Raise algebras/free_algebra.py coverage to 100%

[sagetrac-JStarx]

The attached patch adds a doctest to _coerce_map_from_, which was the only function missing one.

Component: doctest coverage

Keywords: FreeAlgebra

Author: Jim Stark

Reviewer: David Loeffler

Merged: sage-5.0.beta12

Issue created by migration from https://trac.sagemath.org/ticket/12749

[loefflerd]

comment:3

In the list of things coercing into a free algebra, you have

        398	        - Polynomial rings in the same variables over a base with a coercion 
 	399	          map into self.base_ring() 

This is false: a polynomial ring (in which the variables commute) does not, and should not, coerce into a free algebra (in which they don't). Did you mean "free algebras in the same variables..."?

sage: F = FreeAlgebra(ZZ, 3, 'x,y,z')
sage: G = PolynomialRing(ZZ, 3, 'x,y,z')
sage: F.has_coerce_map_from(G)
False

[loefflerd]

Work Issues: correct false statement

[sagetrac-JStarx]

comment:4

Attachment: trac12749.patch.gz

I just copied what was in the comments into the docstring, but you're right it's incorrect. I've fixed the docstring and the comments now.

[sagetrac-JStarx]

Changed work issues from correct false statement to none

[loefflerd]

Reviewer: David Loeffler

[jdemeyer]

Merged: sage-5.0.beta12