/usr/bin/diffoscope --timeout 7200 --html /srv/reproducible-results/rbuild-debian/r-b-build.f3oLyx6B/macaulay2_1.24.11+ds-3.diffoscope.html --text /srv/reproducible-results/rbuild-debian/r-b-build.f3oLyx6B/macaulay2_1.24.11+ds-3.diffoscope.txt --json /srv/reproducible-results/rbuild-debian/r-b-build.f3oLyx6B/macaulay2_1.24.11+ds-3.diffoscope.json --profile=- /srv/reproducible-results/rbuild-debian/r-b-build.f3oLyx6B/b1/macaulay2_1.24.11+ds-3_arm64.changes /srv/reproducible-results/rbuild-debian/r-b-build.f3oLyx6B/b2/macaulay2_1.24.11+ds-3

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Offset 1, 5 lines modified		Offset 1, 5 lines modified

1	·6f4df745b817f1da9bc6f0ce7ebe82fb·60416·editors·optional·elpa-macaulay2_1.24.11+ds-3_all.deb	1	·6f4df745b817f1da9bc6f0ce7ebe82fb·60416·editors·optional·elpa-macaulay2_1.24.11+ds-3_all.deb
2	·2a~~7b8~~c6721e~~b8ca42d~~67f3ac1~~b39ce7b~~·2993~~3064~~·math·optional·macaulay2-common_1.24.11+ds-3_all.deb	2	·394a58ad9c662575be0f67491d5b8099·29934192·math·optional·macaulay2-common_1.24.11+ds-3_all.deb
3	·411a6bc2bb8f8cd194bf9360feec06d9·47930132·debug·optional·macaulay2-dbgsym_1.24.11+ds-3_arm64.deb	3	·411a6bc2bb8f8cd194bf9360feec06d9·47930132·debug·optional·macaulay2-dbgsym_1.24.11+ds-3_arm64.deb
4	·16d1c356ce6be0504e9d8a949024855e·2265704·math·optional·macaulay2_1.24.11+ds-3_arm64.deb	4	·16d1c356ce6be0504e9d8a949024855e·2265704·math·optional·macaulay2_1.24.11+ds-3_arm64.deb


Offset 1, 3 lines modified		Offset 1, 3 lines modified
1	-rw-r--r--···0········0········0········4·2024-11-03·00:49:13.000000·debian-binary	1	-rw-r--r--···0········0········0········4·2024-11-03·00:49:13.000000·debian-binary
2	-rw-r--r--···0········0········0···504~~740~~·2024-11-03·00:49:13.000000·control.tar.xz	2	-rw-r--r--···0········0········0···504828·2024-11-03·00:49:13.000000·control.tar.xz
3	-rw-r--r--···0········0········0·29428132·2024-11-03·00:49:13.000000·data.tar.xz	3	-rw-r--r--···0········0········0·29429172·2024-11-03·00:49:13.000000·data.tar.xz


Offset 1, 13 lines modified		Offset 1, 13 lines modified
1	Package:·macaulay2-common	1	Package:·macaulay2-common
2	Source:·macaulay2	2	Source:·macaulay2
3	Version:·1.24.11+ds-3	3	Version:·1.24.11+ds-3
4	Architecture:·all	4	Architecture:·all
5	Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org>	5	Maintainer:·Debian·Math·Team·<team+math@tracker.debian.org>
6	Installed-Size:·287448	6	Installed-Size:·287442
7	Depends:·fonts-glyphicons-halflings·(>=·1.009~3.4.1+dfsg),·fonts-katex·(>=·0.16.10+~cs6.1.0),·libjs-bootsidemenu·(>=·1.0.0),·libjs-bootstrap·(>=·3.4.1+dfsg),·libjs-d3·(>=·3.5.17),·libjs-jquery·(>=·3.6.1+dfsg+~3.5.14),·libjs-katex·(>=·0.16.10+~cs6.1.0),·libjs-nouislider·(>=·15.8.1+ds),·libjs-three·(>=·111+dfsg1),·node-clipboard·(>=·2.0.11+ds+~cs9.6.11)	7	Depends:·fonts-glyphicons-halflings·(>=·1.009~3.4.1+dfsg),·fonts-katex·(>=·0.16.10+~cs6.1.0),·libjs-bootsidemenu·(>=·1.0.0),·libjs-bootstrap·(>=·3.4.1+dfsg),·libjs-d3·(>=·3.5.17),·libjs-jquery·(>=·3.6.1+dfsg+~3.5.14),·libjs-katex·(>=·0.16.10+~cs6.1.0),·libjs-nouislider·(>=·15.8.1+ds),·libjs-three·(>=·111+dfsg1),·node-clipboard·(>=·2.0.11+ds+~cs9.6.11)
8	Section:·math	8	Section:·math
9	Priority:·optional	9	Priority:·optional
10	Multi-Arch:·foreign	10	Multi-Arch:·foreign
11	Homepage:·http://macaulay2.com	11	Homepage:·http://macaulay2.com
12	Description:·Software·system·for·algebraic·geometry·research·(common·files)	12	Description:·Software·system·for·algebraic·geometry·research·(common·files)
13	·Macaulay·2·is·a·software·system·for·algebraic·geometry·research,·written·by	13	·Macaulay·2·is·a·software·system·for·algebraic·geometry·research,·written·by


Offset 1, 11 lines modified		Offset 1, 11 lines modified
1	#·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sat·Nov··2·12:49:13·2024	1	#·GDBM·dump·file·created·by·GDBM·version·1.24.·02/07/2024·on·Sun·Nov··3·14:49:13·2024
2	#:version=1.1	2	#:version=1.1
3	#:file=rawdocumentation-dcba-8.db	3	#:file=rawdocumentation-dcba-8.db
4	#:uid=~~1111~~,user=pbuilder1,gid=~~1111~~,group=pbuilder1,mode=644	4	#:uid=2222,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	bWFrZURpYWdvbmFsRm9ybQ==	8	bWFrZURpYWdvbmFsRm9ybQ==
9	#:len=2204	9	#:len=2204
10	bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIEdyb3RoZW5kaWVjay1XaXR0IGNs	10	bmV3IEhhc2hUYWJsZSBmcm9tIHtIZWFkbGluZSA9PiAidGhlIEdyb3RoZW5kaWVjay1XaXR0IGNs
11	YXNzIG9mIGEgZGlhZ29uYWwgZm9ybSIsICJsaW5lbnVtIiA9PiAyNSwgSW5wdXRzID0+IHtTUEFO	11	YXNzIG9mIGEgZGlhZ29uYWwgZm9ybSIsICJsaW5lbnVtIiA9PiAyNSwgSW5wdXRzID0+IHtTUEFO


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	·--·3.7656s·elapsed	14	·--·4.86357s·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	·--·4.~~61979~~s·elapsed	21	·--·5.95406s·elapsed

22	······1······3······9······27······81······243······729······2187	22	······1······3······9······27······81······243······729······2187
23	o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R	23	o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
24	·····························································	24	·····························································
25	·····0······1······2······3·······4·······5········6········7	25	·····0······1······2······3·······4·······5········6········7

26	o4·:·Complex	26	o4·:·Complex


Offset 86, 26 lines modified		Offset 86, 26 lines modified
86	o2·=·cokernel·\|·a·b·c·\|	86	o2·=·cokernel·\|·a·b·c·\|

87	····························1	87	····························1
88	o2·:·R-module,·quotient·of·R</code></pre>	88	o2·:·R-module,·quotient·of·R</code></pre>
89	</td>··········</tr>	89	</td>··········</tr>
90	··········<tr>	90	··········<tr>
91	<td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)	91	<td>··············<pre><code·class="language-macaulay2">i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)
92	·--·3.7656s·elapsed	92	·--·4.86357s·elapsed

93	······1······3······9······27······81······243······729······2187	93	······1······3······9······27······81······243······729······2187
94	o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R	94	o3·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
95	·····························································	95	·····························································
96	·····0······1······2······3·······4·······5········6········7	96	·····0······1······2······3·······4·······5········6········7

97	o3·:·Complex</code></pre>	97	o3·:·Complex</code></pre>
98	</td>··········</tr>	98	</td>··········</tr>
99	··········<tr>	99	··········<tr>
100	<td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)	100	<td>··············<pre><code·class="language-macaulay2">i4·:·elapsedTime·burkeResolution(M,·7,·Check·=>·true)
101	·--·4.~~61979~~s·elapsed	101	·--·5.95406s·elapsed

102	······1······3······9······27······81······243······729······2187	102	······1······3······9······27······81······243······729······2187
103	o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R	103	o4·=·R··<--·R··<--·R··<--·R···<--·R···<--·R····<--·R····<--·R
104	·····························································	104	·····························································
105	·····0······1······2······3·······4·······5········6········7	105	·····0······1······2······3·······4·······5········6········7

106	o4·:·Complex</code></pre>	106	o4·:·Complex</code></pre>


Offset 24, 24 lines modified		Offset 24, 24 lines modified
24	i2·:·M·=·coker·vars·R	24	i2·:·M·=·coker·vars·R

25	o2·=·cokernel·\|·a·b·c·\|	25	o2·=·cokernel·\|·a·b·c·\|

26	····························1	26	····························1
27	o2·:·R-module,·quotient·of·R	27	o2·:·R-module,·quotient·of·R
28	i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)	28	i3·:·elapsedTime·burkeResolution(M,·7,·Check·=>·false)
29	·--·3.7656s·elapsed	29	·--·4.86357s·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	·--·4.~~61979~~s·elapsed	35	·--·5.95406s·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, 15 lines modified		Offset 1, 16 lines modified
1	--·--·M2-comint·--·hash:·6456613336951100320	1	--·--·M2-comint·--·hash:·6456613336951100320

2	i1·:·setRandomSeed(currentTime());	2	i1·:·setRandomSeed(currentTime());

3	i2·:·K·=·randomAbstractSimplicialComplex(4)	3	i2·:·K·=·randomAbstractSimplicialComplex(4)

4	o2·=·AbstractSimplicialComplex{-1·=>·{{}}}	4	o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
5	·······························0·=>·{{1}}	5	·······························0·=>·{{1},·{2}}
		6	·······························1·=>·{{1,·2}}

6	o2·:·AbstractSimplicialComplex	7	o2·:·AbstractSimplicialComplex

7	i3·:·prune·HH·simplicialChainComplex·K	8	i3·:·prune·HH·simplicialChainComplex·K

8	·······1	9	·······1
9	o3·=·ZZ	10	o3·=·ZZ
Offset 18, 17 lines modified		Offset 19, 18 lines modified

18	o3·:·Complex	19	o3·:·Complex

19	i4·:·setRandomSeed(currentTime());	20	i4·:·setRandomSeed(currentTime());

20	i5·:·L·=·randomAbstractSimplicialComplex(6,3)	21	i5·:·L·=·randomAbstractSimplicialComplex(6,3)

21	o5·=·AbstractSimplicialComplex{-1·=>·{{}}·····}	22	o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
22	·······························0·=>·{{1},·{5}}	23	·······························0·=>·{{1},·{2},·{3}}
		24	·······························1·=>·{{1,·2},·{1,·3},·{2,·3}}
23	·······························1·=>·{{1,·5}}	25	·······························2·=>·{{1,·2,·3}}

24	o5·:·AbstractSimplicialComplex	26	o5·:·AbstractSimplicialComplex

25	i6·:·prune·HH·simplicialChainComplex·L	27	i6·:·prune·HH·simplicialChainComplex·L

26	·······1	28	·······1
27	o6·=·ZZ	29	o6·=·ZZ
Offset 37, 45 lines modified		Offset 39, 55 lines modified

37	o6·:·Complex	39	o6·:·Complex

38	i7·:·setRandomSeed(currentTime());	40	i7·:·setRandomSeed(currentTime());

39	i8·:·M·=·randomAbstractSimplicialComplex(6,3,2)	41	i8·:·M·=·randomAbstractSimplicialComplex(6,3,2)

40	o8·=·AbstractSimplicialComplex{-1·=>·{{}}···················································~~················~~}	42	o8·=·AbstractSimplicialComplex{-1·=>·{{}}···················································}
41	·······························0·=>·{{1},·{2},·{3},·{4},·{~~5},·{~~6}}	43	·······························0·=>·{{1},·{2},·{3},·{4},·{6}}
42	·······························1·=>·{{1,·4},·{1,·6},·{2,·3},·{2,·4},·{2,·5},·{2,·6},·{3,·6},·{4,·5},·{4,·6}}
43	·······························2·=>·{{1,·4,·6},·{2,·3,·6},·{2,·4,·5}}	44	·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{1,·6},·{2,·3},·{2,·4},·{2,·6}}
		45	·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·2,·6}}

44	o8·:·AbstractSimplicialComplex	46	o8·:·AbstractSimplicialComplex

45	i9·:·prune·HH·simplicialChainComplex·M	47	i9·:·prune·HH·simplicialChainComplex·M

46	·······1·······1
47	o9·=·ZZ··<--·ZZ
48	··············
49	·····~~0·····~~··1	48	·······1
		49	o9·=·ZZ
		50	······
		51	·····0

50	o9·:·Complex	52	o9·:·Complex

51	i10·:·setRandomSeed(currentTime());	53	i10·:·setRandomSeed(currentTime());

52	i11·:·K·=·randomAbstractSimplicialComplex(4)	54	i11·:·K·=·randomAbstractSimplicialComplex(4)

53	o11·=·AbstractSimplicialComplex{-1·=>·{{}}}	55	o11·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
54	································0·=>·{{1}}	56	································0·=>·{{1},·{2}}
		57	································1·=>·{{1,·2}}

55	o11·:·AbstractSimplicialComplex	58	o11·:·AbstractSimplicialComplex

56	i12·:·J·=·randomSubSimplicialComplex(K)	59	i12·:·J·=·randomSubSimplicialComplex(K)

57	o12·=·AbstractSimplicialComplex{-1·=>·{{}}}	60	o12·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
		61	································0·=>·{{1},·{2}}
		62	································1·=>·{{1,·2}}

58	o12·:·AbstractSimplicialComplex	63	o12·:·AbstractSimplicialComplex

59	i13·:·inducedSimplicialChainComplexMap(K,J)	64	i13·:·inducedSimplicialChainComplexMap(K,J)

60	~~o13~~·=·0	65	············2················2
		66	o13·=·0·:·ZZ··<-----------·ZZ··:·0
		67	·················\|·1·0·\|
		68	·················\|·0·1·\|

		69	············1··············1
		70	······1·:·ZZ··<---------·ZZ··:·1
		71	·················\|·1·\|

61	o13·:·ComplexMap	72	o13·:·ComplexMap

62	i14·:·	73	i14·:·


Offset 1, 18 lines modified		Offset 1, 17 lines modified
1	--·--·M2-comint·--·hash:·9222441599761629245	1	--·--·M2-comint·--·hash:·9222441599761629245

2	i1·:·setRandomSeed(currentTime());	2	i1·:·setRandomSeed(currentTime());

3	i2·:·K·=·randomAbstractSimplicialComplex(4)	3	i2·:·K·=·randomAbstractSimplicialComplex(4)

4	o2·=·AbstractSimplicialComplex{-1·=>·{{}}···················~~························~~}	4	o2·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
5	·······························0·=>·{{1},·{2},·{~~3},·{~~4}}	5	·······························0·=>·{{1},·{2},·{4}}
6	·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}}
7	·······························2·=>·{{~~1,·2,·3},·~~{1,·2~~,·4~~},·{1~~,·3~~,·4},·{2~~,·3~~,·4}}	6	·······························1·=>·{{1,·2},·{1,·4},·{2,·4}}
8	·······························3·=>·{{1,·2~~,·3~~,·4}}	7	·······························2·=>·{{1,·2,·4}}

9	o2·:·AbstractSimplicialComplex	8	o2·:·AbstractSimplicialComplex

10	i3·:·setRandomSeed(currentTime());	9	i3·:·setRandomSeed(currentTime());

11	i4·:·L·=·randomAbstractSimplicialComplex(6,3)	10	i4·:·L·=·randomAbstractSimplicialComplex(6,3)

Offset 23, 15 lines modified		Offset 22, 15 lines modified

23	o4·:·AbstractSimplicialComplex	22	o4·:·AbstractSimplicialComplex

24	i5·:·setRandomSeed(currentTime());	23	i5·:·setRandomSeed(currentTime());

25	i6·:·M·=·randomAbstractSimplicialComplex(6,3,2)	24	i6·:·M·=·randomAbstractSimplicialComplex(6,3,2)

26	o6·=·AbstractSimplicialComplex{-1·=>·{{}}···········································~~········~~}	25	o6·=·AbstractSimplicialComplex{-1·=>·{{}}···········································}
27	·······························0·=>·{{1},·{3},·{4},·{~~5},·{~~6}}	26	·······························0·=>·{{1},·{3},·{4},·{6}}
28	·······························1·=>·{{1,·3},·{1,·4},·{1,·~~5},·{1,·~~6},·{3,·4},·{4,·5},·{4,·6}}	27	·······························1·=>·{{1,·3},·{1,·4},·{1,·6},·{3,·4},·{3,·6},·{4,·6}}
29	·······························2·=>·{{1,·3,·4},·{1,·4,·5},·{1,·4,·6}}	28	·······························2·=>·{{1,·3,·4},·{1,·3,·6},·{1,·4,·6}}

30	o6·:·AbstractSimplicialComplex	29	o6·:·AbstractSimplicialComplex

31	i7·:·	30	i7·:·


Offset 1, 18 lines modified		Offset 1, 20 lines modified
1	--·--·M2-comint·--·hash:·13473104809235542297	1	--·--·M2-comint·--·hash:·13473104809235542297

2	i1·:·setRandomSeed(currentTime());	2	i1·:·setRandomSeed(currentTime());

3	i2·:·K·=·randomAbstractSimplicialComplex(4)	3	i2·:·K·=·randomAbstractSimplicialComplex(4)

4	o2·=·AbstractSimplicialComplex{-1·=>·{{}}}	4	o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
5	·······························0·=>·{{1}}	5	·······························0·=>·{{1},·{3}}
		6	·······························1·=>·{{1,·3}}

6	o2·:·AbstractSimplicialComplex	7	o2·:·AbstractSimplicialComplex

7	i3·:·J·=·randomSubSimplicialComplex(K)	8	i3·:·J·=·randomSubSimplicialComplex(K)

8	o3·=·AbstractSimplicialComplex{-1·=>·{{}}}	9	o3·=·AbstractSimplicialComplex{-1·=>·{{}}}
		10	·······························0·=>·{{1}}

9	o3·:·AbstractSimplicialComplex	11	o3·:·AbstractSimplicialComplex

10	i4·:·	12	i4·:·


Offset 52, 16 lines modified		Offset 52, 17 lines modified
52	········<table·class="examples">	52	········<table·class="examples">
53	··········<tr>	53	··········<tr>
54	<td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre>	54	<td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre>
55	</td>··········</tr>	55	</td>··········</tr>
56	··········<tr>	56	··········<tr>
57	<td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4)	57	<td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4)

58	o2·=·AbstractSimplicialComplex{-1·=>·{{}}}	58	o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
59	·······························0·=>·{{1}}	59	·······························0·=>·{{1},·{2}}
		60	·······························1·=>·{{1,·2}}

60	o2·:·AbstractSimplicialComplex</code></pre>	61	o2·:·AbstractSimplicialComplex</code></pre>
61	</td>··········</tr>	62	</td>··········</tr>
62	··········<tr>	63	··········<tr>
63	<td>··············<pre><code·class="language-macaulay2">i3·:·prune·HH·simplicialChainComplex·K	64	<td>··············<pre><code·class="language-macaulay2">i3·:·prune·HH·simplicialChainComplex·K

64	·······1	65	·······1
Offset 78, 17 lines modified		Offset 79, 18 lines modified
78	········<table·class="examples">	79	········<table·class="examples">
79	··········<tr>	80	··········<tr>
80	<td>··············<pre><code·class="language-macaulay2">i4·:·setRandomSeed(currentTime());</code></pre>	81	<td>··············<pre><code·class="language-macaulay2">i4·:·setRandomSeed(currentTime());</code></pre>
81	</td>··········</tr>	82	</td>··········</tr>
82	··········<tr>	83	··········<tr>
83	<td>··············<pre><code·class="language-macaulay2">i5·:·L·=·randomAbstractSimplicialComplex(6,3)	84	<td>··············<pre><code·class="language-macaulay2">i5·:·L·=·randomAbstractSimplicialComplex(6,3)

84	o5·=·AbstractSimplicialComplex{-1·=>·{{}}·····}	85	o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
85	·······························0·=>·{{1},·{5}}	86	·······························0·=>·{{1},·{2},·{3}}
		87	·······························1·=>·{{1,·2},·{1,·3},·{2,·3}}
86	·······························1·=>·{{1,·5}}	88	·······························2·=>·{{1,·2,·3}}

87	o5·:·AbstractSimplicialComplex</code></pre>	89	o5·:·AbstractSimplicialComplex</code></pre>
88	</td>··········</tr>	90	</td>··········</tr>
89	··········<tr>	91	··········<tr>
90	<td>··············<pre><code·class="language-macaulay2">i6·:·prune·HH·simplicialChainComplex·L	92	<td>··············<pre><code·class="language-macaulay2">i6·:·prune·HH·simplicialChainComplex·L

91	·······1	93	·······1
Offset 105, 58 lines modified		Offset 107, 68 lines modified
105	········<table·class="examples">	107	········<table·class="examples">
106	··········<tr>	108	··········<tr>
107	<td>··············<pre><code·class="language-macaulay2">i7·:·setRandomSeed(currentTime());</code></pre>	109	<td>··············<pre><code·class="language-macaulay2">i7·:·setRandomSeed(currentTime());</code></pre>
108	</td>··········</tr>	110	</td>··········</tr>
109	··········<tr>	111	··········<tr>
110	<td>··············<pre><code·class="language-macaulay2">i8·:·M·=·randomAbstractSimplicialComplex(6,3,2)	112	<td>··············<pre><code·class="language-macaulay2">i8·:·M·=·randomAbstractSimplicialComplex(6,3,2)

111	o8·=·AbstractSimplicialComplex{-1·=>·{{}}···················································~~················~~}	113	o8·=·AbstractSimplicialComplex{-1·=>·{{}}···················································}
112	·······························0·=>·{{1},·{2},·{3},·{4},·{~~5},·{~~6}}	114	·······························0·=>·{{1},·{2},·{3},·{4},·{6}}
113	·······························1·=>·{{1,·4},·{1,·6},·{2,·3},·{2,·4},·{2,·5},·{2,·6},·{3,·6},·{4,·5},·{4,·6}}
114	·······························2·=>·{{1,·4,·6},·{2,·3,·6},·{2,·4,·5}}	115	·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{1,·6},·{2,·3},·{2,·4},·{2,·6}}
		116	·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·2,·6}}

115	o8·:·AbstractSimplicialComplex</code></pre>	117	o8·:·AbstractSimplicialComplex</code></pre>
116	</td>··········</tr>	118	</td>··········</tr>
117	··········<tr>	119	··········<tr>
118	<td>··············<pre><code·class="language-macaulay2">i9·:·prune·HH·simplicialChainComplex·M	120	<td>··············<pre><code·class="language-macaulay2">i9·:·prune·HH·simplicialChainComplex·M

119	·······1·······1
120	o9·=·ZZ··<--·ZZ
121	··············
122	·····~~0·····~~··1	121	·······1
		122	o9·=·ZZ
		123	······
		124	·····0

123	o9·:·Complex</code></pre>	125	o9·:·Complex</code></pre>
124	</td>··········</tr>	126	</td>··········</tr>
125	········</table>	127	········</table>
126	········<div>	128	········<div>
127	··········<p>Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex.</p>	129	··········<p>Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex.</p>
128	········</div>	130	········</div>
129	········<table·class="examples">	131	········<table·class="examples">
130	··········<tr>	132	··········<tr>
131	<td>··············<pre><code·class="language-macaulay2">i10·:·setRandomSeed(currentTime());</code></pre>	133	<td>··············<pre><code·class="language-macaulay2">i10·:·setRandomSeed(currentTime());</code></pre>
132	</td>··········</tr>	134	</td>··········</tr>
133	··········<tr>	135	··········<tr>
134	<td>··············<pre><code·class="language-macaulay2">i11·:·K·=·randomAbstractSimplicialComplex(4)	136	<td>··············<pre><code·class="language-macaulay2">i11·:·K·=·randomAbstractSimplicialComplex(4)

135	o11·=·AbstractSimplicialComplex{-1·=>·{{}}}	137	o11·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
136	································0·=>·{{1}}	138	································0·=>·{{1},·{2}}
		139	································1·=>·{{1,·2}}

137	o11·:·AbstractSimplicialComplex</code></pre>	140	o11·:·AbstractSimplicialComplex</code></pre>
138	</td>··········</tr>	141	</td>··········</tr>
139	··········<tr>	142	··········<tr>
140	<td>··············<pre><code·class="language-macaulay2">i12·:·J·=·randomSubSimplicialComplex(K)	143	<td>··············<pre><code·class="language-macaulay2">i12·:·J·=·randomSubSimplicialComplex(K)

141	o12·=·AbstractSimplicialComplex{-1·=>·{{}}}	144	o12·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
		145	································0·=>·{{1},·{2}}
		146	································1·=>·{{1,·2}}

142	o12·:·AbstractSimplicialComplex</code></pre>	147	o12·:·AbstractSimplicialComplex</code></pre>
143	</td>··········</tr>	148	</td>··········</tr>
144	··········<tr>	149	··········<tr>
145	<td>··············<pre><code·class="language-macaulay2">i13·:·inducedSimplicialChainComplexMap(K,J)	150	<td>··············<pre><code·class="language-macaulay2">i13·:·inducedSimplicialChainComplexMap(K,J)

146	~~o13~~·=·0	151	············2················2
		152	o13·=·0·:·ZZ··<-----------·ZZ··:·0
		153	·················\|·1·0·\|
		154	·················\|·0·1·\|

		155	············1··············1
		156	······1·:·ZZ··<---------·ZZ··:·1
		157	·················\|·1·\|

147	o13·:·ComplexMap</code></pre>	158	o13·:·ComplexMap</code></pre>
148	</td>··········</tr>	159	</td>··········</tr>
149	········</table>	160	········</table>
150	······</div>	161	······</div>
151	····</div>	162	····</div>
152	··</body>	163	··</body>


Offset 9, 33 lines modified		Offset 9, 35 lines modified
9	In·what·follows·we·illustrate·a·collection·of·homological·calculations·that·can	9	In·what·follows·we·illustrate·a·collection·of·homological·calculations·that·can
10	be·performed·on·random·simplicial·complexes.	10	be·performed·on·random·simplicial·complexes.
11	Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset	11	Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset
12	of·[n]·=·{1,...,n}.	12	of·[n]·=·{1,...,n}.
13	i1·:·setRandomSeed(currentTime());	13	i1·:·setRandomSeed(currentTime());
14	i2·:·K·=·randomAbstractSimplicialComplex(4)	14	i2·:·K·=·randomAbstractSimplicialComplex(4)

15	o2·=·AbstractSimplicialComplex{-1·=>·{{}}}	15	o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
16	·······························0·=>·{{1}}	16	·······························0·=>·{{1},·{2}}
		17	·······························1·=>·{{1,·2}}

17	o2·:·AbstractSimplicialComplex	18	o2·:·AbstractSimplicialComplex
18	i3·:·prune·HH·simplicialChainComplex·K	19	i3·:·prune·HH·simplicialChainComplex·K

19	·······1	20	·······1
20	o3·=·ZZ	21	o3·=·ZZ

21	·····0	22	·····0

22	o3·:·Complex	23	o3·:·Complex
23	Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.	24	Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.
24	i4·:·setRandomSeed(currentTime());	25	i4·:·setRandomSeed(currentTime());
25	i5·:·L·=·randomAbstractSimplicialComplex(6,3)	26	i5·:·L·=·randomAbstractSimplicialComplex(6,3)

26	o5·=·AbstractSimplicialComplex{-1·=>·{{}}·····}	27	o5·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
27	·······························0·=>·{{1},·{5}}	28	·······························0·=>·{{1},·{2},·{3}}
		29	·······························1·=>·{{1,·2},·{1,·3},·{2,·3}}
28	·······························1·=>·{{1,·5}}	30	·······························2·=>·{{1,·2,·3}}

29	o5·:·AbstractSimplicialComplex	31	o5·:·AbstractSimplicialComplex
30	i6·:·prune·HH·simplicialChainComplex·L	32	i6·:·prune·HH·simplicialChainComplex·L

31	·······1	33	·······1
32	o6·=·ZZ	34	o6·=·ZZ

Offset 46, 39 lines modified		Offset 48, 49 lines modified
46	1)-skeleton,·and·has·exactly·m·dimension·d·faces,·chosen·at·random·from·all	48	1)-skeleton,·and·has·exactly·m·dimension·d·faces,·chosen·at·random·from·all
47	binomial(binomial(n,d+1),m)·possibilities.	49	binomial(binomial(n,d+1),m)·possibilities.
48	i7·:·setRandomSeed(currentTime());	50	i7·:·setRandomSeed(currentTime());
49	i8·:·M·=·randomAbstractSimplicialComplex(6,3,2)	51	i8·:·M·=·randomAbstractSimplicialComplex(6,3,2)

50	o8·=·AbstractSimplicialComplex{-1·=>·{{}}	52	o8·=·AbstractSimplicialComplex{-1·=>·{{}}
51	}	53	}
52	·······························0·=>·{{1},·{2},·{3},·{4},·{~~5},·{~~6}}	54	·······························0·=>·{{1},·{2},·{3},·{4},·{6}}
53	·······························1·=>·{{1,·4},·{1,·6},·{2,·3},·{2,·4},·{2,·5},	55	·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{1,·6},·{2,·3},
54	{2,·6},·{3,·6},·{4,·5},·{4,·6}}
55	~~·······························2·=>·{~~{1,·4~~,·6~~},·{2~~,·3~~,·6~~},·{2,·4,·5~~}}	56	{2,·4},·{2,·6}}
		57	·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·2,·6}}

56	o8·:·AbstractSimplicialComplex	58	o8·:·AbstractSimplicialComplex
57	i9·:·prune·HH·simplicialChainComplex·M	59	i9·:·prune·HH·simplicialChainComplex·M

58	·······1·······1
59	o9·=·ZZ··<--·ZZ	60	·······1
		61	o9·=·ZZ

60	·····0~~·······1~~	62	·····0

61	o9·:·Complex	63	o9·:·Complex
62	Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex.	64	Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex.
63	i10·:·setRandomSeed(currentTime());	65	i10·:·setRandomSeed(currentTime());
64	i11·:·K·=·randomAbstractSimplicialComplex(4)	66	i11·:·K·=·randomAbstractSimplicialComplex(4)

65	o11·=·AbstractSimplicialComplex{-1·=>·{{}}}	67	o11·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
66	································0·=>·{{1}}	68	································0·=>·{{1},·{2}}
		69	································1·=>·{{1,·2}}

67	o11·:·AbstractSimplicialComplex	70	o11·:·AbstractSimplicialComplex
68	i12·:·J·=·randomSubSimplicialComplex(K)	71	i12·:·J·=·randomSubSimplicialComplex(K)

69	o12·=·AbstractSimplicialComplex{-1·=>·{{}}}	72	o12·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
		73	································0·=>·{{1},·{2}}
		74	································1·=>·{{1,·2}}

70	o12·:·AbstractSimplicialComplex	75	o12·:·AbstractSimplicialComplex
71	i13·:·inducedSimplicialChainComplexMap(K,J)	76	i13·:·inducedSimplicialChainComplexMap(K,J)

72	~~o13~~·=·0	77	············2················2
		78	o13·=·0·:·ZZ··<-----------·ZZ··:·0
		79	·················\|·1·0·\|
		80	·················\|·0·1·\|

		81	············1··············1
		82	······1·:·ZZ··<---------·ZZ··:·1
		83	·················\|·1·\|

73	o13·:·ComplexMap	84	o13·:·ComplexMap


Offset 50, 19 lines modified		Offset 50, 18 lines modified
50	········<table·class="examples">	50	········<table·class="examples">
51	··········<tr>	51	··········<tr>
52	<td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre>	52	<td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre>
53	</td>··········</tr>	53	</td>··········</tr>
54	··········<tr>	54	··········<tr>
55	<td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4)	55	<td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4)

56	o2·=·AbstractSimplicialComplex{-1·=>·{{}}···················~~························~~}	56	o2·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
57	·······························0·=>·{{1},·{2},·{~~3},·{~~4}}	57	·······························0·=>·{{1},·{2},·{4}}
58	·······························1·=>·{{1,·2},·{1,·3},·{1,·4},·{2,·3},·{2,·4},·{3,·4}}
59	·······························2·=>·{{~~1,·2,·3},·~~{1,·2~~,·4~~},·{1~~,·3~~,·4},·{2~~,·3~~,·4}}	58	·······························1·=>·{{1,·2},·{1,·4},·{2,·4}}
60	·······························3·=>·{{1,·2~~,·3~~,·4}}	59	·······························2·=>·{{1,·2,·4}}

61	o2·:·AbstractSimplicialComplex</code></pre>	60	o2·:·AbstractSimplicialComplex</code></pre>
62	</td>··········</tr>	61	</td>··········</tr>
63	········</table>	62	········</table>
64	········<div>	63	········<div>
65	··········<p>Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.</p>	64	··········<p>Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.</p>
66	········</div>	65	········</div>
Offset 87, 18 lines modified		Offset 86, 18 lines modified
87	········<table·class="examples">	86	········<table·class="examples">
88	··········<tr>	87	··········<tr>
89	<td>··············<pre><code·class="language-macaulay2">i5·:·setRandomSeed(currentTime());</code></pre>	88	<td>··············<pre><code·class="language-macaulay2">i5·:·setRandomSeed(currentTime());</code></pre>
90	</td>··········</tr>	89	</td>··········</tr>
91	··········<tr>	90	··········<tr>
92	<td>··············<pre><code·class="language-macaulay2">i6·:·M·=·randomAbstractSimplicialComplex(6,3,2)	91	<td>··············<pre><code·class="language-macaulay2">i6·:·M·=·randomAbstractSimplicialComplex(6,3,2)

93	o6·=·AbstractSimplicialComplex{-1·=>·{{}}···········································~~········~~}	92	o6·=·AbstractSimplicialComplex{-1·=>·{{}}···········································}
94	·······························0·=>·{{1},·{3},·{4},·{~~5},·{~~6}}	93	·······························0·=>·{{1},·{3},·{4},·{6}}
95	·······························1·=>·{{1,·3},·{1,·4},·{1,·~~5},·{1,·~~6},·{3,·4},·{4,·5},·{4,·6}}	94	·······························1·=>·{{1,·3},·{1,·4},·{1,·6},·{3,·4},·{3,·6},·{4,·6}}
96	·······························2·=>·{{1,·3,·4},·{1,·4,·5},·{1,·4,·6}}	95	·······························2·=>·{{1,·3,·4},·{1,·3,·6},·{1,·4,·6}}

97	o6·:·AbstractSimplicialComplex</code></pre>	96	o6·:·AbstractSimplicialComplex</code></pre>
98	</td>··········</tr>	97	</td>··········</tr>
99	········</table>	98	········</table>
100	······</div>	99	······</div>
101	······<div>	100	······<div>
102	········<h2>See·also</h2>	101	········<h2>See·also</h2>


Offset 6, 22 lines modified		Offset 6, 18 lines modified
6	\x8\x8\x8\x8\x8\x8·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·s\x8se\x8et\x8t·\x8\x8\x8\x8\x8\x8	6	\x8\x8\x8\x8\x8\x8·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·s\x8se\x8et\x8t·\x8\x8\x8\x8\x8\x8
7	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8	7	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8
8	Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset	8	Create·a·random·abstract·simplicial·complex·with·vertices·supported·on·a·subset
9	of·[n]·=·{1,...,n}.	9	of·[n]·=·{1,...,n}.
10	i1·:·setRandomSeed(currentTime());	10	i1·:·setRandomSeed(currentTime());
11	i2·:·K·=·randomAbstractSimplicialComplex(4)	11	i2·:·K·=·randomAbstractSimplicialComplex(4)

12	o2·=·AbstractSimplicialComplex{-1·=>·{{}}	12	o2·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
13	}
14	·······························0·=>·{{1},·{2},·{~~3},·{~~4}}	13	·······························0·=>·{{1},·{2},·{4}}
15	·······························1·=>·{{1,·2},·{1,·~~3},·{1,·~~4~~},·{2,·3~~},·{2,·4},	14	·······························1·=>·{{1,·2},·{1,·4},·{2,·4}}
16	{3,·4}}
17	·······························2·=>·{{1,·2,·3},·{1,·2,·4},·{1,·3,·4},·{2,·3,
18	4}}
19	·······························3·=>·{{1,·2~~,·3~~,·4}}	15	·······························2·=>·{{1,·2,·4}}

20	o2·:·AbstractSimplicialComplex	16	o2·:·AbstractSimplicialComplex
21	Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.	17	Create·a·random·simplicial·complex·on·[n]·with·dimension·at·most·equal·to·r.
22	i3·:·setRandomSeed(currentTime());	18	i3·:·setRandomSeed(currentTime());
23	i4·:·L·=·randomAbstractSimplicialComplex(6,3)	19	i4·:·L·=·randomAbstractSimplicialComplex(6,3)

24	o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················}	20	o4·=·AbstractSimplicialComplex{-1·=>·{{}}···················}
Offset 34, 18 lines modified		Offset 30, 18 lines modified
34	1)-skeleton,·and·has·exactly·m·d-dimensional·faces,·chosen·at·random·from·all	30	1)-skeleton,·and·has·exactly·m·d-dimensional·faces,·chosen·at·random·from·all
35	binomial(binomial(n,d+1),m)·possibilities.	31	binomial(binomial(n,d+1),m)·possibilities.
36	i5·:·setRandomSeed(currentTime());	32	i5·:·setRandomSeed(currentTime());
37	i6·:·M·=·randomAbstractSimplicialComplex(6,3,2)	33	i6·:·M·=·randomAbstractSimplicialComplex(6,3,2)

38	o6·=·AbstractSimplicialComplex{-1·=>·{{}}	34	o6·=·AbstractSimplicialComplex{-1·=>·{{}}
39	}	35	}
40	·······························0·=>·{{1},·{3},·{4},·{~~5},·{~~6}}	36	·······························0·=>·{{1},·{3},·{4},·{6}}
41	·······························1·=>·{{1,·3},·{1,·4},·{1,·5},·{1,·6},·{3,·4},	37	·······························1·=>·{{1,·3},·{1,·4},·{1,·6},·{3,·4},·{3,·6},
42	{4,·~~5},·{4,·~~6}}	38	{4,·6}}
43	·······························2·=>·{{1,·3,·4},·{1,·4,·5},·{1,·4,·6}}	39	·······························2·=>·{{1,·3,·4},·{1,·3,·6},·{1,·4,·6}}

44	o6·:·AbstractSimplicialComplex	40	o6·:·AbstractSimplicialComplex
45	\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
46	····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·--·get·a·random·object	42	····*·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m·--·get·a·random·object
47	····*·randomSquareFreeMonomialIdeal·(missing·documentation)	43	····*·randomSquareFreeMonomialIdeal·(missing·documentation)
48	\x8\x8\x8\x8\x8·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·\x8\x8\x8\x8\x8	44	\x8\x8\x8\x8\x8·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mA\x8Ab\x8bs\x8st\x8tr\x8ra\x8ac\x8ct\x8tS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·\x8\x8\x8\x8\x8
49	····*·randomAbstractSimplicialComplex(ZZ)	45	····*·randomAbstractSimplicialComplex(ZZ)


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2788	-rw-r--r--···0·root·········(0)·root·········(0)·····9985·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_extract__Blocks.html	2788	-rw-r--r--···0·root·········(0)·root·········(0)·····9985·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_extract__Blocks.html
2789	-rw-r--r--···0·root·········(0)·root·········(0)·····8942·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_golod__Betti.html	2789	-rw-r--r--···0·root·········(0)·root·········(0)·····8942·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_golod__Betti.html
2790	-rw-r--r--···0·root·········(0)·root·········(0)·····5836·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_has__Minimal__Mult.html	2790	-rw-r--r--···0·root·········(0)·root·········(0)·····5836·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_has__Minimal__Mult.html
2791	-rw-r--r--···0·root·········(0)·root·········(0)·····6125·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_is__Golod__A__Inf.html	2791	-rw-r--r--···0·root·········(0)·root·········(0)·····6125·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/_is__Golod__A__Inf.html
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2795	-rw-r--r--···0·root·········(0)·root·········(0)·····5118·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/toc.html	2795	-rw-r--r--···0·root·········(0)·root·········(0)·····5118·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AInfinity/html/toc.html
2796	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/	2796	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/
2797	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/dump/	2797	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/dump/
2798	-rw-r--r--···0·root·········(0)·root·········(0)····37715·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/dump/rawdocumentation.dump	2798	-rw-r--r--···0·root·········(0)·root·········(0)····37715·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/dump/rawdocumentation.dump
2799	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/	2799	drwxr-xr-x···0·root·········(0)·root·········(0)········0·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/
2800	-rw-r--r--···0·root·········(0)·root·········(0)······138·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___Abstract__Simplicial__Complex_sp_eq_eq_sp__Abstract__Simplicial__Complex.out	2800	-rw-r--r--···0·root·········(0)·root·········(0)······138·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___Abstract__Simplicial__Complex_sp_eq_eq_sp__Abstract__Simplicial__Complex.out
2801	-rw-r--r--···0·root·········(0)·root·········(0)······528·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___Abstract__Simplicial__Complex_sp_us_sp__Z__Z.out	2801	-rw-r--r--···0·root·········(0)·root·········(0)······528·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___Abstract__Simplicial__Complex_sp_us_sp__Z__Z.out
2802	-rw-r--r--···0·root·········(0)·root·········(0)·····~~1669~~·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___Calculations_spwith_sprandom_spsimplicial_spcomplexes.out	2802	-rw-r--r--···0·root·········(0)·root·········(0)·····2087·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___Calculations_spwith_sprandom_spsimplicial_spcomplexes.out
2803	-rw-r--r--···0·root·········(0)·root·········(0)·····1728·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___How_spto_spmake_spabstract_spsimplicial_spcomplexes.out	2803	-rw-r--r--···0·root·········(0)·root·········(0)·····1728·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___How_spto_spmake_spabstract_spsimplicial_spcomplexes.out
2804	-rw-r--r--···0·root·········(0)·root·········(0)·····2993·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___How_spto_spmake_spreduced_spand_spnon-reduced_spsimplicial_spchain_spcomplexes.out	2804	-rw-r--r--···0·root·········(0)·root·········(0)·····2993·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___How_spto_spmake_spreduced_spand_spnon-reduced_spsimplicial_spchain_spcomplexes.out
2805	-rw-r--r--···0·root·········(0)·root·········(0)·····1952·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___How_spto_spmake_spsubsimplical_spcomplexes_spand_spinduced_spsimplicial_spchain_spcomplex_spmaps.out	2805	-rw-r--r--···0·root·········(0)·root·········(0)·····1952·2024-11-03·00:49:13.000000·./usr/share/doc/Macaulay2/AbstractSimplicialComplexes/example-output/___How_spto_spmake_spsubsimplical_spcomplexes_spand_spinduced_spsimplicial_spchain_spcomplex_spmaps.out
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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	·--·.~~0580~~415s·elapsed	53	·--·.109749s·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	·--·1.~~5212~~s·elapsed	91	·--·2.03753s·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	·--·15.5241s·elapsed	101	·--·18.9743s·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	·--·.03~~681~~35s·elapsed	84	·--·.0373335s·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	·--·.1~~75279~~s·elapsed	90	·--·.150621s·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	·--·4.~~794~~84s·elapsed	99	·--·6.4278s·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}


Offset 50, 23 lines modified		Offset 50, 25 lines modified
50	········<table·class="examples">	50	········<table·class="examples">
51	··········<tr>	51	··········<tr>
52	<td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre>	52	<td>··············<pre><code·class="language-macaulay2">i1·:·setRandomSeed(currentTime());</code></pre>
53	</td>··········</tr>	53	</td>··········</tr>
54	··········<tr>	54	··········<tr>
55	<td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4)	55	<td>··············<pre><code·class="language-macaulay2">i2·:·K·=·randomAbstractSimplicialComplex(4)

56	o2·=·AbstractSimplicialComplex{-1·=>·{{}}}	56	o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
57	·······························0·=>·{{1}}	57	·······························0·=>·{{1},·{3}}
		58	·······························1·=>·{{1,·3}}

58	o2·:·AbstractSimplicialComplex</code></pre>	59	o2·:·AbstractSimplicialComplex</code></pre>
59	</td>··········</tr>	60	</td>··········</tr>
60	··········<tr>	61	··········<tr>
61	<td>··············<pre><code·class="language-macaulay2">i3·:·J·=·randomSubSimplicialComplex(K)	62	<td>··············<pre><code·class="language-macaulay2">i3·:·J·=·randomSubSimplicialComplex(K)

62	o3·=·AbstractSimplicialComplex{-1·=>·{{}}}	63	o3·=·AbstractSimplicialComplex{-1·=>·{{}}}
		64	·······························0·=>·{{1}}

63	o3·:·AbstractSimplicialComplex</code></pre>	65	o3·:·AbstractSimplicialComplex</code></pre>
64	</td>··········</tr>	66	</td>··········</tr>
65	········</table>	67	········</table>
66	······</div>	68	······</div>
67	······<div·class="waystouse">	69	······<div·class="waystouse">
68	········<h2>Ways·to·use·<span·class="tt">randomSubSimplicialComplex</span>:</h2>	70	········<h2>Ways·to·use·<span·class="tt">randomSubSimplicialComplex</span>:</h2>


Offset 6, 20 lines modified		Offset 6, 22 lines modified
6	\x8\x8\x8\x8\x8\x8·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8su\x8ub\x8b-\x8-s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·c\x8co\x8om\x8mp\x8pl\x8le\x8ex\x8x	6	\x8\x8\x8\x8\x8\x8·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x·-\x8--\x8-·C\x8Cr\x8re\x8ea\x8at\x8te\x8e·a\x8a·r\x8ra\x8an\x8nd\x8do\x8om\x8m·s\x8su\x8ub\x8b-\x8-s\x8si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8l·c\x8co\x8om\x8mp\x8pl\x8le\x8ex\x8x
7	\x8\x8\x8\x8\x8\x8	7	\x8\x8\x8\x8\x8\x8
8	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8	8	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8
9	Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex.	9	Creates·a·random·sub-simplicial·complex·of·a·given·simplicial·complex.
10	i1·:·setRandomSeed(currentTime());	10	i1·:·setRandomSeed(currentTime());
11	i2·:·K·=·randomAbstractSimplicialComplex(4)	11	i2·:·K·=·randomAbstractSimplicialComplex(4)

12	o2·=·AbstractSimplicialComplex{-1·=>·{{}}}	12	o2·=·AbstractSimplicialComplex{-1·=>·{{}}·····}
13	·······························0·=>·{{1}}	13	·······························0·=>·{{1},·{3}}
		14	·······························1·=>·{{1,·3}}

14	o2·:·AbstractSimplicialComplex	15	o2·:·AbstractSimplicialComplex
15	i3·:·J·=·randomSubSimplicialComplex(K)	16	i3·:·J·=·randomSubSimplicialComplex(K)

16	o3·=·AbstractSimplicialComplex{-1·=>·{{}}}	17	o3·=·AbstractSimplicialComplex{-1·=>·{{}}}
		18	·······························0·=>·{{1}}

17	o3·:·AbstractSimplicialComplex	19	o3·:·AbstractSimplicialComplex
18	\x8\x8\x8\x8\x8·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·\x8\x8\x8\x8\x8	20	\x8\x8\x8\x8\x8·W\x8Wa\x8ay\x8ys\x8s·t\x8to\x8o·u\x8us\x8se\x8e·r\x8ra\x8an\x8nd\x8do\x8om\x8mS\x8Su\x8ub\x8bS\x8Si\x8im\x8mp\x8pl\x8li\x8ic\x8ci\x8ia\x8al\x8lC\x8Co\x8om\x8mp\x8pl\x8le\x8ex\x8x:\x8:·\x8\x8\x8\x8\x8
19	····*·randomSubSimplicialComplex(AbstractSimplicialComplex)	21	····*·randomSubSimplicialComplex(AbstractSimplicialComplex)
20	\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
21	The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8u_\x8b_\x8S_\x8i_\x8m_\x8p_\x8l_\x8i_\x8c_\x8i_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.	23	The·object·_\x8r_\x8a_\x8n_\x8d_\x8o_\x8m_\x8S_\x8u_\x8b_\x8S_\x8i_\x8m_\x8p_\x8l_\x8i_\x8c_\x8i_\x8a_\x8l_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·is·a·_\x8m_\x8e_\x8t_\x8h_\x8o_\x8d_\x8·_\x8f_\x8u_\x8n_\x8c_\x8t_\x8i_\x8o_\x8n.


Offset 130, 15 lines modified		Offset 130, 15 lines modified
130	··········<tr>	130	··········<tr>
131	<td>··············<pre><code·class="language-macaulay2">i9·:·c=codim·I	131	<td>··············<pre><code·class="language-macaulay2">i9·:·c=codim·I

132	o9·=·4</code></pre>	132	o9·=·4</code></pre>
133	</td>··········</tr>	133	</td>··········</tr>
134	··········<tr>	134	··········<tr>
135	<td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I	135	<td>··············<pre><code·class="language-macaulay2">i10·:·elapsedTime·fI=res·I
136	·--·.~~0580~~415s·elapsed	136	·--·.109749s·elapsed

137	········1·······14·······33·······28·······8	137	········1·······14·······33·······28·······8
138	o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0	138	o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0
139	··················································	139	··················································
140	······0·······1········2········3········4·······5	140	······0·······1········2········3········4·······5

141	o10·:·ChainComplex</code></pre>	141	o10·:·ChainComplex</code></pre>


Offset 55, 15 lines modified		Offset 55, 15 lines modified
55	·········2:·.·12	55	·········2:·.·12

56	o8·:·BettiTally	56	o8·:·BettiTally
57	i9·:·c=codim·I	57	i9·:·c=codim·I

58	o9·=·4	58	o9·=·4
59	i10·:·elapsedTime·fI=res·I	59	i10·:·elapsedTime·fI=res·I
60	·--·.~~0580~~415s·elapsed	60	·--·.109749s·elapsed

61	········1·······14·······33·······28·······8	61	········1·······14·······33·······28·······8
62	o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0	62	o10·=·Pn··<--·Pn···<--·Pn···<--·Pn···<--·Pn··<--·0

63	······0·······1········2········3········4·······5	63	······0·······1········2········3········4·······5

64	o10·:·ChainComplex	64	o10·:·ChainComplex


Offset 192, 15 lines modified		Offset 192, 15 lines modified
192	··········<tr>	192	··········<tr>
193	<td>··············<pre><code·class="language-macaulay2">i14·:·phi=map(P2,Pn,H);	193	<td>··············<pre><code·class="language-macaulay2">i14·:·phi=map(P2,Pn,H);

194	o14·:·RingMap·P2·<--·Pn</code></pre>	194	o14·:·RingMap·P2·<--·Pn</code></pre>
195	</td>··········</tr>	195	</td>··········</tr>
196	··········<tr>	196	··········<tr>
197	<td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi)	197	<td>··············<pre><code·class="language-macaulay2">i15·:·elapsedTime·betti(I'=trim·ker·phi)
198	·--·1.~~5212~~s·elapsed	198	·--·2.03753s·elapsed

199	·············0··1	199	·············0··1
200	o15·=·total:·1·11	200	o15·=·total:·1·11
201	··········0:·1··.	201	··········0:·1··.
202	··········1:·.··3	202	··········1:·.··3
203	··········2:·.··8	203	··········2:·.··8

Offset 209, 15 lines modified		Offset 209, 15 lines modified
209	··········<tr>	209	··········<tr>
210	<td>··············<pre><code·class="language-macaulay2">i16·:·I'==·I	210	<td>··············<pre><code·class="language-macaulay2">i16·:·I'==·I

211	o16·=·true</code></pre>	211	o16·=·true</code></pre>
212	</td>··········</tr>	212	</td>··········</tr>
213	··········<tr>	213	··········<tr>
214	<td>··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;	214	<td>··············<pre><code·class="language-macaulay2">i17·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
215	·--·15.5241s·elapsed</code></pre>	215	·--·18.9743s·elapsed</code></pre>
216	</td>··········</tr>	216	</td>··········</tr>
217	··········<tr>	217	··········<tr>
218	<td>··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))	218	<td>··············<pre><code·class="language-macaulay2">i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))

219	··························0·1	219	··························0·1
220	o18·=·Tally{(1,·1,·total:·1·2)·=>·5}	220	o18·=·Tally{(1,·1,·total:·1·2)·=>·5}
221	·······················0:·1·2	221	·······················0:·1·2


Offset 111, 28 lines modified		Offset 111, 28 lines modified
111	··········6:·.·7	111	··········6:·.·7

112	o13·:·BettiTally	112	o13·:·BettiTally
113	i14·:·phi=map(P2,Pn,H);	113	i14·:·phi=map(P2,Pn,H);

114	o14·:·RingMap·P2·<--·Pn	114	o14·:·RingMap·P2·<--·Pn
115	i15·:·elapsedTime·betti(I'=trim·ker·phi)	115	i15·:·elapsedTime·betti(I'=trim·ker·phi)
116	·--·1.~~5212~~s·elapsed	116	·--·2.03753s·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	·--·15.5241s·elapsed	126	·--·18.9743s·elapsed
127	i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))	127	i18·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))

128	··························0·1	128	··························0·1
129	o18·=·Tally{(1,·1,·total:·1·2)·=>·5}	129	o18·=·Tally{(1,·1,·total:·1·2)·=>·5}
130	·······················0:·1·2	130	·······················0:·1·2
131	··························0·1	131	··························0·1
132	············(1,·3,·total:·1·3)·=>·8	132	············(1,·3,·total:·1·3)·=>·8


Offset 167, 28 lines modified		Offset 167, 28 lines modified
167	··········2:·.·.	167	··········2:·.·.
168	··········3:·.·8	168	··········3:·.·8

169	o13·:·BettiTally</code></pre>	169	o13·:·BettiTally</code></pre>
170	</td>··········</tr>	170	</td>··········</tr>
171	··········<tr>	171	··········<tr>
172	<td>··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H)	172	<td>··············<pre><code·class="language-macaulay2">i14·:·elapsedTime·sub(I,H)
173	·--·.03~~681~~35s·elapsed	173	·--·.0373335s·elapsed

174	o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)	174	o14·=·ideal·(0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0,·0)

175	o14·:·Ideal·of·P2</code></pre>	175	o14·:·Ideal·of·P2</code></pre>
176	</td>··········</tr>	176	</td>··········</tr>
177	··········<tr>	177	··········<tr>
178	<td>··············<pre><code·class="language-macaulay2">i15·:·phi=map(P2,Pn,H);	178	<td>··············<pre><code·class="language-macaulay2">i15·:·phi=map(P2,Pn,H);

179	o15·:·RingMap·P2·<--·Pn</code></pre>	179	o15·:·RingMap·P2·<--·Pn</code></pre>
180	</td>··········</tr>	180	</td>··········</tr>
181	··········<tr>	181	··········<tr>
182	<td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi)	182	<td>··············<pre><code·class="language-macaulay2">i16·:·elapsedTime·betti(I'=trim·ker·phi)
183	·--·.1~~75279~~s·elapsed	183	·--·.150621s·elapsed

184	·············0··1	184	·············0··1
185	o16·=·total:·1·12	185	o16·=·total:·1·12
186	··········0:·1··.	186	··········0:·1··.
187	··········1:·.·12	187	··········1:·.·12

188	o16·:·BettiTally</code></pre>	188	o16·:·BettiTally</code></pre>
Offset 196, 15 lines modified		Offset 196, 15 lines modified
196	··········<tr>	196	··········<tr>
197	<td>··············<pre><code·class="language-macaulay2">i17·:·I'==·I	197	<td>··············<pre><code·class="language-macaulay2">i17·:·I'==·I

198	o17·=·true</code></pre>	198	o17·=·true</code></pre>
199	</td>··········</tr>	199	</td>··········</tr>
200	··········<tr>	200	··········<tr>
201	<td>··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;	201	<td>··············<pre><code·class="language-macaulay2">i18·:·elapsedTime·basePts=primaryDecomposition·ideal·H;
202	·--·4.~~794~~84s·elapsed</code></pre>	202	·--·6.4278s·elapsed</code></pre>
203	</td>··········</tr>	203	</td>··········</tr>
204	··········<tr>	204	··········<tr>
205	<td>··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))	205	<td>··············<pre><code·class="language-macaulay2">i19·:·tally·apply(basePts,c->(dim·c,·degree·c,·betti·c))

206	···························0··1	206	···························0··1
207	o19·=·Tally{(0,·34,·total:·1·15)·=>·1}	207	o19·=·Tally{(0,·34,·total:·1·15)·=>·1}
208	························0:·1··.	208	························0:·1··.


Offset 83, 36 lines modified		Offset 83, 36 lines modified
83	··········0:·1·.	83	··········0:·1·.
84	··········1:·.·.	84	··········1:·.·.
85	··········2:·.·.	85	··········2:·.·.
86	··········3:·.·8	86	··········3:·.·8

87	o13·:·BettiTally	87	o13·:·BettiTally
88	i14·:·elapsedTime·sub(I,H)	88	i14·:·elapsedTime·sub(I,H)
89	·--·.03~~681~~35s·elapsed	89	·--·.0373335s·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	·--·.1~~75279~~s·elapsed	95	·--·.150621s·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	·--·4.~~794~~84s·elapsed	104	·--·6.4278s·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 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·0.53~~5062~~s·(cpu);·0.392971s·(thread);·0s·(gc)	119	·--·used·0.534204s·(cpu);·0.396217s·(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·0.6~~47888~~s·(cpu);·0.467~~635~~s·(thread);·0s·(gc)	127	·--·used·0.668136s·(cpu);·0.47912s·(thread);·0s·(gc)

128	·············0·1·2	128	·············0·1·2
129	o15·=·total:·3·6·3	129	o15·=·total:·3·6·3
130	··········0:·3·.·.	130	··········0:·3·.·.
131	··········1:·.·6·.	131	··········1:·.·6·.
132	··········2:·.·.·3	132	··········2:·.·.·3


Offset 228, 15 lines modified		Offset 228, 15 lines modified
228	······\|·-10a-29b·39a+21b··-43a-15b·45a-34b··\|	228	······\|·-10a-29b·39a+21b··-43a-15b·45a-34b··\|

229	··············4······4	229	··············4······4
230	o13·:·Matrix·A··<--·A</code></pre>	230	o13·:·Matrix·A··<--·A</code></pre>
231	</td>··········</tr>	231	</td>··········</tr>
232	··········<tr>	232	··········<tr>
233	<td>··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))	233	<td>··············<pre><code·class="language-macaulay2">i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))
234	·--·used·0.53~~5062~~s·(cpu);·0.392971s·(thread);·0s·(gc)	234	·--·used·0.534204s·(cpu);·0.396217s·(thread);·0s·(gc)

235	·············0·1·2	235	·············0·1·2
236	o14·=·total:·3·6·3	236	o14·=·total:·3·6·3
237	··········0:·3·.·.	237	··········0:·3·.·.
238	··········1:·.·6·.	238	··········1:·.·6·.
239	··········2:·.·.·3	239	··········2:·.·.·3

Offset 245, 15 lines modified		Offset 245, 15 lines modified
245	········</table>	245	········</table>
246	········<div>	246	········<div>
247	··········<p>With·the·form·<span·class="tt">pureResolution(p,q,D)</span>·we·can·directly·create·the·situation·of·<span·class="tt">pureResolution(M,D)</span>·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of·linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables·of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in·A·this·runs·much·faster·than·taking·a·random·matrix·M.</p>	247	··········<p>With·the·form·<span·class="tt">pureResolution(p,q,D)</span>·we·can·directly·create·the·situation·of·<span·class="tt">pureResolution(M,D)</span>·where·M·is·generic·product(m_i+1)·x·#D-1+sum(m_i)·matrix·of·linear·forms·defined·over·a·ring·with·product(m_i+1)·*·#D-1+sum(m_i)·variables·of·characteristic·p,·created·by·the·script.·For·a·given·number·of·variables·in·A·this·runs·much·faster·than·taking·a·random·matrix·M.</p>
248	········</div>	248	········</div>
249	········<table·class="examples">	249	········<table·class="examples">
250	··········<tr>	250	··········<tr>
251	<td>··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))	251	<td>··············<pre><code·class="language-macaulay2">i15·:·time·betti·(F·=·pureResolution(11,4,{0,2,4}))
252	·--·used·0.6~~47888~~s·(cpu);·0.467~~635~~s·(thread);·0s·(gc)	252	·--·used·0.668136s·(cpu);·0.47912s·(thread);·0s·(gc)

253	·············0·1·2	253	·············0·1·2
254	o15·=·total:·3·6·3	254	o15·=·total:·3·6·3
255	··········0:·3·.·.	255	··········0:·3·.·.
256	··········1:·.·6·.	256	··········1:·.·6·.
257	··········2:·.·.·3	257	··········2:·.·.·3


Offset 162, 30 lines modified		Offset 162, 30 lines modified
162	······\|·-30a-29b·-29a-24b·-47a-39b·38a+2b···\|	162	······\|·-30a-29b·-29a-24b·-47a-39b·38a+2b···\|
163	······\|·19a+19b··-38a-16b·-18a-13b·16a+22b··\|	163	······\|·19a+19b··-38a-16b·-18a-13b·16a+22b··\|
164	······\|·-10a-29b·39a+21b··-43a-15b·45a-34b··\|	164	······\|·-10a-29b·39a+21b··-43a-15b·45a-34b··\|

165	··············4······4	165	··············4······4
166	o13·:·Matrix·A··<--·A	166	o13·:·Matrix·A··<--·A
167	i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))	167	i14·:·time·betti·(F·=·pureResolution(M,{0,2,4}))
168	·--·used·0.53~~5062~~s·(cpu);·0.392971s·(thread);·0s·(gc)	168	·--·used·0.534204s·(cpu);·0.396217s·(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·0.6~~47888~~s·(cpu);·0.467~~635~~s·(thread);·0s·(gc)	181	·--·used·0.668136s·(cpu);·0.47912s·(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


Offset 1, 10 lines modified		Offset 1, 10 lines modified
1	--·--·M2-comint·--·hash:·1330545576567	1	--·--·M2-comint·--·hash:·1330545576567

2	i1·:·runBenchmarks·"res39"	2	i1·:·runBenchmarks·"res39"
3	--·beginning·computation·~~Thu~~·Dec·11·05:13:31·-12·2025	3	--·beginning·computation·Fri·Dec·12·11:24:46·+14·2025
4	--·Linux·codeth~~ink01-ar~~m64·6.1.0-26-cloud-arm64·#1·SMP·Debian·6.1.112-1·(2024-09-30)·aarch64·GNU/Linux	4	--·Linux·i-capture-the-hostname·6.1.0-26-cloud-arm64·#1·SMP·Debian·6.1.112-1·(2024-09-30)·aarch64·GNU/Linux
5	--·BogoMIPS·50.00··	5	--·BogoMIPS·50.00··
6	--·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0	6	--·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0
7	--·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.1~~51126~~·seconds	7	--·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.143254·seconds

8	i2·:·	8	i2·:·


Offset 73, 19 lines modified		Offset 73, 19 lines modified
73	········<h2>Description</h2>	73	········<h2>Description</h2>
74	········<div>	74	········<div>
75	··········<p>The·tests·available·are:·<br>"deg2generic"·--·gb·of·a·generic·ideal·of·codimension·2·and·degree·2<br>"gb4by4comm"·--·gb·of·the·ideal·of·generic·commuting·4·by·4·matrices·over·ZZ/101<br>"gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables<br>"gbB148"·--·gb·of·Bayesian·graph·ideal·#148<br>"res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101<br>"resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)<br>"yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory<br>"yang-subring"·--·an·example·of·Yang-Hui·He<br></p>	75	··········<p>The·tests·available·are:·<br>"deg2generic"·--·gb·of·a·generic·ideal·of·codimension·2·and·degree·2<br>"gb4by4comm"·--·gb·of·the·ideal·of·generic·commuting·4·by·4·matrices·over·ZZ/101<br>"gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables<br>"gbB148"·--·gb·of·Bayesian·graph·ideal·#148<br>"res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101<br>"resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)<br>"yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory<br>"yang-subring"·--·an·example·of·Yang-Hui·He<br></p>
76	········</div>	76	········</div>
77	········<table·class="examples">	77	········<table·class="examples">
78	··········<tr>	78	··········<tr>
79	<td>··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·"res39"	79	<td>··············<pre><code·class="language-macaulay2">i1·:·runBenchmarks·"res39"
80	--·beginning·computation·~~Thu~~·Dec·11·05:13:31·-12·2025	80	--·beginning·computation·Fri·Dec·12·11:24:46·+14·2025
81	--·Linux·codeth~~ink01-ar~~m64·6.1.0-26-cloud-arm64·#1·SMP·Debian·6.1.112-1·(2024-09-30)·aarch64·GNU/Linux	81	--·Linux·i-capture-the-hostname·6.1.0-26-cloud-arm64·#1·SMP·Debian·6.1.112-1·(2024-09-30)·aarch64·GNU/Linux
82	--·BogoMIPS·50.00··	82	--·BogoMIPS·50.00··
83	--·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0	83	--·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0
84	--·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.1~~51126~~·seconds</code></pre>	84	--·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.143254·seconds</code></pre>
85	</td>··········</tr>	85	</td>··········</tr>
86	········</table>	86	········</table>
87	······</div>	87	······</div>
88	······<div·class="waystouse">	88	······<div·class="waystouse">
89	········<h2>For·the·programmer</h2>	89	········<h2>For·the·programmer</h2>
90	········<p>The·object·<a·href="_run__Benchmarks.html">runBenchmarks</a>·is·<span>a·<a·title="the·class·of·all·commands"·href="../../Macaulay2Doc/html/___Command.html">command</a></span>.</p>	90	········<p>The·object·<a·href="_run__Benchmarks.html">runBenchmarks</a>·is·<span>a·<a·title="the·class·of·all·commands"·href="../../Macaulay2Doc/html/___Command.html">command</a></span>.</p>
91	······</div>	91	······</div>


Offset 24, 15 lines modified		Offset 24, 15 lines modified
24	"gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables	24	"gb3445"·--·gb·of·an·ideal·with·elements·of·degree·3,4,4,5·in·8·variables
25	"gbB148"·--·gb·of·Bayesian·graph·ideal·#148	25	"gbB148"·--·gb·of·Bayesian·graph·ideal·#148
26	"res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101	26	"res39"·--·res·of·a·generic·3·by·9·matrix·over·ZZ/101
27	"resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)	27	"resG25"·--·res·of·the·coordinate·ring·of·Grassmannian(2,5)
28	"yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory	28	"yang-gb1"·--·an·example·of·Yang-Hui·He·arising·in·string·theory
29	"yang-subring"·--·an·example·of·Yang-Hui·He	29	"yang-subring"·--·an·example·of·Yang-Hui·He
30	i1·:·runBenchmarks·"res39"	30	i1·:·runBenchmarks·"res39"
31	--·beginning·computation·~~Thu~~·Dec·11·05:13:31·-12·2025	31	--·beginning·computation·Fri·Dec·12·11:24:46·+14·2025
32	--·Linux·codeth~~ink01-ar~~m64·6.1.0-26-cloud-arm64·#1·SMP·Debian·6.1.112-1~~·(2024-~~	32	--·Linux·i-capture-the-hostname·6.1.0-26-cloud-arm64·#1·SMP·Debian·6.1.112-1
33	09-30)·aarch64·GNU/Linux	33	(2024-09-30)·aarch64·GNU/Linux
34	--·BogoMIPS·50.00	34	--·BogoMIPS·50.00
35	--·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0	35	--·Macaulay2·1.24.11,·compiled·with·gcc·14.2.0
36	--·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.1~~51126~~·seconds	36	--·res39:·res·of·a·generic·3·by·9·matrix·over·ZZ/101:·.143254·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.


Offset 82, 15 lines modified		Offset 82, 15 lines modified
82	<span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]-->	82	<span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniParameterHomotopy,·OutputStyle]-->
83	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li>	83	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li>
84	··············<li>	84	··············<li>
85	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>	85	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>
86	··············<li>	86	··············<li>
87	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>	87	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>
88	··············<li>	88	··············<li>
89	<span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-3~~118901~~-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li>	89	<span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-497316-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li>
90	··············<li>	90	··············<li>
91	<span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li>	91	<span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li>
92	············</ul>	92	············</ul>
93	··········</li>	93	··········</li>
94	··········<li>	94	··········<li>
95	Outputs:············<ul>	95	Outputs:············<ul>
96	··············<li>	96	··············<li>


Offset 27, 15 lines modified		Offset 27, 15 lines modified
27	············"OutPoints",	27	············"OutPoints",
28	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates	28	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates
29	············symbols/strings/variables·that·will·be·set·to·be·a·random·real	29	············symbols/strings/variables·that·will·be·set·to·be·a·random·real
30	············number·or·random·complex·number	30	············number·or·random·complex·number
31	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates	31	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates
32	············symbols/strings/variables·that·will·be·set·to·be·a·random·real	32	············symbols/strings/variables·that·will·be·set·to·be·a·random·real
33	············number·or·random·complex·number	33	············number·or·random·complex·number
34	··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-3~~118901~~-0/0",·Option·to	34	··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-497316-0/0",·Option·to
35	············change·directory·for·file·storage.	35	············change·directory·for·file·storage.
36	··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional	36	··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional
37	············output	37	············output
38	····*·Outputs:	38	····*·Outputs:
39	··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·whose·entries·are·lists·of·solutions·for·each	39	··········o·S,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·whose·entries·are·lists·of·solutions·for·each
40	············target·system	40	············target·system
41	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8	41	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8


Offset 88, 15 lines modified		Offset 88, 15 lines modified
88	··············<li>	88	··············<li>
89	<span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]-->	89	<span><span·class="tt">RandomComplex</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomComplex]-->
90	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li>	90	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li>
91	··············<li>	91	··············<li>
92	<span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]-->	92	<span><span·class="tt">RandomReal</span>·(missing·documentation)<!--tag:·[bertiniUserHomotopy,·RandomReal]-->
93	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li>	93	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span></span></span>··············</li>
94	··············<li>	94	··············<li>
95	<span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-3~~118901~~-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li>	95	<span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-497316-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li>
96	··············<li>	96	··············<li>
97	<span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li>	97	<span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li>
98	············</ul>	98	············</ul>
99	··········</li>	99	··········</li>
100	··········<li>	100	··········<li>
101	Outputs:············<ul>	101	Outputs:············<ul>
102	··············<li>	102	··············<li>


Offset 22, 15 lines modified		Offset 22, 15 lines modified
22	············value·{},	22	············value·{},
23	··········o·HomVariableGroup·(missing·documentation)·=>·...,·default·value·{},	23	··········o·HomVariableGroup·(missing·documentation)·=>·...,·default·value·{},
24	··········o·M2Precision·(missing·documentation)·=>·...,·default·value·53,	24	··········o·M2Precision·(missing·documentation)·=>·...,·default·value·53,
25	··········o·OutputStyle·(missing·documentation)·=>·...,·default·value	25	··········o·OutputStyle·(missing·documentation)·=>·...,·default·value
26	············"OutPoints",	26	············"OutPoints",
27	··········o·RandomComplex·(missing·documentation)·=>·...,·default·value·{},	27	··········o·RandomComplex·(missing·documentation)·=>·...,·default·value·{},
28	··········o·RandomReal·(missing·documentation)·=>·...,·default·value·{},	28	··········o·RandomReal·(missing·documentation)·=>·...,·default·value·{},
29	··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-3~~118901~~-0/0",·Option·to	29	··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-497316-0/0",·Option·to
30	············change·directory·for·file·storage.	30	············change·directory·for·file·storage.
31	··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional	31	··········o·_\x8V_\x8e_\x8r_\x8b_\x8o_\x8s_\x8e·=>·...,·default·value·false,·Option·to·silence·additional
32	············output	32	············output
33	····*·Outputs:	33	····*·Outputs:
34	··········o·S0,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·solutions·to·the·target·system	34	··········o·S0,·a·_\x8l_\x8i_\x8s_\x8t,·a·list·of·solutions·to·the·target·system
35	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8	35	\x8\x8\x8\x8\x8·D\x8De\x8es\x8sc\x8cr\x8ri\x8ip\x8pt\x8ti\x8io\x8on\x8n·\x8\x8\x8\x8\x8
36	This·method·calls·Bertini·to·track·a·user-defined·homotopy.·The·user·needs·to	36	This·method·calls·Bertini·to·track·a·user-defined·homotopy.·The·user·needs·to


Offset 91, 15 lines modified		Offset 91, 15 lines modified
91	<span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]-->	91	<span><span·class="tt">OutputStyle</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·OutputStyle]-->
92	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li>	92	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"OutPoints"</span>,·<span></span></span>··············</li>
93	··············<li>	93	··············<li>
94	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>	94	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomComplex</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>
95	··············<li>	95	··············<li>
96	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>	96	<span><a·title="an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number"·href="___Bertini_spinput_spfile_spdeclarations_co_sprandom_spnumbers.html">RandomReal</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·{}</span>,·<span>an·option·which·designates·symbols/strings/variables·that·will·be·set·to·be·a·random·real·number·or·random·complex·number</span></span>··············</li>
97	··············<li>	97	··············<li>
98	<span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-3~~118901~~-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li>	98	<span><a·title="Option·to·change·directory·for·file·storage."·href="___Top__Directory.html">TopDirectory</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·"/tmp/M2-497316-0/0"</span>,·<span>Option·to·change·directory·for·file·storage.</span></span>··············</li>
99	··············<li>	99	··············<li>
100	<span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]-->	100	<span><span·class="tt">UseRegeneration</span>·(missing·documentation)<!--tag:·[bertiniZeroDimSolve,·UseRegeneration]-->
101	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span>··············</li>	101	<span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·-1</span>,·<span></span></span>··············</li>
102	··············<li>	102	··············<li>
103	<span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li>	103	<span><a·title="Option·to·silence·additional·output"·href="_bertini__Track__Homotopy_lp..._cm__Verbose_eq_gt..._rp.html">Verbose</a><span·class="tt">·=>·</span><span·class="tt">...</span>,·<span>default·value·false</span>,·<span>Option·to·silence·additional·output</span></span>··············</li>
104	············</ul>	104	············</ul>
105	··········</li>	105	··········</li>


Offset 33, 15 lines modified		Offset 33, 15 lines modified
33	············"OutPoints",	33	············"OutPoints",
34	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates	34	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8C_\x8o_\x8m_\x8p_\x8l_\x8e_\x8x·=>·...,·default·value·{},·an·option·which·designates
35	············symbols/strings/variables·that·will·be·set·to·be·a·random·real	35	············symbols/strings/variables·that·will·be·set·to·be·a·random·real
36	············number·or·random·complex·number	36	············number·or·random·complex·number
37	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates	37	··········o·_\x8R_\x8a_\x8n_\x8d_\x8o_\x8m_\x8R_\x8e_\x8a_\x8l·=>·...,·default·value·{},·an·option·which·designates
38	············symbols/strings/variables·that·will·be·set·to·be·a·random·real	38	············symbols/strings/variables·that·will·be·set·to·be·a·random·real
39	············number·or·random·complex·number	39	············number·or·random·complex·number
40	··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-3~~118901~~-0/0",·Option·to	40	··········o·_\x8T_\x8o_\x8p_\x8D_\x8i_\x8r_\x8e_\x8c_\x8t_\x8o_\x8r_\x8y·=>·...,·default·value·"/tmp/M2-497316-0/0",·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