#18678: Implement convolution_product for HopfAlgebras
-------------------------------------+-------------------------------------
       Reporter:  alauve             |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  minor              |    Milestone:  sage-6.9
      Component:  categories         |   Resolution:
       Keywords:  days65,            |    Merged in:
  convolution product                |    Reviewers:  Franco Saliola,
        Authors:  Aaron Lauve,       |  Travis Scrimshaw
  Jean-Baptiste Priez, Amy Pang,     |  Work issues:
  Travis Scrimshaw                   |       Commit:
Report Upstream:  N/A                |  50ecfe4cbfb07f3c681979860f2d69b8508ffd25
         Branch:                     |     Stopgaps:
  public/algebras/convolution_product_hopf_algebras-18678|
   Dependencies:                     |
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * commit:  bf2279ed831a90850e5cc3777dc69ce7ca67f555 =>
     50ecfe4cbfb07f3c681979860f2d69b8508ffd25
 * branch:  u/alauve/implement_convolution_product_for_hopfalgebras =>
     public/algebras/convolution_product_hopf_algebras-18678
 * reviewer:  Franco Saliola => Franco Saliola, Travis Scrimshaw


Comment:

 I've made some changes:

 - I reworked the documentation around a bit.
 - I moved `coproduct_iterated` to `CoalgebrasWithBasis` since it is well-
 defined there.
 - I updated a few doctests for trivial failures (because of the added
 explicit category for `BialgebrasWithBasis`).

 I'm thinking this is in good enough shape to merge into Sage as-is, and if
 there are any issues/improvements, then we can handle those on followup
 tickets. Thoughts?

 ----

 For future reference, we will probably have (and want) to implement a
 custom subclass of `Morphism` for convolution products of morphisms for
 bialgebras without a specified basis (but considering we don't have any in
 Sage currently, I don't think this is a high priority).
 ----
 New commits:
 
||[http://git.sagemath.org/sage.git/commit/?id=a1d962ac30c6d5c8280a2f509900ff462210759c
 a1d962a]||{{{pyflakes cleanup of bialgebras.py.}}}||
 
||[http://git.sagemath.org/sage.git/commit/?id=50ecfe4cbfb07f3c681979860f2d69b8508ffd25
 50ecfe4]||{{{Reviewer changes for #18678.}}}||

--
Ticket URL: <http://trac.sagemath.org/ticket/18678#comment:37>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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