#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:  Add a TestSuite test
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):

 And here is the problem:
 {{{
     def product_on_basis(self, p1, p2):
         FSC = self._free_small_category
         p = FSC(p1)*FSC(p2)
         if p:
             return self.basis()[p]
         else:
             return self.zero()
 }}}

 If p is the invalid path, then it evaluates to False, but still
 `self.basis()[p]!=self.zero()`. I think this is a bug. If one decides to
 distinguish the invalid path from zero, then one must accept the
 consequences also in multiplying elements.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:108>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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