Fusion Ring - Rmatrix

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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

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Branch: public/fusion-rmatrix-30257

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Commit: 637b3fd

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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

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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.

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Description changed:

--- 
+++ 
@@ -1,3 +1,5 @@
 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 the first four examples 5.4.1-4 in Rowell, Stong and Wang but diverge for 5.4.5. The reason for this discrepancy needs to be investigated.
+
+Edit: see [comment:3](#comment%3A3).

[sagetrac-git]

Changed commit from 637b3fd to e42ca5d

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

f22cac0	documentation work
e42ca5d	documentation work

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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.

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Description changed:

--- 
+++ 
@@ -1,5 +1,3 @@
 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 the first four examples 5.4.1-4 in Rowell, Stong and Wang but diverge for 5.4.5. The reason for this discrepancy needs to be investigated.
-
-Edit: see [comment:3](#comment%3A3).
+The results may be compared with calculations in Rowell, Stong and Wang (arXiv:0712.1377) and in Bonderson's thesis. Our results agree for the first four examples 5.4.1-4 in Rowell, Stong and Wang. The reason for this discrepancy was investigated.  (See [comment:3](#comment%3A3).)

[dwbump]

Description changed:

--- 
+++ 
@@ -1,3 +1,3 @@
 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 the first four examples 5.4.1-4 in Rowell, Stong and Wang. The reason for this discrepancy was investigated.  (See [comment:3](#comment%3A3).)
+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](#comment%3A3).)