Iteration over infinite abelian groups

[alexjbest]

Given an AbelianGroup with infinite order generators the __iter__ method silently returns an empty iterator.

sage: for a in AbelianGroup(1,[0]):
....:     print(a)

gives no output.

Either an error should be raised (like for the list method), or ideally an iterator over all elements (by lexicographic order of the powers of generators should be returned, as for

sage: for a in ZZ:
....:     print(a)
....:     if a^2 + a == 30:
....:         break

Component: group theory

Issue created by migration from https://trac.sagemath.org/ticket/30751

[mkoeppe]

comment:2

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.