#18447: Implement dual-quasi-Schur basis in NCSF
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Reporter: zabrocki | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-6.7
Component: combinatorics | Resolution:
Keywords: ncsf, qsym, | Merged in:
quasiSchur | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | 943f817b10d71d867bdc204f06f302780a992ec5
public/combinat/zabrocki/ncsf_quasi_schur_basis/18447| Stopgaps:
Dependencies: #18415 |
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Comment (by zabrocki):
I am slightly concerned that what we call `CompositionTableaux` in Sage
are 'semi-standard reverse composition tableaux' in the literature on
quasisymmetric Schur functions. Moreover, the documentation for
`CompositionTableaux` does not mention the origin of the mathematics of
these objects. As a class in Sage I think that we should have a
definition of a class of objects that one would call composition tableaux
(which would consist of all weakly increasing or decreasing fillings of
composition diagrams) and that SSRCTs are a subclass of this set.
My modification in commit 0ba7a67 makes the change of basis done by
inverting the `_from_complete_on_basis` morphism by triangularity. It
isn't lightening fast, but my test
{{{timeit('dQS[2,2,2,2].coproduct()',number=1,repeat=1)}}} that was
running at 50 some odd seconds now runs in about 19 seconds.
There is still work to be done to speed up the `Quasisymmetric_Schur`
basis by using `number_of_SSRCT` for the `_to_monomial_on_basis` method
and the inversion method by triangularity that I used for the dual to
implement `_from_monomial_by_triangularity`.
--
Ticket URL: <http://trac.sagemath.org/ticket/18447#comment:11>
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