#17435: Cythonise path algebra elements
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       Reporter:  SimonKing          |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.5
      Component:  algebra            |   Resolution:
       Keywords:  path algebra       |    Merged in:
  elements                           |    Reviewers:
        Authors:  Simon King         |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  99da3361014e5397d8bc24a0ec1e2db1df6014f8
  u/SimonKing/cythonise_path_algebra_elements|     Stopgaps:
   Dependencies:  #16453             |
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Comment (by SimonKing):

 I just noticed a problem, most likely in `_sub_`:
 {{{
 sage: P =
 DiGraph({1:{1:['x','y','z']}}).path_semigroup().algebra(GF(25,'t'))
 sage: P.inject_variables()
 Defining e_1, x, y, z
 sage: e_1 + 2*x*y*x*z*z*z*x*y - z*z*x*y*z*z*x*y   # gives wrong result
 e_1 + 3*x*y*x*z*z*z*x*y + 4*z*z*x*y*z*z*x*y
 sage: e_1 - z*z*x*y*z*z*x*y + 2*x*y*x*z*z*z*x*y   # gives correct result
 e_1 + 2*x*y*x*z*z*z*x*y + 4*z*z*x*y*z*z*x*y
 }}}

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Ticket URL: <http://trac.sagemath.org/ticket/17435#comment:6>
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