Fusion Ring Operations; Central Charge

[physicstravels]

This ticket is a successor to #27036.

The Virasoro central charge of a FusionRing is computed using the formula for WZW conformal field theories. This allows us to coerce the square root of the global quantum dimension into the cyclotomic field and normalize the S-matrix. So there are a lot of benfits.

Here is a temporary link to a build of the documentation:

http://match.stanford.edu/reference/combinat/sage/combinat/root_system/fusion_ring.html

Depends on #27036

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

Component: combinatorics

Author: Daniel Bump, Guillermo Aboumrad

Branch/Commit: c3a8036

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29615

[physicstravels]

Branch: u/gh-physicstravels/fusion_ring_operations

[sagetrac-git]

Commit: 50c5ac8

[sagetrac-git]

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

[sagetrac-git]

Changed commit from 50c5ac8 to e77eca1

[sagetrac-git]

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

bbd6ac5	new methods for FusionRings: s-matrix, q_dimension, twists etc
11f0174	created FusionRing.Element class
ef131a0	doctests added, updated q_field, and S-matrix computation
c5a2349	revised doctest
e77eca1	work on revising self.s_ij

[sagetrac-git]

Changed commit from e77eca1 to 48fb1f9

[sagetrac-git]

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

48fb1f9

Update to py3. Fix doctests.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

[sagetrac-git]

Changed commit from 48fb1f9 to 50c5ac8

[sagetrac-git]

Changed commit from 50c5ac8 to 48fb1f9

[sagetrac-git]

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

bbd6ac5	new methods for FusionRings: s-matrix, q_dimension, twists etc
11f0174	created FusionRing.Element class
ef131a0	doctests added, updated q_field, and S-matrix computation
c5a2349	revised doctest
e77eca1	work on revising self.s_ij
48fb1f9	Update to py3. Fix doctests.

[sagetrac-git]

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

16b56a8	new methods for FusionRings: s-matrix, q_dimension, twists etc
dd4f948	created FusionRing.Element class
eb09e3f	doctests added, updated q_field, and S-matrix computation
7be38ba	revised doctest
a5bc48f	work on revising self.s_ij
5438494	Update to py3. Fix doctests.

[sagetrac-git]

Changed commit from 48fb1f9 to 5438494

[dwbump]

Changed commit from 5438494 to b1eff35

[dwbump]

Changed branch from u/gh-physicstravels/fusion_ring_operations to public/fusion_central_charge-29615

[dwbump]

comment:11

I am changing the branch from u/gh-physicstravels/fusion_ring_operations
to public/fusion_central_charge-29615. The original branch was merged into
public/fusion_ring_operations-27036.

---

Last 10 new commits:

0974b08	explain about conjugate in Verlinde formula
e9de384	revision of twists docstring
0e97174	fix newline before docstring
1b6e82f	Merge branch 'public/fusion_ring_operations-27036' of git://trac.sagemath.org/sage into public/fusion_ring_operations-27036
642e80f	Final reviewer changes.
8918e84	remove S = tester.some_elements()
500f767	new method to_field, rewriting s_ij
6640ce6	D_plus and D_minus
db2eaa8	work on central charge
b1eff35	doc revision

[dwbump]

Dependencies: #27036

[sagetrac-git]

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

f06dad2

various improvements

[sagetrac-git]

Changed commit from b1eff35 to f06dad2

[dwbump]

Author: Daniel Bump, Guillermo Aboumrad

[sagetrac-git]

Changed commit from f06dad2 to eb20485

[sagetrac-git]

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

eb20485

test revision

[sagetrac-git]

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

655ec2c

Some reviewer changes.

[sagetrac-git]

Changed commit from eb20485 to 655ec2c

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:18

I made some reviewer changes. Most of them are documentation and coding style, but two important things:

• Renamed to_field to root_of_unity as I feel this is more descriptive of what the method actually does.

• Implemented what appears to generically be a faster normalization of the twist:

  sage: E62 = FusionRing("E6", 2)
  sage: %timeit [x.twist() for x in E62.basis()]
  10000 loops, best of 5: 125 µs per loop
  

  versus before

  10000 loops, best of 5: 128 µs per loop
  

  I am getting these precise timings consistently, so the ~2% speedup is not just noise.

If my changes are good, then you can set a positive review.

[sagetrac-git]

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

377f694	remove two unused variable assignments found by pyflakes
590aeee	Merge branch 'public/fusion_central_charge-29615' of trac.sagemath.org:sage into fusion_central_charge-29615
c3a8036	remove long time from A23 assign so test does not fail

[sagetrac-git]

Changed commit from 655ec2c to c3a8036

[vbraun]

Changed branch from public/fusion_central_charge-29615 to c3a8036