Implement right-angled Artin groups #15137

tscrim · 2013-09-01T18:54:07Z

This patch implements Right-angled Artin groups (RAAG's for short, a.k.a. graph groups or partially commutative groups).

Depends on #15603
Depends on #15669

CC: @vbraun @miguelmarco

Component: group theory

Keywords: Artin group RAAG, days54, sd58

Author: Travis Scrimshaw

Branch/Commit: 473384d

Reviewer: Frédéric Chapoton, Miguel Marco

Issue created by migration from https://trac.sagemath.org/ticket/15137

The text was updated successfully, but these errors were encountered:

tscrim · 2013-09-01T19:01:27Z

comment:1

There is a TODO in that there isn't a good way to create a matrix over ZZ union oo. By default, it coerces into the infinity ring, and explicitly working over the symbolic ring, I couldn't get the equals check to work. I think we'd need a ring for a base ring union infinity as a default coercion.

hughrthomas · 2013-09-08T23:30:09Z

comment:2

Hi Travis--

It's a bit of a hack, but what about using -1 for infinity in the Coxeter matrix?

cheers,

Hugh

tscrim · 2013-09-10T15:28:10Z

comment:3

That's a good idea. It has been done.

fchapoton · 2013-09-10T19:39:36Z

comment:4

Would it be possible to replace the symbolic ring (awful thing in my opinion) by the universal cyclotomic field (see my addon patch in #14816) ?

And how do you interact with #14816 (and also with #9290) ?

tscrim · 2013-09-10T22:49:45Z

comment:5

Replying to @fchapoton:

Would it be possible to replace the symbolic ring (awful thing in my opinion) by the universal cyclotomic field (see my addon patch in #14816) ?

I don't like the symbolic ring either, but I wan't quite sure before about how to make it work with the UCF. I'm thinking we could peel off the necessary portion of your addon patch in #14816 and put it with the Coxeter group code.

And how do you interact with #14816 (and also with #9290) ?

I didn't notice #9290, so shall we move the Coxeter group code there? I also haven't thought completely through yet how I want to interact with #14816 and Weyl groups of root systems.

tscrim · 2013-09-11T02:25:04Z

comment:6

I've split off the Coxeter portion to #9290 since that ticket already is for that. This ticket now focuses solely on a first implementation of RAAG's.

tscrim · 2013-09-11T02:25:04Z

Changed keywords from Coxeter Artin group RAAG to Artin group RAAG

tscrim · 2013-11-07T20:25:25Z

Commit: e8de01f

tscrim · 2013-11-07T20:25:25Z

comment:7

Attachment: trac_15137-groups-ts.patch.gz

New commits:

`[e8de01f](https://github.com/sagemath/sagetrac-mirror/commit/e8de01f)`	`#15137: Implement right-angled Artin groups and general Coxeter groups.`

tscrim · 2013-11-07T20:25:25Z

Branch: public/groups/15137-raags

tscrim · 2013-11-09T00:10:30Z

Changed keywords from Artin group RAAG to Artin group RAAG, days54

sagetrac-git · 2014-01-10T06:10:22Z

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

`4d5091e`	`Merge branch 'public/groups/15137-raags' of trac.sagemath.org:sage into public/groups/15137-raags`
`0f6f1b4`	`Changed to use new immutable graph backend.`

sagetrac-git · 2014-01-10T06:10:22Z

Changed commit from e8de01f to 0f6f1b4

tscrim · 2014-01-10T06:11:30Z

comment:10

Because I think they are a very interesting class of groups (and GAP doesn't have them :p), I'd appreciate a review.

tscrim · 2014-01-10T06:11:30Z

Dependencies: #15603

miguelmarco · 2014-01-10T10:45:15Z

comment:11

Would it make sense to inherit from FinitelyPresentedGroup? Things like the Alexander matrix could be interesting to have.

fchapoton · 2014-01-10T13:32:21Z

comment:12

the following does not work:

sage: G = RightAngledArtinGroup(graphs.EmptyGraph())

it should either fail more gracefully or succeed.

there is a typo "creaing"
maybe the string representation could use the string repr of the graph ? maybe instead of just the number of vertices ?

tscrim · 2014-01-10T20:28:22Z

comment:13

Replying to @miguelmarco:

Would it make sense to inherit from FinitelyPresentedGroup? Things like the Alexander matrix could be interesting to have.

I'm not sure. FinitelyPresentedGroup is a Gap group, this is implementation is pure python/Sage, and I don't know how to mix the two. There should be methods to construct the corresponding FP group, as well as the ability to pass this to Gap (as a FP group).

Replying to @fchapoton:

the following does not work:

sage: G = RightAngledArtinGroup?(graphs.EmptyGraph?())

it should either fail more gracefully or succeed.

Grrr...boarder cases; I'll fix this after I see what would be the most consistent behavior.

there is a typo "creaing"

Will fix.

maybe the string representation could use the string repr of the graph ? maybe instead of just the number of vertices ?

That would be better; will change.

sagetrac-git · 2014-01-13T15:53:27Z

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

`7856bc4`	`Made changes and expanded documentation.`

sagetrac-git · 2014-01-13T15:53:27Z

Changed commit from 0f6f1b4 to 7856bc4

sagetrac-git · 2014-01-13T16:39:58Z

Changed commit from 7856bc4 to 457f00d

tscrim · 2014-01-16T18:15:12Z

Changed dependencies from #15603 to #15603 #15669

sagetrac-git · 2014-01-30T15:10:14Z

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

`a784a50`	`Merge branch 'develop' into public/groups/15137-raags`
`dae53af`	`Merge branch 'develop' into ticket/15623`
`c5b6d59`	`Re-insert a bit of code that had been erroneously deleted in the previous merge commit`
`81fc8a4`	`Merge branch 'u/ncohen/15681' of trac.sagemath.org:sage into u/tscrim/15681`
`c393b58`	`Merge branch 'public/graphs/complement-15699' of trac.sagemath.org:sage into public/graphs/complement-15669`
`744dd52`	`Merge branch 'public/graphs/complement-15669' into public/groups/15137-raags`

sagetrac-git · 2014-01-30T15:10:14Z

Changed commit from 2dff543 to 744dd52

sagetrac-git · 2014-02-16T21:03:16Z

Changed commit from 744dd52 to 0f5b6c8

sagetrac-git · 2014-02-16T21:03:16Z

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

`e1002a5`	`Merge branch 'develop' into public/groups/15137-raags`
`0f5b6c8`	`Merge branch 'develop' into public/groups/15137-raags`

sagetrac-git · 2014-06-16T22:46:09Z

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

`b30ad29`	`Merge branch 'public/groups/15137-raags' of trac.sagemath.org:sage into public/groups/15137-raags`
`6e6d0ef`	`Fixing bad merge and added RAAG's to the catalog.`
`86c8c87`	`Rewrote RAAG as Gap group and did some logic/pickling cleanup of FP groups.`

sagetrac-git · 2014-06-16T22:46:09Z

Changed commit from 0f5b6c8 to 86c8c87

sagetrac-git · 2014-06-17T01:15:48Z

Changed commit from 86c8c87 to d78fc55

sagetrac-git · 2014-06-17T01:15:48Z

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

`d78fc55`	`Improving documentation from talking with Miguel.`

sagetrac-git · 2014-06-17T01:29:51Z

Changed commit from d78fc55 to ce328e8

sagetrac-git · 2014-06-17T01:29:51Z

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

`ce328e8`	`Removed non-ascii character.`

sagetrac-git · 2014-06-17T01:34:27Z

Changed commit from ce328e8 to 473384d

sagetrac-git · 2014-06-17T01:34:27Z

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

`473384d`	`Fixed citation.`

miguelmarco · 2014-06-17T01:39:16Z

comment:27

Looks good.

vbraun · 2014-06-18T12:08:48Z

comment:28

reviewer name

tscrim · 2014-06-18T14:16:34Z

Reviewer: Frédéric Chapoton, Miguel Marco

tscrim · 2014-06-19T00:17:42Z

Changed keywords from Artin group RAAG, days54 to Artin group RAAG, days54, sd58

vbraun · 2014-06-19T13:12:45Z

Changed branch from public/groups/15137-raags to 473384d

tscrim added this to the sage-6.1 milestone Sep 1, 2013

tscrim added c: group theory labels Sep 1, 2013

tscrim self-assigned this Sep 1, 2013

tscrim added the s: needs review label Sep 1, 2013

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tscrim changed the title ~~Implement general Coxeter groups and RAAGs~~ Implement right-angled Artin groups Sep 11, 2013

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.1, sage-6.2 Jan 30, 2014

sagetrac-vbraun-spam mannequin modified the milestones: sage-6.2, sage-6.3 May 6, 2014

miguelmarco added s: positive review and removed s: needs review labels Jun 17, 2014

vbraun added s: needs work and removed s: positive review labels Jun 18, 2014

tscrim added s: positive review and removed s: needs work labels Jun 18, 2014

vbraun removed the s: positive review label Jun 19, 2014

vbraun closed this as completed in e9dd721 Jun 19, 2014

Implement right-angled Artin groups #15137

Implement right-angled Artin groups #15137

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