#18447: Implement dual-quasi-Schur basis in NCSF
-------------------------------------+-------------------------------------
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: | 67263efe75616ab45a6a97e0205462c05612e5c2
public/combinat/zabrocki/ncsf_quasi_schur_basis/18447| Stopgaps:
Dependencies: #18415 |
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Comment (by zabrocki):
I have restored the coercions `_on_basis` (rather than
`_by_triangularity`) using transition matrices. The main difference in
the `QS` basis is that the coercion is to/from the monomial basis instead
of the fundamental basis and the `_from_monomial_transition_matrix` calls
`number_of_SSRCT`. This is significantly faster than creating the
`_from_fundmental_transition_matrix` using `CompositionTableaux`.
Comparing to branch b8cefb8 (with a @cached_method in from of
`_to_monomial_on_basis`)
{{{
sage: timeit('QS[1,2,1]*QS[2,2]',number=1,repeat=1)
1 loops, best of 1: 46.3 s per loop
sage: timeit('QS[1,2,1]*QS[2,3]',number=1,repeat=1)
1 loops, best of 1: 421 s per loop
}}}
Same calculation on current branch
{{{
sage: timeit('QS[1,2,1]*QS[2,2]',number=1,repeat=1)
1 loops, best of 1: 18.7 s per loop
sage: timeit('QS[1,2,1]*QS[2,3]',number=1,repeat=1)
1 loops, best of 1: 90.7 s per loop
}}}
I've optimized here the single calculation, but subsequent calculations
are all cached and will be faster (and faster than my
`_to/from_*_by_triangularity` methods).
--
Ticket URL: <http://trac.sagemath.org/ticket/18447#comment:17>
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