Fix enumeration/cardinality of UnorderedTuples, remove dependency on GAP (for modularization)

[mkoeppe]

That's a gratuitous dependency on a heavy library, which could be rewritten using just itertools.

Part of:

• Meta-ticket: Modularize sagelib into separate distributions (pip-installable packages) sagemath-... for Sage 10.x #29705

[deinst]

I am more than willing to fix this, but I am less than certain what should be done in the case where the underlying iterable has duplicates. For example,

sage: S=[1,1,2,3,4,5]
sage: t = Tuples(S,2)
sage: t.cardinality()
25
sage: len(t.list())
36

My instinct is that Tuples.__iter__() is incorrectly implemented (it should ignore the second '1'), but I don't want to break anyone that might depend on the original behavior.

[mkoeppe]

This does look like a bug to me. @tscrim, @fchapoton, do you agree?

[tscrim]

I agree that it is a bug. As such, @deinst you do not have to fix other people's code relying on bad behavior. I would just implement both iterators with itertools and directly implement the formulas for their cardinality() methods.