#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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Comment (by zabrocki):
Overall the functionality looks good. You covered a lot of ground for a
first implementation. I don't think I will suggest other functionality,
but I will check the ones you have.
What I can see of the map from Sym -> NCSym* seems to work well.
How come you import `SymmetricFunctionsNonCommutingVariables` into the
namespace, but not the dual? It seems as though we can only access it
through `NCSym.dual()`. Is it because there is no name for the dual
space? Actually it is called ΠQSym in "Commutative Combinatorial Hopf
Algebras" `http://arxiv.org/abs/math/0605262`. I think that we can do
better than ΠQSym for a name. This reference seems to realize this space
in the ring of polynomials (see equations (23) and (55) for this
realization), but not clearly where Sym is a subalgebra.
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Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:40>
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