#16926: Merge the features of SymmetricGroupAlgebra and SymmetricGroup.algebra
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       Reporter:  nthiery        |        Owner:
           Type:  enhancement    |       Status:  new
       Priority:  major          |    Milestone:  sage-6.4
      Component:  combinatorics  |   Resolution:
       Keywords:                 |    Merged in:
        Authors:                 |    Reviewers:
Report Upstream:  N/A            |  Work issues:
         Branch:                 |       Commit:
   Dependencies:                 |     Stopgaps:
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Comment (by tscrim):

 Replying to [comment:9 darij]:
 > But we absolutely need to keep the `SGA(p)` syntax working for `SGA` a
 symmetric group algebra and `p` a permutation. And we'd do well to not
 slow it down by any significant amount.

 I agree (and this is easy enough to do with `_element_constructor_`). In
 fact, using the gap group, we'll significantly speed up the
 multiplication. Perhaps being clever by using a hybrid approach, we can
 speed up computing the basis too (IDK yet, haven't tried).

--
Ticket URL: <http://trac.sagemath.org/ticket/16926#comment:10>
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