Tensor product and coefficients

[hivert]

Tensor products of combinatorial free modules still use an old version of
cartesian product. As a consequence extracting a coefficient is not possible:

sage: F = CombinatorialFreeModule(ZZ, [1,2]); F.__custom_name = "F"
sage: G = CombinatorialFreeModule(ZZ, [3,4]); G.__custom_name = "G"
sage: T = tensor([F, G]); T
sage: T.basis()[(1,3)].coefficient((1,3))
...
NotImplementedError:

I fix that. As a side effect, this change the result of an_element so that I
have to fix a few doctests.

Moreover, building the tensor of two infinite dimensional FM now raises a correct
warning:

sage: F = CombinatorialFreeModule(ZZ, NN)
sage: T = tensor([F, F]); T
Free module generated by Non negative integer semiring over Integer Ring ⊗ Free module generated by Non negative integer semiring over Integer Ring
sage: T.an_element()
/home/data/Sage-Install/sage-dev/local/lib/python2.7/site-packages/sage/categories/sets_cat.py:2159: 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 "
2*B[0] ⊗ B[1] + B[0] ⊗ B[0] + 3*B[0] ⊗ B[2] + B[42] ⊗ B[42]

I'm hiding this by asking only finite dim FM.

Depends on #19195

CC: @nthiery @tscrim @mkoeppe

Component: linear algebra

Keywords: tensor product, free modules

Author: Florent Hivert

Branch/Commit: public/cartesian_24900 @ bfa36e7

Issue created by migration from https://trac.sagemath.org/ticket/24900

[hivert]

Branch: u/hivert/tensor_product_and_coefficients

[hivert]

Author: Florent Hivert

[hivert]

Commit: 009c70a

[hivert]

New commits:

009c70a

Fix tensor prod. using old cartesian prod.

[fchapoton]

comment:3

many failing doctests

[fchapoton]

comment:6

rebased, just to see where this stands now

---

New commits:

29190d3

Fix tensor prod. using old cartesian prod.

[fchapoton]

Changed commit from 009c70a to 29190d3

[fchapoton]

Changed branch from u/hivert/tensor_product_and_coefficients to public/cartesian_24900

[sagetrac-git]

Changed commit from 29190d3 to bfa36e7

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

bfa36e7

fix one doctest

[mkoeppe]

Dependencies: #19195