On Sunday 18 November 2007, David Harvey wrote: > On Nov 18, 2007, at 4:16 AM, Robert Bradshaw wrote: > >> #1130 > > > > This seems to rely on an earlier patch. (#1120?) See comments on trac. > > I'm very concerned about this patch. It is not the case that the LCM > of the orders of all elements of E(GF(q)) will equal the order of E(GF > (q)). I haven't tried the code, but if I understand the code > correctly, it will go into an infinite loop on such cases, and it may > well give incorrect results in other cases.
Yes, it should not go in, my bad, sorry. I quickly hacked to together the algorithm in "Elliptic Curves" by Lawrence Washington and apparently screwed up badly on the way. He writes: 7. If we are looking for the #E(F_q), then repeat steps (1)-(6) [finding the order of a point, malb] with randomly chosen points in E(F_q) until the greatest common multiple of the orders divides only one integer N with q + 1 -2*sqrt(q) <= N <= q + 1 + 2*sqrt(q). Then N = #E(F_q). Apparently I overread the 'divides' part. Also, what is a 'greatest common divisor'? I'll fix that for 2.9. Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _www: http://www.informatik.uni-bremen.de/~malb _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
