#9720: Add random echelonizable matrices to matrix/constructor.py
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Reporter: bwonderly | Owner: jason, was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.5.3
Component: linear algebra | Keywords:
Author: Billy Wonderly | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Comment(by bwonderly):
Replying to [comment:2 wdj]:
> Applies fine to 4.5.2.rc0.
>
> Two extremely minor comments off the top of my head:
>
> 1. "Generate a matrix of a desired size and rank, over a desired field,
> whose reduced row-echelon form has only whole values."
> IMHO, "integral" sounds better than "whole".
I agree completely and have made the change in the v2 patch.
> 2. It seems to me that, from the point of view of the functionality,
> using base_ring = ZZ returns the same result as base_ring = QQ.
> (I understand that over QQ the rref algorithm might be different than
over
> ZZ, but it seems to me that for the matrices you compute in the
> random_echelonizable_matrix function, the rref algorithm(s) yield
> the same result either way. Correct?
>
Yes, the rref algorithm yields the same result with base_ring as ZZ or QQ.
However, as these matrices are going to be used primarily as student
example problems I think it would be better to keep the default as QQ.
Although there should be a series of row operations without introducing
fractions that achieves rref, a student will likely want to use fractions
as they row-reduce an output matrix, and the rescale_row or
add_multiple_of_row functions will complain if fractions are introduced
working with a matrix over ZZ.
>
>
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9720#comment:3>
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