Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via `TwoCohomologyGeneric` #3383

hulpke · 2019-03-27T03:13:21Z

Uses rewriting system since pc presentation will not always be available.
This is both code for the cohomology group, and for constructing the extension corresponding to a particular cocycle. Group is constructed by default as Fp group, but there is an option to have it compute a faithful permutation representation.

Also includes improved routines for IrreducibleModules for the non-pc case once such cohomology routines exist, and action of compatible pairs on the cohomology group.

There is a test in testextra that, as application, constructs perfect groups anew. (This could easily go to larger orders, if desired, at the moment two quick tests are in.)

codecov · 2019-03-29T18:54:14Z

Codecov Report

Merging #3383 into master will increase coverage by 0.07%.
The diff coverage is 76.5%.

@@            Coverage Diff             @@
##           master    #3383      +/-   ##
==========================================
+ Coverage   85.17%   85.25%   +0.07%     
==========================================
  Files         699      699              
  Lines      346081   346872     +791     
==========================================
+ Hits       294784   295735     +951     
+ Misses      51297    51137     -160

Impacted Files	Coverage Δ
lib/grp.gd	`100% <100%> (ø)`	⬆️
lib/grppcrep.gi	`96.72% <100%> (+1.11%)`	⬆️
lib/twocohom.gd	`100% <100%> (ø)`	⬆️
lib/ghomfp.gi	`86.45% <100%> (+1.24%)`	⬆️
lib/grpfp.gi	`83.93% <100%> (+2.67%)`	⬆️
lib/meataxe.gi	`87.8% <100%> (+0.08%)`	⬆️
lib/gpprmsya.gi	`78.29% <52.06%> (+1.04%)`	⬆️
lib/grppcext.gi	`70.03% <61.48%> (-0.55%)`	⬇️
lib/grpreps.gi	`84.06% <79.86%> (-13.94%)`	⬇️
lib/gpfpiso.gi	`66.51% <84.61%> (+0.91%)`	⬆️
... and 34 more

doc/ref/grppc.xml

coveralls · 2019-04-08T21:08:59Z

Coverage increased (+0.09%) to 85.08% when pulling ba83355 on hulpke:ah/twocohom into fcbaa66 on gap-system:master.

wilfwilson · 2019-04-15T19:44:15Z

@hulpke I noticed you’ve removed the WIP from the title and the ‘do not review’ label. Just to check, for sure: does this mean that you’d be happy for the PR to be reviewed, and hopefully merged? If so, I’d suggest removing the ‘do not merge’ label because I get the impression it might put people off from reviewing. Sorry I’ve not had chance to look at your PR further yet.

olexandr-konovalov · 2019-04-15T19:54:12Z

Travis reports two manual example diffs:

########> Diff in /home/travis/build/gap-system/gap/doc/ref/../../lib/twocohom\
.gd:273 (/home/travis/build/gap-system/gap/tst/testmanuals/ref-chapter039.tst:
992)
# Input is:
g1:=Image(IsomorphismPermGroup(p));
# Expected output:
<permutation group of size 38880 with 9 generators>
# But found:
<permutation group with 9 generators>
########
########> Diff in /home/travis/build/gap-system/gap/doc/ref/../../lib/twocohom\
.gd:273 (/home/travis/build/gap-system/gap/tst/testmanuals/ref-chapter039.tst:
999)
# Input is:
g2:=Image(IsomorphismPermGroup(p));
# Expected output:
<permutation group of size 38880 with 9 generators>
# But found:
<permutation group with 9 generators>
########

hulpke · 2019-04-16T00:55:44Z

@wilfwilson
At this stage I am happy for comments about potential problems, but there is still some code (basic functionality for compatible pairs and action on the cohomology group) I am still working on and want to add before merging. (There also is a manual bug and a stupid typo in the perfect group construction example that need fixing.)
As there will still be code added (as soon as I fix a bug..), it might be best to wait with formal reviewing.

hulpke · 2019-04-17T15:44:31Z

@wilfwilson OK, now the promised changes are in, and the holds are removed.
Since there is no need to backport, I'm not sure whether there is a need to squash into one commit, but could do so if desired.

fingolfin

Very nice, thank you! Overall, this is of course a very welcome improvement!

Unfortunately I did not yet have time to look at everything (with easter and everything), but I left a few rather minor remarks. I would like to have a closer look at a few more things, I'll try to get this done this week or early next week.

Of course it would be nice to have this in GAP 4.11 -- @alex-konovalov is in charge of that.

lib/gpprmsya.gi

lib/grppcext.gi

lib/grpreps.gi

lib/twocohom.gd

lib/grppcext.gi

fingolfin · 2019-04-27T21:57:04Z

lib/grppcext.gi

-    else
+    if not IsPcgs(Ggens) then
+      elmlist:=fail;
+      epi:=EpimorphismFromFreeGroup(G);


This code section is also untested with testinstall.

Still not covered.

fingolfin · 2019-04-27T21:57:35Z

lib/grppcext.gi

+      until l=1;
+    else
+      #D:=Stabilizer(D,M.generators,gens,genimgs,f);
+      hf:=SparseIntKeyVecListAndMatrix(false,Concatenation(M.generators));


Also not covered by testinstall.

Still not covered.

lib/grpreps.gi

fingolfin · 2019-04-27T21:58:27Z

lib/grpreps.gi

+
+  # The augmentation ideal of a P-normal subgroup lies in the radical
+  if Characteristic(F)=0 then
+    si:=TrivialSubgroup(G);


Also not covered by testinstall.

Still not covered.

lib/twocohom.gi

fingolfin · 2019-04-27T22:01:12Z

lib/twocohom.gi

+          AddSet(hastail,Length(rules));
+      fi;
+    elif Length(r[1])>1 then
+      if Length(r[2])=0 then Error("generator is trivial");fi;


Also not covered by testinstall.

Still not covered.

fingolfin · 2019-04-27T22:01:22Z

lib/twocohom.gi

+  if model<>fail then
+    q:=GQuotients(model,G)[1];
+    pre:=List(gens,x->PreImagesRepresentative(q,x));
+    ker:=KernelOfMultiplicativeGeneralMapping(q);


Also not covered by testinstall.

lib/twocohom.gi

Uses rewriting system since pc presentation will not always be available. Use a rewriting system based on extensions for the factor group (as it is smaller). Rename `PresentationCocycle` to `FpGroupCocycle` and offer to calculate a faithful permutation representation for it. Added test Add info from decomp. Avoid the global Gpword fct. for order issues. ENHANCE: Allow for different presentations for better rewriting Added IsomorphismFpGroupForRewriting and method for alternating groups. ENHANCE: Avoid duplicate test, build on existing permrep first. Examples reflect new code. Make immutable. Simplify presentation before trying permrep. Force natural An for presentation. REBASE: Fix wrong suggestion. ENHANCE: Two-Cohomology for arbitrary finite groups Uses rewriting system since pc presentation will not always be available. Use a rewriting system based on extensions for the factor group (as it is smaller). Rename `PresentationCocycle` to `FpGroupCocycle` and offer to calculate a faithful permutation representation for it. Added test Add info from decomp. Avoid the global Gpword fct. for order issues. ENHANCE: Allow for different presentations for better rewriting Added IsomorphismFpGroupForRewriting and method for alternating groups. ENHANCE: Avoid duplicate test, build on existing permrep first. Examples reflect new code. Make immutable. Simplify presentation before trying permrep. Force natural An for presentation. Simplify presentation before finding subgroup quotients Run Tietze in LargerAbelianQuotient with different heuristics ENHANCE: Two-Cohomology for arbitrary finite groups Uses rewriting system since pc presentation will not always be available. Use a rewriting system based on extensions for the factor group (as it is smaller). Rename `PresentationCocycle` to `FpGroupCocycle` and offer to calculate a faithful permutation representation for it. Added test Add info from decomp. Avoid the global Gpword fct. for order issues. ENHANCE: Allow for different presentations for better rewriting Added IsomorphismFpGroupForRewriting and method for alternating groups. ENHANCE: Avoid duplicate test, build on existing permrep first. Examples reflect new code. Make immutable. Simplify presentation before trying permrep. Force natural An for presentation. REBASE: Fix wrong suggestion. REBASE: Simplify presentation before finding subgroup quotients Run Tietze in LargerAbelianQuotient with different heuristics

Burnside-Brauer method for permutation groups. Generically: Factor out radical part stemming from P-core. Spin submodules spanned by augmentation ideal vectors for first submodul chain and chop, to avoid irreducibility tests in large regular module. Also flag fix for `TrivialModule`.

…space.

Uses Module isomorphism/automorphism code, modeled on Cannon/Holt autom. group paper. Also add action of compatible pairs

Includes action of compatible pairs on cohomology group and model.

fingolfin

Thank you for the added testinstall test. There are still about 300 new lines of code which are not covered by a test in testinstall, and the new code only has a coverage rate of ~76% as a result. I'd prefer if it was higher (not because high coverage by itself is a magic goal, but rather because it would increase my confidence in all those special cases, and also in our ability to keep this code from breaking in the future).

Anyway, I don't think we need to delay this further because of that. So let's merge it soon. (I'll wait for Travis to finish with its current truck loads of builds before merging it).

fingolfin · 2019-05-03T13:33:51Z

lib/grppcext.gi

+      B:=MTX.ModuleAutomorphisms(M);
+      if Size(B)>1 then
+        for i in Set(GeneratorsOfGroup(B)) do
+          Add(pool,DirectProductElement([One(A),i]));


This loop is still not covered.

fingolfin · 2019-05-03T13:34:08Z

lib/grppcext.gi

+
+    if oper=fail then
+      Ggens:=GeneratorsOfGroup(G);
+      oper := GroupHomomorphismByImagesNC( G, Mgrp, Ggens, M.generators );


Still not covered.

fingolfin · 2019-05-03T13:34:50Z

lib/grppcext.gi

-    else
+    if not IsPcgs(Ggens) then
+      elmlist:=fail;
+      epi:=EpimorphismFromFreeGroup(G);


Still not covered.

fingolfin · 2019-05-03T13:35:14Z

lib/grppcext.gi

+      until l=1;
+    else
+      #D:=Stabilizer(D,M.generators,gens,genimgs,f);
+      hf:=SparseIntKeyVecListAndMatrix(false,Concatenation(M.generators));


Still not covered.

fingolfin · 2019-05-03T13:35:54Z

lib/grpreps.gi

+    else
+      a:=MaximalAbelianQuotient(G);
+      si:=List(gens,x->ImagesRepresentative(a,x));
+      sub:=IrreducibleModules(Group(si),F,1);


Still not covered.

fingolfin · 2019-05-03T13:38:14Z

lib/twocohom.gi

+    monreps:=fmgens{[loff+1..off]};
+    monreal:=mgens{[loff+1..off]};
+    if IsBound(m!.rewritingSystem) then
+      k:=m!.rewritingSystem;


This is one of only two lines in this function which is no covered. Very nice!

Yes, this is as a hook for future extensions (RWS for simple groups).

fingolfin · 2019-05-03T13:38:57Z

lib/twocohom.gi

+            else x:=-i/2;fi;
+            # word must be freely cancelled
+            if Length(g)>0 and x=-g[Length(g)] then
+              Unbind(g[Length(g)]);


(This is the other uncovered line).

lib/twocohom.gi

fingolfin · 2019-05-03T13:39:41Z

lib/twocohom.gi

+          AddSet(hastail,Length(rules));
+      fi;
+    elif Length(r[1])>1 then
+      if Length(r[2])=0 then Error("generator is trivial");fi;


Still not covered.

lib/twocohom.gi

hulpke added kind: new feature do not merge PRs which are not yet ready to be merged (e.g. submitted for discussion, or test results) topic: library do not review PRs which are not yet ready for a proper external review (e.g. only submitted for test results) labels Mar 27, 2019

fingolfin reviewed Apr 1, 2019

View reviewed changes

doc/ref/grppc.xml Outdated Show resolved Hide resolved

hulpke force-pushed the ah/twocohom branch 2 times, most recently from 256316b to c26720d Compare April 8, 2019 20:13

hulpke removed the do not review PRs which are not yet ready for a proper external review (e.g. only submitted for test results) label Apr 8, 2019

hulpke added the release notes: to be added PRs introducing changes that should be (but have not yet been) mentioned in the release notes label Apr 9, 2019

hulpke force-pushed the ah/twocohom branch 2 times, most recently from 20233f4 to 2c36816 Compare April 11, 2019 21:59

hulpke changed the title ~~ENHANCE: Two-cohomology routines for non-solvable groups (WIP)~~ Non-solvable extensions: 2-Cohomology and module computation Apr 11, 2019

hulpke force-pushed the ah/twocohom branch from 2c36816 to cde56de Compare April 11, 2019 23:02

hulpke force-pushed the ah/twocohom branch 3 times, most recently from dc4d6f1 to 4b442f2 Compare April 17, 2019 01:49

hulpke removed the do not merge PRs which are not yet ready to be merged (e.g. submitted for discussion, or test results) label Apr 17, 2019

hulpke force-pushed the ah/twocohom branch from 4b442f2 to 2e6ef9e Compare April 20, 2019 01:46

fingolfin requested changes Apr 23, 2019

View reviewed changes

hulpke force-pushed the ah/twocohom branch 2 times, most recently from 7c5e2e3 to aa9bfe4 Compare April 23, 2019 16:22

fingolfin reviewed Apr 27, 2019

View reviewed changes

hulpke force-pushed the ah/twocohom branch from 081b586 to 7dbac5b Compare April 28, 2019 18:58

hulpke added 5 commits April 29, 2019 07:51

ENHANCE: Homomorphisms for 1-dimensional modules just is common eigen…

35bb98b

…space.

ENHANCE: CompatiblePairs also works if group is not solvable

753b4bd

Uses Module isomorphism/automorphism code, modeled on Cannon/Holt autom. group paper. Also add action of compatible pairs

TWOCOHOM: Added tests: Construction of perfect groups

6cdc4d8

Includes action of compatible pairs on cohomology group and model.

CLEANUP: Replace tabs with blanks as requested

ba83355

hulpke force-pushed the ah/twocohom branch from 7dbac5b to ba83355 Compare April 29, 2019 13:51

fingolfin approved these changes May 3, 2019

View reviewed changes

fingolfin merged commit f00ff61 into gap-system:master May 3, 2019

fingolfin changed the title ~~Non-solvable extensions: 2-Cohomology and module computation~~ Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via TwoCohomologyGeneric Aug 21, 2019

DominikBernhardt added release notes: added PRs introducing changes that have since been mentioned in the release notes and removed release notes: to be added PRs introducing changes that should be (but have not yet been) mentioned in the release notes labels Aug 21, 2019

olexandr-konovalov added this to the GAP 4.11.0 milestone Feb 15, 2020

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Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via `TwoCohomologyGeneric` #3383

Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via `TwoCohomologyGeneric` #3383

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Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via TwoCohomologyGeneric #3383

Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via TwoCohomologyGeneric #3383

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Codecov Report

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Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via `TwoCohomologyGeneric` #3383

Implement 2-cohomology and module computations for arbitrary finite groups, not just solvable ones, via `TwoCohomologyGeneric` #3383

hulpke commented Mar 27, 2019 •

edited

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codecov bot commented Mar 29, 2019 •

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coveralls commented Apr 8, 2019 •

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