The original questioner does not say over what field his elliptic curves are defined -- which makes quite a big difference!
Over Q this is easy, partly because of Lutz-Nagell, partly because of Mazur. It's harder to apply those (or their generalizations) over number fields, but at least one could use the canonical height to find out if the point has finite order first, then do something like baby-step-giant-step. Which is also what you would do over a finite field. But I cannot see how one cold possibly implement an Order function which would work over arbitrary fields! John On 8/3/07, William Stein <[EMAIL PROTECTED]> wrote: > > On 8/2/07, biozan <[EMAIL PROTECTED]> wrote: > > > > Hi, > > > > I'm just wondering if there is a command in sage to determine the > > order of a point on an elliptic curve or do I have to define such a > > function? I've looked through all the tutorials, cookbook, programming > > guide etc, but I can't seem to find any. > > > > Thank you. > > > > > > Regards, > > Mandy > > The function to find the order is called "order". Here are some > examples (see below). > Let me know if you have any other questions. > > -- William > > sage: E = EllipticCurve([196, 0]) > sage: P = E([0,0]) > sage: P > (0 : 0 : 1) > sage: P.order() > 2 > sage: P.order? > Type: instancemethod > Base Class: <type 'instancemethod'> > String Form: <bound method EllipticCurvePoint_field.order of (0 : 0 : 1)> > Namespace: Interactive > File: > /home/was/s/local/lib/python2.5/site-packages/sage/schemes/elliptic_curves/ell_point.py > Definition: P.order(self) > Docstring: > > Return the order of this point on the elliptic curve. > If the point has infinite order, returns 0. > > EXAMPLE: > sage: E = EllipticCurve([0,0,1,-1,0]) > sage: P = E([0,0]); P > (0 : 0 : 1) > sage: P.order() > +Infinity > > sage: E = EllipticCurve([0,1]) > sage: P = E([-1,0]) > sage: P.order() > 2 > > > > > > > > > > > > > > > > > -- > William Stein > Associate Professor of Mathematics > University of Washington > http://www.williamstein.org > > > > -- John Cremona --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
