#17798: Create a class for Coxeter matrices and types
-------------------------------------+-------------------------------------
       Reporter:  tscrim             |        Owner:  sage-combinat
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.9
      Component:  group theory       |   Resolution:
       Keywords:  Coxeter groups,    |    Merged in:
  matrices, types, days64            |    Reviewers:  Jean-Philippe Labbé,
        Authors:  Travis Scrimshaw,  |  Travis Scrimshaw
  Jean-Philippe Labbé                |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  4ca434574be9cfc2412a90113cf98968ae347247
  public/combinat/coxeter_matrices-17798|     Stopgaps:
   Dependencies:  #17990, #18152,    |
  #18743                             |
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Comment (by tscrim):

 Okay, so the issue which caused the crystals to infinitely recurse is that
 the type recognition via `subtype()` did not pass along the appropriate
 labels (I'm not 100% sure what was calling `subtype()`...). In particular,
 classical types got relabeled by `[0, 1, ...]`, and KR crystals were
 sensitive to the labellings. I fixed this (which was indicated by the fact
 that we now had to add the relabel to the `subtype` test) and in a
 separate commit I made the KR crystals less sensitive to relabellings (but
 fixing them altogether is an entirely different issue and would deserve a
 separate ticket). What had changed from our previous version was that our
 type recognition system did not support relabelling, but now using Dynkin
 diagrams it does.

 Unfortunately this did not fix the issue for cluster seeds.

--
Ticket URL: <http://trac.sagemath.org/ticket/17798#comment:71>
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