Enhance matrix similarity check

[1d7ec08f-60ae-4512-91a6-8324c06eab9f]

The addition of rational form makes it possible to always compute a canonical equivalence class representative for matrix similarity, using only field operations. Computing the similarity transformation is still limited by the necessity of using Jordan form and the resulting problem of eigenvalues lying outside of the field used for the matrix entries. Various improvements to the code and error-checking have been made.

CC: @ThomasGagne @tscrim @videlec @rbeezer

Component: linear algebra

Keywords: matrix is_similar similarity

Author: Rob Beezer

Branch/Commit: 92aac67

Reviewer: Vincent Delecroix, Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/18505

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 86a80c2 to 6b168e4

[fchapoton]

comment:40

ok, please review

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Changed commit from 6b168e4 to 92aac67

[7ed8c4ca-6d56-4ae9-953a-41e42b4ed313]

Branch pushed to git repo; I updated commit sha1. New commits:

92aac67

trac 18505 fix rubric in doc

[fchapoton]

comment:42

ping ?

[fchapoton]

comment:43

ping !

[fchapoton]

comment:44

P I N G ?

[tscrim]

Changed reviewer from Vincent Delecroix to Vincent Delecroix, Travis Scrimshaw

[tscrim]

comment:45

Everything is good, but I will not set it to a positive review because I disagree with making this raise an error. So if someone else just wants to put this to a positive review, then they can.

[fchapoton]

comment:46

As a motivation for somebody to give a positive review, I have at my disposal and plan to provide an implementation of "is_similar" which gives the change-of-basis matrix over any field, once this ticket is closed.

[videlec]

comment:47

Let it go and happy new year!

[vbraun]

Changed branch from u/chapoton/18505 to 92aac67