Fusion Ring Operations; Central Charge

673da3af-8dd7-47f0-80ed-b9ed01e784ed commented 4 years ago

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

673da3af-8dd7-47f0-80ed-b9ed01e784ed commented 4 years ago

Branch: u/gh-physicstravels/fusion_ring_operations

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Commit: 50c5ac8

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 50c5ac8 to e77eca1

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from e77eca1 to 48fb1f9

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

48fb1f9 Update to py3. Fix doctests.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 48fb1f9 to 50c5ac8

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 50c5ac8 to 48fb1f9

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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.`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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.`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 48fb1f9 to 5438494

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
+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.

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

Changed commit from 5438494 to b1eff35

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

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

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

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`

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

Dependencies: #27036

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

Description changed:

--- 
+++ 
@@ -1,3 +1,7 @@
 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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

f06dad2 various improvements

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from b1eff35 to f06dad2

6bbcde06-8197-41f1-b9a3-c998bb839000 commented 4 years ago

Author: Daniel Bump, Guillermo Aboumrad

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from f06dad2 to eb20485

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

eb20485 test revision

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

655ec2c Some reviewer changes.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from eb20485 to 655ec2c

tscrim commented 4 years ago

Reviewer: Travis Scrimshaw

tscrim commented 4 years ago

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.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 655ec2c to c3a8036

vbraun commented 4 years ago

Changed branch from public/fusion_central_charge-29615 to c3a8036

sagemath / sage

Fusion Ring Operations; Central Charge #29615