FusionRing: Rmatrix revisited

[dwbump]

The R-matrix method of a FusionRing computes R^{ab}_c. If a=b it is somewhat delicate to compute. Previously a method of Leduc and Ram was used, and computation of F-matrices by #30423 seemed to show that there was an error. The difficulty is probably not in the result of Leduc and Ram (actually due to Reshetikhin) but in the implementation. This ticket replaces the algorithm with one of Bonderson, Delaney, Galindo, Rowell, Tran and Wang. Preliminary testing by computing F-matrices seems to show that this method gives correct results. (Thanks to Eric Rowell for suggesting this approach.)

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

Component: combinatorics

Keywords: FusionRing

Author: Daniel Bump, Willie Aboumrad, Travis Scrimshaw

Branch/Commit: 9c6a639

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/31284

[dwbump]

New commits:

470ffac	trac 31183: build scipy on Mac OS X Big Sur.
f88f3a2	Merge branch 'scipy-big-sur' into develop
894f956	revision of r_matrix method

[dwbump]

Branch: public/fusion_rmatrix-31284

[dwbump]

Commit: 894f956

[sagetrac-git]

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

d85f2fe

remove r_matrix_old

[sagetrac-git]

Changed commit from 894f956 to d85f2fe

[sagetrac-git]

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

87cbbdd

correction in r_matrix method

[sagetrac-git]

Changed commit from d85f2fe to 87cbbdd

[dwbump]

Changed author from bump, aboumrad to Daniel Bump, Willie Aboumrad, Travis Scrimshaw

[dwbump]

comment:5

Testing with the F-matrix computations for Type "A2" level 2 shows that this is a good fix: after this change to the R-matrix code, we have consistent hexagon and pentagon relations and are able to compute the F-matrix. This is done not with out of the box F-matrix factory in #30423 but with an improved version of that code.

[dwbump]

Changed work issues from Further testing is needed to Code from #31183 should be removed

[sagetrac-git]

Changed commit from 87cbbdd to 5300a8c

[sagetrac-git]

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

5300a8c

minor documentation edits

[sagetrac-git]

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

f410ecd

removed Leduc-Ram algorithm from r_matrix method

[sagetrac-git]

Changed commit from 5300a8c to f410ecd

[sagetrac-git]

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

9c6a639

Some trivial formatting changes.

[sagetrac-git]

Changed commit from f410ecd to 9c6a639

[tscrim]

Changed work issues from Code from #31183 should be removed to none

[tscrim]

comment:10

I just broke the one big line up into smaller parts to be more PEP8 compliant factored out the self.basis() calls. If my changes are good, then you can set a positive review.

[vbraun]

Changed branch from public/fusion_rmatrix-31284 to 9c6a639