#16931: Elliptic curve point counting over F_q using new PARI
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Reporter: jdemeyer | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: elliptic curves | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #15767, #16927, #8373, #16930 | Stopgaps:
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Old description:
> The new version of PARI (#15767) supports point counting over `F_q`
> instead of `F_p`. We should use this new functionality in Sage!
>
> Sneak preview:
> {{{
> sage: k.<a> = GF(2^5, impl='pari_ffelt')
> sage: E = EllipticCurve_from_j(a)
> sage: timeit('E.cardinality_exhaustive()')
> 5 loops, best of 3: 212 ms per loop
> sage: timeit('E.cardinality_pari()')
> 625 loops, best of 3: 10.6 µs per loop
> }}}
>
> {{{
> sage: k.<a> = GF(5^20)
> sage: E = EllipticCurve_from_j(a)
> sage: timeit('E.cardinality_bsgs()')
> 5 loops, best of 3: 2.18 s per loop
> sage: timeit('E.cardinality_pari()')
> 625 loops, best of 3: 18.8 µs per loop
> }}}
New description:
The new version of PARI (#15767) supports point counting over `F_q`
instead of `F_p`. We should use this new functionality in Sage!
--
Comment (by jdemeyer):
Never mind the timings, PARI does its own caching now...
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Ticket URL: <http://trac.sagemath.org/ticket/16931#comment:4>
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