#15150: Implement NCSym
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       Reporter:  tscrim            |        Owner:  sage-combinat
           Type:  enhancement       |       Status:  needs_review
       Priority:  major             |    Milestone:  sage-5.13
      Component:  combinatorics     |   Resolution:
       Keywords:                    |    Merged in:
        Authors:  Travis Scrimshaw  |    Reviewers:
Report Upstream:  N/A               |  Work issues:
         Branch:                    |       Commit:
   Dependencies:  #15143, #15164    |     Stopgaps:
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Comment (by tscrim):

 Replying to [comment:70 zabrocki]:
 > I think the slice defined in `from_symmetric_function` does not preserve
 the Hopf structure, but the projection preserves both product and
 coproduct.

 If it doesn't preserve the Hopf structure, we can't have it be a coercion
 (including the '''w''' basis to the homogeneous sym funcs). Instead we
 have to make them all conversions. I'll also add in the natural
 conversions (ex. the '''p''' basis to the powersum sym funcs) on the next
 update.

 Best,[[BR]]
 Travis

--
Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:73>
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