#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                |  d0932c325ede70e04db1b659bcfbf86a7b691e06
         Branch:                     |     Stopgaps:
  public/combinat/coxeter_matrices-17798|
   Dependencies:  #17990             |
-------------------------------------+-------------------------------------
Changes (by jipilab):

 * keywords:  Coxeter, groups, matrices, types, days64 => Coxeter groups,
     matrices, types, days64


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.
>
> 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?

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 [X]
 - Remove the inheritance from matrix_generic_dense [X]
 - add _matrix_ method [X]
 - 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:21>
Sage <http://www.sagemath.org>
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