Make tensor of CombinatorialFreeModule use cartesian_product, deprecate CartesianProduct_iters

[videlec]

The last class to use sage.combinat.cartesian_product.CartesianProduct_iters is the CombinatorialFreeModule.

It is not simple to get rid of this since there is no check in constructing element of a combinatorial free module... hence changing the basis from being tuples to be element of a cartesian product might lead to subtle errors (e.g. #18411 comment:24). This is addressed in #18750

This will solve #18849 and probably #24900.

Part of #15425: Meta-ticket: Cleanup cartesian products

Depends on #34374

CC: @nthiery @tscrim @yyyyx4 @videlec @jhpalmieri

Component: combinatorics

Work Issues: fix sage.rings.asymptotic

Author: Frédéric Chapoton, Matthias Koeppe, ...

Issue created by migration from https://trac.sagemath.org/ticket/19195

[fchapoton]

Commit: 1eac71e

[fchapoton]

Branch: public/19195

[fchapoton]

Changed dependencies from #18411 to none

[fchapoton]

New commits:

1eac71e

work on CartesianProduct_iter

[mkoeppe]

comment:3

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

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 The last class to use `sage.combinat.cartesian_product.CartesianProduct_iters` is the `CombinatorialFreeModule`. It is not simple to get rid of this since there is no check in constructing element of a combinatorial free module... hence changing the basis from being tuples to be element of a cartesian product might lead to subtle errors (e.g. [#18411 comment:24](https://github.com/sagemath/sage/issues/18411#comment:24)).
+
+Part of #15425: Meta-ticket: Cleanup cartesian products

[mkoeppe]

Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
-The last class to use `sage.combinat.cartesian_product.CartesianProduct_iters` is the `CombinatorialFreeModule`. It is not simple to get rid of this since there is no check in constructing element of a combinatorial free module... hence changing the basis from being tuples to be element of a cartesian product might lead to subtle errors (e.g. [#18411 comment:24](https://github.com/sagemath/sage/issues/18411#comment:24)).
+The last class to use `sage.combinat.cartesian_product.CartesianProduct_iters` is the `CombinatorialFreeModule`. 
+
+It is not simple to get rid of this since there is no check in constructing element of a combinatorial free module... hence changing the basis from being tuples to be element of a cartesian product might lead to subtle errors (e.g. [#18411 comment:24](https://github.com/sagemath/sage/issues/18411#comment:24)). This is addressed in #18750
 
 Part of #15425: Meta-ticket: Cleanup cartesian products

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

75bf2bd

work on CartesianProduct_iter

[sagetrac-git]

Changed commit from 1eac71e to 75bf2bd

[mkoeppe]

comment:11

Rebased. Some doctests need to be updated. In particular:

**********************************************************************
File "src/sage/combinat/free_module.py", line 1520, in sage.combinat.free_module.CombinatorialFreeModule.CombinatorialFreeModule_Tensor._coerce_map_from_
Failed example:
    S.an_element()
Expected:
    3*B[0] # B[-1] + 2*B[0] # B[0] + 2*B[0] # B[1]
...
    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.
    3*B[0] # B[-1] + B[0] # B[0] + 2*B[0] # B[1] + B[1] # B[1]

[mkoeppe]

Description changed:

--- 
+++ 
@@ -2,4 +2,6 @@
 
 It is not simple to get rid of this since there is no check in constructing element of a combinatorial free module... hence changing the basis from being tuples to be element of a cartesian product might lead to subtle errors (e.g. [#18411 comment:24](https://github.com/sagemath/sage/issues/18411#comment:24)). This is addressed in #18750
 
+This will solve #18849.
+
 Part of #15425: Meta-ticket: Cleanup cartesian products