Implement an rref() function which works over the fraction field of the base ring of a matrix

[jasongrout]

This is a resolution to the issues at #3211.

CC: @williamstein @rbeezer

Component: linear algebra

Author: Jason Grout

Reviewer: Sebastian Pancratz, Minh Van Nguyen, Karl-Dieter Crisman, Rob Beezer

Merged: sage-4.3.4.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8008

[jasongrout]

Attachment: trac-8008-rref.patch.gz

[sagetrac-spancratz]

comment:2

• Perhaps a very short statement about what the row echelon form of matrices over fields look like would be nice.

• line 4035: instead of echelon_form, I think this should be echelon_form or :meth:echelon_form

• line 4085: I'd prefer if this was done in two lines

      F = R.fraction_field()
      return self.change_ring(F).echelon_form()
  

  so that if an error occurs when creating the fraction field, the line number corresponds to the obvious problem. (Of course, this would be clear from the traceback anyway...)

Sebastian

[sagetrac-spancratz]

Reviewer: Sebastian Pancratz

[jasongrout]

apply on top of previous patch

[jasongrout]

comment:3

Attachment: trac-8008-fixes.patch.gz

[jasongrout]

comment:4

The second patch fixes the issues Sebastian brought up.