The simplest workaround, I think, is to set E._point_class = sage.schemes.elliptic_curves.ell_field.EllipticCurve_finite_field
after creating E and before attempting to create points. Example: sage: E6 = EllipticCurve(Integers(6),[0,0,1,-1,0]) sage: E6._point_class = sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field sage: P = E6(0,-1) sage: P (0 : 5 : 1) sage: 2*P (1 : 5 : 1) sage: 3*P (5 : 0 : 1) sage: 4*P (2 : 2 : 1) sage: 5*P boom! but helpfully: ZeroDivisionError: Inverse of 4 does not exist enabling one to find a factorization of 6. For a less trivial example (Taken from my own lecture notes): sage: N = 1715761513 sage: E = EllipticCurve(Integers(N),[3,-13]) sage: E._point_class = sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field sage: P = E(2,1) sage: m = LCM([2..100]) sage: m*P ... ZeroDivisionError: Inverse of 1317188059 does not exist sage: gcd(1317188059, N) 26927 sage: N.factor() 26927 * 63719 John On May 4, 8:59 am, Jeroen Demeyer <jdeme...@cage.ugent.be> wrote: > On 2010-05-03 16:46, Mike Hansen wrote: > > > Hello, > > > On Mon, May 3, 2010 at 1:34 AM, Jeroen Demeyer <jdeme...@cage.ugent.be> > > wrote: > >> I wonder if there is a way to make Sage compute with points on elliptic > >> curves over rings which are not fields. I would like to use it for a > >> very simple implementation of the ECM factoring algorithm for > >> educational purposes. The obvious doesn't work: > > > There is a workaround. Please see: > >http://www.mail-archive.com/sage-support@googlegroups.com/msg18282.html > > Thanks a lot for the pointer! > Jeroen. > > -- > To post to this group, send email to sage-support@googlegroups.com > To unsubscribe from this group, send email to > sage-support+unsubscr...@googlegroups.com > For more options, visit this group > athttp://groups.google.com/group/sage-support > URL:http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
