Opened 8 years ago
Closed 8 years ago
#15137 closed enhancement (fixed)
Implement rightangled Artin groups
Reported by:  tscrim  Owned by:  tscrim 

Priority:  major  Milestone:  sage6.3 
Component:  group theory  Keywords:  Artin group RAAG, days54, sd58 
Cc:  vbraun, mmarco  Merged in:  
Authors:  Travis Scrimshaw  Reviewers:  Frédéric Chapoton, Miguel Marco 
Report Upstream:  N/A  Work issues:  
Branch:  473384d (Commits, GitHub, GitLab)  Commit:  473384d5da5a387464e3ba66d6f2a5ef28bb3ee5 
Dependencies:  #15603 #15669  Stopgaps: 
Description (last modified by )
This patch implements Rightangled Artin groups (RAAG's for short, a.k.a. graph groups or partially commutative groups).
Attachments (1)
Change History (32)
comment:1 Changed 8 years ago by
 Status changed from new to needs_review
comment:2 Changed 8 years ago by
Hi Travis
It's a bit of a hack, but what about using 1 for infinity in the Coxeter matrix?
cheers,
Hugh
comment:4 followup: ↓ 5 Changed 8 years ago by
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) ?
comment:5 in reply to: ↑ 4 Changed 8 years ago by
Replying to chapoton:
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.
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.
comment:6 Changed 8 years ago by
 Description modified (diff)
 Keywords Coxeter removed
 Summary changed from Implement general Coxeter groups and RAAGs to Implement rightangled Artin groups
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.
Changed 8 years ago by
comment:7 Changed 8 years ago by
 Branch set to public/groups/15137raags
 Commit set to e8de01ffac34d7a9bd27a2b81fefe728fad1dbb1
comment:8 Changed 8 years ago by
 Keywords days54 added
comment:9 Changed 8 years ago by
 Commit changed from e8de01ffac34d7a9bd27a2b81fefe728fad1dbb1 to 0f6f1b49532de4b6a55310debeb0a1f0aa6df1ca
comment:10 Changed 8 years ago by
 Cc vbraun mmarco added
 Dependencies set to #15603
Because I think they are a very interesting class of groups (and GAP doesn't have them :p
), I'd appreciate a review.
comment:11 followup: ↓ 13 Changed 8 years ago by
Would it make sense to inherit from FinitelyPresentedGroup?? Things like the Alexander matrix could be interesting to have.
comment:12 Changed 8 years ago by
1) the following does not work:
sage: G = RightAngledArtinGroup?(graphs.EmptyGraph?())
it should either fail more gracefully or succeed.
2) there is a typo "creaing"
3) maybe the string representation could use the string repr of the graph ? maybe instead of just the number of vertices ?
comment:13 in reply to: ↑ 11 Changed 8 years ago by
Replying to mmarco:
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 chapoton:
1) 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.
2) there is a typo "creaing"
Will fix.
3) 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.
comment:14 Changed 8 years ago by
 Commit changed from 0f6f1b49532de4b6a55310debeb0a1f0aa6df1ca to 7856bc45c5c3fd64a7303b7e4465b7add71ef7eb
Branch pushed to git repo; I updated commit sha1. New commits:
7856bc4  Made changes and expanded documentation.

comment:15 Changed 8 years ago by
 Commit changed from 7856bc45c5c3fd64a7303b7e4465b7add71ef7eb to 457f00d48a863dcf34eb93a95243d203ec7c69ad
Branch pushed to git repo; I updated commit sha1. New commits:
457f00d  Added FP group and gap to raag.py.

comment:16 Changed 8 years ago by
I've added a quick way to create a FP group from a RAAG and fixed all of Frederic's comments (the failing was actually uncovered a bug in the graph code).
comment:17 Changed 8 years ago by
 Commit changed from 457f00d48a863dcf34eb93a95243d203ec7c69ad to 2dff54390f37ddca1021cf69c1c5a5a32b52074d
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
30d2132  Merge branch 'develop' into public/groups/15137raags

5b42e19  Fixed complement for immutable graphs.

e2a498c  Fixed doctest output.

b6ed038  trac #15623: Immutable graph backend for Posets

ee8c395  Trac 15623: Let to_graph return an immutable graph

dcb8a0b  trac #15623: rebase on 6.1.beta4

3531566  trac #15623: Rebase on updated #15622

95cecd1  trac #15623: Removing the hack from #15622, update a variable's name

898a8e6  trac #15681: Name of immutable graphs

30dd8dd  Merge branch 'u/ncohen/15681' into public/graphs/complement15699

comment:18 Changed 8 years ago by
 Dependencies changed from #15603 to #15603 #15669
comment:19 Changed 8 years ago by
 Commit changed from 2dff54390f37ddca1021cf69c1c5a5a32b52074d to 744dd52a2bcd661e96c2c4443c66eb690cc7b6d6
Branch pushed to git repo; I updated commit sha1. New commits:
a784a50  Merge branch 'develop' into public/groups/15137raags

dae53af  Merge branch 'develop' into ticket/15623

c5b6d59  Reinsert 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/complement15699' of trac.sagemath.org:sage into public/graphs/complement15669

744dd52  Merge branch 'public/graphs/complement15669' into public/groups/15137raags

comment:20 Changed 8 years ago by
 Milestone changed from sage6.1 to sage6.2
comment:21 Changed 8 years ago by
 Commit changed from 744dd52a2bcd661e96c2c4443c66eb690cc7b6d6 to 0f5b6c84a8f5af5794af5bb91816c344b30dfb5b
comment:22 Changed 8 years ago by
 Milestone changed from sage6.2 to sage6.3
comment:23 Changed 8 years ago by
 Commit changed from 0f5b6c84a8f5af5794af5bb91816c344b30dfb5b to 86c8c872af6c1a1967b1f4045f13e4c3e0f482f6
Branch pushed to git repo; I updated commit sha1. New commits:
b30ad29  Merge branch 'public/groups/15137raags' of trac.sagemath.org:sage into public/groups/15137raags

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.

comment:24 Changed 8 years ago by
 Commit changed from 86c8c872af6c1a1967b1f4045f13e4c3e0f482f6 to d78fc558eed8254313d1aac039e17eb8883cbca9
Branch pushed to git repo; I updated commit sha1. New commits:
d78fc55  Improving documentation from talking with Miguel.

comment:25 Changed 8 years ago by
 Commit changed from d78fc558eed8254313d1aac039e17eb8883cbca9 to ce328e86d829356b8a5d17270b0d615556a86780
Branch pushed to git repo; I updated commit sha1. New commits:
ce328e8  Removed nonascii character.

comment:26 Changed 8 years ago by
 Commit changed from ce328e86d829356b8a5d17270b0d615556a86780 to 473384d5da5a387464e3ba66d6f2a5ef28bb3ee5
Branch pushed to git repo; I updated commit sha1. New commits:
473384d  Fixed citation.

comment:29 Changed 8 years ago by
 Reviewers set to Frédéric Chapoton, Miguel Marco
 Status changed from needs_work to positive_review
comment:30 Changed 8 years ago by
 Keywords sd58 added
comment:31 Changed 8 years ago by
 Branch changed from public/groups/15137raags to 473384d5da5a387464e3ba66d6f2a5ef28bb3ee5
 Resolution set to fixed
 Status changed from positive_review to closed
There is a TODO in that there isn't a good way to create a matrix over
ZZ
unionoo
. 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.