#17798: Create a class for Coxeter matrices and types
-------------------------------------+-------------------------------------
       Reporter:  tscrim             |        Owner:  sage-combinat
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.6
      Component:  group theory       |   Resolution:
       Keywords:  Coxeter, groups,   |    Merged in:
  matrices, types, days64            |    Reviewers:
        Authors:  Travis Scrimshaw,  |  Work issues:
  Jean-Philippe Labbé                |       Commit:
Report Upstream:  N/A                |  86b2d78d02683fee74b77742fee3ffd45ffb2e29
         Branch:                     |     Stopgaps:
  public/combinat/coxeter_matrices-17798|
   Dependencies:  #17990             |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Travis Scrimshaw, Jean-Philippe Labb\xe9', 
'oldvalue': u'Travis Scrimshaw'}):

 * keywords:  Coxeter, groups, matrices, types => Coxeter, groups, matrices,
     types, days64
 * cc: jmichel (added)
 * author:  Travis Scrimshaw => Travis Scrimshaw, Jean-Philippe Labbé


Old description:

> This is a partial step towards #16126, but carries the necessary
> information to speed up #16630 when the input is given as a finite
> !Cartan/Coxeter type.

New description:

 This is a partial step towards #16126, but carries the necessary
 information to speed up #16630 when the input is given as a finite
 !Cartan/Coxeter type.

 There are a few things TO DO in the current patch:

 - Subdivided the init into smaller methods
 - Maybe change the name of CoxeterType.py to type_coxeter?
 - Added doctests
 - Add a __getitem__ method using the index_set
 - Remove the inheritance from matrix_generic_dense
 - add _matrix_ method
 - put is_finite, is_affine in attributes
 - put samples in Coxetertype
 - improve the check_coxeter_type code


 Eventually, maybe create an abstract class for Coxeter matrices and Cartan
 matrices?

--

--
Ticket URL: <http://trac.sagemath.org/ticket/17798#comment:15>
Sage <http://www.sagemath.org>
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