#16926: Merge the features of SymmetricGroupAlgebra and SymmetricGroup.algebra
-------------------------------------+-------------------------------------
       Reporter:  nthiery            |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.4
      Component:  combinatorics      |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Travis Scrimshaw   |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  public/combinat/fix_sga-16926      |  6657c31932284db43898aee3dc33ca3f5558b544
   Dependencies:  #17981             |     Stopgaps:
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Comment (by darij):

 I'm done reviewing the functionality of this patch -- it is a good step
 forward, although I wish it would address the problem in a more systematic
 way (e.g., using `AlgebraWithRealizations` to put the different bases and
 indexing sets for the symmetric group algebra on equal footing, and also
 to get rid of the accursed `mult` global variable). It doesn't introduce
 any new technical debt, though, that's for sure, and it cleans up some of
 the existing.

 On the other hand, I cannot promise that this branch causes no speed
 regressions. Someone who is better at this might want to check this. To me
 it seems that it slows down the product of two `Permutations(n)` elements
 by 50% (refining its parent, though), slows down
 `retract_okounkov_vershik` on symmetric group algebra elements by a bit,
 and speeds up `left_action_product` on a symmetric group algebra
 noticeably.

--
Ticket URL: <http://trac.sagemath.org/ticket/16926#comment:43>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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