#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 Representation, Homspace 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):

 Ah! I just saw that the default `.Hom()` method would fall back to the
 default homset, if `_Hom_` raises a type error. So, this detail is fine.

 But actually, caching of the homspace is done in `sage.categories.homset`.
 So, I see no need to use `UniqueFactory` or `UniqueRepresentation` for
 `QuiverHomspace`. And of course, `QuiverHomspace` should inherit from
 `sage.categories.homset.Homset(WithBasis)`, and not directly from
 `Parent`.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:90>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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