Route sparse integer matrices to a working Smith form

[rbeezer]

Sparse integer matrices get sent to the generic Smith form routine, where they fail (see #10625). They should instead get dense-ified
and routed to the integer-only version. This solves some failures on #10604.

sage: A = matrix(2, range(4), sparse=True)
sage: A.smith_form()
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

/home/sage/sage-4.6.1.alpha2/devel/sage-main/<ipython console> in <module>()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2.Matrix.smith_form (sage/matrix/matrix2.c:37477)()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2._smith_onestep (sage/matrix/matrix2.c:42366)()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2._smith_onestep (sage/matrix/matrix2.c:42181)()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/matrix/matrix2.so in sage.matrix.matrix2._generic_clear_column (sage/matrix/matrix2.c:41049)()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/rings/integer.so in sage.rings.integer.Integer.inverse_mod (sage/rings/integer.c:28740)()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/rings/integer.so in sage.rings.integer.as_Integer (sage/rings/integer.c:6052)()

/home/sage/sage-4.6.1.alpha2/local/lib/python2.6/site-packages/sage/rings/integer.so in sage.rings.integer.Integer.__init__ (sage/rings/integer.c:7312)()

TypeError: unable to coerce <class 'sage.rings.ideal.Ideal_pid'> to an integer

CC: @dandrake @sagetrac-jthurber

Component: linear algebra

Keywords: Smith form

Author: Rob Beezer

Reviewer: David Loeffler

Merged: sage-4.6.2.alpha3

Issue created by migration from https://trac.sagemath.org/ticket/10626

[rbeezer]

Author: Rob Beezer

[rbeezer]

comment:1

Attachment: trac_10626-smith-form-integer-sparse.patch.gz

Patch mirrors docstring for dense matrices and just ships off a dense version of the matrix to that code. matrix/matrix_integer_sparse.pyx is not included into the documentation, so I've added that chore to my list.

[loefflerd]

comment:2

I've just uploaded a patch at #10625, which makes the examples here work. That said, densifying a matrix and calculating Smith form of that using integer-specific routines is going to be much faster than calling a slow generic routine; so this patch should still be applied. Applies fine to 4.6.2.alpha0 and all doctests pass, so positive review.

[loefflerd]

Reviewer: David Loeffler

[loefflerd]

Changed keywords from none to Smith form

[jdemeyer]

Merged: sage-4.6.2.alpha3