#12630: Add representations of quivers and quiver algebras to sage
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       Reporter:  JStarx                                                      | 
        Owner:  AlexGhitza                                            
           Type:  enhancement                                                 | 
       Status:  needs_work                                            
       Priority:  major                                                       | 
    Milestone:  sage-5.11                                             
      Component:  algebra                                                     | 
   Resolution:                                                        
       Keywords:  algebra, quiver, module, days49                             | 
  Work issues:  Use existing infrastructure for Homspase and Morphism.
Report Upstream:  N/A                                                         | 
    Reviewers:                                                        
        Authors:  Jim Stark, Simon King, Mathieu Guay-Paquet, Aladin Virmaux  | 
    Merged in:                                                        
   Dependencies:  #12412, #12413                                              | 
     Stopgaps:                                                        
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Comment (by SimonKing):

 It may be that the last remaining doctest is just a problem with _repr_.
 However, the returned representation really looks fishy, it looks like the
 quiver involved is broken. So, let's investigate what is happening.

 Note that I think the following test should be rewritten anyway. The
 morphism f should be constructed via `f = P2.hom({1:[1, 1], 2:[[1], [1]]},
 M2)` or so, since this is generally the preferred way of creating a
 morphism. Importing and directly calling a class that has a "mutilated"
 name (`QuiverRepHom`) is not what the user is supposed to do. The simple
 reason is that the user would first need to learn where to import it from.
 But `hom` is a method that the user has very likely seen before in Sage.

 {{{
     sage: Q2 = Quiver({1:{2:['a', 'b']}})
     sage: M2 = QuiverRep(QQ, Q2, {1: QQ^2, 2: QQ^1}, {(1, 2, 'a'): [1, 0],
 (1, 2, 'b'): [0, 1]})
     sage: P2 = Q2.P(QQ, 1)
     sage: from sage.quivers.morphism import QuiverRepHom
     sage: f = QuiverRepHom(P2, M2, {1:[1, 1], 2:[[1], [1]]})
     sage: f.linear_dual()
 Expect:
     Homomorphism of representations of Quiver on 2 vertices
 Got:
     Homomorphism of representations of Quiver on Reverse of ()
 }}}

 The underlying problem seems to be this:
 {{{
 sage: Q2.reverse()
 Quiver on Reverse of ()
 }}}

 So, let's have a look at the `reverse()` method.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:80>
Sage <http://www.sagemath.org>
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