Fix and enhancements to isomorphism test

[hulpke]

Ensure the subgroup found so far remains a subgroup of the search space. This fixes the bug from #6537.

Add a documented global function AsAutomorphism(sub,autom), replacing the
local asAutom/asAutomorphism helpers that were duplicated in
AutomorphismGroup and PatheticIsomorphism.

Factor the normal subgroup class stabilization into a local function
stabilizeSubgroupClass, using permutation action and set stabilizer
instead of OrbitStabilizerAlgorithm, lower the index threshold to 10^3 for
using it.

When finding the isomorphism through multiple orbits and stabilizers, reduce
the number of generators.

Clean out some dead code and careless double computation.

Avoid searching hard for special case of 2 generators with few images. if the cost seems high a priori — tune down the special case selection.

Release notes:

A bug in the isomorphism test for groups was fixed, overall performance of the test was improved.

[codecov]

Codecov Report

❌ Patch coverage is 85.26316% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 79.00%. Comparing base (989cc35) to head (5d6329e).

Files with missing lines	Patch %	Lines
lib/autsr.gi	86.36%	12 Missing ⚠️
lib/morpheus.gi	66.66%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6544      +/-   ##
==========================================
+ Coverage   78.98%   79.00%   +0.02%     
==========================================
  Files         684      684              
  Lines      294205   294246      +41     
  Branches     8647     8670      +23     
==========================================
+ Hits       232370   232480     +110     
+ Misses      60028    59959      -69     
  Partials     1807     1807              

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[fingolfin]

Thanks a lot @hulpke . I'll try to review this in detail in the next days, but would appreciate if it was not merged before I had a chance to run some tests and understand what's going on.

[fingolfin]

That doesn't match our naming conventions, it should be, say,

Suggested change

	InstallGlobalFunction(AsAutomorphism,
	InstallGlobalFunction(OnSubgroupsByAutomorphism,

(The rds package already defines an OnSubgroups action, albeit a bit differently, so we can't just use that)

[hulpke]

I know that the name is nonstandard. But this action could be not just on subgroups, but on elements. Maybe OnGroupsAsAutomorphism?

[ThomasBreuer]

With this pull request:

gap> G:= PcGroupCode( 2716742166652831895153946432, 448 );;
gap> PatheticIsomorphism( G, G );
Error, Record Element: '<rec>.makeaqiso' must have an assigned value
Stack trace:
*[1] origa!.makeaqiso(  );
   @ /.../lib/autsr.gi:2330
 [2] makenewa( Length( GeneratorsOfGroup( a ) ) > 12 );
   @ /.../lib/autsr.gi:2354
<function "PatheticIsomorphism">( <arguments> )
 called from read-eval loop at *stdin*:19
you can enter 'quit;' to quit to outer loop

[hulpke]

gap> G:= PcGroupCode( 2716742166652831895153946432, 448 );;
gap> PatheticIsomorphism( G, G );
Error, Record Element: '<rec>.makeaqiso' must have an assigned value

Fixed. (But please note that PatheticIsomorphism is not a user function.)

[ThomasBreuer]

Fixed. (But please note that PatheticIsomorphism is not a user function.)

Thanks a lot, now the code works.

Unfortunately, I get the following timings in a related example.

codes:= [ 14471979246740899087597746358515391646652811741626724220312361444709666170613060394496,
18407730836382948665918351628479071382519842228217209675805892885401437562320551430123222420888927068003840 ];;
grps:= List( codes, c -> PcGroupCode( c, 2^9*7 ) );;
G:= grps[1];;
H:= grps[2];;
IsomorphismGroups( G, H );
time;

• GAP 4.16.0: 16,3 sec.
• GAP 4.16.1: 15,7 sec.
• current master branch: 45,8 sec.

The time increase seems to be due to a longer list of generators in the result of CompatiblePairs, which causes a larger number of LiftInduciblePair calls.

I hope that the longer generators list is not really needed. (In my examples, the actual results of IsomorphismGroups are correct in all three of the abovementioned versions.)