Fix surjectivity testing for free module morphisms

[rbeezer]

Testing for surjectivity of a free module homorphism is probably just fine for vector spaces, but seems to be broken for modules.

sage: V = ZZ^2
sage: m = matrix(ZZ, [[1,2],[0,2]])
sage: phi = V.hom(m, V)
sage: phi.lift(vector(ZZ, [0, 1]))
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)

/sage/dev/devel/sage-main/<ipython console> in <module>()

/sage/dev/local/lib/python2.6/site-packages/sage/modules/free_module_morphism.pyc in lift(self, x)
    375             t = self.domain().linear_combination_of_basis(C)
    376         except TypeError:
--> 377             raise ValueError, "element is not in the image"
    378         assert self(t) == x
    379         return t

ValueError: element is not in the image
sage: phi.is_surjective()
True

Apply:

1. attachment: trac_11552-module-morphism-surjectivity-v2.patch

CC: @simon-king-jena @robertwb @miguelmarco

Component: linear algebra

Author: Rob Beezer

Reviewer: John Palmieri

Merged: sage-4.7.2.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/11552

[rbeezer]

Author: Rob Beezer

[rbeezer]

comment:3

Passes all long tests for me on 4.7.1.alpha3 and patchbot is green-lighting it at the moment.

[rbeezer]

comment:4

Attachment: trac_11552-module-morphism-surjectivity-v2.patch.gz

Version 2 patch tests if a morphism is surjective with the .is_submodule() method. Slower, I guess, but a greater chance of being correct. An example from mmarco has been added to illustrate the non-unique echelon basis for the image. The necessity of these changes is detailed on #11579 (and perhaps, see #11553).

[jhpalmieri]

comment:5

Looks good to me.

[jhpalmieri]

Reviewer: John Palmieri

[rbeezer]

comment:6

Replying to @jhpalmieri:

Looks good to me.

Thanks, John - appreciate you taking the time to look at this. - Rob

[jdemeyer]

Merged: sage-4.7.2.alpha2