#12630: Add representations of quivers and quiver algebras to sage
-------------------------------------+-------------------------------------
       Reporter:  JStarx             |        Owner:  AlexGhitza
           Type:  enhancement        |       Status:  closed
       Priority:  major              |    Milestone:  sage-6.3
      Component:  algebra            |   Resolution:  fixed
       Keywords:  algebra, quiver,   |    Merged in:
  module, days49                     |    Reviewers:  Simon King, Travis
        Authors:  Jim Stark, Simon   |  Scrimshaw
  King, Mathieu Guay-Paquet, Aladin  |  Work issues:
  Virmaux                            |       Commit:
Report Upstream:  N/A                |     Stopgaps:
         Branch:                     |
  f3402ef849622e1f5a7d88205c2911ecd6d03ffa|
   Dependencies:  #12412, #12413,    |
  #14806, #15491, #15623, #15810     |
-------------------------------------+-------------------------------------
Changes (by nthiery):

 * commit:  f3402ef849622e1f5a7d88205c2911ecd6d03ffa =>


Comment:

 Hi!

 With #15801 and this ticket, I am getting the following error:
 {{{
         sage: Q = DiGraph({1:{3:['a']}, 2:{3:['b']}}).path_semigroup()
         sage: spaces = {1: QQ^2, 2: QQ^3, 3: QQ^2}
         sage: maps = {(1, 3, 'a'): (QQ^2).Hom(QQ^2).identity(), (2, 3,
 'b'): [[1, 0], [0, 0], [0, 0]]}
         sage: M = Q.representation(QQ, spaces, maps)
         sage: TestSuite(M).run()
         Failure in _test_category:
         ...
         The following tests failed: _test_category
 }}}

 And indeed:
 {{{
 sage: M in M.category()
 False
 }}}

 This is due to the following (apparent?) inconsistency:
 {{{
 sage: M.category().base_ring()
 Path algebra of Multi-digraph on 3 vertices over Rational Field
 sage: M.base_ring()
 Rational Field
 }}}

 Question: which one do we want to change?

 Cheers,
                                Nicolas

--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:270>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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