#18194: Speedup of calculation of Macdonald H and Ht bases
-------------------------------------+-------------------------------------
Reporter: zabrocki | Owner:
Type: PLEASE CHANGE | Status: new
Priority: minor | Milestone: sage-6.6
Component: combinatorics | Keywords: Macdonald
Merged in: | symmetric functions
Reviewers: | Authors: zabrocki
Work issues: | Report Upstream: N/A
Commit: | Branch:
9ba7893a61e4783b106cd13ad61e1190d77d901d|
public/combinat/zabrocki/mac_speedup
Stopgaps: | Dependencies:
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A formula of F. Bergeron, A. Garsia and M. Haiman gives a Pieri rule for
`h_r^\perp {\tilde H}_\mu` and this formula can be used to compute the `H`
and `Ht` bases much quicker than previous implementations. The current
implementation computes the `H` and `Ht` basis through the `J` basis and
this basis is implemented through creation operators.
For instance a command that takes a relatively long time to compute is
{{{
sage: %time H([3,2]).nabla(q=H.q,t=1/H.t)
CPU times: user 2.75 s, sys: 86.6 ms, total: 2.83 s
Wall time: 2.95 s
q^4/t^2*McdH[3, 2]
}}}
and with the new implementation the same command has the timing
{{{
CPU times: user 184 ms, sys: 18.7 ms, total: 203 ms
Wall time: 196 ms
}}}
One reason that some of the computations in the `H` and `Ht` bases take a
long time is that the entire basis a given degree is cached and so
subsequent computations will be faster. However it seems that the new
implementation is cached more efficiently and is faster.
--
Ticket URL: <http://trac.sagemath.org/ticket/18194>
Sage <http://www.sagemath.org>
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