Retry kernel recognition for missing generators

[fingolfin]

Final verification can expose a missing residual kernel element. Add it to gensN and rerun kernel recognition before aborting.

Co-authored-by: Codex codex@openai.com

[codecov]

Codecov Report

❌ Patch coverage is 75.00000% with 9 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.51%. Comparing base (6bd8e0a) to head (12654e0).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
gap/base/recognition.gi	75.00%	9 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #519      +/-   ##
==========================================
- Coverage   86.51%   86.51%   -0.01%     
==========================================
  Files          45       45              
  Lines       19262    19284      +22     
==========================================
+ Hits        16665    16684      +19     
- Misses       2597     2600       +3     

Files with missing lines	Coverage Δ
gap/base/recognition.gi	72.91% <75.00%> (+0.38%)	⬆️

... and 1 file with indirect coverage changes

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[fingolfin]

Hrm, I guess if this returns fail at this point, we are in deep troubles, and ought to abort. Actually, if we did everything right before getting here, shouldn't this be effectively impossible? Hrm.

[TWiedemann]

I think x could potentially be fail if KernelRecogNode(ImageRecogNode(ri)) is too small. In any case, I agree that we ought to abort in this situation (which is what the code currently does).

[TWiedemann]

Actually, my statement that the code currently aborts in this situation is not entirely correct. I think it does not abort in the following situation:

• The for loop finds some h with SLPforElement(ri, h) = fail, and x := ImageElm(Homom(ri), h) is not fail for this h, and s := SLPforElement(ImageRecogNode(ri), x) is also not fail. This results in done being set to false.
• In a later iteration of the for loop, we find some h with SLPforElement(ri, h) = fail, but this time x := ImageElm(Homom(ri), h) is fail. Since done is still false from a previous iteration, the code does not abort.

[TWiedemann]

Suggested change

	if x <> fail then
	s := SLPforElement(ImageRecogNode(ri), x);
	else
	s := fail;
	fi;
	if s <> fail then
	y := ResultOfStraightLineProgram(s, ri!.pregensfacwithmem);
	z := ri!.gensHmem[i] * y^-1;
	if not isone(ri)(z) and
	not ForAny(gensN(ri), x -> isequal(ri)(x, z)) then
	Add(gensN(ri), z);
	Info(InfoRecog, 2,
	"Final verification found extra kernel ",
	"element (depth=", depth, ").");
	done := false;
	fi;
	fi;
	if done then
	# NiceGens(ri) is too small, abort
	if InfoLevel(InfoRecog) = 1 and depth = 0 then
	Print("\n");
	fi;
	Info(InfoRecog, 1,
	"RecogNode <ri> could not be recognised,",
	" IsReady(<ri>) is not set, recognition aborts");
	return ri;
	fi;
	abort := false;
	if x <> fail then
	s := SLPforElement(ImageRecogNode(ri), x);
	else
	s := fail;
	abort := true;
	fi;
	if s <> fail then
	y := ResultOfStraightLineProgram(s, ri!.pregensfacwithmem);
	z := ri!.gensHmem[i] * y^-1;
	if not isone(ri)(z) and
	not ForAny(gensN(ri), x -> isequal(ri)(x, z)) then
	Add(gensN(ri), z);
	Info(InfoRecog, 2,
	"Final verification found extra kernel ",
	"element (depth=", depth, ").");
	done := false;
	else
	# This should not be possible: If z is one or already in gensN(ri),
	# then we should have been able to find an SLP for h in the first place.
	abort := true;
	fi;
	fi;
	if abort then
	# NiceGens(ri) is too small, abort
	if InfoLevel(InfoRecog) = 1 and depth = 0 then
	Print("\n");
	fi;
	Info(InfoRecog, 1,
	"RecogNode <ri> could not be recognised,",
	" IsReady(<ri>) is not set, recognition aborts");
	return ri;
	fi;

I think this change makes the code abort as it should.