#5876: [with patch, positive review] Vast speedup in P1List construction
---------------------------+------------------------------------------------
Reporter: cremona | Owner: craigcitro
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.4.2
Component: modular forms | Keywords: modular manin symbols
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Comment(by cremona):
For the record, on the same machines the previous timings I now get
{{{
sage: time P1List(10^5)
CPU times: user 0.35 s, sys: 0.01 s, total: 0.36 s
Wall time: 0.35 s
The projective line over the integers modulo 100000
sage: time P1List(10^6)
CPU times: user 7.22 s, sys: 0.13 s, total: 7.35 s
Wall time: 7.35 s
The projective line over the integers modulo 1000000
}}}
Also
{{{
sage: time P1List(1009*1013)
CPU times: user 7.33 s, sys: 0.02 s, total: 7.35 s
Wall time: 7.36 s
The projective line over the integers modulo 1022117
sage: time P1List(1000003)
CPU times: user 8.25 s, sys: 0.03 s, total: 8.28 s
Wall time: 8.28 s
The projective line over the integers modulo 1000003
}}}
We could do a lot better if were allowed to factor N: i nthe last example
(prime just over {{{10^6}}}) there is really nothing to do but it
effectively does trial division up to N/5 !
It might be worth having a version which takes as in put as well as N a
factorization (as a list of (p,e) pairs. Or just a list of divisors of N.
which is a worthwhile extra saving.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5876#comment:5>
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