On 6/13/07, Joseph Hufnagle <> wrote: > Dear Sir, > Is it possible to find the order of a point of an elliptic curve over > a finite field using SAGE? I have been unable to find anything in the > tutorial or reference. > Thank You,
Is the finite field GF(p) or GF(p^n) with n >= 2. If the former, sage: e = EllipticCurve(GF(11),range(5)) sage: P = e([4,2]) sage: P.order() 6 In the latter case, also use the order method: sage: e = EllipticCurve(GF(11^2,'a'),range(5)) sage: P = e([4,2]) sage: P.order() WARNING -- using naive point order finding over finite field! 6 *However* this is very stupidly slow. Fortunately, Martin Albrecht (a sage developer) did send me a patch a few days ago that implements a very fast algorithm for computing the order of a point -- unfortunately, it's not in the current version of SAGE, though it will be in the next version, which will be released within a week. (I can also make the patch available to you if you need it.) William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
