Karim Belabas on Fri, 04 Jun 2004 18:01:19 +0200 |
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
Re: Elliptic curves over finite fields |
* Mc Laughlin, James [2004-06-02 21:33]: > I use to have access to magma and there was a command there that would output what I wanted directly- something like the following, for example: > p:=1123; > r:=3; > E := EllipticCurve([GF(p,r) | 0, 0, 0, 0, 19 ]); > ord:=Order(E); > > ord would be what I wanted. [...] > I know a few extra lines of code would do what I wanted. What I wondered > was if there a command like "Order" in Magma which would do the same thing. > Seems like there should be. Currently, ellap only works for curves defined over the prime field F_p. Introducing a more general function [ or complicating the interface ] is not really useful if it only treats the simplest case, covered by a GP one-liner. I agree general finite fields should be supported, but in a systematic way. None of the (few) current developers are currently working on the 'elliptic curve' module, but I'm more than willing to accept general implementations of point-counting algorithms over finite fields ( not necessarily record-breaking ones :-) So far, I'm aware of an optimized GP implementation of SEA (over F_p), which has not been submitted yet, and a straightforward implementation of Satoh, which can be accessed from my Contributed scripts page http://www.math.u-psud.fr/~belabas/pari/scripts/ Cheers, Karim. -- Karim Belabas Tel: (+33) (0)1 69 15 57 48 Dep. de Mathematiques, Bat. 425 Fax: (+33) (0)1 69 15 60 19 Universite Paris-Sud http://www.math.u-psud.fr/~belabas/ F-91405 Orsay (France) http://pari.math.u-bordeaux.fr/ [PARI/GP]