#12630: Add representations of quivers and quiver algebras to sage
-------------------------------------+-------------------------------------
       Reporter:  JStarx             |        Owner:  AlexGhitza
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  algebra            |   Resolution:
       Keywords:  algebra, quiver,   |    Merged in:
  module, days49                     |    Reviewers:  Simon King
        Authors:  Jim Stark, Simon   |  Work issues:
  King, Mathieu Guay-Paquet, Aladin  |       Commit:
  Virmaux                            |  b2248e0da6dcd8b6c07ff91db00491ce673576e8
Report Upstream:  N/A                |     Stopgaps:
         Branch:                     |
  public/combinat/quivers            |
   Dependencies:  #12412, #12413,    |
  #14806, #15491, #15623, #15810     |
-------------------------------------+-------------------------------------

Comment (by darij):

 I've just pushed a number of minor doc improvements along with the
 occasional sourcecode edit (mainly `base_ring.one()` instead of
 `base_ring(1)`). This is a result of several hours of trying to find bugs,
 unsuccessfully. But there is a code smell which I'm really not happy with,
 despite it being mentioned in several comments in the code:
 {{{
 sage: Q = DiGraph({1:{2:['a'], 3:['b']}, 2:{4:['c']},
 3:{4:['d']}}).path_semigroup()
 sage: P = Q.P(QQ, 2)
 sage: v = P.zero()
 sage: v.set_element([1], 2)
 sage: v._elems
 {1: (), 2: (1), 3: (), 4: (0)}
 sage: P.zero()._elems
 {1: (), 2: (1), 3: (), 4: (0)}
 }}}
 So we can change the cached `P.zero()` by using an exposed set-element
 method. Is there a way to prevent this from happening? I fear just
 mentioning it in comments is not enough; someone *will* trip over this.

 This is as close as I can get to giving this a review (I fear I have
 neither time nor competence to do a systematic review of this). All in
 all, I'm seeing good and well-documented code here; this certainly will be
 a very nice update to Sage.

--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:235>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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