#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 | Stopgaps:
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Comment (by zabrocki):
Here is one that I can see needs to be fixed.
{{{
sage: Sp = SymmetricFunctions(QQ).p()
sage: Np = SymmetricFunctionsNonCommutingVariables(QQ).p()
sage: Nh = SymmetricFunctionsNonCommutingVariables(QQ).h()
sage: Sp(Nh(Np([[1,4],[2,3]])).to_symmetric_function())
45/2*p[1, 1, 1, 1] - p[2, 1, 1] + 1/2*p[2, 2]
sage: Np([[1,4],[2,3]]).to_symmetric_function()
p[2, 2]
sage: Ne = SymmetricFunctionsNonCommutingVariables(QQ).e()
sage: Sp(Ne(Np([[1,4],[2,3]])).to_symmetric_function())
45/2*p[1, 1, 1, 1] + p[2, 1, 1] + 1/2*p[2, 2]
}}}
With '''m''', '''q''', '''x''' the coercion is consistent.
I am fairly sure the problem is with the projection
`to_symmetric_function` in the '''h''' and the '''e''' bases.
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Ticket URL: <http://trac.sagemath.org/ticket/15150#comment:52>
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