#20489: A and B bases for Iwahori-Hecke algebras
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       Reporter:  andrew.mathas      |        Owner:
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-7.2
      Component:  combinatorics      |   Resolution:
       Keywords:  Iwahori-Hecke      |    Merged in:
  algebra                            |    Reviewers:
        Authors:  Andrew Mathas      |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  74ba6e2f2c7cf9cf1a63f654ba8fd108407416f9
  u/andrew.mathas/TwoIwahoriHeckeBases|     Stopgaps:
   Dependencies:                     |
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Comment (by andrew.mathas):

 Replying to [comment:11 tscrim]:
 > Also, do we need corresponding bases in
 `IwahoriHeckeAlgebra_nonstandard`?

 I know that the code actually says on lines 2266-67 that this is necessary
 but as far as I can see it isn't. To check this I wrote some doc-tests
 that involve coercions between the KL-bases and the A/B-basis and they
 work. The way we wrote it `IwahoriHeckeAlgebra_nonstandard` inherits from
 `IwahoriHeckeAlgebra` so it automatically has the `A` and `B` basis
 classes. If you agree then I should delete the comment on lines 2266-67
 (probably the comment should saythat if you want to change any of the
 defaults class then their names etc have to match those in
 `IwahoriHeckeAlgebra`).

--
Ticket URL: <http://trac.sagemath.org/ticket/20489#comment:12>
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