combinat/free module tensor construction

[mantepse]

This branch allows to change the base ring of a tensor product of free modules:

            sage: F = CombinatorialFreeModule(ZZ, ['a','b','c']); F
            sage: T = F.tensor(F); T
            Free module generated by {'a', 'b', 'c'} over Integer Ring # Free module generated by {'a', 'b', 'c'} over Integer Ring
            sage: T.change_ring(QQ)
            Free module generated by {'a', 'b', 'c'} over Rational Field # Free module generated by {'a', 'b', 'c'} over Rational Field

[tscrim]

Should we also do the same for the cartesian_product construction as well?

[tscrim]

LGTM, but what about doing cartesian_product as well?

[mantepse]

LGTM, but what about doing cartesian_product as well?

Like so?

diff --git a/src/sage/combinat/free_module.py b/src/sage/combinat/free_module.py
index 2f153396fc0..5daabd153fb 100644
--- a/src/sage/combinat/free_module.py
+++ b/src/sage/combinat/free_module.py
@@ -505,6 +505,15 @@ class CombinatorialFreeModule(UniqueRepresentation, Module, IndexedGenerators):
             sage: T.change_ring(QQ)
             Free module generated by {'a', 'b', 'c'} over Rational Field
              # Free module generated by {'a', 'b', 'c'} over Rational Field
+
+            sage: G = CombinatorialFreeModule(ZZ, ['x','y']); G
+            Free module generated by {'x', 'y'} over Integer Ring
+            sage: T = F.cartesian_product(G); T
+            Free module generated by {'a', 'b', 'c'} over Integer Ring
+             (+) Free module generated by {'x', 'y'} over Integer Ring
+            sage: T.change_ring(QQ)
+            Free module generated by {'a', 'b', 'c'} over Rational Field
+             (+) Free module generated by {'x', 'y'} over Rational Field
         """
         if R is self.base_ring():
             return self
@@ -515,7 +524,8 @@ class CombinatorialFreeModule(UniqueRepresentation, Module, IndexedGenerators):
             if isinstance(functor, VectorFunctor):
                 return functor(R)
             from sage.categories.tensor import TensorProductFunctor
-            if isinstance(functor, TensorProductFunctor):
+            from sage.categories.cartesian_product import CartesianProductFunctor
+            if isinstance(functor, (TensorProductFunctor, CartesianProductFunctor)):
                 return functor([f.change_ring(R) for f in args])
         raise NotImplementedError('the method change_ring() has not yet been implemented')

[tscrim]

Yes, that's correct.

[mantepse]

ready

[tscrim]

Thank you; once a green bot, then you can set a positive review.

Be aware that the extra large PEP8 stuff might result in a merge conflict. I think there is nothing that will conflict now, but I am not 100% certain.

[github-actions]

Documentation preview for this PR (built with commit c8e1693; changes) is ready! 🎉