#6633: optimize computation of matrices of Hecke operators on modular symbols
spaces
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Reporter: was | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.1.1
Component: modular forms | Keywords:
Reviewer: | Author:
Merged: |
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Compare the following, both on 64-bit OS X:
{{{
SAGE-4.1:
sage: S = ModularSymbols(225,2,sign=1).cuspidal_subspace()
sage: time z = [S.hecke_matrix(n) for n in [1..S.dimension()*2]]
CPU times: user 1.14 s, sys: 0.03 s, total: 1.17 s
Wall time: 1.18 s
and
Magma V2.15-11 Sun Jul 26 2009 15:46:04 on flat [Seed = 672054977]
Type ? for help. Type <Ctrl>-D to quit.
> M := CuspidalSubspace(ModularSymbols(225,2,1));
> time K := [HeckeOperator(M, n) : n in [1..Dimension(M)*2]];
Time: 0.070
>
}}}
Magma is 16.7 times faster at computing those Hecke matrices. I think I
seriously screwed up in deciding on an algorithm for computing Hecke
matrices back in 2005 when I first implemented this stuff. I need to
basically just reimplement tightly in Cython code for doing this (most of
the relevant corresponding magma code for this operation is in C, by the
way). In particular, I use matrix multiplication for reducing modular
the relations, which is evidently very bad.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6633>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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