#12630: Add representations of quivers and quiver algebras to sage
-------------------------------------+-------------------------------------
       Reporter:  JStarx             |        Owner:  AlexGhitza
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  algebra            |   Resolution:
       Keywords:  algebra, quiver,   |    Merged in:
  module, days49                     |    Reviewers:  Simon King, Travis
        Authors:  Jim Stark, Simon   |  Scrimshaw
  King, Mathieu Guay-Paquet, Aladin  |  Work issues:
  Virmaux                            |       Commit:
Report Upstream:  N/A                |  b628ce36bc8f5f67a8eae6db125064a85cd85229
         Branch:                     |     Stopgaps:
  public/combinat/quivers            |
   Dependencies:  #12412, #12413,    |
  #14806, #15491, #15623, #15810     |
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * reviewer:  Simon King => Simon King, Travis Scrimshaw


Comment:

 I've made my pass through it. The first half of the commits are adding the
 files to the doc and doing doc formatting (and 80 width lines). I've made
 three changes:

 1. There was a bug in the `all_paths()` method would consider a single
 edge from `1 -> 2` with label `'abc'` as 3 edges. Fixed.
 2. For a path algebra `A`, the `A[1]` worked. So `list(A)` would not error
 out (in fact, it would run for forever). I added an `__iter__()` so that
 it would iterate over the non-zero graded components.
 3. I made alias for `S` as `simple` for a more natural name. Similarly
 `injective` and `projective` for `I` and `P` respectively.

 If you're happy with my changes, then I believe we can set this to a
 positive review.

--
Ticket URL: <http://trac.sagemath.org/ticket/12630#comment:255>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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