Implement similarity classes over principal ideal local rings of length two

[amritanshu-prasad]

In the paper Similarity of matrices over local rings of length two http://arxiv.org/abs/1212.6157, the similarity classes of n x n matrices with entries in a principal ideal local ring of length two are computed for n = 2, 3, 4. These calculations are being implemented in sage.

Apply:

• attachment: trac_15029-additions-similarity_class_type-ap.patch
• attachment: trac_15029-review-ts.patch

Depends on #14907

CC: @sagetrac-sage-combinat @tscrim

Component: combinatorics

Keywords: similarity classs, matrices, local rings

Author: Amritanshu Prasad

Reviewer: Travis Scrimshaw

Merged: sage-5.13.beta0

Issue created by migration from https://trac.sagemath.org/ticket/15029

[amritanshu-prasad]

Attachment: trac_15029_similarity_local_rings-ap.patch.gz

[amritanshu-prasad]

Dependencies: #14907

[amritanshu-prasad]

Reviewer: tscrim

[tscrim]

comment:2

Hey Amri,

It seems like you've created 2 classes which are basically computing a few methods and don't contain helper methods. I would instead move these to (module-level) functions in similarity_class_type.py which take the data, q, selftranspose, invertible as arguments since there is:

• no complicated internal state across multiple functions,
• no complicated/expensive standardization or preparation needed on the inputs,
• no element classes,
• no classes inheriting from these.

Two other minor points:

• Could you use the arXiv autolink format: :arxiv.org:`1212.6157`?
• Could you remove the [mq]:... line from the patch header by doing a qrefresh -e?

Thanks,

Travis

[tscrim]

Changed reviewer from tscrim to Travis Scrimshaw

[amritanshu-prasad]

Attachment: trac_15029-additions-similarity_class_type-ap.patch.gz

Added functions for similarity over principal ideal local rings of length two

[amritanshu-prasad]

comment:4

As suggested, similarity classes for principal ideal local rings of length two is now implemented as functions in the module similarity_class_type.py

Sorry for all the whitespace changes; please ignore them.

Apply: trac_15029-additions-similarity_class_type-ap.patch

[tscrim]

comment:6

Attachment: trac_15029-review-ts.patch.gz

Hey Amri,

Here's a review patch which does a few things:

• Changes the name of the functions *2 to *_length_two to be a little more explicit.
• Adds INPUT: blocks to some of the functions.
• Fixes some docstring mistakes I didn't catch the first time around in the whole file. I also converted it to use Sage's macro for finite fields \GF{q}.

If you're happy with my changes, go ahead and set this to positive review.

Thanks for your work on this,

Travis

[tscrim]

comment:7

For patchbot:

Apply: trac_15029-additions-similarity_class_type-ap.patch​, trac_15029-review-ts.patch​

[amritanshu-prasad]

comment:8

Thanks Travis, for the considerable work. It looks great now.

Amri.

[jdemeyer]

Merged: sage-5.13.beta0