Use cantor_product for Cartesian products of infinite enumerated sets

[mkoeppe]

(split out from #19195)

CC: @tscrim @yyyyx4 @videlec @jhpalmieri

Component: combinatorics

Author: Matthias Koeppe

Branch/Commit: a20341e

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/34374

[mkoeppe]

Branch: u/mkoeppe/use_cantor_product_for_cartesian_products_of_infinite_enumerated_sets

[mkoeppe]

Author: Matthias Koeppe

[mkoeppe]

New commits:

2edbdba	Sets.CartesianProducts.ParentMethods.__iter__: Use cantor_product if factors other than first are infinite
8890f1e	src/sage/categories/sets_cat.py: Update documentation - cantor_product refines with revlex
a20341e	src/sage/categories/sets_cat.py: Rephrase cartesian product docstring

[mkoeppe]

Commit: a20341e

[jhpalmieri]

comment:3

The behavior of for x in iter(cartesian_product([RR, RR])): print(x) has changed with this ticket, I think in an improvement. Old version:

sage: for x in iter(cartesian_product([RR, RR])): print(x)
/Users/jpalmier/Desktop/Sage/git/sage/src/sage/categories/sets_cat.py:2300: UserWarning: Sage is not able to determine whether the factors of this Cartesian product are finite. The lexicographic ordering might not go through all elements.
  warn("Sage is not able to determine whether the factors of "
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 for x in iter(cartesian_product([RR, RR])): print(x)
...
NotImplementedError: object does not support iteration

New version:

sage: for x in iter(cartesian_product([RR, RR])): print(x)
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)
Input In [1], in <cell line: 1>()
----> 1 for x in iter(cartesian_product([RR, RR])): print(x)
...
NotImplementedError: object does not support iteration

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:4

LGTM.

[mkoeppe]

comment:5

Thanks!

[vbraun]

Changed branch from u/mkoeppe/use_cantor_product_for_cartesian_products_of_infinite_enumerated_sets to a20341e