unstable results of SecondCohomologyDimension

[ThomasBreuer]

Consider the following input for GAP 4.12.2 or the current master branch.

LoadPackage( "cohomolo" );;
G:= GroupWithGenerators( gens );;
chr:= CHR( G, 2, 0, mats );;
SecondCohomologyDimension( chr );

where gens and mats are defined below.

When I enter these lines repeatedly then I get one of the following three outputs.

0

or

Error, 'Cohomolo' failed for some reason.
 at /.../gap/pkg/cohomolo/gap/coho4.g:669 called from
[...]

or

Out of space. Increase RSP.
37

(The output can be changed by calling BaseOfGroup( G ) or Size( G ) before calling CHR, some Random calls seem to be involved.)

Currently I do not see a reason for the differences.

And here are the defining data.

gens:=
[(2,4,9,22)(6,14,36,93)(7,17,43,111)(8,20)(10,25)
(11,27,70,47)(12,30,78,186)(13,33,86,195)(15,39,101,228)
(16,41,106,238)(18,46)(19,49,125,150)(21,54,133,107)
(23,59,127,261)(24,62,90,209)(26,67,105,236)(28,73)
(29,76,161,306)(32,83,194,296)(34,89,206,214)(35,91)
(37,96,219,102)(38,99,148,275)(42,109,198,258)(44,113)
(45,116,249,137)(48,123)(50,120,98,222)(51,129,265,367)
(52,92,212,353)(53,132)(55,136,130,267)(56,139,277,381)
(57,141,281,391)(58,63,151,166)(60,146,287,145)(61,147,289,229)
(64,154,298,250)(65,156,288,345)(66,159,304,310)(68,164)
(69,167,312,292)(71,143)(72,173,104,235)(74,178,144,284)(75,180)
(77,184,313,375)(79,189)(80,160)(82,192,114,202)(84,188,332,402)
(85,134)(87,201,334,331)(88,203)(94,215,245,372)(95,126,260,115)
(97,196,112,244)(100,224)(103,233,333,168)(108,239,183,327)(110,223)
(117,251,323,271)(118,252,376,131)(122,128,263,243)(124,257,343,302)
(135,185,318,279)(138,205)(140,142,282,272)(152,193,274,388)
(153,297,290,319)(155,226,295,393)(157,301)(158,303)(162,300,175,320)
(165,311)(170,308,256,355)(171,283,392,361)(172,247,177,240)
(176,216,294,285)(179,322,341,314)(181,191,299,204)(182,326,401,404)
(190,268)(199,339,362,336)(207,348)(208,350)(210,321,305,246)(211,340)
(213,218)(217,230,364,324)(220,335)(225,359,264,383)(227,360,278,386)
(231,363)(234,349)(237,351)(242,370,253,377)(248,373,262,356)
(259,354,371,269)(266,293)(273,378,385,384)(276,389)(280,346)(291,315)
(307,379)(309,380)(316,366)(328,397,368,374)(329,352)(337,395)
(344,390,396,382)(357,403)(365,400)(369,394),

(1,2,5,12,31,81)(3,7,18,47,121,167)(4,10,26,68,165,301)
(6,15,17,44,114,147)(8,21,55,137,123,256)(9,23,60,78,187,
330)(11,28,74,179,206,346)(13,34,90,58,144,285)(14,37,97,151,
294,111)(16,42)(19,50,128,88,204,177)(20,52,130,103,234,365)
(22,57,142,30,79,190)(24,63,152,296,82,193)(25,65,157,302,293,
370)(27,71,171,314,388,80)(29,77,125,258,251,375)(32,84,196,329,
361,61)(33,87,202,39,102,231)(35,92,213,222,358,400)
(36,94,216,215,86,199)(38,100,226,353,106,120)(40,104,232,355,75,
181)(41,107,49,126,45,117)(43,112,166)(46,119,254,379,387,310)
(48,72,174,319,217,76)(51,53)(54,134)(56,140,279,205,345,401)
(59,145,105,237,311,326)(62,149,292,73,176,304)(64,155,299)
(66,160,163,307,389,322)(67,162,138,185,141,131)(69,143,283,159,244,
286)(70,169,274,369,219,357)(83,195,284,96,93,214)(85,198)(89,207)
(91,95,218,246,221,170)(98,172,208)(99,224,297,212,249,333)
(101,229,363)(108,135,273)(109,240,184,168,313,203)(110,242,132,269,340,
320)(113,245,334,372,228,362)(115,247,122,233,323,350)(116,250,290,133,
271,161)(118,253,378,327,377,381)(124,127,262,287,371,325)(129,266)
(136,275,315,308,220,305)(139,278,390,227,239,367)(146,288,268,257,281,
344)(148,291,235,347,393,230)(150,191,306,154,295,260)(153,210,243,238,
321,298)(156,175,277,373,356,252)(158,276,201,341,402,280)(164,309)
(173,317)(178,188,209,352,392,331)(180,324,197,337,342,200)(182,316,236)
(183,328,385,383,248,359)(186,211,351,380,404,223)(189,300,261,382,272,
354)(194,336)(241,368)(255,259,338,343,405,318)(264,282,374,366,397,391)
(265,384,360,396,386,376)(267,349,395,398,335,364)(270,289,394,332,403,
303)(312,399)(339,348),

(1,3,8)(2,6,16)(4,11,29)
(5,13,35)(7,19,51)(9,24,64)(10,14,38)(12,32,85)
(15,40,105)(17,45,118)(18,48,124)(20,53,121)(21,56,93)
(22,58,117)(23,61,148)(25,66,161)(26,69,168)(27,72,175)
(28,75,182)(30,80,191)(31,82,50)(33,88,205)(34,91,211)
(36,95,165)(37,98,223)(39,103,142)(41,108,74)(42,110,114)
(43,99,225)(44,115,248)(46,120,255)(47,122,157)(49,127,201)
(52,131,83)(54,135,274)(55,138,276)(57,143,180)(59,87,137)
(60,84,197)(62,150,293)(63,153,162)(65,158,251)(67,163,308)
(68,166,116)(70,170,81)(71,172,316)(73,177,237)(76,183,329)
(77,185,199)(78,188,333)(79,147,290)(86,200,340)(89,208,351)
(90,210,311)(92,129,194)(94,217,345)(96,220,326)(97,221,279)
(100,227,361)(101,230,278)(102,232,141)(104,189,334)(106,164,310)
(107,140,280)(109,241,369)(111,243,371)(112,212,354)(113,246,370)
(119,249,265)(123,190,195)(125,259,363)(126,236,294)(128,264,149)
(130,268,379)(132,270,317)(133,187,331)(134,272,196)(136,257,169)
(139,159,305)(144,154,288)(145,286,393)(146,176,321)(151,295,330)
(152,204,344)(155,300,304)(156,292,395)(160,238,360)(167,184,253)
(171,315,327)(173,318,303)(174,281,389)(178,235,186)(179,323,266)
(181,325,289)(192,335,391)(193,306,397)(198,338,219)(202,342,404)
(203,343,394)(206,347,405)(207,349,384)(209,299,277)(213,242,339)
(214,234,366)(215,313,390)(216,355,377)(218,356,245)(222,309,348)
(224,252,362)(226,262,285)(228,337,367)(229,263,261)(231,275,376)
(233,287,283)(239,336,364)(240,302,254)(244,353,359)(247,273,387)
(250,374,346)(256,320,341)(258,380,357)(260,381,322)(267,385,399)
(269,372,365)(271,386,388)(282,284,319)(291,383,402)(296,358,382)
(297,396,352)(298,301,314)(307,398,401)(312,400,368)(324,328,332)
(350,378,403)(373,392,375)];;

mats:=[
[[1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,1,0,1,1,0,1,0,0,0,0,0],
[0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,1,0,1,1,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,1,1,1,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0,1,1,0,1,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1,0,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,1,1,0,0,1,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,1,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,1,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,0,0,1,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,0,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]],

[[0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0,1],
[0,0,1,1,0,0,1,0,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,0],
[1,0,0,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,1,0,0,1,0,1,1,0,0,1,1,0,0,0,1,0,1],
[0,1,0,0,1,0,1,0,1,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0],
[0,0,1,0,1,1,0,1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,1,1,0],
[0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0],
[0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,0,1,1,1,1,1,1],
[0,0,1,0,1,0,0,1,0,1,1,0,0,0,0,1,1,0,0,1,0,1,1,1,1,0],
[0,0,0,1,0,0,0,0,0,0,1,0,0,1,1,0,0,0,1,0,0,0,1,0,0,0],
[0,0,0,1,0,1,0,0,0,0,1,1,0,1,0,1,1,0,0,0,0,0,1,1,0,0],
[0,0,1,0,0,0,1,1,1,1,0,1,0,0,1,1,1,1,0,1,0,1,1,1,1,1],
[0,0,0,0,0,1,0,0,0,0,1,1,0,1,0,0,1,0,1,1,1,1,1,1,1,0],
[0,0,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0,1,1,1,1,0],
[0,0,1,0,0,0,1,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0,1],
[0,0,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1,1,0,1,1,0,0,0,1,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,1,0,0,1,0],
[0,0,1,1,0,0,1,1,1,1,1,1,0,1,0,1,1,0,0,1,1,1,1,1,0,1],
[0,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,1,0,1],
[0,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0,0,1,0],
[0,0,0,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,1,0,1,0,1,0],
[0,0,0,0,0,1,0,0,0,0,1,1,0,1,0,0,1,0,1,1,1,1,1,1,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0]],

[[0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,1,0,0,1,0,1,0,1],
[1,0,1,0,0,1,0,1,1,0,0,1,0,0,0,0,0,0,0,0,0,1,0,1,0,1],
[0,1,0,1,0,0,0,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1,0,0,0],
[1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1,0,0,1,1,0,1,0,0,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0],
[1,0,0,0,0,0,1,0,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,1,1],
[1,0,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,1,1,1,0,1,1,0],
[0,0,1,0,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0,0,0,0,0],
[1,0,0,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,1,1,0],
[0,1,0,0,0,0,1,1,1,0,1,0,1,1,1,1,1,0,1,1,0,1,0,1,0,1],
[0,0,1,0,0,0,1,1,0,0,1,1,0,0,0,0,0,0,1,0,0,0,1,0,1,1],
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,1,1,1,1,1,0,0,0,1,1],
[1,0,0,1,0,1,1,0,0,1,0,1,1,0,0,0,1,1,0,1,1,1,0,1,1,0],
[0,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,1,1,0,0,1,0,0,0],
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0,1,0,0,0,0,0,1,1],
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,1,1,1,1,0,1,0,0,1,1,0,1],
[1,1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,0,0],
[1,1,1,0,1,1,0,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,1],
[1,1,0,1,1,1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0,0,0,0,0,0],
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0,0,1,0,1],
[0,0,1,1,1,0,0,1,0,1,1,0,0,0,0,1,1,1,1,0,1,1,0,1,1,1],
[0,0,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,1],
[0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,0,1,1,1,1,1,0,0,1,1,1]]] * Z(2);;

Perform( mats, x -> ConvertToMatrixRep( x, 2 ) );

[fingolfin]

I can reproduce the issue.

Part of the problem is the user of Exec which does not allow checking the exec code (shameless plug for my GAP PR that adds a better alternative called Exec2).

These should be replaced by calls to Process.

Then I hope the Out of space. Increase RSP. can at least be detected as an error.

Of course that leaves the question whether there is something to be done there, like, well, increasing the hardcoded RSP value.

[fingolfin]

The use of Exec is also a problem in kbmag, I've opened gap-packages/kbmag#33

[ThomasBreuer]

Just for the record:
The function TwoCohomologyGeneric from the GAP library (implemented by @hulpke) confirms that the result 0 is correct. (GAP 4.12.2 is good enough for this computation, and the version from the master branch needs less time.)