Make the is_isomorphic method for AbelianGroup and PermutationGroup work for more groups

[reiniscirpons]

This PR fixes #39893, see also #39890. The crux of the issue is that the G.is_isomorphic(H) method of AbelianGroup returns False if the group H is not an instance of AbelianGroup_class, which caused quite confusing behavior in combination with permutation_group, where G.is_isomorphic(G.permutation_group()) returns False, even though permutation_group in its documentation states that it "Return the permutation group isomorphic to this abelian group".
This seems undesirable, so I've fixed it by making the method use the GAP group isomorphism method when both groups are not instances of AbelianGroup.

Similarly, the PermutationGroup is_isomorphic method seems to reject non-permutation group instances, and then uses the GAP isomorphism function anyway. Since the GAP isomorphism checking function can handle isomorphisms between permutation and non-permutation groups, I relaxed the constraint there, so now G.permutation_group().is_isomorphic(G) also returns true for an AbelianGroup instance G.

📝 Checklist

• The title is concise and informative.
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• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
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[user202729]

I suggest catch it and re-raise NotImplementedError. Avoid exposing too much implementation detail, especially since we don't want upstream catch GAPError.

[reiniscirpons]

Good point. I did see some other parts of the library do throw a GAPError, e.g. the PrimitiveGroups function from permgroups_named.py throws a GAPError when called with too large a degree:

sage: PrimitiveGroups(2^12).cardinality()
Traceback (most recent call last):
...
GAPError: Error, Primitive groups of degree 4096 are not known!

But I see the utility of making the error message more user friendly. I could wrap the isomorphism check in a try-except block as follows:

try:
    iso = left._libgap_().IsomorphismGroups(right)
except GAPError as e:
    raise NotImplementedError(e) from None

This would catch any GAPError and retype it as a NotImplementedError hiding the original exception context. The only issue is that this would catch all GAPErrors indiscriminately, which might cause weird and confusing error messages if there are GAPErrors unrelated to isomorphisms checking of infinite groups. What are your thoughts on this?

[user202729]

is there a way to check if an object is fail in gap itself instead of converting it to str?

[reiniscirpons]

Yes, fail is a boolean in gap so the equality check x = fail; in gap would do this. I took the str(iso) != "fail" code from the is_isomorphic method of PermutationGroup:

sage/src/sage/groups/perm_gps/permgroup.py

Line 4362 in 11baeed

return str(iso) != 'fail'

Similar checking by conversion to string also appears to happen in:

sage/src/sage/libs/gap/libgap.pyx

Line 426 in 11baeed

if str(ret) == 'fail':

sage/src/sage/interfaces/gap.py

Line 451 in 11baeed

if x == 'fail':

Looking around in the codebase, I could avoid the conversion to string if I do iso == libgap.eval('fail') instead. I can implement the change here + in the relevant places in PermutationGroup. Do you think that would be preferable to doing a string conversion?