····------------------------------------------------------------------------ | ||
| 134 | ·····{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, | ||
| 135 | ·····------------------------------------------------------------------------ | ||
| 136 | ·····triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6}, | ||
| 137 | ·····------------------------------------------------------------------------ | ||
| 138 | ·····{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·6}, | ||
| 139 | ·····------------------------------------------------------------------------ | ||
| 140 | ·····{1,·2,·4,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 141 | ·····------------------------------------------------------------------------ | ||
| 142 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·6}, | ||
| 143 | ·····------------------------------------------------------------------------ | ||
| 144 | ·····{1,·5,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},·{0,·2,·4,·5}, | ||
| 145 | ·····------------------------------------------------------------------------ | ||
| 146 | ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·3,·5}, | ||
| 147 | ·····------------------------------------------------------------------------ | ||
| 148 | ·····{0,·2,·3,·6},·{0,·3,·4,·5},·{0,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, | ||
| 149 | ·····------------------------------------------------------------------------ | ||
| 150 | ·····triangulation·{{0,·1,·3,·6},·{0,·1,·5,·6},·{0,·2,·3,·6},·{0,·4,·5,·6}, | ||
| 151 | ·····------------------------------------------------------------------------ | ||
| 152 | ·····{1,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6}, | ||
| 153 | ·····------------------------------------------------------------------------ | ||
| 154 | ·····{0,·4,·5,·6},·{1,·2,·3,·5},·{2,·3,·5,·7},·{2,·5,·6,·7}},·triangulation | ||
| 155 | ·····------------------------------------------------------------------------ | ||
| 156 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·7},·{2,·4,·5,·7}, | ||
| 157 | ·····------------------------------------------------------------------------ | ||
| 158 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·5}, | ||
| 159 | ·····------------------------------------------------------------------------ | ||
| 160 | ·····{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·6}, | ||
| 161 | ·····------------------------------------------------------------------------ | ||
| 162 | ·····{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·5,·6,·7}}, | ||
| 163 | ·····------------------------------------------------------------------------ | ||
| 164 | ·····triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, | ||
| 123 | ·····------------------------------------------------------------------------ | 165 | ·····------------------------------------------------------------------------ |
| 124 | ·····{0,·4,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | 166 | ·····{0,·4,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, |
| 125 | ·····------------------------------------------------------------------------ | 167 | ·····------------------------------------------------------------------------ |
| 126 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation | 168 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation |
| 127 | ·····------------------------------------------------------------------------ | 169 | ·····------------------------------------------------------------------------ |
| 128 | ·····{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·2,·3,·7}, | 170 | ·····{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·2,·3,·7}, |
| 129 | ·····------------------------------------------------------------------------ | 171 | ·····------------------------------------------------------------------------ |
| Offset 281, 64 lines modified | Offset 323, 58 lines modified | ||
| 281 | ·····------------------------------------------------------------------------ | 323 | ·····------------------------------------------------------------------------ |
| 282 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation | 324 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation |
| 283 | ·····------------------------------------------------------------------------ | 325 | ·····------------------------------------------------------------------------ |
| 284 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·6},·{0,·4,·5,·6},·{3,·5,·6,·7}}, | 326 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·6},·{0,·4,·5,·6},·{3,·5,·6,·7}}, |
| 285 | ·····------------------------------------------------------------------------ | 327 | ·····------------------------------------------------------------------------ |
| 286 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·7},·{1,·4,·5,·7}, | 328 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·7},·{1,·4,·5,·7}, |
| 287 | ·····------------------------------------------------------------------------ | 329 | ·····------------------------------------------------------------------------ |
| 288 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7}, | ||
| 289 | ·····------------------------------------------------------------------------ | ||
| 290 | ·····{0,·4,·5,·6},·{0,·5,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7}, | ||
| 291 | ····· | 330 | ·····{2,·4,·6,·7}}} |
| 331 | o4·:·List</code></pre> | ||
| 332 | </td>··········</tr> | ||
| 333 | ··········<tr> | ||
| 334 | <td>··············<pre><code·class="language-macaulay2">i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 292 | · | 335 | o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}, |
| 293 | ·····------------------------------------------------------------------------ | ||
| 294 | ·····triangulation·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7},·{1,·2,·6,·7}, | ||
| 295 | ·····------------------------------------------------------------------------ | 336 | ·····------------------------------------------------------------------------ |
| 296 | ·····{1,· | 337 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·6},·{0,·3,·6,·7}, |
| 297 | ·····------------------------------------------------------------------------ | 338 | ·····------------------------------------------------------------------------ |
| 298 | ·····{ | 339 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7}, |
| 299 | ·····------------------------------------------------------------------------ | 340 | ·····------------------------------------------------------------------------ |
| 300 | ·····{ | 341 | ·····{1,·2,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·4}, |
| 301 | ·····------------------------------------------------------------------------ | 342 | ·····------------------------------------------------------------------------ |
| 302 | ·····{ | 343 | ·····{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·6},·{3,·4,·6,·7}},·{{0,·1,·2,·4}, |
| 303 | ·····------------------------------------------------------------------------ | 344 | ·····------------------------------------------------------------------------ |
| 304 | ·····{ | 345 | ·····{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, |
| 305 | ·····------------------------------------------------------------------------ | 346 | ·····------------------------------------------------------------------------ |
| 306 | ·····{ | 347 | ·····{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6}, |
| 307 | ·····------------------------------------------------------------------------ | 348 | ·····------------------------------------------------------------------------ |
| 308 | ····· | 349 | ·····{3,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·6},·{1,·2,·4,·6},·{1,·3,·6,·7}, |
| 309 | ·····------------------------------------------------------------------------ | 350 | ·····------------------------------------------------------------------------ |
| 310 | ·····{1,·4,·5,·6},·{1,·5,·6,·7}},· | 351 | ·····{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6}, |
| 311 | ·····------------------------------------------------------------------------ | 352 | ·····------------------------------------------------------------------------ |
| 312 | ·····{ | 353 | ·····{1,·2,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·5}, |
| 313 | ·····------------------------------------------------------------------------ | 354 | ·····------------------------------------------------------------------------ |
| 314 | ·····{ | 355 | ·····{0,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·{{0,·1,·3,·5}, |
| 315 | ·····------------------------------------------------------------------------ | 356 | ·····------------------------------------------------------------------------ |
| 316 | ·····{ | 357 | ·····{0,·2,·3,·6},·{0,·3,·4,·5},·{0,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, |
| 317 | ·····------------------------------------------------------------------------ | 358 | ·····------------------------------------------------------------------------ |
| 318 | ·····{0,· | 359 | ·····{{0,·1,·3,·6},·{0,·1,·5,·6},·{0,·2,·3,·6},·{0,·4,·5,·6},·{1,·3,·5,·6}, |
| 319 | ·····------------------------------------------------------------------------ | 360 | ·····------------------------------------------------------------------------ |
| 320 | ·····{ | 361 | ·····{3,·5,·6,·7}},·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, |
| 321 | ·····------------------------------------------------------------------------ | 362 | ·····------------------------------------------------------------------------ |
| 322 | ····· | 363 | ·····{2,·3,·5,·7},·{2,·5,·6,·7}},·{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5}, |
| 323 | ·····------------------------------------------------------------------------ | 364 | ·····------------------------------------------------------------------------ |
| 324 | ·····{2,· | 365 | ·····{2,·3,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·7}, |
| 325 | ·····------------------------------------------------------------------------ | 366 | ·····------------------------------------------------------------------------ |
| 326 | ·····{1,·2,·4,·5},·{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},· | 367 | ·····{1,·2,·4,·5},·{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·2,·6}, |
| 327 | ·····------------------------------------------------------------------------ | 368 | ·····------------------------------------------------------------------------ |
| 328 | ·····{ | 369 | ·····{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·5,·6,·7}}, |
| 329 | ·····------------------------------------------------------------------------ | 370 | ·····------------------------------------------------------------------------ |
| 330 | ·····{1,·5,·6,·7}}} | ||
| 331 | o4·:·List</code></pre> | ||
| 332 | </td>··········</tr> | ||
| 333 | ··········<tr> | ||
| 334 | <td>··············<pre><code·class="language-macaulay2">i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 335 | 371 | ·····{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}, | |
| 336 | ·····------------------------------------------------------------------------ | 372 | ·····------------------------------------------------------------------------ |
| 337 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 373 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 338 | ·····------------------------------------------------------------------------ | 374 | ·····------------------------------------------------------------------------ |
| 339 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7}, | 375 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7}, |
| 340 | ·····------------------------------------------------------------------------ | 376 | ·····------------------------------------------------------------------------ |
| 341 | ·····{0,·4,·6,·7},·{1,·2,·3,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7}, | 377 | ·····{0,·4,·6,·7},·{1,·2,·3,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7}, |
| Max diff block lines reached; 35610/46303 bytes (76.91%) of diff not shown. | |||
| Offset 58, 15 lines modified | Offset 58, 57 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,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,· | 62 | o4·=·{triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·6}, |
| 63 | ·····------------------------------------------------------------------------ | ||
| 64 | ·····{0,·5,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | ||
| 65 | ·····------------------------------------------------------------------------ | ||
| 66 | ·····{0,·2,·3,·6},·{0,·3,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation | ||
| 67 | ·····------------------------------------------------------------------------ | ||
| 68 | ·····{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7},·{1,·2,·6,·7},·{1,·4,·5,·7}, | ||
| 69 | ·····------------------------------------------------------------------------ | ||
| 70 | ·····{1,·4,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·4},·{1,·3,·4,·7}, | ||
| 71 | ·····------------------------------------------------------------------------ | ||
| 72 | ·····{1,·4,·5,·7},·{2,·3,·4,·6},·{3,·4,·6,·7}},·triangulation·{{0,·1,·2,·4}, | ||
| 73 | ·····------------------------------------------------------------------------ | ||
| 74 | ·····{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, | ||
| 75 | ·····------------------------------------------------------------------------ | ||
| 76 | ·····triangulation·{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6}, | ||
| 77 | ·····------------------------------------------------------------------------ | ||
| 78 | ·····{3,·4,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·6}, | ||
| 79 | ·····------------------------------------------------------------------------ | ||
| 80 | ·····{1,·2,·4,·6},·{1,·3,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·triangulation | ||
| 81 | ·····------------------------------------------------------------------------ | ||
| 82 | ·····{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6},·{1,·2,·6,·7},·{1,·4,·5,·6}, | ||
| 83 | ·····------------------------------------------------------------------------ | ||
| 84 | ·····{1,·5,·6,·7}},·triangulation·{{0,·1,·3,·5},·{0,·2,·3,·5},·{0,·2,·4,·5}, | ||
| 85 | ·····------------------------------------------------------------------------ | ||
| 86 | ·····{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·triangulation·{{0,·1,·3,·5}, | ||
| 87 | ·····------------------------------------------------------------------------ | ||
| 88 | ·····{0,·2,·3,·6},·{0,·3,·4,·5},·{0,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, | ||
| 89 | ·····------------------------------------------------------------------------ | ||
| 90 | ·····triangulation·{{0,·1,·3,·6},·{0,·1,·5,·6},·{0,·2,·3,·6},·{0,·4,·5,·6}, | ||
| 91 | ·····------------------------------------------------------------------------ | ||
| 92 | ·····{1,·3,·5,·6},·{3,·5,·6,·7}},·triangulation·{{0,·1,·2,·5},·{0,·2,·5,·6}, | ||
| 93 | ·····------------------------------------------------------------------------ | ||
| 94 | ·····{0,·4,·5,·6},·{1,·2,·3,·5},·{2,·3,·5,·7},·{2,·5,·6,·7}},·triangulation | ||
| 95 | ·····------------------------------------------------------------------------ | ||
| 96 | ·····{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5},·{2,·3,·5,·7},·{2,·4,·5,·7}, | ||
| 97 | ·····------------------------------------------------------------------------ | ||
| 98 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·5}, | ||
| 99 | ·····------------------------------------------------------------------------ | ||
| 100 | ·····{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·6}, | ||
| 101 | ·····------------------------------------------------------------------------ | ||
| 102 | ·····{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·5,·6,·7}}, | ||
| 103 | ·····------------------------------------------------------------------------ | ||
| 104 | ·····triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·7}, | ||
| 63 | ·····------------------------------------------------------------------------ | 105 | ·····------------------------------------------------------------------------ |
| 64 | ·····{0,·4,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, | 106 | ·····{0,·4,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7},·{0,·1,·5,·7}, |
| 65 | ·····------------------------------------------------------------------------ | 107 | ·····------------------------------------------------------------------------ |
| 66 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation | 108 | ·····{0,·2,·3,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}},·triangulation |
| 67 | ·····------------------------------------------------------------------------ | 109 | ·····------------------------------------------------------------------------ |
| 68 | ·····{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·2,·3,·7}, | 110 | ·····{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7},·{0,·4,·6,·7},·{1,·2,·3,·7}, |
| 69 | ·····------------------------------------------------------------------------ | 111 | ·····------------------------------------------------------------------------ |
| Offset 222, 62 lines modified | Offset 264, 56 lines modified | ||
| 222 | ·····------------------------------------------------------------------------ | 264 | ·····------------------------------------------------------------------------ |
| 223 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation | 265 | ·····{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·triangulation |
| 224 | ·····------------------------------------------------------------------------ | 266 | ·····------------------------------------------------------------------------ |
| 225 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·6},·{0,·4,·5,·6},·{3,·5,·6,·7}}, | 267 | ·····{{0,·1,·3,·5},·{0,·2,·3,·6},·{0,·3,·5,·6},·{0,·4,·5,·6},·{3,·5,·6,·7}}, |
| 226 | ·····------------------------------------------------------------------------ | 268 | ·····------------------------------------------------------------------------ |
| 227 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·7},·{1,·4,·5,·7}, | 269 | ·····triangulation·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·7},·{1,·4,·5,·7}, |
| 228 | ·····------------------------------------------------------------------------ | 270 | ·····------------------------------------------------------------------------ |
| 229 | ·····{2,·4,·6,·7}},·triangulation·{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7}, | ||
| 230 | ·····------------------------------------------------------------------------ | ||
| 231 | ·····{0,·4,·5,·6},·{0,·5,·6,·7},·{1,·2,·3,·7}},·triangulation·{{0,·1,·3,·7}, | ||
| 232 | ····· | 271 | ·····{2,·4,·6,·7}}} |
| 272 | o4·:·List | ||
| 273 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 233 | · | 274 | o5·=·{{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·6},·{0,·5,·6,·7}, |
| 234 | ·····------------------------------------------------------------------------ | 275 | ·····------------------------------------------------------------------------ |
| 235 | ····· | 276 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·6},·{0,·3,·6,·7}, |
| 236 | ·····------------------------------------------------------------------------ | 277 | ·····------------------------------------------------------------------------ |
| 237 | ·····{ | 278 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·7}, |
| 238 | ·····------------------------------------------------------------------------ | 279 | ·····------------------------------------------------------------------------ |
| 239 | ·····{1,· | 280 | ·····{1,·2,·6,·7},·{1,·4,·5,·7},·{1,·4,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·4}, |
| 240 | ·····------------------------------------------------------------------------ | 281 | ·····------------------------------------------------------------------------ |
| 241 | ·····{ | 282 | ·····{1,·3,·4,·7},·{1,·4,·5,·7},·{2,·3,·4,·6},·{3,·4,·6,·7}},·{{0,·1,·2,·4}, |
| 242 | ·····------------------------------------------------------------------------ | 283 | ·····------------------------------------------------------------------------ |
| 243 | ·····{ | 284 | ·····{1,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, |
| 244 | ·····------------------------------------------------------------------------ | 285 | ·····------------------------------------------------------------------------ |
| 245 | ·····{ | 286 | ·····{{0,·1,·3,·4},·{0,·2,·3,·4},·{1,·3,·4,·5},·{2,·3,·4,·6},·{3,·4,·5,·6}, |
| 246 | ·····------------------------------------------------------------------------ | 287 | ·····------------------------------------------------------------------------ |
| 247 | ·····{ | 288 | ·····{3,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·6},·{1,·2,·4,·6},·{1,·3,·6,·7}, |
| 248 | ·····------------------------------------------------------------------------ | 289 | ·····------------------------------------------------------------------------ |
| 249 | ····· | 290 | ·····{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·7},·{1,·2,·4,·6}, |
| 250 | ·····------------------------------------------------------------------------ | 291 | ·····------------------------------------------------------------------------ |
| 251 | ·····{1,· | 292 | ·····{1,·2,·6,·7},·{1,·4,·5,·6},·{1,·5,·6,·7}},·{{0,·1,·3,·5},·{0,·2,·3,·5}, |
| 252 | ·····------------------------------------------------------------------------ | 293 | ·····------------------------------------------------------------------------ |
| 253 | ·····{0,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},· | 294 | ·····{0,·2,·4,·5},·{2,·3,·5,·7},·{2,·4,·5,·6},·{2,·5,·6,·7}},·{{0,·1,·3,·5}, |
| 254 | ·····------------------------------------------------------------------------ | 295 | ·····------------------------------------------------------------------------ |
| 255 | ·····{ | 296 | ·····{0,·2,·3,·6},·{0,·3,·4,·5},·{0,·3,·4,·6},·{3,·4,·5,·7},·{3,·4,·6,·7}}, |
| 256 | ·····------------------------------------------------------------------------ | 297 | ·····------------------------------------------------------------------------ |
| 257 | ·····{ | 298 | ·····{{0,·1,·3,·6},·{0,·1,·5,·6},·{0,·2,·3,·6},·{0,·4,·5,·6},·{1,·3,·5,·6}, |
| 258 | ·····------------------------------------------------------------------------ | 299 | ·····------------------------------------------------------------------------ |
| 259 | ·····{ | 300 | ·····{3,·5,·6,·7}},·{{0,·1,·2,·5},·{0,·2,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·5}, |
| 260 | ·····------------------------------------------------------------------------ | 301 | ·····------------------------------------------------------------------------ |
| 261 | ·····{ | 302 | ·····{2,·3,·5,·7},·{2,·5,·6,·7}},·{{0,·1,·2,·5},·{0,·2,·4,·5},·{1,·2,·3,·5}, |
| 262 | ·····------------------------------------------------------------------------ | 303 | ·····------------------------------------------------------------------------ |
| 263 | ····· | 304 | ·····{2,·3,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·2,·4},·{1,·2,·3,·7}, |
| 264 | ·····------------------------------------------------------------------------ | 305 | ·····------------------------------------------------------------------------ |
| 265 | ·····{ | 306 | ·····{1,·2,·4,·5},·{1,·2,·5,·7},·{2,·4,·5,·7},·{2,·4,·6,·7}},·{{0,·1,·2,·6}, |
| 266 | ·····------------------------------------------------------------------------ | 307 | ·····------------------------------------------------------------------------ |
| 267 | ·····{ | 308 | ·····{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7},·{1,·5,·6,·7}}, |
| 268 | ·····------------------------------------------------------------------------ | 309 | ·····------------------------------------------------------------------------ |
| 269 | ·····{{0,·1,·2,·6},·{0,·1,·5,·6},·{0,·4,·5,·6},·{1,·2,·3,·6},·{1,·3,·6,·7}, | ||
| 270 | ·····------------------------------------------------------------------------ | ||
| 271 | ·····{1,·5,·6,·7}}} | ||
| 272 | o4·:·List | ||
| 273 | i5·:·Ts2·=·generateTriangulations(A,·T)·--·list·of·list·of·subsets | ||
| 274 | 310 | ·····{{0,·1,·2,·7},·{0,·1,·5,·7},·{0,·2,·6,·7},·{0,·4,·5,·7},·{0,·4,·6,·7}, | |
| 275 | ·····------------------------------------------------------------------------ | 311 | ·····------------------------------------------------------------------------ |
| 276 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, | 312 | ·····{1,·2,·3,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7},·{0,·2,·3,·7},·{0,·2,·6,·7}, |
| 277 | ·····------------------------------------------------------------------------ | 313 | ·····------------------------------------------------------------------------ |
| 278 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7}, | 314 | ·····{0,·4,·5,·6},·{0,·5,·6,·7}},·{{0,·1,·2,·7},·{0,·1,·4,·7},·{0,·2,·6,·7}, |
| 279 | ·····------------------------------------------------------------------------ | 315 | ·····------------------------------------------------------------------------ |
| 280 | ·····{0,·4,·6,·7},·{1,·2,·3,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7}, | 316 | ·····{0,·4,·6,·7},·{1,·2,·3,·7},·{1,·4,·5,·7}},·{{0,·1,·3,·7},·{0,·1,·5,·7}, |
| 281 | ·····------------------------------------------------------------------------ | 317 | ·····------------------------------------------------------------------------ |
| Offset 409, 56 lines modified | Offset 445, 62 lines modified | ||
| 409 | ·····------------------------------------------------------------------------ | 445 | ·····------------------------------------------------------------------------ |
| 410 | ·····{1,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7}, | 446 | ·····{1,·5,·6,·7}},·{{0,·1,·2,·6},·{0,·1,·4,·6},·{1,·2,·3,·6},·{1,·3,·6,·7}, |
| Max diff block lines reached; 34349/44980 bytes (76.37%) of diff not shown. | |||
| Offset 159, 15 lines modified | Offset 159, 15 lines modified | ||
| 159 | ·····|·1··0··-1·0··0··0·0··0·0·0·| | 159 | ·····|·1··0··-1·0··0··0·0··0·0·0·| |
| 160 | ··············4·······10 | 160 | ··············4·······10 |
| 161 | o2·:·Matrix·ZZ··<--·ZZ</code></pre> | 161 | o2·:·Matrix·ZZ··<--·ZZ</code></pre> |
| 162 | </td>··········</tr> | 162 | </td>··········</tr> |
| 163 | ··········<tr> | 163 | ··········<tr> |
| 164 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); | 164 | <td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·Ts·=·allTriangulations(A,·Fine·=>·true); |
| 165 | ·--·0.1 | 165 | ·--·0.166342·seconds·elapsed</code></pre> |
| 166 | </td>··········</tr> | 166 | </td>··········</tr> |
| 167 | ··········<tr> | 167 | ··········<tr> |
| 168 | <td>··············<pre><code·class="language-macaulay2">i4·:·select(Ts,·T·->·isStar·T) | 168 | <td>··············<pre><code·class="language-macaulay2">i4·:·select(Ts,·T·->·isStar·T) |
| 169 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, | 169 | o4·=·{triangulation·{{0,·1,·2,·3,·9},·{0,·1,·2,·6,·9},·{0,·1,·3,·7,·9},·{0, |
| 170 | ·····------------------------------------------------------------------------ | 170 | ·····------------------------------------------------------------------------ |
| 171 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, | 171 | ·····1,·6,·7,·9},·{0,·2,·3,·6,·9},·{0,·3,·4,·6,·9},·{0,·3,·4,·8,·9},·{0,·3, |
| Offset 197, 15 lines modified | Offset 197, 15 lines modified | ||
| 197 | 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·{{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}} |
| 198 | o7·:·Triangulation</code></pre> | 198 | o7·:·Triangulation</code></pre> |
| 199 | </td>··········</tr> | 199 | </td>··········</tr> |
| 200 | ··········<tr> | 200 | ··········<tr> |
| 201 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·Ts2·=·generateTriangulations·T; | 201 | <td>··············<pre><code·class="language-macaulay2">i8·:·elapsedTime·Ts2·=·generateTriangulations·T; |
| 202 | ·--·1.26 | 202 | ·--·1.12667·seconds·elapsed</code></pre> |
| 203 | </td>··········</tr> | 203 | </td>··········</tr> |
| 204 | ··········<tr> | 204 | ··········<tr> |
| 205 | <td>··············<pre><code·class="language-macaulay2">i9·:·#Ts2·==·#Ts | 205 | <td>··············<pre><code·class="language-macaulay2">i9·:·#Ts2·==·#Ts |
| 206 | o9·=·true</code></pre> | 206 | o9·=·true</code></pre> |
| 207 | </td>··········</tr> | 207 | </td>··········</tr> |
| 208 | ········</table> | 208 | ········</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 | ·--·0.1 | 60 | ·--·0.166342·seconds·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 | ·--·1.26 | 92 | ·--·1.12667·seconds·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 |
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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=10 | 7 | #:len=10 |
| 8 | Y29tbXV0YXRvcg== | 8 | Y29tbXV0YXRvcg== |
| 9 | #:len=3282 | 9 | #:len=3282 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGNvbW11dGF0b3Igb2YgYSBjb2xs | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIGNvbW11dGF0b3Igb2YgYSBjb2xs |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | dGV4KFNWRyk= | 8 | dGV4KFNWRyk= |
| 9 | #:len=181 | 9 | #:len=181 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgwNiwgInVuZG9jdW1lbnRlZCIgPT4g | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHsibGluZW51bSIgPT4gMTgwNiwgInVuZG9jdW1lbnRlZCIgPT4g |
| 11 | dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodGV4LFNW | 11 | dHJ1ZSwgc3ltYm9sIERvY3VtZW50VGFnID0+IG5ldyBEb2N1bWVudFRhZyBmcm9tIHsodGV4LFNW |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 | bGlmdERlZm9ybWF0aW9uKC4uLixWZXJib3NlPT4uLi4p | 8 | bGlmdERlZm9ybWF0aW9uKC4uLixWZXJib3NlPT4uLi4p |
| 9 | #:len=588 | 9 | #:len=588 |
| 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29udHJvbCB0aGUgdmVyYm9zaXR5IG9m | 10 | bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAiY29udHJvbCB0aGUgdmVyYm9zaXR5IG9m |
| 11 | IG91dHB1dCIsIERlc2NyaXB0aW9uID0+IDE6KFBBUkF7VFR7IlZlcmJvc2UifSwiIGlzIHRoZSBu | 11 | IG91dHB1dCIsIERlc2NyaXB0aW9uID0+IDE6KFBBUkF7VFR7IlZlcmJvc2UifSwiIGlzIHRoZSBu |
| 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·0.838962s·(cpu);·0.640153s·(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·0.632042s·(cpu);·0.462123s·(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 60, 15 lines modified | Offset 60, 15 lines modified | ||
| 60 | o2·:·Matrix·S··<--·S</code></pre> | 60 | o2·:·Matrix·S··<--·S</code></pre> |
| 61 | </td>··········</tr> | 61 | </td>··········</tr> |
| 62 | ········</table> | 62 | ········</table> |
| 63 | ········<p>With·the·default·setting·<span·class="tt">SmartLift=>true</span>·we·get·very·nice·equations·for·the·base·space:</p> | 63 | ········<p>With·the·default·setting·<span·class="tt">SmartLift=>true</span>·we·get·very·nice·equations·for·the·base·space:</p> |
| 64 | ········<table·class="examples"> | 64 | ········<table·class="examples"> |
| 65 | ··········<tr> | 65 | ··········<tr> |
| 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(F,R,G,C)=localHilbertScheme(F0); | 66 | <td>··············<pre><code·class="language-macaulay2">i3·:·time·(F,R,G,C)=localHilbertScheme(F0); |
| 67 | ·--·used·0. | 67 | ·--·used·0.838962s·(cpu);·0.640153s·(thread);·0s·(gc)</code></pre> |
| 68 | </td>··········</tr> | 68 | </td>··········</tr> |
| 69 | ··········<tr> | 69 | ··········<tr> |
| 70 | <td>··············<pre><code·class="language-macaulay2">i4·:·T=ring·first·G;</code></pre> | 70 | <td>··············<pre><code·class="language-macaulay2">i4·:·T=ring·first·G;</code></pre> |
| 71 | </td>··········</tr> | 71 | </td>··········</tr> |
| 72 | ··········<tr> | 72 | ··········<tr> |
| 73 | <td>··············<pre><code·class="language-macaulay2">i5·:·sum·G | 73 | <td>··············<pre><code·class="language-macaulay2">i5·:·sum·G |
| Offset 81, 15 lines modified | Offset 81, 15 lines modified | ||
| 81 | o5·:·Matrix·T··<--·T</code></pre> | 81 | o5·:·Matrix·T··<--·T</code></pre> |
| 82 | </td>··········</tr> | 82 | </td>··········</tr> |
| 83 | ········</table> | 83 | ········</table> |
| 84 | ········<p>With·the·setting·<span·class="tt">SmartLift=>false</span>·the·calculation·is·faster,·but·the·equations·are·no·longer·homogeneous:</p> | 84 | ········<p>With·the·setting·<span·class="tt">SmartLift=>false</span>·the·calculation·is·faster,·but·the·equations·are·no·longer·homogeneous:</p> |
| 85 | ········<table·class="examples"> | 85 | ········<table·class="examples"> |
| 86 | ··········<tr> | 86 | ··········<tr> |
| 87 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); | 87 | <td>··············<pre><code·class="language-macaulay2">i6·:·time·(F,R,G,C)=localHilbertScheme(F0,SmartLift=>false); |
| 88 | ·--·used·0. | 88 | ·--·used·0.632042s·(cpu);·0.462123s·(thread);·0s·(gc)</code></pre> |
| 89 | </td>··········</tr> | 89 | </td>··········</tr> |
| 90 | ··········<tr> | 90 | ··········<tr> |
| 91 | <td>··············<pre><code·class="language-macaulay2">i7·:·sum·G | 91 | <td>··············<pre><code·class="language-macaulay2">i7·:·sum·G |
| 92 | o7·=·|·t_1t_16····························································· | 92 | o7·=·|·t_1t_16····························································· |
| 93 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ | 93 | ·····|·2t_5t_10t_11t_16+t_7t_11^2t_16-2t_6t_10t_16+3t_10^2t_16-t_8t_11t_16+ |
| 94 | ·····|·-t_5t_10^2t_16-2t_7t_10t_11t_16-3t_2t_11^2t_16+t_8t_10t_16+2t_3t_11t | 94 | ·····|·-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·0.838962s·(cpu);·0.640153s·(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·0.632042s·(cpu);·0.462123s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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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| 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 |
| 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 |
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| 9 | #:len=1106 | 9 | #:len=1106 |
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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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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 |
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| 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 26, 30 lines modified | Offset 26, 30 lines modified | ||
| 26 | ···········································|·-2·| | 26 | ···········································|·-2·| |
| 27 | ···········································|··1·| | 27 | ···········································|··1·| |
| 28 | o4·:·WeylGroupElement | 28 | o4·:·WeylGroupElement |
| 29 | i5·:·myInterval=intervalBruhat(w1·%·P,w2·%·P) | 29 | i5·:·myInterval=intervalBruhat(w1·%·P,w2·%·P) |
| 30 | o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|},·{1,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{1,·|··2·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}} | ||
| 31 | 30 | o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{1,·|··1·|},·{2,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{2,·|··2·|}}}},·{{We[·...·truncated·by·diffoscope;·len:·244,·SHA:·6f5c82c827615232991ec204e8403822b98a0f8c084cb26b7c14917b27ddab55·...·] | |
| 31 | ··························································|·-3·|········|·0·|·······|··1·|··············································|··3·|········|··1·|·······|··1·|············································|·-1·|········|··2·|·······|·-1·|··············································|·-2·|········|·-1·|············································|··1·|········|··1·|············································|··1·|········|··1·|··············································|·-1·| | ||
| 32 | ··························································|··1·|········|·1·|·······|··1·|··············································|·-2·|········|·-1·|·······|··1·|············································|··3·|········|· | 32 | ··························································|··1·|········|·1·|·······|··1·|··············································|·-2·|········|·-1·|·······|··1·|············································|··3·|········|·-1·|·······|··0·|··············································|··3·|········|··0·|············································|·-2·|········|··1·|············································|··2·|········|·-1·|··············································|··2·| |
| 33 | o5·:·HasseDiagram | 33 | o5·:·HasseDiagram |
| 34 | i6·:·myInterval#1 | 34 | i6·:·myInterval#1 |
| 35 | o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{ | 35 | o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{1,·|··1·|},·{2,·|·-1 |
| 36 | ·············································|··3·|········|··1·|·······|··1 | 36 | ·············································|··3·|········|··1·|·······|··1 |
| 37 | ·············································|·-2·|········|·-1·|·······|··1 | 37 | ·············································|·-2·|········|·-1·|·······|··1 |
| 38 | ·····------------------------------------------------------------------------ | 38 | ·····------------------------------------------------------------------------ |
| 39 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{ | 39 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{2, |
| 40 | ·····|············································|·-1·|········|· | 40 | ·····|············································|·-1·|········|··2·|······ |
| 41 | ·····|············································|··3·|········|· | 41 | ·····|············································|··3·|········|·-1·|······ |
| 42 | ·····------------------------------------------------------------------------ | 42 | ·····------------------------------------------------------------------------ |
| 43 | ·····|· | 43 | ·····|··2·|}}}} |
| 44 | ·····|··2·| | ||
| 45 | ·····|·-1·| | 44 | ·····|·-1·| |
| 45 | ·····|··0·| | ||
| 46 | o6·:·List | 46 | o6·:·List |
| 47 | i7·:· | 47 | i7·:· |
| Offset 4, 16 lines modified | Offset 4, 16 lines modified | ||
| 4 | o1·=·RootSystem{...8...} | 4 | o1·=·RootSystem{...8...} |
| 5 | o1·:·RootSystem | 5 | o1·:·RootSystem |
| 6 | i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R) | 6 | i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R) |
| 7 | o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|},·{1,·|·1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}} | ||
| 8 | 7 | o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1·|},·{1,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|},·{1,·|·1·|}}}},·{{Wey[·...·truncated·by·diffoscope;·len:·178,·SHA:·1e6c76800ad074b8a47615e8559b42657496871815f336a1db2487088304032d·...·] | |
| 8 | ··························································|·-1·|········|·-1·|·······|··2·|··············································|··1·|········|·1·|·······|··2·|············································|·-2·|········|·-1·|·······|·1·|··············································|·-1·|········|··2·|············································|··2·|········|·-1·|··············································|·1·| | ||
| 9 | o2·:·HasseDiagram | 9 | o2·:·HasseDiagram |
| 10 | i3·:·ZZ[x] | 10 | i3·:·ZZ[x] |
| 11 | o3·=·ZZ[x] | 11 | o3·=·ZZ[x] |
| Offset 10, 15 lines modified | Offset 10, 15 lines modified | ||
| 10 | o2·=·set·{1,·2} | 10 | o2·=·set·{1,·2} |
| 11 | o2·:·Parabolic | 11 | o2·:·Parabolic |
| 12 | i3·:·positiveRoots(R,P) | 12 | i3·:·positiveRoots(R,P) |
| 13 | o3·=·set·{|·· | 13 | o3·=·set·{|··1·|,·|··2·|,·|·-1·|} |
| 14 | ··········|··1·|··|·-1·|··|··2·| | ||
| 14 | ··········|·-1·|··|·· | 15 | ··········|·-1·|··|··0·|··|·-1·| |
| 15 | ··········|··0·|··|·-1·|··|·-1·| | ||
| 16 | ··········|··0·|··|··0·|··|··0·| | 16 | ··········|··0·|··|··0·|··|··0·| |
| 17 | o3·:·Set | 17 | o3·:·Set |
| 18 | i4·:· | 18 | i4·:· |
| Offset 97, 35 lines modified | Offset 97, 35 lines modified | ||
| 97 | ···········································|··1·| | 97 | ···········································|··1·| |
| 98 | o3·:·WeylGroupElement</code></pre> | 98 | o3·:·WeylGroupElement</code></pre> |
| 99 | </td>··········</tr> | 99 | </td>··········</tr> |
| 100 | ··········<tr> | 100 | ··········<tr> |
| 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·myInterval=intervalBruhat(w1,w2) | 101 | <td>··············<pre><code·class="language-macaulay2">i4·:·myInterval=intervalBruhat(w1,w2) |
| 102 | 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·|},·{}}}} | ||
| 103 | ··························································|·-2·|········|·-1·|·······|··2·|··············································|·-3·|········|··1·|············································|·-1·|········|·-1·|··············································|·-1·| | ||
| 104 | 102 | 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·...·] | |
| 103 | ··························································|·-2·|········|··2·|·······|·-1·|··············································|·-1·|········|·-1·|············································|·-3·|········|··1·|··············································|·-1·| | ||
| 104 | ··························································|··1·|········|·-1·|·······|··2·|··············································|··2·|········|··2·|············································|··1·|········|··1·|··············································|··3·| | ||
| 105 | o4·:·HasseDiagram</code></pre> | 105 | o4·:·HasseDiagram</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ········</table> | 107 | ········</table> |
| 108 | ········<div> | 108 | ········<div> |
| 109 | ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p> | 109 | ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</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·:·myInterval#1 | 113 | <td>··············<pre><code·class="language-macaulay2">i5·:·myInterval#1 |
| 114 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|· | 114 | o5·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··0·|}}}, |
| 115 | ·············································|·- | 115 | ·············································|·-1·|········|·-1·|···· |
| 116 | ·············································|·· | 116 | ·············································|··2·|········|··2·|···· |
| 117 | ·····------------------------------------------------------------------------ | 117 | ·····------------------------------------------------------------------------ |
| 118 | ·····{WeylGroupElement{RootSystem{...8...},·|· | 118 | ·····{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·-1·|}}}} |
| 119 | ············································|·- | 119 | ············································|·-3·|········|··1·| |
| 120 | ············································|·· | 120 | ············································|··1·|········|··1·| |
| 121 | o5·:·List</code></pre> | 121 | o5·:·List</code></pre> |
| 122 | </td>··········</tr> | 122 | </td>··········</tr> |
| 123 | ········</table> | 123 | ········</table> |
| 124 | ······</div> | 124 | ······</div> |
| 125 | ······<div·class="waystouse"> | 125 | ······<div·class="waystouse"> |
| 126 | ········<h2>Ways·to·use·this·method:</h2> | 126 | ········<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 104, 39 lines modified | Offset 104, 39 lines modified | ||
| 104 | ···········································|··1·| | 104 | ···········································|··1·| |
| 105 | o4·:·WeylGroupElement</code></pre> | 105 | o4·:·WeylGroupElement</code></pre> |
| 106 | </td>··········</tr> | 106 | </td>··········</tr> |
| 107 | ··········<tr> | 107 | ··········<tr> |
| 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·myInterval=intervalBruhat(w1·%·P,w2·%·P) | 108 | <td>··············<pre><code·class="language-macaulay2">i5·:·myInterval=intervalBruhat(w1·%·P,w2·%·P) |
| 109 | o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|},·{1,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{1,·|··2·|},·{2,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}} | ||
| 110 | 109 | o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{1,·|··1·|},·{2,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{2,·|··2·|}}}},·{{We[·...·truncated·by·diffoscope;·len:·244,·SHA:·6f5c82c827615232991ec204e8403822b98a0f8c084cb26b7c14917b27ddab55·...·] | |
| 110 | ··························································|·-3·|········|·0·|·······|··1·|··············································|··3·|········|··1·|·······|··1·|············································|·-1·|········|··2·|·······|·-1·|··············································|·-2·|········|·-1·|············································|··1·|········|··1·|············································|··1·|········|··1·|··············································|·-1·| | ||
| 111 | ··························································|··1·|········|·1·|·······|··1·|··············································|·-2·|········|·-1·|·······|··1·|············································|··3·|········|· | 111 | ··························································|··1·|········|·1·|·······|··1·|··············································|·-2·|········|·-1·|·······|··1·|············································|··3·|········|·-1·|·······|··0·|··············································|··3·|········|··0·|············································|·-2·|········|··1·|············································|··2·|········|·-1·|··············································|··2·| |
| 112 | o5·:·HasseDiagram</code></pre> | 112 | o5·:·HasseDiagram</code></pre> |
| 113 | </td>··········</tr> | 113 | </td>··········</tr> |
| 114 | ········</table> | 114 | ········</table> |
| 115 | ········<div> | 115 | ········<div> |
| 116 | ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p> | 116 | ··········<p>Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length·together·with·their·links·to·the·next·row.</p> |
| 117 | ········</div> | 117 | ········</div> |
| 118 | ········<table·class="examples"> | 118 | ········<table·class="examples"> |
| 119 | ··········<tr> | 119 | ··········<tr> |
| 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·myInterval#1 | 120 | <td>··············<pre><code·class="language-macaulay2">i6·:·myInterval#1 |
| 121 | o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{ | 121 | o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{1,·|··1·|},·{2,·|·-1 |
| 122 | ·············································|··3·|········|··1·|·······|··1 | 122 | ·············································|··3·|········|··1·|·······|··1 |
| 123 | ·············································|·-2·|········|·-1·|·······|··1 | 123 | ·············································|·-2·|········|·-1·|·······|··1 |
| 124 | ·····------------------------------------------------------------------------ | 124 | ·····------------------------------------------------------------------------ |
| 125 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{ | 125 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{2, |
| 126 | ·····|············································|·-1·|········|· | 126 | ·····|············································|·-1·|········|··2·|······ |
| 127 | ·····|············································|··3·|········|· | 127 | ·····|············································|··3·|········|·-1·|······ |
| 128 | ·····------------------------------------------------------------------------ | 128 | ·····------------------------------------------------------------------------ |
| 129 | ·····|· | 129 | ·····|··2·|}}}} |
| 130 | ·····|··2·| | ||
| 131 | ·····|·-1·| | 130 | ·····|·-1·| |
| 131 | ·····|··0·| | ||
| 132 | o6·:·List</code></pre> | 132 | o6·:·List</code></pre> |
| 133 | </td>··········</tr> | 133 | </td>··········</tr> |
| 134 | ········</table> | 134 | ········</table> |
| 135 | ······</div> | 135 | ······</div> |
| 136 | ······<div·class="waystouse"> | 136 | ······<div·class="waystouse"> |
| 137 | ········<h2>Ways·to·use·this·method:</h2> | 137 | ········<h2>Ways·to·use·this·method:</h2> |
| Offset 42, 47 lines modified | Offset 42, 47 lines modified | ||
| 42 | ···········································|·-2·| | 42 | ···········································|·-2·| |
| 43 | ···········································|··1·| | 43 | ···········································|··1·| |
| 44 | o4·:·WeylGroupElement | 44 | o4·:·WeylGroupElement |
| 45 | i5·:·myInterval=intervalBruhat(w1·%·P,w2·%·P) | 45 | i5·:·myInterval=intervalBruhat(w1·%·P,w2·%·P) |
| 46 | o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|}, | 46 | o5·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|·1·|}, |
| 47 | {1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{ | 47 | {1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{1,·|··1·|}, |
| 48 | { | 48 | {2,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|}, |
| 49 | {2,·|· | 49 | {2,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2 |
| 50 | 50 | |}}},·{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}}, | |
| 51 | {WeylGroupElement{RootSystem{...8...},·|· | 51 | {WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|··1·|}}}},·{ |
| 52 | {WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}} | 52 | {WeylGroupElement{RootSystem{...8...},·|··2·|},·{}}}} |
| 53 | ··························································|·-3·|········|·0·| | 53 | ··························································|·-3·|········|·0·| |
| 54 | |··1·|··············································|··3·|········|··1·| | 54 | |··1·|··············································|··3·|········|··1·| |
| 55 | |··1·|············································|·-1·|········|· | 55 | |··1·|············································|·-1·|········|··2·|·······| |
| 56 | 56 | -1·|··············································|·-2·|········|·-1·| | |
| 57 | |··1·|········|··1·|············································|· | 57 | |··1·|········|··1·|············································|··1·|········| |
| 58 | 58 | 1·|··············································|·-1·| | |
| 59 | ··························································|··1·|········|·1·| | 59 | ··························································|··1·|········|·1·| |
| 60 | |··1·|··············································|·-2·|········|·-1·| | 60 | |··1·|··············································|·-2·|········|·-1·| |
| 61 | |··1·|············································|··3·|········|· | 61 | |··1·|············································|··3·|········|·-1·|·······| |
| 62 | 62 | 0·|··············································|··3·|········|··0·| | |
| 63 | |· | 63 | |·-2·|········|··1·|············································|··2·|········| |
| 64 | 64 | -1·|··············································|··2·| | |
| 65 | o5·:·HasseDiagram | 65 | o5·:·HasseDiagram |
| 66 | Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length | 66 | Each·row·of·the·Hasse·diagram·contains·the·elements·of·a·certain·length |
| 67 | together·with·their·links·to·the·next·row. | 67 | together·with·their·links·to·the·next·row. |
| 68 | i6·:·myInterval#1 | 68 | i6·:·myInterval#1 |
| 69 | o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{ | 69 | o6·=·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{1,·|··1·|},·{2,·|·-1 |
| 70 | ·············································|··3·|········|··1·|·······|··1 | 70 | ·············································|··3·|········|··1·|·······|··1 |
| 71 | ·············································|·-2·|········|·-1·|·······|··1 | 71 | ·············································|·-2·|········|·-1·|·······|··1 |
| 72 | ·····------------------------------------------------------------------------ | 72 | ·····------------------------------------------------------------------------ |
| 73 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{ | 73 | ·····|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{2, |
| 74 | ·····|············································|·-1·|········|· | 74 | ·····|············································|·-1·|········|··2·| |
| 75 | ·····|············································|··3·|········|· | 75 | ·····|············································|··3·|········|·-1·| |
| 76 | ·····------------------------------------------------------------------------ | 76 | ·····------------------------------------------------------------------------ |
| 77 | ·····|· | 77 | ·····|··2·|}}}} |
| 78 | ·····|··2·| | ||
| 79 | ·····|·-1·| | 78 | ·····|·-1·| |
| 79 | ·····|··0·| | ||
| 80 | o6·:·List | 80 | o6·:·List |
| 81 | *\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* | 81 | *\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* |
| 82 | ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8L_\x8e_\x8f_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8L_\x8e_\x8f_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8)·--·elements·between | 82 | ····*·_\x8i_\x8n_\x8t_\x8e_\x8r_\x8v_\x8a_\x8l_\x8B_\x8r_\x8u_\x8h_\x8a_\x8t_\x8(_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8L_\x8e_\x8f_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8,_\x8W_\x8e_\x8y_\x8l_\x8G_\x8r_\x8o_\x8u_\x8p_\x8L_\x8e_\x8f_\x8t_\x8C_\x8o_\x8s_\x8e_\x8t_\x8)·--·elements·between |
| 83 | ······two·given·ones·for·the·Bruhat·order·on·a·quotient·of·a·Weyl·group | 83 | ······two·given·ones·for·the·Bruhat·order·on·a·quotient·of·a·Weyl·group |
| Offset 79, 16 lines modified | Offset 79, 16 lines modified | ||
| 79 | o1·=·RootSystem{...8...} | 79 | o1·=·RootSystem{...8...} |
| 80 | o1·:·RootSystem</code></pre> | 80 | o1·:·RootSystem</code></pre> |
| 81 | </td>··········</tr> | 81 | </td>··········</tr> |
| 82 | ··········<tr> | 82 | ··········<tr> |
| 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R) | 83 | <td>··············<pre><code·class="language-macaulay2">i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R) |
| 84 | o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|·-1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|},·{1,·|·1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}} | ||
| 85 | 84 | o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1·|},·{1,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2·|},·{1,·|·1·|}}}},·{{Wey[·...·truncated·by·diffoscope;·len:·178,·SHA:·1e6c76800ad074b8a47615e8559b42657496871815f336a1db2487088304032d·...·] | |
| 85 | ··························································|·-1·|········|·-1·|·······|··2·|··············································|··1·|········|·1·|·······|··2·|············································|·-2·|········|·-1·|·······|·1·|··············································|·-1·|········|··2·|············································|··2·|········|·-1·|··············································|·1·| | ||
| 86 | o2·:·HasseDiagram</code></pre> | 86 | o2·:·HasseDiagram</code></pre> |
| 87 | </td>··········</tr> | 87 | </td>··········</tr> |
| 88 | ··········<tr> | 88 | ··········<tr> |
| 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·ZZ[x] | 89 | <td>··············<pre><code·class="language-macaulay2">i3·:·ZZ[x] |
| 90 | o3·=·ZZ[x] | 90 | o3·=·ZZ[x] |
| Offset 20, 25 lines modified | Offset 20, 25 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·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R) | 23 | i2·:·H=intervalBruhat(neutralWeylGroupElement·R,·longestWeylGroupElement·R) |
| 24 | o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|· | 24 | o2·=·HasseDiagram{{{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2 |
| 25 | 1·|},·{1,·|··2·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·| | ||
| 26 | 25 | |},·{1,·|·-1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|·-2·|},·{{0,·|·1 | |
| 26 | |},·{1,·|·-1·|}}},·{WeylGroupElement{RootSystem{...8...},·|··1·|},·{{0,·|··2 | ||
| 27 | |},·{1,·|· | 27 | |},·{1,·|·1·|}}}},·{{WeylGroupElement{RootSystem{...8...},·|··2·|},·{{0,·|·- |
| 28 | 1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}}},·{ | 28 | 1·|}}},·{WeylGroupElement{RootSystem{...8...},·|·-1·|},·{{0,·|··2·|}}}},·{ |
| 29 | {WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}} | 29 | {WeylGroupElement{RootSystem{...8...},·|·1·|},·{}}}} |
| 30 | ··························································|·-1·|········|· | 30 | ··························································|·-1·|········|·-1·| |
| 31 | |·-1·|··············································|·-2·|········|·-1·| | ||
| 32 | |· | 31 | |··2·|··············································|··1·|········|·1·|·······| |
| 33 | 32 | 2·|············································|·-2·|········|·-1·|·······|·1·| | |
| 33 | |·-1·|········|··2·|············································|··2·|········| | ||
| 34 | 34 | -1·|··············································|·1·| | |
| 35 | o2·:·HasseDiagram | 35 | o2·:·HasseDiagram |
| 36 | i3·:·ZZ[x] | 36 | i3·:·ZZ[x] |
| 37 | o3·=·ZZ[x] | 37 | o3·=·ZZ[x] |
| 38 | o3·:·PolynomialRing | 38 | o3·:·PolynomialRing |
| Offset 86, 17 lines modified | Offset 86, 17 lines modified | ||
| 86 | o2·=·set·{1,·2} | 86 | o2·=·set·{1,·2} |
| 87 | o2·:·Parabolic</code></pre> | 87 | o2·:·Parabolic</code></pre> |
| 88 | </td>··········</tr> | 88 | </td>··········</tr> |
| 89 | ··········<tr> | 89 | ··········<tr> |
| 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·positiveRoots(R,P) | 90 | <td>··············<pre><code·class="language-macaulay2">i3·:·positiveRoots(R,P) |
| 91 | o3·=·set·{|·· | 91 | o3·=·set·{|··1·|,·|··2·|,·|·-1·|} |
| 92 | ··········|··1·|··|·-1·|··|··2·| | ||
| 92 | ··········|·-1·|··|·· | 93 | ··········|·-1·|··|··0·|··|·-1·| |
| 93 | ··········|··0·|··|·-1·|··|·-1·| | ||
| 94 | ··········|··0·|··|··0·|··|··0·| | 94 | ··········|··0·|··|··0·|··|··0·| |
| 95 | o3·:·Set</code></pre> | 95 | o3·:·Set</code></pre> |
| 96 | </td>··········</tr> | 96 | </td>··········</tr> |
| 97 | ········</table> | 97 | ········</table> |
| 98 | ······</div> | 98 | ······</div> |
| 99 | ······<div·class="waystouse"> | 99 | ······<div·class="waystouse"> |
| Offset 24, 16 lines modified | Offset 24, 16 lines modified | ||
| 24 | i2·:·P=parabolic(R,set{1,2}) | 24 | i2·:·P=parabolic(R,set{1,2}) |
| 25 | o2·=·set·{1,·2} | 25 | o2·=·set·{1,·2} |
| 26 | o2·:·Parabolic | 26 | o2·:·Parabolic |
| 27 | i3·:·positiveRoots(R,P) | 27 | i3·:·positiveRoots(R,P) |
| 28 | o3·=·set·{|·· | 28 | o3·=·set·{|··1·|,·|··2·|,·|·-1·|} |
| 29 | ··········|··1·|··|·-1·|··|··2·| | ||
| 29 | ··········|·-1·|··|·· | 30 | ··········|·-1·|··|··0·|··|·-1·| |
| 30 | ··········|··0·|··|·-1·|··|·-1·| | ||
| 31 | ··········|··0·|··|··0·|··|··0·| | 31 | ··········|··0·|··|··0·|··|··0·| |
| 32 | o3·:·Set | 32 | o3·:·Set |
| 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 | ····*·_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8v_\x8e_\x8R_\x8o_\x8o_\x8t_\x8s_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8P_\x8a_\x8r_\x8a_\x8b_\x8o_\x8l_\x8i_\x8c_\x8)·--·the·set·of·all·positive·roots·in·a | 34 | ····*·_\x8p_\x8o_\x8s_\x8i_\x8t_\x8i_\x8v_\x8e_\x8R_\x8o_\x8o_\x8t_\x8s_\x8(_\x8R_\x8o_\x8o_\x8t_\x8S_\x8y_\x8s_\x8t_\x8e_\x8m_\x8,_\x8P_\x8a_\x8r_\x8a_\x8b_\x8o_\x8l_\x8i_\x8c_\x8)·--·the·set·of·all·positive·roots·in·a |
| 35 | ······parabolic·sugroups | 35 | ······parabolic·sugroups |
| Offset 1, 11 lines modified | Offset 1, 11 lines modified | ||
| 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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·1.3 | 95 | ·--·used·1.38248s·(cpu);·0.902197s·(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·3. | 103 | ·--·used·3.88016s·(cpu);·2.48191s·(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· | 111 | ·--·used·4.36645s·(cpu);·2.7709s·(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 223, 45 lines modified | Offset 223, 45 lines modified | ||
| 223 | ········</table> | 223 | ········</table> |
| 224 | ········<div> | 224 | ········<div> |
| 225 | ··········<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 | ··········<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> |
| 226 | ········</div> | 226 | ········</div> |
| 227 | ········<table·class="examples"> | 227 | ········<table·class="examples"> |
| 228 | ··········<tr> | 228 | ··········<tr> |
| 229 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") | 229 | <td>··············<pre><code·class="language-macaulay2">i23·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"singularOnly") |
| 230 | ·--·used·1.3 | 230 | ·--·used·1.38248s·(cpu);·0.902197s·(thread);·0s·(gc) |
| 231 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 231 | o23·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 232 | o23·:·List</code></pre> | 232 | o23·:·List</code></pre> |
| 233 | </td>··········</tr> | 233 | </td>··········</tr> |
| 234 | ··········<tr> | 234 | ··········<tr> |
| 235 | <td>··············<pre><code·class="language-macaulay2">i24·:·peek·last·ms | 235 | <td>··············<pre><code·class="language-macaulay2">i24·:·peek·last·ms |
| 236 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 236 | o24·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 237 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 237 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 238 | ·······················2·=>·{ideal·0}</code></pre> | 238 | ·······················2·=>·{ideal·0}</code></pre> |
| 239 | </td>··········</tr> | 239 | </td>··········</tr> |
| 240 | ··········<tr> | 240 | ··········<tr> |
| 241 | <td>··············<pre><code·class="language-macaulay2">i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") | 241 | <td>··············<pre><code·class="language-macaulay2">i25·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"most") |
| 242 | ·--·used·3. | 242 | ·--·used·3.88016s·(cpu);·2.48191s·(thread);·0s·(gc) |
| 243 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 243 | o25·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 244 | o25·:·List</code></pre> | 244 | o25·:·List</code></pre> |
| 245 | </td>··········</tr> | 245 | </td>··········</tr> |
| 246 | ··········<tr> | 246 | ··········<tr> |
| 247 | <td>··············<pre><code·class="language-macaulay2">i26·:·peek·last·ms | 247 | <td>··············<pre><code·class="language-macaulay2">i26·:·peek·last·ms |
| 248 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} | 248 | o26·=·MutableHashTable{0·=>·{ideal·(P,·M1)}····················} |
| 249 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} | 249 | ·······················1·=>·{ideal·P,·ideal·M1,·ideal(4M1·-·P)} |
| 250 | ·······················2·=>·{ideal·0}</code></pre> | 250 | ·······················2·=>·{ideal·0}</code></pre> |
| 251 | </td>··········</tr> | 251 | </td>··········</tr> |
| 252 | ··········<tr> | 252 | ··········<tr> |
| 253 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") | 253 | <td>··············<pre><code·class="language-macaulay2">i27·:·time·ms=mapStratify(F,Xh,ideal(0_S),StratsToFind=>"all") |
| 254 | ·--·used· | 254 | ·--·used·4.36645s·(cpu);·2.7709s·(thread);·0s·(gc) |
| 255 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} | 255 | o27·=·{MutableHashTable{...5...},·MutableHashTable{...3...}} |
| 256 | o27·:·List</code></pre> | 256 | o27·:·List</code></pre> |
| 257 | </td>··········</tr> | 257 | </td>··········</tr> |
| 258 | ··········<tr> | 258 | ··········<tr> |
| 259 | <td>··············<pre><code·class="language-macaulay2">i28·:·peek·last·ms | 259 | <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·1.3 | 156 | ·--·used·1.38248s·(cpu);·0.902197s·(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·3. | 164 | ·--·used·3.88016s·(cpu);·2.48191s·(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· | 172 | ·--·used·4.36645s·(cpu);·2.7709s·(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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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· | 1 | #·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Mon·Sep··9·14:38:13·2024 |
| 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, 16 lines modified | Offset 17, 16 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 | using·temporary·file·/tmp/M2- | 21 | using·temporary·file·/tmp/M2-2197251-0/172 |
| 22 | running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2- | 22 | running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-2197251-0/172 |
| 23 | 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 | 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. |
| 24 | Options: | 24 | Options: |
| 25 | -g: | 25 | -g: |
| 26 | ·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 | ·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. |
| 27 | --symmetry: | 27 | --symmetry: |
| 28 | ·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. | 28 | ·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 38, 16 lines modified | Offset 38, 16 lines modified | ||
| 38 | ·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 | ·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. |
| 39 | --parameters·value: | 39 | --parameters·value: |
| 40 | ·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 | ·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. |
| 41 | --interrupt·value: | 41 | --interrupt·value: |
| 42 | ·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 | ·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). |
| 43 | using·temporary·file·/tmp/M2- | 43 | using·temporary·file·/tmp/M2-2197251-0/174 |
| 44 | running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2- | 44 | running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-2197251-0/174 |
| 45 | 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 | 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,...]). |
| 46 | Options: | 46 | Options: |
| 47 | -w: | 47 | -w: |
| 48 | ·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 | ·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. |
| 49 | -r: | 49 | -r: |
| 50 | ·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. | 50 | ·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 57, 75 lines modified | Offset 57, 75 lines modified | ||
| 57 | -g: | 57 | -g: |
| 58 | ·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. | 58 | ·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. |
| 59 | --parameters·value: | 59 | --parameters·value: |
| 60 | ·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. | 60 | ·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. |
| 61 | using·temporary·file·/tmp/M2- | 61 | using·temporary·file·/tmp/M2-2197251-0/176 |
| 62 | running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2- | 62 | running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-2197251-0/176 |
| 63 | 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. | 63 | 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. |
| 64 | Options: | 64 | Options: |
| 65 | --remainder: | 65 | --remainder: |
| 66 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. | 66 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. |
| 67 | --multiplier: | 67 | --multiplier: |
| 68 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. | 68 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. |
| 69 | using·temporary·file·/tmp/M2- | 69 | using·temporary·file·/tmp/M2-2197251-0/178 |
| 70 | running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2- | 70 | running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-2197251-0/178 |
| 71 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. | 71 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. |
| 72 | Options: | 72 | Options: |
| 73 | -i1·value: | 73 | -i1·value: |
| 74 | ·Specify·the·name·of·the·first·input·file. | 74 | ·Specify·the·name·of·the·first·input·file. |
| 75 | -i2·value: | 75 | -i2·value: |
| 76 | ·Specify·the·name·of·the·second·input·file. | 76 | ·Specify·the·name·of·the·second·input·file. |
| 77 | --stable: | 77 | --stable: |
| 78 | ·Compute·the·stable·intersection. | 78 | ·Compute·the·stable·intersection. |
| 79 | using·temporary·file·/tmp/M2- | 79 | using·temporary·file·/tmp/M2-2197251-0/180 |
| 80 | running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2- | 80 | running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-2197251-0/180 |
| 81 | 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. | 81 | 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. |
| 82 | Options: | 82 | Options: |
| 83 | -i·value: | 83 | -i·value: |
| 84 | ·Specify·the·name·of·the·input·file. | 84 | ·Specify·the·name·of·the·input·file. |
| 85 | --symmetry: | 85 | --symmetry: |
| 86 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. | 86 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. |
| 87 | --star: | 87 | --star: |
| 88 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. | 88 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. |
| 89 | using·temporary·file·/tmp/M2- | 89 | using·temporary·file·/tmp/M2-2197251-0/182 |
| 90 | running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2- | 90 | running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-2197251-0/182 |
| 91 | This·program·takes·two·polyhedral·fans·and·computes·their·product. | 91 | This·program·takes·two·polyhedral·fans·and·computes·their·product. |
| 92 | Options: | 92 | Options: |
| 93 | -i1·value: | 93 | -i1·value: |
| 94 | ·Specify·the·name·of·the·first·input·file. | 94 | ·Specify·the·name·of·the·first·input·file. |
| 95 | -i2·value: | 95 | -i2·value: |
| 96 | ·Specify·the·name·of·the·second·input·file. | 96 | ·Specify·the·name·of·the·second·input·file. |
| 97 | using·temporary·file·/tmp/M2- | 97 | using·temporary·file·/tmp/M2-2197251-0/184 |
| 98 | running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2- | 98 | running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-2197251-0/184 |
| 99 | 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. | 99 | 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. |
| 100 | Options: | 100 | Options: |
| 101 | --restrict: | 101 | --restrict: |
| 102 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. | 102 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. |
| 103 | --pair: | 103 | --pair: |
| 104 | ·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. | 104 | ·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. |
| 105 | --asfan: | 105 | --asfan: |
| 106 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. | 106 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. |
| 107 | --vectorinput: | 107 | --vectorinput: |
| 108 | ·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. | 108 | ·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. |
| 109 | using·temporary·file·/tmp/M2- | 109 | using·temporary·file·/tmp/M2-2197251-0/186 |
| 110 | running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2- | 110 | running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-2197251-0/186 |
| 111 | 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. | 111 | 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. |
| 112 | Options: | 112 | Options: |
| 113 | using·temporary·file·/tmp/M2- | 113 | using·temporary·file·/tmp/M2-2197251-0/188 |
| 114 | running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2- | 114 | running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-2197251-0/188 |
| 115 | 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. | 115 | 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. |
| 116 | Example: | 116 | Example: |
| 117 | Input: | 117 | Input: |
| 118 | Q[x,y]{y-1} | 118 | Q[x,y]{y-1} |
| 119 | z | 119 | z |
| 120 | Output: | 120 | Output: |
| 121 | Q[x,y,z]{y-z} | 121 | Q[x,y,z]{y-z} |
| Offset 134, 31 lines modified | Offset 134, 31 lines modified | ||
| 134 | ·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. | 134 | ·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. |
| 135 | -w: | 135 | -w: |
| 136 | ·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. | 136 | ·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. |
| 137 | -H: | 137 | -H: |
| 138 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. | 138 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. |
| 139 | using·temporary·file·/tmp/M2- | 139 | using·temporary·file·/tmp/M2-2197251-0/190 |
| 140 | running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2- | 140 | running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2-2197251-0/190 |
| 141 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. | 141 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. |
| 142 | Options: | 142 | Options: |
| 143 | --ideal: | 143 | --ideal: |
| 144 | ·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. | 144 | ·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. |
| 145 | --pair: | 145 | --pair: |
| 146 | ·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. | 146 | ·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. |
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| Offset 92, 16 lines modified | Offset 92, 16 lines modified | ||
| 92 | ········<div> | 92 | ········<div> |
| 93 | ··········<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>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> |
| 94 | ··········<p></p> | 94 | ··········<p></p> |
| 95 | ········</div> | 95 | ········</div> |
| 96 | ········<table·class="examples"> | 96 | ········<table·class="examples"> |
| 97 | ··········<tr> | 97 | ··········<tr> |
| 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true); | 98 | <td>··············<pre><code·class="language-macaulay2">i5·:·loadPackage("gfanInterface",·Configuration·=>·{·"keepfiles"·=>·true,·"verbose"·=>·true},·Reload·=>·true); |
| 99 | using·temporary·file·/tmp/M2- | 99 | using·temporary·file·/tmp/M2-2197251-0/172 |
| 100 | running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2- | 100 | running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-2197251-0/172 |
| 101 | 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. | 101 | 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. |
| 102 | Options: | 102 | Options: |
| 103 | -g: | 103 | -g: |
| 104 | ·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. | 104 | ·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. |
| 105 | --symmetry: | 105 | --symmetry: |
| 106 | ·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. | 106 | ·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 113, 16 lines modified | Offset 113, 16 lines modified | ||
| 113 | ·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. | 113 | ·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. |
| 114 | --parameters·value: | 114 | --parameters·value: |
| 115 | ·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. | 115 | ·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. |
| 116 | --interrupt·value: | 116 | --interrupt·value: |
| 117 | ·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). | 117 | ·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). |
| 118 | using·temporary·file·/tmp/M2- | 118 | using·temporary·file·/tmp/M2-2197251-0/174 |
| 119 | running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2- | 119 | running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-2197251-0/174 |
| 120 | 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,...]). | 120 | 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,...]). |
| 121 | Options: | 121 | Options: |
| 122 | -w: | 122 | -w: |
| 123 | ·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. | 123 | ·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. |
| 124 | -r: | 124 | -r: |
| 125 | ·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. | 125 | ·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 132, 75 lines modified | Offset 132, 75 lines modified | ||
| 132 | -g: | 132 | -g: |
| 133 | ·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. | 133 | ·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. |
| 134 | --parameters·value: | 134 | --parameters·value: |
| 135 | ·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. | 135 | ·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. |
| 136 | using·temporary·file·/tmp/M2- | 136 | using·temporary·file·/tmp/M2-2197251-0/176 |
| 137 | running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2- | 137 | running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-2197251-0/176 |
| 138 | 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. | 138 | 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. |
| 139 | Options: | 139 | Options: |
| 140 | --remainder: | 140 | --remainder: |
| 141 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. | 141 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than·outputting·0·or·1. |
| 142 | --multiplier: | 142 | --multiplier: |
| 143 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. | 143 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided·before·doing·the·division. |
| 144 | using·temporary·file·/tmp/M2- | 144 | using·temporary·file·/tmp/M2-2197251-0/178 |
| 145 | running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2- | 145 | running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-2197251-0/178 |
| 146 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. | 146 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. |
| 147 | Options: | 147 | Options: |
| 148 | -i1·value: | 148 | -i1·value: |
| 149 | ·Specify·the·name·of·the·first·input·file. | 149 | ·Specify·the·name·of·the·first·input·file. |
| 150 | -i2·value: | 150 | -i2·value: |
| 151 | ·Specify·the·name·of·the·second·input·file. | 151 | ·Specify·the·name·of·the·second·input·file. |
| 152 | --stable: | 152 | --stable: |
| 153 | ·Compute·the·stable·intersection. | 153 | ·Compute·the·stable·intersection. |
| 154 | using·temporary·file·/tmp/M2- | 154 | using·temporary·file·/tmp/M2-2197251-0/180 |
| 155 | running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2- | 155 | running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-2197251-0/180 |
| 156 | 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. | 156 | 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. |
| 157 | Options: | 157 | Options: |
| 158 | -i·value: | 158 | -i·value: |
| 159 | ·Specify·the·name·of·the·input·file. | 159 | ·Specify·the·name·of·the·input·file. |
| 160 | --symmetry: | 160 | --symmetry: |
| 161 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. | 161 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must·be·given·on·the·standard·input. |
| 162 | --star: | 162 | --star: |
| 163 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. | 163 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan·containing·all·cones·of·the·original·fan·containing·the·vector. |
| 164 | using·temporary·file·/tmp/M2- | 164 | using·temporary·file·/tmp/M2-2197251-0/182 |
| 165 | running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2- | 165 | running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-2197251-0/182 |
| 166 | This·program·takes·two·polyhedral·fans·and·computes·their·product. | 166 | This·program·takes·two·polyhedral·fans·and·computes·their·product. |
| 167 | Options: | 167 | Options: |
| 168 | -i1·value: | 168 | -i1·value: |
| 169 | ·Specify·the·name·of·the·first·input·file. | 169 | ·Specify·the·name·of·the·first·input·file. |
| 170 | -i2·value: | 170 | -i2·value: |
| 171 | ·Specify·the·name·of·the·second·input·file. | 171 | ·Specify·the·name·of·the·second·input·file. |
| 172 | using·temporary·file·/tmp/M2- | 172 | using·temporary·file·/tmp/M2-2197251-0/184 |
| 173 | running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2- | 173 | running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-2197251-0/184 |
| 174 | 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. | 174 | 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. |
| 175 | Options: | 175 | Options: |
| 176 | --restrict: | 176 | --restrict: |
| 177 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. | 177 | ·Add·an·inequality·for·each·coordinate,·so·that·the·the·cone·is·restricted·to·the·non-negative·orthant. |
| 178 | --pair: | 178 | --pair: |
| 179 | ·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. | 179 | ·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. |
| 180 | --asfan: | 180 | --asfan: |
| 181 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. | 181 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way·the·extreme·rays·of·the·cone·are·also·computed. |
| 182 | --vectorinput: | 182 | --vectorinput: |
| 183 | ·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. | 183 | ·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. |
| 184 | using·temporary·file·/tmp/M2- | 184 | using·temporary·file·/tmp/M2-2197251-0/186 |
| 185 | running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2- | 185 | running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-2197251-0/186 |
| 186 | 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. | 186 | 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. |
| 187 | Options: | 187 | Options: |
| 188 | using·temporary·file·/tmp/M2- | 188 | using·temporary·file·/tmp/M2-2197251-0/188 |
| 189 | running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2- | 189 | running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-2197251-0/188 |
| 190 | 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. | 190 | 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. |
| 191 | Example: | 191 | Example: |
| 192 | Input: | 192 | Input: |
| 193 | Q[x,y]{y-1} | 193 | Q[x,y]{y-1} |
| 194 | z | 194 | z |
| 195 | Output: | 195 | Output: |
| 196 | Q[x,y,z]{y-z} | 196 | Q[x,y,z]{y-z} |
| Offset 209, 31 lines modified | Offset 209, 31 lines modified | ||
| 209 | ·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. | 209 | ·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. |
| 210 | -w: | 210 | -w: |
| 211 | ·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. | 211 | ·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. |
| 212 | -H: | 212 | -H: |
| 213 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. | 213 | ·Let·the·name·of·the·new·variable·be·H·rather·than·reading·in·a·name·from·the·input. |
| 214 | using·temporary·file·/tmp/M2- | 214 | using·temporary·file·/tmp/M2-2197251-0/190 |
| 215 | running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2- | 215 | running:·/usr/bin/gfan·_initialforms·--help·<·/tmp/M2-2197251-0/190 |
| 216 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. | 216 | This·program·converts·a·list·of·polynomials·to·a·list·of·their·initial·forms·with·respect·to·the·vector·given·after·the·list. |
| 217 | Options: | 217 | Options: |
| 218 | --ideal: | 218 | --ideal: |
| 219 | ·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. | 219 | ·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. |
| 220 | --pair: | 220 | --pair: |
| 221 | ·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. | 221 | ·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. |
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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 | using·temporary·file·/tmp/M2- | 46 | using·temporary·file·/tmp/M2-2197251-0/172 |
| 47 | running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2- | 47 | running:·/usr/bin/gfan·gfan·--help·<·/tmp/M2-2197251-0/172 |
| 48 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial | 48 | This·is·a·program·for·computing·all·reduced·Groebner·bases·of·a·polynomial |
| 49 | ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By | 49 | ideal.·It·takes·the·ring·and·a·generating·set·for·the·ideal·as·input.·By |
| 50 | default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the | 50 | default·the·enumeration·is·done·by·an·almost·memoryless·reverse·search.·If·the |
| 51 | ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done | 51 | ideal·is·symmetric·the·symmetry·option·is·useful·and·enumeration·will·be·done |
| 52 | up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting | 52 | up·to·symmetry·using·a·breadth·first·search.·The·program·needs·a·starting |
| 53 | Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it | 53 | Groebner·basis·to·do·its·computations.·If·the·-g·option·is·not·specified·it |
| 54 | will·compute·one·using·Buchberger's·algorithm. | 54 | will·compute·one·using·Buchberger's·algorithm. |
| Offset 79, 16 lines modified | Offset 79, 16 lines modified | ||
| 79 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the | 79 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the |
| 80 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 80 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 81 | --interrupt·value: | 81 | --interrupt·value: |
| 82 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been | 82 | ·Interrupt·the·enumeration·after·a·specified·number·of·facets·have·been |
| 83 | computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for | 83 | computed·(works·for·usual·symmetric·traversals,·but·may·not·work·in·general·for |
| 84 | non-symmetric·traversals·or·for·traversals·restricted·to·fans). | 84 | non-symmetric·traversals·or·for·traversals·restricted·to·fans). |
| 85 | using·temporary·file·/tmp/M2- | 85 | using·temporary·file·/tmp/M2-2197251-0/174 |
| 86 | running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2- | 86 | running:·/usr/bin/gfan·_buchberger·--help·<·/tmp/M2-2197251-0/174 |
| 87 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial | 87 | This·program·computes·a·reduced·lexicographic·Groebner·basis·of·the·polynomial |
| 88 | ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm. | 88 | ideal·given·as·input.·The·default·behavior·is·to·use·Buchberger's·algorithm. |
| 89 | The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q | 89 | The·ordering·of·the·variables·is·$a>b>c...$·(assuming·that·the·ring·is·Q |
| 90 | [a,b,c,...]). | 90 | [a,b,c,...]). |
| 91 | Options: | 91 | Options: |
| 92 | -w: | 92 | -w: |
| 93 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with | 93 | ·Compute·a·Groebner·basis·with·respect·to·a·degree·lexicographic·order·with |
| Offset 110, 41 lines modified | Offset 110, 41 lines modified | ||
| 110 | The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. | 110 | The·target·term·order·is·always·lexicographic.·The·-W·option·must·be·used. |
| 111 | --parameters·value: | 111 | --parameters·value: |
| 112 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters | 112 | ·With·this·option·you·can·specify·how·many·variables·to·treat·as·parameters |
| 113 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the | 113 | instead·of·variables.·This·makes·it·possible·to·do·computations·where·the |
| 114 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. | 114 | coefficient·field·is·the·field·of·rational·functions·in·the·parameters. |
| 115 | using·temporary·file·/tmp/M2- | 115 | using·temporary·file·/tmp/M2-2197251-0/176 |
| 116 | running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2- | 116 | running:·/usr/bin/gfan·_doesidealcontain·--help·<·/tmp/M2-2197251-0/176 |
| 117 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of | 117 | This·program·takes·a·marked·Groebner·basis·of·an·ideal·I·and·a·set·of |
| 118 | polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by | 118 | polynomials·on·its·input·and·tests·if·the·polynomial·set·is·contained·in·I·by |
| 119 | applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and | 119 | applying·the·division·algorithm·for·each·element.·The·output·is·1·for·true·and |
| 120 | 0·for·false. | 120 | 0·for·false. |
| 121 | Options: | 121 | Options: |
| 122 | --remainder: | 122 | --remainder: |
| 123 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than | 123 | ·Tell·the·program·to·output·the·remainders·of·the·divisions·rather·than |
| 124 | outputting·0·or·1. | 124 | outputting·0·or·1. |
| 125 | --multiplier: | 125 | --multiplier: |
| 126 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided | 126 | ·Reads·in·a·polynomial·that·will·be·multiplied·to·the·polynomial·to·be·divided |
| 127 | before·doing·the·division. | 127 | before·doing·the·division. |
| 128 | using·temporary·file·/tmp/M2- | 128 | using·temporary·file·/tmp/M2-2197251-0/178 |
| 129 | running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2- | 129 | running:·/usr/bin/gfan·_fancommonrefinement·--help·<·/tmp/M2-2197251-0/178 |
| 130 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. | 130 | This·program·takes·two·polyhedral·fans·and·computes·their·common·refinement. |
| 131 | Options: | 131 | Options: |
| 132 | -i1·value: | 132 | -i1·value: |
| 133 | ·Specify·the·name·of·the·first·input·file. | 133 | ·Specify·the·name·of·the·first·input·file. |
| 134 | -i2·value: | 134 | -i2·value: |
| 135 | ·Specify·the·name·of·the·second·input·file. | 135 | ·Specify·the·name·of·the·second·input·file. |
| 136 | --stable: | 136 | --stable: |
| 137 | ·Compute·the·stable·intersection. | 137 | ·Compute·the·stable·intersection. |
| 138 | using·temporary·file·/tmp/M2- | 138 | using·temporary·file·/tmp/M2-2197251-0/180 |
| 139 | running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2- | 139 | running:·/usr/bin/gfan·_fanlink·--help·<·/tmp/M2-2197251-0/180 |
| 140 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the | 140 | This·program·takes·a·polyhedral·fan·and·a·vector·and·computes·the·link·of·the |
| 141 | polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension | 141 | polyhedral·fan·around·that·vertex.·The·link·will·have·lineality·space·dimension |
| 142 | equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan | 142 | equal·to·the·dimension·of·the·relative·open·polyhedral·cone·of·the·original·fan |
| 143 | containing·the·vector. | 143 | containing·the·vector. |
| 144 | Options: | 144 | Options: |
| 145 | -i·value: | 145 | -i·value: |
| 146 | ·Specify·the·name·of·the·input·file. | 146 | ·Specify·the·name·of·the·input·file. |
| Offset 152, 25 lines modified | Offset 152, 25 lines modified | ||
| 152 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must | 152 | ·Reads·in·a·fan·stored·with·symmetry.·The·generators·of·the·symmetry·group·must |
| 153 | be·given·on·the·standard·input. | 153 | be·given·on·the·standard·input. |
| 154 | --star: | 154 | --star: |
| 155 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan | 155 | ·Computes·the·star·instead.·The·star·is·defined·as·the·smallest·polyhedral·fan |
| 156 | containing·all·cones·of·the·original·fan·containing·the·vector. | 156 | containing·all·cones·of·the·original·fan·containing·the·vector. |
| 157 | using·temporary·file·/tmp/M2- | 157 | using·temporary·file·/tmp/M2-2197251-0/182 |
| 158 | running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2- | 158 | running:·/usr/bin/gfan·_fanproduct·--help·<·/tmp/M2-2197251-0/182 |
| 159 | This·program·takes·two·polyhedral·fans·and·computes·their·product. | 159 | This·program·takes·two·polyhedral·fans·and·computes·their·product. |
| 160 | Options: | 160 | Options: |
| 161 | -i1·value: | 161 | -i1·value: |
| 162 | ·Specify·the·name·of·the·first·input·file. | 162 | ·Specify·the·name·of·the·first·input·file. |
| 163 | -i2·value: | 163 | -i2·value: |
| 164 | ·Specify·the·name·of·the·second·input·file. | 164 | ·Specify·the·name·of·the·second·input·file. |
| 165 | using·temporary·file·/tmp/M2- | 165 | using·temporary·file·/tmp/M2-2197251-0/184 |
| 166 | running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2- | 166 | running:·/usr/bin/gfan·_groebnercone·--help·<·/tmp/M2-2197251-0/184 |
| 167 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The | 167 | This·program·computes·a·Groebner·cone.·Three·different·cases·are·handled.·The |
| 168 | input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is | 168 | input·may·be·a·marked·reduced·Groebner·basis·in·which·case·its·Groebner·cone·is |
| 169 | computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone | 169 | computed.·The·input·may·be·just·a·marked·minimal·basis·in·which·case·the·cone |
| 170 | computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones | 170 | computed·is·not·a·Groebner·cone·in·the·usual·sense·but·smaller.·(These·cones |
| 171 | are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case | 171 | are·described·in·[Fukuda,·Jensen,·Lauritzen,·Thomas]).·The·third·possible·case |
| 172 | is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of | 172 | is·that·the·Groebner·cone·is·possibly·lower·dimensional·and·given·by·a·pair·of |
| 173 | Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair. | 173 | Groebner·bases·as·it·is·useful·to·do·for·tropical·varieties,·see·option·--pair. |
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| 188 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way | 188 | ·Writes·the·cone·as·a·polyhedral·fan·with·all·its·faces·instead.·In·this·way |
| 189 | the·extreme·rays·of·the·cone·are·also·computed. | 189 | the·extreme·rays·of·the·cone·are·also·computed. |
| 190 | --vectorinput: | 190 | --vectorinput: |
| 191 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The | 191 | ·Compute·a·cone·given·list·of·inequalities·rather·than·a·Groebner·cone.·The |
| 192 | input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list | 192 | input·is·an·integer·which·specifies·the·dimension·of·the·ambient·space,·a·list |
| 193 | of·inequalities·given·as·vectors·and·a·list·of·equations. | 193 | of·inequalities·given·as·vectors·and·a·list·of·equations. |
| 194 | using·temporary·file·/tmp/M2- | 194 | using·temporary·file·/tmp/M2-2197251-0/186 |
| 195 | running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2- | 195 | running:·/usr/bin/gfan·_homogeneityspace·--help·<·/tmp/M2-2197251-0/186 |
| 196 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a | 196 | This·program·computes·the·homogeneity·space·of·a·list·of·polynomials·-·as·a |
| 197 | cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section | 197 | cone.·Thus·generators·for·the·homogeneity·space·are·found·in·the·section |
| 198 | LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first | 198 | LINEALITY_SPACE.·If·you·wish·the·homogeneity·space·of·an·ideal·you·should·first |
| 199 | compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A | 199 | compute·a·set·of·homogeneous·generators·and·call·the·program·on·these.·A |
| 200 | reduced·Groebner·basis·will·always·suffice·for·this·purpose. | 200 | reduced·Groebner·basis·will·always·suffice·for·this·purpose. |
| 201 | Options: | 201 | Options: |
| 202 | using·temporary·file·/tmp/M2- | 202 | using·temporary·file·/tmp/M2-2197251-0/188 |
| 203 | running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2- | 203 | running:·/usr/bin/gfan·_homogenize·--help·<·/tmp/M2-2197251-0/188 |
| 204 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra | 204 | This·program·homogenises·a·list·of·polynomials·by·introducing·an·extra |
| 205 | variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input | 205 | variable.·The·name·of·the·variable·to·be·introduced·is·read·from·the·input |
| 206 | after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done | 206 | after·the·list·of·polynomials.·Without·the·-w·option·the·homogenisation·is·done |
| 207 | with·respect·to·total·degree. | 207 | with·respect·to·total·degree. |
| 208 | Example: | 208 | Example: |
| 209 | Input: | 209 | Input: |
| 210 | Q[x,y]{y-1} | 210 | Q[x,y]{y-1} |
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| 000179d0:·6520·6275·726b·6552·6573·6f6c·7574·696f··e·burkeResolutio | 000179d0:·6520·6275·726b·6552·6573·6f6c·7574·696f··e·burkeResolutio | ||
| 000179e0:·6e28·4d2c·2037·2c20·4368·6563·6b20·3d3e··n(M,·7,·Check·=> | 000179e0:·6e28·4d2c·2037·2c20·4368·6563·6b20·3d3e··n(M,·7,·Check·=> | ||
| 000179f0:·2066·616c·7365·2920·2020·2020·2020·2020···false)········· | 000179f0:·2066·616c·7365·2920·2020·2020·2020·2020···false)········· | ||
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| 00017ca0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00017ca0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
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| 00002af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00002b10:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | 00002b10:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | ||
| 00002b20:·2e30·3 | 00002b20:·2e30·3137·3033·3436·2073·6563·6f6e·6473··.0170346·seconds | ||
| 00002b30:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 00002b30:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
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| 00005f90:·6520·6265·7474·6928·4927·3d74·7269·6d20··e·betti(I'=trim· | 00005f90:·6520·6265·7474·6928·4927·3d74·7269·6d20··e·betti(I'=trim· | ||
| 00005fa0:·6b65·7220·7068·6929·2020·2020·2020·2020··ker·phi)········ | 00005fa0:·6b65·7220·7068·6929·2020·2020·2020·2020··ker·phi)········ | ||
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| 00006300:·6564·5469·6d65·2062·6173·6550·7473·3d70··edTime·basePts=p | 00006300:·6564·5469·6d65·2062·6173·6550·7473·3d70··edTime·basePts=p | ||
| 00006310:·7269·6d61·7279·4465·636f·6d70·6f73·6974··rimaryDecomposit | 00006310:·7269·6d61·7279·4465·636f·6d70·6f73·6974··rimaryDecomposit | ||
| 00006320:·696f·6e20·6964·6561·6c20·483b·207c·0a7c··ion·ideal·H;·|.| | 00006320:·696f·6e20·6964·6561·6c20·483b·207c·0a7c··ion·ideal·H;·|.| | ||
| 00006330:·202d·2d20·3 | 00006330:·202d·2d20·332e·3939·3631·3620·7365·636f···--·3.99616·seco | ||
| 00006340:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | 00006340:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | ||
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| 00006360:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | 00006360:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | ||
| 00006370:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006370:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000063a0:·2d2d·2d2b·0a7c·6931·3820·3a20·7461·6c6c··---+.|i18·:·tall | 000063a0:·2d2d·2d2b·0a7c·6931·3820·3a20·7461·6c6c··---+.|i18·:·tall | ||
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| 00009c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009c40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009c40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009c50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009c50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009c60:·2d2d·2d2d·2d2b·0a7c·6931·3420·3a20·656c··-----+.|i14·:·el | 00009c60:·2d2d·2d2d·2d2b·0a7c·6931·3420·3a20·656c··-----+.|i14·:·el | ||
| 00009c70:·6170·7365·6454·696d·6520·7375·6228·492c··apsedTime·sub(I, | 00009c70:·6170·7365·6454·696d·6520·7375·6228·492c··apsedTime·sub(I, | ||
| 00009c80:·4829·2020·2020·2020·2020·2020·2020·2020··H)·············· | 00009c80:·4829·2020·2020·2020·2020·2020·2020·2020··H)·············· | ||
| 00009c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ca0:·7c0a·7c20·2d2d·2030·2e3 | 00009ca0:·7c0a·7c20·2d2d·2030·2e30·3130·3736·3338··|.|·--·0.0107638 | ||
| 00009cb0:·7365 | 00009cb0:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 00009cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009cd0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00009cd0:·2020·2020·2020·2020·2020·207c·0a7c·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:·2020·2020·2020·7c0a·7c6f·3134·203d·2069········|.|o14·=·i | 00009d10:·2020·2020·2020·7c0a·7c6f·3134·203d·2069········|.|o14·=·i | ||
| 00009d20:·6465·616c·2028·302c·2030·2c20·302c·2030··deal·(0,·0,·0,·0 | 00009d20:·6465·616c·2028·302c·2030·2c20·302c·2030··deal·(0,·0,·0,·0 | ||
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| 00009ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00009ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00009ef0:·7c69·3136·203a·2065·6c61·7073·6564·5469··|i16·:·elapsedTi | 00009ef0:·7c69·3136·203a·2065·6c61·7073·6564·5469··|i16·:·elapsedTi | ||
| 00009f00:·6d65·2062·6574·7469·2849·273d·7472·696d··me·betti(I'=trim | 00009f00:·6d65·2062·6574·7469·2849·273d·7472·696d··me·betti(I'=trim | ||
| 00009f10:·206b·6572·2070·6869·2920·2020·2020·2020···ker·phi)······· | 00009f10:·206b·6572·2070·6869·2920·2020·2020·2020···ker·phi)······· | ||
| 00009f20:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00009f20:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00009f30:·302e·3 | 00009f30:·302e·3034·3431·3038·3620·7365·636f·6e64··0.0441086·second | ||
| 00009f40:·2065 | 00009f40:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00009f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f60:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00009f60:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00009f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00009f90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00009fa0:·0a7c·2020·2020·2020·2020·2020·2020·2030··.|·············0 | 00009fa0:·0a7c·2020·2020·2020·2020·2020·2020·2030··.|·············0 | ||
| 00009fb0:·2020·3120·2020·2020·2020·2020·2020·2020····1············· | 00009fb0:·2020·3120·2020·2020·2020·2020·2020·2020····1············· | ||
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| 0000a1f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a1f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a210:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a220:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3138·203a··--------+.|i18·: | 0000a220:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3138·203a··--------+.|i18·: | ||
| 0000a230:·2065·6c61·7073·6564·5469·6d65·2062·6173···elapsedTime·bas | 0000a230:·2065·6c61·7073·6564·5469·6d65·2062·6173···elapsedTime·bas | ||
| 0000a240:·6550·7473·3d70·7269·6d61·7279·4465·636f··ePts=primaryDeco | 0000a240:·6550·7473·3d70·7269·6d61·7279·4465·636f··ePts=primaryDeco | ||
| 0000a250:·6d70·6f73·6974·696f·6e20·6964·6561·6c20··mposition·ideal· | 0000a250:·6d70·6f73·6974·696f·6e20·6964·6561·6c20··mposition·ideal· | ||
| 0000a260:·483b·207c·0a7c·202d·2d20·3 | 0000a260:·483b·207c·0a7c·202d·2d20·312e·3331·3930··H;·|.|·--·1.3190 | ||
| 0000a270:·3 | 0000a270:·3320·7365·636f·6e64·7320·656c·6170·7365··3·seconds·elapse | ||
| 0000a280:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | 0000a280:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 0000a290:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000a290:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000a2a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 0000a2a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 0000a2b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a2b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a2c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a2c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a2d0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3920··---------+.|i19· | 0000a2d0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3920··---------+.|i19· | ||
| 0000a2e0:·3a20·7461·6c6c·7920·6170·706c·7928·6261··:·tally·apply(ba | 0000a2e0:·3a20·7461·6c6c·7920·6170·706c·7928·6261··:·tally·apply(ba |
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| 00010730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010740:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010740:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00010750:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00010760:·6931·3420·3a20·7469·6d65·2062·6574·7469··i14·:·time·betti | 00010760:·6931·3420·3a20·7469·6d65·2062·6574·7469··i14·:·time·betti | ||
| 00010770:·2028·4620·3d20·7075·7265·5265·736f·6c75···(F·=·pureResolu | 00010770:·2028·4620·3d20·7075·7265·5265·736f·6c75···(F·=·pureResolu | ||
| 00010780:·7469·6f6e·284d·2c7b·302c·322c·347d·2929··tion(M,{0,2,4})) | 00010780:·7469·6f6e·284d·2c7b·302c·322c·347d·2929··tion(M,{0,2,4})) | ||
| 00010790:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 00010790:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 000107a0:·2030·2e3 | 000107a0:·2030·2e34·3933·3938·3873·2028·6370·7529···0.493988s·(cpu) | ||
| 000107b0:·3b20·302e·333 | 000107b0:·3b20·302e·3331·3439·3534·7320·2874·6872··;·0.314954s·(thr | ||
| 000107c0:·6561·6429·3b20·3073·2028·6763·297c·0a7c··ead);·0s·(gc)|.| | 000107c0:·6561·6429·3b20·3073·2028·6763·297c·0a7c··ead);·0s·(gc)|.| | ||
| 000107d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000107d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000107e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000107e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000107f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000107f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010800:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00010800:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00010810:·2020·2020·2030·2031·2032·2020·2020·2020·······0·1·2······ | 00010810:·2020·2020·2030·2031·2032·2020·2020·2020·······0·1·2······ | ||
| 00010820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00010b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010b60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010b60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010b70:·2b0a·7c69·3135·203a·2074·696d·6520·6265··+.|i15·:·time·be | 00010b70:·2b0a·7c69·3135·203a·2074·696d·6520·6265··+.|i15·:·time·be | ||
| 00010b80:·7474·6920·2846·203d·2070·7572·6552·6573··tti·(F·=·pureRes | 00010b80:·7474·6920·2846·203d·2070·7572·6552·6573··tti·(F·=·pureRes | ||
| 00010b90:·6f6c·7574·696f·6e28·3131·2c34·2c7b·302c··olution(11,4,{0, | 00010b90:·6f6c·7574·696f·6e28·3131·2c34·2c7b·302c··olution(11,4,{0, | ||
| 00010ba0:·322c·347d·2929·2020·7c0a·7c20·2d2d·2075··2,4}))··|.|·--·u | 00010ba0:·322c·347d·2929·2020·7c0a·7c20·2d2d·2075··2,4}))··|.|·--·u | ||
| 00010bb0:·7365·6420·302e·343 | 00010bb0:·7365·6420·302e·3437·3231·3632·7320·2863··sed·0.472162s·(c | ||
| 00010bc0:·7075·293b·2030·2e33·3 | 00010bc0:·7075·293b·2030·2e33·3333·3534·3673·2028··pu);·0.333546s·( | ||
| 00010bd0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | 00010bd0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 00010be0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00010be0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00010bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010c10:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00010c10:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00010c20:·2020·2020·2020·2020·3020·3120·3220·2020··········0·1·2··· | 00010c20:·2020·2020·2020·2020·3020·3120·3220·2020··········0·1·2··· | ||
| 00010c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010c30:·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· | 00000980:·6d70·7574·6174·696f·6e20·5765·6420·4f63··mputation·Wed·Oc | ||
| 00000990:·7 | 00000990:·7420·3136·2030·343a·3231·3a34·3620·2b31··t·16·04:21:46·+1 | ||
| 000009a0:·3 | 000009a0:·3420·3230·3234·2020·2020·2020·2020·2020··4·2024·········· | ||
| 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:· | 000009d0:·7572·652d·7468·652d·686f·7374·6e61·6d65··ure-the-hostname | ||
| 000009e0:·2036·2e31·2e30·2d32·362d·636c·6f75·642d···6.1.0-26-cloud- | |||
| 000009 | 000009f0:·616d·6436·3420·2331·2053·4d50·2050·5245··amd64·#1·SMP·PRE | ||
| 00000 | 00000a00:·454d·5054·5f44·594e·414d·4943·2020·7c0a··EMPT_DYNAMIC··|. | ||
| 00000a00:·2044·6562·6961·6e20·2020·2020·2020·7c0a···Debian·······|. | |||
| 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·2032·3139·362e·3638·3820·2020·2020··Hz·2196.688····· | ||
| 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:·3234·2e30·352c·2063·6f6d·7069·6c65·6420··24.05,·compiled· | 00000a70:·3234·2e30·352c·2063·6f6d·7069·6c65·6420··24.05,·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·313 | 00000ae0:·5a2f·3130·313a·202e·3131·3832·3836·2073··Z/101:·.118286·s | ||
| 00000af0:·6563·6f6e·6473·2020·2020·2020·2020·7c0a··econds········|. | 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:·7c36·2e31·302e·3131·2d31·7e62·706f·3132··|6.10.11-1~bpo12 | |||
| 00000b60:·2b31·2028·3230·3234·2d31·302d·3033·2920··+1·(2024-10-03)· | |||
| 00000b | 00000b50:·7c44·6562·6961·6e20·362e·312e·3131·322d··|Debian·6.1.112- | ||
| 00000b60:·3120·2832·3032·342d·3039·2d33·3029·2078··1·(2024-09-30)·x | |||
| 00000b70:·3836·5f36·3420·474e·552f·4c69·6e75·7820··86_64·GNU/Linux· | |||
| 00000b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000b90:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 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··--------------+. |
| Offset 2063, 16 lines modified | Offset 2063, 16 lines modified | ||
| 000080e0:·616c·206e·756d·6265·720a·2020·2020·2020··al·number.······ | 000080e0:·616c·206e·756d·6265·720a·2020·2020·2020··al·number.······ | ||
| 000080f0:·2020·6f72·2072·616e·646f·6d20·636f·6d70····or·random·comp | 000080f0:·2020·6f72·2072·616e·646f·6d20·636f·6d70····or·random·comp | ||
| 00008100:·6c65·7820·6e75·6d62·6572·0a20·2020·2020··lex·number.····· | 00008100:·6c65·7820·6e75·6d62·6572·0a20·2020·2020··lex·number.····· | ||
| 00008110:·202a·202a·6e6f·7465·2054·6f70·4469·7265···*·*note·TopDire | 00008110:·202a·202a·6e6f·7465·2054·6f70·4469·7265···*·*note·TopDire | ||
| 00008120:·6374·6f72·793a·2054·6f70·4469·7265·6374··ctory:·TopDirect | 00008120:·6374·6f72·793a·2054·6f70·4469·7265·6374··ctory:·TopDirect | ||
| 00008130:·6f72·792c·203d·3e20·2e2e·2e2c·2064·6566··ory,·=>·...,·def | 00008130:·6f72·792c·203d·3e20·2e2e·2e2c·2064·6566··ory,·=>·...,·def | ||
| 00008140:·6175·6c74·2076·616c·7565·0a20·2020·2020··ault·value.····· | 00008140:·6175·6c74·2076·616c·7565·0a20·2020·2020··ault·value.····· | ||
| 00008150:·2020·2022·2f74·6d70·2f4d·322d·3 | 00008150:·2020·2022·2f74·6d70·2f4d·322d·3233·3335·····"/tmp/M2-2335 | ||
| 00008160:·3 | 00008160:·3838·372d·302f·3022·2c20·4f70·7469·6f6e··887-0/0",·Option | ||
| 00008170:·2074·6f20·6368·616e·6765·2064·6972·6563···to·change·direc | 00008170:·2074·6f20·6368·616e·6765·2064·6972·6563···to·change·direc | ||
| 00008180:·746f·7279·2066·6f72·2066·696c·6520·7374··tory·for·file·st | 00008180:·746f·7279·2066·6f72·2066·696c·6520·7374··tory·for·file·st | ||
| 00008190:·6f72·6167·652e·0a20·2020·2020·202a·202a··orage..······*·* | 00008190:·6f72·6167·652e·0a20·2020·2020·202a·202a··orage..······*·* | ||
| 000081a0:·6e6f·7465·2056·6572·626f·7365·3a20·6265··note·Verbose:·be | 000081a0:·6e6f·7465·2056·6572·626f·7365·3a20·6265··note·Verbose:·be | ||
| 000081b0:·7274·696e·6954·7261·636b·486f·6d6f·746f··rtiniTrackHomoto | 000081b0:·7274·696e·6954·7261·636b·486f·6d6f·746f··rtiniTrackHomoto | ||
| 000081c0:·7079·5f6c·705f·7064·5f70·645f·7064·5f63··py_lp_pd_pd_pd_c | 000081c0:·7079·5f6c·705f·7064·5f70·645f·7064·5f63··py_lp_pd_pd_pd_c | ||
| 000081d0:·6d56·6572·626f·7365·3d3e·5f70·645f·7064··mVerbose=>_pd_pd | 000081d0:·6d56·6572·626f·7365·3d3e·5f70·645f·7064··mVerbose=>_pd_pd | ||
| Offset 4727, 16 lines modified | Offset 4727, 16 lines modified | ||
| 00012760:·6f63·756d·656e·7461·7469·6f6e·2920·3d3e··ocumentation)·=> | 00012760:·6f63·756d·656e·7461·7469·6f6e·2920·3d3e··ocumentation)·=> | ||
| 00012770:·202e·2e2e·2c20·6465·6661·756c·7420·7661···...,·default·va | 00012770:·202e·2e2e·2c20·6465·6661·756c·7420·7661···...,·default·va | ||
| 00012780:·6c75·6520·7b7d·2c20·0a20·2020·2020·202a··lue·{},·.······* | 00012780:·6c75·6520·7b7d·2c20·0a20·2020·2020·202a··lue·{},·.······* | ||
| 00012790:·202a·6e6f·7465·2054·6f70·4469·7265·6374···*note·TopDirect | 00012790:·202a·6e6f·7465·2054·6f70·4469·7265·6374···*note·TopDirect | ||
| 000127a0:·6f72·793a·2054·6f70·4469·7265·6374·6f72··ory:·TopDirector | 000127a0:·6f72·793a·2054·6f70·4469·7265·6374·6f72··ory:·TopDirector | ||
| 000127b0:·792c·203d·3e20·2e2e·2e2c·2064·6566·6175··y,·=>·...,·defau | 000127b0:·792c·203d·3e20·2e2e·2e2c·2064·6566·6175··y,·=>·...,·defau | ||
| 000127c0:·6c74·2076·616c·7565·0a20·2020·2020·2020··lt·value.······· | 000127c0:·6c74·2076·616c·7565·0a20·2020·2020·2020··lt·value.······· | ||
| 000127d0:·2022·2f74·6d70·2f4d·322d·3 | 000127d0:·2022·2f74·6d70·2f4d·322d·3233·3335·3838···"/tmp/M2-233588 | ||
| 000127e0:·3 | 000127e0:·372d·302f·3022·2c20·4f70·7469·6f6e·2074··7-0/0",·Option·t | ||
| 000127f0:·6f20·6368·616e·6765·2064·6972·6563·746f··o·change·directo | 000127f0:·6f20·6368·616e·6765·2064·6972·6563·746f··o·change·directo | ||
| 00012800:·7279·2066·6f72·2066·696c·6520·7374·6f72··ry·for·file·stor | 00012800:·7279·2066·6f72·2066·696c·6520·7374·6f72··ry·for·file·stor | ||
| 00012810:·6167·652e·0a20·2020·2020·202a·202a·6e6f··age..······*·*no | 00012810:·6167·652e·0a20·2020·2020·202a·202a·6e6f··age..······*·*no | ||
| 00012820:·7465·2056·6572·626f·7365·3a20·6265·7274··te·Verbose:·bert | 00012820:·7465·2056·6572·626f·7365·3a20·6265·7274··te·Verbose:·bert | ||
| 00012830:·696e·6954·7261·636b·486f·6d6f·746f·7079··iniTrackHomotopy | 00012830:·696e·6954·7261·636b·486f·6d6f·746f·7079··iniTrackHomotopy | ||
| 00012840:·5f6c·705f·7064·5f70·645f·7064·5f63·6d56··_lp_pd_pd_pd_cmV | 00012840:·5f6c·705f·7064·5f70·645f·7064·5f63·6d56··_lp_pd_pd_pd_cmV | ||
| 00012850:·6572·626f·7365·3d3e·5f70·645f·7064·5f70··erbose=>_pd_pd_p | 00012850:·6572·626f·7365·3d3e·5f70·645f·7064·5f70··erbose=>_pd_pd_p | ||
| Offset 5217, 16 lines modified | Offset 5217, 16 lines modified | ||
| 00014600:·6c20·6e75·6d62·6572·0a20·2020·2020·2020··l·number.······· | 00014600:·6c20·6e75·6d62·6572·0a20·2020·2020·2020··l·number.······· | ||
| 00014610:·206f·7220·7261·6e64·6f6d·2063·6f6d·706c···or·random·compl | 00014610:·206f·7220·7261·6e64·6f6d·2063·6f6d·706c···or·random·compl | ||
| 00014620:·6578·206e·756d·6265·720a·2020·2020·2020··ex·number.······ | 00014620:·6578·206e·756d·6265·720a·2020·2020·2020··ex·number.······ | ||
| 00014630:·2a20·2a6e·6f74·6520·546f·7044·6972·6563··*·*note·TopDirec | 00014630:·2a20·2a6e·6f74·6520·546f·7044·6972·6563··*·*note·TopDirec | ||
| 00014640:·746f·7279·3a20·546f·7044·6972·6563·746f··tory:·TopDirecto | 00014640:·746f·7279·3a20·546f·7044·6972·6563·746f··tory:·TopDirecto | ||
| 00014650:·7279·2c20·3d3e·202e·2e2e·2c20·6465·6661··ry,·=>·...,·defa | 00014650:·7279·2c20·3d3e·202e·2e2e·2c20·6465·6661··ry,·=>·...,·defa | ||
| 00014660:·756c·7420·7661·6c75·650a·2020·2020·2020··ult·value.······ | 00014660:·756c·7420·7661·6c75·650a·2020·2020·2020··ult·value.······ | ||
| 00014670:·2020·222f·746d·702f·4d32·2d3 | 00014670:·2020·222f·746d·702f·4d32·2d32·3333·3538····"/tmp/M2-23358 | ||
| 00014680:·3 | 00014680:·3837·2d30·2f30·222c·204f·7074·696f·6e20··87-0/0",·Option· | ||
| 00014690:·746f·2063·6861·6e67·6520·6469·7265·6374··to·change·direct | 00014690:·746f·2063·6861·6e67·6520·6469·7265·6374··to·change·direct | ||
| 000146a0:·6f72·7920·666f·7220·6669·6c65·2073·746f··ory·for·file·sto | 000146a0:·6f72·7920·666f·7220·6669·6c65·2073·746f··ory·for·file·sto | ||
| 000146b0:·7261·6765·2e0a·2020·2020·2020·2a20·5573··rage..······*·Us | 000146b0:·7261·6765·2e0a·2020·2020·2020·2a20·5573··rage..······*·Us | ||
| 000146c0:·6552·6567·656e·6572·6174·696f·6e20·286d··eRegeneration·(m | 000146c0:·6552·6567·656e·6572·6174·696f·6e20·286d··eRegeneration·(m | ||
| 000146d0:·6973·7369·6e67·2064·6f63·756d·656e·7461··issing·documenta | 000146d0:·6973·7369·6e67·2064·6f63·756d·656e·7461··issing·documenta | ||
| 000146e0:·7469·6f6e·2920·3d3e·202e·2e2e·2c20·6465··tion)·=>·...,·de | 000146e0:·7469·6f6e·2920·3d3e·202e·2e2e·2c20·6465··tion)·=>·...,·de | ||
| 000146f0:·6661·756c·7420·7661·6c75·6520·2d31·2c20··fault·value·-1,· | 000146f0:·6661·756c·7420·7661·6c75·6520·2d31·2c20··fault·value·-1,· |
| Offset 12415, 15 lines modified | Offset 12415, 15 lines modified | ||
| 000307e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000307e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000307f0:·2d2d·2d2d·2d2d·2d2b·0a7c·6939·203a·2065··-------+.|i9·:·e | 000307f0:·2d2d·2d2d·2d2d·2d2b·0a7c·6939·203a·2065··-------+.|i9·:·e | ||
| 00030800:·6c61·7073·6564·5469·6d65·2063·203d·2063··lapsedTime·c·=·c | 00030800:·6c61·7073·6564·5469·6d65·2063·203d·2063··lapsedTime·c·=·c | ||
| 00030810:·6861·7261·6374·6572·2041·2020·2020·2020··haracter·A······ | 00030810:·6861·7261·6374·6572·2041·2020·2020·2020··haracter·A······ | ||
| 00030820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00030830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00030840:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | 00030840:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | ||
| 00030850:·3 | 00030850:·3332·3433·3535·2073·6563·6f6e·6473·2065··324355·seconds·e | ||
| 00030860:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 00030860:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 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·················· | ||
| 00030890:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00030890:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 000308a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000308a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000308b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000308b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000308c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000308c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 13611, 15 lines modified | Offset 13611, 15 lines modified | ||
| 000352a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000352a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000352b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937··-----------+.|i7 | 000352b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937··-----------+.|i7 | ||
| 000352c0:·203a·2065·6c61·7073·6564·5469·6d65·2063···:·elapsedTime·c | 000352c0:·203a·2065·6c61·7073·6564·5469·6d65·2063···:·elapsedTime·c | ||
| 000352d0:·3d63·6861·7261·6374·6572·2041·2020·2020··=character·A···· | 000352d0:·3d63·6861·7261·6374·6572·2041·2020·2020··=character·A···· | ||
| 000352e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000352e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000352f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000352f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035300:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 00035300:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 00035310:·2d20·302e·3 | 00035310:·2d20·302e·3630·3736·3938·2073·6563·6f6e··-·0.607698·secon | ||
| 00035320:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 00035320:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 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:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00035350:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00035360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00035380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00035380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0003ab40:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | 0003ab40:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | ||
| 0003ab50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ab50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ab60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ab60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ab70:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3230·203a··--------+.|i20·: | 0003ab70:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3230·203a··--------+.|i20·: | ||
| 0003ab80:·2065·6c61·7073·6564·5469·6d65·2061·3120···elapsedTime·a1· | 0003ab80:·2065·6c61·7073·6564·5469·6d65·2061·3120···elapsedTime·a1· | ||
| 0003ab90:·3d20·6368·6172·6163·7465·7220·4131·2020··=·character·A1·· | 0003ab90:·3d20·6368·6172·6163·7465·7220·4131·2020··=·character·A1·· | ||
| 0003aba0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0003aba0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0003abb0:·202d·2d20·302e·3 | 0003abb0:·202d·2d20·302e·3833·3937·3931·2073·6563···--·0.839791·sec | ||
| 0003abc0:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | 0003abc0:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | ||
| 0003abd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003abd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003abe0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 0003abe0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 0003abf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003abf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ac00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ac00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ac10:·2020·2020·2020·207c·0a7c·6f32·3020·3d20·········|.|o20·=· | 0003ac10:·2020·2020·2020·207c·0a7c·6f32·3020·3d20·········|.|o20·=· | ||
| 0003ac20:·4368·6172·6163·7465·7220·6f76·6572·2052··Character·over·R | 0003ac20:·4368·6172·6163·7465·7220·6f76·6572·2052··Character·over·R | ||
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| 0003adc0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 0003adc0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 0003add0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003add0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ade0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ade0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003adf0:·2d2d·2d2d·2b0a·7c69·3231·203a·2065·6c61··----+.|i21·:·ela | 0003adf0:·2d2d·2d2d·2b0a·7c69·3231·203a·2065·6c61··----+.|i21·:·ela | ||
| 0003ae00:·7073·6564·5469·6d65·2061·3220·3d20·6368··psedTime·a2·=·ch | 0003ae00:·7073·6564·5469·6d65·2061·3220·3d20·6368··psedTime·a2·=·ch | ||
| 0003ae10:·6172·6163·7465·7220·4132·2020·2020·2020··aracter·A2······ | 0003ae10:·6172·6163·7465·7220·4132·2020·2020·2020··aracter·A2······ | ||
| 0003ae20:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 0003ae20:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 0003ae30:·3 | 0003ae30:·3435·2e34·3934·2073·6563·6f6e·6473·2065··45.494·seconds·e | ||
| 0003ae40:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 0003ae40:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 0003ae50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0003ae50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0003ae60:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 0003ae60:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 0003ae70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ae70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ae80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003ae80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003ae90:·2020·207c·0a7c·6f32·3120·3d20·4368·6172·····|.|o21·=·Char | 0003ae90:·2020·207c·0a7c·6f32·3120·3d20·4368·6172·····|.|o21·=·Char | ||
| 0003aea0:·6163·7465·7220·6f76·6572·2052·2020·2020··acter·over·R···· | 0003aea0:·6163·7465·7220·6f76·6572·2052·2020·2020··acter·over·R···· | ||
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| 0003ca60:·696f·6e4f·6e47·7261·6465·644d·6f64·756c··ionOnGradedModul | 0003ca60:·696f·6e4f·6e47·7261·6465·644d·6f64·756c··ionOnGradedModul | ||
| 0003ca70:·6520·2020·2020·2020·2020·2020·7c0a·2b2d··e···········|.+- | 0003ca70:·6520·2020·2020·2020·2020·2020·7c0a·2b2d··e···········|.+- | ||
| 0003ca80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ca80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003ca90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003ca90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003caa0:·2d2d·2d2d·2b0a·7c69·3332·203a·2065·6c61··----+.|i32·:·ela | 0003caa0:·2d2d·2d2d·2b0a·7c69·3332·203a·2065·6c61··----+.|i32·:·ela | ||
| 0003cab0:·7073·6564·5469·6d65·2062·203d·2063·6861··psedTime·b·=·cha | 0003cab0:·7073·6564·5469·6d65·2062·203d·2063·6861··psedTime·b·=·cha | ||
| 0003cac0:·7261·6374·6572·2842·2c32·3129·7c0a·7c20··racter(B,21)|.|· | 0003cac0:·7261·6374·6572·2842·2c32·3129·7c0a·7c20··racter(B,21)|.|· | ||
| 0003cad0:·2d2d·2031·3 | 0003cad0:·2d2d·2031·382e·3738·3838·2073·6563·6f6e··--·18.7888·secon | ||
| 0003cae0:·7320 | 0003cae0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 0003caf0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 0003caf0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 0003cb00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003cb00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003cb10:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | 0003cb10:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 0003cb20:·3332·203d·2043·6861·7261·6374·6572·206f··32·=·Character·o | 0003cb20:·3332·203d·2043·6861·7261·6374·6572·206f··32·=·Character·o | ||
| 0003cb30:·7665·7220·5220·2020·2020·2020·2020·2020··ver·R··········· | 0003cb30:·7665·7220·5220·2020·2020·2020·2020·2020··ver·R··········· | ||
| 0003cb40:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 0003cb40:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 0003cb50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003cb50:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00003f90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003f90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003fa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003fa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003fb0:·2d2b·0a7c·6932·3320·3a20·7469·6d65·206a··-+.|i23·:·time·j | 00003fb0:·2d2b·0a7c·6932·3320·3a20·7469·6d65·206a··-+.|i23·:·time·j | ||
| 00003fc0:·3d62·7275·6e73·2046·2e64·645f·333b·2020··=bruns·F.dd_3;·· | 00003fc0:·3d62·7275·6e73·2046·2e64·645f·333b·2020··=bruns·F.dd_3;·· | ||
| 00003fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003fd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004000:·207c·0a7c·202d·2d20·7573·6564·2030·2e3 | 00004000:·207c·0a7c·202d·2d20·7573·6564·2030·2e31···|.|·--·used·0.1 | ||
| 00004010:·3 | 00004010:·3937·3938·3473·2028·6370·7529·3b20·302e··97984s·(cpu);·0. | ||
| 00004020:·313 | 00004020:·3136·3335·3931·7320·2874·6872·6561·6429··163591s·(thread) | ||
| 00004030:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | 00004030:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 00004040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004050:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00004050:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00004060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004090:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00003980:·2028·4365·6c6c·206f·6620·6469·6d65·6e73···(Cell·of·dimens | 00003980:·2028·4365·6c6c·206f·6620·6469·6d65·6e73···(Cell·of·dimens | ||
| 00003990:·696f·6e20·3120·7769·7468·206c·6162·656c··ion·1·with·label | 00003990:·696f·6e20·3120·7769·7468·206c·6162·656c··ion·1·with·label | ||
| 000039a0:·7c0a·7c20·2020·2020·202d·2d2d·2d2d·2d2d··|.|······------- | 000039a0:·7c0a·7c20·2020·2020·202d·2d2d·2d2d·2d2d··|.|······------- | ||
| 000039b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000039b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000039c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000039c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000039d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000039d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000039e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000039e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000039f0:·7c0a·7c20·2020·2020·2031·2c20· | 000039f0:·7c0a·7c20·2020·2020·2031·2c20·2d31·292c··|.|······1,·-1), | ||
| 00003a00:·2843·656c·6c20·6f66·2064·696d·656e·7369··(Cell·of·dimensi | |||
| 00003a10:·6f6e·2031·2077·6974·6820·6c61·6265·6c20··on·1·with·label· | |||
| 00003a20:·312c·202d·3129·2c20·2843·656c·6c20·6f66··1,·-1),·(Cell·of | |||
| 00003a | 00003a00:·2028·4365·6c6c·206f·6620·6469·6d65·6e73···(Cell·of·dimens | ||
| 00003a10:·696f·6e20·3120·7769·7468·206c·6162·656c··ion·1·with·label | |||
| 00003a20:·2031·2c20·2d31·292c·2028·4365·6c6c·206f···1,·-1),·(Cell·o | |||
| 00003a30:·6620·6469·6d65·6e73·696f·6e20·3120·2020··f·dimension·1··· | |||
| 00003a40:·7c0a·7c20·2020·2020·202d·2d2d·2d2d·2d2d··|.|······------- | 00003a40:·7c0a·7c20·2020·2020·202d·2d2d·2d2d·2d2d··|.|······------- | ||
| 00003a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003a70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003a70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003a80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003a80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003a90:·7c0a·7c20·2020·2020·2077·6974·6820·6c61··|.|······with·la | 00003a90:·7c0a·7c20·2020·2020·2077·6974·6820·6c61··|.|······with·la | ||
| 00003aa0:·6265·6c20·312c·20 | 00003aa0:·6265·6c20·312c·2031·297d·2020·2020·2020··bel·1,·1)}······ | ||
| 00003ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003ae0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00003ae0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00003af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003b00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003b00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003b10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00005620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005630:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·6431··-----+.|i10·:·d1 | 00005630:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·6431··-----+.|i10·:·d1 | ||
| 00005640:·203d·2062·6f75·6e64·6172·794d·6170·5f31···=·boundaryMap_1 | 00005640:·203d·2062·6f75·6e64·6172·794d·6170·5f31···=·boundaryMap_1 | ||
| 00005650:·2043·2020·2020·2020·2020·2020·2020·7c0a···C············|. | 00005650:·2043·2020·2020·2020·2020·2020·2020·7c0a···C············|. | ||
| 00005660:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00005660:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00005670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005680:·2020·2020·2020·207c·0a7c·6f31·3020·3d20·········|.|o10·=· | 00005680:·2020·2020·2020·207c·0a7c·6f31·3020·3d20·········|.|o10·=· | ||
| 00005690:·7b31·7d20·7c20·2d7 | 00005690:·7b31·7d20·7c20·2d79·202d·7820·3020·207c··{1}·|·-y·-x·0··| | ||
| 000056a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000056a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000056b0:·7c0a·7c20·2020·2020·207b·317d·207c·20 | 000056b0:·7c0a·7c20·2020·2020·207b·317d·207c·2030··|.|······{1}·|·0 | ||
| 000056c0:·2020·7 | 000056c0:·2020·7a20·2079·2020·7c20·2020·2020·2020····z··y··|······· | ||
| 000056d0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000056d0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000056e0:·2020·7b31·7d20·7c20· | 000056e0:·2020·7b31·7d20·7c20·7a20·2030·2020·2d78····{1}·|·z··0··-x | ||
| 000056f0:·207c·2020·2020·2020·2020·2020·2020·2020···|·············· | 000056f0:·207c·2020·2020·2020·2020·2020·2020·2020···|·············· | ||
| 00005700:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00005700:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00005710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005720:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 00005720:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
| 00005730:·3020·3a20·4d61·7472·6978·2020·2020·2020··0·:·Matrix······ | 00005730:·3020·3a20·4d61·7472·6978·2020·2020·2020··0·:·Matrix······ | ||
| 00005740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005750:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+--------- | 00005750:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+--------- | ||
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| 00005780:·6931·3120·3a20·6432·203d·2062·6f75·6e64··i11·:·d2·=·bound | 00005780:·6931·3120·3a20·6432·203d·2062·6f75·6e64··i11·:·d2·=·bound | ||
| 00005790:·6172·794d·6170·5f32·2043·2020·2020·2020··aryMap_2·C······ | 00005790:·6172·794d·6170·5f32·2043·2020·2020·2020··aryMap_2·C······ | ||
| 000057a0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 000057a0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 000057b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057c0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000057c0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000057d0:·0a7c·6f31·3120·3d20·7b32·7d20·7c20· | 000057d0:·0a7c·6f31·3120·3d20·7b32·7d20·7c20·7820··.|o11·=·{2}·|·x· | ||
| 000057e0:·207c·2020·2020·2020·2020·2020·2020·2020···|·············· | 000057e0:·207c·2020·2020·2020·2020·2020·2020·2020···|·············· | ||
| 000057f0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 000057f0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00005800:·207b·327d·207c·20 | 00005800:·207b·327d·207c·202d·7920·7c20·2020·2020···{2}·|·-y·|····· | ||
| 00005810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005810:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005820:·207c·0a7c·2020·2020·2020·7b32·7d20·7c20···|.|······{2}·|· | 00005820:·207c·0a7c·2020·2020·2020·7b32·7d20·7c20···|.|······{2}·|· | ||
| 00005830:·7 | 00005830:·7a20·207c·2020·2020·2020·2020·2020·2020··z··|············ | ||
| 00005840:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00005840:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00005850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005870:·2020·207c·0a7c·6f31·3120·3a20·4d61·7472·····|.|o11·:·Matr | 00005870:·2020·207c·0a7c·6f31·3120·3a20·4d61·7472·····|.|o11·:·Matr | ||
| 00005880:·6978·2020·2020·2020·2020·2020·2020·2020··ix·············· | 00005880:·6978·2020·2020·2020·2020·2020·2020·2020··ix·············· | ||
| 00005890:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | 00005890:·2020·2020·2020·2020·2020·2020·7c0a·2b2d··············|.+- | ||
| 000058a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000058a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000086c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000086c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000086d0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000086d0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000086e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000086e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000086f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000086f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008710:·2020·2020·2020·2020·2020·7c0a·7c6f·3820············|.|o8· | 00008710:·2020·2020·2020·2020·2020·7c0a·7c6f·3820············|.|o8· | ||
| 00008720:·3d20·5265·6c61·7469·6f6e·204d·6174·7269··=·Relation·Matri | 00008720:·3d20·5265·6c61·7469·6f6e·204d·6174·7269··=·Relation·Matri | ||
| 00008730:·783a·207c·2031·2030·2030·2030·2030·203 | 00008730:·783a·207c·2031·2030·2030·2030·2030·2030··x:·|·1·0·0·0·0·0 | ||
| 00008740:·203 | 00008740:·2031·2030·2031·2031·2031·2030·2030·2031···1·0·1·1·1·0·0·1 | ||
| 00008750:·2031·2031·2031·207c·7c0a·7c20·2020·2020···1·1·1·||.|····· | 00008750:·2031·2031·2031·207c·7c0a·7c20·2020·2020···1·1·1·||.|····· | ||
| 00008760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008770:·207c·2030·2031·2030·2030·2030·203 | 00008770:·207c·2030·2031·2030·2030·2030·2030·2031···|·0·1·0·0·0·0·1 | ||
| 00008780:·2030·2030·2030·203 | 00008780:·2030·2030·2030·2030·2031·2031·2031·2031···0·0·0·0·1·1·1·1 | ||
| 00008790:·2030·2030·207c·7c0a·7c20·2020·2020·2020···0·0·||.|······· | 00008790:·2030·2030·207c·7c0a·7c20·2020·2020·2020···0·0·||.|······· | ||
| 000087a0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000087a0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000087b0:·2030·2030·2031·2030·2030·203 | 000087b0:·2030·2030·2031·2030·2030·2031·2030·2030···0·0·1·0·0·1·0·0 | ||
| 000087c0:·203 | 000087c0:·2031·2030·2030·2031·2030·2031·2030·2031···1·0·0·1·0·1·0·1 | ||
| 000087d0:·2030·207c·7c0a·7c20·2020·2020·2020·2020···0·||.|········· | 000087d0:·2030·207c·7c0a·7c20·2020·2020·2020·2020···0·||.|········· | ||
| 000087e0:·2020·2020·2020·2020·2020·2020·207c·2030···············|·0 | 000087e0:·2020·2020·2020·2020·2020·2020·207c·2030···············|·0 | ||
| 000087f0:·2030·2030·2031·2030·2030·203 | 000087f0:·2030·2030·2031·2030·2030·2030·2031·2030···0·0·1·0·0·0·1·0 | ||
| 00008800:·203 | 00008800:·2031·2030·2030·2031·2030·2031·2030·2031···1·0·0·1·0·1·0·1 | ||
| 00008810:·207c·7c0a·7c20·2020·2020·2020·2020·2020···||.|··········· | 00008810:·207c·7c0a·7c20·2020·2020·2020·2020·2020···||.|··········· | ||
| 00008820:·2020·2020·2020·2020·2020·207c·2030·2030·············|·0·0 | 00008820:·2020·2020·2020·2020·2020·207c·2030·2030·············|·0·0 | ||
| 00008830:·2030·2030·2031·203 | 00008830:·2030·2030·2031·2031·2030·2031·2030·2030···0·0·1·1·0·1·0·0 | ||
| 00008840:·203 | 00008840:·2031·2030·2030·2030·2030·2031·2031·207c···1·0·0·0·0·1·1·| | ||
| 00008850:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00008850:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00008860:·2020·2020·2020·2020·207c·2030·2030·2030···········|·0·0·0 | 00008860:·2020·2020·2020·2020·207c·2030·2030·2030···········|·0·0·0 | ||
| 00008870:·2030·2030·2031·2030·2030·2030·2030·2030···0·0·1·0·0·0·0·0 | 00008870:·2030·2030·2031·2030·2030·2030·2030·2030···0·0·1·0·0·0·0·0 | ||
| 00008880:·2030·2030·203 | 00008880:·2030·2030·2030·2030·2031·2030·207c·7c0a···0·0·0·0·1·0·||. | ||
| 00008890:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00008890:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 000088a0:·2020·2020·2020·207c·2030·2030·2030·2030·········|·0·0·0·0 | 000088a0:·2020·2020·2020·207c·2030·2030·2030·2030·········|·0·0·0·0 | ||
| 000088b0:·2030·2030·2031·2030·2030·2030·2030·2030···0·0·1·0·0·0·0·0 | 000088b0:·2030·2030·2031·2030·2030·2030·2030·2030···0·0·1·0·0·0·0·0 | ||
| 000088c0:·2030·203 | 000088c0:·2030·2031·2031·2030·2030·207c·7c0a·7c20···0·1·1·0·0·||.|· | ||
| 000088d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000088d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000088e0:·2020·2020·207c·2030·2030·2030·2030·2030·······|·0·0·0·0·0 | 000088e0:·2020·2020·207c·2030·2030·2030·2030·2030·······|·0·0·0·0·0 | ||
| 000088f0:·2030·2030·2031·2030·2030·2030·2030·2030···0·0·1·0·0·0·0·0 | 000088f0:·2030·2030·2031·2030·2030·2030·2030·2030···0·0·1·0·0·0·0·0 | ||
| 00008900:·203 | 00008900:·2030·2030·2030·2031·207c·7c0a·7c20·2020···0·0·0·1·||.|··· | ||
| 00008910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008920:·2020·207c·2030·2030·2030·2030·2030·2030·····|·0·0·0·0·0·0 | 00008920:·2020·207c·2030·2030·2030·2030·2030·2030·····|·0·0·0·0·0·0 | ||
| 00008930:·2030·2030·2031·2030·2030·2030·2030·203 | 00008930:·2030·2030·2031·2030·2030·2030·2030·2031···0·0·1·0·0·0·0·1 | ||
| 00008940:·203 | 00008940:·2030·2031·2030·207c·7c0a·7c20·2020·2020···0·1·0·||.|····· | ||
| 00008950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008960:·207c·2030·2030·2030·2030·2030·2030·2030···|·0·0·0·0·0·0·0 | 00008960:·207c·2030·2030·2030·2030·2030·2030·2030···|·0·0·0·0·0·0·0 | ||
| 00008970:·2030·2030·2031·2030·2030·2030·2030·203 | 00008970:·2030·2030·2031·2030·2030·2030·2030·2031···0·0·1·0·0·0·0·1 | ||
| 00008980:·203 | 00008980:·2030·2031·207c·7c0a·7c20·2020·2020·2020···0·1·||.|······· | ||
| 00008990:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00008990:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000089a0:·2030·2030·2030·2030·2030·2030·2030·2030···0·0·0·0·0·0·0·0 | 000089a0:·2030·2030·2030·2030·2030·2030·2030·2030···0·0·0·0·0·0·0·0 | ||
| 000089b0:·2030·2030·2031·2030·2030·203 | 000089b0:·2030·2030·2031·2030·2030·2030·2030·2031···0·0·1·0·0·0·0·1 | ||
| 000089c0:·203 | 000089c0:·2031·207c·7c0a·7c20·2020·2020·2020·2020···1·||.|········· | ||
| 000089d0:·2020·2020·2020·2020·2020·2020·207c·2030···············|·0 | 000089d0:·2020·2020·2020·2020·2020·2020·207c·2030···············|·0 | ||
| 000089e0:·2030·2030·2030·2030·2030·2030·2030·2030···0·0·0·0·0·0·0·0 | 000089e0:·2030·2030·2030·2030·2030·2030·2030·2030···0·0·0·0·0·0·0·0 | ||
| 000089f0:·2030·2030·2031·2030·203 | 000089f0:·2030·2030·2031·2030·2031·2030·2030·2030···0·0·1·0·1·0·0·0 | ||
| 00008a00:·207c·7c0a·7c20·2020·2020·2020·2020·2020···||.|··········· | 00008a00:·207c·7c0a·7c20·2020·2020·2020·2020·2020···||.|··········· | ||
| 00008a10:·2020·2020·2020·2020·2020·207c·2030·2030·············|·0·0 | 00008a10:·2020·2020·2020·2020·2020·207c·2030·2030·············|·0·0 | ||
| 00008a20:·2030·2030·2030·2030·2030·2030·2030·2030···0·0·0·0·0·0·0·0 | 00008a20:·2030·2030·2030·2030·2030·2030·2030·2030···0·0·0·0·0·0·0·0 | ||
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| 00011a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011aa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00011aa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00011ab0:·6931·3320·3a20·7469·6d65·206d·203d·206d··i13·:·time·m·=·m | 00011ab0:·6931·3320·3a20·7469·6d65·206d·203d·206d··i13·:·time·m·=·m | ||
| 00011ac0:·696e·696d·697a·6520·2845·5b31·5d29·3b20··inimize·(E[1]);· | 00011ac0:·696e·696d·697a·6520·2845·5b31·5d29·3b20··inimize·(E[1]);· | ||
| 00011ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011ae0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 00011ae0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 00011af0:·2030·2e32·3 | 00011af0:·2030·2e32·3338·3133·3273·2028·6370·7529···0.238132s·(cpu) | ||
| 00011b00:·3b20·302e·3 | 00011b00:·3b20·302e·3138·3338·3732·7320·2874·6872··;·0.183872s·(thr | ||
| 00011b10:·6561·6429·3b20·3073·2028·6763·297c·0a2b··ead);·0s·(gc)|.+ | 00011b10:·6561·6429·3b20·3073·2028·6763·297c·0a2b··ead);·0s·(gc)|.+ | ||
| 00011b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011b50:·2d2d·2d2d·2d2b·0a7c·6931·3420·3a20·6973··-----+.|i14·:·is | 00011b50:·2d2d·2d2d·2d2b·0a7c·6931·3420·3a20·6973··-----+.|i14·:·is | ||
| 00011b60:·5175·6173·6949·736f·6d6f·7270·6869·736d··QuasiIsomorphism | 00011b60:·5175·6173·6949·736f·6d6f·7270·6869·736d··QuasiIsomorphism | ||
| 00011b70:·206d·2020·2020·2020·2020·2020·2020·2020···m·············· | 00011b70:·206d·2020·2020·2020·2020·2020·2020·2020···m·············· | ||
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| 000183b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000183b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000183c0:·2b0a·7c69·3820·3a20·7469·6d65·206d·203d··+.|i8·:·time·m·= | 000183c0:·2b0a·7c69·3820·3a20·7469·6d65·206d·203d··+.|i8·:·time·m·= | ||
| 000183d0:·2072·6573·6f6c·7574·696f·6e4f·6643·6861···resolutionOfCha | 000183d0:·2072·6573·6f6c·7574·696f·6e4f·6643·6861···resolutionOfCha | ||
| 000183e0:·696e·436f·6d70·6c65·7820·433b·2020·2020··inComplex·C;···· | 000183e0:·696e·436f·6d70·6c65·7820·433b·2020·2020··inComplex·C;···· | ||
| 000183f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000183f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018410:·7c0a·7c20·2d2d·2075·7365·6420·302e·3134··|.|·--·used·0.14 | 00018410:·7c0a·7c20·2d2d·2075·7365·6420·302e·3134··|.|·--·used·0.14 | ||
| 00018420:·3 | 00018420:·3338·3231·7320·2863·7075·293b·2030·2e30··3821s·(cpu);·0.0 | ||
| 00018430:·3 | 00018430:·3934·3237·3733·7320·2874·6872·6561·6429··942773s·(thread) | ||
| 00018440:·2030 | 00018440:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 00018450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018460:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | 00018460:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00018470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000184a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000184a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000184b0:·2b0a·7c69·3920·3a20·7469·6d65·206e·203d··+.|i9·:·time·n·= | 000184b0:·2b0a·7c69·3920·3a20·7469·6d65·206e·203d··+.|i9·:·time·n·= | ||
| 000184c0:·2063·6172·7461·6e45·696c·656e·6265·7267···cartanEilenberg | 000184c0:·2063·6172·7461·6e45·696c·656e·6265·7267···cartanEilenberg | ||
| 000184d0:·5265·736f·6c75·7469·6f6e·2043·3b20·2020··Resolution·C;··· | 000184d0:·5265·736f·6c75·7469·6f6e·2043·3b20·2020··Resolution·C;··· | ||
| 000184e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000184e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000184f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000184f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018500:·7c0a·7c20·2d2d·2075·7365·6420·302e·313 | 00018500:·7c0a·7c20·2d2d·2075·7365·6420·302e·3130··|.|·--·used·0.10 | ||
| 00018510:·3 | 00018510:·3230·3433·7320·2863·7075·293b·2030·2e31··2043s·(cpu);·0.1 | ||
| 00018520:·3 | 00018520:·3032·3539·3173·2028·7468·7265·6164·293b··02591s·(thread); | ||
| 00018530:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 00018530:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 00018540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018550:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | 00018550:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00018560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
| Offset 3799, 30 lines modified | Offset 3799, 30 lines modified | ||
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| 0000ed70:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000ed70:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000ed80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ed80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ed90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ed90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eda0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eda0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000edb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000edb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000edc0:·207c·0a7c·6f34·203d·2045·6c69·6d54·7265···|.|o4·=·ElimTre | 0000edc0:·207c·0a7c·6f34·203d·2045·6c69·6d54·7265···|.|o4·=·ElimTre | ||
| 0000edd0:·657b·6120·3d3e·206 | 0000edd0:·657b·6120·3d3e·2062·2020·207d·2020·2020··e{a·=>·b···}···· | ||
| 0000ede0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ede0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000edf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000edf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ee00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ee00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ee10:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000ee10:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000ee20:·2020·6220·3d3e·2063·2020·2020·2020·2020····b·=>·c········ | 0000ee20:·2020·6220·3d3e·2063·2020·2020·2020·2020····b·=>·c········ | ||
| 0000ee30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ee30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000ee60:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000ee60:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000ee70:·2020·6320·3d3e·2064·2020·2020·2020·2020····c·=>·d········ | 0000ee70:·2020·6320·3d3e·2064·2020·2020·2020·2020····c·=>·d········ | ||
| 0000ee80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ee80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ee90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ee90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eeb0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000eeb0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000eec0:·2020·6420·3d3e·206 | 0000eec0:·2020·6420·3d3e·206e·756c·6c20·2020·2020····d·=>·null····· | ||
| 0000eed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ef00:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000ef00:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000ef10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ef10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ef20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ef20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ef30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ef30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3884, 31 lines modified | Offset 3884, 31 lines modified | ||
| 0000f2b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f2b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f2c0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000f2c0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000f2d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f2d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f2e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f2e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·207c·0a7c·6f37·203d·2043·686f·7264·616c···|.|o7·=·Chordal | 0000f310:·207c·0a7c·6f37·203d·2043·686f·7264·616c···|.|o7·=·Chordal | ||
| 0000f320:·4e65·747b·206 | 0000f320:·4e65·747b·2064·203d·3e20·7b20·2c20·647d··Net{·d·=>·{·,·d} | ||
| 0000f330:·2020·2020·7d20·2020·2020·2020·2020·2020······}··········· | 0000f330:·2020·2020·7d20·2020·2020·2020·2020·2020······}··········· | ||
| 0000f340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f360:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000f360:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000f370:·2020·2020·206 | 0000f370:·2020·2020·2062·203d·3e20·7b62·2c20·202c·······b·=>·{b,··, | ||
| 0000f380:·20 | 0000f380:·2062·7d20·2020·2020·2020·2020·2020·2020···b}············· | ||
| 0000f390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f3a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f3a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f3b0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000f3b0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000f3c0:·2020·2020·206 | 0000f3c0:·2020·2020·2061·203d·3e20·7b61·2c20·207d·······a·=>·{a,··} | ||
| 0000f3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f3e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f3e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f3f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f3f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f400:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000f400:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000f410:·2020·2020·206 | 0000f410:·2020·2020·2063·203d·3e20·7b20·2c20·637d·······c·=>·{·,·c} | ||
| 0000f420:·20 | 0000f420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00013fd0:·2029·2c20·6964·6561·6c20·2878·202c·2078···),·ideal·(x·,·x | 00013fd0:·2029·2c20·6964·6561·6c20·2878·202c·2078···),·ideal·(x·,·x | ||
| 00013fe0:·202c·2078·202c·2078·202c·2078·2029·2c20···,·x·,·x·,·x·),· | 00013fe0:·202c·2078·202c·2078·202c·2078·2029·2c20···,·x·,·x·,·x·),· | ||
| 00013ff0:·6964·6561·6c20·2878·202c·2078·202c·2078··ideal·(x·,·x·,·x | 00013ff0:·6964·6561·6c20·2878·202c·2078·202c·2078··ideal·(x·,·x·,·x | ||
| 00014000:·202c·2078·202c·2078·2029·2c20·6964·6561···,·x·,·x·),·idea | 00014000:·202c·2078·202c·2078·2029·2c20·6964·6561···,·x·,·x·),·idea | ||
| 00014010:·6c20·2878·202c·2020·7c0a·7c20·3720·2020··l·(x·,··|.|·7··· | 00014010:·6c20·2878·202c·2020·7c0a·7c20·3720·2020··l·(x·,··|.|·7··· | ||
| 00014020:·3820·2020·2020·2020·2020·2020·3120·2020··8···········1··· | 00014020:·3820·2020·2020·2020·2020·2020·3120·2020··8···········1··· | ||
| 00014030:·3320·2020·3 | 00014030:·3320·2020·3520·2020·3620·2020·3820·2020··3···5···6···8··· | ||
| 00014040:·2020·2020·2020·2020·3 | 00014040:·2020·2020·2020·2020·3120·2020·3320·2020··········1···3··· | ||
| 00014050:·3 | 00014050:·3420·2020·3620·2020·3820·2020·2020·2020··4···6···8······· | ||
| 00014060:·2020·2020·3 | 00014060:·2020·2020·3220·2020·7c0a·7c2d·2d2d·2d2d······2···|.|----- | ||
| 00014070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000140a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000140a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000140b0:·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020·2020··--------|.|····· | 000140b0:·2d2d·2d2d·2d2d·2d2d·7c0a·7c20·2020·2020··--------|.|····· | ||
| 000140c0:·2020·2020·2020·2020·2020·207d·2020·2020·············}···· | 000140c0:·2020·2020·2020·2020·2020·207d·2020·2020·············}···· | ||
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| Offset 5833, 71 lines modified | Offset 5833, 71 lines modified | ||
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| 00016c90:·2020·2020·2020·2020·6361·6368·6520·3d3e··········cache·=> | 00016c90:·2020·2020·2020·2020·6361·6368·6520·3d3e··········cache·=> | ||
| 00016ca0:·2043·6163·6865·5461·626c·657b·7d20·2020···CacheTable{}··· | 00016ca0:·2043·6163·6865·5461·626c·657b·7d20·2020···CacheTable{}··· | ||
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| 00016ce0:·2020·2020·2020·2020·436f·6465·203d·3e20··········Code·=>· | 00016ce0:·2020·2020·2020·2020·436f·6465·203d·3e20··········Code·=>· | ||
| 00016cf0:·696d·6167·6520·7c20· | 00016cf0:·696d·6167·6520·7c20·612b·3120·3020·2020··image·|·a+1·0··· | ||
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| 00016fb0:·2020·2020·2020·2020·4765·6e65·7261·746f··········Generato | 00016fb0:·2020·2020·2020·2020·4765·6e65·7261·746f··········Generato | ||
| 00016fc0:·724d·6174·7269·7820·3d3e·207c·20 | 00016fc0:·724d·6174·7269·7820·3d3e·207c·2061·2b31··rMatrix·=>·|·a+1 | ||
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| 00017050:·2020·2020·2020·2020·4765·6e65·7261·746f··········Generato | 00017050:·2020·2020·2020·2020·4765·6e65·7261·746f··········Generato | ||
| 00017060:·7273·203d·3e20·7b7b· | 00017060:·7273·203d·3e20·7b7b·6120·2b20·312c·2061··rs·=>·{{a·+·1,·a | ||
| 00017070:·20 | 00017070:·202b·2031·2c20·6120·7c0a·7c20·2020·2020···+·1,·a·|.|····· | ||
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| 000170a0:·2020·2020·2020·2020·5061·7269·7479·4368··········ParityCh | 000170a0:·2020·2020·2020·2020·5061·7269·7479·4368··········ParityCh | ||
| 000170b0:·6563·6b4d·6174·7269·7820·3d3e·207c·2031··eckMatrix·=>·|·1 | 000170b0:·6563·6b4d·6174·7269·7820·3d3e·207c·2031··eckMatrix·=>·|·1 | ||
| 000170c0:·2030·2030·2030·2020·7c0a·7c20·2020·2020···0·0·0··|.|····· | 000170c0:·2030·2030·2030·2020·7c0a·7c20·2020·2020···0·0·0··|.|····· | ||
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| 000170e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000170e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 5931, 18 lines modified | Offset 5931, 18 lines modified | ||
| 000172a0:·2030·2030·2030·2020·7c0a·7c20·2020·2020···0·0·0··|.|····· | 000172a0:·2030·2030·2030·2020·7c0a·7c20·2020·2020···0·0·0··|.|····· | ||
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| 000172d0:·2020·2020·2020·2020·5061·7269·7479·4368··········ParityCh | 000172d0:·2020·2020·2020·2020·5061·7269·7479·4368··········ParityCh | ||
| 000172e0:·6563·6b52·6f77·7320·3d3e·207b·7b31·2c20··eckRows·=>·{{1,· | 000172e0:·6563·6b52·6f77·7320·3d3e·207b·7b31·2c20··eckRows·=>·{{1,· | ||
| 000172f0:·302c·2030·2c20·3020·7c0a·7c20·2020·2020··0,·0,·0·|.|····· | 000172f0:·302c·2030·2c20·3020·7c0a·7c20·2020·2020··0,·0,·0·|.|····· | ||
| 00017300:·2020·2020·2020·2020·2020·2020·2020·2050·················P | 00017300:·2020·2020·2020·2020·2020·2020·2020·2050·················P | ||
| 00017310:·6f69·6e74·7320·3d3e·207b·7b | 00017310:·6f69·6e74·7320·3d3e·207b·7b30·2c20·617d··oints·=>·{{0,·a} | ||
| 00017320:·2c20·7b | 00017320:·2c20·7b61·2c20·307d·2c20·7b31·2c20·617d··,·{a,·0},·{1,·a} | ||
| 00017330:·2c20·7b | 00017330:·2c20·7b61·2c20·317d·2c20·7b61·2c20·617d··,·{a,·1},·{a,·a} | ||
| 00017340:·2c20·7b30·2c20· | 00017340:·2c20·7b30·2c20·3020·7c0a·7c20·2020·2020··,·{0,·0·|.|····· | ||
| 00017350:·2020·2020·2020·2020·2020·2020·2020·2050·················P | 00017350:·2020·2020·2020·2020·2020·2020·2020·2050·················P | ||
| 00017360:·6f6c·796e·6f6d·6961·6c53·6574·203d·3e20··olynomialSet·=>· | 00017360:·6f6c·796e·6f6d·6961·6c53·6574·203d·3e20··olynomialSet·=>· | ||
| 00017370:·7b78·202b·2079·202b·2031·2c20·782a·797d··{x·+·y·+·1,·x*y} | 00017370:·7b78·202b·2079·202b·2031·2c20·782a·797d··{x·+·y·+·1,·x*y} | ||
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| 000173a0:·2020·2020·2020·2020·2020·2020·2020·2053·················S | 000173a0:·2020·2020·2020·2020·2020·2020·2020·2053·················S | ||
| 000173b0:·6574·7320·3d3e·207b·7b30·2c20·312c·2061··ets·=>·{{0,·1,·a | 000173b0:·6574·7320·3d3e·207b·7b30·2c20·312c·2061··ets·=>·{{0,·1,·a | ||
| Offset 6039, 72 lines modified | Offset 6039, 72 lines modified | ||
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| 000179d0:·2020·2020·2020·2020·7c0a·7c | 000179d0:·2020·2020·2020·2020·7c0a·7c61·2031·2020··········|.|a·1·· | ||
| 000179e0:·20 | 000179e0:·2031·2030·2030·2031·207c·2020·2020·2020···1·0·0·1·|······ | ||
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| 000073a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000073a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000073b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000073b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 0000ffb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ffb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ffc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0000ffc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0000ffd0:·0a7c·6937·203a·2074·696d·6520·4720·3d20··.|i7·:·time·G·=· | 0000ffd0:·0a7c·6937·203a·2074·696d·6520·4720·3d20··.|i7·:·time·G·=· | ||
| 0000ffe0:·4569·7365·6e62·7564·5368·616d·6173·6828··EisenbudShamash( | 0000ffe0:·4569·7365·6e62·7564·5368·616d·6173·6828··EisenbudShamash( | ||
| 0000fff0:·6666·2c46·2c6c·656e·2920·2020·2020·2020··ff,F,len)······· | 0000fff0:·6666·2c46·2c6c·656e·2920·2020·2020·2020··ff,F,len)······· | ||
| 00010000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010010:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00010010:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00010020:·0a7c·202d·2d20·7573·6564·2036·2e3 | 00010020:·0a7c·202d·2d20·7573·6564·2036·2e31·3431··.|·--·used·6.141 | ||
| 00010030:·3 | 00010030:·3934·7320·2863·7075·293b·2034·2e31·3634··94s·(cpu);·4.164 | ||
| 00010040:·3 | 00010040:·3639·7320·2874·6872·6561·6429·3b20·3073··69s·(thread);·0s | ||
| 00010050:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 00010050:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00010060:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00010060:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00010070:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00010070:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00010080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000100b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
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| 00012170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012180:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00012190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 000121a0:·6932·3020·3a20·4646·203d·2074·696d·6520··i20·:·FF·=·time· | 000121a0:·6932·3020·3a20·4646·203d·2074·696d·6520··i20·:·FF·=·time· | ||
| 000121b0:·5368·616d·6173·6828·5231·2c46·2c34·2920··Shamash(R1,F,4)· | 000121b0:·5368·616d·6173·6828·5231·2c46·2c34·2920··Shamash(R1,F,4)· | ||
| 000121c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000121c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000121d0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000121d0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000121e0:·0a7c·202d·2d20·7573·6564·2030·2e31·3 | 000121e0:·0a7c·202d·2d20·7573·6564·2030·2e31·3137··.|·--·used·0.117 | ||
| 000121f0:·3334 | 000121f0:·3439·3473·2028·6370·7529·3b20·302e·3038··494s·(cpu);·0.08 | ||
| 00012200:·3 | 00012200:·3336·3139·7320·2874·6872·6561·6429·3b20··3619s·(thread);· | ||
| 00012210:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 00012210:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 00012220:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00012220:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00012230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012260:·2020·207c·0a7c·2020·2020·2020·2020·3120·····|.|········1· | 00012260:·2020·207c·0a7c·2020·2020·2020·2020·3120·····|.|········1· | ||
| 00012270:·2020·2020·2020·3620·2020·2020·2020·3138········6·······18 | 00012270:·2020·2020·2020·3620·2020·2020·2020·3138········6·······18 | ||
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| 00012400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012410:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00012420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00012430:·2d2b·0a7c·6932·3120·3a20·4747·203d·2074··-+.|i21·:·GG·=·t | 00012430:·2d2b·0a7c·6932·3120·3a20·4747·203d·2074··-+.|i21·:·GG·=·t | ||
| 00012440:·696d·6520·4569·7365·6e62·7564·5368·616d··ime·EisenbudSham | 00012440:·696d·6520·4569·7365·6e62·7564·5368·616d··ime·EisenbudSham | ||
| 00012450:·6173·6828·6666·2c46·2c34·2920·2020·2020··ash(ff,F,4)····· | 00012450:·6173·6828·6666·2c46·2c34·2920·2020·2020··ash(ff,F,4)····· | ||
| 00012460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012470:·2020·207c·0a7c·202d·2d20·7573·6564·203 | 00012470:·2020·207c·0a7c·202d·2d20·7573·6564·2031·····|.|·--·used·1 | ||
| 00012480:·2e39·3837·3332·3373·2028·6370·7529·3b20··.987323s·(cpu);· | |||
| 000124 | 00012480:·2e30·3138·3831·7320·2863·7075·293b·2030··.01881s·(cpu);·0 | ||
| 00012490:·2e36·3535·3038·3773·2028·7468·7265·6164··.655087s·(thread | |||
| 000124a0:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | 000124a0:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | ||
| 000124b0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 000124b0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 000124c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000124c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000124d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000124d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000124e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000124e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000124f0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000124f0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00012500:·2f20·525c·3120·2020·2020·2f20·525c·3620··/·R\1·····/·R\6· | 00012500:·2f20·525c·3120·2020·2020·2f20·525c·3620··/·R\1·····/·R\6· | ||
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| 000127a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000127a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000127b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000127b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000127c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932··-----------+.|i2 | 000127c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932··-----------+.|i2 | ||
| 000127d0:·3220·3a20·4747·203d·2074·696d·6520·4569··2·:·GG·=·time·Ei | 000127d0:·3220·3a20·4747·203d·2074·696d·6520·4569··2·:·GG·=·time·Ei | ||
| 000127e0:·7365·6e62·7564·5368·616d·6173·6828·5231··senbudShamash(R1 | 000127e0:·7365·6e62·7564·5368·616d·6173·6828·5231··senbudShamash(R1 | ||
| 000127f0:·2c46·5b32·5d2c·3429·2020·2020·2020·2020··,F[2],4)········ | 000127f0:·2c46·5b32·5d2c·3429·2020·2020·2020·2020··,F[2],4)········ | ||
| 00012800:·2020·7c0a·7c20·2d2d·2075·7365·6420·312e····|.|·--·used·1. | 00012800:·2020·7c0a·7c20·2d2d·2075·7365·6420·312e····|.|·--·used·1. | ||
| 00012810:·303 | 00012810:·3035·3738·3873·2028·6370·7529·3b20·302e··05788s·(cpu);·0. | ||
| 00012820:·3 | 00012820:·3730·3737·3736·7320·2874·6872·6561·6429··707776s·(thread) | ||
| 00012830:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | 00012830:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | ||
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| 00012880:·2020·2036·2020·2020·2020·2031·3820·2020·····6·······18··· | 00012880:·2020·2036·2020·2020·2020·2031·3820·2020·····6·······18··· | ||
| 00012890:·2020·2020·3338·2020·2020·2020·2036·3620······38·······66· | 00012890:·2020·2020·3338·2020·2020·2020·2036·3620······38·······66· | ||
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| 0006bd50:·203d·2052·2f28·6d31·2b6d·3229·2077·6865···=·R/(m1+m2)·whe | 0006bd50:·203d·2052·2f28·6d31·2b6d·3229·2077·6865···=·R/(m1+m2)·whe | ||
| 0006bd60:·7265·206d·3120·616e·6420·6d32·2061·7265··re·m1·and·m2·are | 0006bd60:·7265·206d·3120·616e·6420·6d32·2061·7265··re·m1·and·m2·are | ||
| 0006bd70:·206d·6f6e·6f6d·6961·6c73·206f·6620·7468···monomials·of·th | 0006bd70:·206d·6f6e·6f6d·6961·6c73·206f·6620·7468···monomials·of·th | ||
| 0006bd80:·650a·7361·6d65·2064·6567·7265·652e·0a0a··e.same·degree... | 0006bd80:·650a·7361·6d65·2064·6567·7265·652e·0a0a··e.same·degree... | ||
| 0006bd90:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 0006bd90:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 0006bda0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006bda0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006bdb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006bdb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006bdc0:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·203a· | 0006bdc0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·203a··---------+.|i1·: | ||
| 0006bdd0:·6574·5261·6e64·6f6d·5365·6564·2030· | 0006bdd0:·2073·6574·5261·6e64·6f6d·5365·6564·2030···setRandomSeed·0 | ||
| 0006bde0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006bde0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006bdf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006bdf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006be00:· | 0006be00:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 0006be10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006be10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006be20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006be20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006be30:·2020·2020·2020·2020·207c·0a7c·6f31·203d···········|.|o1·= | |||
| 0006be | 0006be30:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0006be40:·0a7c·6f31·203d·2030·2020·2020·2020·2020··.|o1·=·0········ | |||
| 0006be50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0006be50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0006be70:·2020· | 0006be70:·2020·2020·2020·2020·2020·7c0a·2b2d·2d2d············|.+--- | ||
| 0006be80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006be80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006be90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0006be90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006bea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2 | 0006bea0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0006beb0:·203a·2073·756d·5477·6f4d·6f6e·6f6d·6961···:·sumTwoMonomia | |||
| 0006be | 0006beb0:·2d2d·2d2d·2d2b·0a7c·6932·203a·2073·756d··-----+.|i2·:·sum | ||
| 0006bec0:·5477·6f4d·6f6e·6f6d·6961·6c73·2832·2c33··TwoMonomials(2,3 | |||
| 0006bed0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | |||
| 0006be | 0006bee0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0006be | 0006bef0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3537··|.|·--·used·0.57 | ||
| 0006bef0:·302e·3632·3034·3134·7320·2863·7075·293b··0.620414s·(cpu); | |||
| 0006bf00:· | 0006bf00:·3439·3335·7320·2863·7075·293b·2030·2e33··4935s·(cpu);·0.3 | ||
| 0006bf10:·3533·3633·3573·2028·7468·7265·6164·293b··53635s·(thread); | |||
| 0006bf | 0006bf20:·2030·7320·2867·6329·2020·207c·0a7c·202d···0s·(gc)···|.|·- | ||
| 0006bf | 0006bf30:·2d20·7573·6564·2030·2e31·3239·3873·2028··-·used·0.1298s·( | ||
| 0006bf40:·6370·7529·3b20·302e·3130·3639·3832·7320··cpu);·0.106982s· | |||
| 0006bf30:·3773·2028·6370·7529·3b20·302e·3132·3138··7s·(cpu);·0.1218 | |||
| 0006bf40:·3736·7320·2874·6872·6561·6429·3b20·3073··76s·(thread);·0s | |||
| 0006bf50:·2028·6763·2920·7c0a·7c20·2d2d·2075·7365···(gc)·|.|·--·use | |||
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| Offset 2971, 17 lines modified | Offset 2971, 17 lines modified | ||
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| 000012 | 00001270:·2020·3220·2020·2020·2020·2020·2020·3220····2···········2· | ||
| 00001280:·2020·7c0a·7c6f·3420·3d20·6964·6561·6c28····|.|o4·=·ideal( | |||
| 00001290:·612a·622a·6320·2d20·622a·6320·202d·2061··a*b*c·-·b*c··-·a | |||
| 000012a0:·2064·202b·2061·2a63·2a64·202d·2062·2020···d·+·a*c*d·-·b·· | |||
| 000012b0:·2b20·3262·2a64·202d·2064·2029·2020·7c0a··+·2b*d·-·d·)··|. | |||
| 000012 | 000012c0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00001270:·2020·2020·2020·2032·2020·2020·3220·2020·········2····2··· | |||
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| 00000b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3120··----------+.|i1· | 00000b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3120··----------+.|i1· | ||
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| 00000b50:·6d20·3220·746f·2031·3020·6c69·7374·206c··m·2·to·10·list·l | 00000b50:·6d20·3220·746f·2031·3020·6c69·7374·206c··m·2·to·10·list·l | ||
| 00000b60:·696e·6573·4879·7065·7273·7572·6661·6365··inesHypersurface | 00000b60:·696e·6573·4879·7065·7273·7572·6661·6365··inesHypersurface | ||
| 00000b70:·286e·2920·2020·2020·2020·2020·2020·2020··(n)············· | 00000b70:·286e·2920·2020·2020·2020·2020·2020·2020··(n)············· | ||
| 00000b80:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00000b80:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
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| 00000bb0:· | 00000bb0:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | ||
| 00000bc0:· | 00000bc0:·6763·2920·2020·2020·2020·2020·2020·2020··gc)············· | ||
| 00000bd0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00000bd0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00000be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00000c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00000c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00002240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002250:·2b0a·7c69·3720·3a20·7469·6d65·2066·6f72··+.|i7·:·time·for | 00002250:·2b0a·7c69·3720·3a20·7469·6d65·2066·6f72··+.|i7·:·time·for | ||
| 00002260:·2044·2069·6e20·5420·6c69·7374·2072·6174···D·in·T·list·rat | 00002260:·2044·2069·6e20·5420·6c69·7374·2072·6174···D·in·T·list·rat | ||
| 00002270:·696f·6e61·6c43·7572·7665·2832·2c44·2920··ionalCurve(2,D)· | 00002270:·696f·6e61·6c43·7572·7665·2832·2c44·2920··ionalCurve(2,D)· | ||
| 00002280:·2d20·7261·7469·6f6e·616c·4375·7276·6528··-·rationalCurve( | 00002280:·2d20·7261·7469·6f6e·616c·4375·7276·6528··-·rationalCurve( | ||
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| 000022b0:·293b·2030·2e32·3 | 000022b0:·293b·2030·2e32·3331·3035·3673·2028·7468··);·0.231056s·(th | ||
| 000022c0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 000022c0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 000022d0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000022d0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 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:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002320:·2020·7c0a·7c6f·3720·3d20·7b36·3039·3235····|.|o7·=·{60925 | 00002320:·2020·7c0a·7c6f·3720·3d20·7b36·3039·3235····|.|o7·=·{60925 | ||
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| 00002470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002490:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3820··----------+.|i8· | 00002490:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3820··----------+.|i8· | ||
| 000024a0:·3a20·7469·6d65·2072·6174·696f·6e61·6c43··:·time·rationalC | 000024a0:·3a20·7469·6d65·2072·6174·696f·6e61·6c43··:·time·rationalC | ||
| 000024b0:·7572·7665·2833·2920·2020·2020·2020·2020··urve(3)········· | 000024b0:·7572·7665·2833·2920·2020·2020·2020·2020··urve(3)········· | ||
| 000024c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000024c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000024d0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 000024d0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
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| 000024f0:·2030·2e31·3034·3136·3673·2028·7468·7265···0.104166s·(thre | |||
| 00002 | 000024e0:·2030·2e30·3932·3938·3034·7320·2863·7075···0.0929804s·(cpu | ||
| 000024f0:·293b·2030·2e30·3936·3537·3233·7320·2874··);·0.0965723s·(t | |||
| 00002500:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | |||
| 00002510:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00002510:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00002520:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002520:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002540:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00002540:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00002550:·2020·2038·3536·3435·3735·3030·3020·2020·····8564575000··· | 00002550:·2020·2038·3536·3435·3735·3030·3020·2020·····8564575000··· | ||
| 00002560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00002680:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002680:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002690:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002690:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000026b0:·6939·203a·2074·696d·6520·666f·7220·4420··i9·:·time·for·D· | 000026b0:·6939·203a·2074·696d·6520·666f·7220·4420··i9·:·time·for·D· | ||
| 000026c0:·696e·2054·206c·6973·7420·7261·7469·6f6e··in·T·list·ration | 000026c0:·696e·2054·206c·6973·7420·7261·7469·6f6e··in·T·list·ration | ||
| 000026d0:·616c·4375·7276·6528·332c·4429·2020·2020··alCurve(3,D)···· | 000026d0:·616c·4375·7276·6528·332c·4429·2020·2020··alCurve(3,D)···· | ||
| 000026e0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | 000026e0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2075··········|.|·--·u | ||
| 000026f0:·7365·6420·332e·3 | 000026f0:·7365·6420·332e·3536·3635·3173·2028·6370··sed·3.56651s·(cp | ||
| 00002700:·7529·3b20·332e·3 | 00002700:·7529·3b20·332e·3138·3337·3273·2028·7468··u);·3.18372s·(th | ||
| 00002710:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 00002710:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 00002720:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00002720:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 00002730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002750:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00002750:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00002760:·7c20·2020·2020·2038·3536·3435·3735·3030··|······856457500 | 00002760:·7c20·2020·2020·2038·3536·3435·3735·3030··|······856457500 | ||
| 00002770:·3020·2034·3232·3639·3038·3136·2020·2020··0··422690816···· | 00002770:·3020·2034·3232·3639·3038·3136·2020·2020··0··422690816···· | ||
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| 00002910:·6265·0a63·6f6d·7075·7465·6420·6173·2066··be.computed·as·f | 00002910:·6265·0a63·6f6d·7075·7465·6420·6173·2066··be.computed·as·f | ||
| 00002920:·6f6c·6c6f·7773·3a0a·0a0a·0a2b·2d2d·2d2d··ollows:....+---- | 00002920:·6f6c·6c6f·7773·3a0a·0a0a·0a2b·2d2d·2d2d··ollows:....+---- | ||
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| 00002940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002960:·2d2d·2d2b·0a7c·6931·3020·3a20·7469·6d65··---+.|i10·:·time | |||
| 00002960:·2d2d·2b0a·7c69·3130·203a·2074·696d·6520··--+.|i10·:·time· | |||
| 00002970:·7261·7469·6f6e·616c·4375·7276·6528·3329··rationalCurve(3) | |||
| 000029 | 00002970:·2072·6174·696f·6e61·6c43·7572·7665·2833···rationalCurve(3 | ||
| 00002980:·2920·2d20·7261·7469·6f6e·616c·4375·7276··)·-·rationalCurv | |||
| 00002990:·2831 | 00002990:·6528·3129·2f32·3720·2020·2020·207c·0a7c··e(1)/27······|.| | ||
| 000029a0:·2d20·7573·6564·2030·2e30·393 | 000029a0:·202d·2d20·7573·6564·2030·2e30·3934·3733···--·used·0.09473 | ||
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| 000029 | 000029c0:·3135·3539·7320·2874·6872·6561·6429·3b20··1559s·(thread);· | ||
| 000029d0:·3073·2028·6763·297c·0a7c·2020·2020·2020··0s·(gc)|.|······ | |||
| 000029e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000029e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000029f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000029f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002a00:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00002a10:·6f31·3020·3d20·3331·3732·3036·3337·3520··o10·=·317206375· | |||
| 00002a | 00002a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002a10:·207c·0a7c·6f31·3020·3d20·3331·3732·3036···|.|o10·=·317206 | |||
| 00002a20:·3337·3520·2020·2020·2020·2020·2020·2020··375············· | |||
| 00002a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00002a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002ab0:·2020·2020·2020·2020· | 00002ab0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
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| 000107d0:·2c20·5374·7261·7465·6779·3d3e·5261·6e64··,·Strategy=>Rand | 000107d0:·2c20·5374·7261·7465·6779·3d3e·5261·6e64··,·Strategy=>Rand | ||
| 000107e0:·6f6d·2929·2020·2020·2020·2020·2020·7c0a··om))··········|. | 000107e0:·6f6d·2929·2020·2020·2020·2020·2020·7c0a··om))··········|. | ||
| 000107f0:·7c20·2d2d·2075·7365·6420·302e·3039·3 | 000107f0:·7c20·2d2d·2075·7365·6420·302e·3039·3236··|·--·used·0.0926 | ||
| 00010800:·363 | 00010800:·3634·3773·2028·6370·7529·3b20·302e·3039··647s·(cpu);·0.09 | ||
| 00010810:·3 | 00010810:·3133·3037·3373·2028·7468·7265·6164·293b··13073s·(thread); | ||
| 00010820:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | 00010820:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 00010830:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010830:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010840:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00010840:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00010850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010850:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010880:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010880:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| Offset 4242, 18 lines modified | Offset 4242, 18 lines modified | ||
| 00010910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00010920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00010930:·7c69·3239·203a·2074·696d·6520·6469·6d20··|i29·:·time·dim· | 00010930:·7c69·3239·203a·2074·696d·6520·6469·6d20··|i29·:·time·dim· | ||
| 00010940:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | 00010940:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | ||
| 00010950:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | 00010950:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | ||
| 00010960:·2c20·5374·7261·7465·6779·3d3e·4c65·7853··,·Strategy=>LexS | 00010960:·2c20·5374·7261·7465·6779·3d3e·4c65·7853··,·Strategy=>LexS | ||
| 00010970:·6d61·6c6c·6573·7429·2920·2020·2020·7c0a··mallest))·····|. | 00010970:·6d61·6c6c·6573·7429·2920·2020·2020·7c0a··mallest))·····|. | ||
| 00010980:·7c20·2d2d·2075·7365·6420·302e·323 | 00010980:·7c20·2d2d·2075·7365·6420·302e·3239·3537··|·--·used·0.2957 | ||
| 00010990:·3 | 00010990:·3833·7320·2863·7075·293b·2030·2e31·3738··83s·(cpu);·0.178 | ||
| 000109a0:·3 | 000109a0:·3573·2028·7468·7265·6164·293b·2030·7320··5s·(thread);·0s· | ||
| 000109b0:· | 000109b0:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 000109c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000109c0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000109d0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 000109d0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 000109e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000109e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000109f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000109f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010a10:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010a10:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010a20:·7c6f·3239·203d·2033·2020·2020·2020·2020··|o29·=·3········ | 00010a20:·7c6f·3239·203d·2033·2020·2020·2020·2020··|o29·=·3········ | ||
| Offset 4267, 17 lines modified | Offset 4267, 17 lines modified | ||
| 00010aa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010aa0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010ab0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00010ab0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00010ac0:·7c69·3330·203a·2074·696d·6520·6469·6d20··|i30·:·time·dim· | 00010ac0:·7c69·3330·203a·2074·696d·6520·6469·6d20··|i30·:·time·dim· | ||
| 00010ad0:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | 00010ad0:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | ||
| 00010ae0:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | 00010ae0:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | ||
| 00010af0:·2c20·5374·7261·7465·6779·3d3e·4c65·7853··,·Strategy=>LexS | 00010af0:·2c20·5374·7261·7465·6779·3d3e·4c65·7853··,·Strategy=>LexS | ||
| 00010b00:·6d61·6c6c·6573·7454·6572·6d29·2920·7c0a··mallestTerm))·|. | 00010b00:·6d61·6c6c·6573·7454·6572·6d29·2920·7c0a··mallestTerm))·|. | ||
| 00010b10:·7c20·2d2d·2075·7365·6420·302e·3332·3 | 00010b10:·7c20·2d2d·2075·7365·6420·302e·3332·3934··|·--·used·0.3294 | ||
| 00010b20:·3 | 00010b20:·3031·7320·2863·7075·293b·2030·2e32·3430··01s·(cpu);·0.240 | ||
| 00010b30:·3 | 00010b30:·3031·3873·2028·7468·7265·6164·293b·2030··018s·(thread);·0 | ||
| 00010b40:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | 00010b40:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00010b50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010b50:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010b60:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00010b60:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00010b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010ba0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010ba0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| Offset 4292, 17 lines modified | Offset 4292, 17 lines modified | ||
| 00010c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010c40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00010c40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00010c50:·7c69·3331·203a·2074·696d·6520·6469·6d20··|i31·:·time·dim· | 00010c50:·7c69·3331·203a·2074·696d·6520·6469·6d20··|i31·:·time·dim· | ||
| 00010c60:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | 00010c60:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | ||
| 00010c70:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | 00010c70:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | ||
| 00010c80:·2c20·5374·7261·7465·6779·3d3e·4c65·784c··,·Strategy=>LexL | 00010c80:·2c20·5374·7261·7465·6779·3d3e·4c65·784c··,·Strategy=>LexL | ||
| 00010c90:·6172·6765·7374·2929·2020·2020·2020·7c0a··argest))······|. | 00010c90:·6172·6765·7374·2929·2020·2020·2020·7c0a··argest))······|. | ||
| 00010ca0:·7c20·2d2d·2075·7365·6420·302e·3233·3 | 00010ca0:·7c20·2d2d·2075·7365·6420·302e·3233·3331··|·--·used·0.2331 | ||
| 00010cb0:·3 | 00010cb0:·3973·2028·6370·7529·3b20·302e·3136·3530··9s·(cpu);·0.1650 | ||
| 00010cc0:·3 | 00010cc0:·3437·7320·2874·6872·6561·6429·3b20·3073··47s·(thread);·0s | ||
| 00010cd0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 00010cd0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00010ce0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010ce0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010cf0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00010cf0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00010d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010d30:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010d30:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| Offset 4317, 17 lines modified | Offset 4317, 17 lines modified | ||
| 00010dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00010dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00010de0:·7c69·3332·203a·2074·696d·6520·6469·6d20··|i32·:·time·dim· | 00010de0:·7c69·3332·203a·2074·696d·6520·6469·6d20··|i32·:·time·dim· | ||
| 00010df0:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | 00010df0:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | ||
| 00010e00:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | 00010e00:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | ||
| 00010e10:·2c20·5374·7261·7465·6779·3d3e·4752·6576··,·Strategy=>GRev | 00010e10:·2c20·5374·7261·7465·6779·3d3e·4752·6576··,·Strategy=>GRev | ||
| 00010e20:·4c65·7853·6d61·6c6c·6573·7429·2920·7c0a··LexSmallest))·|. | 00010e20:·4c65·7853·6d61·6c6c·6573·7429·2920·7c0a··LexSmallest))·|. | ||
| 00010e30:·7c20·2d2d·2075·7365·6420·302e·3233·373 | 00010e30:·7c20·2d2d·2075·7365·6420·302e·3233·3730··|·--·used·0.2370 | ||
| 00010e40:·3 | 00010e40:·3135·7320·2863·7075·293b·2030·2e31·3530··15s·(cpu);·0.150 | ||
| 00010e50:·3 | 00010e50:·3733·3973·2028·7468·7265·6164·293b·2030··739s·(thread);·0 | ||
| 00010e60:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | 00010e60:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00010e70:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010e70:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010e80:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00010e80:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00010e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010ec0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010ec0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| Offset 4342, 17 lines modified | Offset 4342, 17 lines modified | ||
| 00010f50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010f50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00010f60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00010f70:·7c69·3333·203a·2074·696d·6520·6469·6d20··|i33·:·time·dim· | 00010f70:·7c69·3333·203a·2074·696d·6520·6469·6d20··|i33·:·time·dim· | ||
| 00010f80:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | 00010f80:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | ||
| 00010f90:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | 00010f90:·696e·6f72·7328·382c·2036·2c20·4d2c·204a··inors(8,·6,·M,·J | ||
| 00010fa0:·2c20·2020·2020·2020·2020·2020·2020·2020··,··············· | 00010fa0:·2c20·2020·2020·2020·2020·2020·2020·2020··,··············· | ||
| 00010fb0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00010fb0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00010fc0:·7c20·2d2d·2075·7365·6420·302e·3 | 00010fc0:·7c20·2d2d·2075·7365·6420·302e·3139·3835··|·--·used·0.1985 | ||
| 00010fd0:·3 | 00010fd0:·3132·7320·2863·7075·293b·2030·2e31·3635··12s·(cpu);·0.165 | ||
| 00010fe0:·3 | 00010fe0:·3339·3873·2028·7468·7265·6164·293b·2030··398s·(thread);·0 | ||
| 00010ff0:·7320·2020·2020·2020·2020·2020·2020·2020··s··············· | 00010ff0:·7320·2020·2020·2020·2020·2020·2020·2020··s··············· | ||
| 00011000:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00011000:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00011010:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00011010:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00011020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011050:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00011050:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| Offset 4382, 17 lines modified | Offset 4382, 17 lines modified | ||
| 000111d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000111d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000111e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 000111e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 000111f0:·7c69·3334·203a·2074·696d·6520·6469·6d20··|i34·:·time·dim· | 000111f0:·7c69·3334·203a·2074·696d·6520·6469·6d20··|i34·:·time·dim· | ||
| 00011200:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | 00011200:·284a·202b·2063·686f·6f73·6547·6f6f·644d··(J·+·chooseGoodM | ||
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| 00011280:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00011280:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00011290:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00011290:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 000112a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000112a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000039c0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 000039c0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 000039d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000039d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000039e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000039e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00003a00:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00003a00:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 00003b90:·6520·4a3d·6669·7474·696e·6749·6465·616c··e·J=fittingIdeal | 00003b90:·6520·4a3d·6669·7474·696e·6749·6465·616c··e·J=fittingIdeal | ||
| 00003ba0:·2832·2d31·2c63·6f6b·6572·204b·3329·3b20··(2-1,coker·K3);· | 00003ba0:·2832·2d31·2c63·6f6b·6572·204b·3329·3b20··(2-1,coker·K3);· | ||
| 00003bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003bc0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00003bc0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
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| 00003 | 00003be0:·3538·3936·3773·2028·6370·7529·3b20·302e··58967s·(cpu);·0. | ||
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| 00003c10:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00003c10:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00003c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·2020·2020·207c·0a7c·6f31·3620·3a20·4964·······|.|o16·:·Id | 00003c60:·2020·2020·207c·0a7c·6f31·3620·3a20·4964·······|.|o16·:·Id | ||
| 00003c70:·6561·6c20·6f66·2052·2020·2020·2020·2020··eal·of·R········ | 00003c70:·6561·6c20·6f66·2052·2020·2020·2020·2020··eal·of·R········ |
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| 00005910:·2069·6e74·3332·7c0a·2b2d·2d2d·2d2d·2d2d···int32|.+------- | 00005910:·2069·6e74·3332·7c0a·2b2d·2d2d·2d2d·2d2d···int32|.+------- | ||
| 00005920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005930:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a··---------+.|i2·: | 00005930:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a··---------+.|i2·: | ||
| 00005940:·2070·7472·203d·2061·6464·7265·7373·2078···ptr·=·address·x | 00005940:·2070·7472·203d·2061·6464·7265·7373·2078···ptr·=·address·x | ||
| 00005950:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00005950:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00005960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005970:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00005970:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00005980:·0a7c·6f32·203d·2030·7837·66 | 00005980:·0a7c·6f32·203d·2030·7837·6636·3965·3134··.|o2·=·0x7f69e14 | ||
| 00005990:· | 00005990:·3537·6138·3020·2020·2020·2020·2020·2020··57a80··········· | ||
| 000059a0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 000059a0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 000059b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000059b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000059c0:·2020·2020·207c·0a7c·6f32·203a·2050·6f69·······|.|o2·:·Poi | 000059c0:·2020·2020·207c·0a7c·6f32·203a·2050·6f69·······|.|o2·:·Poi | ||
| 000059d0:·6e74·6572·2020·2020·2020·2020·2020·2020··nter············ | 000059d0:·6e74·6572·2020·2020·2020·2020·2020·2020··nter············ | ||
| 000059e0:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | 000059e0:·2020·2020·2020·2020·7c0a·2b2d·2d2d·2d2d··········|.+----- | ||
| 000059f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000059f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933··-----------+.|i3 | 00005a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933··-----------+.|i3 | ||
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| 000060e0:·7479·7065·2073·7472·7563·740a·7573·6564··type·struct.used | 000060e0:·7479·7065·2073·7472·7563·740a·7573·6564··type·struct.used | ||
| 000060f0:·2062·7920·6c69·6266·6669·2074·6f20·6964···by·libffi·to·id | 000060f0:·2062·7920·6c69·6266·6669·2074·6f20·6964···by·libffi·to·id | ||
| 00006100:·656e·7469·6679·2074·6865·2074·7970·652e··entify·the·type. | 00006100:·656e·7469·6679·2074·6865·2074·7970·652e··entify·the·type. | ||
| 00006110:·0a0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··..+------------- | 00006110:·0a0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··..+------------- | ||
| 00006120:·2d2d·2d2d·2d2d·2b0a·7c69·3120·3a20·6164··------+.|i1·:·ad | 00006120:·2d2d·2d2d·2d2d·2b0a·7c69·3120·3a20·6164··------+.|i1·:·ad | ||
| 00006130:·6472·6573·7320·696e·7420·2020·7c0a·7c20··dress·int···|.|· | 00006130:·6472·6573·7320·696e·7420·2020·7c0a·7c20··dress·int···|.|· | ||
| 00006140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00006160:·33 | 00006160:·3334·6436·3831·6530·7c0a·7c20·2020·2020··34d681e0|.|····· | ||
| 00006170:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00006170:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00006180:·7c6f·3120·3a20·506f·696e·7465·7220·2020··|o1·:·Pointer··· | 00006180:·7c6f·3120·3a20·506f·696e·7465·7220·2020··|o1·:·Pointer··· | ||
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| 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·0a49·6620··----------+..If· | 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·0a49·6620··----------+..If· | ||
| 000061b0:·7820·6973·2061·2066·6f72·6569·676e·206f··x·is·a·foreign·o | 000061b0:·7820·6973·2061·2066·6f72·6569·676e·206f··x·is·a·foreign·o | ||
| 000061c0:·626a·6563·742c·2074·6865·6e20·7468·6973··bject,·then·this | 000061c0:·626a·6563·742c·2074·6865·6e20·7468·6973··bject,·then·this | ||
| 000061d0:·2072·6574·7572·6e73·2074·6865·2061·6464···returns·the·add | 000061d0:·2072·6574·7572·6e73·2074·6865·2061·6464···returns·the·add | ||
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| 00006200:·6c69·6b65·2074·6865·2026·2022·6164·6472··like·the·&·"addr | 00006200:·6c69·6b65·2074·6865·2026·2022·6164·6472··like·the·&·"addr | ||
| 00006210:·6573·732d·6f66·2220·6f70·6572·6174·6f72··ess-of"·operator | 00006210:·6573·732d·6f66·2220·6f70·6572·6174·6f72··ess-of"·operator | ||
| 00006220:·2069·6e20·432e·0a0a·2b2d·2d2d·2d2d·2d2d···in·C...+------- | 00006220:·2069·6e20·432e·0a0a·2b2d·2d2d·2d2d·2d2d···in·C...+------- | ||
| 00006230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00006230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00006240:·3220·3a20·6164·6472·6573·7320·696e·7420··2·:·address·int· | 00006240:·3220·3a20·6164·6472·6573·7320·696e·7420··2·:·address·int· | ||
| 00006250:·3520·7c0a·7c20·2020·2020·2020·2020·2020··5·|.|··········· | 00006250:·3520·7c0a·7c20·2020·2020·2020·2020·2020··5·|.|··········· | ||
| 00006260:·2020·2020·2020·2020·7c0a·7c6f·3220·3d20··········|.|o2·=· | 00006260:·2020·2020·2020·2020·7c0a·7c6f·3220·3d20··········|.|o2·=· | ||
| 00006270:·3078·3766·3 | 00006270:·3078·3766·3933·3937·3461·3139·3330·7c0a··0x7f93974a1930|. | ||
| 00006280:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00006280:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00006290:·2020·2020·7c0a·7c6f·3220·3a20·506f·696e······|.|o2·:·Poin | 00006290:·2020·2020·7c0a·7c6f·3220·3a20·506f·696e······|.|o2·:·Poin | ||
| 000062a0:·7465·7220·2020·2020·2020·7c0a·2b2d·2d2d··ter·······|.+--- | 000062a0:·7465·7220·2020·2020·2020·7c0a·2b2d·2d2d··ter·······|.+--- | ||
| 000062b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000062b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000062c0:·2b0a·0a57·6179·7320·746f·2075·7365·2061··+..Ways·to·use·a | 000062c0:·2b0a·0a57·6179·7320·746f·2075·7365·2061··+..Ways·to·use·a | ||
| 000062d0:·6464·7265·7373·203a·0a3d·3d3d·3d3d·3d3d··ddress·:.======= | 000062d0:·6464·7265·7373·203a·0a3d·3d3d·3d3d·3d3d··ddress·:.======= | ||
| 000062e0:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·0a0a··==============.. | 000062e0:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·0a0a··==============.. | ||
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| 0000a160:·203d·206d·616c·6c6f·6320·3820·2020·2020···=·malloc·8····· | 0000a160:·203d·206d·616c·6c6f·6320·3820·2020·2020···=·malloc·8····· | ||
| 0000a170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 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·················· | ||
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| 0000e320:·203d·207b·3078·3766·6 | 0000e320:·203d·207b·3078·3766·6461·6532·3438·3231···=·{0x7fdae24821 | ||
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| 0000fda0:·207b·6164·6472·6573·7320·696e·7420·302c···{address·int·0, | 0000fda0:·207b·6164·6472·6573·7320·696e·7420·302c···{address·int·0, | ||
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| 00003090:·2020·7c0a·7c6f·3520·3d20·2f74·6d70·2f4d····|.|o5·=·/tmp/M | 00003090:·2020·7c0a·7c6f·3520·3d20·2f74·6d70·2f4d····|.|o5·=·/tmp/M | ||
| 000030a0:·322d·3 | 000030a0:·322d·3231·3338·3838·342d·302f·3020·2020··2-2138884-0/0··· | ||
| 000030b0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000030b0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 000030c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000030d0:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | 000030d0:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 000030e0:·3520·3a20·4669·6c65·2020·2020·2020·2020··5·:·File········ | 000030e0:·3520·3a20·4669·6c65·2020·2020·2020·2020··5·:·File········ | ||
| 000030f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003100:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | 00003100:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
| 00003110:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003110:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00009cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009cf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00009d00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00009d10:·0a7c·6932·3720·3a20·7469·6d65·206e·756d··.|i27·:·time·num | 00009d10:·0a7c·6932·3720·3a20·7469·6d65·206e·756d··.|i27·:·time·num | ||
| 00009d20:·6572·6963·2066·7074·2866·2c20·4465·7074··eric·fpt(f,·Dept | 00009d20:·6572·6963·2066·7074·2866·2c20·4465·7074··eric·fpt(f,·Dept | ||
| 00009d30:·684f·6653·6561·7263·6820·3d3e·2033·2c20··hOfSearch·=>·3,· | 00009d30:·684f·6653·6561·7263·6820·3d3e·2033·2c20··hOfSearch·=>·3,· | ||
| 00009d40:·4669·6e61·6c41·7474·656d·7074·203d·3e20··FinalAttempt·=>· | 00009d40:·4669·6e61·6c41·7474·656d·7074·203d·3e20··FinalAttempt·=>· | ||
| 00009d50:·7472·7565·297c·0a7c·202d·2d20·7573·6564··true)|.|·--·used | 00009d50:·7472·7565·297c·0a7c·202d·2d20·7573·6564··true)|.|·--·used | ||
| 00009d60:·2031·2e37·3 | 00009d60:·2031·2e37·3731·3639·7320·2863·7075·293b···1.77169s·(cpu); | ||
| 00009d70:·2031·2e3 | 00009d70:·2031·2e30·3339·3731·7320·2874·6872·6561···1.03971s·(threa | ||
| 00009d80:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | 00009d80:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 00009d90:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00009d90:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00009da0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009da0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009db0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009db0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·207c·0a7c·6f32·3720·3d20·7b2e·3134·3230···|.|o27·=·{.1420 | 00009de0:·207c·0a7c·6f32·3720·3d20·7b2e·3134·3230···|.|o27·=·{.1420 | ||
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| 00009ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009ed0:·2d2d·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·2d2b·0a7c·6932·3820··---------+.|i28· | 00009ef0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3820··---------+.|i28· | ||
| 00009f00:·3a20·7469·6d65·2066·7074·2866·2c20·4465··:·time·fpt(f,·De | 00009f00:·3a20·7469·6d65·2066·7074·2866·2c20·4465··:·time·fpt(f,·De | ||
| 00009f10:·7074·684f·6653·6561·7263·6820·3d3e·2033··pthOfSearch·=>·3 | 00009f10:·7074·684f·6653·6561·7263·6820·3d3e·2033··pthOfSearch·=>·3 | ||
| 00009f20:·2c20·4174·7465·6d70·7473·203d·3e20·3729··,·Attempts·=>·7) | 00009f20:·2c20·4174·7465·6d70·7473·203d·3e20·3729··,·Attempts·=>·7) | ||
| 00009f30:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00009f30:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00009f40:·0a7c·202d·2d20·7573·6564·2031·2e30·3 | 00009f40:·0a7c·202d·2d20·7573·6564·2031·2e30·3032··.|·--·used·1.002 | ||
| 00009f50:·3 | 00009f50:·3134·7320·2863·7075·293b·2030·2e36·3337··14s·(cpu);·0.637 | ||
| 00009f60:·3 | 00009f60:·3936·3973·2028·7468·7265·6164·293b·2030··969s·(thread);·0 | ||
| 00009f70:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | 00009f70:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00009f80:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00009f80:·2020·2020·207c·0a7c·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:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009fc0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00009fc0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00009fd0:·2020·2020·3120·2020·2020·2020·2020·2020······1··········· | 00009fd0:·2020·2020·3120·2020·2020·2020·2020·2020······1··········· | ||
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| 0000a150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0000a160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0000a170:·0a7c·6932·3920·3a20·7469·6d65·2066·7074··.|i29·:·time·fpt | 0000a170:·0a7c·6932·3920·3a20·7469·6d65·2066·7074··.|i29·:·time·fpt | ||
| 0000a180:·2866·2c20·4465·7074·684f·6653·6561·7263··(f,·DepthOfSearc | 0000a180:·2866·2c20·4465·7074·684f·6653·6561·7263··(f,·DepthOfSearc | ||
| 0000a190:·6820·3d3e·2034·2920·2020·2020·2020·2020··h·=>·4)········· | 0000a190:·6820·3d3e·2034·2920·2020·2020·2020·2020··h·=>·4)········· | ||
| 0000a1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a1b0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 0000a1b0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 0000a1c0:·2030·2e38·3 | 0000a1c0:·2030·2e38·3435·3736·3673·2028·6370·7529···0.845766s·(cpu) | ||
| 0000a1d0:·3b20·302e·353 | 0000a1d0:·3b20·302e·3534·3137·3332·7320·2874·6872··;·0.541732s·(thr | ||
| 0000a1e0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | 0000a1e0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 0000a1f0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 0000a1f0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 0000a200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·207c·0a7c·2020·2020·2020·3120·2020·2020···|.|······1····· | 0000a240:·207c·0a7c·2020·2020·2020·3120·2020·2020···|.|······1····· | ||
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| 0000d940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d940:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d960:·2d2d·2d2b·0a7c·6931·3520·3a20·7469·6d65··---+.|i15·:·time | 0000d960:·2d2d·2d2b·0a7c·6931·3520·3a20·7469·6d65··---+.|i15·:·time | ||
| 0000d970:·2066·726f·6265·6e69·7573·4e75·2833·2c20···frobeniusNu(3,· | 0000d970:·2066·726f·6265·6e69·7573·4e75·2833·2c20···frobeniusNu(3,· | ||
| 0000d980:·6629·2020·2020·2020·2020·2020·2020·2020··f)·············· | 0000d980:·6629·2020·2020·2020·2020·2020·2020·2020··f)·············· | ||
| 0000d990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d9a0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 0000d9a0:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 0000d9b0:·303 | 0000d9b0:·3034·3134·3135·3473·2028·6370·7529·3b20··0414154s·(cpu);· | ||
| 0000d9c0:·302e·3030·3 | 0000d9c0:·302e·3030·3337·3633·3234·7320·2874·6872··0.00376324s·(thr | ||
| 0000d9d0:·6561·6429·3b20·3073·2028·6763·2920·207c··ead);·0s·(gc)··| | 0000d9d0:·6561·6429·3b20·3073·2028·6763·2920·207c··ead);·0s·(gc)··| | ||
| 0000d9e0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 0000d9e0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 0000d9f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d9f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000da00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000da00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000da10:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000da10:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000da20:·6f31·3520·3d20·3337·3536·2020·2020·2020··o15·=·3756······ | 0000da20:·6f31·3520·3d20·3337·3536·2020·2020·2020··o15·=·3756······ | ||
| 0000da30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000da30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000da70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000da70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000da80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000da80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000da90:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3620··---------+.|i16· | 0000da90:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3620··---------+.|i16· | ||
| 0000daa0:·3a20·7469·6d65·2066·726f·6265·6e69·7573··:·time·frobenius | 0000daa0:·3a20·7469·6d65·2066·726f·6265·6e69·7573··:·time·frobenius | ||
| 0000dab0:·4e75·2833·2c20·662c·2055·7365·5370·6563··Nu(3,·f,·UseSpec | 0000dab0:·4e75·2833·2c20·662c·2055·7365·5370·6563··Nu(3,·f,·UseSpec | ||
| 0000dac0:·6961·6c41·6c67·6f72·6974·686d·7320·3d3e··ialAlgorithms·=> | 0000dac0:·6961·6c41·6c67·6f72·6974·686d·7320·3d3e··ialAlgorithms·=> | ||
| 0000dad0:·2066·616c·7365·297c·0a7c·202d·2d20·7573···false)|.|·--·us | 0000dad0:·2066·616c·7365·297c·0a7c·202d·2d20·7573···false)|.|·--·us | ||
| 0000dae0:·6564·2030·2e33·333 | 0000dae0:·6564·2030·2e33·3333·3637·3373·2028·6370··ed·0.333673s·(cp | ||
| 0000daf0:·7529·3b20·302e·323 | 0000daf0:·7529·3b20·302e·3231·3435·3433·7320·2874··u);·0.214543s·(t | ||
| 0000db00:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 0000db00:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 0000db10:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 0000db10:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 0000db20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000db30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000db40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000db50:·2020·207c·0a7c·6f31·3620·3d20·3337·3536·····|.|o16·=·3756 | 0000db50:·2020·207c·0a7c·6f31·3620·3d20·3337·3536·····|.|o16·=·3756 | ||
| 0000db60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000db60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e1b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e1b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e1c0:·2d2d·2d2b·0a7c·6931·3920·3a20·7469·6d65··---+.|i19·:·time | 0000e1c0:·2d2d·2d2b·0a7c·6931·3920·3a20·7469·6d65··---+.|i19·:·time | ||
| 0000e1d0:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | 0000e1d0:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | ||
| 0000e1e0:·6629·202d·2d20·436f·6e74·6169·6e6d·656e··f)·--·Containmen | 0000e1e0:·6629·202d·2d20·436f·6e74·6169·6e6d·656e··f)·--·Containmen | ||
| 0000e1f0:·7454·6573·7420·6973·2073·6574·2074·6f20··tTest·is·set·to· | 0000e1f0:·7454·6573·7420·6973·2073·6574·2074·6f20··tTest·is·set·to· | ||
| 0000e200:·4672·6f62·656e·6975·7352·6f6f·742c·2062··FrobeniusRoot,·b | 0000e200:·4672·6f62·656e·6975·7352·6f6f·742c·2062··FrobeniusRoot,·b | ||
| 0000e210:·7920·207c·0a7c·202d·2d20·7573·6564·2030··y··|.|·--·used·0 | 0000e210:·7920·207c·0a7c·202d·2d20·7573·6564·2030··y··|.|·--·used·0 | ||
| 0000e220:·2e32·3 | 0000e220:·2e32·3430·3835·3173·2028·6370·7529·3b20··.240851s·(cpu);· | ||
| 0000e230:·302e·313 | 0000e230:·302e·3136·3035·3434·7320·2874·6872·6561··0.160544s·(threa | ||
| 0000e240:·293b | 0000e240:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 0000e250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e260:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0000e260:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0000e270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·2020·207c·0a7c·6f31·3920·3d20·3439·3920·····|.|o19·=·499· | 0000e2b0:·2020·207c·0a7c·6f31·3920·3d20·3439·3920·····|.|o19·=·499· | ||
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| 0000e3f0:·2d2d·2d2b·0a7c·6932·3020·3a20·7469·6d65··---+.|i20·:·time | 0000e3f0:·2d2d·2d2b·0a7c·6932·3020·3a20·7469·6d65··---+.|i20·:·time | ||
| 0000e400:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | 0000e400:·2066·726f·6265·6e69·7573·4e75·2834·2c20···frobeniusNu(4,· | ||
| 0000e410:·662c·2043·6f6e·7461·696e·6d65·6e74·5465··f,·ContainmentTe | 0000e410:·662c·2043·6f6e·7461·696e·6d65·6e74·5465··f,·ContainmentTe | ||
| 0000e420:·7374·203d·3e20·5374·616e·6461·7264·506f··st·=>·StandardPo | 0000e420:·7374·203d·3e20·5374·616e·6461·7264·506f··st·=>·StandardPo | ||
| 0000e430:·7765·7229·2020·2020·2020·2020·2020·2020··wer)············ | 0000e430:·7765·7229·2020·2020·2020·2020·2020·2020··wer)············ | ||
| 0000e440:·2020·207c·0a7c·202d·2d20·7573·6564·2031·····|.|·--·used·1 | 0000e440:·2020·207c·0a7c·202d·2d20·7573·6564·2031·····|.|·--·used·1 | ||
| 0000e450:·2e30·3 | 0000e450:·2e30·3232·3039·7320·2863·7075·293b·2030··.02209s·(cpu);·0 | ||
| 0000e460:·2e3 | 0000e460:·2e38·3536·3435·7320·2874·6872·6561·6429··.85645s·(thread) | ||
| 0000e470:· | 0000e470:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 0000e480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e490:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 0000e490:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0000e4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e4b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e4b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·2020·207c·0a7c·6f32·3020·3d20·3439·3920·····|.|o20·=·499· | 0000e4e0:·2020·207c·0a7c·6f32·3020·3d20·3439·3920·····|.|o20·=·499· | ||
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| 0000eee0:·2d2d·2b0a·7c69·3237·203a·2074·696d·6520··--+.|i27·:·time· | 0000eee0:·2d2d·2b0a·7c69·3237·203a·2074·696d·6520··--+.|i27·:·time· | ||
| 0000eef0:·6672·6f62·656e·6975·734e·7528·352c·2066··frobeniusNu(5,·f | 0000eef0:·6672·6f62·656e·6975·734e·7528·352c·2066··frobeniusNu(5,·f | ||
| 0000ef00:·2920·2d2d·2075·7365·7320·6269·6e61·7279··)·--·uses·binary | 0000ef00:·2920·2d2d·2075·7365·7320·6269·6e61·7279··)·--·uses·binary | ||
| 0000ef10:·2073·6561·7263·6820·2864·6566·6175·6c74···search·(default | 0000ef10:·2073·6561·7263·6820·2864·6566·6175·6c74···search·(default | ||
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| 00042150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00042150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00042160:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3237··----------+.|i27 | 00042160:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3237··----------+.|i27 | ||
| 00042170:·203a·2074·696d·6520·4320·3d20·6f72·6269···:·time·C·=·orbi | 00042170:·203a·2074·696d·6520·4320·3d20·6f72·6269···:·time·C·=·orbi | ||
| 00042180:·7443·6c6f·7375·7265·2858·2c4d·6174·2920··tClosure(X,Mat)· | 00042180:·7443·6c6f·7375·7265·2858·2c4d·6174·2920··tClosure(X,Mat)· | ||
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| 000421b0:·2075·7365·6420·302e·3536·3 | 000421b0:·2075·7365·6420·302e·3536·3834·3232·7320···used·0.568422s· | ||
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| 00042230:·203d·2061·6e20·2265·7175·6976·6172·6961···=·an·"equivaria | 00042230:·203d·2061·6e20·2265·7175·6976·6172·6961···=·an·"equivaria | ||
| 00042240:·6e74·204b·2d63·6c61·7373·2220·6f6e·2061··nt·K-class"·on·a | 00042240:·6e74·204b·2d63·6c61·7373·2220·6f6e·2061··nt·K-class"·on·a | ||
| 00042250:·2047·4b4d·2076·6172·6965·7479·2020·2020···GKM·variety···· | 00042250:·2047·4b4d·2076·6172·6965·7479·2020·2020···GKM·variety···· | ||
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| 00042310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00042310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00042320:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3238··----------+.|i28 | 00042320:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3238··----------+.|i28 | ||
| 00042330:·203a·2074·696d·6520·4320·3d20·6f72·6269···:·time·C·=·orbi | 00042330:·203a·2074·696d·6520·4320·3d20·6f72·6269···:·time·C·=·orbi | ||
| 00042340:·7443·6c6f·7375·7265·2858·2c4d·6174·2c20··tClosure(X,Mat,· | 00042340:·7443·6c6f·7375·7265·2858·2c4d·6174·2c20··tClosure(X,Mat,· | ||
| 00042350:·5252·4546·4d65·7468·6f64·203d·3e20·7472··RREFMethod·=>·tr | 00042350:·5252·4546·4d65·7468·6f64·203d·3e20·7472··RREFMethod·=>·tr | ||
| 00042360:·7565·2920·2020·2020·2020·7c0a·7c20·2d2d··ue)·······|.|·-- | 00042360:·7565·2920·2020·2020·2020·7c0a·7c20·2d2d··ue)·······|.|·-- | ||
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| 00042380:·6370·7529·3b20·302e·3839·3734·3031·7320··cpu);·0.897401s· | |||
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| 00042390:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | |||
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| 000423e0:·2020·2020·2020·2020·2020·7c0a·7c6f·3238············|.|o28 | 000423e0:·2020·2020·2020·2020·2020·7c0a·7c6f·3238············|.|o28 | ||
| 000423f0:·203d·2061·6e20·2265·7175·6976·6172·6961···=·an·"equivaria | 000423f0:·203d·2061·6e20·2265·7175·6976·6172·6961···=·an·"equivaria | ||
| 00042400:·6e74·204b·2d63·6c61·7373·2220·6f6e·2061··nt·K-class"·on·a | 00042400:·6e74·204b·2d63·6c61·7373·2220·6f6e·2061··nt·K-class"·on·a | ||
| 00042410:·2047·4b4d·2076·6172·6965·7479·2020·2020···GKM·variety···· | 00042410:·2047·4b4d·2076·6172·6965·7479·2020·2020···GKM·variety···· |
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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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| 00000d60:·3 | 00000d60:·3138·3139·2073·6563·6f6e·6473·2065·6c61··1819·seconds·ela | ||
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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 | ||
| 00000fc0:·6e65·7257·616c·6b28·6762·2049·312c·2052··nerWalk(gb·I1,·R | 00000fc0:·6e65·7257·616c·6b28·6762·2049·312c·2052··nerWalk(gb·I1,·R | ||
| 00000fd0:·3229·2020·2020·2020·2020·2020·2020·2020··2)·············· | 00000fd0:·3229·2020·2020·2020·2020·2020·2020·2020··2)·············· | ||
| 00000fe0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00000fe0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00000ff0:·7c20·2d2d·203 | 00000ff0:·7c20·2d2d·2031·2e35·3635·3635·2073·6563··|·--·1.56565·sec | ||
| 00001000:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | 00001000:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | ||
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| 0000ef10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ef10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ef20:·2d2d·2d2d·2b0a·7c69·3620·3a20·6e65·744c··----+.|i6·:·netL | 0000ef20:·2d2d·2d2d·2b0a·7c69·3620·3a20·6e65·744c··----+.|i6·:·netL | ||
| 0000ef30:·6973·7420·6373·734c·6561·6454·6572·6d28··ist·cssLeadTerm( | 0000ef30:·6973·7420·6373·734c·6561·6454·6572·6d28··ist·cssLeadTerm( | ||
| 0000ef40:·4862·6574·612c·2077·2920·2020·2020·2020··Hbeta,·w)······· | 0000ef40:·4862·6574·612c·2077·2920·2020·2020·2020··Hbeta,·w)······· | ||
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| 0000ef80:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | 0000ef80:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | ||
| 0000ef90:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 0000ef90:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
| 0000efa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000efa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000efd0:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | 0000efd0:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | ||
| 0000efe0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 0000efe0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
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| 0000f020:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | 0000f020:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | ||
| 0000f030:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 0000f030:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
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| 0000f070:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | 0000f070:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | ||
| 0000f080:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 0000f080:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
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| 0000f0b0:·2020·2020·7c0a·7c20·2d2d·203 | 0000f0b0:·2020·2020·7c0a·7c20·2d2d·2034·2e34·3137······|.|·--·4.417 | ||
| 0000f0c0:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | 0000f0c0:·652d·3036·2073·6563·6f6e·6473·2065·6c61··e-06·seconds·ela | ||
| 0000f0d0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | 0000f0d0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
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| 0000f100:·2020·2020·7c0a·7c57·6172·6e69·6e67·3a20······|.|Warning:· | 0000f100:·2020·2020·7c0a·7c57·6172·6e69·6e67·3a20······|.|Warning:· | ||
| 0000f110:·2046·3420·416c·676f·7269·7468·6d20·6e6f···F4·Algorithm·no | 0000f110:·2046·3420·416c·676f·7269·7468·6d20·6e6f···F4·Algorithm·no | ||
| 0000f120:·7420·6176·6169·6c61·626c·6520·6f76·6572··t·available·over | 0000f120:·7420·6176·6169·6c61·626c·6520·6f76·6572··t·available·over | ||
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| 00014d50:·2073·6f6c·7665·4672·6f62·656e·6975·7349···solveFrobeniusI | 00014d50:·2073·6f6c·7665·4672·6f62·656e·6975·7349···solveFrobeniusI | ||
| 00014d60:·6465·616c·2049·2020·2020·2020·2020·2020··deal·I·········· | 00014d60:·6465·616c·2049·2020·2020·2020·2020·2020··deal·I·········· | ||
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| 00014da0:·3 | 00014da0:·352e·3131·3865·2d30·3620·7365·636f·6e64··5.118e-06·second | ||
| 00014db0:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00014db0:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
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| 00014de0:·2020·2020·2020·2020·207c·0a7c·5761·726e···········|.|Warn | 00014de0:·2020·2020·2020·2020·207c·0a7c·5761·726e···········|.|Warn | ||
| 00014df0:·696e·673a·2020·4634·2041·6c67·6f72·6974··ing:··F4·Algorit | 00014df0:·696e·673a·2020·4634·2041·6c67·6f72·6974··ing:··F4·Algorit | ||
| 00014e00:·686d·206e·6f74·2061·7661·696c·6162·6c65··hm·not·available | 00014e00:·686d·206e·6f74·2061·7661·696c·6162·6c65··hm·not·available | ||
| 00014e10:·206f·7665·7220·6375·7272·656e·7420·636f···over·current·co | 00014e10:·206f·7665·7220·6375·7272·656e·7420·636f···over·current·co | ||
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| 000154c0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | 000154c0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | ||
| 000154d0:·2073·6f6c·7665·4672·6f62·656e·6975·7349···solveFrobeniusI | 000154d0:·2073·6f6c·7665·4672·6f62·656e·6975·7349···solveFrobeniusI | ||
| 000154e0:·6465·616c·2849·2c20·5729·2020·2020·2020··deal(I,·W)······ | 000154e0:·6465·616c·2849·2c20·5729·2020·2020·2020··deal(I,·W)······ | ||
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| 00015520:·342e·3 | 00015520:·342e·3732·3765·2d30·3620·7365·636f·6e64··4.727e-06·second | ||
| 00015530:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00015530:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
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| 00015560:·2020·2020·2020·2020·207c·0a7c·5761·726e···········|.|Warn | 00015560:·2020·2020·2020·2020·207c·0a7c·5761·726e···········|.|Warn | ||
| 00015570:·696e·673a·2020·4634·2041·6c67·6f72·6974··ing:··F4·Algorit | 00015570:·696e·673a·2020·4634·2041·6c67·6f72·6974··ing:··F4·Algorit | ||
| 00015580:·686d·206e·6f74·2061·7661·696c·6162·6c65··hm·not·available | 00015580:·686d·206e·6f74·2061·7661·696c·6162·6c65··hm·not·available | ||
| 00015590:·206f·7665·7220·6375·7272·656e·7420·636f···over·current·co | 00015590:·206f·7665·7220·6375·7272·656e·7420·636f···over·current·co |
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| 00025970:·4127·272c·6d27·2729·203d·2065·756c·6572··A'',m'')·=·euler | 00025970:·4127·272c·6d27·2729·203d·2065·756c·6572··A'',m'')·=·euler | ||
| 00025980:·5265·7374·7269·6374·696f·6e28·412c·6d2c··Restriction(A,m, | 00025980:·5265·7374·7269·6374·696f·6e28·412c·6d2c··Restriction(A,m, | ||
| 00025990:·3329·2020·7c0a·7c20·2020·2020·2020·2020··3)··|.|········· | 00025990:·3329·2020·7c0a·7c20·2020·2020·2020·2020··3)··|.|········· | ||
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| 000259d0:·2 | 000259d0:·2c20·7a2c·2079·7d2c·207b·312c·2032·2c20··,·z,·y},·{1,·2,· | ||
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| 00026000:·203d·2028·7b78·202 | 00026000:·203d·2028·7b78·202c·2078·2020·2b20·7820···=·({x·,·x··+·x· | ||
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| 000260d0:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 000260d0:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
| 000260e0:·3320·3a20·5365·7175·656e·6365·2020·2020··3·:·Sequence···· | 000260e0:·3320·3a20·5365·7175·656e·6365·2020·2020··3·:·Sequence···· | ||
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| 00044c90:·2020·2020·7c0a·7c6f·3320·3a20·4879·7065······|.|o3·:·Hype | 00044c90:·2020·2020·7c0a·7c6f·3320·3a20·4879·7065······|.|o3·:·Hype |
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| 000117a0:·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20·7469··------+.|i4·:·ti | 000117a0:·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20·7469··------+.|i4·:·ti | ||
| 000117b0:·6d65·2052·2720·3d20·696e·7465·6772·616c··me·R'·=·integral | 000117b0:·6d65·2052·2720·3d20·696e·7465·6772·616c··me·R'·=·integral | ||
| 000117c0:·436c·6f73·7572·6520·5220·2020·2020·2020··Closure·R······· | 000117c0:·436c·6f73·7572·6520·5220·2020·2020·2020··Closure·R······· | ||
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| 00011800:·6420·302e·3 | 00011800:·6420·302e·3636·3532·3735·7320·2863·7075··d·0.665275s·(cpu | ||
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| 00011890:·2020·2020·2020·7c0a·7c6f·3420·3d20·5227········|.|o4·=·R' | 00011890:·2020·2020·2020·7c0a·7c6f·3420·3d20·5227········|.|o4·=·R' | ||
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| 00013640:·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a·2074··------+.|i10·:·t | 00013640:·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a·2074··------+.|i10·:·t | ||
| 00013650:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | 00013650:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | ||
| 00013660:·6c43·6c6f·7375·7265·2852·2c20·5374·7261··lClosure(R,·Stra | 00013660:·6c43·6c6f·7375·7265·2852·2c20·5374·7261··lClosure(R,·Stra | ||
| 00013670:·7465·6779·203d·3e20·5261·6469·6361·6c29··tegy·=>·Radical) | 00013670:·7465·6779·203d·3e20·5261·6469·6361·6c29··tegy·=>·Radical) | ||
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| 000136a0:·6420·302e·3 | 000136a0:·6420·302e·3730·3136·3433·7320·2863·7075··d·0.701643s·(cpu | ||
| 000136b0:·293b·2030·2e34·3 | 000136b0:·293b·2030·2e34·3334·3931·3673·2028·7468··);·0.434916s·(th | ||
| 000136c0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 000136c0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
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| 000154e0:·2d2d·2d2d·2d2d·2b0a·7c69·3136·203a·2074··------+.|i16·:·t | 000154e0:·2d2d·2d2d·2d2d·2b0a·7c69·3136·203a·2074··------+.|i16·:·t | ||
| 000154f0:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | 000154f0:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | ||
| 00015500:·6c43·6c6f·7375·7265·2852·2c20·5374·7261··lClosure(R,·Stra | 00015500:·6c43·6c6f·7375·7265·2852·2c20·5374·7261··lClosure(R,·Stra | ||
| 00015510:·7465·6779·203d·3e20·416c·6c43·6f64·696d··tegy·=>·AllCodim | 00015510:·7465·6779·203d·3e20·416c·6c43·6f64·696d··tegy·=>·AllCodim | ||
| 00015520:·656e·7369·6f6e·7329·2020·2020·2020·2020··ensions)········ | 00015520:·656e·7369·6f6e·7329·2020·2020·2020·2020··ensions)········ | ||
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| 00015540:·6420·302e·3638·3 | 00015540:·6420·302e·3638·3732·3535·7320·2863·7075··d·0.687255s·(cpu | ||
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| 00015560:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 00015560:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
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| 000170a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000170a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000170b0:·2d2d·2d2d·2d2d·2b0a·7c69·3231·203a·2074··------+.|i21·:·t | 000170b0:·2d2d·2d2d·2d2d·2b0a·7c69·3231·203a·2074··------+.|i21·:·t | ||
| 000170c0:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | 000170c0:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | ||
| 000170d0:·6c43·6c6f·7375·7265·2852·2c20·5374·7261··lClosure(R,·Stra | 000170d0:·6c43·6c6f·7375·7265·2852·2c20·5374·7261··lClosure(R,·Stra | ||
| 000170e0:·7465·6779·203d·3e20·5369·6d70·6c69·6679··tegy·=>·Simplify | 000170e0:·7465·6779·203d·3e20·5369·6d70·6c69·6679··tegy·=>·Simplify | ||
| 000170f0:·4672·6163·7469·6f6e·7329·2020·2020·2020··Fractions)······ | 000170f0:·4672·6163·7469·6f6e·7329·2020·2020·2020··Fractions)······ | ||
| 00017100:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00017100:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00017110:·6420·302e·373 | 00017110:·6420·302e·3737·3033·3532·7320·2863·7075··d·0.770352s·(cpu | ||
| 00017120:·293b·2030·2e34·3 | 00017120:·293b·2030·2e34·3830·3233·7320·2874·6872··);·0.48023s·(thr | ||
| 00017130:· | 00017130:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 00017140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017150:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00017150:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00017160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017190:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000171a0:·2020·2020·2020·7c0a·7c6f·3231·203d·2052········|.|o21·=·R | 000171a0:·2020·2020·2020·7c0a·7c6f·3231·203d·2052········|.|o21·=·R | ||
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| 00018c70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00018c70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00018c80:·2d2d·2d2d·2d2d·2b0a·7c69·3236·203a·2074··------+.|i26·:·t | 00018c80:·2d2d·2d2d·2d2d·2b0a·7c69·3236·203a·2074··------+.|i26·:·t | ||
| 00018c90:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | 00018c90:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | ||
| 00018ca0:·6c43·6c6f·7375·7265·2028·522c·2053·7472··lClosure·(R,·Str | 00018ca0:·6c43·6c6f·7375·7265·2028·522c·2053·7472··lClosure·(R,·Str | ||
| 00018cb0:·6174·6567·7920·3d3e·2052·6164·6963·616c··ategy·=>·Radical | 00018cb0:·6174·6567·7920·3d3e·2052·6164·6963·616c··ategy·=>·Radical | ||
| 00018cc0:·436f·6469·6d31·2920·2020·2020·2020·2020··Codim1)········· | 00018cc0:·436f·6469·6d31·2920·2020·2020·2020·2020··Codim1)········· | ||
| 00018cd0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00018cd0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00018ce0:·6420·312e·313 | 00018ce0:·6420·312e·3138·3235·3273·2028·6370·7529··d·1.18252s·(cpu) | ||
| 00018cf0:·3b20·302e·363 | 00018cf0:·3b20·302e·3639·3138·3134·7320·2874·6872··;·0.691814s·(thr | ||
| 00018d00:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | 00018d00:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | ||
| 00018d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018d20:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00018d20:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00018d30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018d30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00018d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00018d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0001a840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001a840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001a850:·2d2d·2d2d·2d2d·2b0a·7c69·3331·203a·2074··------+.|i31·:·t | 0001a850:·2d2d·2d2d·2d2d·2b0a·7c69·3331·203a·2074··------+.|i31·:·t | ||
| 0001a860:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | 0001a860:·696d·6520·5227·203d·2069·6e74·6567·7261··ime·R'·=·integra | ||
| 0001a870:·6c43·6c6f·7375·7265·2028·522c·2053·7472··lClosure·(R,·Str | 0001a870:·6c43·6c6f·7375·7265·2028·522c·2053·7472··lClosure·(R,·Str | ||
| 0001a880:·6174·6567·7920·3d3e·2056·6173·636f·6e63··ategy·=>·Vasconc | 0001a880:·6174·6567·7920·3d3e·2056·6173·636f·6e63··ategy·=>·Vasconc | ||
| 0001a890:·656c·6f73·2920·2020·2020·2020·2020·2020··elos)··········· | 0001a890:·656c·6f73·2920·2020·2020·2020·2020·2020··elos)··········· | ||
| 0001a8a0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 0001a8a0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 0001a8b0:·6420·302e·3 | 0001a8b0:·6420·302e·3833·3138·3838·7320·2863·7075··d·0.831888s·(cpu | ||
| 0001a8c0:·293b·2030·2e34·3 | 0001a8c0:·293b·2030·2e34·3530·3334·3773·2028·7468··);·0.450347s·(th | ||
| 0001a8d0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 0001a8d0:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 0001a8e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001a8e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001a8f0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 0001a8f0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 0001a900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001a900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001a910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001a910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001a920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001a920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001a930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001a930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0001c250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001c250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001c260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001c260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001c270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001c270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001c280:·2d2d·2b0a·7c69·3336·203a·2074·696d·6520··--+.|i36·:·time· | 0001c280:·2d2d·2b0a·7c69·3336·203a·2074·696d·6520··--+.|i36·:·time· | ||
| 0001c290:·5227·203d·2069·6e74·6567·7261·6c43·6c6f··R'·=·integralClo | 0001c290:·5227·203d·2069·6e74·6567·7261·6c43·6c6f··R'·=·integralClo | ||
| 0001c2a0:·7375·7265·2052·2020·2020·2020·2020·2020··sure·R·········· | 0001c2a0:·7375·7265·2052·2020·2020·2020·2020·2020··sure·R·········· | ||
| 0001c2b0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0001c2b0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0001c2c0:·202d·2d20·7573·6564·2030·2e30·393 | 0001c2c0:·202d·2d20·7573·6564·2030·2e30·3938·3033···--·used·0.09803 | ||
| 0001c2d0:·3536·7320·2863·7075·293b·2030·2e30·3 | 0001c2d0:·3536·7320·2863·7075·293b·2030·2e30·3439··56s·(cpu);·0.049 | ||
| 0001c2e0:·3 | 0001c2e0:·3834·7320·2874·6872·6561·6429·3b20·3073··84s·(thread);·0s | ||
| 0001c2f0:· | 0001c2f0:·2028·6763·2920·2020·7c0a·7c20·2020·2020···(gc)···|.|····· | ||
| 0001c300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c330:·2020·207c·0a7c·6f33·3620·3d20·5227·2020·····|.|o36·=·R'·· | 0001c330:·2020·207c·0a7c·6f33·3620·3d20·5227·2020·····|.|o36·=·R'·· | ||
| 0001c340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001c350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001c360:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0001c360:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 0001ce30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001ce30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001ce40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001ce40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001ce50:·2d2d·2d2d·2d2d·2b0a·7c69·3431·203a·2074··------+.|i41·:·t | 0001ce50:·2d2d·2d2d·2d2d·2b0a·7c69·3431·203a·2074··------+.|i41·:·t | ||
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| 0000bed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000bed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000bee0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | 0000bee0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | ||
| 0000bef0:·2065·6c61·7073·6564·5469·6d65·2065·7175···elapsedTime·equ | 0000bef0:·2065·6c61·7073·6564·5469·6d65·2065·7175···elapsedTime·equ | ||
| 0000bf00:·6976·6172·6961·6e74·4869·6c62·6572·7453··ivariantHilbertS | 0000bf00:·6976·6172·6961·6e74·4869·6c62·6572·7453··ivariantHilbertS | ||
| 0000bf10:·6572·6965·7328·542c·204f·7264·6572·203d··eries(T,·Order·= | 0000bf10:·6572·6965·7328·542c·204f·7264·6572·203d··eries(T,·Order·= | ||
| 0000bf20:·3e20·3529·2020·2020·2020·2020·2020·2020··>·5)············ | 0000bf20:·3e20·3529·2020·2020·2020·2020·2020·2020··>·5)············ | ||
| 0000bf30:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 0000bf30:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 0000bf40:·302e·3030·3230·3 | 0000bf40:·302e·3030·3230·3532·3320·7365·636f·6e64··0.0020523·second | ||
| 0000bf50:· | 0000bf50:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 0000bf60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000bf60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000bf70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000bf70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000bf80:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 0000bf80:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 0000bf90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000bf90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000bfa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000bfa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000bfb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000bfb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000bfc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000bfc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000c6f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000c6f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000c700:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·: | 0000c700:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·: | ||
| 0000c710:·2065·6c61·7073·6564·5469·6d65·2065·7175···elapsedTime·equ | 0000c710:·2065·6c61·7073·6564·5469·6d65·2065·7175···elapsedTime·equ | ||
| 0000c720:·6976·6172·6961·6e74·4869·6c62·6572·7453··ivariantHilbertS | 0000c720:·6976·6172·6961·6e74·4869·6c62·6572·7453··ivariantHilbertS | ||
| 0000c730:·6572·6965·7328·542c·204f·7264·6572·203d··eries(T,·Order·= | 0000c730:·6572·6965·7328·542c·204f·7264·6572·203d··eries(T,·Order·= | ||
| 0000c740:·3e20·3529·3b20·2020·2020·2020·2020·2020··>·5);··········· | 0000c740:·3e20·3529·3b20·2020·2020·2020·2020·2020··>·5);··········· | ||
| 0000c750:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 0000c750:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 0000c760:·302e·3030·3835·3635·3032·2073·6563·6f6e··0.00856502·secon | |||
| 0000c7 | 0000c760:·302e·3030·3034·3032·3233·3720·7365·636f··0.000402237·seco | ||
| 0000c770:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | |||
| 0000c780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000c790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000c7a0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | 0000c7a0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 0000c7b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000c7b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000c7c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000c7c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000c7d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000c7d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 000016b0:·5d22·203c·3c20·656e·646c·203c·3c20·636c··]"·<<·endl·<<·cl | 000016b0:·5d22·203c·3c20·656e·646c·203c·3c20·636c··]"·<<·endl·<<·cl | ||
| 000016c0:·6f73·657c·0a7c·2020·2020·2020·2020·2020··ose|.|·········· | 000016c0:·6f73·657c·0a7c·2020·2020·2020·2020·2020··ose|.|·········· | ||
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| 000016f0:·2020·2020·7c0a·7c6f·3130·203d·202f·746d······|.|o10·=·/tm | 000016f0:·2020·2020·7c0a·7c6f·3130·203d·202f·746d······|.|o10·=·/tm | ||
| 00001700:·702f·4d32·2d3 | 00001700:·702f·4d32·2d32·3533·3436·3930·2d30·2f30··p/M2-2534690-0/0 | ||
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| 00012580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00012580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00012590:·7c69·3420·3a20·656c·6170·7365·6454·696d··|i4·:·elapsedTim | 00012590:·7c69·3420·3a20·656c·6170·7365·6454·696d··|i4·:·elapsedTim | ||
| 000125a0:·6520·6a65·7473·5261·6469·6361·6c28·322c··e·jetsRadical(2, | 000125a0:·6520·6a65·7473·5261·6469·6361·6c28·322c··e·jetsRadical(2, | ||
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| 0001afe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0001afe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
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| 0001d950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001d950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0001e450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001e450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001e460:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3720··---------+.|i27· | 0001e460:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3720··---------+.|i27· | ||
| 0001e470:·3a20·656c·6170·7365·6454·696d·6520·6a65··:·elapsedTime·je | 0001e470:·3a20·656c·6170·7365·6454·696d·6520·6a65··:·elapsedTime·je | ||
| 0001e480:·7473·2832·2c66·2920·2020·2020·2020·2020··ts(2,f)········· | 0001e480:·7473·2832·2c66·2920·2020·2020·2020·2020··ts(2,f)········· | ||
| 0001e490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001e4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001e4b0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 0001e4b0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 0001e4c0:·302e·3030·3 | 0001e4c0:·302e·3030·3132·3435·3032·2073·6563·6f6e··0.00124502·secon | ||
| 0001e4d0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 0001e4d0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 0001e4e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e4e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001e4f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e4f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001e500:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 0001e500:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 0001e510:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e510:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001e520:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e520:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001e530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001e530:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00007060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00007070:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00007080:·0a7c·6934·203a·204c·203d·2061·6e61·6c79··.|i4·:·L·=·analy | 00007080:·0a7c·6934·203a·204c·203d·2061·6e61·6c79··.|i4·:·L·=·analy | ||
| 00007090:·7a65·5374·7261·6e64·2846·2c61·293b·2023··zeStrand(F,a);·# | 00007090:·7a65·5374·7261·6e64·2846·2c61·293b·2023··zeStrand(F,a);·# | ||
| 000070a0:·4c20·2020·2020·2020·2020·2020·2020·2020··L··············· | 000070a0:·4c20·2020·2020·2020·2020·2020·2020·2020··L··············· | ||
| 000070b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000070b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000070c0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000070c0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000070d0:·0a7c·202d·2d20·302e·303 | 000070d0:·0a7c·202d·2d20·302e·3031·3834·3637·3420··.|·--·0.0184674· | ||
| 000070e0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·elapsed· | 000070e0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·elapsed· | ||
| 000070f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000070f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007110:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00007110:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00007120:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00007120:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00007130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007140:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 1934, 35 lines modified | Offset 1934, 35 lines modified | ||
| 000078d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000078d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000078e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 000078e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 000078f0:·0a7c·6931·3020·3a20·6361·7270·6574·4265··.|i10·:·carpetBe | 000078f0:·0a7c·6931·3020·3a20·6361·7270·6574·4265··.|i10·:·carpetBe | ||
| 00007900:·7474·6954·6162·6c65·2861·2c62·2c33·2920··ttiTable(a,b,3)· | 00007900:·7474·6954·6162·6c65·2861·2c62·2c33·2920··ttiTable(a,b,3)· | ||
| 00007910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007930:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00007930:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00007940:·0a7c·202d·2d20·302e·3030·3 | 00007940:·0a7c·202d·2d20·302e·3030·3330·3533·3436··.|·--·0.00305346 | ||
| 00007950:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | 00007950:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 00007960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007980:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00007980:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00007990:·0a7c·202d·2d20·302e·3030·3 | 00007990:·0a7c·202d·2d20·302e·3030·3531·3336·3820··.|·--·0.0051368· | ||
| 000079a0:· | 000079a0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·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:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000079d0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000079e0:·0a7c·202d·2d20·302e·3032·3 | 000079e0:·0a7c·202d·2d20·302e·3032·3034·3832·3320··.|·--·0.0204823· | ||
| 000079f0:·6563 | 000079f0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·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:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00007a20:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00007a30:·0a7c·202d·2d20·302e·303 | 00007a30:·0a7c·202d·2d20·302e·3030·3832·3036·3638··.|·--·0.00820668 | ||
| 00007a40:·7365 | 00007a40:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·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:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00007a70:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00007a80:·0a7c·202d·2d20·302e·3030·3 | 00007a80:·0a7c·202d·2d20·302e·3030·3238·3330·3332··.|·--·0.00283032 | ||
| 00007a90:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | 00007a90:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·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:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00007ac0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00007ad0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00007ad0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00007ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000df10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000df10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000df20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000df20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000df30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000df30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000df40:·2d2d·2d2d·2b0a·7c69·3220·3a20·656c·6170··----+.|i2·:·elap | 0000df40:·2d2d·2d2d·2b0a·7c69·3220·3a20·656c·6170··----+.|i2·:·elap | ||
| 0000df50:·7365·6454·696d·6520·543d·6361·7270·6574··sedTime·T=carpet | 0000df50:·7365·6454·696d·6520·543d·6361·7270·6574··sedTime·T=carpet | ||
| 0000df60:·4265·7474·6954·6162·6c65·2861·2c62·2c33··BettiTable(a,b,3 | 0000df60:·4265·7474·6954·6162·6c65·2861·2c62·2c33··BettiTable(a,b,3 | ||
| 0000df70:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 0000df70:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 0000df80:·207c·0a7c·202d·2d20·302e·3030·3 | 0000df80:·207c·0a7c·202d·2d20·302e·3030·3137·3336···|.|·--·0.001736 | ||
| 0000df90:·3 | 0000df90:·3433·2073·6563·6f6e·6473·2065·6c61·7073··43·seconds·elaps | ||
| 0000dfa0:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | 0000dfa0:·6564·2020·2020·2020·2020·2020·2020·2020··ed·············· | ||
| 0000dfb0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000dfb0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000dfc0:·7c20·2d2d·2030·2e30·303 | 0000dfc0:·7c20·2d2d·2030·2e30·3035·3338·3031·3520··|·--·0.00538015· | ||
| 0000dfd0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·elapsed· | 0000dfd0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·elapsed· | ||
| 0000dfe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dfe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000dff0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 0000dff0:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 0000e000:·2d20·302e·303 | 0000e000:·2d20·302e·3031·3836·3231·3420·7365·636f··-·0.0186214·seco | ||
| 0000e010:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | 0000e010:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | ||
| 0000e020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e030:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | 0000e030:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | ||
| 0000e040:·2e30·3 | 0000e040:·2e30·3038·3731·3432·3520·7365·636f·6e64··.00871425·second | ||
| 0000e050:·2065 | 0000e050:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 0000e060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e070:·2020·2020·207c·0a7c·202d·2d20·302e·3030·······|.|·--·0.00 | 0000e070:·2020·2020·207c·0a7c·202d·2d20·302e·3030·······|.|·--·0.00 | ||
| 0000e080:·3 | 0000e080:·3238·3837·3737·2073·6563·6f6e·6473·2065··288777·seconds·e | ||
| 0000e090:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 0000e090:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 0000e0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e0a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e0b0:·2020·7c0a·7c20·2d2d·2030·2e3 | 0000e0b0:·2020·7c0a·7c20·2d2d·2030·2e32·3436·3534····|.|·--·0.24654 | ||
| 0000e0c0:·3 | 0000e0c0:·3920·7365·636f·6e64·7320·656c·6170·7365··9·seconds·elapse | ||
| 0000e0d0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | 0000e0d0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 0000e0e0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000e0e0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000e0f0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 0000e0f0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 0000e100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e120:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000e120:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0000e130:·2020·2020·2020·2020·2020·2030·2020·3120·············0··1· | 0000e130:·2020·2020·2020·2020·2020·2030·2020·3120·············0··1· | ||
| Offset 3658, 15 lines modified | Offset 3658, 15 lines modified | ||
| 0000e490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e4a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e4a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e4b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0000e4b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0000e4c0:·0a7c·6934·203a·2065·6c61·7073·6564·5469··.|i4·:·elapsedTi | 0000e4c0:·0a7c·6934·203a·2065·6c61·7073·6564·5469··.|i4·:·elapsedTi | ||
| 0000e4d0:·6d65·2054·273d·6d69·6e69·6d61·6c42·6574··me·T'=minimalBet | 0000e4d0:·6d65·2054·273d·6d69·6e69·6d61·6c42·6574··me·T'=minimalBet | ||
| 0000e4e0:·7469·204a·2020·2020·2020·2020·2020·2020··ti·J············ | 0000e4e0:·7469·204a·2020·2020·2020·2020·2020·2020··ti·J············ | ||
| 0000e4f0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000e4f0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
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| 0000e9e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e9e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e9f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 0000e9f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
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| 0000ea10:·2068·3d63·6172·7065·7442·6574·7469·5461···h=carpetBettiTa | 0000ea10:·2068·3d63·6172·7065·7442·6574·7469·5461···h=carpetBettiTa | ||
| 0000ea20:·626c·6573·2836·2c36·293b·2020·2020·2020··bles(6,6);······ | 0000ea20:·626c·6573·2836·2c36·293b·2020·2020·2020··bles(6,6);······ | ||
| 0000ea30:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 0000ea30:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 0000ea40:·2030·2e30·3033·3933·3 | 0000ea40:·2030·2e30·3033·3933·3231·3120·7365·636f···0.00393211·seco | ||
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| 0000ea60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ea60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000ea80:·303 | 0000ea80:·3031·3537·3439·3220·7365·636f·6e64·7320··0157492·seconds· | ||
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| 0000eaa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eaa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000eac0:·3 | 0000eac0:·3837·3120·7365·636f·6e64·7320·656c·6170··871·seconds·elap | ||
| 0000ead0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | 0000ead0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 0000eae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eaf0:·207c·0a7c·202d·2d20·3 | 0000eaf0:·207c·0a7c·202d·2d20·302e·3833·3139·3836···|.|·--·0.831986 | ||
| 0000eb00:·6563·6f6e·6473·2065·6c61·7073·6564· | 0000eb00:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 0000eb10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eb10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eb20:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000eb20:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000eb30:·7c20·2d2d·2030·2e3 | 0000eb30:·7c20·2d2d·2030·2e32·3531·3737·3920·7365··|·--·0.251779·se | ||
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| 00009150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933··-----------+.|i3 | 00009150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933··-----------+.|i3 | ||
| 00009160:·203a·2074·696d·6520·4c4c·4c20·6d3b·2020···:·time·LLL·m;·· | 00009160:·203a·2074·696d·6520·4c4c·4c20·6d3b·2020···:·time·LLL·m;·· | ||
| 00009170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000091a0:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | 000091a0:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | ||
| 000091b0:·3030·3439·3931·3636·7320·2863·7075·293b··00499166s·(cpu); | |||
| 000091c0:·2030·2e30·3037·3537·3837·3473·2028·7468···0.00757874s·(th | |||
| 000091 | 000091b0:·3030·3739·3133·3973·2028·6370·7529·3b20··0079139s·(cpu);· | ||
| 000091c0:·302e·3030·3730·3733·3439·7320·2874·6872··0.00707349s·(thr | |||
| 000091d0:·6561·6429·3b20·3073·2028·6763·2920·2020··ead);·0s·(gc)··· | |||
| 000091e0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000091e0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000091f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000091f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00009230:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00009230:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00009240:·2035·3020·2020·2020·2020·3437·2020·2020···50·······47···· | 00009240:·2035·3020·2020·2020·2020·3437·2020·2020···50·······47···· | ||
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| 000092e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000092e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000092f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000092f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009300:·2d2d·2d2d·2d2b·0a7c·6934·203a·2074·696d··-----+.|i4·:·tim | 00009300:·2d2d·2d2d·2d2b·0a7c·6934·203a·2074·696d··-----+.|i4·:·tim | ||
| 00009310:·6520·4c4c·4c28·6d2c·2053·7472·6174·6567··e·LLL(m,·Strateg | 00009310:·6520·4c4c·4c28·6d2c·2053·7472·6174·6567··e·LLL(m,·Strateg | ||
| 00009320:·793d·3e43·6f68·656e·456e·6769·6e65·293b··y=>CohenEngine); | 00009320:·793d·3e43·6f68·656e·456e·6769·6e65·293b··y=>CohenEngine); | ||
| 00009330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009340:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00009340:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00009350:·2d2d·2075·7365·6420·302e·303 | 00009350:·2d2d·2075·7365·6420·302e·3031·3937·3931··--·used·0.019791 | ||
| 00009360:·3 | 00009360:·3273·2028·6370·7529·3b20·302e·3032·3333··2s·(cpu);·0.0233 | ||
| 00009370:·3 | 00009370:·3337·3873·2028·7468·7265·6164·293b·2030··378s·(thread);·0 | ||
| 00009380:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | 00009380:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00009390:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00009390:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 000093a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000093a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000093b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000093b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000093c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000093c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000093d0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 000093d0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 000093e0:·2020·2020·2020·2020·2020·2035·3020·2020·············50··· | 000093e0:·2020·2020·2020·2020·2020·2035·3020·2020·············50··· | ||
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| 00009490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000094a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 000094a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 000094b0:·0a7c·6935·203a·2074·696d·6520·4c4c·4c28··.|i5·:·time·LLL( | 000094b0:·0a7c·6935·203a·2074·696d·6520·4c4c·4c28··.|i5·:·time·LLL( | ||
| 000094c0:·6d2c·2053·7472·6174·6567·793d·3e43·6f68··m,·Strategy=>Coh | 000094c0:·6d2c·2053·7472·6174·6567·793d·3e43·6f68··m,·Strategy=>Coh | ||
| 000094d0:·656e·546f·704c·6576·656c·293b·2020·2020··enTopLevel);···· | 000094d0:·656e·546f·704c·6576·656c·293b·2020·2020··enTopLevel);···· | ||
| 000094e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000094e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000094f0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 000094f0:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00009500:·6420·302e·3130·3638·3535·7320·2863·7075··d·0.106855s·(cpu | |||
| 000095 | 00009500:·6420·302e·3039·3635·3034·3773·2028·6370··d·0.0965047s·(cp | ||
| 00009510:·7529·3b20·302e·3039·3635·3130·3873·2028··u);·0.0965108s·( | |||
| 00009520:·7265·6164·293b·2030·7320·2867·6329· | 00009520:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | ||
| 00009530:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00009530:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00009540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009540:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009560:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009570:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009580:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00009580:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00009590:·2020·2020·2035·3020·2020·2020·2020·3437·······50·······47 | 00009590:·2020·2020·2035·3020·2020·2020·2020·3437·······50·······47 | ||
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| 00009630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009650:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | 00009650:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | ||
| 00009660:·2074·696d·6520·4c4c·4c28·6d2c·2053·7472···time·LLL(m,·Str | 00009660:·2074·696d·6520·4c4c·4c28·6d2c·2053·7472···time·LLL(m,·Str | ||
| 00009670:·6174·6567·793d·3e7b·4769·7665·6e73·2c52··ategy=>{Givens,R | 00009670:·6174·6567·793d·3e7b·4769·7665·6e73·2c52··ategy=>{Givens,R | ||
| 00009680:·6561·6c46·507d·293b·2020·2020·2020·2020··ealFP});········ | 00009680:·6561·6c46·507d·293b·2020·2020·2020·2020··ealFP});········ | ||
| 00009690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000096a0:·7c0a·7c20·2d2d·2075·7365·6420·302e·303 | 000096a0:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 000096b0:·3033·3937·3773·2028·6370·7529·3b20·302e··03977s·(cpu);·0. | |||
| 000096 | 000096b0:·3933·3831·3538·7320·2863·7075·293b·2030··938158s·(cpu);·0 | ||
| 000096c0:·2e30·3039·3931·3632·3473·2028·7468·7265··.00991624s·(thre | |||
| 000096d0:·293b·2030·7320·2867·6329·2020·2020· | 000096d0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 000096e0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000096e0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 000096f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000096f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00009720:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00009720:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00009730:·7c20·2020·2020·2020·2020·2020·2020·2035··|··············5 | 00009730:·7c20·2020·2020·2020·2020·2020·2020·2035··|··············5 | ||
| 00009740:·3020·2020·2020·2020·3437·2020·2020·2020··0·······47······ | 00009740:·3020·2020·2020·2020·3437·2020·2020·2020··0·······47······ | ||
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| 000097f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000097f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009800:·2d2d·2d2b·0a7c·6937·203a·2074·696d·6520··---+.|i7·:·time· | 00009800:·2d2d·2d2b·0a7c·6937·203a·2074·696d·6520··---+.|i7·:·time· | ||
| 00009810:·4c4c·4c28·6d2c·2053·7472·6174·6567·793d··LLL(m,·Strategy= | 00009810:·4c4c·4c28·6d2c·2053·7472·6174·6567·793d··LLL(m,·Strategy= | ||
| 00009820:·3e7b·4769·7665·6e73·2c52·6561·6c51·507d··>{Givens,RealQP} | 00009820:·3e7b·4769·7665·6e73·2c52·6561·6c51·507d··>{Givens,RealQP} | ||
| 00009830:·293b·2020·2020·2020·2020·2020·2020·2020··);·············· | 00009830:·293b·2020·2020·2020·2020·2020·2020·2020··);·············· | ||
| 00009840:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00009840:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00009850:·2075·7365·6420·302e·303 | 00009850:·2075·7365·6420·302e·3034·3935·3436·3273···used·0.0495462s | ||
| 00009860:·2028·6370·7529·3b20·302e·3035·3 | 00009860:·2028·6370·7529·3b20·302e·3035·3137·3432···(cpu);·0.051742 | ||
| 00009870:·3473·2028·7468·7265·6164·293b·2030·7320··4s·(thread);·0s· | 00009870:·3473·2028·7468·7265·6164·293b·2030·7320··4s·(thread);·0s· | ||
| 00009880:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | 00009880:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 00009890:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00009890:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 000098a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000098a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000098b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000098b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000098c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000098c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000098d0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 000098d0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
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| 000099a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 000099a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 000099b0:·6938·203a·2074·696d·6520·4c4c·4c28·6d2c··i8·:·time·LLL(m, | 000099b0:·6938·203a·2074·696d·6520·4c4c·4c28·6d2c··i8·:·time·LLL(m, | ||
| 000099c0:·2053·7472·6174·6567·793d·3e7b·4769·7665···Strategy=>{Give | 000099c0:·2053·7472·6174·6567·793d·3e7b·4769·7665···Strategy=>{Give | ||
| 000099d0:·6e73·2c52·6561·6c58·447d·293b·2020·2020··ns,RealXD});···· | 000099d0:·6e73·2c52·6561·6c58·447d·293b·2020·2020··ns,RealXD});···· | ||
| 000099e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000099e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000099f0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 000099f0:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
| 00009a00:·302e·303 | 00009a00:·302e·3035·3137·3338·3473·2028·6370·7529··0.0517384s·(cpu) | ||
| 00009a10:·3b20·302e·3035·313 | 00009a10:·3b20·302e·3035·3139·3830·3573·2028·7468··;·0.0519805s·(th | ||
| 00009a20:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 00009a20:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 00009a30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00009a30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00009a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009a80:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00009a80:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
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| 00009b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009b50:·2d2d·2d2d·2d2d·2d2b·0a7c·6939·203a·2074··-------+.|i9·:·t | 00009b50:·2d2d·2d2d·2d2d·2d2b·0a7c·6939·203a·2074··-------+.|i9·:·t | ||
| 00009b60:·696d·6520·4c4c·4c28·6d2c·2053·7472·6174··ime·LLL(m,·Strat | 00009b60:·696d·6520·4c4c·4c28·6d2c·2053·7472·6174··ime·LLL(m,·Strat | ||
| 00009b70:·6567·793d·3e7b·4769·7665·6e73·2c52·6561··egy=>{Givens,Rea | 00009b70:·6567·793d·3e7b·4769·7665·6e73·2c52·6561··egy=>{Givens,Rea | ||
| 00009b80:·6c52·527d·293b·2020·2020·2020·2020·2020··lRR});·········· | 00009b80:·6c52·527d·293b·2020·2020·2020·2020·2020··lRR});·········· | ||
| 00009b90:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00009b90:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 00009be0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00009be0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00009bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c20:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00009c20:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
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| 00004560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00004560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00004570:·7c69·3620·3a20·7469·6d65·2061·7265·4973··|i6·:·time·areIs | 00004570:·7c69·3620·3a20·7469·6d65·2061·7265·4973··|i6·:·time·areIs | ||
| 00004580:·6f6d·6f72·7068·6963·2850·2c50·293b·2020··omorphic(P,P);·· | 00004580:·6f6d·6f72·7068·6963·2850·2c50·293b·2020··omorphic(P,P);·· | ||
| 00004590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000045a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000045a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000045b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000045b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 000045f0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | 000045f0:·7320·2867·6329·2020·2020·2020·2020·2020··s·(gc)·········· | ||
| 00004600:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00004600:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00004610:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 00004610:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | ||
| 00004620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00004670:·6f6d·6f72·7068·6963·2850·2c50·2c73·6d6f··omorphic(P,P,smo | 00004670:·6f6d·6f72·7068·6963·2850·2c50·2c73·6d6f··omorphic(P,P,smo | ||
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| 00004690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000046a0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000046a0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 000046f0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000046f0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 00004720:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004720:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004730:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00004750:·0a57·6179·7320·746f·2075·7365·2061·7265··.Ways·to·use·are | 00004750:·0a57·6179·7320·746f·2075·7365·2061·7265··.Ways·to·use·are |
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| 00007fa0:·287b·7b30·2c30·7d2c·7b34·2c34·7d7d·2c4d··({{0,0},{4,4}},M | 00007fa0:·287b·7b30·2c30·7d2c·7b34·2c34·7d7d·2c4d··({{0,0},{4,4}},M | ||
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| 00007fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00007ff0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | 00007ff0:·6420·2020·2020·2020·2020·2020·2020·2020··d··············· | ||
| 00008000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00008030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000081d0:·287b·7b30·2c30·7d2c·7b34·2c34·7d7d·2c4d··({{0,0},{4,4}},M | 000081d0:·287b·7b30·2c30·7d2c·7b34·2c34·7d7d·2c4d··({{0,0},{4,4}},M | ||
| 000081e0:·2c66·2c49·6e6e·6572·3d3e·7b7b·312c·327d··,f,Inner=>{{1,2} | 000081e0:·2c66·2c49·6e6e·6572·3d3e·7b7b·312c·327d··,f,Inner=>{{1,2} | ||
| 000081f0:·2c7b·332c·317d·7d2c·4f75·7465·723d·3e7b··,{3,1}},Outer=>{ | 000081f0:·2c7b·332c·317d·7d2c·4f75·7465·723d·3e7b··,{3,1}},Outer=>{ | ||
| 00008200:·7b31·7c0a·7c20·2d2d·2030·2e30·3 | 00008200:·7b31·7c0a·7c20·2d2d·2030·2e30·3039·3130··{1|.|·--·0.00910 | ||
| 00008210:·3338 | 00008210:·3736·3820·7365·636f·6e64·7320·656c·6170··768·seconds·elap | ||
| 00008220:· | 00008220:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 00008230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008250:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00008250:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00008260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008290:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0000f3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0000f3e0:·0a7c·6936·203a·2065·6c61·7073·6564·5469··.|i6·:·elapsedTi | 0000f3e0:·0a7c·6936·203a·2065·6c61·7073·6564·5469··.|i6·:·elapsedTi | ||
| 0000f3f0:·6d65·206c·696e·6561·7254·7275·6e63·6174··me·linearTruncat | 0000f3f0:·6d65·206c·696e·6561·7254·7275·6e63·6174··me·linearTruncat | ||
| 0000f400:·696f·6e73·287b·7b32·2c32·2c32·7d2c·7b34··ions({{2,2,2},{4 | 0000f400:·696f·6e73·287b·7b32·2c32·2c32·7d2c·7b34··ions({{2,2,2},{4 | ||
| 0000f410:·2c34·2c34·7d7d·2c20·4d29·7c0a·7c20·2d2d··,4,4}},·M)|.|·-- | 0000f410:·2c34·2c34·7d7d·2c20·4d29·7c0a·7c20·2d2d··,4,4}},·M)|.|·-- | ||
| 0000f420:·203 | 0000f420:·2031·322e·3836·3639·2073·6563·6f6e·6473···12.8669·seconds | ||
| 0000f430:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | 0000f430:·2065·6c61·7073·6564·2020·2020·2020·2020···elapsed········ | ||
| 0000f440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f450:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 0000f450:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 0000f460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f480:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f490:·7c0a·7c6f·3620·3d20·7b7b·342c·2033·2c20··|.|o6·=·{{4,·3,· | 0000f490:·7c0a·7c6f·3620·3d20·7b7b·342c·2033·2c20··|.|o6·=·{{4,·3,· | ||
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| 0000f550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f550:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0000f570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0000f580:·3720·3a20·656c·6170·7365·6454·696d·6520··7·:·elapsedTime· | 0000f580:·3720·3a20·656c·6170·7365·6454·696d·6520··7·:·elapsedTime· | ||
| 0000f590:·6c69·6e65·6172·5472·756e·6361·7469·6f6e··linearTruncation | 0000f590:·6c69·6e65·6172·5472·756e·6361·7469·6f6e··linearTruncation | ||
| 0000f5a0:·7342·6f75·6e64·204d·2020·2020·2020·2020··sBound·M········ | 0000f5a0:·7342·6f75·6e64·204d·2020·2020·2020·2020··sBound·M········ | ||
| 0000f5b0:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | 0000f5b0:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | ||
| 0000f5c0:·3 | 0000f5c0:·3131·3035·3333·2073·6563·6f6e·6473·2065··110533·seconds·e | ||
| 0000f5d0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 0000f5d0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 0000f5e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f5e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f5f0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 0000f5f0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 0000f600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f620:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0000f620:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0000f630:·6f37·203d·207b·7b34·2c20·332c·2033·7d2c··o7·=·{{4,·3,·3}, | 0000f630:·6f37·203d·207b·7b34·2c20·332c·2033·7d2c··o7·=·{{4,·3,·3}, |
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| 00009610:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | 00009610:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 00009620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009620:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009630:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00009640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00009650:·7c69·3520·3a20·656c·6170·7365·6454·696d··|i5·:·elapsedTim | 00009650:·7c69·3520·3a20·656c·6170·7365·6454·696d··|i5·:·elapsedTim | ||
| 00009660:·6520·6869·6c62·6572·7453·616d·7565·6c46··e·hilbertSamuelF | 00009660:·6520·6869·6c62·6572·7453·616d·7565·6c46··e·hilbertSamuelF | ||
| 00009670:·756e·6374·696f·6e28·4d2c·2030·2c20·3629··unction(M,·0,·6) | 00009670:·756e·6374·696f·6e28·4d2c·2030·2c20·3629··unction(M,·0,·6) | ||
| 00009680:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e3 | 00009680:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e32········|.|·--·0.2 | ||
| 00009690:·3 | 00009690:·3035·3438·3920·7365·636f·6e64·7320·656c··05489·seconds·el | ||
| 000096a0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 000096a0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 000096b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000096b0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000096c0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 000096c0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 000096d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000096d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000096e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000096e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000096f0:·2020·2020·2020·7c0a·7c6f·3520·3d20·7b31········|.|o5·=·{1 | 000096f0:·2020·2020·2020·7c0a·7c6f·3520·3d20·7b31········|.|o5·=·{1 | ||
| 00009700:·2c20·332c·2036·2c20·372c·2036·2c20·332c··,·3,·6,·7,·6,·3, | 00009700:·2c20·332c·2036·2c20·372c·2036·2c20·332c··,·3,·6,·7,·6,·3, | ||
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| 00009eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00009ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00009ed0:·0a7c·6931·3120·3a20·656c·6170·7365·6454··.|i11·:·elapsedT | 00009ed0:·0a7c·6931·3120·3a20·656c·6170·7365·6454··.|i11·:·elapsedT | ||
| 00009ee0:·696d·6520·6869·6c62·6572·7453·616d·7565··ime·hilbertSamue | 00009ee0:·696d·6520·6869·6c62·6572·7453·616d·7565··ime·hilbertSamue | ||
| 00009ef0:·6c46·756e·6374·696f·6e28·4e2c·2030·2c20··lFunction(N,·0,· | 00009ef0:·6c46·756e·6374·696f·6e28·4e2c·2030·2c20··lFunction(N,·0,· | ||
| 00009f00:·3529·202d·2d20·6e2b·3120·2d2d·2030·2e30··5)·--·n+1·--·0.0 | 00009f00:·3529·202d·2d20·6e2b·3120·2d2d·2030·2e30··5)·--·n+1·--·0.0 | ||
| 00009f10:·3220·7365·636f·6e64·7320·2020·2020·207c··2·seconds······| | 00009f10:·3220·7365·636f·6e64·7320·2020·2020·207c··2·seconds······| | ||
| 00009f20:·0a7c·202d·2d20·302e·303 | 00009f20:·0a7c·202d·2d20·302e·3030·3938·3936·3638··.|·--·0.00989668 | ||
| 00009f30:·7365 | 00009f30:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 00009f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009f60:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00009f60:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00009f70:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00009f70:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 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:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000a0e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a0e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a0f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0000a0f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0000a100:·0a7c·6931·3220·3a20·656c·6170·7365·6454··.|i12·:·elapsedT | 0000a100:·0a7c·6931·3220·3a20·656c·6170·7365·6454··.|i12·:·elapsedT | ||
| 0000a110:·696d·6520·6869·6c62·6572·7453·616d·7565··ime·hilbertSamue | 0000a110:·696d·6520·6869·6c62·6572·7453·616d·7565··ime·hilbertSamue | ||
| 0000a120:·6c46·756e·6374·696f·6e28·712c·204e·2c20··lFunction(q,·N,· | 0000a120:·6c46·756e·6374·696f·6e28·712c·204e·2c20··lFunction(q,·N,· | ||
| 0000a130:·302c·2035·2920·2d2d·2036·286e·2b31·2920··0,·5)·--·6(n+1)· | 0000a130:·302c·2035·2920·2d2d·2036·286e·2b31·2920··0,·5)·--·6(n+1)· | ||
| 0000a140:·2d2d·2030·2e33·3220·7365·636f·6e64·737c··--·0.32·seconds| | 0000a140:·2d2d·2030·2e33·3220·7365·636f·6e64·737c··--·0.32·seconds| | ||
| 0000a150:·0a7c·202d·2d20·302e·3 | 0000a150:·0a7c·202d·2d20·302e·3332·3339·3338·2073··.|·--·0.323938·s | ||
| 0000a160:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | 0000a160:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | ||
| 0000a170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a190:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000a190:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0000a1a0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 0000a1a0:·0a7c·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·················· |
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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·2d20·7573·6564·2032·2e35·3635··.|·--·used·2.565 | ||
| 00002480:·3 | 00002480:·3435·7320·2863·7075·293b·2031·2e32·3632··45s·(cpu);·1.262 | ||
| 00002490:·3 | 00002490:·3437·7320·2874·6872·6561·6429·3b20·3073··47s·(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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| 000176f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000176f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017710:·2d2d·2b0a·7c69·3220·3a20·7469·6d65·2067··--+.|i2·:·time·g | 00017710:·2d2d·2b0a·7c69·3220·3a20·7469·6d65·2067··--+.|i2·:·time·g | ||
| 00017720:·726f·7468·656e·6469·6563·6b50·6f6c·796e··rothendieckPolyn | 00017720:·726f·7468·656e·6469·6563·6b50·6f6c·796e··rothendieckPolyn | ||
| 00017730:·6f6d·6961·6c20·7720·2020·2020·2020·2020··omial·w········· | 00017730:·6f6d·6961·6c20·7720·2020·2020·2020·2020··omial·w········· | ||
| 00017740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017750:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | 00017750:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 00017760:·3 | 00017760:·3038·3937·3731·3173·2028·6370·7529·3b20··0897711s·(cpu);· | ||
| 00017770:· | 00017770:·302e·3030·3334·3533·3373·2028·7468·7265··0.0034533s·(thre | ||
| 00017780:·6164·293b·2030·7320·2867·6329·2020·7c0a··ad);·0s·(gc)··|. | 00017780:·6164·293b·2030·7320·2867·6329·2020·7c0a··ad);·0s·(gc)··|. | ||
| 00017790:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00017790:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 000177a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000177a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000177b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000177b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000177c0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 000177c0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 000177d0:·2020·2020·2032·2020·2020·2020·2020·3220·······2········2· | 000177d0:·2020·2020·2032·2020·2020·2020·2020·3220·······2········2· | ||
| 000177e0:·2020·2020·2032·2020·2020·2020·2020·2020·······2·········· | 000177e0:·2020·2020·2032·2020·2020·2020·2020·2020·······2·········· | ||
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| 00017950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017950:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017960:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00017960:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00017970:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00017970:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00017980:·7c69·3320·3a20·7469·6d65·2067·726f·7468··|i3·:·time·groth | 00017980:·7c69·3320·3a20·7469·6d65·2067·726f·7468··|i3·:·time·groth | ||
| 00017990:·656e·6469·6563·6b50·6f6c·796e·6f6d·6961··endieckPolynomia | 00017990:·656e·6469·6563·6b50·6f6c·796e·6f6d·6961··endieckPolynomia | ||
| 000179a0:·6c20·2877·2c41·6c67·6f72·6974·686d·3d3e··l·(w,Algorithm=> | 000179a0:·6c20·2877·2c41·6c67·6f72·6974·686d·3d3e··l·(w,Algorithm=> | ||
| 000179b0:·2250·6970·6544·7265·616d·2229·7c0a·7c20··"PipeDream")|.|· | 000179b0:·2250·6970·6544·7265·616d·2229·7c0a·7c20··"PipeDream")|.|· | ||
| 000179c0:·2d2d·2075·7365·6420·302e·3030·303 | 000179c0:·2d2d·2075·7365·6420·302e·3030·3032·3232··--·used·0.000222 | ||
| 000179d0:·3 | 000179d0:·3436·3573·2028·6370·7529·3b20·302e·3030··465s·(cpu);·0.00 | ||
| 000179e0:·313 | 000179e0:·3137·3733·3337·7320·2874·6872·6561·6429··177337s·(thread) | ||
| 000179f0:·3b20·3073·2028·6763·2920·7c0a·7c20·2020··;·0s·(gc)·|.|··· | 000179f0:·3b20·3073·2028·6763·2920·7c0a·7c20·2020··;·0s·(gc)·|.|··· | ||
| 00017a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00017a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00017a30:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00017a30:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00017a40:·2032·2020·2020·2020·2020·3220·2020·2020···2········2····· | 00017a40:·2032·2020·2020·2020·2020·3220·2020·2020···2········2····· | ||
| 00017a50:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | 00017a50:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | ||
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| 000229e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000229e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000229f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000229f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022a00:·2d2d·2d2d·2d2d·2b0a·7c69·3233·203a·2074··------+.|i23·:·t | 00022a00:·2d2d·2d2d·2d2d·2b0a·7c69·3233·203a·2074··------+.|i23·:·t | ||
| 00022a10:·696d·6520·7363·6875·6265·7274·5265·6775··ime·schubertRegu | 00022a10:·696d·6520·7363·6875·6265·7274·5265·6775··ime·schubertRegu | ||
| 00022a20:·6c61·7269·7479·2042·2020·2020·2020·2020··larity·B········ | 00022a20:·6c61·7269·7479·2042·2020·2020·2020·2020··larity·B········ | ||
| 00022a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022a40:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | 00022a40:·2020·2020·7c0a·7c20·2d2d·2075·7365·6420······|.|·--·used· | ||
| 00022a50:·302e·3031·3 | 00022a50:·302e·3031·3139·3632·3473·2028·6370·7529··0.0119624s·(cpu) | ||
| 00022a60:·3b20·302e·3031·3 | 00022a60:·3b20·302e·3031·3336·3639·3773·2028·7468··;·0.0136697s·(th | ||
| 00022a70:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | 00022a70:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 00022a80:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00022a80:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00022a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022ac0:·7c0a·7c6f·3233·203d·2031·2020·2020·2020··|.|o23·=·1······ | 00022ac0:·7c0a·7c6f·3233·203d·2031·2020·2020·2020··|.|o23·=·1······ | ||
| 00022ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022ad0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00022b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022b10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022b20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00022b30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00022b40:·3234·203a·2074·696d·6520·7265·6775·6c61··24·:·time·regula | 00022b40:·3234·203a·2074·696d·6520·7265·6775·6c61··24·:·time·regula | ||
| 00022b50:·7269·7479·2063·6f6d·6f64·756c·6520·7363··rity·comodule·sc | 00022b50:·7269·7479·2063·6f6d·6f64·756c·6520·7363··rity·comodule·sc | ||
| 00022b60:·6875·6265·7274·4465·7465·726d·696e·616e··hubertDeterminan | 00022b60:·6875·6265·7274·4465·7465·726d·696e·616e··hubertDeterminan | ||
| 00022b70:·7461·6c49·6465·616c·2042·7c0a·7c20·2d2d··talIdeal·B|.|·-- | 00022b70:·7461·6c49·6465·616c·2042·7c0a·7c20·2d2d··talIdeal·B|.|·-- | ||
| 00022b80:·2075·7365·6420·302e·3031·3 | 00022b80:·2075·7365·6420·302e·3031·3334·3432·3573···used·0.0134425s | ||
| 00022b90:·2863·7075·293b·2030·2e30·3137·3237·3231··(cpu);·0.0172721 | |||
| 00022b | 00022b90:·2028·6370·7529·3b20·302e·3031·3339·3339···(cpu);·0.013939 | ||
| 00022ba0:·3573·2028·7468·7265·6164·293b·2030·7320··5s·(thread);·0s· | |||
| 00022bb0:· | 00022bb0:·2867·6329·2020·2020·7c0a·7c20·2020·2020··(gc)····|.|····· | ||
| 00022bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022bf0:·2020·2020·2020·7c0a·7c6f·3234·203d·2031········|.|o24·=·1 | 00022bf0:·2020·2020·2020·7c0a·7c6f·3234·203d·2031········|.|o24·=·1 | ||
| 00022c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022c20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0003b640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003b640:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003b650:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003b650:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003b660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0003b660:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0003b670:·0a7c·6931·3520·3a20·7469·6d65·2073·6368··.|i15·:·time·sch | 0003b670:·0a7c·6931·3520·3a20·7469·6d65·2073·6368··.|i15·:·time·sch | ||
| 0003b680:·7562·6572·7452·6567·756c·6172·6974·7920··ubertRegularity· | 0003b680:·7562·6572·7452·6567·756c·6172·6974·7920··ubertRegularity· | ||
| 0003b690:·7020·2020·2020·2020·2020·2020·2020·2020··p··············· | 0003b690:·7020·2020·2020·2020·2020·2020·2020·2020··p··············· | ||
| 0003b6a0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0003b6a0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0003b6b0:·2d2d·2075·7365·6420·302e·3030·313 | 0003b6b0:·2d2d·2075·7365·6420·302e·3030·3137·3037··--·used·0.001707 | ||
| 0003b6c0:·323 | 0003b6c0:·3236·7320·2863·7075·293b·2030·2e30·3030··26s·(cpu);·0.000 | ||
| 0003b6d0:·3 | 0003b6d0:·3231·3335·3331·7320·2874·6872·6561·6429··213531s·(thread) | ||
| 0003b6e0:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | 0003b6e0:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | ||
| 0003b6f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b6f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b700:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b720:·2020·2020·2020·7c0a·7c6f·3135·203d·2035········|.|o15·=·5 | 0003b720:·2020·2020·2020·7c0a·7c6f·3135·203d·2035········|.|o15·=·5 | ||
| 0003b730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b740:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0003b770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003b770:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003b780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003b780:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003b790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0003b790:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0003b7a0:·2b0a·7c69·3136·203a·2074·696d·6520·7265··+.|i16·:·time·re | 0003b7a0:·2b0a·7c69·3136·203a·2074·696d·6520·7265··+.|i16·:·time·re | ||
| 0003b7b0:·6775·6c61·7269·7479·2063·6f6d·6f64·756c··gularity·comodul | 0003b7b0:·6775·6c61·7269·7479·2063·6f6d·6f64·756c··gularity·comodul | ||
| 0003b7c0:·6520·4920·2020·2020·2020·2020·2020·2020··e·I············· | 0003b7c0:·6520·4920·2020·2020·2020·2020·2020·2020··e·I············· | ||
| 0003b7d0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 0003b7d0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 0003b7e0:·202d·2d20·7573·6564·2030·2e30·313 | 0003b7e0:·202d·2d20·7573·6564·2030·2e30·3134·3037···--·used·0.01407 | ||
| 0003b7f0:·3 | 0003b7f0:·3338·7320·2863·7075·293b·2030·2e30·3134··38s·(cpu);·0.014 | ||
| 0003b800:·3 | 0003b800:·3237·3732·7320·2874·6872·6561·6429·3b20··2772s·(thread);· | ||
| 0003b810:·3073·2028·6763·2920·2020·7c0a·7c20·2020··0s·(gc)···|.|··· | 0003b810:·3073·2028·6763·2920·2020·7c0a·7c20·2020··0s·(gc)···|.|··· | ||
| 0003b820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b830:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0003b850:·2020·2020·2020·207c·0a7c·6f31·3620·3d20·········|.|o16·=· | 0003b850:·2020·2020·2020·207c·0a7c·6f31·3620·3d20·········|.|o16·=· | ||
| 0003b860:·3520·2020·2020·2020·2020·2020·2020·2020··5··············· | 0003b860:·3520·2020·2020·2020·2020·2020·2020·2020··5··············· | ||
| 0003b870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0003b870:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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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·2b0a·7c69··------------+.|i | 00005000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00005010:·3620·3a20·656c·6170·7365·6454·696d·6520··6·:·elapsedTime· | 00005010:·3620·3a20·656c·6170·7365·6454·696d·6520··6·:·elapsedTime· | ||
| 00005020:·7261·6469·6361·6c28·6964·6561·6c20·495f··radical(ideal·I_ | 00005020:·7261·6469·6361·6c28·6964·6561·6c20·495f··radical(ideal·I_ | ||
| 00005030:·2a2c·2053·7472·6174·6567·7920·3d3e·204d··*,·Strategy·=>·M | 00005030:·2a2c·2053·7472·6174·6567·7920·3d3e·204d··*,·Strategy·=>·M | ||
| 00005040:·6f6e·6f6d·6961·6c29·7c0a·7c20·2d2d·2030··onomial)|.|·--·0 | 00005040:·6f6e·6f6d·6961·6c29·7c0a·7c20·2d2d·2030··onomial)|.|·--·0 | ||
| 00005050:·2e30·3030·3 | 00005050:·2e30·3030·3335·3336·3033·2073·6563·6f6e··.000353603·secon | ||
| 00005060:·7320 | 00005060:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 00005070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005080:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00005080:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00005090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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:·7c0a·7c6f·3620·3d20·6964·6561·6c20·2861··|.|o6·=·ideal·(a | 000050c0:·7c0a·7c6f·3620·3d20·6964·6561·6c20·2861··|.|o6·=·ideal·(a | ||
| 000050d0:·2c20·622c·2063·2920·2020·2020·2020·2020··,·b,·c)········· | 000050d0:·2c20·622c·2063·2920·2020·2020·2020·2020··,·b,·c)········· | ||
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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·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:·2b0a·7c69·3720·3a20·656c·6170·7365·6454··+.|i7·:·elapsedT | 000051b0:·2b0a·7c69·3720·3a20·656c·6170·7365·6454··+.|i7·:·elapsedT | ||
| 000051c0:·696d·6520·7261·6469·6361·6c28·6964·6561··ime·radical(idea | 000051c0:·696d·6520·7261·6469·6361·6c28·6964·6561··ime·radical(idea | ||
| 000051d0:·6c20·495f·2a2c·2055·6e6d·6978·6564·203d··l·I_*,·Unmixed·= | 000051d0:·6c20·495f·2a2c·2055·6e6d·6978·6564·203d··l·I_*,·Unmixed·= | ||
| 000051e0:·3e20·7472·7565·2920·2020·2020·7c0a·7c20··>·true)·····|.|· | 000051e0:·3e20·7472·7565·2920·2020·2020·7c0a·7c20··>·true)·····|.|· | ||
| 000051f0:·2d2d·2030·2e30·3 | 000051f0:·2d2d·2030·2e30·3137·3538·3233·2073·6563··--·0.0175823·sec | ||
| 00005200:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | 00005200:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | ||
| 00005210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005220:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00005220:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 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:·2020·2020·7c0a·7c6f·3720·3d20·6964·6561······|.|o7·=·idea | 00005260:·2020·2020·7c0a·7c6f·3720·3d20·6964·6561······|.|o7·=·idea | ||
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| 00006860:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006860:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006870:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006870:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006880:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·656c··------+.|i7·:·el | 00006880:·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20·656c··------+.|i7·:·el | ||
| 00006890:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | 00006890:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | ||
| 000068a0:·6c43·6f6e·7461·696e·6d65·6e74·2878·5f30··lContainment(x_0 | 000068a0:·6c43·6f6e·7461·696e·6d65·6e74·2878·5f30··lContainment(x_0 | ||
| 000068b0:·2c20·4929·2020·2020·2020·2020·2020·2020··,·I)············ | 000068b0:·2c20·4929·2020·2020·2020·2020·2020·2020··,·I)············ | ||
| 000068c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000068c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000068d0:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e3 | 000068d0:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e31········|.|·--·0.1 | ||
| 000068e0:·363 | 000068e0:·3631·3738·3320·7365·636f·6e64·7320·656c··61783·seconds·el | ||
| 000068f0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 000068f0:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 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:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00006920:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00006930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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·················· | ||
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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·2b0a·7c69·3820·3a20·656c··------+.|i8·:·el | 00006a10:·2d2d·2d2d·2d2d·2b0a·7c69·3820·3a20·656c··------+.|i8·:·el | ||
| 00006a20:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | 00006a20:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | ||
| 00006a30:·6c43·6f6e·7461·696e·6d65·6e74·2878·5f30··lContainment(x_0 | 00006a30:·6c43·6f6e·7461·696e·6d65·6e74·2878·5f30··lContainment(x_0 | ||
| 00006a40:·2c20·492c·2053·7472·6174·6567·7920·3d3e··,·I,·Strategy·=> | 00006a40:·2c20·492c·2053·7472·6174·6567·7920·3d3e··,·I,·Strategy·=> | ||
| 00006a50:·2022·4b6f·6c6c·6172·2229·2020·2020·2020···"Kollar")······ | 00006a50:·2022·4b6f·6c6c·6172·2229·2020·2020·2020···"Kollar")······ | ||
| 00006a60:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e30········|.|·--·0.0 | 00006a60:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e30········|.|·--·0.0 | ||
| 00006a70:·3 | 00006a70:·3134·3232·3534·2073·6563·6f6e·6473·2065··142254·seconds·e | ||
| 00006a80:·6 | 00006a80:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 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:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00006ab0:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00006ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ac0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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·2b0a·7c69·3920·3a20·656c··------+.|i9·:·el | 00006ba0:·2d2d·2d2d·2d2d·2b0a·7c69·3920·3a20·656c··------+.|i9·:·el | ||
| 00006bb0:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | 00006bb0:·6170·7365·6454·696d·6520·7261·6469·6361··apsedTime·radica | ||
| 00006bc0:·6c43·6f6e·7461·696e·6d65·6e74·2878·5f6e··lContainment(x_n | 00006bc0:·6c43·6f6e·7461·696e·6d65·6e74·2878·5f6e··lContainment(x_n | ||
| 00006bd0:·2c20·492c·2053·7472·6174·6567·7920·3d3e··,·I,·Strategy·=> | 00006bd0:·2c20·492c·2053·7472·6174·6567·7920·3d3e··,·I,·Strategy·=> | ||
| 00006be0:·2022·4b6f·6c6c·6172·2229·2020·2020·2020···"Kollar")······ | 00006be0:·2022·4b6f·6c6c·6172·2229·2020·2020·2020···"Kollar")······ | ||
| 00006bf0:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e30········|.|·--·0.0 | 00006bf0:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e30········|.|·--·0.0 | ||
| 00006c00:·3 | 00006c00:·3030·3938·3330·3934·2073·6563·6f6e·6473··00983094·seconds | ||
| 00006c10:·6c61·7073·6564·2020·2020·2020·2020· | 00006c10:·2065·6c61·7073·6564·2020·2020·2020·2020···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:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00006c40:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00006c50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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·················· | ||
| 00006c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2164, 34 lines modified | Offset 2164, 34 lines modified | ||
| 00008730:·2020·5374·7261·7465·6779·3a20·4c69·6e65····Strategy:·Line | 00008730:·2020·5374·7261·7465·6779·3a20·4c69·6e65····Strategy:·Line | ||
| 00008740:·6172·2020·2020·2020·2020·2020·2020·2874··ar············(t | 00008740:·6172·2020·2020·2020·2020·2020·2020·2874··ar············(t | ||
| 00008750:·696d·6520·3029·2020·2020·2020·2020·2023··ime·0)·········# | 00008750:·696d·6520·3029·2020·2020·2020·2020·2023··ime·0)·········# | ||
| 00008760:·7072·696d·6573·2020·2020·2020·2020·2020··primes·········· | 00008760:·7072·696d·6573·2020·2020·2020·2020·2020··primes·········· | ||
| 00008770:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00008770:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00008780:·2020·5374·7261·7465·6779·3a20·4269·7261····Strategy:·Bira | 00008780:·2020·5374·7261·7465·6779·3a20·4269·7261····Strategy:·Bira | ||
| 00008790:·7469·6f6e·616c·2020·2020·2020·2020·2874··tional········(t | 00008790:·7469·6f6e·616c·2020·2020·2020·2020·2874··tional········(t | ||
| 000087a0:·696d·6520·2e30·313 | 000087a0:·696d·6520·2e30·3131·3931·3937·2920·2023··ime·.0119197)··# | ||
| 000087b0:·7072·696d·6573·2020·2020·2020·2020·2020··primes·········· | 000087b0:·7072·696d·6573·2020·2020·2020·2020·2020··primes·········· | ||
| 000087c0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000087c0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 000087d0:·2020·5374·7261·7465·6779·3a20·4661·6374····Strategy:·Fact | 000087d0:·2020·5374·7261·7465·6779·3a20·4661·6374····Strategy:·Fact | ||
| 000087e0:·6f72·697a·6174·696f·6e20·2020·2020·2874··orization·····(t | 000087e0:·6f72·697a·6174·696f·6e20·2020·2020·2874··orization·····(t | ||
| 000087f0:·696d·6520· | 000087f0:·696d·6520·2e30·3032·3732·3132·2920·2023··ime·.0027212)··# | ||
| 00008800:·7072·696d·6573·2020·2020·2020·2020·2020··primes·········· | 00008800:·7072·696d·6573·2020·2020·2020·2020·2020··primes·········· | ||
| 00008810:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00008810:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00008820:·2020·5374·7261·7465·6779·3a20·4465·636f····Strategy:·Deco | 00008820:·2020·5374·7261·7465·6779·3a20·4465·636f····Strategy:·Deco | ||
| 00008830:·6d70·6f73·654d·6f6e·6f6d·6961·6c73·202d··mposeMonomials·- | 00008830:·6d70·6f73·654d·6f6e·6f6d·6961·6c73·202d··mposeMonomials·- | ||
| 00008840:·2d20·436f·6e76·6572·7469·6e67·2061·6e6e··-·Converting·ann | 00008840:·2d20·436f·6e76·6572·7469·6e67·2061·6e6e··-·Converting·ann | ||
| 00008850:·6f74·6174·6564·2020·2020·2020·2020·2020··otated·········· | 00008850:·6f74·6174·6564·2020·2020·2020·2020·2020··otated·········· | ||
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| 00008920:·2023·7072·696d·6573·203d·2031·2023·7072···#primes·=·1·#pr | 00008920:·2023·7072·696d·6573·203d·2031·2023·7072···#primes·=·1·#pr | ||
| 00008930:·756e·6564·5669·6143·6f64·696d·203d·2030··unedViaCodim·=·0 | 00008930:·756e·6564·5669·6143·6f64·696d·203d·2030··unedViaCodim·=·0 | ||
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| 00006fe0:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·7469··-----+.|i10·:·ti | 00006fe0:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·7469··-----+.|i10·:·ti | ||
| 00006ff0:·6d65·206d·756c·7469·5265·6573·4964·6561··me·multiReesIdea | 00006ff0:·6d65·206d·756c·7469·5265·6573·4964·6561··me·multiReesIdea | ||
| 00007000:·6c20·4a20·2020·2020·2020·2020·2020·2020··l·J············· | 00007000:·6c20·4a20·2020·2020·2020·2020·2020·2020··l·J············· | ||
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| 00007040:·2030·2e31·333 | 00007040:·2030·2e31·3336·3034·3773·2028·6370·7529···0.136047s·(cpu) | ||
| 00007050:·3b20·302e·3 | 00007050:·3b20·302e·3039·3438·3530·3373·2028·7468··;·0.0948503s·(th | ||
| 00007060:·6561 | 00007060:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
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| 00007440:·2d2d·2d2d·2d2b·0a7c·6931·3120·3a20·7469··-----+.|i11·:·ti | 00007440:·2d2d·2d2d·2d2b·0a7c·6931·3120·3a20·7469··-----+.|i11·:·ti | ||
| 00007450:·6d65·206d·756c·7469·5265·6573·4964·6561··me·multiReesIdea | 00007450:·6d65·206d·756c·7469·5265·6573·4964·6561··me·multiReesIdea | ||
| 00007460:·6c20·284a·2c20·6129·2020·2020·2020·2020··l·(J,·a)········ | 00007460:·6c20·284a·2c20·6129·2020·2020·2020·2020··l·(J,·a)········ | ||
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| 000074a0:·2030·2e30·3 | 000074a0:·2030·2e30·3039·3134·3136·3273·2028·6370···0.00914162s·(cp | ||
| 000074b0:·293b | 000074b0:·7529·3b20·302e·3030·3938·3332·3632·7320··u);·0.00983262s· | ||
| 000074c0:·6872·6561·6429·3b20·3073·2028·6763· | 000074c0:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 000074d0:·2 | 000074d0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
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| 00003c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00003c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00003ca0:·6938·203a·2028·532c·4e29·203d·2074·696d··i8·:·(S,N)·=·tim | 00003ca0:·6938·203a·2028·532c·4e29·203d·2074·696d··i8·:·(S,N)·=·tim | ||
| 00003cb0:·6520·6465·666f·726d·4d43·4d4d·6f64·756c··e·deformMCMModul | 00003cb0:·6520·6465·666f·726d·4d43·4d4d·6f64·756c··e·deformMCMModul | ||
| 00003cc0:·6520·4e30·2020·2020·2020·2020·2020·2020··e·N0············ | 00003cc0:·6520·4e30·2020·2020·2020·2020·2020·2020··e·N0············ | ||
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| 00003cf0:·202d·2d20·7573·6564·2031·2e31·3 | 00003cf0:·202d·2d20·7573·6564·2031·2e31·3239·3835···--·used·1.12985 | ||
| 00003d00:·7320·2863·7075·293b·2030·2e39·3 | 00003d00:·7320·2863·7075·293b·2030·2e39·3234·3335··s·(cpu);·0.92435 | ||
| 00003d10:·3773·2028·7468·7265·6164·293b·2030·7320··7s·(thread);·0s· | 00003d10:·3773·2028·7468·7265·6164·293b·2030·7320··7s·(thread);·0s· | ||
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| 00004830:·2d2b·0a7c·6931·3120·3a20·2853·272c·4e27··-+.|i11·:·(S',N' | 00004830:·2d2b·0a7c·6931·3120·3a20·2853·272c·4e27··-+.|i11·:·(S',N' | ||
| 00004840:·2920·3d20·7469·6d65·2064·6566·6f72·6d4d··)·=·time·deformM | 00004840:·2920·3d20·7469·6d65·2064·6566·6f72·6d4d··)·=·time·deformM | ||
| 00004850:·434d·4d6f·6475·6c65·204e·3027·2020·2020··CMModule·N0'···· | 00004850:·434d·4d6f·6475·6c65·204e·3027·2020·2020··CMModule·N0'···· | ||
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| 00004890:·3 | 00004890:·3037·3233·7320·2863·7075·293b·2031·2e31··0723s·(cpu);·1.1 | ||
| 000048a0:·3 | 000048a0:·3031·3439·7320·2874·6872·6561·6429·3b20··0149s·(thread);· | ||
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| 00005b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005b40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005b50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005b60:·2d2d·2d2d·2b0a·7c69·3420·3a20·284c·2c20··----+.|i4·:·(L,· | 00005b60:·2d2d·2d2d·2b0a·7c69·3420·3a20·284c·2c20··----+.|i4·:·(L,· | ||
| 00005b70:·6e70·6174·6873·2920·3d20·6479·6e61·6d69··npaths)·=·dynami | 00005b70:·6e70·6174·6873·2920·3d20·6479·6e61·6d69··npaths)·=·dynami | ||
| 00005b80:·6346·6c6f·7765·7253·6f6c·7665·2870·6f6c··cFlowerSolve(pol | 00005b80:·6346·6c6f·7765·7253·6f6c·7665·2870·6f6c··cFlowerSolve(pol | ||
| 00005b90:·7973·2e50·6f6c·794d·6170·2c70·302c·7b78··ys.PolyMap,p0,{x | 00005b90:·7973·2e50·6f6c·794d·6170·2c70·302c·7b78··ys.PolyMap,p0,{x | ||
| 00005ba0:·307d·297c·0a7c·202d·2d20·302e·3030·323 | 00005ba0:·307d·297c·0a7c·202d·2d20·302e·3030·3236··0})|.|·--·0.0026 | ||
| 00005bb0:·3 | 00005bb0:·3630·3134·2073·6563·6f6e·6473·2065·6c61··6014·seconds·ela | ||
| 00005bc0:·7 | 00005bc0:·7073·6564·2020·2020·2020·2020·2020·2020··psed············ | ||
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| 00005bf0:·303 | 00005bf0:·3032·3120·7365·636f·6e64·7320·656c·6170··021·seconds·elap | ||
| 00005c00:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | 00005c00:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
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| 00005c30:·3 | 00005c30:·3138·2073·6563·6f6e·6473·2065·6c61·7073··18·seconds·elaps | ||
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| 00005c70:·3 | 00005c70:·3620·7365·636f·6e64·7320·656c·6170·7365··6·seconds·elapse | ||
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| 00005ca0:·0a7c·202d·2d20·302e·3030·323 | 00005ca0:·0a7c·202d·2d20·302e·3030·3236·3037·3235··.|·--·0.00260725 | ||
| 00005cb0:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | 00005cb0:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 00005cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005cc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005cd0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00005cd0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00005ce0:·7c20·2d2d·2030·2e30·3030·323 | 00005ce0:·7c20·2d2d·2030·2e30·3030·3232·3737·3333··|·--·0.000227733 | ||
| 00005cf0:·7365 | 00005cf0:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 00005d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005d10:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00005d10:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00005d20:·202d·2d20·302e·3030·323 | 00005d20:·202d·2d20·302e·3030·3239·3433·3334·2073···--·0.00294334·s | ||
| 00005d30:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | 00005d30:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | ||
| 00005d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005d50:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00005d50:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00005d60:·2d2d·2030·2e30·3032·3 | 00005d60:·2d2d·2030·2e30·3032·3631·3338·3520·7365··--·0.00261385·se | ||
| 00005d70:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | 00005d70:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | ||
| 00005d80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005d80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005d90:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | 00005d90:·2020·2020·2020·2020·2020·207c·0a7c·202d·············|.|·- | ||
| 00005da0:·2d20·302e·3030·3032·3433·3 | 00005da0:·2d20·302e·3030·3032·3433·3136·3720·7365··-·0.000243167·se | ||
| 00005db0:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | 00005db0:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | ||
| 00005dc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005dc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005dd0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 00005dd0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 00005de0:·2030·2e30·3032·3 | 00005de0:·2030·2e30·3032·3434·3830·3120·7365·636f···0.00244801·seco | ||
| 00005df0:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | 00005df0:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | ||
| 00005e00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005e00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005e10:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00005e10:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00005e20:·302e·3030·323 | 00005e20:·302e·3030·3235·3338·3235·2073·6563·6f6e··0.00253825·secon | ||
| 00005e30:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 00005e30:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 00005e40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005e40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005e50:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | 00005e50:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | ||
| 00005e60:·2e30·3030·323 | 00005e60:·2e30·3030·3234·3737·3834·2073·6563·6f6e··.000247784·secon | ||
| 00005e70:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 00005e70:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 00005e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005e90:·2020·2020·2020·207c·0a7c·2d2d·6261·636b·········|.|--back | 00005e90:·2020·2020·2020·207c·0a7c·2d2d·6261·636b·········|.|--back | ||
| 00005ea0:·7570·2064·6972·6563·746f·7279·2063·7265··up·directory·cre | 00005ea0:·7570·2064·6972·6563·746f·7279·2063·7265··up·directory·cre | ||
| 00005eb0:·6174·6564·3a20·2f74·6d70·2f4d·322d·3 | 00005eb0:·6174·6564·3a20·2f74·6d70·2f4d·322d·3233··ated:·/tmp/M2-23 | ||
| 00005ec0:·3 | 00005ec0:·3937·3533·332d·302f·3120·2020·2020·2020··97533-0/1······· | ||
| 00005ed0:·2020·2020·2020·7c0a·7c20·2048·3031·3a20········|.|··H01:· | 00005ed0:·2020·2020·2020·7c0a·7c20·2048·3031·3a20········|.|··H01:· | ||
| 00005ee0:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | 00005ee0:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | ||
| 00005ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f10:·2020·2020·207c·0a7c·2020·4831·303a·2031·······|.|··H10:·1 | 00005f10:·2020·2020·207c·0a7c·2020·4831·303a·2031·······|.|··H10:·1 | ||
| 00005f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 1023, 42 lines modified | Offset 1023, 42 lines modified | ||
| 00003fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003fe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003ff0:·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d····|.+----------- | 00003ff0:·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d····|.+----------- | ||
| 00004000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00004010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00004020:·3320·3a20·656c·6170·7365·6454·696d·6520··3·:·elapsedTime· | 00004020:·3320·3a20·656c·6170·7365·6454·696d·6520··3·:·elapsedTime· | ||
| 00004030:·6a4d·756c·7420·4920·2020·2020·2020·2020··jMult·I········· | 00004030:·6a4d·756c·7420·4920·2020·2020·2020·2020··jMult·I········· | ||
| 00004040:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e30········|.|·--·0.0 | 00004040:·2020·2020·2020·7c0a·7c20·2d2d·2030·2e30········|.|·--·0.0 | ||
| 00004050:·3 | 00004050:·3232·3139·3839·2073·6563·6f6e·6473·2065··221989·seconds·e | ||
| 00004060:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 00004060:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 00004070:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 00004070:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 00004080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004090:·2020·2020·2020·2020·2020·7c0a·7c6f·3320············|.|o3· | 00004090:·2020·2020·2020·2020·2020·7c0a·7c6f·3320············|.|o3· | ||
| 000040a0:·3d20·3220·2020·2020·2020·2020·2020·2020··=·2············· | 000040a0:·3d20·3220·2020·2020·2020·2020·2020·2020··=·2············· | ||
| 000040b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000040b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000040c0:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+--------- | 000040c0:·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d······|.+--------- | ||
| 000040d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000040d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000040e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 000040e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 000040f0:·7c69·3420·3a20·656c·6170·7365·6454·696d··|i4·:·elapsedTim | 000040f0:·7c69·3420·3a20·656c·6170·7365·6454·696d··|i4·:·elapsedTim | ||
| 00004100:·6520·6d6f·6e6a·4d75·6c74·2049·2020·2020··e·monjMult·I···· | 00004100:·6520·6d6f·6e6a·4d75·6c74·2049·2020·2020··e·monjMult·I···· | ||
| 00004110:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | 00004110:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | ||
| 00004120:·2e3 | 00004120:·2e31·3637·3636·3620·7365·636f·6e64·7320··.167666·seconds· | ||
| 00004130:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | 00004130:·656c·6170·7365·6420·2020·2020·2020·2020··elapsed········· | ||
| 00004140:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00004140:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00004150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004160:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | 00004160:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 00004170:·3420·3d20·3220·2020·2020·2020·2020·2020··4·=·2··········· | 00004170:·3420·3d20·3220·2020·2020·2020·2020·2020··4·=·2··········· | ||
| 00004180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004190:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | 00004190:·2020·2020·2020·7c0a·2b2d·2d2d·2d2d·2d2d········|.+------- | ||
| 000041a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000041a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000041b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000041b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000041c0:·2b0a·7c69·3520·3a20·656c·6170·7365·6454··+.|i5·:·elapsedT | 000041c0:·2b0a·7c69·3520·3a20·656c·6170·7365·6454··+.|i5·:·elapsedT | ||
| 000041d0:·696d·6520·6d75·6c74·6970·6c69·6369·7479··ime·multiplicity | 000041d0:·696d·6520·6d75·6c74·6970·6c69·6369·7479··ime·multiplicity | ||
| 000041e0:·5365·7175·656e·6365·2049·7c0a·7c20·2d2d··Sequence·I|.|·-- | 000041e0:·5365·7175·656e·6365·2049·7c0a·7c20·2d2d··Sequence·I|.|·-- | ||
| 000041f0:·2030·2e31·3 | 000041f0:·2030·2e31·3635·3534·3420·7365·636f·6e64···0.165544·second | ||
| 00004200:·2065 | 00004200:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00004210:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00004210:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00004220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004220:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004230:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00004230:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00004240:·7c6f·3520·3d20·4861·7368·5461·626c·657b··|o5·=·HashTable{ | 00004240:·7c6f·3520·3d20·4861·7368·5461·626c·657b··|o5·=·HashTable{ | ||
| 00004250:·3220·3d3e·2033·7d20·2020·2020·2020·2020··2·=>·3}········· | 00004250:·3220·3d3e·2033·7d20·2020·2020·2020·2020··2·=>·3}········· | ||
| 00004260:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00004260:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00004270:·2020·2020·2020·2020·2020·3320·3d3e·2032············3·=>·2 | 00004270:·2020·2020·2020·2020·2020·3320·3d3e·2032············3·=>·2 | ||
| Offset 1168, 15 lines modified | Offset 1168, 15 lines modified | ||
| 000048f0:·4964·6561·6c20·6f66·2052·2020·2020·2020··Ideal·of·R······ | 000048f0:·4964·6561·6c20·6f66·2052·2020·2020·2020··Ideal·of·R······ | ||
| 00004900:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00004900:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00004910:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 00004910:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 00004920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004930:·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20·656c··------+.|i3·:·el | 00004930:·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20·656c··------+.|i3·:·el | ||
| 00004940:·6170·7365·6454·696d·6520·6d6f·6e41·6e61··apsedTime·monAna | 00004940:·6170·7365·6454·696d·6520·6d6f·6e41·6e61··apsedTime·monAna | ||
| 00004950:·6c79·7469·6353·7072·6561·6420·497c·0a7c··lyticSpread·I|.| | 00004950:·6c79·7469·6353·7072·6561·6420·497c·0a7c··lyticSpread·I|.| | ||
| 00004960:·202d·2d20·302e·3 | 00004960:·202d·2d20·302e·3132·3337·3833·2073·6563···--·0.123783·sec | ||
| 00004970:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | 00004970:·6f6e·6473·2065·6c61·7073·6564·2020·2020··onds·elapsed···· | ||
| 00004980:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 00004980:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 00004990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000049a0:·2020·2020·2020·2020·2020·207c·0a7c·6f33·············|.|o3 | 000049a0:·2020·2020·2020·2020·2020·207c·0a7c·6f33·············|.|o3 | ||
| 000049b0:·203d·2032·2020·2020·2020·2020·2020·2020···=·2············ | 000049b0:·203d·2032·2020·2020·2020·2020·2020·2020···=·2············ | ||
| 000049c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000049c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000049d0:·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d····|.+----------- | 000049d0:·2020·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d····|.+----------- | ||
| Offset 1322, 15 lines modified | Offset 1322, 15 lines modified | ||
| 00005290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000052a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 000052a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 000052b0:·0a7c·6933·203a·2065·6c61·7073·6564·5469··.|i3·:·elapsedTi | 000052b0:·0a7c·6933·203a·2065·6c61·7073·6564·5469··.|i3·:·elapsedTi | ||
| 000052c0:·6d65·206d·6f6e·6a4d·756c·7420·4920·2020··me·monjMult·I··· | 000052c0:·6d65·206d·6f6e·6a4d·756c·7420·4920·2020··me·monjMult·I··· | ||
| 000052d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000052d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000052e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000052e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000052f0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000052f0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00005300:·0a7c·202d·2d20·302e·3 | 00005300:·0a7c·202d·2d20·302e·3236·3230·3836·2073··.|·--·0.262086·s | ||
| 00005310:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | 00005310:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | ||
| 00005320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005340:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00005340:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00005350:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00005350:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00005360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 1347, 15 lines modified | Offset 1347, 15 lines modified | ||
| 00005420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005420:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005430:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 00005430:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 00005440:·0a7c·6934·203a·2065·6c61·7073·6564·5469··.|i4·:·elapsedTi | 00005440:·0a7c·6934·203a·2065·6c61·7073·6564·5469··.|i4·:·elapsedTi | ||
| 00005450:·6d65·206a·4d75·6c74·2049·2020·2020·2020··me·jMult·I······ | 00005450:·6d65·206a·4d75·6c74·2049·2020·2020·2020··me·jMult·I······ | ||
| 00005460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005480:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00005480:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00005490:·0a7c·202d·2d20·312e·3 | 00005490:·0a7c·202d·2d20·312e·3133·3335·3320·7365··.|·--·1.13353·se | ||
| 000054a0:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | 000054a0:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | ||
| 000054b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000054c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000054d0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 000054d0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 000054e0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 000054e0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 000054f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005500:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005500:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 9217, 17 lines modified | Offset 9217, 17 lines modified | ||
| 00024000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00024000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00024010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00024010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00024020:·6933·203a·2074·696d·6520·6465·6772·6565··i3·:·time·degree | 00024020:·6933·203a·2074·696d·6520·6465·6772·6565··i3·:·time·degree | ||
| 00024030:·2050·6869·2020·2020·2020·2020·2020·2020···Phi············ | 00024030:·2050·6869·2020·2020·2020·2020·2020·2020···Phi············ | ||
| 00024040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024060:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00024060:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00024070:·202d·2d20·7573·6564·2030·2e3 | 00024070:·202d·2d20·7573·6564·2030·2e34·3435·3035···--·used·0.44505 | ||
| 00024080:·3 | 00024080:·3373·2028·6370·7529·3b20·302e·3333·3734··3s·(cpu);·0.3374 | ||
| 00024090:·3 | 00024090:·3233·7320·2874·6872·6561·6429·3b20·3073··23s·(thread);·0s | ||
| 000240a0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 000240a0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 000240b0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000240b0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 000240c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000240c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000240d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000240d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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···············|.| | ||
| Offset 9444, 16 lines modified | Offset 9444, 16 lines modified | ||
| 00024e30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00024e30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00024e40:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | 00024e40:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 00024e50:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | 00024e50:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | ||
| 00024e60:·2c53·7472·6174·6567·793d·3e22·7261·6e64··,Strategy=>"rand | 00024e60:·2c53·7472·6174·6567·793d·3e22·7261·6e64··,Strategy=>"rand | ||
| 00024e70:·6f6d·2070·6f69·6e74·2229·2020·2020·2020··om·point")······ | 00024e70:·6f6d·2070·6f69·6e74·2229·2020·2020·2020··om·point")······ | ||
| 00024e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024e90:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00024e90:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00024ea0:·7573·6564·203 | 00024ea0:·7573·6564·2032·2e36·3839·3831·7320·2863··used·2.68981s·(c | ||
| 00024eb0:·7075·293b·2032·2e3 | 00024eb0:·7075·293b·2032·2e31·3437·3737·7320·2874··pu);·2.14777s·(t | ||
| 00024ec0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00024ec0:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00024ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024ed0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024ee0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00024ee0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00024ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024ef0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00024f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00024f20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 9469, 18 lines modified | Offset 9469, 18 lines modified | ||
| 00024fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00024fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00024fd0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | 00024fd0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | ||
| 00024fe0:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | 00024fe0:·2074·696d·6520·6465·6772·6565·2850·6869···time·degree(Phi | ||
| 00024ff0:·2c53·7472·6174·6567·793d·3e22·302d·7468··,Strategy=>"0-th | 00024ff0:·2c53·7472·6174·6567·793d·3e22·302d·7468··,Strategy=>"0-th | ||
| 00025000:·2070·726f·6a65·6374·6976·6520·6465·6772···projective·degr | 00025000:·2070·726f·6a65·6374·6976·6520·6465·6772···projective·degr | ||
| 00025010:·6565·2229·2020·2020·2020·2020·2020·2020··ee")············ | 00025010:·6565·2229·2020·2020·2020·2020·2020·2020··ee")············ | ||
| 00025020:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00025020:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00025030:·7573·6564·2030·2e32·3 | 00025030:·7573·6564·2030·2e32·3832·3633·3973·2028··used·0.282639s·( | ||
| 00025040:·6370·7529·3b20·302e·3232·3 | 00025040:·6370·7529·3b20·302e·3232·3834·3032·7320··cpu);·0.228402s· | ||
| 00025050:·7468 | 00025050:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 00025060:·2 | 00025060:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00025070:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00025070:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00025080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000250a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000250a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000250b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000250b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000250c0:·2020·2020·2020·2020·207c·0a7c·6f35·203d···········|.|o5·= | 000250c0:·2020·2020·2020·2020·207c·0a7c·6f35·203d···········|.|o5·= | ||
| 000250d0:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | 000250d0:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | ||
| Offset 9494, 18 lines modified | Offset 9494, 18 lines modified | ||
| 00025150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00025150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025160:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | 00025160:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6936·203a··---------+.|i6·: | ||
| 00025170:·2074·696d·6520·6465·6772·6565·2050·6869···time·degree·Phi | 00025170:·2074·696d·6520·6465·6772·6565·2050·6869···time·degree·Phi | ||
| 00025180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025180:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000251a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000251a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000251b0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000251b0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 000251c0:·7573·6564·2030·2e32·3 | 000251c0:·7573·6564·2030·2e32·3238·3937·3873·2028··used·0.228978s·( | ||
| 000251d0:·7075 | 000251d0:·6370·7529·3b20·302e·3233·3038·3139·7320··cpu);·0.230819s· | ||
| 000251e0:·6872·6561·6429·3b20·3073·2028·6763· | 000251e0:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 000251f0:·2 | 000251f0:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00025200:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00025200:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
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| 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·6f36·203d···········|.|o6·= | 00025250:·2020·2020·2020·2020·207c·0a7c·6f36·203d···········|.|o6·= | ||
| 00025260:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | 00025260:·2032·2020·2020·2020·2020·2020·2020·2020···2·············· | ||
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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·2b0a·7c69·3220··----------+.|i2· | 00027950:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3220··----------+.|i2· | ||
| 00027960:·3a20·7469·6d65·203f·2050·6869·2020·2020··:·time·?·Phi···· | 00027960:·3a20·7469·6d65·203f·2050·6869·2020·2020··:·time·?·Phi···· | ||
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| 000279a0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 000279a0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 000279b0:·2075·7365·6420·3 | 000279b0:·2075·7365·6420·362e·3437·3137·652d·3035···used·6.4717e-05 | ||
| 000279c0:·7320·2863·7075·293b·2030·2e30·3030·313 | 000279c0:·7320·2863·7075·293b·2030·2e30·3030·3138··s·(cpu);·0.00018 | ||
| 000279d0:·3 | 000279d0:·3334·3736·7320·2874·6872·6561·6429·3b20··3476s·(thread);· | ||
| 000279e0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 000279e0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 000279f0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 000279f0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00027a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00027a00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000121e0:·6e67·2220·3d3e·2052·2020·2020·2020·2020··ng"·=>·R········ | 000121e0:·6e67·2220·3d3e·2052·2020·2020·2020·2020··ng"·=>·R········ | ||
| 000121f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000121f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00012220:·7c20·2020·2020·2020·2020·2020·2022·7665··|············"ve | 00012220:·7c20·2020·2020·2020·2020·2020·2022·7665··|············"ve | ||
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| 000122f0:·7b6 | 000122f0:·7b61·2c20·657d·2c20·7b64·2c20·657d·7d7d··{a,·e},·{d,·e}}} | ||
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| 00012310:·7c20·2020·2020·2020·2020·2020·2272·696e··|···········"rin | 00012310:·7c20·2020·2020·2020·2020·2020·2272·696e··|···········"rin | ||
| 00012320:·6722·203d·3e20·5220·2020·2020·2020·2020··g"·=>·R········· | 00012320:·6722·203d·3e20·5220·2020·2020·2020·2020··g"·=>·R········· | ||
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| 00012360:·7c20·2020·2020·2020·2020·2020·2276·6572··|···········"ver | 00012360:·7c20·2020·2020·2020·2020·2020·2276·6572··|···········"ver | ||
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| 00012400:·7c20·2020·2020·4772·6170·687b·2265·6467··|·····Graph{"edg | 00012400:·7c20·2020·2020·4772·6170·687b·2265·6467··|·····Graph{"edg | ||
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| 00012450:·7c20·2020·2020·2020·2020·2020·2272·696e··|···········"rin | 00012450:·7c20·2020·2020·2020·2020·2020·2272·696e··|···········"rin | ||
| 00012460:·6722·203d·3e20·5220·2020·2020·2020·2020··g"·=>·R········· | 00012460:·6722·203d·3e20·5220·2020·2020·2020·2020··g"·=>·R········· | ||
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| 0000aae0:·6220·6e29·297c·0a7c·2020·2020·2020·2020··b·n))|.|········ | 0000aae0:·6220·6e29·297c·0a7c·2020·2020·2020·2020··b·n))|.|········ | ||
| 0000aaf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000aaf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ab00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ab00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ab10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ab10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ab20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ab20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000abb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000abb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000abc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000abc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 0000ac20:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 0000ac20:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 0000ac30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ac30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ac40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ac40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ac50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ac50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ac60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ac60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ac70:·2020·2020·207c·0a7c·6f39·203a·2053·6571·······|.|o9·:·Seq | 0000ac70:·2020·2020·207c·0a7c·6f39·203a·2053·6571·······|.|o9·:·Seq | ||
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| 0000ae00:·206e·292f·327c·0a7c·2020·2020·2020·2020···n)/2|.|········ | 0000ae00:·206e·292f·327c·0a7c·2020·2020·2020·2020···n)/2|.|········ | ||
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| 0000ae30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ae30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000ae50:·2020·2020·207c·0a7c·6f31·3020·3d20·2831·······|.|o10·=·(1 | 0000ae50:·2020·2020·207c·0a7c·6f31·3020·3d20·2831·······|.|o10·=·(1 | ||
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| 0000aec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000aec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000aed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000aed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000aee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000aee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000aef0:·2d2d·2d2d·2d7c·0a7c·2020·2020·2020·302c··-----|.|······0, | 0000aef0:·2d2d·2d2d·2d7c·0a7c·2020·2020·2020·302c··-----|.|······0, | ||
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| 0000af10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000af10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e0a0:·2020·2020·2020·2020·207c·0a7c·6f32·203d···········|.|o2·= | 0000e0a0:·2020·2020·2020·2020·207c·0a7c·6f32·203d···········|.|o2·= | ||
| 0000e0b0:·207b·44 | 0000e0b0:·207b·4476·672c·2044·6653·2c20·445f·532c···{Dvg,·DfS,·D_S, | ||
| 0000e0c0:·2044· | 0000e0c0:·2044·7b73·2c20·4453·6b7d·2020·2020·2020···D{s,·DSk}······ | ||
| 0000e0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e0e0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000e0e0:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000e0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e0f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e110:·2020·2020·2020·2020·207c·0a7c·6f32·203a···········|.|o2·: | 0000e110:·2020·2020·2020·2020·207c·0a7c·6f32·203a···········|.|o2·: | ||
| 0000e120:·204c·6973·7420·2020·2020·2020·2020·2020···List··········· | 0000e120:·204c·6973·7420·2020·2020·2020·2020·2020···List··········· | ||
| 0000e130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3763, 15 lines modified | Offset 3763, 15 lines modified | ||
| 0000eb20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000eb20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000eb30:·2d2d·2d2b·0a7c·6931·203a·2067·656e·6572··---+.|i1·:·gener | 0000eb30:·2d2d·2d2b·0a7c·6931·203a·2067·656e·6572··---+.|i1·:·gener | ||
| 0000eb40:·6174·6552·616e·646f·6d52·6567·756c·6172··ateRandomRegular | 0000eb40:·6174·6552·616e·646f·6d52·6567·756c·6172··ateRandomRegular | ||
| 0000eb50:·4772·6170·6873·2835·2c20·332c·2032·297c··Graphs(5,·3,·2)| | 0000eb50:·4772·6170·6873·2835·2c20·332c·2032·297c··Graphs(5,·3,·2)| | ||
| 0000eb60:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 0000eb60:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 0000eb70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eb70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eb80:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | 0000eb80:·2020·2020·2020·2020·2020·207c·0a7c·6f31·············|.|o1 | ||
| 0000eb90:·203d·207b·44 | 0000eb90:·203d·207b·4464·572c·2044·5b53·2c20·4455···=·{DdW,·D[S,·DU | ||
| 0000eba0:·577d·2020·2020·2020·2020·2020·2020·2020··W}·············· | 0000eba0:·577d·2020·2020·2020·2020·2020·2020·2020··W}·············· | ||
| 0000ebb0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 0000ebb0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 0000ebc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ebd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ebe0:·2020·207c·0a7c·6f31·203a·204c·6973·7420·····|.|o1·:·List· | 0000ebe0:·2020·207c·0a7c·6f31·203a·204c·6973·7420·····|.|o1·:·List· | ||
| 0000ebf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec00:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0000ec00:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| Offset 4101, 29 lines modified | Offset 4101, 29 lines modified | ||
| 00010040:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010040:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010050:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010050:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00010060:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00010070:·6934·203a·2074·696d·6520·6772·6170·6843··i4·:·time·graphC | 00010070:·6934·203a·2074·696d·6520·6772·6170·6843··i4·:·time·graphC | ||
| 00010080:·6f6d·706c·656d·656e·7420·473b·2020·2020··omplement·G;···· | 00010080:·6f6d·706c·656d·656e·7420·473b·2020·2020··omplement·G;···· | ||
| 00010090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000100a0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | 000100a0:·2020·2020·2020·2020·2020·7c0a·7c20·2d2d············|.|·-- | ||
| 000100b0:·2075·7365·6420·302e·3030·303 | 000100b0:·2075·7365·6420·302e·3030·3035·3031·3132···used·0.00050112 | ||
| 000100c0:·3473·2028·6370·7529·3b20·302e·3030·303 | 000100c0:·3473·2028·6370·7529·3b20·302e·3030·3034··4s·(cpu);·0.0004 | ||
| 000100d0:·3 | 000100d0:·3132·3533·7320·2874·6872·6561·6429·3b20··1253s·(thread);· | ||
| 000100e0:·3073·2028·6763·297c·0a2b·2d2d·2d2d·2d2d··0s·(gc)|.+------ | 000100e0:·3073·2028·6763·297c·0a2b·2d2d·2d2d·2d2d··0s·(gc)|.+------ | ||
| 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·2d2d·2d2d·2d2d·2d2d··---------------- | 00010110:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010120:·2d2d·2d2d·2b0a·7c69·3520·3a20·7469·6d65··----+.|i5·:·time | 00010120:·2d2d·2d2d·2b0a·7c69·3520·3a20·7469·6d65··----+.|i5·:·time | ||
| 00010130:·2028·6772·6170·6843·6f6d·706c·656d·656e···(graphComplemen | 00010130:·2028·6772·6170·6843·6f6d·706c·656d·656e···(graphComplemen | ||
| 00010140:·7420·5c20·4729·3b20·2020·2020·2020·2020··t·\·G);········· | 00010140:·7420·5c20·4729·3b20·2020·2020·2020·2020··t·\·G);········· | ||
| 00010150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010150:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010160:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 00010160:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 00010170:·373 | 00010170:·3730·3938·7320·2863·7075·293b·2030·2e30··7098s·(cpu);·0.0 | ||
| 00010180:· | 00010180:·3638·3933·3738·7320·2874·6872·6561·6429··689378s·(thread) | ||
| 00010190:· | 00010190:·3b20·3073·2028·6763·2920·2020·2020·7c0a··;·0s·(gc)·····|. | ||
| 000101a0:·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··+--------------- | 000101a0:·2b2d·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·2d2d·2d2d·2d2b·0a0a·5761··-----------+..Wa | 000101d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a0a·5761··-----------+..Wa | ||
| 000101e0:·7973·2074·6f20·7573·6520·6772·6170·6843··ys·to·use·graphC | 000101e0:·7973·2074·6f20·7573·6520·6772·6170·6843··ys·to·use·graphC | ||
| 000101f0:·6f6d·706c·656d·656e·7420·3a0a·3d3d·3d3d··omplement·:.==== | 000101f0:·6f6d·706c·656d·656e·7420·3a0a·3d3d·3d3d··omplement·:.==== | ||
| 00010200:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ | 00010200:·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d·3d3d··================ |
| Offset 13464, 15 lines modified | Offset 13464, 15 lines modified | ||
| 00034970:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00034970:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00034980:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00034980:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00034990:·3620·3a20·656c·6170·7365·6454·696d·6520··6·:·elapsedTime· | 00034990:·3620·3a20·656c·6170·7365·6454·696d·6520··6·:·elapsedTime· | ||
| 000349a0:·6e6f·6574·6865·7269·616e·4f70·6572·6174··noetherianOperat | 000349a0:·6e6f·6574·6865·7269·616e·4f70·6572·6174··noetherianOperat | ||
| 000349b0:·6f72·7328·512c·2053·7472·6174·6567·7920··ors(Q,·Strategy· | 000349b0:·6f72·7328·512c·2053·7472·6174·6567·7920··ors(Q,·Strategy· | ||
| 000349c0:·3d3e·2022·5075·6e63·7475·616c·5175·6f74··=>·"PunctualQuot | 000349c0:·3d3e·2022·5075·6e63·7475·616c·5175·6f74··=>·"PunctualQuot | ||
| 000349d0:·2229·2020·2020·2020·2020·2020·7c0a·7c20··")··········|.|· | 000349d0:·2229·2020·2020·2020·2020·2020·7c0a·7c20··")··········|.|· | ||
| 000349e0:·2d2d·2030·2e3 | 000349e0:·2d2d·2030·2e31·3034·3336·3120·7365·636f··--·0.104361·seco | ||
| 000349f0:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | 000349f0:·6e64·7320·656c·6170·7365·6420·2020·2020··nds·elapsed····· | ||
| 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:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00034a20:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00034a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00034a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00034a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00034a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00034a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00034a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 7985, 17 lines modified | Offset 7985, 17 lines modified | ||
| 0001f300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0001f310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0001f320:·0a7c·6931·3420·3a20·5920·3d20·7469·6d65··.|i14·:·Y·=·time | 0001f320:·0a7c·6931·3420·3a20·5920·3d20·7469·6d65··.|i14·:·Y·=·time | ||
| 0001f330:·2073·6d6f·6f74·6846·616e·6f54·6f72·6963···smoothFanoToric | 0001f330:·2073·6d6f·6f74·6846·616e·6f54·6f72·6963···smoothFanoToric | ||
| 0001f340:·5661·7269·6574·7928·352c·3130·3029·3b20··Variety(5,100);· | 0001f340:·5661·7269·6574·7928·352c·3130·3029·3b20··Variety(5,100);· | ||
| 0001f350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0001f350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0001f360:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0001f360:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0001f370:·0a7c·202d·2d20·7573·6564·2030·2e31·3 | 0001f370:·0a7c·202d·2d20·7573·6564·2030·2e31·3339··.|·--·used·0.139 | ||
| 0001f380:·3 | 0001f380:·3032·3273·2028·6370·7529·3b20·302e·3133··022s·(cpu);·0.13 | ||
| 0001f390:·3 | 0001f390:·3932·3439·7320·2874·6872·6561·6429·3b20··9249s·(thread);· | ||
| 0001f3a0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 0001f3a0:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 0001f3b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0001f3b0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0001f3c0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | 0001f3c0:·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··.+-------------- | ||
| 0001f3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f3e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f3e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f3f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001f3f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001f400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0001f400:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| Offset 8180, 43 lines modified | Offset 8180, 43 lines modified | ||
| 0001ff30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0001ff30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0001ff40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | 0001ff40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 0001ff50:·0a7c·6931·3920·3a20·666f·7220·6920·746f··.|i19·:·for·i·to | 0001ff50:·0a7c·6931·3920·3a20·666f·7220·6920·746f··.|i19·:·for·i·to | ||
| 0001ff60:·2064·696d·2059·206c·6973·7420·7469·6d65···dim·Y·list·time | 0001ff60:·2064·696d·2059·206c·6973·7420·7469·6d65···dim·Y·list·time | ||
| 0001ff70:·2068·696c·6265·7274·4675·6e63·7469·6f6e···hilbertFunction | 0001ff70:·2068·696c·6265·7274·4675·6e63·7469·6f6e···hilbertFunction | ||
| 0001ff80:·2028·692c·2041·3229·2020·2020·2020·2020···(i,·A2)········ | 0001ff80:·2028·692c·2041·3229·2020·2020·2020·2020···(i,·A2)········ | ||
| 0001ff90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0001ff90:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0001ffa0:·0a7c·202d·2d20·7573·6564·2030·2e30·303 | 0001ffa0:·0a7c·202d·2d20·7573·6564·2030·2e30·3030··.|·--·used·0.000 | ||
| 0001ffb0:·3939·3636·3873·2028·6370·7529·3b20·302e··99668s·(cpu);·0. | |||
| 0001ff | 0001ffb0:·3536·3534·3331·7320·2863·7075·293b·2030··565431s·(cpu);·0 | ||
| 0001ffc0:·2e30·3031·3037·3239·3273·2028·7468·7265··.00107292s·(thre | |||
| 0001ffd0:·6429 | 0001ffd0:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 0001ffe0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 0001ffe0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 0001fff0:·0a7c·202d·2d20·7573·6564·2032·2e3 | 0001fff0:·0a7c·202d·2d20·7573·6564·2032·2e31·3435··.|·--·used·2.145 | ||
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| 0007b550:·3d20·656c·6170·7365·6454·696d·6520·6d6f··=·elapsedTime·mo | 0007b550:·3d20·656c·6170·7365·6454·696d·6520·6d6f··=·elapsedTime·mo | ||
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| 0007b5a0:·3 | 0007b5a0:·3336·3432·2073·6563·6f6e·6473·2065·6c61··3642·seconds·ela | ||
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| 0007b970:·2873·6574·204d·3120·3d3d·3d20·7365·7420··(set·M1·===·set· | 0007b970:·2873·6574·204d·3120·3d3d·3d20·7365·7420··(set·M1·===·set· | ||
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| 00005600:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | 00005600:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | ||
| 00005610:·2d20·7573·6564·202e·3030·3 | 00005610:·2d20·7573·6564·202e·3030·3639·3830·3231··-·used·.00698021 | ||
| 00005620:·2073·6563·6f6e·6473·2020·2020·2020·2020···seconds········ | 00005620:·2073·6563·6f6e·6473·2020·2020·2020·2020···seconds········ | ||
| 00005630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005650:·2020·2020·2020·207c·0a7c·5065·7266·6f72·········|.|Perfor | 00005650:·2020·2020·2020·207c·0a7c·5065·7266·6f72·········|.|Perfor | ||
| 00005660:·6d69·6e67·206e·6f72·6d61·6c69·7a61·7469··ming·normalizati | 00005660:·6d69·6e67·206e·6f72·6d61·6c69·7a61·7469··ming·normalizati | ||
| 00005670:·6f6e·2070·7265·636f·6e64·6974·696f·6e69··on·preconditioni | 00005670:·6f6e·2070·7265·636f·6e64·6974·696f·6e69··on·preconditioni | ||
| 00005680:·6e67·202e·2e2e·2020·2020·2020·2020·2020··ng·...·········· | 00005680:·6e67·202e·2e2e·2020·2020·2020·2020·2020··ng·...·········· | ||
| 00005690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000056a0:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | 000056a0:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | ||
| 000056b0:·2d20·7573·6564·2030·2073·6563·6f6e·6473··-·used·0·seconds | |||
| 000056 | 000056b0:·2d20·7573·6564·202e·3030·3232·3236·3420··-·used·.0022264· | ||
| 000056c0:·7365·636f·6e64·7320·2020·2020·2020·2020··seconds········· | |||
| 000056d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000056d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000056e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000056e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000056f0:·2020·2020·2020·207c·0a7c·436f·6d70·7574·········|.|Comput | 000056f0:·2020·2020·2020·207c·0a7c·436f·6d70·7574·········|.|Comput | ||
| 00005700:·696e·6720·6e75·6d65·7269·6361·6c20·6b65··ing·numerical·ke | 00005700:·696e·6720·6e75·6d65·7269·6361·6c20·6b65··ing·numerical·ke | ||
| 00005710:·726e·656c·202e·2e2e·2020·2020·2020·2020··rnel·...········ | 00005710:·726e·656c·202e·2e2e·2020·2020·2020·2020··rnel·...········ | ||
| 00005720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005740:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | 00005740:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | ||
| 00005750:·2d20·7573·6564·2030·2073·6563·6f6e·6473··-·used·0·seconds | |||
| 000057 | 00005750:·2d20·7573·6564·202e·3030·3039·3832·3434··-·used·.00098244 | ||
| 00005760:·3820·7365·636f·6e64·7320·2020·2020·2020··8·seconds······· | |||
| 00005770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005790:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00005790:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 000057a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000057d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000057d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 1686, 24 lines modified | Offset 1686, 24 lines modified | ||
| 00006950:·6964·6561·6c20·305f·522c·2032·2c20·4174··ideal·0_R,·2,·At | 00006950:·6964·6561·6c20·305f·522c·2032·2c20·4174··ideal·0_R,·2,·At | ||
| 00006960:·7465·6d70·745a·5a20·3d3e·2074·7275·6529··temptZZ·=>·true) | 00006960:·7465·6d70·745a·5a20·3d3e·2074·7275·6529··temptZZ·=>·true) | ||
| 00006970:·2020·7c0a·7c53·616d·706c·696e·6720·696d····|.|Sampling·im | 00006970:·2020·7c0a·7c53·616d·706c·696e·6720·696d····|.|Sampling·im | ||
| 00006980:·6167·6520·706f·696e·7473·202e·2e2e·2020··age·points·...·· | 00006980:·6167·6520·706f·696e·7473·202e·2e2e·2020··age·points·...·· | ||
| 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·················· | ||
| 000069b0:·2020·2020·207c·0a7c·2020·2020·202d·2d20·······|.|·····--· | 000069b0:·2020·2020·207c·0a7c·2020·2020·202d·2d20·······|.|·····--· | ||
| 000069c0:·7573·6564·202e·3030·3 | 000069c0:·7573·6564·202e·3030·3431·3839·3835·2073··used·.00418985·s | ||
| 000069d0:· | 000069d0:·6563·6f6e·6473·2020·2020·2020·2020·2020··econds·········· | ||
| 000069e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000069e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000069f0:·2020·2020·2020·2020·7c0a·7c43·7265·6174··········|.|Creat | 000069f0:·2020·2020·2020·2020·7c0a·7c43·7265·6174··········|.|Creat | ||
| 00006a00:·696e·6720·696e·7465·7270·6f6c·6174·696f··ing·interpolatio | 00006a00:·696e·6720·696e·7465·7270·6f6c·6174·696f··ing·interpolatio | ||
| 00006a10:·6e20·6d61·7472·6978·202e·2e2e·2020·2020··n·matrix·...···· | 00006a10:·6e20·6d61·7472·6978·202e·2e2e·2020·2020··n·matrix·...···· | ||
| 00006a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006a30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00006a30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00006a40:·2020·202d·2d20·7573·6564·202e·3030·3 | 00006a40:·2020·202d·2d20·7573·6564·202e·3030·3135·····--·used·.0015 | ||
| 00006a50:·303 | 00006a50:·3039·3638·2073·6563·6f6e·6473·2020·2020··0968·seconds···· | ||
| 00006a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006a70:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00006a70:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00006a80:·7c50·6572·666f·726d·696e·6720·6e6f·726d··|Performing·norm | 00006a80:·7c50·6572·666f·726d·696e·6720·6e6f·726d··|Performing·norm | ||
| 00006a90:·616c·697a·6174·696f·6e20·7072·6563·6f6e··alization·precon | 00006a90:·616c·697a·6174·696f·6e20·7072·6563·6f6e··alization·precon | ||
| 00006aa0:·6469·7469·6f6e·696e·6720·2e2e·2e20·2020··ditioning·...··· | 00006aa0:·6469·7469·6f6e·696e·6720·2e2e·2e20·2020··ditioning·...··· | ||
| 00006ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ab0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ac0:·207c·0a7c·2020·2020·202d·2d20·7573·6564···|.|·····--·used | 00006ac0:·207c·0a7c·2020·2020·202d·2d20·7573·6564···|.|·····--·used | ||
| Offset 1711, 16 lines modified | Offset 1711, 16 lines modified | ||
| 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·················· | ||
| 00006b00:·2020·2020·7c0a·7c43·6f6d·7075·7469·6e67······|.|Computing | 00006b00:·2020·2020·7c0a·7c43·6f6d·7075·7469·6e67······|.|Computing | ||
| 00006b10:·206e·756d·6572·6963·616c·206b·6572·6e65···numerical·kerne | 00006b10:·206e·756d·6572·6963·616c·206b·6572·6e65···numerical·kerne | ||
| 00006b20:·6c20·2e2e·2e20·2020·2020·2020·2020·2020··l·...··········· | 00006b20:·6c20·2e2e·2e20·2020·2020·2020·2020·2020··l·...··········· | ||
| 00006b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006b40:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | 00006b40:·2020·2020·2020·207c·0a7c·2020·2020·202d·········|.|·····- | ||
| 00006b50:·2d20·7573·6564·2030·2073·6563·6f6e·6473··-·used·0·seconds | |||
| 00006b | 00006b50:·2d20·7573·6564·202e·3030·3339·3432·3820··-·used·.0039428· | ||
| 00006b60:·7365·636f·6e64·7320·2020·2020·2020·2020··seconds········· | |||
| 00006b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006b80:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 00006b80:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 00006b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006ba0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006bc0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00006bc0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00006bd0:·6f33·203d·207c·2079·5f31·5e32·2d79·5f30··o3·=·|·y_1^2-y_0 | 00006bd0:·6f33·203d·207c·2079·5f31·5e32·2d79·5f30··o3·=·|·y_1^2-y_0 | ||
| Offset 2646, 35 lines modified | Offset 2646, 35 lines modified | ||
| 0000a550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a550:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a560:·2020·2020·2020·2020·7c0a·7c53·616d·706c··········|.|Sampl | 0000a560:·2020·2020·2020·2020·7c0a·7c53·616d·706c··········|.|Sampl | ||
| 0000a570:·696e·6720·696d·6167·6520·706f·696e·7473··ing·image·points | 0000a570:·696e·6720·696d·6167·6520·706f·696e·7473··ing·image·points | ||
| 0000a580:·202e·2e2e·2020·2020·2020·2020·2020·2020···...············ | 0000a580:·202e·2e2e·2020·2020·2020·2020·2020·2020···...············ | ||
| 0000a590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a590:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a5a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a5a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a5b0:·2020·2020·2020·7c0a·7c20·2020·2020·2d2d········|.|·····-- | 0000a5b0:·2020·2020·2020·7c0a·7c20·2020·2020·2d2d········|.|·····-- | ||
| 0000a5c0:·2075·7365·6420·2e30·313 | 0000a5c0:·2075·7365·6420·2e30·3130·3535·3431·2073···used·.0105541·s | ||
| 0000a5d0:·6563·6f6e·6473·2020·2020·2020·2020·2020··econds·········· | 0000a5d0:·6563·6f6e·6473·2020·2020·2020·2020·2020··econds·········· | ||
| 0000a5e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a5e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a5f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a5f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a600:·2020·2020·7c0a·7c43·7265·6174·696e·6720······|.|Creating· | 0000a600:·2020·2020·7c0a·7c43·7265·6174·696e·6720······|.|Creating· | ||
| 0000a610:·696e·7465·7270·6f6c·6174·696f·6e20·6d61··interpolation·ma | 0000a610:·696e·7465·7270·6f6c·6174·696f·6e20·6d61··interpolation·ma | ||
| 0000a620:·7472·6978·202e·2e2e·2020·2020·2020·2020··trix·...········ | 0000a620:·7472·6978·202e·2e2e·2020·2020·2020·2020··trix·...········ | ||
| 0000a630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a640:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a650:·2020·7c0a·7c20·2020·2020·2d2d·2075·7365····|.|·····--·use | 0000a650:·2020·7c0a·7c20·2020·2020·2d2d·2075·7365····|.|·····--·use | ||
| 0000a660:·6420·2e30·313 | 0000a660:·6420·2e30·3131·3930·3834·2073·6563·6f6e··d·.0119084·secon | ||
| 0000a670:·6473·2020·2020·2020·2020·2020·2020·2020··ds·············· | 0000a670:·6473·2020·2020·2020·2020·2020·2020·2020··ds·············· | ||
| 0000a680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a6a0:·7c0a·7c50·6572·666f·726d·696e·6720·6e6f··|.|Performing·no | 0000a6a0:·7c0a·7c50·6572·666f·726d·696e·6720·6e6f··|.|Performing·no | ||
| 0000a6b0:·726d·616c·697a·6174·696f·6e20·7072·6563··rmalization·prec | 0000a6b0:·726d·616c·697a·6174·696f·6e20·7072·6563··rmalization·prec | ||
| 0000a6c0:·6f6e·6469·7469·6f6e·696e·6720·2e2e·2e20··onditioning·...· | 0000a6c0:·6f6e·6469·7469·6f6e·696e·6720·2e2e·2e20··onditioning·...· | ||
| 0000a6d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a6d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a6e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 0000a6e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 0000a6f0:·7c20·2020·2020·2d2d·2075·7365·6420·2e30··|·····--·used·.0 | 0000a6f0:·7c20·2020·2020·2d2d·2075·7365·6420·2e30··|·····--·used·.0 | ||
| 0000a700:·303 | 0000a700:·3035·3636·3734·3720·7365·636f·6e64·7320··0566747·seconds· | ||
| 0000a710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a730:·2020·2020·2020·2020·2020·2020·7c0a·7c43··············|.|C | 0000a730:·2020·2020·2020·2020·2020·2020·7c0a·7c43··············|.|C | ||
| 0000a740:·6f6d·7075·7469·6e67·206e·756d·6572·6963··omputing·numeric | 0000a740:·6f6d·7075·7469·6e67·206e·756d·6572·6963··omputing·numeric | ||
| 0000a750:·616c·206b·6572·6e65·6c20·2e2e·2e20·2020··al·kernel·...··· | 0000a750:·616c·206b·6572·6e65·6c20·2e2e·2e20·2020··al·kernel·...··· | ||
| 0000a760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Max diff block lines reached; 5361/14865 bytes (36.06%) of diff not shown. | |||
| Offset 5434, 32 lines modified | Offset 5434, 32 lines modified | ||
| 00015390:·313a·2028·6531·2c20·7b35·2c20·357d·2c20··1:·(e1,·{5,·5},· | 00015390:·313a·2028·6531·2c20·7b35·2c20·357d·2c20··1:·(e1,·{5,·5},· | ||
| 000153a0:·7b2d·332c·202d·347d·2920·2020·2020·2020··{-3,·-4})······· | 000153a0:·7b2d·332c·202d·347d·2920·2020·2020·2020··{-3,·-4})······· | ||
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| 00026570:·7c69·3920·3a20·7469·6d65·2042·203d·206f··|i9·:·time·B·=·o | 00026570:·7c69·3920·3a20·7469·6d65·2042·203d·206f··|i9·:·time·B·=·o | ||
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| 00026590:·7261·7465·6779·203d·3e20·4661·7374·4e6f··rategy·=>·FastNo | 00026590:·7261·7465·6779·203d·3e20·4661·7374·4e6f··rategy·=>·FastNo | ||
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| 000298f0:·207c·0a7c·202d·2d20·7573·6564·2030·2e31···|.|·--·used·0.1 | 000298f0:·207c·0a7c·202d·2d20·7573·6564·2030·2e31···|.|·--·used·0.1 | ||
| 00029900:·3 | 00029900:·3139·3731·3373·2028·6370·7529·3b20·302e··19713s·(cpu);·0. | ||
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| 00029930:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00029930:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00029940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029940:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029960:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029970:·2020·2020·2020·2020·207c·0a7c·6f35·203d···········|.|o5·= | 00029970:·2020·2020·2020·2020·207c·0a7c·6f35·203d···········|.|o5·= | ||
| 00029980:·2030·3a20·2865·302c·207b·327d·2c20·7b2d···0:·(e0,·{2},·{- | 00029980:·2030·3a20·2865·302c·207b·327d·2c20·7b2d···0:·(e0,·{2},·{- | ||
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| 0002aa60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0002aa60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0002aa70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0002aa70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0002aa80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0002aa80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
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| 00054360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00054360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00054370:·6933·203a·2061·7070·6c79·286d·6178·436f··i3·:·apply(maxCo | 00054370:·6933·203a·2061·7070·6c79·286d·6178·436f··i3·:·apply(maxCo | ||
| 00054380:·6e65·7320·462c·7261·7973·2920·2020·2020··nes·F,rays)····· | 00054380:·6e65·7320·462c·7261·7973·2920·2020·2020··nes·F,rays)····· | ||
| 00054390:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00054390:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 000543a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000543a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000543b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000543b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000543c0:·2020·2020·2020·2020·207c·0a7c·6f33·203d···········|.|o3·= | 000543c0:·2020·2020·2020·2020·207c·0a7c·6f33·203d···········|.|o3·= | ||
| 000543d0:·207b·7c20·3120· | 000543d0:·207b·7c20·3120·3020·7c2c·207c·202d·3120···{|·1·0·|,·|·-1· | ||
| 000543e0:·3020·7c2c·207c·20 | 000543e0:·3020·7c2c·207c·2031·202d·3120·7c7d·2020··0·|,·|·1·-1·|}·· | ||
| 000543f0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000543f0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00054400:·7c20·3020· | 00054400:·7c20·3020·3120·7c20·207c·202d·3120·3120··|·0·1·|··|·-1·1· | ||
| 00054410:·7c20·207c·20 | 00054410:·7c20·207c·2030·202d·3120·7c20·2020·2020··|··|·0·-1·|····· | ||
| 00054420:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00054420:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00054430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00054430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00054440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00054440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00054450:·2020·207c·0a7c·6f33·203a·204c·6973·7420·····|.|o3·:·List· | 00054450:·2020·207c·0a7c·6f33·203a·204c·6973·7420·····|.|o3·:·List· | ||
| 00054460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00054460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00054470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00054470:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00054480:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | 00054480:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
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| 0007c230:·6973·506f·6c79·746f·7061·6c20·4620·2020··isPolytopal·F··· | 0007c230:·6973·506f·6c79·746f·7061·6c20·4620·2020··isPolytopal·F··· | ||
| 0007c240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0007c240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0007c250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0007c250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0007c260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0007c260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0007c270:·2020·2020·2020·207c·0a7c·7b28·7b61·6d62·········|.|{({amb | 0007c270:·2020·2020·2020·207c·0a7c·7b28·7b61·6d62·········|.|{({amb | ||
| 0007c280:·6965·6e74·2064·696d·656e·7369·6f6e·203d··ient·dimension·= | 0007c280:·6965·6e74·2064·696d·656e·7369·6f6e·203d··ient·dimension·= | ||
| 0007c290:·3e20·3320·2020·2020·2020·2020·2020·7d2c··>·3···········}, | 0007c290:·3e20·3320·2020·2020·2020·2020·2020·7d2c··>·3···········}, | ||
| 0007c2a0:·207b·322c·2033·2c20·3 | 0007c2a0:·207b·322c·2033·2c20·347d·292c·2028·7b61···{2,·3,·4}),·({a | ||
| 0007c2b0:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | 0007c2b0:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | ||
| 0007c2c0:·203d·3e20·3320·207c·0a7c·2020·2064·696d···=>·3··|.|···dim | 0007c2c0:·203d·3e20·3320·207c·0a7c·2020·2064·696d···=>·3··|.|···dim | ||
| 0007c2d0:·656e·7369·6f6e·206f·6620·6c69·6e65·616c··ension·of·lineal | 0007c2d0:·656e·7369·6f6e·206f·6620·6c69·6e65·616c··ension·of·lineal | ||
| 0007c2e0:·6974·7920·7370·6163·6520·3d3e·2030·2020··ity·space·=>·0·· | 0007c2e0:·6974·7920·7370·6163·6520·3d3e·2030·2020··ity·space·=>·0·· | ||
| 0007c2f0:·2020·2020·2020·2020·2020·2020·2020·2064·················d | 0007c2f0:·2020·2020·2020·2020·2020·2020·2020·2064·················d | ||
| 0007c300:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | 0007c300:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | ||
| 0007c310:·616c·6974·7920·207c·0a7c·2020·2064·696d··ality··|.|···dim | 0007c310:·616c·6974·7920·207c·0a7c·2020·2064·696d··ality··|.|···dim | ||
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| 0007c4c0:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | 0007c4c0:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | ||
| 0007c4d0:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | 0007c4d0:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | ||
| 0007c4e0:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | 0007c4e0:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | ||
| 0007c4f0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c4f0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c500:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | 0007c500:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | ||
| 0007c510:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | 0007c510:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | ||
| 0007c520:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | 0007c520:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | ||
| 0007c530:·6365·7473·203d·3e20·3 | 0007c530:·6365·7473·203d·3e20·3420·2020·2020·2020··cets·=>·4······· | ||
| 0007c540:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c540:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c550:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | 0007c550:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | ||
| 0007c560:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | 0007c560:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | ||
| 0007c570:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | 0007c570:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | ||
| 0007c580:·7973·203d·3e20·3 | 0007c580:·7973·203d·3e20·3420·2020·2020·2020·2020··ys·=>·4········· | ||
| 0007c590:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | 0007c590:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | ||
| 0007c5a0:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | 0007c5a0:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | ||
| 0007c5b0:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | 0007c5b0:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | ||
| 0007c5c0:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | 0007c5c0:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | ||
| 0007c5d0:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | 0007c5d0:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | ||
| 0007c5e0:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | 0007c5e0:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | ||
| 0007c5f0:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | 0007c5f0:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | ||
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| 0007c650:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | 0007c650:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | ||
| 0007c660:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | 0007c660:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | ||
| 0007c670:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | 0007c670:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | ||
| 0007c680:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c680:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c690:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | 0007c690:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | ||
| 0007c6a0:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | 0007c6a0:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | ||
| 0007c6b0:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | 0007c6b0:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | ||
| 0007c6c0:·6365·7473·203d·3e20·3 | 0007c6c0:·6365·7473·203d·3e20·3420·2020·2020·2020··cets·=>·4······· | ||
| 0007c6d0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c6d0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c6e0:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | 0007c6e0:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | ||
| 0007c6f0:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | 0007c6f0:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | ||
| 0007c700:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | 0007c700:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | ||
| 0007c710:·7973·203d·3e20·3 | 0007c710:·7973·203d·3e20·3420·2020·2020·2020·2020··ys·=>·4········· | ||
| 0007c720:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | 0007c720:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | ||
| 0007c730:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | 0007c730:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | ||
| 0007c740:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | 0007c740:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | ||
| 0007c750:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | 0007c750:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | ||
| 0007c760:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | 0007c760:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | ||
| 0007c770:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | 0007c770:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | ||
| 0007c780:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | 0007c780:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | ||
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| 0007c7e0:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | 0007c7e0:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | ||
| 0007c7f0:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | 0007c7f0:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | ||
| 0007c800:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | 0007c800:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | ||
| 0007c810:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c810:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c820:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | 0007c820:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | ||
| 0007c830:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | 0007c830:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | ||
| 0007c840:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | 0007c840:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | ||
| 0007c850:·6365·7473·203d·3e20·3 | 0007c850:·6365·7473·203d·3e20·3420·2020·2020·2020··cets·=>·4······· | ||
| 0007c860:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c860:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c870:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | 0007c870:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | ||
| 0007c880:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | 0007c880:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | ||
| 0007c890:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | 0007c890:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | ||
| 0007c8a0:·7973·203d·3e20·3 | 0007c8a0:·7973·203d·3e20·3420·2020·2020·2020·2020··ys·=>·4········· | ||
| 0007c8b0:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | 0007c8b0:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | ||
| 0007c8c0:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | 0007c8c0:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | ||
| 0007c8d0:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | 0007c8d0:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | ||
| 0007c8e0:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | 0007c8e0:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | ||
| 0007c8f0:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | 0007c8f0:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | ||
| 0007c900:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | 0007c900:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | ||
| 0007c910:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | 0007c910:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | ||
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| 0007c970:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | 0007c970:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | ||
| 0007c980:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | 0007c980:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | ||
| 0007c990:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | 0007c990:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | ||
| 0007c9a0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c9a0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007c9b0:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | 0007c9b0:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | ||
| 0007c9c0:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | 0007c9c0:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | ||
| 0007c9d0:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | 0007c9d0:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | ||
| 0007c9e0:·6365·7473·203d·3e20·3 | 0007c9e0:·6365·7473·203d·3e20·3420·2020·2020·2020··cets·=>·4······· | ||
| 0007c9f0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007c9f0:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007ca00:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | 0007ca00:·756d·6265·7220·6f66·2072·6179·7320·3d3e··umber·of·rays·=> | ||
| 0007ca10:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | 0007ca10:·2034·2020·2020·2020·2020·2020·2020·2020···4·············· | ||
| 0007ca20:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | 0007ca20:·2020·2020·6e75·6d62·6572·206f·6620·7261······number·of·ra | ||
| 0007ca30:·7973·203d·3e20·3 | 0007ca30:·7973·203d·3e20·3420·2020·2020·2020·2020··ys·=>·4········· | ||
| 0007ca40:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | 0007ca40:·2020·2020·2020·207c·0a7c·763a·207b·7b61·········|.|v:·{{a | ||
| 0007ca50:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | 0007ca50:·6d62·6965·6e74·2064·696d·656e·7369·6f6e··mbient·dimension | ||
| 0007ca60:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | 0007ca60:·203d·3e20·3320·2020·2020·2020·2020·2020···=>·3··········· | ||
| 0007ca70:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | 0007ca70:·7d2c·207b·616d·6269·656e·7420·6469·6d65··},·{ambient·dime | ||
| 0007ca80:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | 0007ca80:·6e73·696f·6e20·3d3e·2033·2020·2020·2020··nsion·=>·3······ | ||
| 0007ca90:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | 0007ca90:·2020·2020·2020·207c·0a7c·2020·2020·2064·········|.|·····d | ||
| 0007caa0:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | 0007caa0:·696d·656e·7369·6f6e·206f·6620·6c69·6e65··imension·of·line | ||
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| 0007cb00:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | 0007cb00:·636f·6e65·203d·3e20·3320·2020·2020·2020··cone·=>·3······· | ||
| 0007cb10:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | 0007cb10:·2020·2020·6469·6d65·6e73·696f·6e20·6f66······dimension·of | ||
| 0007cb20:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | 0007cb20:·2074·6865·2063·6f6e·6520·3d3e·2033·2020···the·cone·=>·3·· | ||
| 0007cb30:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | 0007cb30:·2020·2020·2020·207c·0a7c·2020·2020·206e·········|.|·····n | ||
| 0007cb40:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | 0007cb40:·756d·6265·7220·6f66·2066·6163·6574·7320··umber·of·facets· | ||
| 0007cb50:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | 0007cb50:·3d3e·2034·2020·2020·2020·2020·2020·2020··=>·4············ | ||
| 0007cb60:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | 0007cb60:·2020·2020·6e75·6d62·6572·206f·6620·6661······number·of·fa | ||
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| 00029b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00029b90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00029ba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00029ba0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00029bb0:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3120·3a20··-------+.|i11·:· | 00029bb0:·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3120·3a20··-------+.|i11·:· | ||
| 00029bc0:·656c·6170·7365·6454·696d·6520·556c·7220··elapsedTime·Ulr· | 00029bc0:·656c·6170·7365·6454·696d·6520·556c·7220··elapsedTime·Ulr· | ||
| 00029bd0:·3d20·7365·6172·6368·556c·7269·6368·284d··=·searchUlrich(M | 00029bd0:·3d20·7365·6172·6368·556c·7269·6368·284d··=·searchUlrich(M | ||
| 00029be0:·2c53·293b·2020·2020·2020·2020·2020·2020··,S);············ | 00029be0:·2c53·293b·2020·2020·2020·2020·2020·2020··,S);············ | ||
| 00029bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029c00:·2020·2020·2020·207c·0a7c·202d·2d20·3 | 00029c00:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | ||
| 00029c10:·3 | 00029c10:·3730·3730·3737·2073·6563·6f6e·6473·2065··707077·seconds·e | ||
| 00029c20:·6170 | 00029c20:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 00029c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029c30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029c40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029c50:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 00029c50:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00029c60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00029c60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00029c70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00029c70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00029c80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00029c80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00029c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00029c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- |
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| 00003530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003530:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003540:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003550:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·656c··-----+.|i10·:·el | 00003550:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·656c··-----+.|i10·:·el | ||
| 00003560:·6170·7365·6454·696d·6520·2851·2c69·6e47··apsedTime·(Q,inG | 00003560:·6170·7365·6454·696d·6520·2851·2c69·6e47··apsedTime·(Q,inG | ||
| 00003570:·2c47·2920·3d20·6166·6669·6e65·4661·7450··,G)·=·affineFatP | 00003570:·2c47·2920·3d20·6166·6669·6e65·4661·7450··,G)·=·affineFatP | ||
| 00003580:·6f69·6e74·7328·4d2c·6d75·6c74·732c·5229··oints(M,mults,R) | 00003580:·6f69·6e74·7328·4d2c·6d75·6c74·732c·5229··oints(M,mults,R) | ||
| 00003590:·3b20·2020·2020·2020·2020·2020·2020·2020··;··············· | 00003590:·3b20·2020·2020·2020·2020·2020·2020·2020··;··············· | ||
| 000035a0:·2020·2020·207c·0a7c·202d·2d20·332e·3 | 000035a0:·2020·2020·207c·0a7c·202d·2d20·332e·3632·······|.|·--·3.62 | ||
| 000035b0:·3 | 000035b0:·3937·3920·7365·636f·6e64·7320·656c·6170··979·seconds·elap | ||
| 000035c0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | 000035c0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 000035d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000035d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000035e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000035e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000035f0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | 000035f0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
| 00003600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003600:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·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·2d2b·0a7c·6931·3120·3a20·656c··-----+.|i11·:·el | 00003640:·2d2d·2d2d·2d2b·0a7c·6931·3120·3a20·656c··-----+.|i11·:·el | ||
| 00003650:·6170·7365·6454·696d·6520·4820·3d20·6166··apsedTime·H·=·af | 00003650:·6170·7365·6454·696d·6520·4820·3d20·6166··apsedTime·H·=·af | ||
| 00003660:·6669·6e65·4661·7450·6f69·6e74·7342·7949··fineFatPointsByI | 00003660:·6669·6e65·4661·7450·6f69·6e74·7342·7949··fineFatPointsByI | ||
| 00003670:·6e74·6572·7365·6374·696f·6e28·4d2c·6d75··ntersection(M,mu | 00003670:·6e74·6572·7365·6374·696f·6e28·4d2c·6d75··ntersection(M,mu | ||
| 00003680:·6c74·732c·5229·3b20·2020·2020·2020·2020··lts,R);········· | 00003680:·6c74·732c·5229·3b20·2020·2020·2020·2020··lts,R);········· | ||
| 00003690:·2020·2020·207c·0a7c·202d·2d20·332e·3 | 00003690:·2020·2020·207c·0a7c·202d·2d20·332e·3332·······|.|·--·3.32 | ||
| 000036a0:·3 | 000036a0:·3239·3120·7365·636f·6e64·7320·656c·6170··291·seconds·elap | ||
| 000036b0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | 000036b0:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 000036c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000036c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000036d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000036d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000036e0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | 000036e0:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
| 000036f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000036f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·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··---------------- |
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| 00001ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001ff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002000:·2020·7c0a·7c6f·3420·3d20·6964·6561·6c20····|.|o4·=·ideal· | 00002000:·2020·7c0a·7c6f·3420·3d20·6964·6561·6c20····|.|o4·=·ideal· | ||
| 00002010:·2878·2020·2078·2020·2020·2d20·7820·2020··(x···x····-·x··· | 00002010:·2878·2020·2078·2020·2020·2d20·7820·2020··(x···x····-·x··· | ||
| 00002020:·7820·2020·2c20·7820·2020·7820·2020·202d··x···,·x···x····- | 00002020:·7820·2020·2c20·7820·2020·7820·2020·202d··x···,·x···x····- | ||
| 00002030:·2078·2020·2078·2020·202c·2078·2020·2078···x···x···,·x···x | 00002030:·2078·2020·2078·2020·202c·2078·2020·2078···x···x···,·x···x | ||
| 00002040:·2020·2020·2d20·7820·2020·7820·2020·2c20······-·x···x···,· | 00002040:·2020·2020·2d20·7820·2020·7820·2020·2c20······-·x···x···,· | ||
| 00002050:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00002050:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00002060:·2020·3 | 00002060:·2020·342c·3420·322c·3320·2020·2034·2c33····4,4·2,3····4,3 | ||
| 00002070:·203 | 00002070:·2032·2c34·2020·2032·2c32·2031·2c31·2020···2,4···2,2·1,1·· | ||
| 00002080:·2020·322c·3120·312c·3 | 00002080:·2020·322c·3120·312c·3220·2020·342c·3220····2,1·1,2···4,2· | ||
| 00002090:·332c·3120·2020·2034·2c31·2033·2c3 | 00002090:·332c·3120·2020·2034·2c31·2033·2c32·2020··3,1····4,1·3,2·· | ||
| 000020a0:·2020·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d····|.|·····------ | 000020a0:·2020·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d····|.|·····------ | ||
| 000020b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000020b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000020c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000020c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000020d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000020d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000020e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000020e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000020f0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | 000020f0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | ||
| 00002100:·2020·202d·2078·2020·2078·2020·202c·2078·····-·x···x···,·x | 00002100:·2020·202d·2078·2020·2078·2020·202c·2078·····-·x···x···,·x | ||
| 00002110:·2020·2078·2020·2020·2d20·7820·2020·7820·····x····-·x···x· | 00002110:·2020·2078·2020·2020·2d20·7820·2020·7820·····x····-·x···x· | ||
| 00002120:·2020·2c20·7820·2020·7820·2020·202d·2078····,·x···x····-·x | 00002120:·2020·2c20·7820·2020·7820·2020·202d·2078····,·x···x····-·x | ||
| 00002130:·2020·2078·2020·202c·2078·2020·2078·2020·····x···,·x···x·· | 00002130:·2020·2078·2020·202c·2078·2020·2078·2020·····x···,·x···x·· | ||
| 00002140:·2020·7c0a·7c20·2020·2020·203 | 00002140:·2020·7c0a·7c20·2020·2020·2032·2c33·2031····|.|······2,3·1 | ||
| 00002150:·2c3 | 00002150:·2c31·2020·2020·322c·3120·312c·3320·2020··,1····2,1·1,3··· | ||
| 00002160:·3 | 00002160:·342c·3320·332c·3120·2020·2034·2c31·2033··4,3·3,1····4,1·3 | ||
| 00002170:·2c3 | 00002170:·2c33·2020·2034·2c34·2031·2c33·2020·2020··,3···4,4·1,3···· | ||
| 00002180:·3 | 00002180:·342c·3320·312c·3420·2020·332c·3420·322c··4,3·1,4···3,4·2, | ||
| 00002190:·3 | 00002190:·3320·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d··3·|.|·····------ | ||
| 000021a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000021a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000021b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000021b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000021c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000021c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000021d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000021d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000021e0:·2d2d·7c0a·7c20·2020·2020·2d20·7820·2020··--|.|·····-·x··· | 000021e0:·2d2d·7c0a·7c20·2020·2020·2d20·7820·2020··--|.|·····-·x··· | ||
| 000021f0:·7820·2020·2c20·7820·2020·7820·2020·202d··x···,·x···x····- | 000021f0:·7820·2020·2c20·7820·2020·7820·2020·202d··x···,·x···x····- | ||
| 00002200:·2078·2020·2078·2020·202c·2078·2020·2078···x···x···,·x···x | 00002200:·2078·2020·2078·2020·202c·2078·2020·2078···x···x···,·x···x | ||
| 00002210:·2020·2020·2d20·7820·2020·7820·2020·2c20······-·x···x···,· | 00002210:·2020·2020·2d20·7820·2020·7820·2020·2c20······-·x···x···,· | ||
| 00002220:·7820·2020·7820·2020·202d·2020·2020·2020··x···x····-······ | 00002220:·7820·2020·7820·2020·202d·2020·2020·2020··x···x····-······ | ||
| 00002230:·2020·7c0a·7c20·2020·2020·2020·203 | 00002230:·2020·7c0a·7c20·2020·2020·2020·2033·2c33····|.|········3,3 | ||
| 00002240:·2031·2c32·2020·2032·2c34·2031·2c32·2020···1,2···2,4·1,2·· | |||
| 000022 | 00002240:·2032·2c34·2020·2034·2c32·2032·2c31·2020···2,4···4,2·2,1·· | ||
| 00002250:·2020·342c·3120·322c·3220·2020·322c·3320····4,1·2,2···2,3· | |||
| 00002260:·3 | 00002260:·312c·3220·2020·2032·2c32·2031·2c33·2020··1,2····2,2·1,3·· | ||
| 00002270:·2032·2c34·2031·2c3 | 00002270:·2032·2c34·2031·2c31·2020·2020·2020·2020···2,4·1,1········ | ||
| 00002280:·2020·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d····|.|·····------ | 00002280:·2020·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d····|.|·····------ | ||
| 00002290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000022a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000022a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000022b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000022b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000022c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000022c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000022d0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | 000022d0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | ||
| 000022e0:·2020·2c20·7820·2020·7820·2020·202d·2078····,·x···x····-·x | 000022e0:·2020·2c20·7820·2020·7820·2020·202d·2078····,·x···x····-·x | ||
| 000022f0:·2020·2078·2020·202c·2078·2020·2078·2020·····x···,·x···x·· | 000022f0:·2020·2078·2020·202c·2078·2020·2078·2020·····x···,·x···x·· | ||
| 00002300:·2020·2d20·7820·2020·7820·2020·2c20·7820····-·x···x···,·x· | 00002300:·2020·2d20·7820·2020·7820·2020·2c20·7820····-·x···x···,·x· | ||
| 00002310:·2020·7820·2020·202d·2078·2020·2078·2020····x····-·x···x·· | 00002310:·2020·7820·2020·202d·2078·2020·2078·2020····x····-·x···x·· | ||
| 00002320:·202c·7c0a·7c20·2020·2020·2032·2c3 | 00002320:·202c·7c0a·7c20·2020·2020·2032·2c31·2031···,|.|······2,1·1 | ||
| 00002330:·2c34·2020·2034·2c34·2033·2c3 | 00002330:·2c34·2020·2034·2c34·2033·2c31·2020·2020··,4···4,4·3,1···· | ||
| 00002340:·342c·3320·332c·3420·2020·332c·3220·312c··4,3·3,4···3,2·1, | |||
| 000023 | 00002340:·342c·3120·332c·3420·2020·342c·3320·332c··4,1·3,4···4,3·3, | ||
| 00002350:·3220·2020·2034·2c32·2033·2c33·2020·2033··2····4,2·3,3···3 | |||
| 00002360:·2c34·203 | 00002360:·2c34·2031·2c33·2020·2020·332c·3320·312c··,4·1,3····3,3·1, | ||
| 00002370:·3420·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d··4·|.|·····------ | 00002370:·3420·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d··4·|.|·····------ | ||
| 00002380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002380:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000023a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000023a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000023b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000023b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000023c0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | 000023c0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | ||
| 000023d0:·2020·202d·2078·2020·2078·2020·202c·2078·····-·x···x···,·x | 000023d0:·2020·202d·2078·2020·2078·2020·202c·2078·····-·x···x···,·x | ||
| 000023e0:·2020·2078·2020·2020·2d20·7820·2020·7820·····x····-·x···x· | 000023e0:·2020·2078·2020·2020·2d20·7820·2020·7820·····x····-·x···x· | ||
| 000023f0:·2020·2c20·7820·2020·7820·2020·202d·2078····,·x···x····-·x | 000023f0:·2020·2c20·7820·2020·7820·2020·202d·2078····,·x···x····-·x | ||
| 00002400:·2020·2078·2020·202c·2078·2020·2078·2020·····x···,·x···x·· | 00002400:·2020·2078·2020·202c·2078·2020·2078·2020·····x···,·x···x·· | ||
| 00002410:·2020·7c0a·7c20·2020·2020·203 | 00002410:·2020·7c0a·7c20·2020·2020·2033·2c32·2032····|.|······3,2·2 | ||
| 00002420:·2c31·2020·2020·3 | 00002420:·2c31·2020·2020·332c·3120·322c·3220·2020··,1····3,1·2,2··· | ||
| 00002430:·342c·3220·3 | 00002430:·342c·3220·312c·3120·2020·2034·2c31·2031··4,2·1,1····4,1·1 | ||
| 00002440:·2c32·2020·2032·2c3 | 00002440:·2c32·2020·2032·2c34·2031·2c32·2020·2020··,2···2,4·1,2···· | ||
| 00002450:·322c·3 | 00002450:·322c·3220·312c·3420·2020·342c·3420·332c··2,2·1,4···4,4·3, | ||
| 00002460:·3 | 00002460:·3220·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d··2·|.|·····------ | ||
| 00002470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002480:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002490:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000024a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000024a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000024b0:·2d2d·7c0a·7c20·2020·2020·2d20·7820·2020··--|.|·····-·x··· | 000024b0:·2d2d·7c0a·7c20·2020·2020·2d20·7820·2020··--|.|·····-·x··· | ||
| 000024c0:·7820·2020·2c20·7820·2020·7820·2020·202d··x···,·x···x····- | 000024c0:·7820·2020·2c20·7820·2020·7820·2020·202d··x···,·x···x····- | ||
| 000024d0:·2078·2020·2078·2020·202c·2078·2020·2078···x···x···,·x···x | 000024d0:·2078·2020·2078·2020·202c·2078·2020·2078···x···x···,·x···x | ||
| 000024e0:·2020·2020·2d20·7820·2020·7820·2020·2c20······-·x···x···,· | 000024e0:·2020·2020·2d20·7820·2020·7820·2020·2c20······-·x···x···,· | ||
| 000024f0:·7820·2020·7820·2020·202d·2020·2020·2020··x···x····-······ | 000024f0:·7820·2020·7820·2020·202d·2020·2020·2020··x···x····-······ | ||
| 00002500:·2020·7c0a·7c20·2020·2020·2020·2034·2c3 | 00002500:·2020·7c0a·7c20·2020·2020·2020·2034·2c32····|.|········4,2 | ||
| 00002510:·2033·2c3 | 00002510:·2033·2c34·2020·2032·2c34·2031·2c33·2020···3,4···2,4·1,3·· | ||
| 00002520:·2020·3 | 00002520:·2020·322c·3320·312c·3420·2020·342c·3420····2,3·1,4···4,4· | ||
| 00002530:·3 | 00002530:·332c·3320·2020·2034·2c33·2033·2c34·2020··3,3····4,3·3,4·· | ||
| 00002540:·203 | 00002540:·2033·2c32·2031·2c31·2020·2020·2020·2020···3,2·1,1········ | ||
| 00002550:·2020·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d····|.|·····------ | 00002550:·2020·7c0a·7c20·2020·2020·2d2d·2d2d·2d2d····|.|·····------ | ||
| 00002560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002560:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002590:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000025a0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | 000025a0:·2d2d·7c0a·7c20·2020·2020·7820·2020·7820··--|.|·····x···x· | ||
| 000025b0:·2020·2920·2020·2020·2020·2020·2020·2020····)············· | 000025b0:·2020·2920·2020·2020·2020·2020·2020·2020····)············· | ||
| 000025c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000025c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000025d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000025d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000025e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000025e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000025f0:·2020·7c0a·7c20·2020·2020·203 | 000025f0:·2020·7c0a·7c20·2020·2020·2033·2c31·2031····|.|······3,1·1 | ||
| 00002600:·2c32·2020·2020·2020·2020·2020·2020·2020··,2·············· | 00002600:·2c32·2020·2020·2020·2020·2020·2020·2020··,2·············· | ||
| 00002610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002620:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002630:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002640:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00002640:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00002650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002660:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 8745, 17 lines modified | Offset 8745, 17 lines modified | ||
| 00022280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000222a0:·2d2d·2d2d·2b0a·7c69·3420·3a20·7469·6d65··----+.|i4·:·time | 000222a0:·2d2d·2d2d·2b0a·7c69·3420·3a20·7469·6d65··----+.|i4·:·time | ||
| 000222b0:·2067·7265·656e·654b·6c65·6974·6d61·6e50···greeneKleitmanP | 000222b0:·2067·7265·656e·654b·6c65·6974·6d61·6e50···greeneKleitmanP | ||
| 000222c0:·6172·7469·7469·6f6e·2844·2c20·5374·7261··artition(D,·Stra | 000222c0:·6172·7469·7469·6f6e·2844·2c20·5374·7261··artition(D,·Stra | ||
| 000222d0:·7465·6779·203d·3e20·2261·6e74·6963·6861··tegy·=>·"anticha | 000222d0:·7465·6779·203d·3e20·2261·6e74·6963·6861··tegy·=>·"anticha | ||
| 000222e0:·696e·7322·297c·0a7c·202d·2d20·7573·6564··ins")|.|·--·used | 000222e0:·696e·7322·297c·0a7c·202d·2d20·7573·6564··ins")|.|·--·used | ||
| 000222f0:·2030·2e35·3 | 000222f0:·2030·2e35·3331·3335·3273·2028·6370·7529···0.531352s·(cpu) | ||
| 00022300:·3b20·302e·323 | 00022300:·3b20·302e·3235·3431·3873·2028·7468·7265··;·0.25418s·(thre | ||
| 00022310:·6 | 00022310:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00022320:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 00022320:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 00022330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022330:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022340:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022350:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022360:·2020·2020·2020·207c·0a7c·6f34·203d·2050·········|.|o4·=·P | 00022360:·2020·2020·2020·207c·0a7c·6f34·203d·2050·········|.|o4·=·P | ||
| 00022370:·6172·7469·7469·6f6e·7b39·2c20·327d·2020··artition{9,·2}·· | 00022370:·6172·7469·7469·6f6e·7b39·2c20·327d·2020··artition{9,·2}·· | ||
| 00022380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00022440:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022440:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00022450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00022460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935··-----------+.|i5 | 00022460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935··-----------+.|i5 | ||
| 00022470:·203a·2074·696d·6520·6772·6565·6e65·4b6c···:·time·greeneKl | 00022470:·203a·2074·696d·6520·6772·6565·6e65·4b6c···:·time·greeneKl | ||
| 00022480:·6569·746d·616e·5061·7274·6974·696f·6e28··eitmanPartition( | 00022480:·6569·746d·616e·5061·7274·6974·696f·6e28··eitmanPartition( | ||
| 00022490:·442c·2053·7472·6174·6567·7920·3d3e·2022··D,·Strategy·=>·" | 00022490:·442c·2053·7472·6174·6567·7920·3d3e·2022··D,·Strategy·=>·" | ||
| 000224a0:·6368·6169·6e73·2229·2020·2020·7c0a·7c20··chains")····|.|· | 000224a0:·6368·6169·6e73·2229·2020·2020·7c0a·7c20··chains")····|.|· | ||
| 000224b0:·2d2d·2075·7365·6420·302e·3030·303 | 000224b0:·2d2d·2075·7365·6420·302e·3030·3033·3439··--·used·0.000349 | ||
| 000224c0:·3 | 000224c0:·3036·3573·2028·6370·7529·3b20·372e·3134··065s·(cpu);·7.14 | ||
| 000224d0:·3 | 000224d0:·3165·2d30·3673·2028·7468·7265·6164·293b··1e-06s·(thread); | ||
| 000224e0:·2030·7320·2867·6329·2020·2020·207c·0a7c···0s·(gc)·····|.| | 000224e0:·2030·7320·2867·6329·2020·2020·207c·0a7c···0s·(gc)·····|.| | ||
| 000224f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000224f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022500:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022500:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022510:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00022510:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00022520:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00022520:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00022530:·7c6f·3520·3d20·5061·7274·6974·696f·6e7b··|o5·=·Partition{ | 00022530:·7c6f·3520·3d20·5061·7274·6974·696f·6e7b··|o5·=·Partition{ | ||
| 00022540:·392c·2032·7d20·2020·2020·2020·2020·2020··9,·2}··········· | 00022540:·392c·2032·7d20·2020·2020·2020·2020·2020··9,·2}··········· | ||
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| 000481e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000481e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000481f0:·2d2b·0a7c·6937·203a·2074·696d·6520·6973··-+.|i7·:·time·is | 000481f0:·2d2b·0a7c·6937·203a·2074·696d·6520·6973··-+.|i7·:·time·is | ||
| 00048200:·4469·7374·7269·6275·7469·7665·2043·2020··Distributive·C·· | 00048200:·4469·7374·7269·6275·7469·7665·2043·2020··Distributive·C·· | ||
| 00048210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00048230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00048240:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | 00048240:·207c·0a7c·202d·2d20·7573·6564·2030·2e30···|.|·--·used·0.0 | ||
| 00048250:·303 | 00048250:·3033·3533·3330·3773·2028·6370·7529·3b20··0353307s·(cpu);· | ||
| 00048260:·3 | 00048260:·372e·3430·3165·2d30·3673·2028·7468·7265··7.401e-06s·(thre | ||
| 00048270:·6429 | 00048270:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 00048280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00048290:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00048290:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 000482a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000482a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000482b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000482b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000482c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000482c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000482d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000482d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000482e0:·207c·0a7c·6f37·203d·2074·7275·6520·2020···|.|o7·=·true··· | 000482e0:·207c·0a7c·6f37·203d·2074·7275·6520·2020···|.|o7·=·true··· | ||
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| 00048360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00048360:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00048370:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00048370:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00048380:·2d2b·0a7c·6938·203a·2074·696d·6520·6973··-+.|i8·:·time·is | 00048380:·2d2b·0a7c·6938·203a·2074·696d·6520·6973··-+.|i8·:·time·is | ||
| 00048390:·4469·7374·7269·6275·7469·7665·2050·2020··Distributive·P·· | 00048390:·4469·7374·7269·6275·7469·7665·2050·2020··Distributive·P·· | ||
| 000483a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000483a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000483b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000483b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000483c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000483c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000483d0:·207c·0a7c·202d·2d20·7573·6564·203 | 000483d0:·207c·0a7c·202d·2d20·7573·6564·2031·302e···|.|·--·used·10. | ||
| 000483e0:·3 | 000483e0:·3236·3433·7320·2863·7075·293b·2034·2e34··2643s·(cpu);·4.4 | ||
| 000483f0:·3 | 000483f0:·3138·3631·7320·2874·6872·6561·6429·3b20··1861s·(thread);· | ||
| 00048400:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 00048400:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 00048410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00048420:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 00048420:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 00048430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00048460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00048460:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00048670:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00048670:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00048680:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·7469··-----+.|i10·:·ti | 00048680:·2d2d·2d2d·2d2b·0a7c·6931·3020·3a20·7469··-----+.|i10·:·ti | ||
| 00048690:·6d65·2069·7344·6973·7472·6962·7574·6976··me·isDistributiv | 00048690:·6d65·2069·7344·6973·7472·6962·7574·6976··me·isDistributiv | ||
| 000486a0:·6520·4327·2020·2020·2020·2020·2020·2020··e·C'············ | 000486a0:·6520·4327·2020·2020·2020·2020·2020·2020··e·C'············ | ||
| 000486b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000486b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000486c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000486c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000486d0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 000486d0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 000486e0:·2030·2e30·3030·3 | 000486e0:·2030·2e30·3030·3331·3033·3137·7320·2863···0.000310317s·(c | ||
| 000486f0:·7075·293b·203 | 000486f0:·7075·293b·2035·2e31·3538·652d·3036·7320··pu);·5.158e-06s· | ||
| 00048700:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | 00048700:·2874·6872·6561·6429·3b20·3073·2028·6763··(thread);·0s·(gc | ||
| 00048710:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | 00048710:·2920·2020·2020·2020·2020·2020·2020·2020··)··············· | ||
| 00048720:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00048720:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
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| 0000e270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e290:·2b0a·7c69·3420·3a20·656c·6170·7365·6454··+.|i4·:·elapsedT | 0000e290:·2b0a·7c69·3420·3a20·656c·6170·7365·6454··+.|i4·:·elapsedT | ||
| 0000e2a0:·696d·6520·6b65·726e·656c·4f66·4c6f·6361··ime·kernelOfLoca | 0000e2a0:·696d·6520·6b65·726e·656c·4f66·4c6f·6361··ime·kernelOfLoca | ||
| 0000e2b0:·6c69·7a61·7469·6f6e·284d·2c20·4931·2920··lization(M,·I1)· | 0000e2b0:·6c69·7a61·7469·6f6e·284d·2c20·4931·2920··lization(M,·I1)· | ||
| 0000e2c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e2c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e2d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e2d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e2e0:·7c0a·7c20·2d2d·2030·2e3 | 0000e2e0:·7c0a·7c20·2d2d·2030·2e34·3535·3538·2073··|.|·--·0.45558·s | ||
| 0000e2f0:· | 0000e2f0:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | ||
| 0000e300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e320:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e330:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0000e330:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 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·················· | ||
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| 0000e6d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e6d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e6e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e6e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e6f0:·2b0a·7c69·3520·3a20·656c·6170·7365·6454··+.|i5·:·elapsedT | 0000e6f0:·2b0a·7c69·3520·3a20·656c·6170·7365·6454··+.|i5·:·elapsedT | ||
| 0000e700:·696d·6520·6b65·726e·656c·4f66·4c6f·6361··ime·kernelOfLoca | 0000e700:·696d·6520·6b65·726e·656c·4f66·4c6f·6361··ime·kernelOfLoca | ||
| 0000e710:·6c69·7a61·7469·6f6e·284d·2c20·4932·2920··lization(M,·I2)· | 0000e710:·6c69·7a61·7469·6f6e·284d·2c20·4932·2920··lization(M,·I2)· | ||
| 0000e720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e720:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e740:·7c0a·7c20·2d2d·2030·2e30·3 | 0000e740:·7c0a·7c20·2d2d·2030·2e30·3233·3338·3735··|.|·--·0.0233875 | ||
| 0000e750:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | 0000e750:·2073·6563·6f6e·6473·2065·6c61·7073·6564···seconds·elapsed | ||
| 0000e760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e790:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0000e790:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 0000e7a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e7a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e7b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e7b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000eb30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000eb30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000eb40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000eb40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000eb50:·2b0a·7c69·3620·3a20·656c·6170·7365·6454··+.|i6·:·elapsedT | 0000eb50:·2b0a·7c69·3620·3a20·656c·6170·7365·6454··+.|i6·:·elapsedT | ||
| 0000eb60:·696d·6520·6b65·726e·656c·4f66·4c6f·6361··ime·kernelOfLoca | 0000eb60:·696d·6520·6b65·726e·656c·4f66·4c6f·6361··ime·kernelOfLoca | ||
| 0000eb70:·6c69·7a61·7469·6f6e·284d·2c20·4933·2920··lization(M,·I3)· | 0000eb70:·6c69·7a61·7469·6f6e·284d·2c20·4933·2920··lization(M,·I3)· | ||
| 0000eb80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eb80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eb90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000eb90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000eba0:·7c0a·7c20·2d2d·2030·2e3 | 0000eba0:·7c0a·7c20·2d2d·2030·2e31·3331·3838·3820··|.|·--·0.131888· | ||
| 0000ebb0:· | 0000ebb0:·7365·636f·6e64·7320·656c·6170·7365·6420··seconds·elapsed· | ||
| 0000ebc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ebd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ebe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ebe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ebf0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | 0000ebf0:·7c0a·7c20·2020·2020·2020·2020·2020·2020··|.|············· | ||
| 0000ec00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ec20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ec20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00014a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014a50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00014a60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00014a70:·7c69·3320·3a20·656c·6170·7365·6454·696d··|i3·:·elapsedTim | 00014a70:·7c69·3320·3a20·656c·6170·7365·6454·696d··|i3·:·elapsedTim | ||
| 00014a80:·6520·7265·6753·6571·496e·4964·6561·6c20··e·regSeqInIdeal· | 00014a80:·6520·7265·6753·6571·496e·4964·6561·6c20··e·regSeqInIdeal· | ||
| 00014a90:·4920·2020·2020·2020·2020·2020·2020·2020··I··············· | 00014a90:·4920·2020·2020·2020·2020·2020·2020·2020··I··············· | ||
| 00014aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014ab0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00014ab0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00014ac0:·7c20·2d2d·2030·2e3 | 00014ac0:·7c20·2d2d·2030·2e31·3533·3039·3920·7365··|·--·0.153099·se | ||
| 00014ad0:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | 00014ad0:·636f·6e64·7320·656c·6170·7365·6420·2020··conds·elapsed··· | ||
| 00014ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014ae0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014af0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b00:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00014b00:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00014b10:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00014b10:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00014b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014b30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00015570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00015570:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00015580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00015580:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00015590:·2d2d·2d2b·0a7c·6937·203a·2065·6c61·7073··---+.|i7·:·elaps | 00015590:·2d2d·2d2b·0a7c·6937·203a·2065·6c61·7073··---+.|i7·:·elaps | ||
| 000155a0:·6564·5469·6d65·2072·6567·5365·7149·6e49··edTime·regSeqInI | 000155a0:·6564·5469·6d65·2072·6567·5365·7149·6e49··edTime·regSeqInI | ||
| 000155b0:·6465·616c·2849·2c20·332c·2033·2c20·3129··deal(I,·3,·3,·1) | 000155b0:·6465·616c·2849·2c20·332c·2033·2c20·3129··deal(I,·3,·3,·1) | ||
| 000155c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000155c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000155d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000155d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000155e0:·2020·207c·0a7c·202d·2d20·302e·3031·3 | 000155e0:·2020·207c·0a7c·202d·2d20·302e·3031·3936·····|.|·--·0.0196 | ||
| 000155f0:·3 | 000155f0:·3532·3220·7365·636f·6e64·7320·656c·6170··522·seconds·elap | ||
| 00015600:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | 00015600:·7365·6420·2020·2020·2020·2020·2020·2020··sed············· | ||
| 00015610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00015630:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00015630:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
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| 00015660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015660:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 000090d0:·203d·2069·7465·7261·746f·7220·7820·2020···=·iterator·x··· | 000090d0:·203d·2069·7465·7261·746f·7220·7820·2020···=·iterator·x··· | ||
| 000090e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000090e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000090f0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 000090f0:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00009100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009120:·2020·2020·2020·2020·207c·0a7c·6f32·203d···········|.|o2·= | 00009120:·2020·2020·2020·2020·207c·0a7c·6f32·203d···········|.|o2·= | ||
| 00009130:·203c·7261·6e67·655f·6974·6572·6174·6f72···<range_iterator | 00009130:·203c·7261·6e67·655f·6974·6572·6174·6f72···<range_iterator | ||
| 00009140:·206f·626a·6563·7420·6174·2030·7837·66 | 00009140:·206f·626a·6563·7420·6174·2030·7837·6666···object·at·0x7ff | ||
| 00009150:·393 | 00009150:·3931·6162·6231·6362·303e·7c0a·7c20·2020··91abb1cb0>|.|··· | ||
| 00009160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009160:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009170:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009180:·2020·2020·2020·2020·2020·207c·0a7c·6f32·············|.|o2 | 00009180:·2020·2020·2020·2020·2020·207c·0a7c·6f32·············|.|o2 | ||
| 00009190:·203a·2050·7974·686f·6e4f·626a·6563·7420···:·PythonObject· | 00009190:·203a·2050·7974·686f·6e4f·626a·6563·7420···:·PythonObject· | ||
| 000091a0:·6f66·2063·6c61·7373·2072·616e·6765·5f69··of·class·range_i | 000091a0:·6f66·2063·6c61·7373·2072·616e·6765·5f69··of·class·range_i | ||
| 000091b0:·7465·7261·746f·7220·2020·2020·7c0a·2b2d··terator·····|.+- | 000091b0:·7465·7261·746f·7220·2020·2020·7c0a·2b2d··terator·····|.+- | ||
| 000091c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000091c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00009b60:·2078·2020·2020·2020·2020·2020·2020·2020···x·············· | 00009b60:·2078·2020·2020·2020·2020·2020·2020·2020···x·············· | ||
| 00009b70:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00009b70:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00009b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009b80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009ba0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00009ba0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00009bb0:·7c6f·3220·3d20·3c72·616e·6765·5f69·7465··|o2·=·<range_ite | 00009bb0:·7c6f·3220·3d20·3c72·616e·6765·5f69·7465··|o2·=·<range_ite | ||
| 00009bc0:·7261·746f·7220·6f62·6a65·6374·2061·7420··rator·object·at· | 00009bc0:·7261·746f·7220·6f62·6a65·6374·2061·7420··rator·object·at· | ||
| 00009bd0:·3078·3766·636 | 00009bd0:·3078·3766·6365·3437·3366·3963·6230·3e7c··0x7fce473f9cb0>| | ||
| 00009be0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 00009be0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 00009bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009bf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009c00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009c10:·7c0a·7c6f·3220·3a20·5079·7468·6f6e·4f62··|.|o2·:·PythonOb | 00009c10:·7c0a·7c6f·3220·3a20·5079·7468·6f6e·4f62··|.|o2·:·PythonOb | ||
| 00009c20:·6a65·6374·206f·6620·636c·6173·7320·7261··ject·of·class·ra | 00009c20:·6a65·6374·206f·6620·636c·6173·7320·7261··ject·of·class·ra | ||
| 00009c30:·6e67·655f·6974·6572·6174·6f72·2020·2020··nge_iterator···· | 00009c30:·6e67·655f·6974·6572·6174·6f72·2020·2020··nge_iterator···· | ||
| 00009c40:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | 00009c40:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
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| 00012090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000120a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000120a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000120b0:·2020·2020·207c·0a7c·6f31·3320·3d20·3c62·······|.|o13·=·<b | 000120b0:·2020·2020·207c·0a7c·6f31·3320·3d20·3c62·······|.|o13·=·<b | ||
| 000120c0:·7569·6c74·2d69·6e20·6d65·7468·6f64·206d··uilt-in·method·m | 000120c0:·7569·6c74·2d69·6e20·6d65·7468·6f64·206d··uilt-in·method·m | ||
| 000120d0:·3273·7172·7420·6f66·2050·7943·6170·7375··2sqrt·of·PyCapsu | 000120d0:·3273·7172·7420·6f66·2050·7943·6170·7375··2sqrt·of·PyCapsu | ||
| 000120e0:·6c65·206f·626a·6563·7420·6174·2030·7837··le·object·at·0x7 | 000120e0:·6c65·206f·626a·6563·7420·6174·2030·7837··le·object·at·0x7 | ||
| 000120f0:·6638· | 000120f0:·6638·3465·3530·3739·6536·303e·7c0a·7c20··f84e5079e60>|.|· | ||
| 00012100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012110:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00012130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012140:·2020·207c·0a7c·6f31·3320·3a20·5079·7468·····|.|o13·:·Pyth | 00012140:·2020·207c·0a7c·6f31·3320·3a20·5079·7468·····|.|o13·:·Pyth | ||
| 00012150:·6f6e·4f62·6a65·6374·206f·6620·636c·6173··onObject·of·clas | 00012150:·6f6e·4f62·6a65·6374·206f·6620·636c·6173··onObject·of·clas | ||
| 00012160:·7320·6275·696c·7469·6e5f·6675·6e63·7469··s·builtin_functi | 00012160:·7320·6275·696c·7469·6e5f·6675·6e63·7469··s·builtin_functi |
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| 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·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00000af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00000b00:·6935·203a·2074·696d·6520·6265·7474·6928··i5·:·time·betti( | 00000b00:·6935·203a·2074·696d·6520·6265·7474·6928··i5·:·time·betti( | ||
| 00000b10:·493d·2872·616e·646f·6d20·6361·6e6f·6e69··I=(random·canoni | 00000b10:·493d·2872·616e·646f·6d20·6361·6e6f·6e69··I=(random·canoni | ||
| 00000b20:·6361·6c43·7572·7665·2928·672c·5229·2920··calCurve)(g,R))· | 00000b20:·6361·6c43·7572·7665·2928·672c·5229·2920··calCurve)(g,R))· | ||
| 00000b30:·2020·207c·0a7c·202d·2d20·7573·6564·2035·····|.|·--·used·5 | 00000b30:·2020·207c·0a7c·202d·2d20·7573·6564·2035·····|.|·--·used·5 | ||
| 00000b40:·2e3 | 00000b40:·2e34·3336·3638·7320·2863·7075·293b·2034··.43668s·(cpu);·4 | ||
| 00000b50:·2e3 | 00000b50:·2e35·3531·3737·7320·2874·6872·6561·6429··.55177s·(thread) | ||
| 00000b60:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | 00000b60:·3b20·3073·2028·6763·297c·0a7c·2020·2020··;·0s·(gc)|.|···· | ||
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| 00006080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000060a0:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a··--------+.|i10·: | 000060a0:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3130·203a··--------+.|i10·: | ||
| 000060b0:·2065·6c61·7073·6564·5469·6d65·2877·6869···elapsedTime(whi | 000060b0:·2065·6c61·7073·6564·5469·6d65·2877·6869···elapsedTime(whi | ||
| 000060c0:·6c65·2028·6920·3c20·3130·2920·616e·6420··le·(i·<·10)·and· | 000060c0:·6c65·2028·6920·3c20·3130·2920·616e·6420··le·(i·<·10)·and· | ||
| 000060d0:·6469·6d20·4a20·3e20·3120·646f·2028·6920··dim·J·>·1·do·(i· | 000060d0:·6469·6d20·4a20·3e20·3120·646f·2028·6920··dim·J·>·1·do·(i· | ||
| 000060e0:·3d20·692b·313b·204a·203d·2020·2020·2020··=·i+1;·J·=······ | 000060e0:·3d20·692b·313b·204a·203d·2020·2020·2020··=·i+1;·J·=······ | ||
| 000060f0:·2020·2020·2020·2020·7c0a·7c20·2d2d·203 | 000060f0:·2020·2020·2020·2020·7c0a·7c20·2d2d·2031··········|.|·--·1 | ||
| 00006100:·2e3 | 00006100:·2e33·3234·3737·2073·6563·6f6e·6473·2065··.32477·seconds·e | ||
| 00006110:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 00006110:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 00006120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006120:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006130:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006140:·2020·2020·2020·2020·7c0a·7c2d·2d2d·2d2d··········|.|----- | 00006140:·2020·2020·2020·2020·7c0a·7c2d·2d2d·2d2d··········|.|----- | ||
| 00006150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006150:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| Offset 4498, 15 lines modified | Offset 4498, 15 lines modified | ||
| 00011910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6938··-----------+.|i8 | 00011920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6938··-----------+.|i8 | ||
| 00011930:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | 00011930:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | ||
| 00011940:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | 00011940:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | ||
| 00011950:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | 00011950:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | ||
| 00011960:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | 00011960:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | ||
| 00011970:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | 00011970:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | ||
| 00011980:·2d20·3 | 00011980:·2d20·322e·3433·3733·3120·7365·636f·6e64··-·2.43731·second | ||
| 00011990:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00011990:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 000119a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000119a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000119b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000119b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000119c0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 000119c0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 000119d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000119d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000119e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000119e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000119f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000119f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 4553, 15 lines modified | Offset 4553, 15 lines modified | ||
| 00011c80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00011c80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00011c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6939··-----------+.|i9 | 00011c90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6939··-----------+.|i9 | ||
| 00011ca0:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | 00011ca0:·203a·2065·6c61·7073·6564·5469·6d65·2072···:·elapsedTime·r | ||
| 00011cb0:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | 00011cb0:·616e·646f·6d50·6f69·6e74·7328·492c·2053··andomPoints(I,·S | ||
| 00011cc0:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | 00011cc0:·7472·6174·6567·793d·3e4c·696e·6561·7249··trategy=>LinearI | ||
| 00011cd0:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | 00011cd0:·6e74·6572·7365·6374·696f·6e2c·2044·6563··ntersection,·Dec | ||
| 00011ce0:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | 00011ce0:·6f6d·706f·7369·7469·6f6e·537c·0a7c·202d··ompositionS|.|·- | ||
| 00011cf0:·2d20·3 | 00011cf0:·2d20·312e·3837·3732·3320·7365·636f·6e64··-·1.87723·second | ||
| 00011d00:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00011d00:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00011d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011d30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 00011d30:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 00011d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011d40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00011d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00011d60:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 2217, 18 lines modified | Offset 2217, 18 lines modified | ||
| 00008a80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00008a80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00008a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00008a90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 00008aa0:·3134·203a·2074·696d·6520·696e·7665·7273··14·:·time·invers | 00008aa0:·3134·203a·2074·696d·6520·696e·7665·7273··14·:·time·invers | ||
| 00008ab0:·654f·664d·6170·2870·6869·2c43·6865·636b··eOfMap(phi,Check | 00008ab0:·654f·664d·6170·2870·6869·2c43·6865·636b··eOfMap(phi,Check | ||
| 00008ac0:·4269·7261·7469·6f6e·616c·3d3e·6661·6c73··Birational=>fals | 00008ac0:·4269·7261·7469·6f6e·616c·3d3e·6661·6c73··Birational=>fals | ||
| 00008ad0:·652c·2056·6572·626f·7369·7479·3d3e·3029··e,·Verbosity=>0) | 00008ad0:·652c·2056·6572·626f·7369·7479·3d3e·3029··e,·Verbosity=>0) | ||
| 00008ae0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00008ae0:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00008af0:·2d2d·2075·7365·6420·302e·3 | 00008af0:·2d2d·2075·7365·6420·302e·3436·3230·3239··--·used·0.462029 | ||
| 00008b00:·7320·2863·7075·293b·2030·2e3 | 00008b00:·7320·2863·7075·293b·2030·2e33·3335·3832··s·(cpu);·0.33582 | ||
| 00008b10:· | 00008b10:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | ||
| 00008b20:· | 00008b20:·6763·2920·2020·2020·2020·2020·2020·2020··gc)············· | ||
| 00008b30:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00008b30:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00008b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008b40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008b50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008b60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008b60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008b80:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 00008b80:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 00008b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008b90:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
| Offset 1200, 18 lines modified | Offset 1200, 18 lines modified | ||
| 00004af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004af0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004b00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004b10:·2d2d·2d2d·2b0a·7c69·3134·203a·2074·696d··----+.|i14·:·tim | 00004b10:·2d2d·2d2d·2b0a·7c69·3134·203a·2074·696d··----+.|i14·:·tim | ||
| 00004b20:·6520·7261·7469·6f6e·616c·506f·696e·7473··e·rationalPoints | 00004b20:·6520·7261·7469·6f6e·616c·506f·696e·7473··e·rationalPoints | ||
| 00004b30:·2849·2c20·416d·6f75·6e74·203d·3e20·7472··(I,·Amount·=>·tr | 00004b30:·2849·2c20·416d·6f75·6e74·203d·3e20·7472··(I,·Amount·=>·tr | ||
| 00004b40:·7565·2920·2020·2020·2020·2020·2020·2020··ue)············· | 00004b40:·7565·2920·2020·2020·2020·2020·2020·2020··ue)············· | ||
| 00004b50:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00004b50:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00004b60:·7573·6564·2030·2e30·303 | 00004b60:·7573·6564·2030·2e30·3034·3033·3033·3673··used·0.00403036s | ||
| 00004b70:·2863·7075·293b·2030·2e30·3032·3635·3934··(cpu);·0.0026594 | |||
| 00004b | 00004b70:·2028·6370·7529·3b20·302e·3030·3237·3139···(cpu);·0.002719 | ||
| 00004b80:·3633·7320·2874·6872·6561·6429·3b20·3073··63s·(thread);·0s | |||
| 00004b90:·2 | 00004b90:·2028·6763·2920·2020·2020·2020·2020·7c0a···(gc)·········|. | ||
| 00004ba0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00004ba0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00004bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004bb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004bc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004bd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004be0:·2020·207c·0a7c·6f31·3420·3d20·3131·3034·····|.|o14·=·1104 | 00004be0:·2020·207c·0a7c·6f31·3420·3d20·3131·3034·····|.|o14·=·1104 | ||
| 00004bf0:·3632·3231·3235·3431·3132·3034·3531·3030··6221254112045100 | 00004bf0:·3632·3231·3235·3431·3132·3034·3531·3030··6221254112045100 | ||
| 00004c00:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | 00004c00:·3120·2020·2020·2020·2020·2020·2020·2020··1··············· | ||
| Offset 1773, 17 lines modified | Offset 1773, 17 lines modified | ||
| 00006ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00006ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00006ee0:·6933·3220·3a20·7469·6d65·2072·6174·696f··i32·:·time·ratio | 00006ee0:·6933·3220·3a20·7469·6d65·2072·6174·696f··i32·:·time·ratio | ||
| 00006ef0:·6e61·6c50·6f69·6e74·7328·7661·7269·6574··nalPoints(variet | 00006ef0:·6e61·6c50·6f69·6e74·7328·7661·7269·6574··nalPoints(variet | ||
| 00006f00:·7920·6e6f·6465·732c·2053·706c·6974·3d3e··y·nodes,·Split=> | 00006f00:·7920·6e6f·6465·732c·2053·706c·6974·3d3e··y·nodes,·Split=> | ||
| 00006f10:·7472·7565·2c20·5665·7262·6f73·653d·3e74··true,·Verbose=>t | 00006f10:·7472·7565·2c20·5665·7262·6f73·653d·3e74··true,·Verbose=>t | ||
| 00006f20:·7275·6529·3b20·2020·2020·2020·207c·0a7c··rue);········|.| | 00006f20:·7275·6529·3b20·2020·2020·2020·207c·0a7c··rue);········|.| | ||
| 00006f30:·202d·2d20·7573·6564·2030·2e3 | 00006f30:·202d·2d20·7573·6564·2030·2e38·3134·3035···--·used·0.81405 | ||
| 00006f40:·3 | 00006f40:·3773·2028·6370·7529·3b20·302e·3639·3339··7s·(cpu);·0.6939 | ||
| 00006f50:·3 | 00006f50:·3134·7320·2874·6872·6561·6429·3b20·3073··14s·(thread);·0s | ||
| 00006f60:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 00006f60:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00006f70:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00006f70:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00006f80:·2d2d·2062·6173·6520·6368·616e·6765·2074··--·base·change·t | 00006f80:·2d2d·2062·6173·6520·6368·616e·6765·2074··--·base·change·t | ||
| 00006f90:·6f20·7468·6520·6669·656c·6420·5151·5b61··o·the·field·QQ[a | 00006f90:·6f20·7468·6520·6669·656c·6420·5151·5b61··o·the·field·QQ[a | ||
| 00006fa0:·5d2f·2861·5e38·2d34·302a·615e·362b·3233··]/(a^8-40*a^6+23 | 00006fa0:·5d2f·2861·5e38·2d34·302a·615e·362b·3233··]/(a^8-40*a^6+23 | ||
| 00006fb0:·302a·615e·342d·3230·302a·615e·322b·3235··0*a^4-200*a^2+25 | 00006fb0:·302a·615e·342d·3230·302a·615e·322b·3235··0*a^4-200*a^2+25 | ||
| 00006fc0:·2920·2020·2020·2020·2020·2020·207c·0a2b··)············|.+ | 00006fc0:·2920·2020·2020·2020·2020·2020·207c·0a2b··)············|.+ | ||
| Offset 1840, 16 lines modified | Offset 1840, 16 lines modified | ||
| 000072f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000072f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00007300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00007310:·2d2d·2b0a·7c69·3335·203a·2074·696d·6520··--+.|i35·:·time· | 00007310:·2d2d·2b0a·7c69·3335·203a·2074·696d·6520··--+.|i35·:·time· | ||
| 00007320:·2372·6174·696f·6e61·6c50·6f69·6e74·7328··#rationalPoints( | 00007320:·2372·6174·696f·6e61·6c50·6f69·6e74·7328··#rationalPoints( | ||
| 00007330:·7661·7269·6574·7920·6e6f·6465·7327·2c20··variety·nodes',· | 00007330:·7661·7269·6574·7920·6e6f·6465·7327·2c20··variety·nodes',· | ||
| 00007340:·5370·6c69·743d·3e74·7275·652c·2056·6572··Split=>true,·Ver | 00007340:·5370·6c69·743d·3e74·7275·652c·2056·6572··Split=>true,·Ver | ||
| 00007350:·626f·7365·3d3e·7472·7565·297c·0a7c·202d··bose=>true)|.|·- | 00007350:·626f·7365·3d3e·7472·7565·297c·0a7c·202d··bose=>true)|.|·- | ||
| 00007360:·2d20·7573·6564·2030·2e32·323 | 00007360:·2d20·7573·6564·2030·2e32·3234·3836·3773··-·used·0.224867s | ||
| 00007370:·2028·6370·7529·3b20·302e·313 | 00007370:·2028·6370·7529·3b20·302e·3136·3630·3538···(cpu);·0.166058 | ||
| 00007380:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | 00007380:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | ||
| 00007390:·6763·2920·2020·2020·2020·2020·2020·2020··gc)············· | 00007390:·6763·2920·2020·2020·2020·2020·2020·2020··gc)············· | ||
| 000073a0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 000073a0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 000073b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000073b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000073c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000073c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000073d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000073d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000073e0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000073e0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| |
| Offset 645, 15 lines modified | Offset 645, 15 lines modified | ||
| 00002840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002840:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002850:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 00002850:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00002860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002860:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002880:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000028a0:·2020·2020·2020·207c·0a7c·6f38·203d·202e·········|.|o8·=·. | 000028a0:·2020·2020·2020·207c·0a7c·6f38·203d·202e·········|.|o8·=·. | ||
| 000028b0:·3137·3 | 000028b0:·3137·3632·3539·3531·3333·3735·2020·2020··176259513375···· | ||
| 000028c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000028c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000028d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000028d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000028e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000028e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000028f0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000028f0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00002900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002910:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002920:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 744, 16 lines modified | Offset 744, 16 lines modified | ||
| 00002e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002e70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002e80:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00002e80:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00002e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002ea0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002eb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002ec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002ed0:·2020·2020·2020·2020·207c·0a7c·6f31·3120···········|.|o11· | 00002ed0:·2020·2020·2020·2020·207c·0a7c·6f31·3120···········|.|o11· | ||
| 00002ee0:·3d20·2e30·353 | 00002ee0:·3d20·2e30·3531·3033·3836·3339·3435·3333··=·.0510386394533 | ||
| 00002ef0:·3 | 00002ef0:·3333·3420·2020·2020·2020·2020·2020·2020··334············· | ||
| 00002f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f20:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00002f20:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00002f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00002f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00002f60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00003000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00003000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00003010:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3220··---------+.|i12· | 00003010:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3220··---------+.|i12· | ||
| 00003020:·3a20·7469·6d65·2072·6567·756c·6172·6974··:·time·regularit | 00003020:·3a20·7469·6d65·2072·6567·756c·6172·6974··:·time·regularit | ||
| 00003030:·7920·4932·2020·2020·2020·2020·2020·2020··y·I2············ | 00003030:·7920·4932·2020·2020·2020·2020·2020·2020··y·I2············ | ||
| 00003040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00003050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003060:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00003060:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00003070:·7573·6564·2030·2e30·303 | 00003070:·7573·6564·2030·2e30·3032·3037·3331·3773··used·0.00207317s | ||
| 00003080:·2028·6370·7529·3b20·302e·3030·3 | 00003080:·2028·6370·7529·3b20·302e·3030·3139·3933···(cpu);·0.001993 | ||
| 00003090:·3 | 00003090:·3438·7320·2874·6872·6561·6429·3b20·3073··48s·(thread);·0s | ||
| 000030a0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 000030a0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 000030b0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000030b0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000030c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000030d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000030e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000030f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000030f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00003100:·2020·2020·2020·2020·207c·0a7c·6f31·3220···········|.|o12· | 00003100:·2020·2020·2020·2020·207c·0a7c·6f31·3220···········|.|o12· |
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| 00005dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005de0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·: | 00005de0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·: | ||
| 00005df0:·2074·696d·6520·2850·3178·5031·7850·322c···time·(P1xP1xP2, | 00005df0:·2074·696d·6520·2850·3178·5031·7850·322c···time·(P1xP1xP2, | ||
| 00005e00:·5031·7850·3178·5032·2729·203d·2063·6179··P1xP1xP2')·=·cay | 00005e00:·5031·7850·3178·5032·2729·203d·2063·6179··P1xP1xP2')·=·cay | ||
| 00005e10:·6c65·7954·7269·636b·2850·3178·5031·2c32··leyTrick(P1xP1,2 | 00005e10:·6c65·7954·7269·636b·2850·3178·5031·2c32··leyTrick(P1xP1,2 | ||
| 00005e20:·293b·207c·0a7c·202d·2d20·7573·6564·2030··);·|.|·--·used·0 | 00005e20:·293b·207c·0a7c·202d·2d20·7573·6564·2030··);·|.|·--·used·0 | ||
| 00005e30:·2e30·3 | 00005e30:·2e30·3337·3833·3038·7320·2863·7075·293b··.0378308s·(cpu); | ||
| 00005e40:·2030·2e30·3 | 00005e40:·2030·2e30·3337·3939·3533·7320·2874·6872···0.0379953s·(thr | ||
| 00005e50:·6561·6429·3b20·3073·2028·6763·297c·0a2b··ead);·0s·(gc)|.+ | 00005e50:·6561·6429·3b20·3073·2028·6763·297c·0a2b··ead);·0s·(gc)|.+ | ||
| 00005e60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005e60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005e70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005e70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005e80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005e80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005e90:·2d2d·2d2d·2d2d·2d2b·0a0a·496e·2074·6865··-------+..In·the | 00005e90:·2d2d·2d2d·2d2d·2d2b·0a0a·496e·2074·6865··-------+..In·the | ||
| 00005ea0:·206e·6578·7420·6578·616d·706c·652c·2077···next·example,·w | 00005ea0:·206e·6578·7420·6578·616d·706c·652c·2077···next·example,·w | ||
| 00005eb0:·6520·6361·6c63·756c·6174·6520·7468·6520··e·calculate·the· | 00005eb0:·6520·6361·6c63·756c·6174·6520·7468·6520··e·calculate·the· | ||
| Offset 1528, 16 lines modified | Offset 1528, 16 lines modified | ||
| 00005f70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005f70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005f80:·2d2d·2d2d·2d2b·0a7c·6934·203a·2074·696d··-----+.|i4·:·tim | 00005f80:·2d2d·2d2d·2d2b·0a7c·6934·203a·2074·696d··-----+.|i4·:·tim | ||
| 00005f90:·6520·2850·3178·5031·7850·312c·5031·7850··e·(P1xP1xP1,P1xP | 00005f90:·6520·2850·3178·5031·7850·312c·5031·7850··e·(P1xP1xP1,P1xP | ||
| 00005fa0:·3178·5031·2729·203d·2063·6179·6c65·7954··1xP1')·=·cayleyT | 00005fa0:·3178·5031·2729·203d·2063·6179·6c65·7954··1xP1')·=·cayleyT | ||
| 00005fb0:·7269·636b·2850·3178·5031·2c31·2920·2020··rick(P1xP1,1)··· | 00005fb0:·7269·636b·2850·3178·5031·2c31·2920·2020··rick(P1xP1,1)··· | ||
| 00005fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005fd0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 00005fd0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 00005fe0:·2030·2e30·3 | 00005fe0:·2030·2e30·3437·3239·3838·7320·2863·7075···0.0472988s·(cpu | ||
| 00005ff0:·293b·2030·2e30·3 | 00005ff0:·293b·2030·2e30·3438·3235·3738·7320·2874··);·0.0482578s·(t | ||
| 00006000:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00006000:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00006010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006020:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00006020:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00006030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 1681, 16 lines modified | Offset 1681, 16 lines modified | ||
| 00006900:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006900:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006930:·2d2b·0a7c·6935·203a·2074·696d·6520·6361··-+.|i5·:·time·ca | 00006930:·2d2b·0a7c·6935·203a·2074·696d·6520·6361··-+.|i5·:·time·ca | ||
| 00006940:·796c·6579·5472·6963·6b28·5031·7850·312c··yleyTrick(P1xP1, | 00006940:·796c·6579·5472·6963·6b28·5031·7850·312c··yleyTrick(P1xP1, | ||
| 00006950:·312c·4475·616c·6974·793d·3e74·7275·6529··1,Duality=>true) | 00006950:·312c·4475·616c·6974·793d·3e74·7275·6529··1,Duality=>true) | ||
| 00006960:·3b20·2020·2020·2020·2020·7c0a·7c20·2d2d··;·········|.|·-- | 00006960:·3b20·2020·2020·2020·2020·7c0a·7c20·2d2d··;·········|.|·-- | ||
| 00006970:·2075·7365·6420·302e·313 | 00006970:·2075·7365·6420·302e·3131·3331·3535·7320···used·0.113155s· | ||
| 00006980:·2863·7075·293b·2030·2e30·3 | 00006980:·2863·7075·293b·2030·2e30·3738·3234·3739··(cpu);·0.0782479 | ||
| 00006990:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | 00006990:·7320·2874·6872·6561·6429·3b20·3073·2028··s·(thread);·0s·( | ||
| 000069a0:·6763·297c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d··gc)|.+---------- | 000069a0:·6763·297c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d··gc)|.+---------- | ||
| 000069b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000069b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000069c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000069c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000069d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 000069d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 000069e0:·3620·3a20·6173·7365·7274·286f·6f20·3d3d··6·:·assert(oo·== | 000069e0:·3620·3a20·6173·7365·7274·286f·6f20·3d3d··6·:·assert(oo·== | ||
| 000069f0:·2028·5031·7850·3178·5031·2c50·3178·5031···(P1xP1xP1,P1xP1 | 000069f0:·2028·5031·7850·3178·5031·2c50·3178·5031···(P1xP1xP1,P1xP1 | ||
| Offset 1699, 17 lines modified | Offset 1699, 17 lines modified | ||
| 00006a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006a30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006a30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | 00006a40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 00006a50:·7c69·3720·3a20·7469·6d65·2063·6179·6c65··|i7·:·time·cayle | 00006a50:·7c69·3720·3a20·7469·6d65·2063·6179·6c65··|i7·:·time·cayle | ||
| 00006a60:·7954·7269·636b·2850·3178·5031·2c32·2c44··yTrick(P1xP1,2,D | 00006a60:·7954·7269·636b·2850·3178·5031·2c32·2c44··yTrick(P1xP1,2,D | ||
| 00006a70:·7561·6c69·7479·3d3e·7472·7565·293b·2020··uality=>true);·· | 00006a70:·7561·6c69·7479·3d3e·7472·7565·293b·2020··uality=>true);·· | ||
| 00006a80:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | 00006a80:·2020·2020·2020·207c·0a7c·202d·2d20·7573·········|.|·--·us | ||
| 00006a90:·6564·2030·2e31·313 | 00006a90:·6564·2030·2e31·3137·3431·3773·2028·6370··ed·0.117417s·(cp | ||
| 00006aa0:·293b·2030·2e30·3830·3938·3133·7320·2874··);·0.0809813s·(t | |||
| 00006a | 00006aa0:·7529·3b20·302e·3037·3638·3237·3973·2028··u);·0.0768279s·( | ||
| 00006ab0:·7468·7265·6164·293b·2030·7320·2867·6329··thread);·0s·(gc) | |||
| 00006ac0:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | 00006ac0:·7c0a·2b2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··|.+------------- | ||
| 00006ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006ae0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006af0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6938·203a··---------+.|i8·: | 00006af0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6938·203a··---------+.|i8·: | ||
| 00006b00:·2061·7373·6572·7428·6f6f·203d·3d20·2850···assert(oo·==·(P | 00006b00:·2061·7373·6572·7428·6f6f·203d·3d20·2850···assert(oo·==·(P | ||
| 00006b10:·3178·5031·7850·322c·5031·7850·3178·5032··1xP1xP2,P1xP1xP2 | 00006b10:·3178·5031·7850·322c·5031·7850·3178·5032··1xP1xP2,P1xP1xP2 | ||
| 00006b20:·2729·2920·2020·2020·2020·2020·2020·2020··'))············· | 00006b20:·2729·2920·2020·2020·2020·2020·2020·2020··'))············· | ||
| Offset 1885, 16 lines modified | Offset 1885, 16 lines modified | ||
| 000075c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000075c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000075d0:·2020·2020·207c·0a7c·2020·2020·2074·696d·······|.|·····tim | 000075d0:·2020·2020·207c·0a7c·2020·2020·2074·696d·······|.|·····tim | ||
| 000075e0:·6520·6571·7343·203d·2063·686f·7745·7175··e·eqsC·=·chowEqu | 000075e0:·6520·6571·7343·203d·2063·686f·7745·7175··e·eqsC·=·chowEqu | ||
| 000075f0:·6174·696f·6e73·2063·686f·7746·6f72·6d20··ations·chowForm· | 000075f0:·6174·696f·6e73·2063·686f·7746·6f72·6d20··ations·chowForm· | ||
| 00007600:·4320·2020·2020·2020·2020·2020·2020·2020··C··············· | 00007600:·4320·2020·2020·2020·2020·2020·2020·2020··C··············· | ||
| 00007610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007610:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007620:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 00007620:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 00007630:·2030·2e30·3 | 00007630:·2030·2e30·3430·3932·3136·7320·2863·7075···0.0409216s·(cpu | ||
| 00007640:·293b·2030·2e30·3 | 00007640:·293b·2030·2e30·3433·3130·3137·7320·2874··);·0.0431017s·(t | ||
| 00007650:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00007650:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00007660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007660:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007670:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00007670:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00007680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000076b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000076b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2200, 16 lines modified | Offset 2200, 16 lines modified | ||
| 00008970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008980:·2020·2020·207c·0a7c·2020·2020·2074·696d·······|.|·····tim | 00008980:·2020·2020·207c·0a7c·2020·2020·2074·696d·······|.|·····tim | ||
| 00008990:·6520·6571·7344·203d·2063·686f·7745·7175··e·eqsD·=·chowEqu | 00008990:·6520·6571·7344·203d·2063·686f·7745·7175··e·eqsD·=·chowEqu | ||
| 000089a0:·6174·696f·6e73·2063·686f·7746·6f72·6d20··ations·chowForm· | 000089a0:·6174·696f·6e73·2063·686f·7746·6f72·6d20··ations·chowForm· | ||
| 000089b0:·4420·2020·2020·2020·2020·2020·2020·2020··D··············· | 000089b0:·4420·2020·2020·2020·2020·2020·2020·2020··D··············· | ||
| 000089c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000089c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000089d0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | 000089d0:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 000089e0:·2030·2e30·333 | 000089e0:·2030·2e30·3333·3430·3135·7320·2863·7075···0.0334015s·(cpu | ||
| 000089f0:·293b·2030·2e30·333 | 000089f0:·293b·2030·2e30·3334·3034·3631·7320·2874··);·0.0340461s·(t | ||
| 00008a00:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00008a00:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00008a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008a10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008a20:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | 00008a20:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | ||
| 00008a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008a30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008a60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2460, 16 lines modified | Offset 2460, 16 lines modified | ||
| 000099b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000099b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000099c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 000099c0:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 000099d0:·2020·7469·6d65·2028·5730·2c57·312c·5732····time·(W0,W1,W2 | 000099d0:·2020·7469·6d65·2028·5730·2c57·312c·5732····time·(W0,W1,W2 | ||
| 000099e0:·2920·3d20·2874·616e·6765·6e74·6961·6c43··)·=·(tangentialC | 000099e0:·2920·3d20·2874·616e·6765·6e74·6961·6c43··)·=·(tangentialC | ||
| 000099f0:·686f·7746·6f72·6d28·512c·3029·2c74·616e··howForm(Q,0),tan | 000099f0:·686f·7746·6f72·6d28·512c·3029·2c74·616e··howForm(Q,0),tan | ||
| 00009a00:·6765·6e74·6961·6c43·686f·7746·6f72·6d28··gentialChowForm( | 00009a00:·6765·6e74·6961·6c43·686f·7746·6f72·6d28··gentialChowForm( | ||
| 00009a10:·512c·3129·2c74·616e·677c·0a7c·202d·2d20··Q,1),tang|.|·--· | 00009a10:·512c·3129·2c74·616e·677c·0a7c·202d·2d20··Q,1),tang|.|·--· | ||
| 00009a20:·7573·6564·2030·2e31·3 | 00009a20:·7573·6564·2030·2e31·3035·3233·3973·2028··used·0.105239s·( | ||
| 00009a30:·6370·7529·3b20·302e·303 | 00009a30:·6370·7529·3b20·302e·3037·3638·3231·3873··cpu);·0.0768218s | ||
| 00009a40:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | 00009a40:·2028·7468·7265·6164·293b·2030·7320·2867···(thread);·0s·(g | ||
| 00009a50:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | 00009a50:·6329·2020·2020·2020·2020·2020·2020·2020··c)·············· | ||
| 00009a60:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00009a60:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00009a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00009aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00009aa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 2530, 18 lines modified | Offset 2530, 18 lines modified | ||
| 00009e10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00009e10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00009e20:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3120··---------+.|i11· | 00009e20:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3120··---------+.|i11· | ||
| 00009e30:·3a20·7469·6d65·2028·512c·512c·5129·203d··:·time·(Q,Q,Q)·= | 00009e30:·3a20·7469·6d65·2028·512c·512c·5129·203d··:·time·(Q,Q,Q)·= | ||
| 00009e40:·3d20·2863·686f·7745·7175·6174·696f·6e73··=·(chowEquations | 00009e40:·3d20·2863·686f·7745·7175·6174·696f·6e73··=·(chowEquations | ||
| 00009e50:·2857·302c·3029·2c63·686f·7745·7175·6174··(W0,0),chowEquat | 00009e50:·2857·302c·3029·2c63·686f·7745·7175·6174··(W0,0),chowEquat | ||
| 00009e60:·696f·6e73·2857·312c·3129·2c63·686f·7745··ions(W1,1),chowE | 00009e60:·696f·6e73·2857·312c·3129·2c63·686f·7745··ions(W1,1),chowE | ||
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| 000027d0:·6e74·6c79·2061·7661·696c·6162·6c65·2074··ntly·available·t | 000027d0:·6e74·6c79·2061·7661·696c·6162·6c65·2074··ntly·available·t | ||
| 000027e0:·6f20·7468·650a·4d61·6361·756c·6179·3220··o·the.Macaulay2· | 000027e0:·6f20·7468·650a·4d61·6361·756c·6179·3220··o·the.Macaulay2· | ||
| 000027f0:·7072·6f63·6573·7320·6279·2075·7369·6e67··process·by·using | 000027f0:·7072·6f63·6573·7320·6279·2075·7369·6e67··process·by·using | ||
| 00002800:·2074·6865·202a·6e6f·7465·2072·756e·3a20···the·*note·run:· | 00002800:·2074·6865·202a·6e6f·7465·2072·756e·3a20···the·*note·run:· | ||
| 00002810:·284d·6163·6175·6c61·7932·446f·6329·7275··(Macaulay2Doc)ru | 00002810:·284d·6163·6175·6c61·7932·446f·6329·7275··(Macaulay2Doc)ru | ||
| 00002820:·6e2c·2063·6f6d·6d61·6e64·3a0a·0a2b·2d2d··n,·command:..+-- | 00002820:·6e2c·2063·6f6d·6d61·6e64·3a0a·0a2b·2d2d··n,·command:..+-- | ||
| 00002830:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00002830:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00002840:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | |||
| 00002850:·3120·3a20·7275·6e28·2275·6c69·6d69·7420··1·:·run("ulimit· | |||
| 00002860:·2d61·2229·2020·2020·2020·2020·207c·0a7c··-a")·········|.| | |||
| 00002870:·7469·6d65·2873·6563·6f6e·6473·2920·2020··time(seconds)··· | |||
| 00002880:·2020·2020·2037·3030·2020·2020·2020·7c0a·······700······|. | |||
| 00002890:·7c66·696c·6528·626c·6f63·6b73·2920·2020··|file(blocks)··· | |||
| 000028a0:·2020·2020·2020·756e·6c69·6d69·7465·647c········unlimited| | |||
| 000028b0:·0a7c·6461·7461·286b·6279·7465·7329·2020··.|data(kbytes)·· | |||
| 000028c0:·2020·2020·2020·2075·6e6c·696d·6974·6564·········unlimited | |||
| 000028d0:·7c0a·7c73·7461·636b·286b·6279·7465·7329··|.|stack(kbytes) | |||
| 000028e0:·2020·2020·2020·2020·3831·3932·2020·2020··········8192···· | |||
| 000028f0:·207c·0a7c·636f·7265·6475·6d70·2862·6c6f···|.|coredump(blo | |||
| 00002900:·636b·7329·2020·2020·2030·2020·2020·2020··cks)·····0······ | |||
| 00002910:·2020·7c0a·7c6d·656d·6f72·7928·6b62·7974····|.|memory(kbyt | |||
| 00002920:·6573·2920·2020·2020·2020·3835·3030·3030··es)·······850000 | |||
| 00002930:·2020·207c·0a7c·6c6f·636b·6564·206d·656d·····|.|locked·mem | |||
| 00002940:·6f72·7928·6b62·7974·6573·2920·3330·3736··ory(kbytes)·3076 | |||
| 00002950:·3835·3620·7c0a·7c70·726f·6365·7373·2020··856·|.|process·· | |||
| 00002960:·2020·2020·2020·2020·2020·2020·3935·3939··············9599 | |||
| 00002970:·3120·2020·207c·0a7c·6e6f·6669·6c65·7320··1····|.|nofiles· | |||
| 00002980:·2020·2020·2020·2020·2020·2020·2035·3132···············512 | |||
| 00002990:·2020·2020·2020·7c0a·7c76·6d65·6d6f·7279········|.|vmemory | |||
| 000029a0:·286b·6279·7465·7329·2020·2020·2020·756e··(kbytes)······un | |||
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| 000123b0:·3 | 000123b0:·3220·2020·2020·2020·2020·2020·2020·207c··2··············| | ||
| 000123c0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | 000123c0:·0a7c·2020·2020·2020·2020·2020·2020·2020··.|·············· | ||
| 000123d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000123d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000123e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000123e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000123f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000123f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00012400:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00012400:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
| 00012410:·0a7c·6f38·203a·2063·6f2d·636f·6d70·6c65··.|o8·:·co-comple | 00012410:·0a7c·6f38·203a·2063·6f2d·636f·6d70·6c65··.|o8·:·co-comple | ||
| 00012420:·7820·6f66·2064·696d·2032·2065·6d62·6564··x·of·dim·2·embed | 00012420:·7820·6f66·2064·696d·2032·2065·6d62·6564··x·of·dim·2·embed |
| Offset 3327, 16 lines modified | Offset 3327, 16 lines modified | ||
| 0000cfe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cfe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000cff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d000:·2d2d·2d2d·2b0a·7c69·3520·3a20·656c·6170··----+.|i5·:·elap | 0000d000:·2d2d·2d2d·2b0a·7c69·3520·3a20·656c·6170··----+.|i5·:·elap | ||
| 0000d010:·7365·6454·696d·6520·433d·7261·6e64·6f6d··sedTime·C=random | 0000d010:·7365·6454·696d·6520·433d·7261·6e64·6f6d··sedTime·C=random | ||
| 0000d020:·4368·6169·6e43·6f6d·706c·6578·2868·2c72··ChainComplex(h,r | 0000d020:·4368·6169·6e43·6f6d·706c·6578·2868·2c72··ChainComplex(h,r | ||
| 0000d030:·2c48·6569·6768·743d·3e31·3030·2c5a·6572··,Height=>100,Zer | 0000d030:·2c48·6569·6768·743d·3e31·3030·2c5a·6572··,Height=>100,Zer | ||
| 0000d040:·6f4d·6561·6e3d·3e74·7275·6529·2020·2020··oMean=>true)···· | 0000d040:·6f4d·6561·6e3d·3e74·7275·6529·2020·2020··oMean=>true)···· | ||
| 0000d050:·2020·2020·7c0a·7c20·2d2d·2030·2e30·303 | 0000d050:·2020·2020·7c0a·7c20·2d2d·2030·2e30·3033······|.|·--·0.003 | ||
| 0000d060:·3 | 0000d060:·3136·3431·3920·7365·636f·6e64·7320·656c··16419·seconds·el | ||
| 0000d070:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 0000d070:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 0000d080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0a0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | 0000d0a0:·2020·2020·7c0a·7c20·2020·2020·2020·2020······|.|········· | ||
| 0000d0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 3864, 15 lines modified | Offset 3864, 15 lines modified | ||
| 0000f170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f180:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | 0000f180:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | ||
| 0000f190:·2065·6c61·7073·6564·5469·6d65·2043·3d72···elapsedTime·C=r | 0000f190:·2065·6c61·7073·6564·5469·6d65·2043·3d72···elapsedTime·C=r | ||
| 0000f1a0:·616e·646f·6d43·6861·696e·436f·6d70·6c65··andomChainComple | 0000f1a0:·616e·646f·6d43·6861·696e·436f·6d70·6c65··andomChainComple | ||
| 0000f1b0:·7828·682c·722c·4865·6967·6874·3d3e·352c··x(h,r,Height=>5, | 0000f1b0:·7828·682c·722c·4865·6967·6874·3d3e·352c··x(h,r,Height=>5, | ||
| 0000f1c0:·5a65·726f·4d65·616e·3d3e·7472·7565·2920··ZeroMean=>true)· | 0000f1c0:·5a65·726f·4d65·616e·3d3e·7472·7565·2920··ZeroMean=>true)· | ||
| 0000f1d0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 0000f1d0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 0000f1e0:·302e·3030·323 | 0000f1e0:·302e·3030·3232·3034·3035·2073·6563·6f6e··0.00220405·secon | ||
| 0000f1f0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 0000f1f0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 0000f200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f220:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 0000f220:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 0000f230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f240:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 6512, 15 lines modified | Offset 6512, 15 lines modified | ||
| 000196f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000196f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00019700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 00019700:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00019710:·6935·203a·2065·6c61·7073·6564·5469·6d65··i5·:·elapsedTime | 00019710:·6935·203a·2065·6c61·7073·6564·5469·6d65··i5·:·elapsedTime | ||
| 00019720:·2043·3d72·616e·646f·6d43·6861·696e·436f···C=randomChainCo | 00019720:·2043·3d72·616e·646f·6d43·6861·696e·436f···C=randomChainCo | ||
| 00019730:·6d70·6c65·7828·682c·722c·4865·6967·6874··mplex(h,r,Height | 00019730:·6d70·6c65·7828·682c·722c·4865·6967·6874··mplex(h,r,Height | ||
| 00019740:·3d3e·352c·5a65·726f·4d65·616e·3d3e·7472··=>5,ZeroMean=>tr | 00019740:·3d3e·352c·5a65·726f·4d65·616e·3d3e·7472··=>5,ZeroMean=>tr | ||
| 00019750:·7565·2920·2020·2020·2020·2020·207c·0a7c··ue)··········|.| | 00019750:·7565·2920·2020·2020·2020·2020·207c·0a7c··ue)··········|.| | ||
| 00019760:·202d·2d20·302e·3030·3 | 00019760:·202d·2d20·302e·3030·3234·3938·3734·2073···--·0.00249874·s | ||
| 00019770:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | 00019770:·6563·6f6e·6473·2065·6c61·7073·6564·2020··econds·elapsed·· | ||
| 00019780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00019780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00019790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00019790:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000197a0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000197a0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 000197b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000197b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000197c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000197c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000197d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000197d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 9708, 15 lines modified | Offset 9708, 15 lines modified | ||
| 00025eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00025eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00025ec0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | 00025ec0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 00025ed0:·2065·6c61·7073·6564·5469·6d65·2043·3d72···elapsedTime·C=r | 00025ed0:·2065·6c61·7073·6564·5469·6d65·2043·3d72···elapsedTime·C=r | ||
| 00025ee0:·616e·646f·6d43·6861·696e·436f·6d70·6c65··andomChainComple | 00025ee0:·616e·646f·6d43·6861·696e·436f·6d70·6c65··andomChainComple | ||
| 00025ef0:·7828·682c·722c·4865·6967·6874·3d3e·3429··x(h,r,Height=>4) | 00025ef0:·7828·682c·722c·4865·6967·6874·3d3e·3429··x(h,r,Height=>4) | ||
| 00025f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025f00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025f10:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00025f10:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00025f20:·302e·3030·3 | 00025f20:·302e·3030·3535·3130·3035·2073·6563·6f6e··0.00551005·secon | ||
| 00025f30:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 00025f30:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 00025f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025f40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025f50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025f60:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00025f60:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00025f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00025f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00025f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| Offset 9888, 15 lines modified | Offset 9888, 15 lines modified | ||
| 000269f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000269f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00026a00:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·: | 00026a00:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6937·203a··---------+.|i7·: | ||
| 00026a10:·2065·6c61·7073·6564·5469·6d65·2028·682c···elapsedTime·(h, | 00026a10:·2065·6c61·7073·6564·5469·6d65·2028·682c···elapsedTime·(h, | ||
| 00026a20:·5529·3d53·5644·436f·6d70·6c65·7820·4352··U)=SVDComplex·CR | 00026a20:·5529·3d53·5644·436f·6d70·6c65·7820·4352··U)=SVDComplex·CR | ||
| 00026a30:·3b20·2020·2020·2020·2020·2020·2020·2020··;··············· | 00026a30:·3b20·2020·2020·2020·2020·2020·2020·2020··;··············· | ||
| 00026a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026a40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026a50:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 00026a50:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00026a60:·302e·3030·323 | 00026a60:·302e·3030·3230·3737·3433·2073·6563·6f6e··0.00207743·secon | ||
| 00026a70:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 00026a70:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 00026a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00026a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00026aa0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | 00026aa0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 00026ab0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00026ab0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00026ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00026ac0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00026ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00026ad0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| Offset 10118, 15 lines modified | Offset 10118, 15 lines modified | ||
| 00027850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027850:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00027860:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3320··---------+.|i13· | 00027860:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6931·3320··---------+.|i13· | ||
| 00027870:·3a20·656c·6170·7365·6454·696d·6520·2868··:·elapsedTime·(h | 00027870:·3a20·656c·6170·7365·6454·696d·6520·2868··:·elapsedTime·(h | ||
| 00027880:·4c2c·5529·3d53·5644·436f·6d70·6c65·7828··L,U)=SVDComplex( | 00027880:·4c2c·5529·3d53·5644·436f·6d70·6c65·7828··L,U)=SVDComplex( | ||
| 00027890:·4352·2c53·7472·6174·6567·793d·3e4c·6170··CR,Strategy=>Lap | 00027890:·4352·2c53·7472·6174·6567·793d·3e4c·6170··CR,Strategy=>Lap | ||
| 000278a0:·6c61·6369·616e·293b·2020·2020·2020·2020··lacian);········ | 000278a0:·6c61·6369·616e·293b·2020·2020·2020·2020··lacian);········ | ||
| 000278b0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000278b0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 000278c0:·302e·3030·3 | 000278c0:·302e·3030·3339·3839·3932·2073·6563·6f6e··0.00398992·secon | ||
| 000278d0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 000278d0:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 000278e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000278e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000278f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000278f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00027900:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | 00027900:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 00027910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00027920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027920:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00027930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00027930:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00028ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00028ee0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00028ef0:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:· | 00028ef0:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3420·3a20··--------+.|i4·:· | ||
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| 00028f10:·6e64·6f6d·4368·6169·6e43·6f6d·706c·6578··ndomChainComplex | 00028f10:·6e64·6f6d·4368·6169·6e43·6f6d·706c·6578··ndomChainComplex | ||
| 00028f20:·2868·2c72·2c48·6569·6768·743d·3e35·2c5a··(h,r,Height=>5,Z | 00028f20:·2868·2c72·2c48·6569·6768·743d·3e35·2c5a··(h,r,Height=>5,Z | ||
| 00028f30:·6572·6f4d·6561·6e3d·3e74·7275·6529·2020··eroMean=>true)·· | 00028f30:·6572·6f4d·6561·6e3d·3e74·7275·6529·2020··eroMean=>true)·· | ||
| 00028f40:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | 00028f40:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | ||
| 00028f50:·2e30·3032·3 | 00028f50:·2e30·3032·3232·3632·3520·7365·636f·6e64··.00222625·second | ||
| 00028f60:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | 00028f60:·7320·656c·6170·7365·6420·2020·2020·2020··s·elapsed······· | ||
| 00028f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00028f70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00028f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00028f80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00028f90:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00028f90:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 00028fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00028fa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00028fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00028fb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00028fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00028fc0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000298f0:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20··--------+.|i7·:· | 000298f0:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3720·3a20··--------+.|i7·:· | ||
| 00029900:·656c·6170·7365·6454·696d·6520·2868·2c68··elapsedTime·(h,h | 00029900:·656c·6170·7365·6454·696d·6520·2868·2c68··elapsedTime·(h,h | ||
| 00029910:·3129·3d53·5644·486f·6d6f·6c6f·6779·2043··1)=SVDHomology·C | 00029910:·3129·3d53·5644·486f·6d6f·6c6f·6779·2043··1)=SVDHomology·C | ||
| 00029920:·5220·2020·2020·2020·2020·2020·2020·2020··R··············· | 00029920:·5220·2020·2020·2020·2020·2020·2020·2020··R··············· | ||
| 00029930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029930:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029940:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | 00029940:·2020·2020·2020·2020·7c0a·7c20·2d2d·2030··········|.|·--·0 | ||
| 00029950:·2e30·3030·3 | 00029950:·2e30·3030·3437·3839·3433·2073·6563·6f6e··.000478943·secon | ||
| 00029960:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | 00029960:·6473·2065·6c61·7073·6564·2020·2020·2020··ds·elapsed······ | ||
| 00029970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00029980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00029990:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 00029990:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 000299a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000299a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000299b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000299b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000db80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000db80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000db90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 0000db90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
| 0000dba0:·3720·3a20·7469·6d65·2071·756f·7469·656e··7·:·time·quotien | 0000dba0:·3720·3a20·7469·6d65·2071·756f·7469·656e··7·:·time·quotien | ||
| 0000dbb0:·7428·495e·332c·204a·5e32·2c20·5374·7261··t(I^3,·J^2,·Stra | 0000dbb0:·7428·495e·332c·204a·5e32·2c20·5374·7261··t(I^3,·J^2,·Stra | ||
| 0000dbc0:·7465·6779·203d·3e20·4974·6572·6174·6529··tegy·=>·Iterate) | 0000dbc0:·7465·6779·203d·3e20·4974·6572·6174·6529··tegy·=>·Iterate) | ||
| 0000dbd0:·3b20·2020·7c0a·7c20·2d2d·2075·7365·6420··;···|.|·--·used· | 0000dbd0:·3b20·2020·7c0a·7c20·2d2d·2075·7365·6420··;···|.|·--·used· | ||
| 0000dbe0:·302e·3 | 0000dbe0:·302e·3332·3237·3037·7320·2863·7075·293b··0.322707s·(cpu); | ||
| 0000dbf0:·2030·2e3 | 0000dbf0:·2030·2e32·3832·3735·3873·2028·7468·7265···0.282758s·(thre | ||
| 0000dc00:·6164·293b·2030·7320·2867·6329·7c0a·7c20··ad);·0s·(gc)|.|· | 0000dc00:·6164·293b·2030·7320·2867·6329·7c0a·7c20··ad);·0s·(gc)|.|· | ||
| 0000dc10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dc10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000dc20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dc20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000dc30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dc30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000dc40:·2020·2020·7c0a·7c6f·3720·3a20·4964·6561······|.|o7·:·Idea | 0000dc40:·2020·2020·7c0a·7c6f·3720·3a20·4964·6561······|.|o7·:·Idea | ||
| 0000dc50:·6c20·6f66·2053·2020·2020·2020·2020·2020··l·of·S·········· | 0000dc50:·6c20·6f66·2053·2020·2020·2020·2020·2020··l·of·S·········· | ||
| 0000dc60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dc60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000dc80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000dc80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000dc90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000dc90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000dca0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000dca0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000dcb0:·2d2d·2d2d·2b0a·7c69·3820·3a20·7469·6d65··----+.|i8·:·time | 0000dcb0:·2d2d·2d2d·2b0a·7c69·3820·3a20·7469·6d65··----+.|i8·:·time | ||
| 0000dcc0:·2071·756f·7469·656e·7428·495e·332c·204a···quotient(I^3,·J | 0000dcc0:·2071·756f·7469·656e·7428·495e·332c·204a···quotient(I^3,·J | ||
| 0000dcd0:·5e32·2c20·5374·7261·7465·6779·203d·3e20··^2,·Strategy·=>· | 0000dcd0:·5e32·2c20·5374·7261·7465·6779·203d·3e20··^2,·Strategy·=>· | ||
| 0000dce0:·5175·6f74·6965·6e74·293b·2020·7c0a·7c20··Quotient);··|.|· | 0000dce0:·5175·6f74·6965·6e74·293b·2020·7c0a·7c20··Quotient);··|.|· | ||
| 0000dcf0:·2d2d·2075·7365·6420·302e·353 | 0000dcf0:·2d2d·2075·7365·6420·302e·3531·3533·3135··--·used·0.515315 | ||
| 0000dd00:·7320·2863·7075·293b·2030·2e3 | 0000dd00:·7320·2863·7075·293b·2030·2e34·3835·3838··s·(cpu);·0.48588 | ||
| 0000dd10:·3673·2028·7468·7265·6164·293b·2030·7320··6s·(thread);·0s· | 0000dd10:·3673·2028·7468·7265·6164·293b·2030·7320··6s·(thread);·0s· | ||
| 0000dd20:·2867·6329·7c0a·7c20·2020·2020·2020·2020··(gc)|.|········· | 0000dd20:·2867·6329·7c0a·7c20·2020·2020·2020·2020··(gc)|.|········· | ||
| 0000dd30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dd30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000dd40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dd40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000dd50:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | 0000dd50:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | ||
| 0000dd60:·3820·3a20·4964·6561·6c20·6f66·2053·2020··8·:·Ideal·of·S·· | 0000dd60:·3820·3a20·4964·6561·6c20·6f66·2053·2020··8·:·Ideal·of·S·· | ||
| 0000dd70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000dd70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 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·2d2d·2d2d·2d2d·2d2d··---------------- | 0000df90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000dfa0:·2d2b·0a7c·6931·3120·3a20·7469·6d65·2071··-+.|i11·:·time·q | 0000dfa0:·2d2b·0a7c·6931·3120·3a20·7469·6d65·2071··-+.|i11·:·time·q | ||
| 0000dfb0:·756f·7469·656e·7428·495e·352c·2049·5e33··uotient(I^5,·I^3 | 0000dfb0:·756f·7469·656e·7428·495e·352c·2049·5e33··uotient(I^5,·I^3 | ||
| 0000dfc0:·2c20·5374·7261·7465·6779·203d·3e20·4974··,·Strategy·=>·It | 0000dfc0:·2c20·5374·7261·7465·6779·203d·3e20·4974··,·Strategy·=>·It | ||
| 0000dfd0:·6572·6174·6529·3b20·2020·2020·207c·0a7c··erate);······|.| | 0000dfd0:·6572·6174·6529·3b20·2020·2020·207c·0a7c··erate);······|.| | ||
| 0000dfe0:·202d·2d20·7573·6564·2030·2e30·3 | 0000dfe0:·202d·2d20·7573·6564·2030·2e30·3135·3933···--·used·0.01593 | ||
| 0000dff0:·3373 | 0000dff0:·3338·7320·2863·7075·293b·2030·2e30·3136··38s·(cpu);·0.016 | ||
| 0000e000:·3 | 0000e000:·3339·3636·7320·2874·6872·6561·6429·3b20··3966s·(thread);· | ||
| 0000e010:·7320 | 0000e010:·3073·2028·6763·2920·207c·0a7c·2020·2020··0s·(gc)··|.|···· | ||
| 0000e020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e030:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e050:·2020·2020·207c·0a7c·6f31·3120·3a20·4964·······|.|o11·:·Id | 0000e050:·2020·2020·207c·0a7c·6f31·3120·3a20·4964·······|.|o11·:·Id | ||
| 0000e060:·6561·6c20·6f66·2053·2020·2020·2020·2020··eal·of·S········ | 0000e060:·6561·6c20·6f66·2053·2020·2020·2020·2020··eal·of·S········ | ||
| 0000e070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000e080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000e0a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e0a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e0b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000e0b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000e0c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | 0000e0c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 0000e0d0:·6931·3220·3a20·7469·6d65·2071·756f·7469··i12·:·time·quoti | 0000e0d0:·6931·3220·3a20·7469·6d65·2071·756f·7469··i12·:·time·quoti | ||
| 0000e0e0:·656e·7428·495e·352c·2049·5e33·2c20·5374··ent(I^5,·I^3,·St | 0000e0e0:·656e·7428·495e·352c·2049·5e33·2c20·5374··ent(I^5,·I^3,·St | ||
| 0000e0f0:·7261·7465·6779·203d·3e20·5175·6f74·6965··rategy·=>·Quotie | 0000e0f0:·7261·7465·6779·203d·3e20·5175·6f74·6965··rategy·=>·Quotie | ||
| 0000e100:·6e74·293b·2020·2020·207c·0a7c·202d·2d20··nt);·····|.|·--· | 0000e100:·6e74·293b·2020·2020·207c·0a7c·202d·2d20··nt);·····|.|·--· | ||
| 0000e110:·7573·6564·2030·2e30·303 | 0000e110:·7573·6564·2030·2e30·3033·3230·3939·3873··used·0.00320998s | ||
| 0000e120:·2028·6370·7529·3b20·302e·3030·3 | 0000e120:·2028·6370·7529·3b20·302e·3030·3633·3234···(cpu);·0.006324 | ||
| 0000e130:·3 | 0000e130:·3932·7320·2874·6872·6561·6429·3b20·3073··92s·(thread);·0s | ||
| 0000e140:·2028·6763·297c·0a7c·2020·2020·2020·2020···(gc)|.|········ | 0000e140:·2028·6763·297c·0a7c·2020·2020·2020·2020···(gc)|.|········ | ||
| 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:·207c·0a7c·6f31·3220·3a20·4964·6561·6c20···|.|o12·:·Ideal· | 0000e180:·207c·0a7c·6f31·3220·3a20·4964·6561·6c20···|.|o12·:·Ideal· | ||
| 0000e190:·6f66·2053·2020·2020·2020·2020·2020·2020··of·S············ | 0000e190:·6f66·2053·2020·2020·2020·2020·2020·2020··of·S············ | ||
| 0000e1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000e1a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00008dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00008dc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00008dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | 00008dd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69··------------+.|i | ||
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| 00008df0:·2074·6f20·3130·206c·6973·7420·7469·6d65···to·10·list·time | 00008df0:·2074·6f20·3130·206c·6973·7420·7469·6d65···to·10·list·time | ||
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| 00007800:·6528·592c·4229·2c73·6174·7572·6174·6528··e(Y,B),saturate( | 00007800:·6528·592c·4229·2c73·6174·7572·6174·6528··e(Y,B),saturate( | ||
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| 00007820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007820:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007830:·2020·7c0a·7c20·2d2d·2075·7365·6420·3 | 00007830:·2020·7c0a·7c20·2d2d·2075·7365·6420·3436····|.|·--·used·46 | ||
| 00007840:·2e3 | 00007840:·2e38·3931·3973·2028·6370·7529·3b20·3434··.8919s·(cpu);·44 | ||
| 00007850:·2e3 | 00007850:·2e37·3533·3873·2028·7468·7265·6164·293b··.7538s·(thread); | ||
| 00007860:·3073 | 00007860:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 00007870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007870:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007880:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00007880:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00007890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007890:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000078a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000078a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000078b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000078b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000078c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000078c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000078d0:·2020·7c0a·7c6f·3134·203d·2074·7275·6520····|.|o14·=·true· | 000078d0:·2020·7c0a·7c6f·3134·203d·2074·7275·6520····|.|o14·=·true· | ||
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| 0000fc30:·782e·2e2e·785c·5050·5e7b·6e5f·6d7d·2e20··x...x\PP^{n_m}.· | 0000fc30:·782e·2e2e·785c·5050·5e7b·6e5f·6d7d·2e20··x...x\PP^{n_m}.· | ||
| 0000fc40:·5468·6973·2069·7320·6661·7374·6572·2074··This·is·faster·t | 0000fc40:·5468·6973·2069·7320·6661·7374·6572·2074··This·is·faster·t | ||
| 0000fc50:·6861·6e20·636f·6d70·7574·696e·6720·7468··han·computing·th | 0000fc50:·6861·6e20·636f·6d70·7574·696e·6720·7468··han·computing·th | ||
| 0000fc60:·6520·656e·7469·7265·2053·6567·7265·0a63··e·entire·Segre.c | 0000fc60:·6520·656e·7469·7265·2053·6567·7265·0a63··e·entire·Segre.c | ||
| 0000fc70:·6c61·7373·2e0a·0a2b·2d2d·2d2d·2d2d·2d2d··lass...+-------- | 0000fc70:·6c61·7373·2e0a·0a2b·2d2d·2d2d·2d2d·2d2d··lass...+-------- | ||
| 0000fc80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fc80:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fc90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fc90:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fca0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2 | 0000fca0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 0000fcb0:·6931 | 0000fcb0:·7c69·3120·3a20·5220·3d20·6d61·6b65·5072··|i1·:·R·=·makePr | ||
| 0000fcc0:·6475 | 0000fcc0:·6f64·7563·7452·696e·6728·7b32·2c32·7d29··oductRing({2,2}) | ||
| 0000fcd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fcd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fce0:·2020·2020·207c·0a7c·2020·2020·2020· | 0000fce0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 0000fcf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fcf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fd00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fd00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fd10:·2020·2020·2020·2020·2020·2020·20 | 0000fd10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fd20:· | 0000fd20:·7c0a·7c6f·3120·3d20·5220·2020·2020·2020··|.|o1·=·R······· | ||
| 0000fd30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fd30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000fd50:·2020·2020·20 | 0000fd50:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
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| 0000fd80:·2020·2020·2020·2020·2020·2020·20 | 0000fd80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fd90:·6f31·203a·2050·6f6c·796e·6f6d·6961·6c52··o1·:·PolynomialR | |||
| 0000fd | 0000fd90:·2020·7c0a·7c6f·3120·3a20·506f·6c79·6e6f····|.|o1·:·Polyno | ||
| 0000fda0:·6d69·616c·5269·6e67·2020·2020·2020·2020··mialRing········ | |||
| 0000fdb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fdb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fdc0:·2020·2020·20 | 0000fdc0:·2020·2020·2020·2020·2020·207c·0a2b·2d2d·············|.+-- | ||
| 0000fdd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fdd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fde0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000fde0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fdf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2 | 0000fdf0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000fe00:·6932·203a·2078·203d·2067·656e·7328·5229··i2·:·x·=·gens(R) | |||
| 0000fe | 0000fe00:·2d2d·2d2d·2b0a·7c69·3220·3a20·7820·3d20··----+.|i2·:·x·=· | ||
| 0000fe10:·6765·6e73·2852·2920·2020·2020·2020·2020··gens(R)········· | |||
| 0000fe20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fe20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fe30:·2020·2020·20 | 0000fe30:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 0000fe50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000fe50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fe60:·2020·2020·2020·2020·2020·2020·20 | 0000fe60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fe70:·6f32·203d·207b·612c·2062·2c20·632c·2064··o2·=·{a,·b,·c,·d | |||
| 0000fe | 0000fe70:·2020·2020·2020·7c0a·7c6f·3220·3d20·7b61········|.|o2·=·{a | ||
| 0000fe80:·2c20·622c·2063·2c20·642c·2065·2c20·667d··,·b,·c,·d,·e,·f} | |||
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| 0000fea0:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | |||
| 0000fe | 0000fea0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
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| 0000fed0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 0000fee0:·6f32·203a·204c·6973·7420·2020·2020·2020··o2·:·List······· | |||
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| 0000fee0:·2020·2020·2020·2020·7c0a·7c6f·3220·3a20··········|.|o2·:· | |||
| 0000fef0:·4c69·7374·2020·2020·2020·2020·2020·2020··List············ | |||
| 0000ff00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ff00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ff10:·2020·2020·20 | 0000ff10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ff20:·2 | 0000ff20:·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d···|.+------------ | ||
| 0000ff30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000ff30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ff40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2 | 0000ff40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000ff50:·6933·203a·2059·203d·2069·6465·616c·2872··i3·:·Y·=·ideal(r | |||
| 0000ff | 0000ff50:·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3320··----------+.|i3· | ||
| 0000ff60:·3a20·5920·3d20·6964·6561·6c28·7261·6e64··:·Y·=·ideal(rand | |||
| 0000ff70:·6f6d·287b·322c·327d·2c52·2929·3b20·2020··om({2,2},R));··· | |||
| 0000ff | 0000ff80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ff | 0000ff90:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 0000ff90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 0000ffa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ffa0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ffb0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 0000ffc0:·6f33·203a·2049·6465·616c·206f·6620·5220··o3·:·Ideal·of·R· | |||
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| 0000ffc0:·2020·2020·2020·2020·2020·2020·7c0a·7c6f··············|.|o | |||
| 0000ffd0:·3320·3a20·4964·6561·6c20·6f66·2052·2020··3·:·Ideal·of·R·· | |||
| 0000ffe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ffe0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000fff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000 | 00010000:·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·······|.+-------- | ||
| 00010000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 00010010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
| 000100 | 00010030:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a··--------------+. | ||
| 000100 | 00010040:·7c69·3420·3a20·5820·3d20·592b·6964·6561··|i4·:·X·=·Y+idea | ||
| 000100 | 00010050:·6c28·785f·302a·785f·332b·785f·312a·785f··l(x_0*x_3+x_1*x_ | ||
| 000100 | 00010060:·3429·3b20·2020·2020·2020·2020·2020·2020··4);············· | ||
| 000100 | 00010070:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 00010070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 00010080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010090:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 000100a0:·6f34·203a·2049·6465·616c·206f·6620·5220··o4·:·Ideal·of·R· | |||
| 000100 | 00010090:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000100 | 000100a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000100b0:·7c0a·7c6f·3420·3a20·4964·6561·6c20·6f66··|.|o4·:·Ideal·of | |||
| 000100c0:·2052·2020·2020·2020·2020·2020·2020·2020···R·············· | |||
| 000100d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | |||
| 000100 | 000100e0:·2020·2020·2020·2020·207c·0a2b·2d2d·2d2d···········|.+---- | ||
| 000100e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | |||
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| 0000a300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000a320:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | 0000a320:·2020·2020·2020·2020·2020·2020·7c0a·7c20··············|.|· | ||
| 0000a330:·2d2d·2063·6170·7475·7269·6e67·2063·6865··--·capturing·che | 0000a330:·2d2d·2063·6170·7475·7269·6e67·2063·6865··--·capturing·che | ||
| 0000a340:·636b·2830·2c20·2253·696d·706c·6544·6f63··ck(0,·"SimpleDoc | 0000a340:·636b·2830·2c20·2253·696d·706c·6544·6f63··ck(0,·"SimpleDoc | ||
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| 0000a360:·302e·313 | 0000a360:·302e·3138·3936·3032·2073·6563·6f6e·6473··0.189602·seconds | ||
| 0000a370:·2065·6c61·7073·6564·7c0a·2b2d·2d2d·2d2d···elapsed|.+----- | 0000a370:·2065·6c61·7073·6564·7c0a·2b2d·2d2d·2d2d···elapsed|.+----- | ||
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| 0000a390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a390:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a3c0:·2d2d·2d2d·2b0a·0a53·6565·2061·6c73·6f0a··----+..See·also. | 0000a3c0:·2d2d·2d2d·2b0a·0a53·6565·2061·6c73·6f0a··----+..See·also. | ||
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| 0002f390:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0002f390:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0002f3a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f3a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f3b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f3b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f3c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f3c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f3d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f3e0:·2020·2020·2020·2020·2020·7c0a·7c6f·3320············|.|o3· | 0002f3e0:·2020·2020·2020·2020·2020·7c0a·7c6f·3320············|.|o3· | ||
| 0002f3f0:·3d20·287c·2030·2031·20 | 0002f3f0:·3d20·287c·2030·2031·2030·2020·2031·207c··=·(|·0·1·0···1·| | ||
| 0002f400:·2c20·4772·6170·687b·2265·6467·6573·2220··,·Graph{"edges"· | 0002f400:·2c20·4772·6170·687b·2265·6467·6573·2220··,·Graph{"edges"· | ||
| 0002f410:·3d3e·207b·7b79·202c·2079·207d·2c20·7b79··=>·{{y·,·y·},·{y | 0002f410:·3d3e·207b·7b79·202c·2079·207d·2c20·7b79··=>·{{y·,·y·},·{y | ||
| 0002f420:·202c·2079·207d·2c20·7b79·202c·2079·207d···,·y·},·{y·,·y·} | 0002f420:·202c·2079·207d·2c20·7b79·202c·2079·207d···,·y·},·{y·,·y·} | ||
| 0002f430:·2c20·7b79·202c·2020·2020·7c0a·7c20·2020··,·{y·,····|.|··· | 0002f430:·2c20·7b79·202c·2020·2020·7c0a·7c20·2020··,·{y·,····|.|··· | ||
| 0002f440:·2020·207c·2031·2030·20 | 0002f440:·2020·207c·2031·2030·2030·2020·2031·207c·····|·1·0·0···1·| | ||
| 0002f450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f460:·2020·2020·2020·3120·2020·3420·2020·2020········1···4····· | 0002f460:·2020·2020·2020·3120·2020·3420·2020·2020········1···4····· | ||
| 0002f470:·3320·2020·3420·2020·2020·3020·2020·3520··3···4·····0···5· | 0002f470:·3320·2020·3420·2020·2020·3020·2020·3520··3···4·····0···5· | ||
| 0002f480:·2020·2020·3220·2020·2020·7c0a·7c20·2020······2·····|.|··· | 0002f480:·2020·2020·3220·2020·2020·7c0a·7c20·2020······2·····|.|··· | ||
| 0002f490:·2020·207c·2030·20 | 0002f490:·2020·207c·2030·2031·2031·2020·2030·207c·····|·0·1·1···0·| | ||
| 0002f4a0:·2020·2020·2020·2020·2272·696e·6722·203d··········"ring"·= | 0002f4a0:·2020·2020·2020·2020·2272·696e·6722·203d··········"ring"·= | ||
| 0002f4b0:·3e20·5151·5b79·202e·2e79·205d·2020·2020··>·QQ[y·..y·]···· | 0002f4b0:·3e20·5151·5b79·202e·2e79·205d·2020·2020··>·QQ[y·..y·]···· | ||
| 0002f4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f4c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0002f4f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f4f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f500:·2020·2020·2020·3020·2020·3720·2020·2020········0···7····· | 0002f500:·2020·2020·2020·3020·2020·3720·2020·2020········0···7····· | ||
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| 0002f530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f530:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f540:·2020·2020·2020·2020·2276·6572·7469·6365··········"vertice | 0002f540:·2020·2020·2020·2020·2276·6572·7469·6365··········"vertice | ||
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| 0002f670:·2020·203 | 0002f670:·2020·2035·2020·2020·2032·2020·2036·2020·····5·····2···6·· | ||
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| 0002f690:·2037·2020·2020·2020·2020·2020·2020·2020···7·············· | 0002f690:·2037·2020·2020·2020·2020·2020·2020·2020···7·············· | ||
| 0002f6a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f6a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f6b0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | 0002f6b0:·2020·2020·2020·2020·2020·7c0a·7c20·2020············|.|··· | ||
| 0002f6c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f6c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f6d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f6d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002f6e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002f6e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00004000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004010:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a··---------+.|i2·: | 00004010:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·203a··---------+.|i2·: | ||
| 00004020:·2074·696d·6520·6465·6772·6565·4465·7465···time·degreeDete | 00004020:·2074·696d·6520·6465·6772·6565·4465·7465···time·degreeDete | ||
| 00004030:·726d·696e·616e·7420·6e20·2020·2020·2020··rminant·n······· | 00004030:·726d·696e·616e·7420·6e20·2020·2020·2020··rminant·n······· | ||
| 00004040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004040:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004060:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | 00004060:·7c0a·7c20·2d2d·2075·7365·6420·302e·3030··|.|·--·used·0.00 | ||
| 00004070:·3038·3637·3137·3673·2028·6370·7529·3b20··0867176s·(cpu);· | |||
| 00004080:·352e·3138·3737·652d·3035·7320·2874·6872··5.1877e-05s·(thr | |||
| 000040 | 00004070:·3136·3335·3134·7320·2863·7075·293b·2035··163514s·(cpu);·5 | ||
| 00004080:·2e33·3938·3165·2d30·3573·2028·7468·7265··.3981e-05s·(thre | |||
| 00004090:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | |||
| 000040a0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | 000040a0:·2020·2020·2020·207c·0a7c·2020·2020·2020·········|.|······ | ||
| 000040b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000040b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000040c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000040c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000040d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000040d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000040e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 000040e0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 000040f0:·7c6f·3220·3d20·3620·2020·2020·2020·2020··|o2·=·6········· | 000040f0:·7c6f·3220·3d20·3620·2020·2020·2020·2020··|o2·=·6········· | ||
| 00004100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 000042c0:·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·2d2b··---------------+ | 000042d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b··---------------+ | ||
| 000042e0:·0a7c·6934·203a·2074·696d·6520·6465·6772··.|i4·:·time·degr | 000042e0:·0a7c·6934·203a·2074·696d·6520·6465·6772··.|i4·:·time·degr | ||
| 000042f0:·6565·2064·6574·6572·6d69·6e61·6e74·204d··ee·determinant·M | 000042f0:·6565·2064·6574·6572·6d69·6e61·6e74·204d··ee·determinant·M | ||
| 00004300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004300:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004310:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004320:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 00004320:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 00004330:·6420·302e·313 | 00004330:·6420·302e·3132·3837·3934·7320·2863·7075··d·0.128794s·(cpu | ||
| 00004340:·3b20 | 00004340:·293b·2030·2e31·3030·3431·3873·2028·7468··);·0.100418s·(th | ||
| 00004350:·6561 | 00004350:·7265·6164·293b·2030·7320·2867·6329·2020··read);·0s·(gc)·· | ||
| 00004360:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00004360:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00004370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000043a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000043a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000043b0:·2020·2020·7c0a·7c6f·3420·3d20·7b36·7d20······|.|o4·=·{6}· | 000043b0:·2020·2020·7c0a·7c6f·3420·3d20·7b36·7d20······|.|o4·=·{6}· | ||
| 000043c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000043c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00004c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004c30:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00004c40:·2d2d·2b0a·7c69·3220·3a20·7469·6d65·2044··--+.|i2·:·time·D | 00004c40:·2d2d·2b0a·7c69·3220·3a20·7469·6d65·2044··--+.|i2·:·time·D | ||
| 00004c50:·6973·6320·3d20·6465·6e73·6544·6973·6372··isc·=·denseDiscr | 00004c50:·6973·6320·3d20·6465·6e73·6544·6973·6372··isc·=·denseDiscr | ||
| 00004c60:·696d·696e·616e·7428·642c·6e29·2020·2020··iminant(d,n)···· | 00004c60:·696d·696e·616e·7428·642c·6e29·2020·2020··iminant(d,n)···· | ||
| 00004c70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004c70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004c80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004c90:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | 00004c90:·2020·7c0a·7c20·2d2d·2075·7365·6420·302e····|.|·--·used·0. | ||
| 00004ca0:·323 | 00004ca0:·3238·3034·3634·7320·2863·7075·293b·2030··280464s·(cpu);·0 | ||
| 00004cb0:·2e32·303 | 00004cb0:·2e32·3039·3531·3773·2028·7468·7265·6164··.209517s·(thread | ||
| 00004cc0:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | 00004cc0:·293b·2030·7320·2867·6329·2020·2020·2020··);·0s·(gc)······ | ||
| 00004cd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004cd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004ce0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | 00004ce0:·2020·7c0a·7c20·2020·2020·2020·2020·2020····|.|··········· | ||
| 00004cf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004cf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00004d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00005ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005f00:·2d2d·2d2b·0a7c·6932·203a·2074·696d·6520··---+.|i2·:·time· | 00005f00:·2d2d·2d2b·0a7c·6932·203a·2074·696d·6520··---+.|i2·:·time· | ||
| 00005f10:·6465·6e73·6552·6573·756c·7461·6e74·2866··denseResultant(f | 00005f10:·6465·6e73·6552·6573·756c·7461·6e74·2866··denseResultant(f | ||
| 00005f20:·302c·6631·2c66·3229·3b20·2d2d·2075·7369··0,f1,f2);·--·usi | 00005f20:·302c·6631·2c66·3229·3b20·2d2d·2075·7369··0,f1,f2);·--·usi | ||
| 00005f30:·6e67·2050·6f69·7373·6f6e·2066·6f72·6d75··ng·Poisson·formu | 00005f30:·6e67·2050·6f69·7373·6f6e·2066·6f72·6d75··ng·Poisson·formu | ||
| 00005f40:·6c61·2020·2020·2020·2020·2020·2020·2020··la·············· | 00005f40:·6c61·2020·2020·2020·2020·2020·2020·2020··la·············· | ||
| 00005f50:·2020·207c·0a7c·202d·2d20·7573·6564·2030·····|.|·--·used·0 | 00005f50:·2020·207c·0a7c·202d·2d20·7573·6564·2030·····|.|·--·used·0 | ||
| 00005f60:·2e31·3 | 00005f60:·2e31·3438·3430·3273·2028·6370·7529·3b20··.148402s·(cpu);· | ||
| 00005f70:·302e·3131·3 | 00005f70:·302e·3131·3639·3633·7320·2874·6872·6561··0.116963s·(threa | ||
| 00005f80:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | 00005f80:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 00005f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005f90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005fa0:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | 00005fa0:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | ||
| 00005fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005fb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005fc0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005fd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005fd0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005fe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00005ff0:·2d2d·2d2b·0a7c·6933·203a·2074·696d·6520··---+.|i3·:·time· | 00005ff0:·2d2d·2d2b·0a7c·6933·203a·2074·696d·6520··---+.|i3·:·time· | ||
| 00006000:·6465·6e73·6552·6573·756c·7461·6e74·2866··denseResultant(f | 00006000:·6465·6e73·6552·6573·756c·7461·6e74·2866··denseResultant(f | ||
| 00006010:·302c·6631·2c66·322c·416c·676f·7269·7468··0,f1,f2,Algorith | 00006010:·302c·6631·2c66·322c·416c·676f·7269·7468··0,f1,f2,Algorith | ||
| 00006020:·6d3d·3e22·4d61·6361·756c·6179·2229·3b20··m=>"Macaulay");· | 00006020:·6d3d·3e22·4d61·6361·756c·6179·2229·3b20··m=>"Macaulay");· | ||
| 00006030:·2d2d·2075·7369·6e67·204d·6163·6175·6c61··--·using·Macaula | 00006030:·2d2d·2075·7369·6e67·204d·6163·6175·6c61··--·using·Macaula | ||
| 00006040:·7920·207c·0a7c·202d·2d20·7573·6564·2030··y··|.|·--·used·0 | 00006040:·7920·207c·0a7c·202d·2d20·7573·6564·2030··y··|.|·--·used·0 | ||
| 00006050:·2e3 | 00006050:·2e32·3330·3835·3473·2028·6370·7529·3b20··.230854s·(cpu);· | ||
| 00006060:·302e·323 | 00006060:·302e·3230·3038·3335·7320·2874·6872·6561··0.200835s·(threa | ||
| 00006070:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | 00006070:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 00006080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006090:·2020·207c·0a7c·2d2d·2d2d·2d2d·2d2d·2d2d·····|.|---------- | 00006090:·2020·207c·0a7c·2d2d·2d2d·2d2d·2d2d·2d2d·····|.|---------- | ||
| 000060a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000060b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000060c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000060d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000060d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00006170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006180:·2d2d·2d2b·0a7c·6934·203a·2074·696d·6520··---+.|i4·:·time· | 00006180:·2d2d·2d2b·0a7c·6934·203a·2074·696d·6520··---+.|i4·:·time· | ||
| 00006190:·2864·656e·7365·5265·7375·6c74·616e·7428··(denseResultant( | 00006190:·2864·656e·7365·5265·7375·6c74·616e·7428··(denseResultant( | ||
| 000061a0:·312c·322c·3229·2920·2866·302c·6631·2c66··1,2,2))·(f0,f1,f | 000061a0:·312c·322c·3229·2920·2866·302c·6631·2c66··1,2,2))·(f0,f1,f | ||
| 000061b0:·3229·3b20·2d2d·2075·7369·6e67·2073·7061··2);·--·using·spa | 000061b0:·3229·3b20·2d2d·2075·7369·6e67·2073·7061··2);·--·using·spa | ||
| 000061c0:·7273·6552·6573·756c·7461·6e74·2020·2020··rseResultant···· | 000061c0:·7273·6552·6573·756c·7461·6e74·2020·2020··rseResultant···· | ||
| 000061d0:·2020·207c·0a7c·202d·2d20·7573·6564·2030·····|.|·--·used·0 | 000061d0:·2020·207c·0a7c·202d·2d20·7573·6564·2030·····|.|·--·used·0 | ||
| 000061e0:·2e32·3 | 000061e0:·2e32·3236·3135·3673·2028·6370·7529·3b20··.226156s·(cpu);· | ||
| 000061f0:·302e·323 | 000061f0:·302e·3232·3934·3938·7320·2874·6872·6561··0.229498s·(threa | ||
| 00006200:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | 00006200:·6429·3b20·3073·2028·6763·2920·2020·2020··d);·0s·(gc)····· | ||
| 00006210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006210:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006220:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | 00006220:·2020·207c·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·····|.+---------- | ||
| 00006230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006230:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006240:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006250:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00006260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00014fb0:·6572·5370·6563·6874·506f·6c79·6e6f·6d69··erSpechtPolynomi | 00014fb0:·6572·5370·6563·6874·506f·6c79·6e6f·6d69··erSpechtPolynomi | ||
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| 00014fe0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | 00014fe0:·2020·2020·2020·2020·2020·2020·2020·207c·················| | ||
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| 00015050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00015050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0002a9c0:·6172·7949·6e76·6172·6961·6e74·7328·6765··aryInvariants(ge | 0002a9c0:·6172·7949·6e76·6172·6961·6e74·7328·6765··aryInvariants(ge | ||
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| 0002aa60:·4469·6d65·6e73·696f·6e2c·2031·2c20·5261··Dimension,·1,·Ra | 0002aa60:·4469·6d65·6e73·696f·6e2c·2031·2c20·5261··Dimension,·1,·Ra | ||
| 0002aa70:·6e6b·2c20·3129·2020·2020·2020·2020·2020··nk,·1)·········· | 0002aa70:·6e6b·2c20·3129·2020·2020·2020·2020·2020··nk,·1)·········· | ||
| 0002aa80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002aa80:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 000072d0:·7373·6f63·6961·7465·6443·6173·7465·6c6e··ssociatedCasteln | 000072d0:·7373·6f63·6961·7465·6443·6173·7465·6c6e··ssociatedCasteln | ||
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| 000072f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000072f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007300:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00007300:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00007310:·202d·2d20·7573·6564·203 | 00007310:·202d·2d20·7573·6564·2031·2e37·3531·3136···--·used·1.75116 | ||
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| 00007330:·3 | 00007330:·3773·2028·7468·7265·6164·293b·2030·7320··7s·(thread);·0s· | ||
| 00007340:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | 00007340:·2867·6329·2020·2020·2020·2020·2020·2020··(gc)············ | ||
| 00007350:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00007350:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00007360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007360:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007370:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007380:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00007390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00007390:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000073a0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 000073a0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
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| 00008d30:·6173·736f·6369·6174·6564·4b33·7375·7266··associatedK3surf | 00008d30:·6173·736f·6369·6174·6564·4b33·7375·7266··associatedK3surf | ||
| 00008d40:·6163·6520·583b·2020·2020·2020·2020·2020··ace·X;·········· | 00008d40:·6163·6520·583b·2020·2020·2020·2020·2020··ace·X;·········· | ||
| 00008d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008d50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008d60:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00008d60:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00008d70:·7c20·2d2d·2075·7365·6420·312e·3 | 00008d70:·7c20·2d2d·2075·7365·6420·312e·3637·3139··|·--·used·1.6719 | ||
| 00008d80:·3 | 00008d80:·3273·2028·6370·7529·3b20·302e·3932·3537··2s·(cpu);·0.9257 | ||
| 00008d90:·3 | 00008d90:·3638·7320·2874·6872·6561·6429·3b20·3073··68s·(thread);·0s | ||
| 00008da0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | 00008da0:·2028·6763·2920·2020·2020·2020·2020·2020···(gc)··········· | ||
| 00008db0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00008db0:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
| 00008dc0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | 00008dc0:·7c20·2020·2020·2020·2020·2020·2020·2020··|··············· | ||
| 00008dd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008dd0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008de0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00008df0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00008e00:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | 00008e00:·2020·2020·2020·2020·2020·2020·2020·7c0a················|. | ||
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| 0000a5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000a5b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000a5c0:·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20·7469··------+.|i3·:·ti | 0000a5c0:·2d2d·2d2d·2d2d·2b0a·7c69·3320·3a20·7469··------+.|i3·:·ti | ||
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| 0000a5e0:·6564·4b33·7375·7266·6163·6520·583b·2020··edK3surface·X;·· | 0000a5e0:·6564·4b33·7375·7266·6163·6520·583b·2020··edK3surface·X;·· | ||
| 0000a5f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a5f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a600:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a610:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | 0000a610:·2020·2020·2020·7c0a·7c20·2d2d·2075·7365········|.|·--·use | ||
| 0000a620:·6420·3 | 0000a620:·6420·352e·3339·3135·3773·2028·6370·7529··d·5.39157s·(cpu) | ||
| 0000a630:·3b20·332e·3 | 0000a630:·3b20·332e·3630·3230·3273·2028·7468·7265··;·3.60202s·(thre | ||
| 0000a640:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | 0000a640:·6164·293b·2030·7320·2867·6329·2020·2020··ad);·0s·(gc)···· | ||
| 0000a650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a650:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a660:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | 0000a660:·2020·2020·2020·7c0a·7c20·2020·2020·2020········|.|······· | ||
| 0000a670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a670:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a680:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a690:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000a6a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000a6a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 0000f3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f3c0:·2d2b·0a7c·6933·203a·2074·696d·6520·6620··-+.|i3·:·time·f· | 0000f3c0:·2d2b·0a7c·6933·203a·2074·696d·6520·6620··-+.|i3·:·time·f· | ||
| 0000f3d0:·3d20·6465·7465·6374·436f·6e67·7275·656e··=·detectCongruen | 0000f3d0:·3d20·6465·7465·6374·436f·6e67·7275·656e··=·detectCongruen | ||
| 0000f3e0:·6365·2858·2c56·6572·626f·7365·3d3e·7472··ce(X,Verbose=>tr | 0000f3e0:·6365·2858·2c56·6572·626f·7365·3d3e·7472··ce(X,Verbose=>tr | ||
| 0000f3f0:·7565·293b·2020·2020·2020·2020·2020·2020··ue);············ | 0000f3f0:·7565·293b·2020·2020·2020·2020·2020·2020··ue);············ | ||
| 0000f400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f400:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f410:·207c·0a7c·202d·2d20·7573·6564·203 | 0000f410:·207c·0a7c·202d·2d20·7573·6564·2033·2e30···|.|·--·used·3.0 | ||
| 0000f420:·3 | 0000f420:·3238·3832·7320·2863·7075·293b·2031·2e36··2882s·(cpu);·1.6 | ||
| 0000f430:·3 | 0000f430:·3737·3233·7320·2874·6872·6561·6429·3b20··7723s·(thread);· | ||
| 0000f440:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | 0000f440:·3073·2028·6763·2920·2020·2020·2020·2020··0s·(gc)········· | ||
| 0000f450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f460:·207c·0a7c·6e75·6d62·6572·206c·696e·6573···|.|number·lines | 0000f460:·207c·0a7c·6e75·6d62·6572·206c·696e·6573···|.|number·lines | ||
| 0000f470:·2063·6f6e·7461·696e·6564·2069·6e20·7468···contained·in·th | 0000f470:·2063·6f6e·7461·696e·6564·2069·6e20·7468···contained·in·th | ||
| 0000f480:·6520·696d·6167·6520·6f66·2074·6865·2063··e·image·of·the·c | 0000f480:·6520·696d·6167·6520·6f66·2074·6865·2063··e·image·of·the·c | ||
| 0000f490:·7562·6963·206d·6170·2061·6e64·2070·6173··ubic·map·and·pas | 0000f490:·7562·6963·206d·6170·2061·6e64·2070·6173··ubic·map·and·pas | ||
| 0000f4a0:·7369·6e67·2074·6872·6f75·6768·2061·2020··sing·through·a·· | 0000f4a0:·7369·6e67·2074·6872·6f75·6768·2061·2020··sing·through·a·· | ||
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| 0000f8b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000f8b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000f8c0:·2d2b·0a7c·6935·203a·2074·696d·6520·4320··-+.|i5·:·time·C· | 0000f8c0:·2d2b·0a7c·6935·203a·2074·696d·6520·4320··-+.|i5·:·time·C· | ||
| 0000f8d0:·3d20·6620·703b·202d·2d20·352d·7365·6361··=·f·p;·--·5-seca | 0000f8d0:·3d20·6620·703b·202d·2d20·352d·7365·6361··=·f·p;·--·5-seca | ||
| 0000f8e0:·6e74·2063·6f6e·6963·2074·6f20·7468·6520··nt·conic·to·the· | 0000f8e0:·6e74·2063·6f6e·6963·2074·6f20·7468·6520··nt·conic·to·the· | ||
| 0000f8f0:·7375·7266·6163·6520·2020·2020·2020·2020··surface········· | 0000f8f0:·7375·7266·6163·6520·2020·2020·2020·2020··surface········· | ||
| 0000f900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f900:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f910:·207c·0a7c·202d·2d20·7573·6564·2030·2e33···|.|·--·used·0.3 | 0000f910:·207c·0a7c·202d·2d20·7573·6564·2030·2e33···|.|·--·used·0.3 | ||
| 0000f920:·3931·3 | 0000f920:·3931·3137·3473·2028·6370·7529·3b20·302e··91174s·(cpu);·0. | ||
| 0000f930:·323 | 0000f930:·3238·3832·3131·7320·2874·6872·6561·6429··288211s·(thread) | ||
| 0000f940:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | 0000f940:·3b20·3073·2028·6763·2920·2020·2020·2020··;·0s·(gc)······· | ||
| 0000f950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f950:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f960:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | 0000f960:·207c·0a7c·2020·2020·2020·2020·2020·2020···|.|············ | ||
| 0000f970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f970:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f980:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f990:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000f9a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000f9a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
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| 00010980:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00010980:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00010990:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·: | 00010990:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a··---------+.|i3·: | ||
| 000109a0:·2074·696d·6520·6620·3d20·6465·7465·6374···time·f·=·detect | 000109a0:·2074·696d·6520·6620·3d20·6465·7465·6374···time·f·=·detect | ||
| 000109b0:·436f·6e67·7275·656e·6365·2858·2c56·6572··Congruence(X,Ver | 000109b0:·436f·6e67·7275·656e·6365·2858·2c56·6572··Congruence(X,Ver | ||
| 000109c0:·626f·7365·3d3e·7472·7565·293b·2020·2020··bose=>true);···· | 000109c0:·626f·7365·3d3e·7472·7565·293b·2020·2020··bose=>true);···· | ||
| 000109d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000109d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000109e0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000109e0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 000109f0:·7573·6564·2031·3 | 000109f0:·7573·6564·2031·332e·3931·3036·7320·2863··used·13.9106s·(c | ||
| 00010a00:·7075·293b·2036·2e37·3836·3773·2028·7468··pu);·6.7867s·(th | |||
| 00010a | 00010a00:·7075·293b·2035·2e36·3530·3035·7320·2874··pu);·5.65005s·(t | ||
| 00010a10:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | |||
| 00010a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00010a20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00010a30:·2020·2020·2020·2020·207c·0a7c·6e75·6d62···········|.|numb | 00010a30:·2020·2020·2020·2020·207c·0a7c·6e75·6d62···········|.|numb | ||
| 00010a40:·6572·206c·696e·6573·2063·6f6e·7461·696e··er·lines·contain | 00010a40:·6572·206c·696e·6573·2063·6f6e·7461·696e··er·lines·contain | ||
| 00010a50:·6564·2069·6e20·7468·6520·696d·6167·6520··ed·in·the·image· | 00010a50:·6564·2069·6e20·7468·6520·696d·6167·6520··ed·in·the·image· | ||
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| 00001710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001710:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001720:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00001720:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
| 00001730:·2020·2020·2020·2020·2832·2c20·3329·203d··········(2,·3)·= | |||
| 000017 | 00001730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001740:·2020·2030·2035·2020·2020·3320·3220·2020·····0·5····3·2··· | |||
| 00001750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001770:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | 00001770:·2020·207c·0a7c·2020·2020·2020·2020·2020·····|.|·········· | ||
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| 00006190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006190:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | 000061a0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6934·203a··---------+.|i4·: | ||
| 000061b0:·2074·696d·6520·6564·4465·6728·4129·2020···time·edDeg(A)·· | 000061b0:·2074·696d·6520·6564·4465·6728·4129·2020···time·edDeg(A)·· | ||
| 000061c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000061c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000061d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000061d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000061e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000061e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000061f0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000061f0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00006200:·7573·6564·203 | 00006200:·7573·6564·2030·2e39·3537·3335·7320·2863··used·0.95735s·(c | ||
| 00006210:·7075·293b·2030·2e3 | 00006210:·7075·293b·2030·2e36·3634·3835·7320·2874··pu);·0.66485s·(t | ||
| 00006220:· | 00006220:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00006230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006230:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006240:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00006240:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00006250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006250:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006260:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006270:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006280:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006290:·2020·2020·2020·2020·207c·0a7c·5468·6520···········|.|The· | 00006290:·2020·2020·2020·2020·207c·0a7c·5468·6520···········|.|The· | ||
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| 00006690:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00006690:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000066a0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | 000066a0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6935·203a··---------+.|i5·: | ||
| 000066b0:·2074·696d·6520·6564·4465·6728·412c·466f···time·edDeg(A,Fo | 000066b0:·2074·696d·6520·6564·4465·6728·412c·466f···time·edDeg(A,Fo | ||
| 000066c0:·7263·6541·6d61·743d·3e74·7275·6529·2020··rceAmat=>true)·· | 000066c0:·7263·6541·6d61·743d·3e74·7275·6529·2020··rceAmat=>true)·· | ||
| 000066d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000066d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000066e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000066e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000066f0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | 000066f0:·2020·2020·2020·2020·207c·0a7c·202d·2d20···········|.|·--· | ||
| 00006700:·7573·6564·2033·2e3 | 00006700:·7573·6564·2033·2e36·3332·3033·7320·2863··used·3.63203s·(c | ||
| 00006710:·7075·293b·2032·2e3 | 00006710:·7075·293b·2032·2e35·3232·3037·7320·2874··pu);·2.52207s·(t | ||
| 00006720:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | 00006720:·6872·6561·6429·3b20·3073·2028·6763·2920··hread);·0s·(gc)· | ||
| 00006730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006730:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006740:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00006740:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00006750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006750:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006760:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006770:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00006780:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00006780:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 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·2064·2c20·662c·2068·7d2c·207b··{{c,·d,·f,·h},·{ | |||
| 00000520:·622c·2064·2c20·652c·2066·7d2c·207b·612a··b,·d,·e,·f},·{a* | |||
| 000005 | 00000530:·6420·2d20·622a·632c·2065·2c20·667d·202f··d·-·b*c,·e,·f}·/ | ||
| 000005 | 00000540:·2064·2c20·7b61·2a64·202d·2062·2a63·2c20···d,·{a*d·-·b*c,· | ||
| 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:·632a·6620·2d20·2020·7c0a·7c20·2020·2020··c*f·-···|.|····· | ||
| 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:·7b63·2c20·642c·2066·2c20·687d·2c20·7b63··{c,·d,·f,·h},·{c | |||
| 000005 | 000005b0:·642a·652c·2065·2a68·202d·2066·2a67·7d20··d*e,·e*h·-·f*g}· | ||
| 000005d0:·2f20·682c·207b·622c·2064·2c20·652c·2066··/·h,·{b,·d,·e,·f | |||
| 000005 | 000005c0:·2f20·7b64·2c20·662c·2068·7d2c·207b·632c··/·{d,·f,·h},·{c, | ||
| 000005d0:·2064·2c20·652a·6820·2d20·662a·677d·202f···d,·e*h·-·f*g}·/ | |||
| 000005e0:·2068·2c20·7b63·2c20·642c·2065·2c20·667d···h,·{c,·d,·e,·f} | |||
| 000005f0:·207b | 000005f0:·2c20·7b61·2a64·202d·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:·622a·632c·2063·2a66·202d·2064·2a65·2c20··b*c,·c*f·-·d*e,· | 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},· | 00000660:·672c·2068·7d20·2f20·7b64·2c20·667d·2c20··g,·h}·/·{d,·f},· | ||
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| 0000cfe0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 0000cfe0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 0000cff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cff0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d000:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d010:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d020:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d030:·2020·2020·2020·2020·2020·207c·0a7c·6f33·············|.|o3 | 0000d030:·2020·2020·2020·2020·2020·207c·0a7c·6f33·············|.|o3 | ||
| 0000d040:·203d·207b·7b63·2c20·642c·2065·2c20·667d···=·{{c,·d,·e,·f} | 0000d040:·203d·207b·7b63·2c20·642c·2065·2c20·667d···=·{{c,·d,·e,·f} | ||
| 0000d050:·2c20·7b61·2a64·202d·2062·2a63·2c20·6 | 0000d050:·2c20·7b61·2a64·202d·2062·2a63·2c20·632a··,·{a*d·-·b*c,·c* | ||
| 0000d060:·2066·7d20·2f20·642c·207b·612a·6420·2d20···f}·/·d,·{a*d·-· | |||
| 0000d0 | 0000d060:·6620·2d20·642a·652c·2067·2c20·687d·202f··f·-·d*e,·g,·h}·/ | ||
| 0000d070:·207b·642c·2066·7d2c·207b·622c·2064·2c20···{d,·f},·{b,·d,· | |||
| 0000d080:·6 | 0000d080:·662c·2068·7d2c·207b·632c·207c·0a7c·2020··f,·h},·{c,·|.|·· | ||
| 0000d090:·2020·202d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····------------- | 0000d090:·2020·202d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····------------- | ||
| 0000d0a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d0a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d0b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d0b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d0c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d0c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d0d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·2020··-----------|.|·· | 0000d0d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·2020··-----------|.|·· | ||
| 0000d0e0:·2020·2066·7d2c·207b·612a·6420·2d20·622a·····f},·{a*d·-·b* | |||
| 0000d0f0:·632c·2063·2a66·202d·2064·2a65·2c20·652a··c,·c*f·-·d*e,·e* | |||
| 0000d100:·6820·2d20·662a·677d·202f·207b·642c·2066··h·-·f*g}·/·{d,·f | |||
| 0000d110:·2c20·687d·2c20·7b62·2c20·642c·2066·2c20··,·h},·{b,·d,·f,· | |||
| 0000d | 0000d0e0:·2020·2064·2c20·672c·2068·7d2c·207b·612a·····d,·g,·h},·{a* | ||
| 0000d0f0:·6420·2d20·622a·632c·2065·2c20·667d·202f··d·-·b*c,·e,·f}·/ | |||
| 0000d100:·2064·2c20·7b61·2a64·202d·2062·2a63·2c20···d,·{a*d·-·b*c,· | |||
| 0000d110:·632a·6620·2d20·642a·652c·2065·2a68·202d··c*f·-·d*e,·e*h·- | |||
| 0000d120:·2066·2a67·7d20·2f20·7b64·2c7c·0a7c·2020···f*g}·/·{d,|.|·· | |||
| 0000d130:·2020·202d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·····------------- | 0000d130:·2020·202d·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·2d2d··---------------- | 0000d160:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·2020··-----------|.|·· | 0000d170:·2d2d·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·2020··-----------|.|·· | ||
| 0000d180:·2020·2066·2c20·687d·2c20·7b63·2c20·642c·····f,·h},·{c,·d, | |||
| 0000d1 | 0000d190:·2065·2a68·202d·2066·2a67·7d20·2f20·682c···e*h·-·f*g}·/·h, | ||
| 0000d190:·682c·207b·632c·2064·2c20·672c·2068·7d2c··h,·{c,·d,·g,·h}, | |||
| 0000d1a0:·207b·632c·2064·2c20·662c·2068·7d2c·207b···{c,·d,·f,·h},·{ | 0000d1a0:·207b·632c·2064·2c20·662c·2068·7d2c·207b···{c,·d,·f,·h},·{ | ||
| 0000d1b0:·622c·2064·2c20·652c·2066·7d7d·2020·2020··b,·d,·e,·f}}···· | 0000d1b0:·622c·2064·2c20·652c·2066·7d7d·2020·2020··b,·d,·e,·f}}···· | ||
| 0000d1c0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 0000d1c0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 0000d1d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d1d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d1e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d1e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d1f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d1f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000d200:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000d200:·2020·2020·2020·2020·2020·2020·2020·2020·················· |
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| 00001120:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001120:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001130:·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a·2065··-------+.|i3·:·e | 00001130:·2d2d·2d2d·2d2d·2d2b·0a7c·6933·203a·2065··-------+.|i3·:·e | ||
| 00001140:·6c61·7073·6564·5469·6d65·2054·7320·3d20··lapsedTime·Ts·=· | 00001140:·6c61·7073·6564·5469·6d65·2054·7320·3d20··lapsedTime·Ts·=· | ||
| 00001150:·616c·6c54·7269·616e·6775·6c61·7469·6f6e··allTriangulation | 00001150:·616c·6c54·7269·616e·6775·6c61·7469·6f6e··allTriangulation | ||
| 00001160:·7328·412c·2046·696e·6520·3d3e·2074·7275··s(A,·Fine·=>·tru | 00001160:·7328·412c·2046·696e·6520·3d3e·2074·7275··s(A,·Fine·=>·tru | ||
| 00001170:·6529·3b20·2020·2020·2020·2020·2020·2020··e);············· | 00001170:·6529·3b20·2020·2020·2020·2020·2020·2020··e);············· | ||
| 00001180:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | 00001180:·2020·2020·2020·207c·0a7c·202d·2d20·302e·········|.|·--·0. | ||
| 00001190:·313 | 00001190:·3136·3633·3432·2073·6563·6f6e·6473·2065··166342·seconds·e | ||
| 000011a0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | 000011a0:·6c61·7073·6564·2020·2020·2020·2020·2020··lapsed·········· | ||
| 000011b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000011b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000011c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000011c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000011d0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 000011d0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 000011e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000011e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000011f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000011f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001200:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| Offset 480, 15 lines modified | Offset 480, 15 lines modified | ||
| 00001df0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001df0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001e00:·2d2d·2d2d·2d2d·2d2b·0a7c·6938·203a·2065··-------+.|i8·:·e | 00001e00:·2d2d·2d2d·2d2d·2d2b·0a7c·6938·203a·2065··-------+.|i8·:·e | ||
| 00001e10:·6c61·7073·6564·5469·6d65·2054·7332·203d··lapsedTime·Ts2·= | 00001e10:·6c61·7073·6564·5469·6d65·2054·7332·203d··lapsedTime·Ts2·= | ||
| 00001e20:·2067·656e·6572·6174·6554·7269·616e·6775···generateTriangu | 00001e20:·2067·656e·6572·6174·6554·7269·616e·6775···generateTriangu | ||
| 00001e30:·6c61·7469·6f6e·7320·543b·2020·2020·2020··lations·T;······ | 00001e30:·6c61·7469·6f6e·7320·543b·2020·2020·2020··lations·T;······ | ||
| 00001e40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001e40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001e50:·2020·2020·2020·207c·0a7c·202d·2d20·312e·········|.|·--·1. | 00001e50:·2020·2020·2020·207c·0a7c·202d·2d20·312e·········|.|·--·1. | ||
| 00001e60:·3 | 00001e60:·3132·3636·3720·7365·636f·6e64·7320·656c··12667·seconds·el | ||
| 00001e70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | 00001e70:·6170·7365·6420·2020·2020·2020·2020·2020··apsed··········· | ||
| 00001e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001e80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00001e90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00001ea0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | 00001ea0:·2020·2020·2020·207c·0a2b·2d2d·2d2d·2d2d·········|.+------ | ||
| 00001eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001eb0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001ec0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00001ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00001ed0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| Offset 3308, 351 lines modified | Offset 3308, 351 lines modified | ||
| 0000ceb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ceb0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000cec0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000ced0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0000ced0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0000cee0:·207c·0a7c·6f34·203d·207b·7472·6961·6e67···|.|o4·=·{triang | 0000cee0:·207c·0a7c·6f34·203d·207b·7472·6961·6e67···|.|o4·=·{triang | ||
| 0000cef0:·756c·6174·696f·6e20·7b7b·302c·2031·2c20··ulation·{{0,·1,· | 0000cef0:·756c·6174·696f·6e20·7b7b·302c·2031·2c20··ulation·{{0,·1,· | ||
| 0000cf00:·322c·2037·7d2c·207b·302c·2031·2c20·352c··2,·7},·{0,·1,·5, | 0000cf00:·322c·2037·7d2c·207b·302c·2031·2c20·352c··2,·7},·{0,·1,·5, | ||
| 0000cf10:·2037·7d2c·207b·302c·2032·2c20·362c·2037···7},·{0,·2,·6,·7 | 0000cf10:·2037·7d2c·207b·302c·2032·2c20·362c·2037···7},·{0,·2,·6,·7 | ||
| 0000cf20:·7d2c·207b·302c·2034·2c20·352c·203 | 0000cf20:·7d2c·207b·302c·2034·2c20·352c·2036·7d2c··},·{0,·4,·5,·6}, | ||
| 0000cf30:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000cf30:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000cf40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cf40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000cf50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cf50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000cf60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cf60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000cf70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cf70:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000cf80:·2d7c·0a7c·2020·2020·207b·302c·203 | 0000cf80:·2d7c·0a7c·2020·2020·207b·302c·2035·2c20··-|.|·····{0,·5,· | ||
| 0000cf90:·362c·2037·7d2c·207b·312c·2032·2c20·332c··6,·7},·{1,·2,·3, | 0000cf90:·362c·2037·7d2c·207b·312c·2032·2c20·332c··6,·7},·{1,·2,·3, | ||
| 0000cfa0:·2037·7d7d·2c20·7472·6961·6e67·756c·6174···7}},·triangulat | 0000cfa0:·2037·7d7d·2c20·7472·6961·6e67·756c·6174···7}},·triangulat | ||
| 0000cfb0:·696f·6e20·7b7b·302c·2031·2c20·332c·2037··ion·{{0,·1,·3,·7 | 0000cfb0:·696f·6e20·7b7b·302c·2031·2c20·332c·2037··ion·{{0,·1,·3,·7 | ||
| 0000cfc0:·7d2c·207b·302c·2031·2c20·352c·2037·7d2c··},·{0,·1,·5,·7}, | 0000cfc0:·7d2c·207b·302c·2031·2c20·352c·2037·7d2c··},·{0,·1,·5,·7}, | ||
| 0000cfd0:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000cfd0:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000cfe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cfe0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000cff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000cff0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d000:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d010:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d020:·2d7c·0a7c·2020·2020·207b·302c·2032·2c20··-|.|·····{0,·2,· | 0000d020:·2d7c·0a7c·2020·2020·207b·302c·2032·2c20··-|.|·····{0,·2,· | ||
| 0000d030:·332c·203 | 0000d030:·332c·2036·7d2c·207b·302c·2033·2c20·362c··3,·6},·{0,·3,·6, | ||
| 0000d040:·2037·7d2c·207b·302c·2034·2c20·352c·2036···7},·{0,·4,·5,·6 | 0000d040:·2037·7d2c·207b·302c·2034·2c20·352c·2036···7},·{0,·4,·5,·6 | ||
| 0000d050:·7d2c·207b·302c·2035·2c20·362c·2037·7d7d··},·{0,·5,·6,·7}} | 0000d050:·7d2c·207b·302c·2035·2c20·362c·2037·7d7d··},·{0,·5,·6,·7}} | ||
| 0000d060:·2c20·7472·6961·6e67·756c·6174·696f·6e20··,·triangulation· | 0000d060:·2c20·7472·6961·6e67·756c·6174·696f·6e20··,·triangulation· | ||
| 0000d070:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d070:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d080:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d090:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d0a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d0a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d0b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d0b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d0c0:·2d7c·0a7c·2020·2020·207b·7b30·2c20·312c··-|.|·····{{0,·1, | 0000d0c0:·2d7c·0a7c·2020·2020·207b·7b30·2c20·312c··-|.|·····{{0,·1, | ||
| 0000d0d0:·2032·2c20·3 | 0000d0d0:·2032·2c20·367d·2c20·7b30·2c20·312c·2034···2,·6},·{0,·1,·4 | ||
| 0000d0e0:·2c20·3 | 0000d0e0:·2c20·367d·2c20·7b31·2c20·322c·2033·2c20··,·6},·{1,·2,·3,· | ||
| 0000d0f0:·377d·2c20·7b3 | 0000d0f0:·377d·2c20·7b31·2c20·322c·2036·2c20·377d··7},·{1,·2,·6,·7} | ||
| 0000d100:·2c20·7b31·2c20·3 | 0000d100:·2c20·7b31·2c20·342c·2035·2c20·377d·2c20··,·{1,·4,·5,·7},· | ||
| 0000d110:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d110:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d120:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d120:·2d2d·2d2d·2d2d·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:·2d7c·0a7c·2020·2020·207b·312c·2034·2c20··-|.|·····{1,·4,· | 0000d160:·2d7c·0a7c·2020·2020·207b·312c·2034·2c20··-|.|·····{1,·4,· | ||
| 0000d170:·3 | 0000d170:·362c·2037·7d7d·2c20·7472·6961·6e67·756c··6,·7}},·triangul | ||
| 0000d180:·6174·696f·6e20·7b7b·302c·2031·2c20·3 | 0000d180:·6174·696f·6e20·7b7b·302c·2031·2c20·322c··ation·{{0,·1,·2, | ||
| 0000d190:·203 | 0000d190:·2034·7d2c·207b·312c·2032·2c20·332c·2034···4},·{1,·2,·3,·4 | ||
| 0000d1a0:·7d2c·207b·3 | 0000d1a0:·7d2c·207b·312c·2033·2c20·342c·2037·7d2c··},·{1,·3,·4,·7}, | ||
| 0000d1b0:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d1b0:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d1c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d1c0:·2d2d·2d2d·2d2d·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:·2d7c·0a7c·2020·2020·207b·3 | 0000d200:·2d7c·0a7c·2020·2020·207b·312c·2034·2c20··-|.|·····{1,·4,· | ||
| 0000d210:·3 | 0000d210:·352c·2037·7d2c·207b·322c·2033·2c20·342c··5,·7},·{2,·3,·4, | ||
| 0000d220:·203 | 0000d220:·2036·7d2c·207b·332c·2034·2c20·362c·2037···6},·{3,·4,·6,·7 | ||
| 0000d230:·7d7d·2c20·7472·6961·6e67·756c·6174·696f··}},·triangulatio | 0000d230:·7d7d·2c20·7472·6961·6e67·756c·6174·696f··}},·triangulatio | ||
| 0000d240:·6e20·7b7b·302c·2031·2c20·322c·203 | 0000d240:·6e20·7b7b·302c·2031·2c20·322c·2034·7d2c··n·{{0,·1,·2,·4}, | ||
| 0000d250:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d250:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d260:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d270:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d280:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d290:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d2a0:·2d7c·0a7c·2020·2020·207b·3 | 0000d2a0:·2d7c·0a7c·2020·2020·207b·312c·2032·2c20··-|.|·····{1,·2,· | ||
| 0000d2b0:·3 | 0000d2b0:·332c·2034·7d2c·207b·312c·2033·2c20·342c··3,·4},·{1,·3,·4, | ||
| 0000d2c0:·203 | 0000d2c0:·2035·7d2c·207b·322c·2033·2c20·342c·2036···5},·{2,·3,·4,·6 | ||
| 0000d2d0:·7d2c·207b·3 | 0000d2d0:·7d2c·207b·332c·2034·2c20·352c·2037·7d2c··},·{3,·4,·5,·7}, | ||
| 0000d2e0:·207b·3 | 0000d2e0:·207b·332c·2034·2c20·362c·2037·7d7d·2c20···{3,·4,·6,·7}},· | ||
| 0000d2f0:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d2f0:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d300:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d310:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d320:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d330:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d330:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d340:·2d7c·0a7c·2020·2020·2074·7269·616e·6775··-|.|·····triangu | 0000d340:·2d7c·0a7c·2020·2020·2074·7269·616e·6775··-|.|·····triangu | ||
| 0000d350:·6c61·7469·6f6e·207b·7b30·2c20·312c·2033··lation·{{0,·1,·3 | 0000d350:·6c61·7469·6f6e·207b·7b30·2c20·312c·2033··lation·{{0,·1,·3 | ||
| 0000d360:·2c20·3 | 0000d360:·2c20·347d·2c20·7b30·2c20·322c·2033·2c20··,·4},·{0,·2,·3,· | ||
| 0000d370:·3 | 0000d370:·347d·2c20·7b31·2c20·332c·2034·2c20·357d··4},·{1,·3,·4,·5} | ||
| 0000d380:·2c20·7b3 | 0000d380:·2c20·7b32·2c20·332c·2034·2c20·367d·2c20··,·{2,·3,·4,·6},· | ||
| 0000d390:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d390:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d3a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d3b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d3c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d3d0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d3e0:·2d7c·0a7c·2020·2020·207b·3 | 0000d3e0:·2d7c·0a7c·2020·2020·207b·332c·2034·2c20··-|.|·····{3,·4,· | ||
| 0000d3f0:·352c·203 | 0000d3f0:·352c·2036·7d2c·207b·332c·2035·2c20·362c··5,·6},·{3,·5,·6, | ||
| 0000d400:·2037·7d7d·2c20·7472·6961·6e67·756c·6174···7}},·triangulat | 0000d400:·2037·7d7d·2c20·7472·6961·6e67·756c·6174···7}},·triangulat | ||
| 0000d410:·696f·6e20·7b7b·302c·2031·2c20·3 | 0000d410:·696f·6e20·7b7b·302c·2031·2c20·322c·2034··ion·{{0,·1,·2,·4 | ||
| 0000d420:·7d2c·207b·3 | 0000d420:·7d2c·207b·312c·2032·2c20·332c·2036·7d2c··},·{1,·2,·3,·6}, | ||
| 0000d430:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | 0000d430:·207c·0a7c·2020·2020·202d·2d2d·2d2d·2d2d···|.|·····------- | ||
| 0000d440:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d440:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d450:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d460:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 0000d470:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 0000d480:·2d7c·0a7c·2020·2020·207b·3 | 0000d480:·2d7c·0a7c·2020·2020·207b·312c·2032·2c20··-|.|·····{1,·2,· | ||
| 0000d490:·342c·203 | 0000d490:·342c·2036·7d2c·207b·312c·2033·2c20·362c··4,·6},·{1,·3,·6, | ||
| Max diff block lines reached; 441515/452694 bytes (97.53%) of diff not shown. | |||
| Offset 5259, 2765 lines modified | Offset 5259, 2766 lines modified | ||
| 000148a0:·6574·7469·6e67·2053·6d61·7274·4c69·6674··etting·SmartLift | 000148a0:·6574·7469·6e67·2053·6d61·7274·4c69·6674··etting·SmartLift | ||
| 000148b0:·3d3e·7472·7565·2077·6520·6765·7420·7665··=>true·we·get·ve | 000148b0:·3d3e·7472·7565·2077·6520·6765·7420·7665··=>true·we·get·ve | ||
| 000148c0:·7279·206e·6963·6520·6571·7561·7469·6f6e··ry·nice·equation | 000148c0:·7279·206e·6963·6520·6571·7561·7469·6f6e··ry·nice·equation | ||
| 000148d0:·7320·666f·7220·7468·650a·6261·7365·2073··s·for·the.base·s | 000148d0:·7320·666f·7220·7468·650a·6261·7365·2073··s·for·the.base·s | ||
| 000148e0:·7061·6365·3a0a·0a2b·2d2d·2d2d·2d2d·2d2d··pace:..+-------- | 000148e0:·7061·6365·3a0a·0a2b·2d2d·2d2d·2d2d·2d2d··pace:..+-------- | ||
| 000148f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000148f0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014900:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014900:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2b0a | 00014910:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c··-------------+.| | ||
| 00014920:·3320·3a20·7469·6d65·2028·462c·522c·472c··3·:·time·(F,R,G, | |||
| 000149 | 00014920:·6933·203a·2074·696d·6520·2846·2c52·2c47··i3·:·time·(F,R,G | ||
| 00014930:·2c43·293d·6c6f·6361·6c48·696c·6265·7274··,C)=localHilbert | |||
| 00014940:·6368 | 00014940:·5363·6865·6d65·2846·3029·3b20·2020·2020··Scheme(F0);····· | ||
| 00014950:·2020·207c·0a7c·202d·2d20·7573·6564· | 00014950:·2020·2020·207c·0a7c·202d·2d20·7573·6564·······|.|·--·used | ||
| 00014960:·2e39·3838·3339·7320·2863·7075·293b·2030··.98839s·(cpu);·0 | |||
| 00014970:·2e37·3333·3339·3773·2028·7468·7265·6164··.733397s·(thread | |||
| 000149 | 00014960:·2030·2e38·3338·3936·3273·2028·6370·7529···0.838962s·(cpu) | ||
| 00014970:·3b20·302e·3634·3031·3533·7320·2874·6872··;·0.640153s·(thr | |||
| 00014980:·6561·6429·3b20·3073·2028·6763·297c·0a2b··ead);·0s·(gc)|.+ | |||
| 00014990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014990:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000149a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000149a0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000149b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000149b0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000149c0:·2d2b·0a7c·6934·203a·2054·3d72· | 000149c0:·2d2d·2d2d·2d2b·0a7c·6934·203a·2054·3d72··-----+.|i4·:·T=r | ||
| 000149d0:·6669·7273·7420·473b·2020·2020· | 000149d0:·696e·6720·6669·7273·7420·473b·2020·2020··ing·first·G;···· | ||
| 000149e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000149e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000149f0:·2020·2020·2020·2020· | 000149f0:·2020·2020·2020·2020·2020·2020·207c·0a2b···············|.+ | ||
| 00014a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014a00:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014a10:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2 | 00014a20:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014a30:·0a7c·6935·203a·2073·756d | 00014a30:·2d2d·2d2d·2d2b·0a7c·6935·203a·2073·756d··-----+.|i5·:·sum | ||
| 00014a40:·20 | 00014a40:·2047·2020·2020·2020·2020·2020·2020·2020···G·············· | ||
| 00014a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014a50:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014a60:·2020·2020·2020· | 00014a60:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00014a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014a70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00014a80:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014a90:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00014aa0:·6f35·203d·207c·2074·5f31·745f·3136·2020··o5·=·|·t_1t_16·· | |||
| 00014ab0:·2020·2020·2020·2020·2020·207c·2020·2020·············|···· | |||
| 00014a | 00014a90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014a | 00014aa0:·2020·2020·207c·0a7c·6f35·203d·207c·2074·······|.|o5·=·|·t | ||
| 00014a | 00014ab0:·5f31·745f·3136·2020·2020·2020·2020·2020··_1t_16·········· | ||
| 00014a | 00014ac0:·2020·207c·2020·2020·2020·2020·2020·2020·····|············ | ||
| 00014ad0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | |||
| 00014ae0:·2020·2020·207c·2074·5f39·745f·3136·2020·······|·t_9t_16·· | |||
| 00014 | 00014af0:·2020·2020·2020·2020·2020·207c·2020·2020·············|···· | ||
| 00014b10:·2020·207c·202d·745f·3474·5f31·3620·2020·····|·-t_4t_16··· | |||
| 00014b20:·2020·2020·2020·2020·207c·2020·2020·2020···········|······ | |||
| 00014b | 00014b00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b40:·2020·7c0a·7c20·2020·2020·7c20·2d32·745f····|.|·····|·-2t_ | |||
| 00014b | 00014b10:·2020·2020·207c·0a7c·2020·2020·207c·202d·······|.|·····|·- | ||
| 00014b20:·745f·3474·5f31·3620·2020·2020·2020·2020··t_4t_16········· | |||
| 00014b | 00014b30:·2020·207c·2020·2020·2020·2020·2020·2020·····|············ | ||
| 00014b | 00014b40:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00014b50:·2020·2020·207c·202d·3274·5f31·3474·5f31·······|·-2t_14t_1 | |||
| 00014b60:·362b·745f·3135·745f·3136·207c·2020·2020··6+t_15t_16·|···· | |||
| 00014b | 00014b70:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b80:·2020·2020·207c·0a7c·2020·2020·2020·2020·······|.|········ | |||
| 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:· | 00014bb0:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00014bc0:·2020·2020·2020·2020·2020·2020·2034·2020···············4·· | |||
| 00014b | 00014bd0:·2020·2020·3120·2020·2020·2020·2020·2020······1··········· | ||
| 00014b | 00014be0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014b | 00014bf0:·2020·2020·207c·0a7c·6f35·203a·204d·6174·······|.|o5·:·Mat | ||
| 00014 | 00014c00:·7269·7820·5420·203c·2d2d·2054·2020·2020··rix·T··<--·T···· | ||
| 00014c | 00014c10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00014c | 00014c20:·2020·2020·2020·2020·2020·2020·207c·0a2b···············|.+ | ||
| 00014c20:·2b2d·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··---------------- | ||
| 00014c40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00014c40:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014c50:·2d2d·2d2d·2d2b·0a0a·5769·7468·2074·6865··-----+..With·the | |||
| 00014c60:·2073·6574·7469·6e67·2053·6d61·7274·4c69···setting·SmartLi | |||
| 00014c70:·6674·3d3e·6661·6c73·6520·7468·6520·6361··ft=>false·the·ca | |||
| 00014c80:·6c63·756c·6174·696f·6e20·6973·2066·6173··lculation·is·fas | |||
| 00014c90:·7465·722c·2062·7574·2074·6865·2065·7175··ter,·but·the·equ | |||
| 00014ca0:·6174·696f·6e73·0a61·7265·206e·6f20·6c6f··ations.are·no·lo | |||
| 00014cb0:·6e67·6572·2068·6f6d·6f67·656e·656f·7573··nger·homogeneous | |||
| 00014cc0:·3a0a·0a2b·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··:..+------------ | |||
| 00014c | 00014c50:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 00014c60:·2d2d·2d2d·2d2b·0a0a·5769·7468·2074·6865··-----+..With·the | |||
| 00014c70:·2073·6574·7469·6e67·2053·6d61·7274·4c69···setting·SmartLi | |||
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| 00025ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·7b7b··-----------|.|{{ | 00025ef0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d7c·0a7c·7b7b··-----------|.|{{ | ||
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| 000262c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000262c0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00004c60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00004c60:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00004c90:·7928·462c·5868·2c69·6465·616c·2830·5f53··y(F,Xh,ideal(0_S | 00004c90:·7928·462c·5868·2c69·6465·616c·2830·5f53··y(F,Xh,ideal(0_S | ||
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| 00004d00:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | 00004d00:·2020·2020·2020·2020·207c·0a7c·2020·2020···········|.|···· | ||
| 00004d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00004d10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 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·················· | ||
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| 00005020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 00005020:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
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| 00005050:·6966·7928·462c·5868·2c69·6465·616c·2830··ify(F,Xh,ideal(0 | 00005050:·6966·7928·462c·5868·2c69·6465·616c·2830··ify(F,Xh,ideal(0 | ||
| 00005060:·5f53·292c·5374·7261·7473·546f·4669·6e64··_S),StratsToFind | 00005060:·5f53·292c·5374·7261·7473·546f·4669·6e64··_S),StratsToFind | ||
| 00005070:·3d3e·226d·6f73·7422·2920·2020·2020·2020··=>"most")······· | 00005070:·3d3e·226d·6f73·7422·2920·2020·2020·2020··=>"most")······· | ||
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| 000050c0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | 000050c0:·2020·2020·2020·2020·2020·207c·0a7c·2020·············|.|·· | ||
| 000050d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000050d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000050e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000050e0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000050f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000050f0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005100:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 00005110:·2020·2020·207c·0a7c·6f32·3520·3d20·7b4d·······|.|o25·=·{M | 00005110:·2020·2020·207c·0a7c·6f32·3520·3d20·7b4d·······|.|o25·=·{M | ||
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| 000053e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | 000053e0:·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d·2d2d··---------------- | ||
| 000053f0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3720··---------+.|i27· | 000053f0:·2d2d·2d2d·2d2d·2d2d·2d2b·0a7c·6932·3720··---------+.|i27· | ||
| 00005400:·3a20·7469·6d65·206d·733d·6d61·7053·7472··:·time·ms=mapStr | 00005400:·3a20·7469·6d65·206d·733d·6d61·7053·7472··:·time·ms=mapStr | ||
| 00005410:·6174·6966·7928·462c·5868·2c69·6465·616c··atify(F,Xh,ideal | 00005410:·6174·6966·7928·462c·5868·2c69·6465·616c··atify(F,Xh,ideal | ||
| 00005420:·2830·5f53·292c·5374·7261·7473·546f·4669··(0_S),StratsToFi | 00005420:·2830·5f53·292c·5374·7261·7473·546f·4669··(0_S),StratsToFi | ||
| 00005430:·6e64·3d3e·2261·6c6c·2229·2020·2020·2020··nd=>"all")······ | 00005430:·6e64·3d3e·2261·6c6c·2229·2020·2020·2020··nd=>"all")······ | ||
| 00005440:·2020·207c·0a7c·202d·2d20·7573·6564·203 | 00005440:·2020·207c·0a7c·202d·2d20·7573·6564·2034·····|.|·--·used·4 | ||
| 00005450:·2e3 | 00005450:·2e33·3636·3435·7320·2863·7075·293b·2032··.36645s·(cpu);·2 | ||
| 00005460:·2e3 | 00005460:·2e37·3730·3973·2028·7468·7265·6164·293b··.7709s·(thread); | ||
| 00005470:· | 00005470:·2030·7320·2867·6329·2020·2020·2020·2020···0s·(gc)········ | ||
| 00005480:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | 00005480:·2020·2020·2020·2020·2020·2020·207c·0a7c···············|.| | ||
| 00005490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 00005490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000054a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000054b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054b0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000054c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 000054c0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 000054d0:·2020·2020·2020·207c·0a7c·6f32·3720·3d20·········|.|o27·=· | 000054d0:·2020·2020·2020·207c·0a7c·6f32·3720·3d20·········|.|o27·=· | ||
| 000054e0:·7b4d·7574·6162·6c65·4861·7368·5461·626c··{MutableHashTabl | 000054e0:·7b4d·7574·6162·6c65·4861·7368·5461·626c··{MutableHashTabl |
| Offset 11481, 21 lines modified | Offset 11481, 21 lines modified | ||
| 0002cd80:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20··--------+.|i5·:· | 0002cd80:·2d2d·2d2d·2d2d·2d2d·2b0a·7c69·3520·3a20··--------+.|i5·:· | ||
| 0002cd90:·6c6f·6164·5061·636b·6167·6528·2267·6661··loadPackage("gfa | 0002cd90:·6c6f·6164·5061·636b·6167·6528·2267·6661··loadPackage("gfa | ||
| 0002cda0:·6e49·6e74·6572·6661·6365·222c·2043·6f6e··nInterface",·Con | 0002cda0:·6e49·6e74·6572·6661·6365·222c·2043·6f6e··nInterface",·Con | ||
| 0002cdb0:·6669·6775·7261·7469·6f6e·203d·3e20·7b20··figuration·=>·{· | 0002cdb0:·6669·6775·7261·7469·6f6e·203d·3e20·7b20··figuration·=>·{· | ||
| 0002cdc0:·226b·6565·7066·696c·6573·2220·3d3e·2074··"keepfiles"·=>·t | 0002cdc0:·226b·6565·7066·696c·6573·2220·3d3e·2074··"keepfiles"·=>·t | ||
| 0002cdd0:·7275·652c·2022·7665·7c0a·7c75·7369·6e67··rue,·"ve|.|using | 0002cdd0:·7275·652c·2022·7665·7c0a·7c75·7369·6e67··rue,·"ve|.|using | ||
| 0002cde0:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | 0002cde0:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | ||
| 0002cdf0:·2f74·6d70·2f4d·322d·3 | 0002cdf0:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002ce00:·302f·3137·3220·2020·2020·2020·2020·2020··0/172··········· | 0002ce00:·302f·3137·3220·2020·2020·2020·2020·2020··0/172··········· | ||
| 0002ce10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002ce10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002ce20:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | 0002ce20:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | ||
| 0002ce30:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | 0002ce30:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | ||
| 0002ce40:·6e20·6766·616e·202d·2d68·656c·7020·3c20··n·gfan·--help·<· | 0002ce40:·6e20·6766·616e·202d·2d68·656c·7020·3c20··n·gfan·--help·<· | ||
| 0002ce50:·2f74·6d70·2f4d·322d·3 | 0002ce50:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002ce60:·302f·3137·3220·2020·2020·2020·2020·2020··0/172··········· | 0002ce60:·302f·3137·3220·2020·2020·2020·2020·2020··0/172··········· | ||
| 0002ce70:·2020·2020·2020·2020·7c0a·7c54·6869·7320··········|.|This· | 0002ce70:·2020·2020·2020·2020·7c0a·7c54·6869·7320··········|.|This· | ||
| 0002ce80:·6973·2061·2070·726f·6772·616d·2066·6f72··is·a·program·for | 0002ce80:·6973·2061·2070·726f·6772·616d·2066·6f72··is·a·program·for | ||
| 0002ce90:·2063·6f6d·7075·7469·6e67·2061·6c6c·2072···computing·all·r | 0002ce90:·2063·6f6d·7075·7469·6e67·2061·6c6c·2072···computing·all·r | ||
| 0002cea0:·6564·7563·6564·2047·726f·6562·6e65·7220··educed·Groebner· | 0002cea0:·6564·7563·6564·2047·726f·6562·6e65·7220··educed·Groebner· | ||
| 0002ceb0:·6261·7365·7320·6f66·2061·2070·6f6c·796e··bases·of·a·polyn | 0002ceb0:·6261·7365·7320·6f66·2061·2070·6f6c·796e··bases·of·a·polyn | ||
| 0002cec0:·6f6d·6961·6c20·6964·7c0a·7c4f·7074·696f··omial·id|.|Optio | 0002cec0:·6f6d·6961·6c20·6964·7c0a·7c4f·7074·696f··omial·id|.|Optio | ||
| Offset 11586, 22 lines modified | Offset 11586, 22 lines modified | ||
| 0002d410:·656e·2063·6f6d·7075·7c0a·7c20·2020·2020··en·compu|.|····· | 0002d410:·656e·2063·6f6d·7075·7c0a·7c20·2020·2020··en·compu|.|····· | ||
| 0002d420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002d420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002d430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002d430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002d440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002d440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002d450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002d450:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002d460:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | 0002d460:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | ||
| 0002d470:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | 0002d470:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | ||
| 0002d480:·2f74·6d70·2f4d·322d·3 | 0002d480:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002d490:·302f·3137·3420·2020·2020·2020·2020·2020··0/174··········· | 0002d490:·302f·3137·3420·2020·2020·2020·2020·2020··0/174··········· | ||
| 0002d4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002d4a0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002d4b0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | 0002d4b0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | ||
| 0002d4c0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | 0002d4c0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | ||
| 0002d4d0:·6e20·5f62·7563·6862·6572·6765·7220·2d2d··n·_buchberger·-- | 0002d4d0:·6e20·5f62·7563·6862·6572·6765·7220·2d2d··n·_buchberger·-- | ||
| 0002d4e0:·6865·6c70·203c·202f·746d·702f·4d32·2d3 | 0002d4e0:·6865·6c70·203c·202f·746d·702f·4d32·2d32··help·<·/tmp/M2-2 | ||
| 0002d4f0:·3 | 0002d4f0:·3139·3732·3531·2d30·2f31·3734·2020·2020··197251-0/174···· | ||
| 0002d500:·2020·2020·2020·2020·7c0a·7c54·6869·7320··········|.|This· | 0002d500:·2020·2020·2020·2020·7c0a·7c54·6869·7320··········|.|This· | ||
| 0002d510:·7072·6f67·7261·6d20·636f·6d70·7574·6573··program·computes | 0002d510:·7072·6f67·7261·6d20·636f·6d70·7574·6573··program·computes | ||
| 0002d520:·2061·2072·6564·7563·6564·206c·6578·6963···a·reduced·lexic | 0002d520:·2061·2072·6564·7563·6564·206c·6578·6963···a·reduced·lexic | ||
| 0002d530:·6f67·7261·7068·6963·2047·726f·6562·6e65··ographic·Groebne | 0002d530:·6f67·7261·7068·6963·2047·726f·6562·6e65··ographic·Groebne | ||
| 0002d540:·7220·6261·7369·7320·6f66·2074·6865·2070··r·basis·of·the·p | 0002d540:·7220·6261·7369·7320·6f66·2074·6865·2070··r·basis·of·the·p | ||
| 0002d550:·6f6c·796e·6f6d·6961·7c0a·7c4f·7074·696f··olynomia|.|Optio | 0002d550:·6f6c·796e·6f6d·6961·7c0a·7c4f·7074·696f··olynomia|.|Optio | ||
| 0002d560:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | 0002d560:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | ||
| Offset 11681, 22 lines modified | Offset 11681, 22 lines modified | ||
| 0002da00:·6d65·7465·7273·2069·7c0a·7c20·2020·2020··meters·i|.|····· | 0002da00:·6d65·7465·7273·2069·7c0a·7c20·2020·2020··meters·i|.|····· | ||
| 0002da10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002da10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002da20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002da20:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002da30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002da30:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002da40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002da40:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002da50:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | 0002da50:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | ||
| 0002da60:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | 0002da60:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | ||
| 0002da70:·2f74·6d70·2f4d·322d·3 | 0002da70:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002da80:·302f·3137·3620·2020·2020·2020·2020·2020··0/176··········· | 0002da80:·302f·3137·3620·2020·2020·2020·2020·2020··0/176··········· | ||
| 0002da90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002da90:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002daa0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | 0002daa0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | ||
| 0002dab0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | 0002dab0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | ||
| 0002dac0:·6e20·5f64·6f65·7369·6465·616c·636f·6e74··n·_doesidealcont | 0002dac0:·6e20·5f64·6f65·7369·6465·616c·636f·6e74··n·_doesidealcont | ||
| 0002dad0:·6169·6e20·2d2d·6865·6c70·203c·202f·746d··ain·--help·<·/tm | 0002dad0:·6169·6e20·2d2d·6865·6c70·203c·202f·746d··ain·--help·<·/tm | ||
| 0002dae0:·702f·4d32·2d3 | 0002dae0:·702f·4d32·2d32·3139·3732·3531·2d30·2f31··p/M2-2197251-0/1 | ||
| 0002daf0:·3736·2020·2020·2020·7c0a·7c54·6869·7320··76······|.|This· | 0002daf0:·3736·2020·2020·2020·7c0a·7c54·6869·7320··76······|.|This· | ||
| 0002db00:·7072·6f67·7261·6d20·7461·6b65·7320·6120··program·takes·a· | 0002db00:·7072·6f67·7261·6d20·7461·6b65·7320·6120··program·takes·a· | ||
| 0002db10:·6d61·726b·6564·2047·726f·6562·6e65·7220··marked·Groebner· | 0002db10:·6d61·726b·6564·2047·726f·6562·6e65·7220··marked·Groebner· | ||
| 0002db20:·6261·7369·7320·6f66·2061·6e20·6964·6561··basis·of·an·idea | 0002db20:·6261·7369·7320·6f66·2061·6e20·6964·6561··basis·of·an·idea | ||
| 0002db30:·6c20·4920·616e·6420·6120·7365·7420·6f66··l·I·and·a·set·of | 0002db30:·6c20·4920·616e·6420·6120·7365·7420·6f66··l·I·and·a·set·of | ||
| 0002db40:·2070·6f6c·796e·6f6d·7c0a·7c4f·7074·696f···polynom|.|Optio | 0002db40:·2070·6f6c·796e·6f6d·7c0a·7c4f·7074·696f···polynom|.|Optio | ||
| 0002db50:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | 0002db50:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | ||
| Offset 11726, 22 lines modified | Offset 11726, 22 lines modified | ||
| 0002dcd0:·6520·6469·7669·6465·7c0a·7c20·2020·2020··e·divide|.|····· | 0002dcd0:·6520·6469·7669·6465·7c0a·7c20·2020·2020··e·divide|.|····· | ||
| 0002dce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002dce0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002dcf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002dcf0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002dd00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002dd00:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002dd10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002dd10:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002dd20:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | 0002dd20:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | ||
| 0002dd30:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | 0002dd30:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | ||
| 0002dd40:·2f74·6d70·2f4d·322d·3 | 0002dd40:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002dd50:·302f·3137·3820·2020·2020·2020·2020·2020··0/178··········· | 0002dd50:·302f·3137·3820·2020·2020·2020·2020·2020··0/178··········· | ||
| 0002dd60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002dd60:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002dd70:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | 0002dd70:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | ||
| 0002dd80:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | 0002dd80:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | ||
| 0002dd90:·6e20·5f66·616e·636f·6d6d·6f6e·7265·6669··n·_fancommonrefi | 0002dd90:·6e20·5f66·616e·636f·6d6d·6f6e·7265·6669··n·_fancommonrefi | ||
| 0002dda0:·6e65·6d65·6e74·202d·2d68·656c·7020·3c20··nement·--help·<· | 0002dda0:·6e65·6d65·6e74·202d·2d68·656c·7020·3c20··nement·--help·<· | ||
| 0002ddb0:·2f74·6d70·2f4d·322d·3 | 0002ddb0:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002ddc0:·302f·3137·3820·2020·7c0a·7c54·6869·7320··0/178···|.|This· | 0002ddc0:·302f·3137·3820·2020·7c0a·7c54·6869·7320··0/178···|.|This· | ||
| 0002ddd0:·7072·6f67·7261·6d20·7461·6b65·7320·7477··program·takes·tw | 0002ddd0:·7072·6f67·7261·6d20·7461·6b65·7320·7477··program·takes·tw | ||
| 0002dde0:·6f20·706f·6c79·6865·6472·616c·2066·616e··o·polyhedral·fan | 0002dde0:·6f20·706f·6c79·6865·6472·616c·2066·616e··o·polyhedral·fan | ||
| 0002ddf0:·7320·616e·6420·636f·6d70·7574·6573·2074··s·and·computes·t | 0002ddf0:·7320·616e·6420·636f·6d70·7574·6573·2074··s·and·computes·t | ||
| 0002de00:·6865·6972·2063·6f6d·6d6f·6e20·7265·6669··heir·common·refi | 0002de00:·6865·6972·2063·6f6d·6d6f·6e20·7265·6669··heir·common·refi | ||
| 0002de10:·6e65·6d65·6e74·2e20·7c0a·7c4f·7074·696f··nement.·|.|Optio | 0002de10:·6e65·6d65·6e74·2e20·7c0a·7c4f·7074·696f··nement.·|.|Optio | ||
| 0002de20:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | 0002de20:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | ||
| Offset 11781, 22 lines modified | Offset 11781, 22 lines modified | ||
| 0002e040:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | 0002e040:·2020·2020·2020·2020·7c0a·7c20·2020·2020··········|.|····· | ||
| 0002e050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e050:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e060:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e070:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e080:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e090:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | 0002e090:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | ||
| 0002e0a0:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | 0002e0a0:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | ||
| 0002e0b0:·2f74·6d70·2f4d·322d·3 | 0002e0b0:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002e0c0:·302f·3138·3020·2020·2020·2020·2020·2020··0/180··········· | 0002e0c0:·302f·3138·3020·2020·2020·2020·2020·2020··0/180··········· | ||
| 0002e0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e0d0:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e0e0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | 0002e0e0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | ||
| 0002e0f0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | 0002e0f0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | ||
| 0002e100:·6e20·5f66·616e·6c69·6e6b·202d·2d68·656c··n·_fanlink·--hel | 0002e100:·6e20·5f66·616e·6c69·6e6b·202d·2d68·656c··n·_fanlink·--hel | ||
| 0002e110:·7020·3c20·2f74·6d70·2f4d·322d·3 | 0002e110:·7020·3c20·2f74·6d70·2f4d·322d·3231·3937··p·<·/tmp/M2-2197 | ||
| 0002e120:·3 | 0002e120:·3235·312d·302f·3138·3020·2020·2020·2020··251-0/180······· | ||
| 0002e130:·2020·2020·2020·2020·7c0a·7c54·6869·7320··········|.|This· | 0002e130:·2020·2020·2020·2020·7c0a·7c54·6869·7320··········|.|This· | ||
| 0002e140:·7072·6f67·7261·6d20·7461·6b65·7320·6120··program·takes·a· | 0002e140:·7072·6f67·7261·6d20·7461·6b65·7320·6120··program·takes·a· | ||
| 0002e150:·706f·6c79·6865·6472·616c·2066·616e·2061··polyhedral·fan·a | 0002e150:·706f·6c79·6865·6472·616c·2066·616e·2061··polyhedral·fan·a | ||
| 0002e160:·6e64·2061·2076·6563·746f·7220·616e·6420··nd·a·vector·and· | 0002e160:·6e64·2061·2076·6563·746f·7220·616e·6420··nd·a·vector·and· | ||
| 0002e170:·636f·6d70·7574·6573·2074·6865·206c·696e··computes·the·lin | 0002e170:·636f·6d70·7574·6573·2074·6865·206c·696e··computes·the·lin | ||
| 0002e180:·6b20·6f66·2074·6865·7c0a·7c4f·7074·696f··k·of·the|.|Optio | 0002e180:·6b20·6f66·2074·6865·7c0a·7c4f·7074·696f··k·of·the|.|Optio | ||
| 0002e190:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | 0002e190:·6e73·3a20·2020·2020·2020·2020·2020·2020··ns:············· | ||
| Offset 11841, 22 lines modified | Offset 11841, 22 lines modified | ||
| 0002e400:·6564·7261·6c20·6661·7c0a·7c20·2020·2020··edral·fa|.|····· | 0002e400:·6564·7261·6c20·6661·7c0a·7c20·2020·2020··edral·fa|.|····· | ||
| 0002e410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e410:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e420:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e430:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e440:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e450:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | 0002e450:·2020·2020·2020·2020·7c0a·7c75·7369·6e67··········|.|using | ||
| 0002e460:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | 0002e460:·2074·656d·706f·7261·7279·2066·696c·6520···temporary·file· | ||
| 0002e470:·2f74·6d70·2f4d·322d·3 | 0002e470:·2f74·6d70·2f4d·322d·3231·3937·3235·312d··/tmp/M2-2197251- | ||
| 0002e480:·302f·3138·3220·2020·2020·2020·2020·2020··0/182··········· | 0002e480:·302f·3138·3220·2020·2020·2020·2020·2020··0/182··········· | ||
| 0002e490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | 0002e490:·2020·2020·2020·2020·2020·2020·2020·2020·················· | ||
| 0002e4a0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | 0002e4a0:·2020·2020·2020·2020·7c0a·7c72·756e·6e69··········|.|runni | ||
| 0002e4b0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | 0002e4b0:·6e67·3a20·2f75·7372·2f62·696e·2f67·6661··ng:·/usr/bin/gfa | ||
| 0002e4c0:·6e20·5f66·616e·7072·6f64·7563·7420·2d2d··n·_fanproduct·-- | 0002e4c0:·6e20·5f66·616e·7072·6f64·7563·7420·2d2d··n·_fanproduct·-- | ||
| Max diff block lines reached; 64442/74258 bytes (86.78%) of diff not shown. | |||
| Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
| 1 | -rw-r--r--···0········0········0········4·2024-09-09·00:38:13.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2024-09-09·00:38:13.000000·debian-binary |
| 2 | -rw-r--r--···0········0········0·····2092·2024-09-09·00:38:13.000000·control.tar.xz | 2 | -rw-r--r--···0········0········0·····2092·2024-09-09·00:38:13.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0··2564 | 3 | -rw-r--r--···0········0········0··2564736·2024-09-09·00:38:13.000000·data.tar.xz |
| Offset 3496, 42 lines modified | Offset 3496, 42 lines modified | ||
| 3496 | 000000000083e818··0000000000000008·R_X86_64_RELATIVE·························84c340 | 3496 | 000000000083e818··0000000000000008·R_X86_64_RELATIVE·························84c340 |
| 3497 | 000000000083e820··0000000000000008·R_X86_64_RELATIVE·························84c430 | 3497 | 000000000083e820··0000000000000008·R_X86_64_RELATIVE·························84c430 |
| 3498 | 000000000083e828··0000000000000008·R_X86_64_RELATIVE·························84c2c8 | 3498 | 000000000083e828··0000000000000008·R_X86_64_RELATIVE·························84c2c8 |
| 3499 | 000000000083e830··0000000000000008·R_X86_64_RELATIVE·························6f31a0 | 3499 | 000000000083e830··0000000000000008·R_X86_64_RELATIVE·························6f31a0 |
| 3500 | 000000000083e838··0000000000000008·R_X86_64_RELATIVE·························5508d0 | 3500 | 000000000083e838··0000000000000008·R_X86_64_RELATIVE·························5508d0 |
| 3501 | 000000000083e840··0000000000000008·R_X86_64_RELATIVE·························5508f0 | 3501 | 000000000083e840··0000000000000008·R_X86_64_RELATIVE·························5508f0 |
| 3502 | 000000000083e848··0000000000000008·R_X86_64_RELATIVE·························5533a0 | 3502 | 000000000083e848··0000000000000008·R_X86_64_RELATIVE·························5533a0 |
| 3503 | 000000000083e860··0000000000000008·R_X86_64_RELATIVE·························6cc11 | 3503 | 000000000083e860··0000000000000008·R_X86_64_RELATIVE·························6cc118 |
| 3504 | 000000000083e868··0000000000000008·R_X86_64_RELATIVE·························6cc11 | 3504 | 000000000083e868··0000000000000008·R_X86_64_RELATIVE·························6cc118 |
| 3505 | 000000000083e870··0000000000000008·R_X86_64_RELATIVE·························6cc14 | 3505 | 000000000083e870··0000000000000008·R_X86_64_RELATIVE·························6cc145 |
| 3506 | 000000000083e878··0000000000000008·R_X86_64_RELATIVE·························6cc11 | 3506 | 000000000083e878··0000000000000008·R_X86_64_RELATIVE·························6cc11f |
| 3507 | 000000000083e880··0000000000000008·R_X86_64_RELATIVE·························6cc3c | 3507 | 000000000083e880··0000000000000008·R_X86_64_RELATIVE·························6cc3c5 |
| 3508 | 000000000083e888··0000000000000008·R_X86_64_RELATIVE·························6cc3c | 3508 | 000000000083e888··0000000000000008·R_X86_64_RELATIVE·························6cc3c8 |
| 3509 | 000000000083e890··0000000000000008·R_X86_64_RELATIVE·························6cc3c | 3509 | 000000000083e890··0000000000000008·R_X86_64_RELATIVE·························6cc3cc |
| 3510 | 000000000083e898··0000000000000008·R_X86_64_RELATIVE·························6cc3 | 3510 | 000000000083e898··0000000000000008·R_X86_64_RELATIVE·························6cc3d0 |
| 3511 | 000000000083e8a0··0000000000000008·R_X86_64_RELATIVE·························6cc3d | 3511 | 000000000083e8a0··0000000000000008·R_X86_64_RELATIVE·························6cc3d5 |
| 3512 | 000000000083e8a8··0000000000000008·R_X86_64_RELATIVE·························6cc3d | 3512 | 000000000083e8a8··0000000000000008·R_X86_64_RELATIVE·························6cc3db |
| 3513 | 000000000083e8b0··0000000000000008·R_X86_64_RELATIVE·························6cc3 | 3513 | 000000000083e8b0··0000000000000008·R_X86_64_RELATIVE·························6cc3e2 |
| 3514 | 000000000083e8b8··0000000000000008·R_X86_64_RELATIVE·························6cc3e | 3514 | 000000000083e8b8··0000000000000008·R_X86_64_RELATIVE·························6cc3ea |
| 3515 | 000000000083e8c0··0000000000000008·R_X86_64_RELATIVE·························6cc3f | 3515 | 000000000083e8c0··0000000000000008·R_X86_64_RELATIVE·························6cc3f3 |
| 3516 | 000000000083e8c8··0000000000000008·R_X86_64_RELATIVE·························6cc3f | 3516 | 000000000083e8c8··0000000000000008·R_X86_64_RELATIVE·························6cc3fd |
| 3517 | 000000000083e8d0··0000000000000008·R_X86_64_RELATIVE·························6cc40 | 3517 | 000000000083e8d0··0000000000000008·R_X86_64_RELATIVE·························6cc408 |
| 3518 | 000000000083e8d8··0000000000000008·R_X86_64_RELATIVE·························6cc41 | 3518 | 000000000083e8d8··0000000000000008·R_X86_64_RELATIVE·························6cc414 |
| 3519 | 000000000083e8e0··0000000000000008·R_X86_64_RELATIVE·························6cc4 | 3519 | 000000000083e8e0··0000000000000008·R_X86_64_RELATIVE·························6cc422 |
| 3520 | 000000000083e8e8··0000000000000008·R_X86_64_RELATIVE·························6cc4 | 3520 | 000000000083e8e8··0000000000000008·R_X86_64_RELATIVE·························6cc431 |
| 3521 | 000000000083e8f0··0000000000000008·R_X86_64_RELATIVE·························6cc4 | 3521 | 000000000083e8f0··0000000000000008·R_X86_64_RELATIVE·························6cc441 |
| 3522 | 000000000083e8f8··0000000000000008·R_X86_64_RELATIVE·························6cc4 | 3522 | 000000000083e8f8··0000000000000008·R_X86_64_RELATIVE·························6cc452 |
| 3523 | 000000000083e900··0000000000000008·R_X86_64_RELATIVE·························6cc46 | 3523 | 000000000083e900··0000000000000008·R_X86_64_RELATIVE·························6cc465 |
| 3524 | 000000000083e908··0000000000000008·R_X86_64_RELATIVE·························6cc47 | 3524 | 000000000083e908··0000000000000008·R_X86_64_RELATIVE·························6cc479 |
| 3525 | 000000000083e910··0000000000000008·R_X86_64_RELATIVE·························6cc48 | 3525 | 000000000083e910··0000000000000008·R_X86_64_RELATIVE·························6cc48e |
| 3526 | 000000000083e918··0000000000000008·R_X86_64_RELATIVE·························6cc4a | 3526 | 000000000083e918··0000000000000008·R_X86_64_RELATIVE·························6cc4a5 |
| 3527 | 000000000083e920··0000000000000008·R_X86_64_RELATIVE·························6cc4b | 3527 | 000000000083e920··0000000000000008·R_X86_64_RELATIVE·························6cc4bd |
| 3528 | 000000000083e928··0000000000000008·R_X86_64_RELATIVE·························6cc4d | 3528 | 000000000083e928··0000000000000008·R_X86_64_RELATIVE·························6cc4d6 |
| 3529 | 000000000083e930··0000000000000008·R_X86_64_RELATIVE·························6cc4 | 3529 | 000000000083e930··0000000000000008·R_X86_64_RELATIVE·························6cc4f1 |
| 3530 | 000000000083e938··0000000000000008·R_X86_64_RELATIVE·························6cc50 | 3530 | 000000000083e938··0000000000000008·R_X86_64_RELATIVE·························6cc50d |
| 3531 | 000000000083e940··0000000000000008·R_X86_64_RELATIVE·························6e9db8 | 3531 | 000000000083e940··0000000000000008·R_X86_64_RELATIVE·························6e9db8 |
| 3532 | 000000000083e948··0000000000000008·R_X86_64_RELATIVE·························6e9dd8 | 3532 | 000000000083e948··0000000000000008·R_X86_64_RELATIVE·························6e9dd8 |
| 3533 | 000000000083e950··0000000000000008·R_X86_64_RELATIVE·························6e9df8 | 3533 | 000000000083e950··0000000000000008·R_X86_64_RELATIVE·························6e9df8 |
| 3534 | 000000000083e958··0000000000000008·R_X86_64_RELATIVE·························6e9e20 | 3534 | 000000000083e958··0000000000000008·R_X86_64_RELATIVE·························6e9e20 |
| 3535 | 000000000083e960··0000000000000008·R_X86_64_RELATIVE·························6e9e48 | 3535 | 000000000083e960··0000000000000008·R_X86_64_RELATIVE·························6e9e48 |
| 3536 | 000000000083e968··0000000000000008·R_X86_64_RELATIVE·························6e9e70 | 3536 | 000000000083e968··0000000000000008·R_X86_64_RELATIVE·························6e9e70 |
| 3537 | 000000000083e970··0000000000000008·R_X86_64_RELATIVE·························6e9e98 | 3537 | 000000000083e970··0000000000000008·R_X86_64_RELATIVE·························6e9e98 |
| Offset 9772, 28 lines modified | Offset 9772, 28 lines modified | ||
| 9772 | 000000000084f290··0000000000000008·R_X86_64_RELATIVE·························6c9e05 | 9772 | 000000000084f290··0000000000000008·R_X86_64_RELATIVE·························6c9e05 |
| 9773 | 000000000084f298··0000000000000008·R_X86_64_RELATIVE·························6c9298 | 9773 | 000000000084f298··0000000000000008·R_X86_64_RELATIVE·························6c9298 |
| 9774 | 000000000084f2a0··0000000000000008·R_X86_64_RELATIVE·························6cb648 | 9774 | 000000000084f2a0··0000000000000008·R_X86_64_RELATIVE·························6cb648 |
| 9775 | 000000000084f2a8··0000000000000008·R_X86_64_RELATIVE·························6cba32 | 9775 | 000000000084f2a8··0000000000000008·R_X86_64_RELATIVE·························6cba32 |
| 9776 | 000000000084f2b0··0000000000000008·R_X86_64_RELATIVE·························6cbae8 | 9776 | 000000000084f2b0··0000000000000008·R_X86_64_RELATIVE·························6cbae8 |
| 9777 | 000000000084f2b8··0000000000000008·R_X86_64_RELATIVE·························6ca5c9 | 9777 | 000000000084f2b8··0000000000000008·R_X86_64_RELATIVE·························6ca5c9 |
| 9778 | 000000000084f2c0··0000000000000008·R_X86_64_RELATIVE·························6ca513 | 9778 | 000000000084f2c0··0000000000000008·R_X86_64_RELATIVE·························6ca513 |
| 9779 | 000000000084f2c8··0000000000000008·R_X86_64_RELATIVE·························6cc22 | 9779 | 000000000084f2c8··0000000000000008·R_X86_64_RELATIVE·························6cc22c |
| 9780 | 000000000084f2d0··0000000000000008·R_X86_64_RELATIVE·························6c9d36 | 9780 | 000000000084f2d0··0000000000000008·R_X86_64_RELATIVE·························6c9d36 |
| 9781 | 000000000084f2d8··0000000000000008·R_X86_64_RELATIVE·························6c9d36 | 9781 | 000000000084f2d8··0000000000000008·R_X86_64_RELATIVE·························6c9d36 |
| 9782 | 000000000084f2e0··0000000000000008·R_X86_64_RELATIVE·························6cba3d | 9782 | 000000000084f2e0··0000000000000008·R_X86_64_RELATIVE·························6cba3d |
| 9783 | 000000000084f2e8··0000000000000008·R_X86_64_RELATIVE·························6cba40 | 9783 | 000000000084f2e8··0000000000000008·R_X86_64_RELATIVE·························6cba40 |
| 9784 | 000000000084f2f0··0000000000000008·R_X86_64_RELATIVE·························6c9d35 | 9784 | 000000000084f2f0··0000000000000008·R_X86_64_RELATIVE·························6c9d35 |
| 9785 | 000000000084f2f8··0000000000000008·R_X86_64_RELATIVE·························6c91d0 | 9785 | 000000000084f2f8··0000000000000008·R_X86_64_RELATIVE·························6c91d0 |
| 9786 | 000000000084f300··0000000000000008·R_X86_64_RELATIVE·························6cbbdd | 9786 | 000000000084f300··0000000000000008·R_X86_64_RELATIVE·························6cbbdd |
| 9787 | 000000000084f308··0000000000000008·R_X86_64_RELATIVE·························6ca99f | 9787 | 000000000084f308··0000000000000008·R_X86_64_RELATIVE·························6ca99f |
| 9788 | 000000000084f310··0000000000000008·R_X86_64_RELATIVE·························6cc55 | 9788 | 000000000084f310··0000000000000008·R_X86_64_RELATIVE·························6cc555 |
| 9789 | 000000000084f318··0000000000000008·R_X86_64_RELATIVE·························6ca685 | 9789 | 000000000084f318··0000000000000008·R_X86_64_RELATIVE·························6ca685 |
| 9790 | 000000000084f320··0000000000000008·R_X86_64_RELATIVE·························6ca52b | 9790 | 000000000084f320··0000000000000008·R_X86_64_RELATIVE·························6ca52b |
| 9791 | 000000000084f328··0000000000000008·R_X86_64_RELATIVE·························6cba43 | 9791 | 000000000084f328··0000000000000008·R_X86_64_RELATIVE·························6cba43 |
| 9792 | 000000000084f330··0000000000000008·R_X86_64_RELATIVE·························6cc1c | 9792 | 000000000084f330··0000000000000008·R_X86_64_RELATIVE·························6cc1c3 |
| 9793 | 000000000084f338··0000000000000008·R_X86_64_RELATIVE·························6cbe34 | 9793 | 000000000084f338··0000000000000008·R_X86_64_RELATIVE·························6cbe34 |
| 9794 | 000000000084f340··0000000000000008·R_X86_64_RELATIVE·························6caacf | 9794 | 000000000084f340··0000000000000008·R_X86_64_RELATIVE·························6caacf |
| 9795 | 000000000084f348··0000000000000008·R_X86_64_RELATIVE·························6cb26c | 9795 | 000000000084f348··0000000000000008·R_X86_64_RELATIVE·························6cb26c |
| 9796 | 000000000084f350··0000000000000008·R_X86_64_RELATIVE·························6cb323 | 9796 | 000000000084f350··0000000000000008·R_X86_64_RELATIVE·························6cb323 |
| 9797 | 000000000084f358··0000000000000008·R_X86_64_RELATIVE·························6c9d36 | 9797 | 000000000084f358··0000000000000008·R_X86_64_RELATIVE·························6c9d36 |
| 9798 | 000000000084f360··0000000000000008·R_X86_64_RELATIVE·························6c9d36 | 9798 | 000000000084f360··0000000000000008·R_X86_64_RELATIVE·························6c9d36 |
| 9799 | 000000000084f368··0000000000000008·R_X86_64_RELATIVE·························6c9d36 | 9799 | 000000000084f368··0000000000000008·R_X86_64_RELATIVE·························6c9d36 |
| Offset 9805, 15 lines modified | Offset 9805, 15 lines modified | ||
| 9805 | 000000000084f398··0000000000000008·R_X86_64_RELATIVE·························6cba7a | 9805 | 000000000084f398··0000000000000008·R_X86_64_RELATIVE·························6cba7a |
| 9806 | 000000000084f3a0··0000000000000008·R_X86_64_RELATIVE·························6cbabf | 9806 | 000000000084f3a0··0000000000000008·R_X86_64_RELATIVE·························6cbabf |
| 9807 | 000000000084f3a8··0000000000000008·R_X86_64_RELATIVE·························6ca66b | 9807 | 000000000084f3a8··0000000000000008·R_X86_64_RELATIVE·························6ca66b |
| 9808 | 000000000084f3b0··0000000000000008·R_X86_64_RELATIVE·························6cb901 | 9808 | 000000000084f3b0··0000000000000008·R_X86_64_RELATIVE·························6cb901 |
| 9809 | 000000000084f3b8··0000000000000008·R_X86_64_RELATIVE·························6cba9e | 9809 | 000000000084f3b8··0000000000000008·R_X86_64_RELATIVE·························6cba9e |
| 9810 | 000000000084f3c0··0000000000000008·R_X86_64_RELATIVE·························6cba45 | 9810 | 000000000084f3c0··0000000000000008·R_X86_64_RELATIVE·························6cba45 |
| 9811 | 000000000084f3c8··0000000000000008·R_X86_64_RELATIVE·························6c9eb6 | 9811 | 000000000084f3c8··0000000000000008·R_X86_64_RELATIVE·························6c9eb6 |
| 9812 | 000000000084f3d0··0000000000000008·R_X86_64_RELATIVE·························6cc1a | 9812 | 000000000084f3d0··0000000000000008·R_X86_64_RELATIVE·························6cc1aa |
| 9813 | 000000000084f3d8··0000000000000008·R_X86_64_RELATIVE·························6cba01 | 9813 | 000000000084f3d8··0000000000000008·R_X86_64_RELATIVE·························6cba01 |
| 9814 | 000000000084f3e0··0000000000000008·R_X86_64_RELATIVE·························6cbb2c | 9814 | 000000000084f3e0··0000000000000008·R_X86_64_RELATIVE·························6cbb2c |
| 9815 | 000000000084f3e8··0000000000000008·R_X86_64_RELATIVE·························6cba47 | 9815 | 000000000084f3e8··0000000000000008·R_X86_64_RELATIVE·························6cba47 |
| 9816 | 000000000084f3f0··0000000000000008·R_X86_64_RELATIVE·························6cbb20 | 9816 | 000000000084f3f0··0000000000000008·R_X86_64_RELATIVE·························6cbb20 |
| 9817 | 000000000084f3f8··0000000000000008·R_X86_64_RELATIVE·························6ca67b | 9817 | 000000000084f3f8··0000000000000008·R_X86_64_RELATIVE·························6ca67b |
| 9818 | 000000000084f400··0000000000000008·R_X86_64_RELATIVE·························6cba73 | 9818 | 000000000084f400··0000000000000008·R_X86_64_RELATIVE·························6cba73 |
| 9819 | 000000000084f408··0000000000000008·R_X86_64_RELATIVE·························6cba76 | 9819 | 000000000084f408··0000000000000008·R_X86_64_RELATIVE·························6cba76 |
| Offset 9943, 26 lines modified | Offset 9943, 26 lines modified | ||
| 9943 | 000000000084f7f8··0000000000000008·R_X86_64_RELATIVE·························6cac95 | 9943 | 000000000084f7f8··0000000000000008·R_X86_64_RELATIVE·························6cac95 |
| 9944 | 000000000084f800··0000000000000008·R_X86_64_RELATIVE·························6cba7d | 9944 | 000000000084f800··0000000000000008·R_X86_64_RELATIVE·························6cba7d |
| 9945 | 000000000084f808··0000000000000008·R_X86_64_RELATIVE·························6cb8e6 | 9945 | 000000000084f808··0000000000000008·R_X86_64_RELATIVE·························6cb8e6 |
| 9946 | 000000000084f810··0000000000000008·R_X86_64_RELATIVE·························6cbaa4 | 9946 | 000000000084f810··0000000000000008·R_X86_64_RELATIVE·························6cbaa4 |
| 9947 | 000000000084f818··0000000000000008·R_X86_64_RELATIVE·························6cba48 | 9947 | 000000000084f818··0000000000000008·R_X86_64_RELATIVE·························6cba48 |
| 9948 | 000000000084f820··0000000000000008·R_X86_64_RELATIVE·························6cba83 | 9948 | 000000000084f820··0000000000000008·R_X86_64_RELATIVE·························6cba83 |
| 9949 | 000000000084f828··0000000000000008·R_X86_64_RELATIVE·························6cbe55 | 9949 | 000000000084f828··0000000000000008·R_X86_64_RELATIVE·························6cbe55 |
| 9950 | 000000000084f830··0000000000000008·R_X86_64_RELATIVE·························6cc55 | 9950 | 000000000084f830··0000000000000008·R_X86_64_RELATIVE·························6cc555 |
| 9951 | 000000000084f838··0000000000000008·R_X86_64_RELATIVE·························6ca58c | 9951 | 000000000084f838··0000000000000008·R_X86_64_RELATIVE·························6ca58c |
| 9952 | 000000000084f840··0000000000000008·R_X86_64_RELATIVE·························6cc1a | 9952 | 000000000084f840··0000000000000008·R_X86_64_RELATIVE·························6cc1aa |
| 9953 | 000000000084f848··0000000000000008·R_X86_64_RELATIVE·························6cc1 | 9953 | 000000000084f848··0000000000000008·R_X86_64_RELATIVE·························6cc1b1 |
| 9954 | 000000000084f850··0000000000000008·R_X86_64_RELATIVE·························6ca685 | 9954 | 000000000084f850··0000000000000008·R_X86_64_RELATIVE·························6ca685 |
| 9955 | 000000000084f858··0000000000000008·R_X86_64_RELATIVE·························6ca181 | 9955 | 000000000084f858··0000000000000008·R_X86_64_RELATIVE·························6ca181 |
| 9956 | 000000000084f860··0000000000000008·R_X86_64_RELATIVE·························6ca52b | 9956 | 000000000084f860··0000000000000008·R_X86_64_RELATIVE·························6ca52b |
| 9957 | 000000000084f868··0000000000000008·R_X86_64_RELATIVE·························6ca9a7 | 9957 | 000000000084f868··0000000000000008·R_X86_64_RELATIVE·························6ca9a7 |
| 9958 | 000000000084f870··0000000000000008·R_X86_64_RELATIVE·························6cba43 | 9958 | 000000000084f870··0000000000000008·R_X86_64_RELATIVE·························6cba43 |
| 9959 | 000000000084f878··0000000000000008·R_X86_64_RELATIVE·························6cbda5 | 9959 | 000000000084f878··0000000000000008·R_X86_64_RELATIVE·························6cbda5 |
| 9960 | 000000000084f880··0000000000000008·R_X86_64_RELATIVE·························6cc1c | 9960 | 000000000084f880··0000000000000008·R_X86_64_RELATIVE·························6cc1c3 |
| 9961 | 000000000084f888··0000000000000008·R_X86_64_RELATIVE·························6cc1 | 9961 | 000000000084f888··0000000000000008·R_X86_64_RELATIVE·························6cc192 |
| 9962 | 000000000084f890··0000000000000008·R_X86_64_RELATIVE·························6cba9b | 9962 | 000000000084f890··0000000000000008·R_X86_64_RELATIVE·························6cba9b |
| 9963 | 000000000084f898··0000000000000008·R_X86_64_RELATIVE·························6cbcc9 | 9963 | 000000000084f898··0000000000000008·R_X86_64_RELATIVE·························6cbcc9 |
| 9964 | 000000000084f8a0··0000000000000008·R_X86_64_RELATIVE·························6cbcdc | 9964 | 000000000084f8a0··0000000000000008·R_X86_64_RELATIVE·························6cbcdc |
| 9965 | 000000000084f8a8··0000000000000008·R_X86_64_RELATIVE·························6cbcea | 9965 | 000000000084f8a8··0000000000000008·R_X86_64_RELATIVE·························6cbcea |
| 9966 | 000000000084f8b0··0000000000000008·R_X86_64_RELATIVE·························6cbcfe | 9966 | 000000000084f8b0··0000000000000008·R_X86_64_RELATIVE·························6cbcfe |
| 9967 | 000000000084f8b8··0000000000000008·R_X86_64_RELATIVE·························6cbd04 | 9967 | 000000000084f8b8··0000000000000008·R_X86_64_RELATIVE·························6cbd04 |
| 9968 | 000000000084f8c0··0000000000000008·R_X86_64_RELATIVE·························6c9d36 | 9968 | 000000000084f8c0··0000000000000008·R_X86_64_RELATIVE·························6c9d36 |
| Offset 9970, 33 lines modified | Offset 9970, 33 lines modified | ||
| 9970 | 000000000084f9c8··0000000000000008·R_X86_64_RELATIVE·························6cbe52 | 9970 | 000000000084f9c8··0000000000000008·R_X86_64_RELATIVE·························6cbe52 |
| 9971 | 000000000084f9e0··0000000000000008·R_X86_64_RELATIVE·························84fa20 | 9971 | 000000000084f9e0··0000000000000008·R_X86_64_RELATIVE·························84fa20 |
| 9972 | 000000000084fa20··0000000000000008·R_X86_64_RELATIVE·························6cbe57 | 9972 | 000000000084fa20··0000000000000008·R_X86_64_RELATIVE·························6cbe57 |
| 9973 | 000000000084fa28··0000000000000008·R_X86_64_RELATIVE·························53a980 | 9973 | 000000000084fa28··0000000000000008·R_X86_64_RELATIVE·························53a980 |
| 9974 | 000000000084fa38··0000000000000008·R_X86_64_RELATIVE·························6cbe5e | 9974 | 000000000084fa38··0000000000000008·R_X86_64_RELATIVE·························6cbe5e |
| 9975 | 000000000084fa70··0000000000000008·R_X86_64_RELATIVE·························6e9c80 | 9975 | 000000000084fa70··0000000000000008·R_X86_64_RELATIVE·························6e9c80 |
| 9976 | 000000000084fa78··0000000000000008·R_X86_64_RELATIVE·························6e9ca8 | 9976 | 000000000084fa78··0000000000000008·R_X86_64_RELATIVE·························6e9ca8 |
| 9977 | 000000000084fa80··0000000000000008·R_X86_64_RELATIVE·························6cc57 | 9977 | 000000000084fa80··0000000000000008·R_X86_64_RELATIVE·························6cc57b |
| 9978 | 000000000084fa88··0000000000000008·R_X86_64_RELATIVE·························6cc29 | 9978 | 000000000084fa88··0000000000000008·R_X86_64_RELATIVE·························6cc296 |
| 9979 | 000000000084fa90··0000000000000008·R_X86_64_RELATIVE·························6cc38 | 9979 | 000000000084fa90··0000000000000008·R_X86_64_RELATIVE·························6cc383 |
| 9980 | 000000000084fa98··0000000000000008·R_X86_64_RELATIVE·························6e9708 | 9980 | 000000000084fa98··0000000000000008·R_X86_64_RELATIVE·························6e9708 |
| 9981 | 000000000084faa0··0000000000000008·R_X86_64_RELATIVE·························6e9cd0 | 9981 | 000000000084faa0··0000000000000008·R_X86_64_RELATIVE·························6e9cd0 |
| Max diff block lines reached; 1785/16185 bytes (11.03%) 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:· | 6 | ··GNU··················0x00000014» NT_GNU_BUILD_ID·(unique·build·ID·bitstring)» ····Build·ID:·a9325dda796b02c22279357bc970c528549b4c63 |
| 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 12542, 15 lines modified | Offset 12542, 15 lines modified | ||
| 12542 | evaluate_evalSequenceHadError | 12542 | evaluate_evalSequenceHadError |
| 12543 | errorreturn | 12543 | errorreturn |
| 12544 | evaluate_backtrace | 12544 | evaluate_backtrace |
| 12545 | lastCode | 12545 | lastCode |
| 12546 | tryEvalSuccess | 12546 | tryEvalSuccess |
| 12547 | gcc·14.2.0 | 12547 | gcc·14.2.0 |
| 12548 | x86_64-Linux-Debian-trixie | 12548 | x86_64-Linux-Debian-trixie |
| 12549 | 6.10 | 12549 | 6.1.0-26-cloud-amd64 |
| 12550 | m2-compile-node | 12550 | m2-compile-node |
| 12551 | %d.%d.%d | 12551 | %d.%d.%d |
| 12552 | not·present | 12552 | not·present |
| 12553 | x86_64-pc-linux-gnu | 12553 | x86_64-pc-linux-gnu |
| 12554 | version-1.24.05-16-ec9e9ac60 | 12554 | version-1.24.05-16-ec9e9ac60 |
| 12555 | whichway | 12555 | whichway |
| 12556 | sortlist | 12556 | sortlist |
| Offset 71209, 15 lines modified | Offset 71209, 15 lines modified | ||
| 71209 | » endbr64 | 71209 | » endbr64 |
| 71210 | » push···%rbp | 71210 | » push···%rbp |
| 71211 | » mov····$0x10,%edi | 71211 | » mov····$0x10,%edi |
| 71212 | » push···%rbx | 71212 | » push···%rbx |
| 71213 | » push···%rax | 71213 | » push···%rax |
| 71214 | » call···57410·<__cxa_allocate_exception@plt> | 71214 | » call···57410·<__cxa_allocate_exception@plt> |
| 71215 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39·(discriminator·1) | 71215 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39·(discriminator·1) |
| 71216 | » lea····0x63b1 | 71216 | » lea····0x63b1e2(%rip),%rsi········ |
| 71217 | » mov····%rax,%rdi | 71217 | » mov····%rax,%rdi |
| 71218 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39 | 71218 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39 |
| 71219 | » mov····%rax,%rbx | 71219 | » mov····%rax,%rbx |
| 71220 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39·(discriminator·1) | 71220 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39·(discriminator·1) |
| 71221 | » call···56c20·<std::runtime_error::runtime_error(char·const*)@plt> | 71221 | » call···56c20·<std::runtime_error::runtime_error(char·const*)@plt> |
| 71222 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39·(discriminator·2) | 71222 | ./M2/Macaulay2/d/./M2/Macaulay2/d/interface.dd:39·(discriminator·2) |
| 71223 | » mov····0x7bdf96(%rip),%rdx········ | 71223 | » mov····0x7bdf96(%rip),%rdx········ |
| Offset 71265, 15 lines modified | Offset 71265, 15 lines modified | ||
| 71265 | /usr/include/c++/14/bits/basic_string.h:2032 | 71265 | /usr/include/c++/14/bits/basic_string.h:2032 |
| 71266 | » push···%rax | 71266 | » push···%rax |
| 71267 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::_M_check(unsigned·long,·char·const*)·const: | 71267 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::_M_check(unsigned·long,·char·const*)·const: |
| 71268 | /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1) | 71268 | /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1) |
| 71269 | » mov····%rsi,%rdx | 71269 | » mov····%rsi,%rdx |
| 71270 | » lea····0x65319b(%rip),%rdi········ | 71270 | » lea····0x65319b(%rip),%rdi········ |
| 71271 | » xor····%eax,%eax | 71271 | » xor····%eax,%eax |
| 71272 | » lea····0x63b15 | 71272 | » lea····0x63b159(%rip),%rsi········ |
| 71273 | » call···561d0·<std::__throw_out_of_range_fmt(char·const*,·...)@plt> | 71273 | » call···561d0·<std::__throw_out_of_range_fmt(char·const*,·...)@plt> |
| 71274 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::insert(unsigned·long,·unsigned·long,·char)·[clone·.isra.0]·[clone·.cold]: | 71274 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::insert(unsigned·long,·unsigned·long,·char)·[clone·.isra.0]·[clone·.cold]: |
| 71275 | /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1) | 71275 | /usr/include/c++/14/bits/basic_string.h:394·(discriminator·1) |
| 71276 | » nop | 71276 | » nop |
| 71277 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::basic_string(char·const*,·std::allocator<char>·const&): | 71277 | std::__cxx11::basic_string<char,·std::char_traits<char>,·std::allocator<char>·>::basic_string(char·const*,·std::allocator<char>·const&): |
| 71278 | /usr/include/c++/14/bits/basic_string.h:651 | 71278 | /usr/include/c++/14/bits/basic_string.h:651 |
| 71279 | » mov····0x8(%rsp),%rax | 71279 | » mov····0x8(%rsp),%rax |
| Offset 130702, 15 lines modified | Offset 130702, 15 lines modified | ||
| 130702 | » mov····0xb79e27(%rip),%rdi········#·c3a358·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea378> | 130702 | » mov····0xb79e27(%rip),%rdi········#·c3a358·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea378> |
| 130703 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 | 130703 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 |
| 130704 | » movw···$0x7,(%rbx) | 130704 | » movw···$0x7,(%rbx) |
| 130705 | » movl···$0x2,0x4(%rbx) | 130705 | » movl···$0x2,0x4(%rbx) |
| 130706 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 130706 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 130707 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130707 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| 130708 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130708 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130709 | » lea····0x60bb | 130709 | » lea····0x60bba0(%rip),%rdi········ |
| 130710 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 130710 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 130711 | » mov····%rax,0x8(%rbx) | 130711 | » mov····%rax,0x8(%rbx) |
| 130712 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130712 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130713 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> | 130713 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> |
| 130714 | » mov····%rax,%rdi | 130714 | » mov····%rax,%rdi |
| 130715 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 130715 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 130716 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130716 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| Offset 130746, 15 lines modified | Offset 130746, 15 lines modified | ||
| 130746 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:76 | 130746 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:76 |
| 130747 | » shr····$0x10,%r9d | 130747 | » shr····$0x10,%r9d |
| 130748 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:79 | 130748 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:79 |
| 130749 | » cmp····$0xff,%eax | 130749 | » cmp····$0xff,%eax |
| 130750 | » je·····c139c·<CanonicalForm::~CanonicalForm()@plt+0x66dc4> | 130750 | » je·····c139c·<CanonicalForm::~CanonicalForm()@plt+0x66dc4> |
| 130751 | /usr/include/x86_64-linux-gnu/bits/stdio2.h:68·(discriminator·1) | 130751 | /usr/include/x86_64-linux-gnu/bits/stdio2.h:68·(discriminator·1) |
| 130752 | » push···%rax | 130752 | » push···%rax |
| 130753 | » lea····0x60bb3 | 130753 | » lea····0x60bb3f(%rip),%r8········ |
| 130754 | » push···%rdx | 130754 | » push···%rdx |
| 130755 | » lea····0xb79e5e(%rip),%rbx········#·c3a420·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea440> | 130755 | » lea····0xb79e5e(%rip),%rbx········#·c3a420·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea440> |
| 130756 | » mov····$0x28,%ecx | 130756 | » mov····$0x28,%ecx |
| 130757 | » mov····$0x1,%edx | 130757 | » mov····$0x1,%edx |
| 130758 | » xor····%eax,%eax | 130758 | » xor····%eax,%eax |
| 130759 | » mov····$0x28,%esi | 130759 | » mov····$0x28,%esi |
| 130760 | » mov····%rbx,%rdi | 130760 | » mov····%rbx,%rdi |
| Offset 130783, 15 lines modified | Offset 130783, 15 lines modified | ||
| 130783 | » test···%rax,%rax | 130783 | » test···%rax,%rax |
| 130784 | » je·····c13b0·<CanonicalForm::~CanonicalForm()@plt+0x66dd8> | 130784 | » je·····c13b0·<CanonicalForm::~CanonicalForm()@plt+0x66dd8> |
| 130785 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:158 | 130785 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:158 |
| 130786 | » mov····0x58(%rsp),%r14 | 130786 | » mov····0x58(%rsp),%r14 |
| 130787 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 130787 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 130788 | » mov····0xb79d2d(%rip),%rdi········#·c3a348·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea368> | 130788 | » mov····0xb79d2d(%rip),%rdi········#·c3a348·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea368> |
| 130789 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130789 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130790 | » lea····0x60ba | 130790 | » lea····0x60bae0(%rip),%rbx········ |
| 130791 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:158 | 130791 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:158 |
| 130792 | » movw···$0x7,(%r14) | 130792 | » movw···$0x7,(%r14) |
| 130793 | » movl···$0x2,0x4(%r14) | 130793 | » movl···$0x2,0x4(%r14) |
| 130794 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 130794 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 130795 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130795 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| 130796 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130796 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130797 | » mov····%rbx,%rdi | 130797 | » mov····%rbx,%rdi |
| Offset 130818, 15 lines modified | Offset 130818, 15 lines modified | ||
| 130818 | » mov····0xb79ccf(%rip),%rdi········#·c3a340·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea360> | 130818 | » mov····0xb79ccf(%rip),%rdi········#·c3a340·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea360> |
| 130819 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 | 130819 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 |
| 130820 | » movw···$0x7,(%r15) | 130820 | » movw···$0x7,(%r15) |
| 130821 | » movl···$0x2,0x4(%r15) | 130821 | » movl···$0x2,0x4(%r15) |
| 130822 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 130822 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 130823 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130823 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| 130824 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 130824 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 130825 | » lea····0x60ba8 | 130825 | » lea····0x60ba83(%rip),%rdi········ |
| 130826 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 130826 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 130827 | » mov····%rax,0x8(%r15) | 130827 | » mov····%rax,0x8(%r15) |
| 130828 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 130828 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 130829 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> | 130829 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> |
| 130830 | » mov····%rax,%rdi | 130830 | » mov····%rax,%rdi |
| 130831 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·2) | 130831 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·2) |
| 130832 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130832 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| Offset 130846, 15 lines modified | Offset 130846, 15 lines modified | ||
| 130846 | » mov····0xb79c74(%rip),%rdi········#·c3a338·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea358> | 130846 | » mov····0xb79c74(%rip),%rdi········#·c3a338·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea358> |
| 130847 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:166 | 130847 | ./M2/Macaulay2/d/./M2/Macaulay2/d/version.dd:166 |
| 130848 | » movw···$0x7,(%r14) | 130848 | » movw···$0x7,(%r14) |
| 130849 | » movl···$0x2,0x4(%r14) | 130849 | » movl···$0x2,0x4(%r14) |
| 130850 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 130850 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 130851 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130851 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| 130852 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130852 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130853 | » lea····0x60ba3 | 130853 | » lea····0x60ba36(%rip),%rdi········ |
| 130854 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 130854 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 130855 | » mov····%rax,0x8(%r14) | 130855 | » mov····%rax,0x8(%r14) |
| 130856 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130856 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130857 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> | 130857 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> |
| 130858 | » mov····%rax,%rdi | 130858 | » mov····%rax,%rdi |
| 130859 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 130859 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 130860 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130860 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| Offset 130874, 15 lines modified | Offset 130874, 15 lines modified | ||
| 130874 | » mov····0xb79c19(%rip),%rdi········#·c3a330·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea350> | 130874 | » mov····0xb79c19(%rip),%rdi········#·c3a330·<std::__cxx11::numpunct<char>::id@GLIBCXX_3.4.21+0x3ea350> |
| 130875 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 | 130875 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:63 |
| 130876 | » movw···$0x7,(%r15) | 130876 | » movw···$0x7,(%r15) |
| 130877 | » movl···$0x2,0x4(%r15) | 130877 | » movl···$0x2,0x4(%r15) |
| 130878 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 | 130878 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59 |
| 130879 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130879 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| 130880 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130880 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130881 | » lea····0x60b9e | 130881 | » lea····0x60b9e9(%rip),%rdi········ |
| 130882 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) | 130882 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:59·(discriminator·1) |
| 130883 | » mov····%rax,0x8(%r15) | 130883 | » mov····%rax,0x8(%r15) |
| 130884 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 | 130884 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62 |
| 130885 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> | 130885 | » call···53ae60·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0xe6e0> |
| 130886 | » mov····%rax,%rdi | 130886 | » mov····%rax,%rdi |
| 130887 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) | 130887 | ./M2/Macaulay2/d/./M2/Macaulay2/d/hashtables.sig:62·(discriminator·1) |
| 130888 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> | 130888 | » call···567600·<std::_Vector_base<char,·std::allocator<char>·>::~_Vector_base()@@Base+0x3ae80> |
| Max diff block lines reached; 251996/258718 bytes (97.40%) of diff not shown. | |||
| Offset 777, 91 lines modified | Offset 777, 91 lines modified | ||
| 777 | ··0x006cc060·72726574·75726e00·6576616c·75617465·rreturn.evaluate | 777 | ··0x006cc060·72726574·75726e00·6576616c·75617465·rreturn.evaluate |
| 778 | ··0x006cc070·5f626163·6b747261·6365006c·61737443·_backtrace.lastC | 778 | ··0x006cc070·5f626163·6b747261·6365006c·61737443·_backtrace.lastC |
| 779 | ··0x006cc080·6f646500·74727945·76616c53·75636365·ode.tryEvalSucce | 779 | ··0x006cc080·6f646500·74727945·76616c53·75636365·ode.tryEvalSucce |
| 780 | ··0x006cc090·73730031·2e32342e·30350034·2e342e30·ss.1.24.05.4.4.0 | 780 | ··0x006cc090·73730031·2e32342e·30350034·2e342e30·ss.1.24.05.4.4.0 |
| 781 | ··0x006cc0a0·00676363·2031342e·322e3000·7838365f·.gcc·14.2.0.x86_ | 781 | ··0x006cc0a0·00676363·2031342e·322e3000·7838365f·.gcc·14.2.0.x86_ |
| 782 | ··0x006cc0b0·36340078·38365f36·342d4c69·6e75782d·64.x86_64-Linux- | 782 | ··0x006cc0b0·36340078·38365f36·342d4c69·6e75782d·64.x86_64-Linux- |
| 783 | ··0x006cc0c0·44656269·616e2d74·72697869·65004c69·Debian-trixie.Li | 783 | ··0x006cc0c0·44656269·616e2d74·72697869·65004c69·Debian-trixie.Li |
| 784 | ··0x006cc0d0·6e757800·362e3130 | 784 | ··0x006cc0d0·6e757800·362e312e·302d3236·2d636c6f·nux.6.1.0-26-clo |
| 785 | ··0x006cc0e0·616d6436 | 785 | ··0x006cc0e0·75642d61·6d643634·006d322d·636f6d70·ud-amd64.m2-comp |
| 786 | ··0x006cc0f0·2d6e6f64 | 786 | ··0x006cc0f0·696c652d·6e6f6465·0025642e·25642e25·ile-node.%d.%d.% |
| 787 | ··0x006cc100·6f742070 | 787 | ··0x006cc100·64006e6f·74207072·6573656e·7400322e·d.not·present.2. |
| 788 | ··0x006cc110·00332e32 | 788 | ··0x006cc110·352e3000·332e322e·3100332e·31322e36·5.0.3.2.1.3.12.6 |
| 789 | ··0x006cc120·2e352e31 | 789 | ··0x006cc120·0031312e·352e3100·332e312e·3000315f·.11.5.1.3.1.0.1_ |
| 790 | ··0x006cc130·342e322e | 790 | ··0x006cc130·38330034·2e322e31·00312e35·2e340032·83.4.2.1.1.5.4.2 |
| 791 | ··0x006cc140·2e313200 | 791 | ··0x006cc140·3032312e·31320033·2e342e30·00332e34·021.12.3.4.0.3.4 |
| 792 | ··0x006cc150·7838365f | 792 | ··0x006cc150·2e360078·38365f36·342d7063·2d6c696e·.6.x86_64-pc-lin |
| 793 | ··0x006cc160·676e7500 | 793 | ··0x006cc160·75782d67·6e750076·65727369·6f6e2d31·ux-gnu.version-1 |
| 794 | ··0x006cc170·2e30352d | 794 | ··0x006cc170·2e32342e·30352d31·362d6563·39653961·.24.05-16-ec9e9a |
| 795 | ··0x006cc180·004d3254 | 795 | ··0x006cc180·63363000·4d325461·736b0077·68696368·c60.M2Task.which |
| 796 | ··0x006cc190·00736f72 | 796 | ··0x006cc190·77617900·736f7274·6c697374·006c6f63·way.sortlist.loc |
| 797 | ··0x006cc1a0·64436f64 | 797 | ··0x006cc1a0·61746564·436f6465·00257000·68616473·atedCode.%p.hads |
| 798 | ··0x006cc1b0·64656570 | 798 | ··0x006cc1b0·65710064·65657073·65710064·65657069·eq.deepseq.deepi |
| 799 | ··0x006cc1c0·78007265 | 799 | ··0x006cc1c0·6e646578·00726573·65747661·72730077·ndex.resetvars.w |
| 800 | ··0x006cc1d0·70656420 | 800 | ··0x006cc1d0·72617070·6564204d·61636175·6c617932·rapped·Macaulay2 |
| 801 | ··0x006cc1e0·6e637469 | 801 | ··0x006cc1e0·2066756e·6374696f·6e007465·73740062··function.test.b |
| 802 | ··0x006cc1f0·635f7374 | 802 | ··0x006cc1f0·61736963·5f737472·696e673a·3a696e73·asic_string::ins |
| 803 | ··0x006cc200·004f7665 | 803 | ··0x006cc200·65727400·4f766572·666c6f77·20457272·ert.Overflow·Err |
| 804 | ··0x006cc210·63627274 | 804 | ··0x006cc210·6f720063·6272743c·2531253e·28253125·or.cbrt<%1%>(%1% |
| 805 | ··0x006cc220·67616d6d | 805 | ··0x006cc220·29006c67·616d6d61·3c253125·3e00626f·).lgamma<%1%>.bo |
| 806 | ··0x006cc230·3a3a6d61 | 806 | ··0x006cc230·6f73743a·3a6d6174·683a3a65·78706d31·ost::math::expm1 |
| 807 | ··0x006cc240·253e2825 | 807 | ··0x006cc240·3c253125·3e282531·2529006e·756d6572·<%1%>(%1%).numer |
| 808 | ··0x006cc250·6f766572 | 808 | ··0x006cc250·6963206f·76657266·6c6f7700·626f6f73·ic·overflow.boos |
| 809 | ··0x006cc260·6d617468 | 809 | ··0x006cc260·743a3a6d·6174683a·3a6c6f67·31703c25·t::math::log1p<% |
| 810 | ··0x006cc270·28253125 | 810 | ··0x006cc270·31253e28·25312529·00457661·6c756174·1%>(%1%).Evaluat |
| 811 | ··0x006cc280·206f6620 | 811 | ··0x006cc280·696f6e20·6f66206c·67616d6d·61206174·ion·of·lgamma·at |
| 812 | ··0x006cc290·20253125·2e00626f·6f73743a·3a6d6174··%1%..boost::mat | ||
| 813 | ··0x006cc2a0·683a3a6c·67616d6d·613c2531·253e2825·h::lgamma<%1%>(% | ||
| 814 | ··0x006cc2b0·31252900·6f706572·61746f72·3d00556e·1%).operator=.Un | ||
| 815 | ··0x006cc2c0·61626c65·20746f20·70617273·65207374·able·to·parse·st | ||
| 816 | ··0x006cc2d0·72696e67·20220062·6f6f7374·3a3a6d61·ring·".boost::ma | ||
| 817 | ··0x006cc2e0·74683a3a·6572665f·696e763c·2531253e·th::erf_inv<%1%> | ||
| 818 | ··0x006cc2f0·00457661·6c756174·696f6e20·6f662074·.Evaluation·of·t | ||
| 819 | ··0x006cc300·67616d6d·61206174·20253125·2e00626f·gamma·at·%1%..bo | ||
| 820 | ··0x006cc310·6f73743a·3a6d6174·683a3a69·7472756e·ost::math::itrun | ||
| 821 | ··0x006cc320·633c2531·253e2825·31252900·20616e64·c<%1%>(%1%).·and | ||
| 822 | ··0x006cc330·2078203d·20253125·00626f6f·73743a3a··x·=·%1%.boost:: | ||
| 823 | ··0x006cc340·6d617468·3a3a7a65·74613c25·31253e28·math::zeta<%1%>( | ||
| 824 | ··0x006cc350·25312529·0067616d·6d615f70·3c253125·%1%).gamma_p<%1% | ||
| 825 | ··0x006cc360·3e282531·252c2025·31252900·67616d6d·>(%1%,·%1%).gamm | ||
| 826 | ··0x006cc370·615f713c·2531253e·28253125·2c202531·a_q<%1%>(%1%,·%1 | ||
| 812 | ··0x006cc | 827 | ··0x006cc380·25290062·6f6f7374·3a3a6d61·74683a3a·%).boost::math:: |
| 813 | ··0x006cc2a0·6c67616d·6d613c25·31253e28·25312529·lgamma<%1%>(%1%) | ||
| 814 | ··0x006cc2b0·006f7065·7261746f·723d0055·6e61626c·.operator=.Unabl | ||
| 815 | ··0x006cc2c0·6520746f·20706172·73652073·7472696e·e·to·parse·strin | ||
| 816 | ··0x006cc2d0·67202200·626f6f73·743a3a6d·6174683a·g·".boost::math: | ||
| 817 | ··0x006cc2e0·3a657266·5f696e76·3c253125·3e004576·:erf_inv<%1%>.Ev | ||
| 818 | ··0x006cc2f0·616c7561·74696f6e·206f6620·7467616d·aluation·of·tgam | ||
| 819 | ··0x006cc300·6d612061·74202531·252e0062·6f6f7374·ma·at·%1%..boost | ||
| 820 | ··0x006cc310·3a3a6d61·74683a3a·69747275·6e633c25·::math::itrunc<% | ||
| 821 | ··0x006cc320·31253e28·25312529·0020616e·64207820·1%>(%1%).·and·x· | ||
| 822 | ··0x006cc330·3d202531·2500626f·6f73743a·3a6d6174·=·%1%.boost::mat | ||
| 823 | ··0x006cc340·683a3a7a·6574613c·2531253e·28253125·h::zeta<%1%>(%1% | ||
| 824 | ··0x006cc350·29006761·6d6d615f·703c2531·253e2825·).gamma_p<%1%>(% | ||
| 825 | ··0x006cc360·31252c20·25312529·0067616d·6d615f71·1%,·%1%).gamma_q | ||
| 826 | ··0x006cc370·3c253125·3e282531·252c2025·31252900·<%1%>(%1%,·%1%). | ||
| 827 | ··0x006cc380·626f6f73·743a3a6d·6174683a·3a7a6574·boost::math::zet | ||
| 828 | ··0x006cc390·613c2531 | 828 | ··0x006cc390·7a657461·3c253125·3e00666c·6f61745f·zeta<%1%>.float_ |
| 829 | ··0x006cc3a0·6f723c25 | 829 | ··0x006cc3a0·7072696f·723c2531·253e2825·31252900·prior<%1%>(%1%). |
| 830 | ··0x006cc3b0·61745f6e | 830 | ··0x006cc3b0·666c6f61·745f6e65·78743c25·31253e28·float_next<%1%>( |
| 831 | ··0x006cc3c0·29003234 | 831 | ··0x006cc3c0·25312529·00323400·31323000·37323000·%1%).24.120.720. |
| 832 | ··0x006cc3d0·30003430 | 832 | ··0x006cc3d0·35303430·00343033·32300033·36323838·5040.40320.36288 |
| 833 | ··0x006cc3e0·36323838 | 833 | ··0x006cc3e0·30003336·32383830·30003339·39313638·0.3628800.399168 |
| 834 | ··0x006cc3f0·34373930 | 834 | ··0x006cc3f0·30300034·37393030·31363030·00363232·00.479001600.622 |
| 835 | ··0x006cc400·30383030 | 835 | ··0x006cc400·37303230·38303000·38373137·38323931·7020800.87178291 |
| 836 | ··0x006cc410·00313330 | 836 | ··0x006cc410·32303000·31333037·36373433·36383030·200.130767436800 |
| 837 | ··0x006cc420·30 | 837 | ··0x006cc420·30003230·39323237·38393838·38303030·0.20922789888000 |
| 838 | ··0x006cc430·35363837 | 838 | ··0x006cc430·00333535·36383734·32383039·36303030·.355687428096000 |
| 839 | ··0x006cc440· | 839 | ··0x006cc440·00363430·32333733·37303537·32383030·.640237370572800 |
| 840 | ··0x006cc450·32313634 | 840 | ··0x006cc450·30003132·31363435·31303034·30383833·0.12164510040883 |
| 841 | ··0x006cc460·3 | 841 | ··0x006cc460·32303030·00323433·32393032·30303831·2000.24329020081 |
| 842 | ··0x006cc470·3 | 842 | ··0x006cc470·37363634·30303030·00353130·39303934·76640000.5109094 |
| 843 | ··0x006cc480·31373039 | 843 | ··0x006cc480·32313731·37303934·34303030·30003131·2171709440000.11 |
| 844 | ··0x006cc490·3 | 844 | ··0x006cc490·32343030·30373237·37373736·30373638·2400072777760768 |
| 845 | ··0x006cc4a0·30003235 | 845 | ··0x006cc4a0·30303030·00323538·35323031·36373338·0000.25852016738 |
| 846 | ··0x006cc4b0·39373636 | 846 | ··0x006cc4b0·38383439·37363634·30303030·00363230·884976640000.620 |
| 847 | ··0x006cc4c0·343 | 847 | ··0x006cc4c0·34343834·30313733·33323339·34333933·4484017332394393 |
| 848 | ··0x006cc4d0·3 | 848 | ··0x006cc4d0·36303030·30003135·35313132·31303034·60000.1551121004 |
| 849 | ··0x006cc4e0·3 | 849 | ··0x006cc4e0·33333330·39383539·38343030·30303030·3330985984000000 |
| 850 | ··0x006cc4f0· | 850 | ··0x006cc4f0·00343033·32393134·36313132·36363035·.403291461126605 |
| 851 | ··0x006cc500·3 | 851 | ··0x006cc500·36333535·38343030·30303030·00313038·635584000000.108 |
| 852 | ··0x006cc510·3 | 852 | ··0x006cc510·38383836·39343530·34313833·35323136·8886945041835216 |
| 853 | ··0x006cc520·38303030 | 853 | ··0x006cc520·30373638·30303030·30300062·61736963·0768000000.basic |
| 854 | ··0x006cc530·72696e67 | 854 | ··0x006cc530·5f737472·696e673a·3a726570·6c616365·_string::replace |
| 855 | ··0x006cc540·30300030 | 855 | ··0x006cc540·00652b30·3000302e·002d696e·66002b69·.e+00.0..-inf.+i |
| 856 | ··0x006cc550·6e616e00 | 856 | ··0x006cc550·6e66006e·616e002d·30004361·75736520·nf.nan.-0.Cause· |
| 857 | ··0x006cc560·6e6f776e | 857 | ··0x006cc560·756e6b6e·6f776e00·4572726f·7220696e·unknown.Error·in |
| 858 | ··0x006cc570·6e637469 | 858 | ··0x006cc570·2066756e·6374696f·6e200062·6f6f7374··function·.boost |
| 859 | ··0x006cc580·6174683a | 859 | ··0x006cc580·3a3a6d61·74683a3a·7467616d·6d613c25·::math::tgamma<% |
| 860 | ··0x006cc590· | 860 | ··0x006cc590·31253e28·25312529·00000000·00000000·1%>(%1%)........ |
| 861 | ··0x006cc5a0·01000000·00000000·00000000·00000000·................ | 861 | ··0x006cc5a0·01000000·00000000·00000000·00000000·................ |
| 862 | ··0x006cc5b0·30303031·30323033·30343035·30363037·0001020304050607 | 862 | ··0x006cc5b0·30303031·30323033·30343035·30363037·0001020304050607 |
| 863 | ··0x006cc5c0·30383039·31303131·31323133·31343135·0809101112131415 | 863 | ··0x006cc5c0·30383039·31303131·31323133·31343135·0809101112131415 |
| 864 | ··0x006cc5d0·31363137·31383139·32303231·32323233·1617181920212223 | 864 | ··0x006cc5d0·31363137·31383139·32303231·32323233·1617181920212223 |
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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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| 66 | ··0x0084f3f0·20bb6c00·00000000·7ba66c00·00000000··.l.....{.l..... | 66 | ··0x0084f3f0·20bb6c00·00000000·7ba66c00·00000000··.l.....{.l..... |
| 67 | ··0x0084f400·73ba6c00·00000000·76ba6c00·00000000·s.l.....v.l..... | 67 | ··0x0084f400·73ba6c00·00000000·76ba6c00·00000000·s.l.....v.l..... |
| 68 | ··0x0084f410·79ba6c00·00000000·0ebd6c00·00000000·y.l.......l..... | 68 | ··0x0084f410·79ba6c00·00000000·0ebd6c00·00000000·y.l.......l..... |
| 69 | ··0x0084f420·7cba6c00·00000000·7fba6c00·00000000·|.l.......l..... | 69 | ··0x0084f420·7cba6c00·00000000·7fba6c00·00000000·|.l.......l..... |
| 70 | ··0x0084f430·9c986c00·00000000·82ba6c00·00000000·..l.......l..... | 70 | ··0x0084f430·9c986c00·00000000·82ba6c00·00000000·..l.......l..... |
| 71 | ··0x0084f440·85ba6c00·00000000·48926c00·00000000·..l.....H.l..... | 71 | ··0x0084f440·85ba6c00·00000000·48926c00·00000000·..l.....H.l..... |
| Offset 127, 20 lines modified | Offset 127, 20 lines modified | ||
| 127 | ··0x0084f7c0·bcbc6c00·00000000·ddbb6c00·00000000·..l.......l..... | 127 | ··0x0084f7c0·bcbc6c00·00000000·ddbb6c00·00000000·..l.......l..... |
| 128 | ··0x0084f7d0·e8ba6c00·00000000·34be6c00·00000000·..l.....4.l..... | 128 | ··0x0084f7d0·e8ba6c00·00000000·34be6c00·00000000·..l.....4.l..... |
| 129 | ··0x0084f7e0·2a966c00·00000000·23b36c00·00000000·*.l.....#.l..... | 129 | ··0x0084f7e0·2a966c00·00000000·23b36c00·00000000·*.l.....#.l..... |
| 130 | ··0x0084f7f0·9fa96c00·00000000·95ac6c00·00000000·..l.......l..... | 130 | ··0x0084f7f0·9fa96c00·00000000·95ac6c00·00000000·..l.......l..... |
| 131 | ··0x0084f800·7dba6c00·00000000·e6b86c00·00000000·}.l.......l..... | 131 | ··0x0084f800·7dba6c00·00000000·e6b86c00·00000000·}.l.......l..... |
| 132 | ··0x0084f810·a4ba6c00·00000000·48ba6c00·00000000·..l.....H.l..... | 132 | ··0x0084f810·a4ba6c00·00000000·48ba6c00·00000000·..l.....H.l..... |
| 133 | ··0x0084f820·83ba6c00·00000000·55be6c00·00000000·..l.....U.l..... | 133 | ··0x0084f820·83ba6c00·00000000·55be6c00·00000000·..l.....U.l..... |
| 134 | ··0x0084f830·5 | 134 | ··0x0084f830·55c56c00·00000000·8ca56c00·00000000·U.l.......l..... |
| 135 | ··0x0084f840·a | 135 | ··0x0084f840·aac16c00·00000000·b1c16c00·00000000·..l.......l..... |
| 136 | ··0x0084f850·85a66c00·00000000·81a16c00·00000000·..l.......l..... | 136 | ··0x0084f850·85a66c00·00000000·81a16c00·00000000·..l.......l..... |
| 137 | ··0x0084f860·2ba56c00·00000000·a7a96c00·00000000·+.l.......l..... | 137 | ··0x0084f860·2ba56c00·00000000·a7a96c00·00000000·+.l.......l..... |
| 138 | ··0x0084f870·43ba6c00·00000000·a5bd6c00·00000000·C.l.......l..... | 138 | ··0x0084f870·43ba6c00·00000000·a5bd6c00·00000000·C.l.......l..... |
| 139 | ··0x0084f880·c | 139 | ··0x0084f880·c3c16c00·00000000·92c16c00·00000000·..l.......l..... |
| 140 | ··0x0084f890·9bba6c00·00000000·c9bc6c00·00000000·..l.......l..... | 140 | ··0x0084f890·9bba6c00·00000000·c9bc6c00·00000000·..l.......l..... |
| 141 | ··0x0084f8a0·dcbc6c00·00000000·eabc6c00·00000000·..l.......l..... | 141 | ··0x0084f8a0·dcbc6c00·00000000·eabc6c00·00000000·..l.......l..... |
| 142 | ··0x0084f8b0·febc6c00·00000000·04bd6c00·00000000·..l.......l..... | 142 | ··0x0084f8b0·febc6c00·00000000·04bd6c00·00000000·..l.......l..... |
| 143 | ··0x0084f8c0·369d6c00·00000000·00000000·00000000·6.l............. | 143 | ··0x0084f8c0·369d6c00·00000000·00000000·00000000·6.l............. |
| 144 | ··0x0084f8d0·25733a25·643a2065·72726f72·3a202573·%s:%d:·error:·%s | 144 | ··0x0084f8d0·25733a25·643a2065·72726f72·3a202573·%s:%d:·error:·%s |
| 145 | ··0x0084f8e0·00000000·00000000·00000000·00000000·................ | 145 | ··0x0084f8e0·00000000·00000000·00000000·00000000·................ |
| 146 | ··0x0084f8f0·25733a25·643a2564·3a206572·726f723a·%s:%d:%d:·error: | 146 | ··0x0084f8f0·25733a25·643a2564·3a206572·726f723a·%s:%d:%d:·error: |
| Offset 164, 23 lines modified | Offset 164, 23 lines modified | ||
| 164 | ··0x0084fa10·00000000·00000000·00000000·00000000·................ | 164 | ··0x0084fa10·00000000·00000000·00000000·00000000·................ |
| 165 | ··0x0084fa20·57be6c00·00000000·80a95300·00000000·W.l.......S..... | 165 | ··0x0084fa20·57be6c00·00000000·80a95300·00000000·W.l.......S..... |
| 166 | ··0x0084fa30·01000000·00000000·5ebe6c00·00000000·........^.l..... | 166 | ··0x0084fa30·01000000·00000000·5ebe6c00·00000000·........^.l..... |
| 167 | ··0x0084fa40·00000000·00000000·00000000·00000000·................ | 167 | ··0x0084fa40·00000000·00000000·00000000·00000000·................ |
| 168 | ··0x0084fa50·00000000·00000000·00000000·00000000·................ | 168 | ··0x0084fa50·00000000·00000000·00000000·00000000·................ |
| 169 | ··0x0084fa60·0a000000·00000000·64636261·00000000·........dcba.... | 169 | ··0x0084fa60·0a000000·00000000·64636261·00000000·........dcba.... |
| 170 | ··0x0084fa70·809c6e00·00000000·a89c6e00·00000000·..n.......n..... | 170 | ··0x0084fa70·809c6e00·00000000·a89c6e00·00000000·..n.......n..... |
| 171 | ··0x0084fa80·7 | 171 | ··0x0084fa80·7bc56c00·00000000·96c26c00·00000000·{.l.......l..... |
| 172 | ··0x0084fa90·8 | 172 | ··0x0084fa90·83c36c00·00000000·08976e00·00000000·..l.......n..... |
| 173 | ··0x0084faa0·d09c6e00·00000000·9 | 173 | ··0x0084faa0·d09c6e00·00000000·9ac36c00·00000000·..n.......l..... |
| 174 | ··0x0084fab0· | 174 | ··0x0084fab0·b0c36c00·00000000·f89c6e00·00000000·..l.......n..... |
| 175 | ··0x0084fac0·209d6e00·00000000·489d6e00·00000000··.n.....H.n..... | 175 | ··0x0084fac0·209d6e00·00000000·489d6e00·00000000··.n.....H.n..... |
| 176 | ··0x0084fad0·789d6e00·00000000·809c6e00·00000000·x.n.......n..... | 176 | ··0x0084fad0·789d6e00·00000000·809c6e00·00000000·x.n.......n..... |
| 177 | ··0x0084fae0·7 | 177 | ··0x0084fae0·7bc56c00·00000000·96c26c00·00000000·{.l.......l..... |
| 178 | ··0x0084faf0·f0b86e00·00000000·18b96e00·00000000·..n.......n..... | 178 | ··0x0084faf0·f0b86e00·00000000·18b96e00·00000000·..n.......n..... |
| 179 | ··0x0084fb00·d09c6e00·00000000·f0b86e00·00000000·..n.......n..... | 179 | ··0x0084fb00·d09c6e00·00000000·f0b86e00·00000000·..n.......n..... |
| 180 | ··0x0084fb10·5 | 180 | ··0x0084fb10·5cc26c00·00000000·d09c6e00·00000000·\.l.......n..... |
| 181 | ··0x0084fb20·d09c6e00·00000000·409b6e00·00000000·..n.....@.n..... | 181 | ··0x0084fb20·d09c6e00·00000000·409b6e00·00000000·..n.....@.n..... |
| 182 | ··0x0084fb30·209d6e00·00000000·40b96e00·00000000··.n.....@.n..... | 182 | ··0x0084fb30·209d6e00·00000000·40b96e00·00000000··.n.....@.n..... |
| 183 | ··0x0084fb40·68b96e00·00000000·18b96e00·00000000·h.n.......n..... | 183 | ··0x0084fb40·68b96e00·00000000·18b96e00·00000000·h.n.......n..... |
| 184 | ··0x0084fb50·03000000·14000000·48c58400·00000000·........H....... | 184 | ··0x0084fb50·03000000·14000000·48c58400·00000000·........H....... |
| 185 | ··0x0084fb60·00000000·00000000···················........ | 185 | ··0x0084fb60·00000000·00000000···················........ |
| 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 | ··0x00000000·61663730·35663565·35383964·62383061·af705f5e589db80a | ||
| 3 | ··0x000000 | 2 | ··0x00000000·33323564·64613739·36623032·63323232·325dda796b02c222 |
| 3 | ··0x00000010·37393335·37626339·37306335·32383534·79357bc970c52854 | ||
| 4 | ··0x00000020·3 | 4 | ··0x00000020·39623463·36332e64·65627567·00000000·9b4c63.debug.... |
| 5 | ··0x00000030· | 5 | ··0x00000030·8dca0051····························...Q |
| Offset 1, 3 lines modified | Offset 1, 3 lines modified | ||
| 1 | -rw-r--r--···0········0········0········4·2024-09-09·00:38:13.000000·debian-binary | 1 | -rw-r--r--···0········0········0········4·2024-09-09·00:38:13.000000·debian-binary |
| 2 | -rw-r--r--···0········0········0······53 | 2 | -rw-r--r--···0········0········0······532·2024-09-09·00:38:13.000000·control.tar.xz |
| 3 | -rw-r--r--···0········0········0·4852 | 3 | -rw-r--r--···0········0········0·48521796·2024-09-09·00:38:13.000000·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:·49729 | 7 | Installed-Size:·49729 |
| 8 | Depends:·macaulay2·(=·1.24.05+ds-5) | 8 | Depends:·macaulay2·(=·1.24.05+ds-5) |
| 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:· | 12 | Build-Ids:·a9325dda796b02c22279357bc970c528549b4c63 |
| Offset 1, 10 lines modified | Offset 1, 10 lines modified | ||
| 1 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./ | 1 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./ |
| 2 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/ | 2 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/ |
| 3 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/ | 3 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/ |
| 4 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/debug/ | 4 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/debug/ |
| 5 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/debug/.build-id/ | 5 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/debug/.build-id/ |
| 6 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/debug/.build-id/ | 6 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/lib/debug/.build-id/a9/ |
| 7 | -rw-r--r--···0·root·········(0)·root·········(0)·509122 | 7 | -rw-r--r--···0·root·········(0)·root·········(0)·50912208·2024-09-09·00:38:13.000000·./usr/lib/debug/.build-id/a9/325dda796b02c22279357bc970c528549b4c63.debug |
| 8 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/ | 8 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/ |
| 9 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/ | 9 | drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/ |
| 10 | lrwxrwxrwx···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./usr/share/doc/macaulay2-dbgsym·->·macaulay2 | 10 | lrwxrwxrwx···0·root·········(0)·root·········(0)········0·2024-09-09·00:38:13.000000·./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:···············0xec6a0 | 11 | ··Entry·point·address:···············0xec6a0 |
| 12 | ··Start·of·program·headers:··········64·(bytes·into·file) | 12 | ··Start·of·program·headers:··········64·(bytes·into·file) |
| 13 | ··Start·of·section·headers:··········509095 | 13 | ··Start·of·section·headers:··········50909520·(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·0x308d1 | 1 | There·are·42·section·headers,·starting·at·offset·0x308d150: |
| 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··········00000000008376a0·001330·015218·00··WA··0···0·32 | 29 | ··[24]·.data.rel.ro······NOBITS··········00000000008376a0·001330·015218·00··WA··0···0·32 |
| 30 | ··[25]·.dynamic··········NOBITS··········000000000084c8b8·001330·0003a0·10··WA··7···0··8 | 30 | ··[25]·.dynamic··········NOBITS··········000000000084c8b8·001330·0003a0·10··WA··7···0··8 |
| 31 | ··[26]·.got··············NOBITS··········000000000084cc58·001330·0023a0·08··WA··0···0··8 | 31 | ··[26]·.got··············NOBITS··········000000000084cc58·001330·0023a0·08··WA··0···0··8 |
| 32 | ··[27]·.data·············NOBITS··········000000000084f000·001330·000b68·00··WA··0···0·32 | 32 | ··[27]·.data·············NOBITS··········000000000084f000·001330·000b68·00··WA··0···0·32 |
| 33 | ··[28]·.bss··············NOBITS··········000000000084fb80·001330·3f0170·00··WA··0···0·64 | 33 | ··[28]·.bss··············NOBITS··········000000000084fb80·001330·3f0170·00··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········0000000000000000·0003f8·0097ef·00···C··0···0··8 | 35 | ··[30]·.debug_aranges····PROGBITS········0000000000000000·0003f8·0097ef·00···C··0···0··8 |
| 36 | ··[31]·.debug_info·······PROGBITS········0000000000000000·009be8·1aa51 | 36 | ··[31]·.debug_info·······PROGBITS········0000000000000000·009be8·1aa5160·00···C··0···0··8 |
| 37 | ··[32]·.debug_abbrev·····PROGBITS········0000000000000000·1aaed | 37 | ··[32]·.debug_abbrev·····PROGBITS········0000000000000000·1aaed48·03a80c·00···C··0···0··8 |
| 38 | ··[33]·.debug_line·······PROGBITS········0000000000000000·1ae95 | 38 | ··[33]·.debug_line·······PROGBITS········0000000000000000·1ae9558·290b77·00···C··0···0··8 |
| 39 | ··[34]·.debug_str········PROGBITS········0000000000000000·1d7a | 39 | ··[34]·.debug_str········PROGBITS········0000000000000000·1d7a0d0·8ea0d7·01·MSC··0···0··8 |
| 40 | ··[35]·.debug_line_str···PROGBITS········0000000000000000·26641 | 40 | ··[35]·.debug_line_str···PROGBITS········0000000000000000·26641a8·00348c·01·MSC··0···0··8 |
| 41 | ··[36]·.debug_loclists···PROGBITS········0000000000000000·26676 | 41 | ··[36]·.debug_loclists···PROGBITS········0000000000000000·2667638·59d835·00···C··0···0··8 |
| 42 | ··[37]·.debug_macro······PROGBITS········0000000000000000·2c04e | 42 | ··[37]·.debug_macro······PROGBITS········0000000000000000·2c04e70·0deab4·00···C··0···0··8 |
| 43 | ··[38]·.debug_rnglists···PROGBITS········0000000000000000·2ce39 | 43 | ··[38]·.debug_rnglists···PROGBITS········0000000000000000·2ce3928·13db1d·00···C··0···0··8 |
| 44 | ··[39]·.symtab···········SYMTAB··········0000000000000000·2e214 | 44 | ··[39]·.symtab···········SYMTAB··········0000000000000000·2e21448·08e3b0·18·····40·8656··8 |
| 45 | ··[40]·.strtab···········STRTAB··········0000000000000000·2eaf | 45 | ··[40]·.strtab···········STRTAB··········0000000000000000·2eaf7f8·1dd79f·00······0···0··1 |
| 46 | ··[41]·.shstrtab·········STRTAB··········0000000000000000·308cf | 46 | ··[41]·.shstrtab·········STRTAB··········0000000000000000·308cf97·0001b3·00······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:· | 6 | ··GNU··················0x00000014» NT_GNU_BUILD_ID·(unique·build·ID·bitstring)» ····Build·ID:·a9325dda796b02c22279357bc970c528549b4c63 |
| 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 11506, 15 lines modified | Offset 11506, 15 lines modified | ||
| 11506 | ·DW_MACRO_define_strp·-·lineno·:·311·macro·:·PACKAGE_BUGREPORT·"https://github.com/Macaulay2/M2/issues" | 11506 | ·DW_MACRO_define_strp·-·lineno·:·311·macro·:·PACKAGE_BUGREPORT·"https://github.com/Macaulay2/M2/issues" |
| 11507 | ·DW_MACRO_define_strp·-·lineno·:·314·macro·:·PACKAGE_NAME·"Macaulay2" | 11507 | ·DW_MACRO_define_strp·-·lineno·:·314·macro·:·PACKAGE_NAME·"Macaulay2" |
| 11508 | ·DW_MACRO_define_strp·-·lineno·:·317·macro·:·PACKAGE_STRING·"Macaulay2·1.24.05" | 11508 | ·DW_MACRO_define_strp·-·lineno·:·317·macro·:·PACKAGE_STRING·"Macaulay2·1.24.05" |
| 11509 | ·DW_MACRO_define_strp·-·lineno·:·320·macro·:·PACKAGE_TARNAME·"Macaulay2" | 11509 | ·DW_MACRO_define_strp·-·lineno·:·320·macro·:·PACKAGE_TARNAME·"Macaulay2" |
| 11510 | ·DW_MACRO_define_strp·-·lineno·:·323·macro·:·PACKAGE_URL·"https://macaulay2.com/" | 11510 | ·DW_MACRO_define_strp·-·lineno·:·323·macro·:·PACKAGE_URL·"https://macaulay2.com/" |
| 11511 | ·DW_MACRO_define_strp·-·lineno·:·326·macro·:·PACKAGE_VERSION·"1.24.05" | 11511 | ·DW_MACRO_define_strp·-·lineno·:·326·macro·:·PACKAGE_VERSION·"1.24.05" |
| 11512 | ·DW_MACRO_define_strp·-·lineno·:·329·macro·:·PROFILING·0 | 11512 | ·DW_MACRO_define_strp·-·lineno·:·329·macro·:·PROFILING·0 |
| 11513 | ·DW_MACRO_define_strp·-·lineno·:·332·macro·:·REL·"6.10 | 11513 | ·DW_MACRO_define_strp·-·lineno·:·332·macro·:·REL·"6.1.0-26-cloud-amd64" |
| 11514 | ·DW_MACRO_define_strp·-·lineno·:·335·macro·:·SIZEOF_INT_P·8 | 11514 | ·DW_MACRO_define_strp·-·lineno·:·335·macro·:·SIZEOF_INT_P·8 |
| 11515 | ·DW_MACRO_define_strp·-·lineno·:·338·macro·:·SIZEOF_LONG·8 | 11515 | ·DW_MACRO_define_strp·-·lineno·:·338·macro·:·SIZEOF_LONG·8 |
| 11516 | ·DW_MACRO_define_strp·-·lineno·:·341·macro·:·SOCKLEN_T· | 11516 | ·DW_MACRO_define_strp·-·lineno·:·341·macro·:·SOCKLEN_T· |
| 11517 | ·DW_MACRO_define_strp·-·lineno·:·354·macro·:·STDC_HEADERS·1 | 11517 | ·DW_MACRO_define_strp·-·lineno·:·354·macro·:·STDC_HEADERS·1 |
| 11518 | ·DW_MACRO_define_strp·-·lineno·:·357·macro·:·USING_MPIR·0 | 11518 | ·DW_MACRO_define_strp·-·lineno·:·357·macro·:·USING_MPIR·0 |
| 11519 | ·DW_MACRO_define_strp·-·lineno·:·363·macro·:·WITH_NEWLINE_CR·0 | 11519 | ·DW_MACRO_define_strp·-·lineno·:·363·macro·:·WITH_NEWLINE_CR·0 |
| 11520 | ·DW_MACRO_define_strp·-·lineno·:·366·macro·:·WITH_NEWLINE_CRLF·0 | 11520 | ·DW_MACRO_define_strp·-·lineno·:·366·macro·:·WITH_NEWLINE_CRLF·0 |
| Offset 2641262, 15 lines modified | Offset 2641262, 15 lines modified | ||
| 2641262 | ····00779ae6·v000000000000001·v000000000000000·views·at·00779ae4·for: | 2641262 | ····00779ae6·v000000000000001·v000000000000000·views·at·00779ae4·for: |
| 2641263 | ·············00000000002c54bd·00000000002c54db·(DW_OP_reg6·(rbp)) | 2641263 | ·············00000000002c54bd·00000000002c54db·(DW_OP_reg6·(rbp)) |
| 2641264 | ····00779af2·<End·of·list> | 2641264 | ····00779af2·<End·of·list> |
| 2641265 | ····00779af3·v000000000000001·v000000000000000·location·view·pair | 2641265 | ····00779af3·v000000000000001·v000000000000000·location·view·pair |
| 2641266 | ····00779af5·v000000000000001·v000000000000000·views·at·00779af3·for: | 2641266 | ····00779af5·v000000000000001·v000000000000000·views·at·00779af3·for: |
| 2641267 | ·············00000000002c54bd·00000000002c54db·(DW_OP_addr:·6cc11 | 2641267 | ·············00000000002c54bd·00000000002c54db·(DW_OP_addr:·6cc118;·DW_OP_stack_value) |
| 2641268 | ····00779b0a·<End·of·list> | 2641268 | ····00779b0a·<End·of·list> |
| 2641269 | ····00779b0b·v000000000000002·v000000000000001·location·view·pair | 2641269 | ····00779b0b·v000000000000002·v000000000000001·location·view·pair |
| 2641270 | ····00779b0d·v000000000000002·v000000000000001·views·at·00779b0b·for: | 2641270 | ····00779b0d·v000000000000002·v000000000000001·views·at·00779b0b·for: |
| 2641271 | ·············00000000002c5574·00000000002c5585·(DW_OP_reg6·(rbp)) | 2641271 | ·············00000000002c5574·00000000002c5585·(DW_OP_reg6·(rbp)) |
| 2641272 | ····00779b19·<End·of·list> | 2641272 | ····00779b19·<End·of·list> |
| Offset 2711046, 15 lines modified | Offset 2711046, 15 lines modified | ||
| 2711046 | ····007ad790·v000000000000001·v000000000000001·views·at·007ad78e·for: | 2711046 | ····007ad790·v000000000000001·v000000000000001·views·at·007ad78e·for: |
| 2711047 | ·············00000000002d8e18·00000000002d8e27·(DW_OP_reg3·(rbx)) | 2711047 | ·············00000000002d8e18·00000000002d8e27·(DW_OP_reg3·(rbx)) |
| 2711048 | ····007ad79c·<End·of·list> | 2711048 | ····007ad79c·<End·of·list> |
| 2711049 | ····007ad79d·v000000000000001·v000000000000001·location·view·pair | 2711049 | ····007ad79d·v000000000000001·v000000000000001·location·view·pair |
| 2711050 | ····007ad79f·v000000000000001·v000000000000001·views·at·007ad79d·for: | 2711050 | ····007ad79f·v000000000000001·v000000000000001·views·at·007ad79d·for: |
| 2711051 | ·············00000000002d8e18·00000000002d8e27·(DW_OP_addr:·6cc1c | 2711051 | ·············00000000002d8e18·00000000002d8e27·(DW_OP_addr:·6cc1c3;·DW_OP_stack_value) |
| 2711052 | ····007ad7b4·<End·of·list> | 2711052 | ····007ad7b4·<End·of·list> |
| 2711053 | ····007ad7b5·v000000000000001·v000000000000001·location·view·pair | 2711053 | ····007ad7b5·v000000000000001·v000000000000001·location·view·pair |
| 2711054 | ····007ad7b7·v000000000000001·v000000000000001·views·at·007ad7b5·for: | 2711054 | ····007ad7b7·v000000000000001·v000000000000001·views·at·007ad7b5·for: |
| 2711055 | ·············00000000002d8e27·00000000002d8e33·(DW_OP_reg3·(rbx)) | 2711055 | ·············00000000002d8e27·00000000002d8e33·(DW_OP_reg3·(rbx)) |
| 2711056 | ····007ad7c3·<End·of·list> | 2711056 | ····007ad7c3·<End·of·list> |
| Offset 3224603, 15 lines modified | Offset 3224603, 15 lines modified | ||
| 3224603 | ····00929ad5·v000000000000001·v000000000000001·views·at·00929ad3·for: | 3224603 | ····00929ad5·v000000000000001·v000000000000001·views·at·00929ad3·for: |
| 3224604 | ·············000000000036dcd4·000000000036dce3·(DW_OP_reg6·(rbp)) | 3224604 | ·············000000000036dcd4·000000000036dce3·(DW_OP_reg6·(rbp)) |
| 3224605 | ····00929ae1·<End·of·list> | 3224605 | ····00929ae1·<End·of·list> |
| 3224606 | ····00929ae2·v000000000000001·v000000000000001·location·view·pair | 3224606 | ····00929ae2·v000000000000001·v000000000000001·location·view·pair |
| 3224607 | ····00929ae4·v000000000000001·v000000000000001·views·at·00929ae2·for: | 3224607 | ····00929ae4·v000000000000001·v000000000000001·views·at·00929ae2·for: |
| 3224608 | ·············000000000036dcd4·000000000036dce3·(DW_OP_addr:·6cc22 | 3224608 | ·············000000000036dcd4·000000000036dce3·(DW_OP_addr:·6cc22c;·DW_OP_stack_value) |
| 3224609 | ····00929af9·<End·of·list> | 3224609 | ····00929af9·<End·of·list> |
| 3224610 | ····00929afa·v000000000000001·v000000000000000·location·view·pair | 3224610 | ····00929afa·v000000000000001·v000000000000000·location·view·pair |
| 3224611 | ····00929afc·v000000000000000·v000000000000000·location·view·pair | 3224611 | ····00929afc·v000000000000000·v000000000000000·location·view·pair |
| 3224612 | ····00929afe·v000000000000000·v000000000000000·location·view·pair | 3224612 | ····00929afe·v000000000000000·v000000000000000·location·view·pair |
| 3224613 | ····00929b00·000000000036dd4f·(base·address) | 3224613 | ····00929b00·000000000036dd4f·(base·address) |
| Offset 3252468, 15 lines modified | Offset 3252468, 15 lines modified | ||
| 3252468 | ····0093f544·v000000000000001·v000000000000001·views·at·0093f542·for: | 3252468 | ····0093f544·v000000000000001·v000000000000001·views·at·0093f542·for: |
| 3252469 | ·············0000000000375d33·0000000000375d42·(DW_OP_reg6·(rbp)) | 3252469 | ·············0000000000375d33·0000000000375d42·(DW_OP_reg6·(rbp)) |
| 3252470 | ····0093f550·<End·of·list> | 3252470 | ····0093f550·<End·of·list> |
| 3252471 | ····0093f551·v000000000000001·v000000000000001·location·view·pair | 3252471 | ····0093f551·v000000000000001·v000000000000001·location·view·pair |
| 3252472 | ····0093f553·v000000000000001·v000000000000001·views·at·0093f551·for: | 3252472 | ····0093f553·v000000000000001·v000000000000001·views·at·0093f551·for: |
| 3252473 | ·············0000000000375d33·0000000000375d42·(DW_OP_addr:·6cc22 | 3252473 | ·············0000000000375d33·0000000000375d42·(DW_OP_addr:·6cc22c;·DW_OP_stack_value) |
| 3252474 | ····0093f568·<End·of·list> | 3252474 | ····0093f568·<End·of·list> |
| 3252475 | ····0093f569·v000000000000001·v000000000000000·location·view·pair | 3252475 | ····0093f569·v000000000000001·v000000000000000·location·view·pair |
| 3252476 | ····0093f56b·v000000000000000·v000000000000000·location·view·pair | 3252476 | ····0093f56b·v000000000000000·v000000000000000·location·view·pair |
| 3252477 | ····0093f56d·v000000000000000·v000000000000000·location·view·pair | 3252477 | ····0093f56d·v000000000000000·v000000000000000·location·view·pair |
| 3252478 | ····0093f56f·0000000000375daf·(base·address) | 3252478 | ····0093f56f·0000000000375daf·(base·address) |
| Offset 3540398, 15 lines modified | Offset 3540398, 15 lines modified | ||
| 3540398 | ····00a19bdb·v000000000000001·v000000000000001·views·at·00a19bd9·for: | 3540398 | ····00a19bdb·v000000000000001·v000000000000001·views·at·00a19bd9·for: |
| 3540399 | ·············00000000003b336c·00000000003b337b·(DW_OP_reg6·(rbp)) | 3540399 | ·············00000000003b336c·00000000003b337b·(DW_OP_reg6·(rbp)) |
| 3540400 | ····00a19be7·<End·of·list> | 3540400 | ····00a19be7·<End·of·list> |
| 3540401 | ····00a19be8·v000000000000001·v000000000000001·location·view·pair | 3540401 | ····00a19be8·v000000000000001·v000000000000001·location·view·pair |
| 3540402 | ····00a19bea·v000000000000001·v000000000000001·views·at·00a19be8·for: | 3540402 | ····00a19bea·v000000000000001·v000000000000001·views·at·00a19be8·for: |
| 3540403 | ·············00000000003b336c·00000000003b337b·(DW_OP_addr:·6cc22 | 3540403 | ·············00000000003b336c·00000000003b337b·(DW_OP_addr:·6cc22c;·DW_OP_stack_value) |
| 3540404 | ····00a19bff·<End·of·list> | 3540404 | ····00a19bff·<End·of·list> |
| 3540405 | ····00a19c00·v000000000000001·v000000000000000·location·view·pair | 3540405 | ····00a19c00·v000000000000001·v000000000000000·location·view·pair |
| 3540406 | ····00a19c02·v000000000000001·v000000000000000·views·at·00a19c00·for: | 3540406 | ····00a19c02·v000000000000001·v000000000000000·views·at·00a19c00·for: |
| 3540407 | ·············00000000003b33d4·00000000003b33df·(DW_OP_reg6·(rbp)) | 3540407 | ·············00000000003b33d4·00000000003b33df·(DW_OP_reg6·(rbp)) |
| 3540408 | ····00a19c0e·<End·of·list> | 3540408 | ····00a19c0e·<End·of·list> |
| Offset 3627256, 15 lines modified | Offset 3627256, 15 lines modified | ||
| 3627256 | ····00a5ace6·v000000000000001·v000000000000000·views·at·00a5ace4·for: | 3627256 | ····00a5ace6·v000000000000001·v000000000000000·views·at·00a5ace4·for: |
| 3627257 | ·············00000000003c8a8c·00000000003c8a93·(DW_OP_reg6·(rbp)) | 3627257 | ·············00000000003c8a8c·00000000003c8a93·(DW_OP_reg6·(rbp)) |
| 3627258 | ····00a5acf2·<End·of·list> | 3627258 | ····00a5acf2·<End·of·list> |
| 3627259 | ····00a5acf3·v000000000000001·v000000000000000·location·view·pair | 3627259 | ····00a5acf3·v000000000000001·v000000000000000·location·view·pair |
| 3627260 | ····00a5acf5·v000000000000001·v000000000000000·views·at·00a5acf3·for: | 3627260 | ····00a5acf5·v000000000000001·v000000000000000·views·at·00a5acf3·for: |
| 3627261 | ·············00000000003c8a8c·00000000003c8a93·(DW_OP_addr:·6cc11 | 3627261 | ·············00000000003c8a8c·00000000003c8a93·(DW_OP_addr:·6cc118;·DW_OP_stack_value) |
| 3627262 | ····00a5ad0a·<End·of·list> | 3627262 | ····00a5ad0a·<End·of·list> |
| 3627263 | ····00a5ad0b·v000000000000000·v000000000000000·location·view·pair | 3627263 | ····00a5ad0b·v000000000000000·v000000000000000·location·view·pair |
| 3627264 | ····00a5ad0d·v000000000000000·v000000000000000·location·view·pair | 3627264 | ····00a5ad0d·v000000000000000·v000000000000000·location·view·pair |
| 3627265 | ····00a5ad0f·v000000000000000·v000000000000000·location·view·pair | 3627265 | ····00a5ad0f·v000000000000000·v000000000000000·location·view·pair |
| 3627266 | ····00a5ad11·00000000003c8fc0·(base·address) | 3627266 | ····00a5ad11·00000000003c8fc0·(base·address) |
| Offset 3628632, 15 lines modified | Offset 3628632, 15 lines modified | ||
| 3628632 | ····00a5bbfa·v000000000000000·v000000000000000·views·at·00a5bbf8·for: | 3628632 | ····00a5bbfa·v000000000000000·v000000000000000·views·at·00a5bbf8·for: |
| 3628633 | ·············00000000003c8229·00000000003c8238·(DW_OP_reg6·(rbp)) | 3628633 | ·············00000000003c8229·00000000003c8238·(DW_OP_reg6·(rbp)) |
| 3628634 | ····00a5bc06·<End·of·list> | 3628634 | ····00a5bc06·<End·of·list> |
| 3628635 | ····00a5bc07·v000000000000000·v000000000000000·location·view·pair | 3628635 | ····00a5bc07·v000000000000000·v000000000000000·location·view·pair |
| 3628636 | ····00a5bc09·v000000000000000·v000000000000000·views·at·00a5bc07·for: | 3628636 | ····00a5bc09·v000000000000000·v000000000000000·views·at·00a5bc07·for: |
| 3628637 | ·············00000000003c8229·00000000003c8238·(DW_OP_addr:·6cc11 | 3628637 | ·············00000000003c8229·00000000003c8238·(DW_OP_addr:·6cc118;·DW_OP_stack_value) |
| 3628638 | ····00a5bc1e·<End·of·list> | 3628638 | ····00a5bc1e·<End·of·list> |
| 3628639 | ····00a5bc1f·v000000000000000·v000000000000000·location·view·pair | 3628639 | ····00a5bc1f·v000000000000000·v000000000000000·location·view·pair |
| 3628640 | ····00a5bc21·v000000000000000·v000000000000000·location·view·pair | 3628640 | ····00a5bc21·v000000000000000·v000000000000000·location·view·pair |
| 3628641 | ····00a5bc23·v000000000000000·v000000000000000·location·view·pair | 3628641 | ····00a5bc23·v000000000000000·v000000000000000·location·view·pair |
| 3628642 | ····00a5bc25·00000000003c8274·(base·address) | 3628642 | ····00a5bc25·00000000003c8274·(base·address) |
| Offset 3648885, 15 lines modified | Offset 3648885, 15 lines modified | ||
| 3648885 | ····00a6af96·v000000000000001·v000000000000001·views·at·00a6af94·for: | 3648885 | ····00a6af96·v000000000000001·v000000000000001·views·at·00a6af94·for: |
| 3648886 | ·············00000000003cd296·00000000003cd2b3·(DW_OP_fbreg:·-152) | 3648886 | ·············00000000003cd296·00000000003cd2b3·(DW_OP_fbreg:·-152) |
| 3648887 | ····00a6afa4·<End·of·list> | 3648887 | ····00a6afa4·<End·of·list> |
| 3648888 | ····00a6afa5·v000000000000001·v000000000000001·location·view·pair | 3648888 | ····00a6afa5·v000000000000001·v000000000000001·location·view·pair |
| 3648889 | ····00a6afa7·v000000000000001·v000000000000001·views·at·00a6afa5·for: | 3648889 | ····00a6afa7·v000000000000001·v000000000000001·views·at·00a6afa5·for: |
| 3648890 | ·············00000000003cd296·00000000003cd2b3·(DW_OP_addr:·6cc11 | 3648890 | ·············00000000003cd296·00000000003cd2b3·(DW_OP_addr:·6cc118;·DW_OP_stack_value) |
| 3648891 | ····00a6afbc·<End·of·list> | 3648891 | ····00a6afbc·<End·of·list> |
| 3648892 | ····00a6afbd·v000000000000000·v000000000000000·location·view·pair | 3648892 | ····00a6afbd·v000000000000000·v000000000000000·location·view·pair |
| 3648893 | ····00a6afbf·v000000000000000·v000000000000000·location·view·pair | 3648893 | ····00a6afbf·v000000000000000·v000000000000000·location·view·pair |
| 3648894 | ····00a6afc1·v000000000000000·v000000000000000·location·view·pair | 3648894 | ····00a6afc1·v000000000000000·v000000000000000·location·view·pair |
| 3648895 | ····00a6afc3·v000000000000000·v000000000000000·location·view·pair | 3648895 | ····00a6afc3·v000000000000000·v000000000000000·location·view·pair |
| 3648896 | ····00a6afc5·v000000000000000·v000000000000000·location·view·pair | 3648896 | ····00a6afc5·v000000000000000·v000000000000000·location·view·pair |
| Max diff block lines reached; 2185/8604 bytes (25.40%) of diff not shown. | |||
| Offset 1, 6449 lines modified | Offset 1, 6401 lines modified | ||
| 1 | GCC:·(Debian·14.2.0-6)·14.2.0 | 1 | GCC:·(Debian·14.2.0-6)·14.2.0 |
| 2 | AaQI%[QJe%! | 2 | AaQI%[QJe%! |
| 3 | vM-o;Z~kU | 3 | vM-o;Z~kU |
| 4 | 7808482868 | 4 | 7808482868 |
| 5 | f(OD9<S1rmY | ||
| 6 | aMMNZ-n,! | ||
| 7 | OWIz(Z]s | ||
| 8 | :G%W&yM%Wf | ||
| 9 | 5 | d"SK}&f+ | |
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