#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):

 The next problem uncovered by test suites is this:
 {{{
 sage: Q = Quiver({1:{2:['a']}, 2:{3:['b']}})
 sage: A = Q.algebra(GF(7))
 age: A.one()
 e_1 + e_2 + e_3
 sage: A.an_element()
 invalid path + e_1 + 2*e_2 + 3*e_3
 sage: A.an_element()*A.one()
 e_1 + 2*e_2 + 3*e_3
 sage: A.an_element()*A.one() == A.an_element()
 False
 }}}
 So, that's very bad. Apparently, an invalid path summand vanishes when
 multiplying, but the equality test does take them into account.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12630#comment:107>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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