F-Matrix Factory

[dwbump]

The FusionRing and its methods contain nearly complete information about the underlying modular tensor category. However information is lost about the associator, and this is captured by the F-matrix or 6j symbols. This ticket adds a method to compute the F-matrices.

This may be tested on the rank <=4 examples in the paper of Rowell, Stong and Wang (arXiv:0712.1377). It is able to compute F-matrices for these examples except the last one, G2 at level 2.

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

Component: combinatorics

Keywords: Fusion Ring, F-matrix

Author: Daniel Bump, Guillermo Aboumrad, Galit Anikeeva

Branch: 57825e9

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/30423

[dwbump]

New commits:

1b99dcc	added FMatrix code
2de3efb	work on doctest
559a4c8	doc revision

[dwbump]

Commit: 559a4c8

[dwbump]

Branch: public/fusion_fmatrix-30423

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

062b694

bugfix in sreduce

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6093b1e

missing import

[tscrim]

comment:4

Just a quick comment: you can use itertools.product rather than the nested for loops in hexagon and pentagon:

sage: from itertools import product
sage: list(product([1,2], repeat=3))                                                                                           
[(1, 1, 1), (1, 1, 2), (1, 2, 1), (1, 2, 2),
 (2, 1, 1), (2, 1, 2), (2, 2, 1), (2, 2, 2)]

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

7065b18

use itertools.product

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

36aafea

some doctests

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0f322ee

indentation tweak

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

0cf69fd

some of Willie's improvements

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

4ed0ec9

fix variable injection, add some of Willie's improvement's, observation of Galit reducing number of pentagon equations. Doctests are currently broke, will fix later

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

434a5c6

doctest revisions, right-handed hexagon relations

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

ec1f943

singletons, and only consider 2-term equations in substitute_degree_one

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[mkoeppe]

comment:13

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

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

80c84f7

updating shm_managers to new FMatrix interface

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Changed commit from 80c84f7 to 696742c

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

10b5e11	updating pyx files to use new FMatrix interface
696742c	pyx files now use updated FMatrix interface

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

ed9fb97

Fixing some last little details.

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

589a5b8

Just a few more polish.

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

5c29d60

back out change to fusion_ring root_of_unity method

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Changed commit from 589a5b8 to 5c29d60

[dwbump]

comment:130

The commit 589a5b8 changed the behavior of the root_of_unity method, causing a doctest failure, so I reverted this change.

[tscrim]

comment:131

I am going to insist that this raise a ValueError as None as the latter does not make sense to be returned. It should fail because the input doesn't make sense (unless you are not going to special case it, in which case the garbage-in-garbage-out rule applies). I am going to change the test.

Curiously, this was not failing for me when I was running the tests yesterday via

./sage -btp --long --warn-long src/sage/algebras/fusion_rings/

but now I can reproduce the failure.

[tscrim]

Changed branch from public/new_fmatrix-30423 to public/algebra/fmatrix-30423

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New commits:

0d6e803

Fixing failing test due to change.

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

0be29f7

Changing to a more accurate error message.

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

57825e9

Updating the documentation.

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Changed commit from 0be29f7 to 57825e9

[tscrim]

comment:135

Checked by Dan and Willie.

[vbraun]

Changed branch from public/algebra/fmatrix-30423 to 57825e9

[fchapoton]

comment:137

this broke the linter by adding final empty lines, see #34781

[fchapoton]

Changed commit from 57825e9 to none