Introduce extension of scalars coercion of CombinatorialFreeModules

[tscrim]

Currently, CombinatorialFreeModule does not allow coercion from another CombinatorialFreeModule with the same indices but with a base ring coercion:

sage: C = CombinatorialFreeModule(ZZ, Set([1,2]))
sage: CQ = CombinatorialFreeModule(QQ, Set([1,2]))
sage: CQ.has_coerce_map_from(C)
False

In this ticket, we introduce such a coercion and also implement C.change_ring(QQ) (which also makes C.base_extend(QQ) work).

CC: @sagetrac-sage-combinat @nthiery @darijgr @fchapoton

Component: combinatorics

Keywords: combinatorial free module

Author: Travis Scrimshaw, Matthias Koeppe

Reviewer: Darij Grinberg

Issue created by migration from https://trac.sagemath.org/ticket/21405

[darijgr]

comment:1

Ah! That said, your example is backwards. :P

[tscrim]

Commit: 7906f74

[tscrim]

Branch: public/combinat/CFM_base_ring_coercion-21405

[tscrim]

Description changed:

--- 
+++ 
@@ -3,7 +3,7 @@
 ```sage
 sage: C = CombinatorialFreeModule(ZZ, Set([1,2]))
 sage: CQ = CombinatorialFreeModule(QQ, Set([1,2]))
-sage: C.has_coerce_map_from(CQ)
+sage: CQ.has_coerce_map_from(C)
 False
 ```
 We plan to introduce such a coercion.

[tscrim]

New commits:

7906f74

Initial version of introducing coercion of base rings.

[sagetrac-git]

Changed commit from 7906f74 to 286883e

[sagetrac-git]

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

286883e

review

[darijgr]

comment:4

See commit msg. Other than this, LGTM!

[darijgr]

Reviewer: Darij Grinberg

[tscrim]

comment:6

Nicolas, any comments or concerns? I would like your opinion on this before setting it to a positive review (Darij, I'm happy with your changes).