#6671: [with patch, needs review] Speed of Victor Miller basis
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Reporter: mraum | Owner: mraum
Type: enhancement | Status: new
Priority: minor | Milestone: sage-4.1.1
Component: modular forms | Keywords:
Reviewer: | Author:
Merged: |
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This cythonfies Eisenstein series and uses FLINT instead of NTL to speed
up Victor Miller basis by factor 2 and Eisenstein series even more.
Old
{{{
sage: %timeit eisenstein_series_qexp(18, 1000)
10 loops, best of 3: 19.3 ms per loop
sage: %timeit victor_miller_basis(18, 1000)
10 loops, best of 3: 51 ms per loop
sage: %timeit victor_miller_basis(18, 10000)
10 loops, best of 3: 711 ms per loop
sage: %timeit victor_miller_basis(18, 100000)
10 loops, best of 3: 9.86 s per loop
}}}
New
{{{
sage: %timeit eisenstein_series_qexp(18, 1000)
100 loops, best of 3: 4.17 ms per loop
sage: %timeit victor_miller_basis(18, 1000)
10 loops, best of 3: 22.9 ms per loop
sage: %timeit victor_miller_basis(18, 10000)
10 loops, best of 3: 263 ms per loop
sage: %timeit victor_miller_basis(18, 100000)
10 loops, best of 3: 4.29 s per loop
}}}
This also has some effect on echelon basis of modular forms.
Old
{{{
sage: %time h = ModularForms(1, 18).echelon_basis()[0].qexp(10000)
CPU times: user 5.00 s, sys: 0.12 s, total: 5.12 s
Wall time: 5.13 s
}}}
New
{{{
sage: %time h = ModularForms(1, 18).echelon_basis()[0].qexp(10000)
CPU times: user 4.70 s, sys: 0.09 s, total: 4.79 s
Wall time: 4.80 s
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6671>
Sage <http://sagemath.org/>
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