#15150: Implement NCSym
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       Reporter:  tscrim            |        Owner:  sage-combinat
           Type:  enhancement       |       Status:  needs_review
       Priority:  major             |    Milestone:  sage-5.12
      Component:  combinatorics     |   Resolution:
       Keywords:                    |    Merged in:
        Authors:  Travis Scrimshaw  |    Reviewers:
Report Upstream:  N/A               |  Work issues:
         Branch:                    |       Commit:
   Dependencies:  #15143            |     Stopgaps:
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Changes (by tscrim):

 * status:  new => needs_review


Comment:

 Okay, the patch is now ready for first review. It has full doctest
 coverage and all tests pass for me. I've removed some of the coercions in
 the old version since I was worried about possibly breaking coercion
 commutative diagrams.

 Some of the things I'm not perfectly happy about (but can live with
 currently):

 - A descriptive name of the '''q''', '''x''', and '''w''' bases.
 - No antipode for the '''w''' basis.
 - Creating the `SymmetricFunctions` base object when creating
 `SymmetricFunctionNonCommutingVariables` in order to set up the coercion.
 - Is it safe to put the natural maps `Sym -> NCSym` and `NSym -> NCSym` as
 coercions?

 The references I used are included in the documentation now too.

--
Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:7>
Sage <http://www.sagemath.org>
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