#13217: Expand the Dedekind eta function more efficiently
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Reporter: arminstraub | Owner: craigcitro
Type: enhancement | Status: new
Priority: minor | Milestone: sage-5.2
Component: modular forms | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors: Armin Straub
Merged in: | Dependencies:
Stopgaps: |
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Currently, the Dedekind eta function is expanded by multiplying out its
defining truncated product. With the attached patch, Euler's identity is
used instead for a significant increase in speed.
Before:
{{{
sage: %timeit qexp_eta(ZZ[['q']],10)
625 loops, best of 3: 1.41 ms per loop
sage: %timeit qexp_eta(ZZ[['q']],100)
25 loops, best of 3: 21.4 ms per loop
sage: %timeit qexp_eta(ZZ[['q']],1000)
5 loops, best of 3: 937 ms per loop
}}}
After:
{{{
sage: %timeit qexp_eta(ZZ[['q']],10)
625 loops, best of 3: 155 µs per loop
sage: %timeit qexp_eta(ZZ[['q']],100)
625 loops, best of 3: 221 µs per loop
sage: %timeit qexp_eta(ZZ[['q']],1000)
625 loops, best of 3: 873 µs per loop
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13217>
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