Iteration over infinite abelian groups

[DaveWitteMorris]

Fixes #30751.

This PR adds code to the __iter__ method of AbelianGroup to handle infinite groups. For backward compatibility (and because the finite case is simpler and probably more efficient), the code for the finite case has been retained.

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[mantepse]

I think that this can be simplified slightly:

Suggested change

	if 0 not in invs:
	# The group is finite
	for t in mrange(invs):
	yield self(t)
	else:
	# A similar approach works for infinite groups.
	# (This would also work for finite groups, but is more complicated.)
	from sage.misc.mrange import cantor_product
	for t in cantor_product(*[range(n) if n > 0 else ZZ for n in invs]):
	yield self(t)
	if 0 not in invs:
	# The group is finite
	yield from map(self, mrange(invs))
	else:
	# A similar approach works for infinite groups.
	# (This would also work for finite groups, but is more complicated.)
	from sage.misc.mrange import cantor_product
	yield from map(self, cantor_product(*[range(n) if n else ZZ for n in invs]))

I suppose that negative orders should not be allowed, although:

sage: G = AbelianGroup([-4])
sage: G.cardinality()
-4

[DaveWitteMorris]

I agree that your code is an improvement, so I made the changes. (At least, I think I did, but I don't really understand github.)

[DaveWitteMorris]

I opened issue #38967 to correct the problem with negative orders.

[mantepse]

Perfekt!

[DaveWitteMorris]

Thanks for the review and your comments!