#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:  Make HomSpace inherit from Homset; remove UniqueFactory of 
Homspace, Homspace.__contains__, make TestSuite work
Report Upstream:  N/A                                                         | 
    Reviewers:  Simon King                                                      
                                               
        Authors:  Jim Stark, Simon King, Mathieu Guay-Paquet, Aladin Virmaux  | 
    Merged in:                                                                  
                                               
   Dependencies:  #12412, #12413                                              | 
     Stopgaps:                                                                  
                                               
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Comment (by SimonKing):

 Replying to [comment:102 SimonKing]:
 > It might be reasonable ''for now'' to overload `__call__`, by first
 trying what is now done in the `_element_constructor_`, but using an
 element_class. And only if this fails, `Homset.__call__` should be called.

 The update of the third patch implements this short term solution.

 Still TODO:

 - I found that still some tests start with importing Quiver. This is not
 needed. Quiver, in contrast to everything else of the new stuff, is in the
 global namespace.
 - Get rid of the unique factory
 - Now, as element_class is available for the Homspaces, use it! Hence, do
 not create `QuiverRepHom`, but always create homomorphisms by means of the
 element_class.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:103>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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