#15082: speedup of k-Schur functions at t=1
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Reporter: zabrocki | Owner:
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.12
Component: combinatorics | Keywords:
Merged in: | Authors: Mike Zabrocki
Reviewers: Anne Schilling | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This patch will implement two improvements to the k-Schur functions at
t=1. The first is a change to `_to_schur_on_basis` and the second is a
change to how the product is calculated. Both will improve the algorithm
for doing these calculations by factoring out k-rectangles which are known
to multiply by the rule `s_R*s^{(k)}_\lambda = s^{(k)}_{\lambda\cup R}`.
Currently `_to_schur_on_basis` is computed by determining the tableau in
the k-atom of a given shape. Factoring out maximal rectangles seems to
reduce the computation by orders of magnitude for large examples.
Before:
{{{
sage: Sym = SymmetricFunctions(QQ); ks3 = Sym.kschur(3,1); s = Sym.s()
sage: timeit("s(ks3([3,3,3,2,2,1,1,1]))", number = 1, repeat = 1)
1 loops, best of 1: 7.43 s per loop
}}}
After:
{{{
sage: Sym = SymmetricFunctions(QQ); ks3 = Sym.kschur(3,1); s = Sym.s()
sage: timeit("s(ks3([3,3,3,2,2,1,1,1]))", number = 1, repeat = 1)
1 loops, best of 1: 55.5 ms per loop
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/15082>
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