#13461: Another WeylCharacterRing speedup
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Reporter: bump
| Owner: bump
Type: enhancement
| Status: needs_review
Priority: major
| Milestone: sage-5.4
Component: combinatorics
| Resolution:
Keywords: Weyl character ring, Demazure characters, Demazure-Lusztig
operators | Work issues:
Report Upstream: N/A
| Reviewers: Anne Schilling
Authors: Daniel Bump
| Merged in:
Dependencies:
| Stopgaps:
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Changes (by bump):
* status: needs_work => needs_review
Old description:
> After trac_13461-demazure-speedup.patch, if a WeylCharacterRing is
> created with style="coroots",
> characters are computed using not the Freudenthal multiplicity formula,
> but
> rather the Demazure character formula. This can be done using only
> integer
> addition and subtraction. If we run {{{sage -t --long
> weyl_characters.py}}},
> it is more than twice as fast (26 seconds versus 69 seconds) as
> previously.
> If we omit {{{--long}}} it is slightly slower, so there is a speedup for
> big computations and a slight penalty for small ones.
>
> Demazure characters are added as a method of WeylCharacterRing and the
> Demazure operators are implemented as methods of WeightRing elements.
>
> The second patch trac_13461-demazure-lusztig.patch implements Demazure-
> Lusztig
> operators as a method of the weight ring. For documentation see:
>
> http://sporadic.stanford.edu/bump/reference-5.4.beta1/sage/combinat/root_system/weyl_characters.html
>
> Apply:
> {{{
> trac_13461-demazure-speedup.patch
> trac_13461-demazure-lusztig.patch
> }}}
New description:
After trac_13461-demazure-speedup.patch, if a WeylCharacterRing is created
with style="coroots",
characters are computed using not the Freudenthal multiplicity formula,
but
rather the Demazure character formula. This can be done using only integer
addition and subtraction. If we run {{{sage -t --long
weyl_characters.py}}},
it is more than twice as fast (26 seconds versus 69 seconds) as
previously.
If we omit {{{--long}}} it is slightly slower, so there is a speedup for
big computations and a slight penalty for small ones.
Demazure characters are added as a method of WeylCharacterRing and the
Demazure operators and Demazure-Lusztig operators are implemented as
methods
of WeightRing elements.
For documentation see:
http://sporadic.stanford.edu/bump/reference-5.4.beta1/sage/combinat/root_system/weyl_characters.html
Apply:
{{{
trac_13461-demazure-speedup.patch
}}}
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13461#comment:13>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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