Fusion Ring - Rmatrix

[dwbump]

The FusionRing method captures much of the structure of a modular tensor category. One aspect that it does not capture is the R-matrix, which is implemented in this ticket.

The results may be compared with calculations in Rowell, Stong and Wang (arXiv:0712.1377) and in Bonderson's thesis. Our results agree for several examples in Rowell, Stong and Wang. The reason for an apparent discrepancy in Example 5.4.5 was investigated. (See comment:3.)

CC: @tscrim @sagetrac-sage-combinat @dwbump @willieab @physicstravels

Component: combinatorics

Keywords: FusionRing, R-matrix

Author: Daniel Bump, Guillermo Aboumrad

Branch/Commit: db68965

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/30257

[dwbump]

Branch: public/fusion-rmatrix-30257

[dwbump]

Commit: 637b3fd

[dwbump]

New commits:

f498480	new method rmatrix
6344585	bugfix in q_dimension
ca2562c	Merge branch 'cyclotomic' into rmatrix
f15e39d	doctest
39f894d	bugfix: don't reduce twist
5fe4524	use theta method in a few places
637b3fd	work on documentation

[dwbump]

comment:3

Rowell, Stong and Wang was corrected in arXiv version 4 and Example 5.4.5 agrees with our code in the corrected version.

[sagetrac-git]

Changed commit from 637b3fd to e42ca5d

[sagetrac-git]

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

f22cac0	documentation work
e42ca5d	documentation work

[dwbump]

comment:6

This method has been tested a lot in the past couple of days in computing F-matrices (using the hexagon relations). I think it is reliable.

[sagetrac-git]

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

4165a9c

pyflakes and pycodestyle requested revisions

[sagetrac-git]

Changed commit from e42ca5d to 4165a9c

[sagetrac-git]

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

ad0a2f3

more pyflakes revisions

[sagetrac-git]

Changed commit from 4165a9c to ad0a2f3

[sagetrac-git]

Changed commit from ad0a2f3 to db68965

[sagetrac-git]

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

eb257ab	Merge branch 'public/fusion-rmatrix-30257' of git://trac.sagemath.org/sage into public/fusion-rmatrix-30257
db68965	Refactored rmatrix() -> r_matrix(). Some other reviewer changes.

[tscrim]

comment:12

I renamed rmatrix() to r_matrix() to be consistent with s_matrix() and I think this is easier to read.

I renamed twist parameter reduce to reduced to avoid a conflict with the reduce builtin Python method.

I also made some minor changes to the docstrings.

If my changes are good, then positive review.

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from public/fusion-rmatrix-30257 to db68965